id	sid	tid	token	lemma	pos
ejpam-5993	1	1	european	european	PROPN
ejpam-5993	1	2	journal	journal	PROPN
ejpam-5993	1	3	of	of	ADP
ejpam-5993	1	4	pure	pure	ADJ
ejpam-5993	1	5	and	and	CCONJ
ejpam-5993	1	6	applied	applied	ADJ
ejpam-5993	1	7	mathematics	mathematic	NOUN
ejpam-5993	1	8	2025	2025	NUM
ejpam-5993	1	9	,	,	PUNCT
ejpam-5993	1	10	vol	vol	NOUN
ejpam-5993	1	11	.	.	PROPN
ejpam-5993	1	12	18	18	NUM
ejpam-5993	1	13	,	,	PUNCT
ejpam-5993	1	14	issue	issue	NOUN
ejpam-5993	1	15	2	2	NUM
ejpam-5993	1	16	,	,	PUNCT
ejpam-5993	1	17	article	article	NOUN
ejpam-5993	1	18	number	number	NOUN
ejpam-5993	1	19	5993	5993	NUM
ejpam-5993	1	20	issn	issn	VERB
ejpam-5993	1	21	1307	1307	NUM
ejpam-5993	1	22	-	-	SYM
ejpam-5993	1	23	5543	5543	NUM
ejpam-5993	1	24	–	–	PUNCT
ejpam-5993	1	25	ejpam.com	ejpam.com	X
ejpam-5993	1	26	published	publish	VERB
ejpam-5993	1	27	by	by	ADP
ejpam-5993	1	28	new	new	PROPN
ejpam-5993	1	29	york	york	PROPN
ejpam-5993	1	30	business	business	PROPN
ejpam-5993	1	31	global	global	ADJ
ejpam-5993	1	32	1	1	NUM
ejpam-5993	1	33	finite	finite	ADJ
ejpam-5993	1	34	groups	group	NOUN
ejpam-5993	1	35	with	with	ADP
ejpam-5993	1	36	certain	certain	ADJ
ejpam-5993	1	37	ssh	ssh	NOUN
ejpam-5993	1	38	-	-	PUNCT
ejpam-5993	1	39	subgroups2	subgroups2	NOUN
ejpam-5993	1	40	a.	a.	NOUN
ejpam-5993	1	41	s.	s.	PROPN
ejpam-5993	1	42	allehyani3	allehyani3	PROPN
ejpam-5993	2	1	department	department	PROPN
ejpam-5993	2	2	of	of	ADP
ejpam-5993	2	3	mathematics	mathematic	NOUN
ejpam-5993	2	4	,	,	PUNCT
ejpam-5993	2	5	faculty	faculty	NOUN
ejpam-5993	2	6	of	of	ADP
ejpam-5993	2	7	science	science	NOUN
ejpam-5993	2	8	,	,	PUNCT
ejpam-5993	2	9	king	king	PROPN
ejpam-5993	2	10	abdulaziz	abdulaziz	PROPN
ejpam-5993	2	11	university	university	PROPN
ejpam-5993	2	12	,	,	PUNCT
ejpam-5993	2	13	jeddah,4	jeddah,4	VERB
ejpam-5993	2	14	saudi	saudi	ADJ
ejpam-5993	2	15	arabia5	arabia5	PROPN
ejpam-5993	2	16	6	6	NUM
ejpam-5993	2	17	abstract	abstract	NOUN
ejpam-5993	2	18	.	.	PUNCT
ejpam-5993	3	1	let	let	VERB
ejpam-5993	3	2	g	g	PRON
ejpam-5993	3	3	be	be	AUX
ejpam-5993	3	4	a	a	DET
ejpam-5993	3	5	finite	finite	ADJ
ejpam-5993	3	6	group	group	NOUN
ejpam-5993	3	7	.	.	PUNCT
ejpam-5993	4	1	a	a	DET
ejpam-5993	4	2	subgroup	subgroup	NOUN
ejpam-5993	4	3	h	h	NOUN
ejpam-5993	4	4	of	of	ADP
ejpam-5993	4	5	g	g	PROPN
ejpam-5993	4	6	is	be	AUX
ejpam-5993	4	7	s	s	NOUN
ejpam-5993	4	8	-	-	NOUN
ejpam-5993	4	9	permutable	permutable	ADJ
ejpam-5993	4	10	in	in	ADP
ejpam-5993	4	11	g	g	PROPN
ejpam-5993	4	12	if	if	SCONJ
ejpam-5993	4	13	h	h	NOUN
ejpam-5993	4	14	permutes	permute	VERB
ejpam-5993	4	15	with	with	ADP
ejpam-5993	4	16	every	every	DET
ejpam-5993	4	17	sylow	sylow	NOUN
ejpam-5993	4	18	subgroup	subgroup	NOUN
ejpam-5993	4	19	of	of	ADP
ejpam-5993	4	20	g.	g.	PROPN
ejpam-5993	4	21	a	a	DET
ejpam-5993	4	22	subgroup	subgroup	NOUN
ejpam-5993	4	23	h	h	NOUN
ejpam-5993	4	24	of	of	ADP
ejpam-5993	4	25	g	g	PROPN
ejpam-5993	4	26	is	be	AUX
ejpam-5993	4	27	called	call	VERB
ejpam-5993	4	28	an	an	DET
ejpam-5993	4	29	ssh	ssh	NOUN
ejpam-5993	4	30	-	-	PUNCT
ejpam-5993	4	31	subgroup	subgroup	NOUN
ejpam-5993	4	32	in	in	ADP
ejpam-5993	4	33	g	g	PROPN
ejpam-5993	4	34	if	if	SCONJ
ejpam-5993	4	35	g	g	PROPN
ejpam-5993	4	36	has	have	VERB
ejpam-5993	4	37	an	an	DET
ejpam-5993	4	38	s	s	NOUN
ejpam-5993	4	39	-	-	PUNCT
ejpam-5993	4	40	permutable	permutable	ADJ
ejpam-5993	4	41	subgroup	subgroup	NOUN
ejpam-5993	4	42	k	k	PROPN
ejpam-5993	4	43	such	such	ADJ
ejpam-5993	4	44	that	that	DET
ejpam-5993	4	45	hsg	hsg	NOUN
ejpam-5993	4	46	=	=	PUNCT
ejpam-5993	4	47	hk	hk	PROPN
ejpam-5993	4	48	and	and	CCONJ
ejpam-5993	4	49	hg∩nk(h	hg∩nk(h	ADJ
ejpam-5993	4	50	)	)	PUNCT
ejpam-5993	4	51	⩽	⩽	ADJ
ejpam-5993	4	52	h	h	NOUN
ejpam-5993	4	53	,	,	PUNCT
ejpam-5993	4	54	for	for	ADP
ejpam-5993	4	55	all	all	PRON
ejpam-5993	4	56	g	g	PROPN
ejpam-5993	4	57	∈	∈	PROPN
ejpam-5993	4	58	g	g	NOUN
ejpam-5993	4	59	,	,	PUNCT
ejpam-5993	4	60	where	where	SCONJ
ejpam-5993	4	61	hsg	hsg	NOUN
ejpam-5993	4	62	is	be	AUX
ejpam-5993	4	63	the	the	DET
ejpam-5993	4	64	intersection	intersection	NOUN
ejpam-5993	4	65	of	of	ADP
ejpam-5993	4	66	all	all	DET
ejpam-5993	4	67	s	s	NOUN
ejpam-5993	4	68	-	-	ADJ
ejpam-5993	4	69	permutable	permutable	ADJ
ejpam-5993	4	70	subgroups	subgroup	NOUN
ejpam-5993	4	71	of	of	ADP
ejpam-5993	4	72	g	g	NOUN
ejpam-5993	4	73	containing	contain	VERB
ejpam-5993	4	74	h.	h.	NOUN
ejpam-5993	4	75	in	in	ADP
ejpam-5993	4	76	this	this	DET
ejpam-5993	4	77	paper	paper	NOUN
ejpam-5993	4	78	,	,	PUNCT
ejpam-5993	4	79	we	we	PRON
ejpam-5993	4	80	investigate	investigate	VERB
ejpam-5993	4	81	the	the	DET
ejpam-5993	4	82	structure	structure	NOUN
ejpam-5993	4	83	of	of	ADP
ejpam-5993	4	84	a	a	DET
ejpam-5993	4	85	finite	finite	ADJ
ejpam-5993	4	86	group	group	NOUN
ejpam-5993	4	87	g	g	PROPN
ejpam-5993	4	88	under	under	ADP
ejpam-5993	4	89	the	the	DET
ejpam-5993	4	90	assumption	assumption	NOUN
ejpam-5993	4	91	that	that	SCONJ
ejpam-5993	4	92	certain	certain	ADJ
ejpam-5993	4	93	subgroups	subgroup	NOUN
ejpam-5993	4	94	of	of	ADP
ejpam-5993	4	95	prime	prime	ADJ
ejpam-5993	4	96	power	power	NOUN
ejpam-5993	4	97	orders	order	NOUN
ejpam-5993	4	98	are	be	AUX
ejpam-5993	4	99	ssh	ssh	NOUN
ejpam-5993	4	100	-	-	PUNCT
ejpam-5993	4	101	subgroups	subgroup	NOUN
ejpam-5993	4	102	of	of	ADP
ejpam-5993	4	103	g.	g.	PROPN
ejpam-5993	4	104	2020	2020	NUM
ejpam-5993	4	105	mathematics	mathematics	PROPN
ejpam-5993	4	106	subject	subject	NOUN
ejpam-5993	4	107	classifications	classification	NOUN
ejpam-5993	4	108	:	:	PUNCT
ejpam-5993	4	109	20d10	20d10	NUM
ejpam-5993	4	110	,	,	PUNCT
ejpam-5993	4	111	20d207	20d207	PROPN
ejpam-5993	4	112	key	key	ADJ
ejpam-5993	4	113	words	word	NOUN
ejpam-5993	4	114	and	and	CCONJ
ejpam-5993	4	115	phrases	phrase	NOUN
ejpam-5993	4	116	:	:	PUNCT
ejpam-5993	4	117	s	s	X
ejpam-5993	4	118	-	-	PUNCT
ejpam-5993	4	119	permutable	permutable	ADJ
ejpam-5993	4	120	subgroups	subgroup	NOUN
ejpam-5993	4	121	,	,	PUNCT
ejpam-5993	4	122	c	c	X
ejpam-5993	4	123	-	-	ADJ
ejpam-5993	4	124	normal	normal	ADJ
ejpam-5993	4	125	subgroups	subgroup	NOUN
ejpam-5993	4	126	,	,	PUNCT
ejpam-5993	4	127	h	h	NOUN
ejpam-5993	4	128	-	-	PUNCT
ejpam-5993	4	129	subgroups	subgroup	NOUN
ejpam-5993	4	130	,	,	PUNCT
ejpam-5993	4	131	hc-8	hc-8	PROPN
ejpam-5993	4	132	subgroups	subgroup	NOUN
ejpam-5993	4	133	,	,	PUNCT
ejpam-5993	4	134	ssh	ssh	NOUN
ejpam-5993	4	135	-	-	PUNCT
ejpam-5993	4	136	subgroups	subgroup	NOUN
ejpam-5993	4	137	,	,	PUNCT
ejpam-5993	4	138	supersolvable	supersolvable	ADJ
ejpam-5993	4	139	groups	group	NOUN
ejpam-5993	4	140	,	,	PUNCT
ejpam-5993	4	141	saturated	saturate	VERB
ejpam-5993	4	142	formations9	formations9	NOUN
ejpam-5993	4	143	10	10	NUM
ejpam-5993	4	144	1	1	NUM
ejpam-5993	4	145	.	.	PUNCT
ejpam-5993	4	146	introduction11	introduction11	PROPN
ejpam-5993	4	147	throughout	throughout	ADP
ejpam-5993	4	148	this	this	DET
ejpam-5993	4	149	paper	paper	NOUN
ejpam-5993	4	150	,	,	PUNCT
ejpam-5993	4	151	we	we	PRON
ejpam-5993	4	152	assume	assume	VERB
ejpam-5993	4	153	that	that	SCONJ
ejpam-5993	4	154	all	all	DET
ejpam-5993	4	155	groups	group	NOUN
ejpam-5993	4	156	in	in	ADP
ejpam-5993	4	157	this	this	DET
ejpam-5993	4	158	paper	paper	NOUN
ejpam-5993	4	159	are	be	AUX
ejpam-5993	4	160	finite	finite	ADJ
ejpam-5993	4	161	and	and	CCONJ
ejpam-5993	4	162	g	g	PROPN
ejpam-5993	4	163	always12	always12	NOUN
ejpam-5993	4	164	denotes	denote	VERB
ejpam-5993	4	165	a	a	DET
ejpam-5993	4	166	group	group	NOUN
ejpam-5993	4	167	.	.	PUNCT
ejpam-5993	5	1	recall	recall	VERB
ejpam-5993	5	2	that	that	SCONJ
ejpam-5993	5	3	a	a	DET
ejpam-5993	5	4	subgroup	subgroup	NOUN
ejpam-5993	5	5	h	h	NOUN
ejpam-5993	5	6	of	of	ADP
ejpam-5993	5	7	g	g	PROPN
ejpam-5993	5	8	is	be	AUX
ejpam-5993	5	9	called	call	VERB
ejpam-5993	5	10	permutable	permutable	ADJ
ejpam-5993	5	11	in	in	ADP
ejpam-5993	5	12	g	g	PROPN
ejpam-5993	5	13	if	if	SCONJ
ejpam-5993	5	14	h	h	NOUN
ejpam-5993	5	15	permutes13	permutes13	NOUN
ejpam-5993	5	16	with	with	ADP
ejpam-5993	5	17	every	every	DET
ejpam-5993	5	18	subgroup	subgroup	NOUN
ejpam-5993	5	19	of	of	ADP
ejpam-5993	5	20	g	g	PROPN
ejpam-5993	5	21	,	,	PUNCT
ejpam-5993	5	22	that	that	ADV
ejpam-5993	5	23	is	is	ADV
ejpam-5993	5	24	,	,	PUNCT
ejpam-5993	5	25	hk	hk	PROPN
ejpam-5993	5	26	⩽	⩽	NOUN
ejpam-5993	5	27	g	g	PROPN
ejpam-5993	5	28	,	,	PUNCT
ejpam-5993	5	29	for	for	ADP
ejpam-5993	5	30	all	all	DET
ejpam-5993	5	31	k	k	PROPN
ejpam-5993	5	32	⩽	⩽	PROPN
ejpam-5993	5	33	g	g	NOUN
ejpam-5993	5	34	;	;	PUNCT
ejpam-5993	5	35	and	and	CCONJ
ejpam-5993	5	36	a	a	DET
ejpam-5993	5	37	subgroup	subgroup	NOUN
ejpam-5993	5	38	h	h	NOUN
ejpam-5993	5	39	is	be	AUX
ejpam-5993	5	40	said14	said14	NOUN
ejpam-5993	5	41	to	to	PART
ejpam-5993	5	42	be	be	AUX
ejpam-5993	5	43	s	s	NOUN
ejpam-5993	5	44	-	-	NOUN
ejpam-5993	5	45	permutable	permutable	ADJ
ejpam-5993	5	46	in	in	ADP
ejpam-5993	5	47	g	g	PROPN
ejpam-5993	5	48	if	if	SCONJ
ejpam-5993	5	49	h	h	NOUN
ejpam-5993	5	50	permutes	permute	VERB
ejpam-5993	5	51	with	with	ADP
ejpam-5993	5	52	every	every	DET
ejpam-5993	5	53	sylow	sylow	NOUN
ejpam-5993	5	54	subgroup	subgroup	NOUN
ejpam-5993	5	55	of	of	ADP
ejpam-5993	5	56	g.	g.	PROPN
ejpam-5993	5	57	the	the	DET
ejpam-5993	5	58	concept	concept	NOUN
ejpam-5993	5	59	of15	of15	PROPN
ejpam-5993	5	60	s	s	NOUN
ejpam-5993	5	61	-	-	NOUN
ejpam-5993	5	62	permutability	permutability	NOUN
ejpam-5993	5	63	as	as	ADP
ejpam-5993	5	64	generalization	generalization	NOUN
ejpam-5993	5	65	of	of	ADP
ejpam-5993	5	66	normality	normality	NOUN
ejpam-5993	5	67	and	and	CCONJ
ejpam-5993	5	68	permutability	permutability	NOUN
ejpam-5993	5	69	was	be	AUX
ejpam-5993	5	70	defined	define	VERB
ejpam-5993	5	71	by	by	ADP
ejpam-5993	5	72	kegel	kegel	PROPN
ejpam-5993	6	1	[	[	X
ejpam-5993	6	2	1]16	1]16	NOUN
ejpam-5993	6	3	in	in	ADP
ejpam-5993	6	4	1962.17	1962.17	NUM
ejpam-5993	6	5	18	18	NUM
ejpam-5993	6	6	another	another	DET
ejpam-5993	6	7	generalization	generalization	NOUN
ejpam-5993	6	8	of	of	ADP
ejpam-5993	6	9	normality	normality	NOUN
ejpam-5993	6	10	was	be	AUX
ejpam-5993	6	11	given	give	VERB
ejpam-5993	6	12	by	by	ADP
ejpam-5993	6	13	wang	wang	PROPN
ejpam-5993	7	1	[	[	X
ejpam-5993	7	2	2	2	NUM
ejpam-5993	7	3	]	]	PUNCT
ejpam-5993	7	4	in	in	ADP
ejpam-5993	7	5	1996	1996	NUM
ejpam-5993	7	6	as	as	SCONJ
ejpam-5993	7	7	follows	follow	VERB
ejpam-5993	7	8	:	:	PUNCT
ejpam-5993	7	9	a19	a19	PROPN
ejpam-5993	7	10	subgroup	subgroup	PROPN
ejpam-5993	7	11	h	h	PROPN
ejpam-5993	7	12	of	of	ADP
ejpam-5993	7	13	g	g	PROPN
ejpam-5993	7	14	is	be	AUX
ejpam-5993	7	15	said	say	VERB
ejpam-5993	7	16	to	to	PART
ejpam-5993	7	17	be	be	AUX
ejpam-5993	7	18	c	c	NOUN
ejpam-5993	7	19	-	-	ADJ
ejpam-5993	7	20	normal	normal	ADJ
ejpam-5993	7	21	in	in	ADP
ejpam-5993	7	22	g	g	PROPN
ejpam-5993	7	23	if	if	SCONJ
ejpam-5993	7	24	g	g	PROPN
ejpam-5993	7	25	has	have	VERB
ejpam-5993	7	26	a	a	DET
ejpam-5993	7	27	normal	normal	ADJ
ejpam-5993	7	28	subgroup	subgroup	NOUN
ejpam-5993	7	29	k	k	PROPN
ejpam-5993	7	30	such	such	ADJ
ejpam-5993	7	31	that20	that20	NOUN
ejpam-5993	7	32	g	g	PROPN
ejpam-5993	7	33	=	=	PUNCT
ejpam-5993	7	34	hk	hk	PROPN
ejpam-5993	7	35	and	and	CCONJ
ejpam-5993	7	36	h	h	PROPN
ejpam-5993	7	37	∩	∩	PROPN
ejpam-5993	7	38	k	k	PROPN
ejpam-5993	7	39	⩽	⩽	PROPN
ejpam-5993	7	40	hg	hg	PROPN
ejpam-5993	7	41	,	,	PUNCT
ejpam-5993	7	42	where	where	SCONJ
ejpam-5993	7	43	hg	hg	PROPN
ejpam-5993	7	44	=	=	PUNCT
ejpam-5993	7	45	coreg(h	coreg(h	PROPN
ejpam-5993	7	46	)	)	PUNCT
ejpam-5993	7	47	=	=	PUNCT
ejpam-5993	8	1	∩g∈gh	∩g∈gh	ADP
ejpam-5993	8	2	g	g	NOUN
ejpam-5993	8	3	is	be	AUX
ejpam-5993	8	4	the	the	DET
ejpam-5993	8	5	largest	large	ADJ
ejpam-5993	8	6	normal21	normal21	NOUN
ejpam-5993	8	7	subgroup	subgroup	NOUN
ejpam-5993	8	8	of	of	ADP
ejpam-5993	8	9	g	g	PROPN
ejpam-5993	8	10	contained	contain	VERB
ejpam-5993	8	11	in	in	ADP
ejpam-5993	8	12	h.	h.	PROPN
ejpam-5993	8	13	in	in	ADP
ejpam-5993	8	14	2000	2000	NUM
ejpam-5993	8	15	,	,	PUNCT
ejpam-5993	8	16	the	the	DET
ejpam-5993	8	17	concept	concept	NOUN
ejpam-5993	8	18	of	of	ADP
ejpam-5993	8	19	h	h	NOUN
ejpam-5993	8	20	-	-	PUNCT
ejpam-5993	8	21	subgroup	subgroup	NOUN
ejpam-5993	8	22	was	be	AUX
ejpam-5993	8	23	introduced	introduce	VERB
ejpam-5993	8	24	by22	by22	PROPN
ejpam-5993	8	25	bianchi	bianchi	NOUN
ejpam-5993	8	26	et	et	PROPN
ejpam-5993	8	27	al	al	PROPN
ejpam-5993	8	28	.	.	PUNCT
ejpam-5993	9	1	in	in	ADP
ejpam-5993	9	2	[	[	X
ejpam-5993	9	3	3	3	X
ejpam-5993	9	4	]	]	PUNCT
ejpam-5993	9	5	as	as	SCONJ
ejpam-5993	9	6	follows	follow	VERB
ejpam-5993	9	7	:	:	PUNCT
ejpam-5993	9	8	a	a	DET
ejpam-5993	9	9	subgroup	subgroup	NOUN
ejpam-5993	9	10	h	h	NOUN
ejpam-5993	9	11	of	of	ADP
ejpam-5993	9	12	g	g	PROPN
ejpam-5993	9	13	is	be	AUX
ejpam-5993	9	14	called	call	VERB
ejpam-5993	9	15	an	an	DET
ejpam-5993	9	16	h	h	NOUN
ejpam-5993	9	17	-	-	NOUN
ejpam-5993	9	18	subgroup	subgroup	NOUN
ejpam-5993	9	19	in	in	ADP
ejpam-5993	9	20	g	g	PROPN
ejpam-5993	9	21	if23	if23	PROPN
ejpam-5993	9	22	hg	hg	PROPN
ejpam-5993	9	23	∩ng(h	∩ng(h	PROPN
ejpam-5993	9	24	)	)	PUNCT
ejpam-5993	9	25	⩽	⩽	PROPN
ejpam-5993	9	26	h	h	NOUN
ejpam-5993	9	27	,	,	PUNCT
ejpam-5993	9	28	for	for	ADP
ejpam-5993	9	29	all	all	DET
ejpam-5993	9	30	g	g	PROPN
ejpam-5993	9	31	∈	∈	PROPN
ejpam-5993	9	32	g.24	g.24	PROPN
ejpam-5993	9	33	wei	wei	PROPN
ejpam-5993	9	34	and	and	CCONJ
ejpam-5993	9	35	guo	guo	PROPN
ejpam-5993	10	1	[	[	X
ejpam-5993	10	2	4	4	NUM
ejpam-5993	10	3	]	]	PUNCT
ejpam-5993	10	4	,	,	PUNCT
ejpam-5993	10	5	in	in	ADP
ejpam-5993	10	6	2012	2012	NUM
ejpam-5993	10	7	,	,	PUNCT
ejpam-5993	10	8	defined	define	VERB
ejpam-5993	10	9	a	a	DET
ejpam-5993	10	10	new	new	ADJ
ejpam-5993	10	11	concept	concept	NOUN
ejpam-5993	10	12	,	,	PUNCT
ejpam-5993	10	13	named	name	VERB
ejpam-5993	10	14	hc	hc	NOUN
ejpam-5993	10	15	-	-	PUNCT
ejpam-5993	10	16	subgroup	subgroup	NOUN
ejpam-5993	10	17	,	,	PUNCT
ejpam-5993	10	18	which	which	PRON
ejpam-5993	10	19	is	be	AUX
ejpam-5993	10	20	a25	a25	NOUN
ejpam-5993	10	21	generalization	generalization	NOUN
ejpam-5993	10	22	of	of	ADP
ejpam-5993	10	23	c	c	NOUN
ejpam-5993	10	24	-	-	PUNCT
ejpam-5993	10	25	normality	normality	NOUN
ejpam-5993	10	26	and	and	CCONJ
ejpam-5993	10	27	h	h	NOUN
ejpam-5993	10	28	-	-	PUNCT
ejpam-5993	10	29	subgroup	subgroup	NOUN
ejpam-5993	10	30	as	as	SCONJ
ejpam-5993	10	31	follows	follow	VERB
ejpam-5993	10	32	:	:	PUNCT
ejpam-5993	10	33	a	a	DET
ejpam-5993	10	34	subgroup	subgroup	NOUN
ejpam-5993	10	35	h	h	NOUN
ejpam-5993	10	36	of	of	ADP
ejpam-5993	10	37	g	g	PROPN
ejpam-5993	10	38	is	be	AUX
ejpam-5993	10	39	said	say	VERB
ejpam-5993	10	40	to26	to26	PROPN
ejpam-5993	10	41	be	be	AUX
ejpam-5993	10	42	an	an	DET
ejpam-5993	10	43	hc	hc	NOUN
ejpam-5993	10	44	-	-	PUNCT
ejpam-5993	10	45	subgroup	subgroup	NOUN
ejpam-5993	10	46	of	of	ADP
ejpam-5993	10	47	g	g	PROPN
ejpam-5993	10	48	if	if	SCONJ
ejpam-5993	10	49	there	there	PRON
ejpam-5993	10	50	exists	exist	VERB
ejpam-5993	10	51	a	a	DET
ejpam-5993	10	52	normal	normal	ADJ
ejpam-5993	10	53	subgroup	subgroup	NOUN
ejpam-5993	10	54	k	k	PROPN
ejpam-5993	10	55	of	of	ADP
ejpam-5993	10	56	g	g	PROPN
ejpam-5993	11	1	such	such	ADJ
ejpam-5993	11	2	that	that	SCONJ
ejpam-5993	11	3	g	g	PROPN
ejpam-5993	11	4	=	=	PUNCT
ejpam-5993	11	5	hk27	hk27	PROPN
ejpam-5993	11	6	doi	doi	NOUN
ejpam-5993	11	7	:	:	PUNCT
ejpam-5993	11	8	https://doi.org/10.29020/nybg.ejpam.v18i2.5993	https://doi.org/10.29020/nybg.ejpam.v18i2.5993	PRON
ejpam-5993	11	9	email	email	NOUN
ejpam-5993	11	10	address	address	NOUN
ejpam-5993	11	11	:	:	PUNCT
ejpam-5993	11	12	asaeedallehyani@stu.kau.edu.sa	asaeedallehyani@stu.kau.edu.sa	PROPN
ejpam-5993	11	13	(	(	PUNCT
ejpam-5993	11	14	a.	a.	PROPN
ejpam-5993	11	15	s.	s.	PROPN
ejpam-5993	11	16	allehyani	allehyani	PROPN
ejpam-5993	11	17	)	)	PUNCT
ejpam-5993	11	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5993	12	1	1	1	NUM
ejpam-5993	12	2	copyright	copyright	NOUN
ejpam-5993	12	3	:	:	PUNCT
ejpam-5993	12	4	©	©	PROPN
ejpam-5993	12	5	2025	2025	NUM
ejpam-5993	12	6	the	the	DET
ejpam-5993	12	7	author(s	author(s	NOUN
ejpam-5993	12	8	)	)	PUNCT
ejpam-5993	12	9	.	.	PUNCT
ejpam-5993	13	1	(	(	PUNCT
ejpam-5993	13	2	cc	cc	NOUN
ejpam-5993	13	3	by	by	ADP
ejpam-5993	13	4	-	-	PUNCT
ejpam-5993	13	5	nc	nc	PROPN
ejpam-5993	13	6	4.0	4.0	NUM
ejpam-5993	13	7	)	)	PUNCT
ejpam-5993	13	8	a.	a.	NOUN
ejpam-5993	13	9	s.	s.	PROPN
ejpam-5993	13	10	allehyani	allehyani	PROPN
ejpam-5993	13	11	/	/	SYM
ejpam-5993	13	12	eur	eur	PROPN
ejpam-5993	13	13	.	.	PUNCT
ejpam-5993	14	1	j.	j.	PROPN
ejpam-5993	14	2	pure	pure	PROPN
ejpam-5993	14	3	appl	appl	PROPN
ejpam-5993	14	4	.	.	PROPN
ejpam-5993	14	5	math	math	PROPN
ejpam-5993	14	6	,	,	PUNCT
ejpam-5993	14	7	18	18	NUM
ejpam-5993	14	8	(	(	PUNCT
ejpam-5993	14	9	2	2	NUM
ejpam-5993	14	10	)	)	PUNCT
ejpam-5993	14	11	(	(	PUNCT
ejpam-5993	14	12	2025	2025	NUM
ejpam-5993	14	13	)	)	PUNCT
ejpam-5993	14	14	,	,	PUNCT
ejpam-5993	14	15	5993	5993	NUM
ejpam-5993	14	16	2	2	NUM
ejpam-5993	14	17	of	of	ADP
ejpam-5993	14	18	13	13	NUM
ejpam-5993	14	19	and	and	CCONJ
ejpam-5993	14	20	hg	hg	NOUN
ejpam-5993	14	21	∩	∩	NOUN
ejpam-5993	14	22	nk(h	nk(h	CCONJ
ejpam-5993	14	23	)	)	PUNCT
ejpam-5993	14	24	≤	≤	NUM
ejpam-5993	14	25	h	h	NOUN
ejpam-5993	14	26	,	,	PUNCT
ejpam-5993	14	27	for	for	ADP
ejpam-5993	14	28	all	all	DET
ejpam-5993	14	29	g	g	PROPN
ejpam-5993	14	30	∈	∈	PROPN
ejpam-5993	14	31	g.	g.	NOUN
ejpam-5993	14	32	clearly	clearly	ADV
ejpam-5993	14	33	,	,	PUNCT
ejpam-5993	14	34	every	every	DET
ejpam-5993	14	35	c	c	NOUN
ejpam-5993	14	36	-	-	ADJ
ejpam-5993	14	37	normal	normal	ADJ
ejpam-5993	14	38	subgroup	subgroup	NOUN
ejpam-5993	14	39	of	of	ADP
ejpam-5993	14	40	g	g	PROPN
ejpam-5993	14	41	is	be	AUX
ejpam-5993	14	42	an	an	DET
ejpam-5993	14	43	hc-28	hc-28	ADJ
ejpam-5993	14	44	subgroup	subgroup	NOUN
ejpam-5993	14	45	of	of	ADP
ejpam-5993	14	46	g	g	NOUN
ejpam-5993	14	47	;	;	PUNCT
ejpam-5993	14	48	to	to	PART
ejpam-5993	14	49	see	see	VERB
ejpam-5993	14	50	that	that	SCONJ
ejpam-5993	14	51	,	,	PUNCT
ejpam-5993	14	52	if	if	SCONJ
ejpam-5993	14	53	h	h	NOUN
ejpam-5993	14	54	is	be	AUX
ejpam-5993	14	55	a	a	DET
ejpam-5993	14	56	c	c	NOUN
ejpam-5993	14	57	-	-	ADJ
ejpam-5993	14	58	normal	normal	ADJ
ejpam-5993	14	59	subgroup	subgroup	NOUN
ejpam-5993	14	60	of	of	ADP
ejpam-5993	14	61	g	g	PROPN
ejpam-5993	14	62	,	,	PUNCT
ejpam-5993	14	63	then	then	ADV
ejpam-5993	14	64	there	there	PRON
ejpam-5993	14	65	exists	exist	VERB
ejpam-5993	14	66	a	a	DET
ejpam-5993	14	67	normal29	normal29	NOUN
ejpam-5993	14	68	subgroup	subgroup	NOUN
ejpam-5993	14	69	k	k	PROPN
ejpam-5993	14	70	of	of	ADP
ejpam-5993	14	71	g	g	PROPN
ejpam-5993	14	72	such	such	ADJ
ejpam-5993	14	73	that	that	SCONJ
ejpam-5993	14	74	g	g	PROPN
ejpam-5993	14	75	=	=	PUNCT
ejpam-5993	14	76	hk	hk	PROPN
ejpam-5993	14	77	and	and	CCONJ
ejpam-5993	14	78	h	h	PROPN
ejpam-5993	14	79	∩	∩	NOUN
ejpam-5993	14	80	k	k	PROPN
ejpam-5993	14	81	≤	≤	NUM
ejpam-5993	14	82	coreg(h	coreg(h	NOUN
ejpam-5993	14	83	)	)	PUNCT
ejpam-5993	14	84	.	.	PUNCT
ejpam-5993	15	1	thus	thus	ADV
ejpam-5993	15	2	hg	hg	NOUN
ejpam-5993	15	3	∩	∩	NOUN
ejpam-5993	15	4	nk(h	nk(h	NUM
ejpam-5993	15	5	)	)	PUNCT
ejpam-5993	15	6	=	=	SYM
ejpam-5993	15	7	30	30	NUM
ejpam-5993	15	8	(	(	PUNCT
ejpam-5993	15	9	h	h	NOUN
ejpam-5993	15	10	∩k)g	∩k)g	PROPN
ejpam-5993	15	11	∩ng(h	∩ng(h	PROPN
ejpam-5993	15	12	)	)	PUNCT
ejpam-5993	15	13	≤	≤	NUM
ejpam-5993	15	14	h	h	NOUN
ejpam-5993	15	15	,	,	PUNCT
ejpam-5993	15	16	for	for	ADP
ejpam-5993	15	17	all	all	DET
ejpam-5993	15	18	g	g	PROPN
ejpam-5993	15	19	∈	∈	PROPN
ejpam-5993	15	20	g	g	NOUN
ejpam-5993	15	21	and	and	CCONJ
ejpam-5993	15	22	so	so	ADV
ejpam-5993	15	23	h	h	NOUN
ejpam-5993	15	24	is	be	AUX
ejpam-5993	15	25	an	an	DET
ejpam-5993	15	26	hc	hc	NOUN
ejpam-5993	15	27	-	-	PUNCT
ejpam-5993	15	28	subgroup	subgroup	NOUN
ejpam-5993	15	29	of	of	ADP
ejpam-5993	15	30	g.	g.	PROPN
ejpam-5993	15	31	however	however	ADV
ejpam-5993	15	32	,	,	PUNCT
ejpam-5993	15	33	the31	the31	NOUN
ejpam-5993	15	34	converse	converse	NOUN
ejpam-5993	15	35	is	be	AUX
ejpam-5993	15	36	not	not	PART
ejpam-5993	15	37	true	true	ADJ
ejpam-5993	15	38	in	in	ADP
ejpam-5993	15	39	general	general	ADJ
ejpam-5993	15	40	(	(	PUNCT
ejpam-5993	15	41	see	see	VERB
ejpam-5993	15	42	[	[	X
ejpam-5993	15	43	4	4	NUM
ejpam-5993	15	44	,	,	PUNCT
ejpam-5993	15	45	example	example	NOUN
ejpam-5993	15	46	1	1	NUM
ejpam-5993	15	47	]	]	NUM
ejpam-5993	15	48	)	)	PUNCT
ejpam-5993	15	49	.	.	PUNCT
ejpam-5993	16	1	moreover	moreover	ADV
ejpam-5993	16	2	,	,	PUNCT
ejpam-5993	16	3	it	it	PRON
ejpam-5993	16	4	is	be	AUX
ejpam-5993	16	5	easy	easy	ADJ
ejpam-5993	16	6	to	to	PART
ejpam-5993	16	7	see	see	VERB
ejpam-5993	16	8	that	that	DET
ejpam-5993	16	9	every32	every32	NOUN
ejpam-5993	16	10	h	h	NOUN
ejpam-5993	16	11	-	-	PUNCT
ejpam-5993	16	12	subgroup	subgroup	NOUN
ejpam-5993	16	13	of	of	ADP
ejpam-5993	16	14	g	g	PROPN
ejpam-5993	16	15	is	be	AUX
ejpam-5993	16	16	an	an	DET
ejpam-5993	16	17	hc	hc	NOUN
ejpam-5993	16	18	-	-	PUNCT
ejpam-5993	16	19	subgroup	subgroup	NOUN
ejpam-5993	16	20	of	of	ADP
ejpam-5993	16	21	g	g	PROPN
ejpam-5993	16	22	,	,	PUNCT
ejpam-5993	16	23	but	but	CCONJ
ejpam-5993	16	24	the	the	DET
ejpam-5993	16	25	converse	converse	NOUN
ejpam-5993	16	26	is	be	AUX
ejpam-5993	16	27	not	not	PART
ejpam-5993	16	28	true	true	ADJ
ejpam-5993	16	29	in	in	ADP
ejpam-5993	16	30	general	general	ADJ
ejpam-5993	16	31	(	(	PUNCT
ejpam-5993	16	32	see	see	VERB
ejpam-5993	16	33	[	[	X
ejpam-5993	16	34	4,33	4,33	DET
ejpam-5993	16	35	example	example	NOUN
ejpam-5993	17	1	2]).34	2]).34	NUM
ejpam-5993	17	2	35	35	NUM
ejpam-5993	17	3	in	in	ADP
ejpam-5993	17	4	2016	2016	NUM
ejpam-5993	17	5	,	,	PUNCT
ejpam-5993	17	6	asaad	asaad	NOUN
ejpam-5993	17	7	and	and	CCONJ
ejpam-5993	17	8	ramadan	ramadan	PROPN
ejpam-5993	18	1	[	[	X
ejpam-5993	18	2	5	5	NUM
ejpam-5993	18	3	]	]	PUNCT
ejpam-5993	18	4	introduced	introduce	VERB
ejpam-5993	18	5	the	the	DET
ejpam-5993	18	6	concept	concept	NOUN
ejpam-5993	18	7	of	of	ADP
ejpam-5993	18	8	weakly	weakly	ADJ
ejpam-5993	18	9	hc	hc	ADV
ejpam-5993	18	10	-	-	PUNCT
ejpam-5993	18	11	embedded	embed	VERB
ejpam-5993	18	12	sub-36	sub-36	NOUN
ejpam-5993	18	13	group	group	NOUN
ejpam-5993	18	14	as	as	ADP
ejpam-5993	18	15	a	a	DET
ejpam-5993	18	16	generalization	generalization	NOUN
ejpam-5993	18	17	of	of	ADP
ejpam-5993	18	18	hc	hc	PROPN
ejpam-5993	18	19	-	-	PUNCT
ejpam-5993	18	20	subgroup	subgroup	NOUN
ejpam-5993	18	21	as	as	SCONJ
ejpam-5993	18	22	follows	follow	VERB
ejpam-5993	18	23	:	:	PUNCT
ejpam-5993	18	24	a	a	DET
ejpam-5993	18	25	subgroup	subgroup	NOUN
ejpam-5993	18	26	h	h	NOUN
ejpam-5993	18	27	of	of	ADP
ejpam-5993	18	28	g	g	PROPN
ejpam-5993	18	29	is	be	AUX
ejpam-5993	18	30	said	say	VERB
ejpam-5993	18	31	to	to	ADP
ejpam-5993	18	32	be37	be37	PROPN
ejpam-5993	18	33	weakly	weakly	ADJ
ejpam-5993	18	34	hc	hc	ADV
ejpam-5993	18	35	-	-	PUNCT
ejpam-5993	18	36	embedded	embed	VERB
ejpam-5993	18	37	in	in	ADP
ejpam-5993	18	38	g	g	PROPN
ejpam-5993	18	39	if	if	SCONJ
ejpam-5993	18	40	there	there	PRON
ejpam-5993	18	41	exists	exist	VERB
ejpam-5993	18	42	a	a	DET
ejpam-5993	18	43	normal	normal	ADJ
ejpam-5993	18	44	subgroup	subgroup	NOUN
ejpam-5993	18	45	k	k	PROPN
ejpam-5993	18	46	of	of	ADP
ejpam-5993	18	47	g	g	PROPN
ejpam-5993	18	48	such	such	ADJ
ejpam-5993	18	49	that	that	DET
ejpam-5993	18	50	hg	hg	NOUN
ejpam-5993	18	51	=	=	PUNCT
ejpam-5993	18	52	hk38	hk38	PROPN
ejpam-5993	18	53	and	and	CCONJ
ejpam-5993	18	54	hg	hg	NOUN
ejpam-5993	18	55	∩	∩	NOUN
ejpam-5993	18	56	nk(h	nk(h	CCONJ
ejpam-5993	18	57	)	)	PUNCT
ejpam-5993	18	58	≤	≤	NUM
ejpam-5993	18	59	h	h	NOUN
ejpam-5993	18	60	,	,	PUNCT
ejpam-5993	18	61	for	for	ADP
ejpam-5993	18	62	all	all	PRON
ejpam-5993	18	63	g	g	PROPN
ejpam-5993	18	64	∈	∈	PROPN
ejpam-5993	18	65	g	g	NOUN
ejpam-5993	18	66	,	,	PUNCT
ejpam-5993	18	67	where	where	SCONJ
ejpam-5993	19	1	hg	hg	PROPN
ejpam-5993	19	2	=	=	PUNCT
ejpam-5993	19	3	∩{n	∩{n	INTJ
ejpam-5993	19	4	:	:	PUNCT
ejpam-5993	19	5	n	n	NOUN
ejpam-5993	19	6	⊴	⊴	ADP
ejpam-5993	19	7	g	g	PROPN
ejpam-5993	19	8	and	and	CCONJ
ejpam-5993	19	9	h	h	NOUN
ejpam-5993	19	10	≤	≤	NOUN
ejpam-5993	19	11	n	n	CCONJ
ejpam-5993	19	12	}	}	PUNCT
ejpam-5993	19	13	is	be	AUX
ejpam-5993	19	14	the39	the39	VERB
ejpam-5993	19	15	normal	normal	ADJ
ejpam-5993	19	16	closure	closure	NOUN
ejpam-5993	19	17	of	of	ADP
ejpam-5993	19	18	h	h	NOUN
ejpam-5993	19	19	in	in	ADP
ejpam-5993	19	20	g.40	g.40	DET
ejpam-5993	19	21	41	41	NUM
ejpam-5993	19	22	in	in	ADP
ejpam-5993	19	23	2018	2018	NUM
ejpam-5993	19	24	,	,	PUNCT
ejpam-5993	19	25	al	al	PROPN
ejpam-5993	19	26	-	-	PUNCT
ejpam-5993	19	27	gafri	gafri	PROPN
ejpam-5993	19	28	and	and	CCONJ
ejpam-5993	19	29	nauman	nauman	NOUN
ejpam-5993	20	1	[	[	X
ejpam-5993	20	2	6	6	NUM
ejpam-5993	20	3	]	]	PUNCT
ejpam-5993	20	4	introduced	introduce	VERB
ejpam-5993	20	5	the	the	DET
ejpam-5993	20	6	concept	concept	NOUN
ejpam-5993	20	7	of	of	ADP
ejpam-5993	20	8	ssh	ssh	PROPN
ejpam-5993	20	9	-	-	PUNCT
ejpam-5993	20	10	subgroup	subgroup	NOUN
ejpam-5993	20	11	which42	which42	NOUN
ejpam-5993	20	12	is	be	AUX
ejpam-5993	20	13	a	a	DET
ejpam-5993	20	14	generalization	generalization	NOUN
ejpam-5993	20	15	of	of	ADP
ejpam-5993	20	16	weakly	weakly	ADJ
ejpam-5993	20	17	hc	hc	ADV
ejpam-5993	20	18	-	-	PUNCT
ejpam-5993	20	19	embedded	embed	VERB
ejpam-5993	20	20	subgroup	subgroup	NOUN
ejpam-5993	20	21	as	as	SCONJ
ejpam-5993	20	22	follows	follow	VERB
ejpam-5993	20	23	:	:	PUNCT
ejpam-5993	20	24	a	a	DET
ejpam-5993	20	25	subgroup	subgroup	NOUN
ejpam-5993	20	26	h	h	NOUN
ejpam-5993	20	27	of	of	ADP
ejpam-5993	20	28	g43	g43	NOUN
ejpam-5993	20	29	is	be	AUX
ejpam-5993	20	30	said	say	VERB
ejpam-5993	20	31	to	to	PART
ejpam-5993	20	32	be	be	AUX
ejpam-5993	20	33	an	an	DET
ejpam-5993	20	34	ssh	ssh	NOUN
ejpam-5993	20	35	-	-	PUNCT
ejpam-5993	20	36	subgroup	subgroup	NOUN
ejpam-5993	20	37	in	in	ADP
ejpam-5993	20	38	g	g	PROPN
ejpam-5993	20	39	if	if	SCONJ
ejpam-5993	20	40	g	g	PROPN
ejpam-5993	20	41	has	have	VERB
ejpam-5993	20	42	an	an	DET
ejpam-5993	20	43	s	s	NOUN
ejpam-5993	20	44	-	-	PUNCT
ejpam-5993	20	45	permutable	permutable	ADJ
ejpam-5993	20	46	subgroup	subgroup	NOUN
ejpam-5993	20	47	k	k	PROPN
ejpam-5993	20	48	such	such	ADJ
ejpam-5993	20	49	that44	that44	NOUN
ejpam-5993	20	50	hsg	hsg	NOUN
ejpam-5993	20	51	=	=	SYM
ejpam-5993	20	52	hk	hk	PROPN
ejpam-5993	20	53	and	and	CCONJ
ejpam-5993	20	54	hg	hg	NOUN
ejpam-5993	20	55	∩	∩	NOUN
ejpam-5993	20	56	nk(h	nk(h	NUM
ejpam-5993	20	57	)	)	PUNCT
ejpam-5993	20	58	⩽	⩽	ADJ
ejpam-5993	20	59	h	h	NOUN
ejpam-5993	20	60	,	,	PUNCT
ejpam-5993	20	61	for	for	ADP
ejpam-5993	20	62	all	all	PRON
ejpam-5993	20	63	g	g	PROPN
ejpam-5993	20	64	∈	∈	PROPN
ejpam-5993	20	65	g	g	NOUN
ejpam-5993	20	66	,	,	PUNCT
ejpam-5993	20	67	where	where	SCONJ
ejpam-5993	20	68	hsg	hsg	NOUN
ejpam-5993	20	69	is	be	AUX
ejpam-5993	20	70	the	the	DET
ejpam-5993	20	71	intersection45	intersection45	NOUN
ejpam-5993	20	72	of	of	ADP
ejpam-5993	20	73	all	all	DET
ejpam-5993	20	74	s	s	NOUN
ejpam-5993	20	75	-	-	ADJ
ejpam-5993	20	76	permutable	permutable	ADJ
ejpam-5993	20	77	subgroups	subgroup	NOUN
ejpam-5993	20	78	of	of	ADP
ejpam-5993	20	79	g	g	NOUN
ejpam-5993	20	80	containing	contain	VERB
ejpam-5993	20	81	h	h	NOUN
ejpam-5993	20	82	,	,	PUNCT
ejpam-5993	20	83	that	that	ADV
ejpam-5993	20	84	is	is	ADV
ejpam-5993	20	85	,	,	PUNCT
ejpam-5993	20	86	hsg	hsg	NOUN
ejpam-5993	20	87	=	=	SYM
ejpam-5993	20	88	∩{l	∩{l	ADV
ejpam-5993	20	89	≤	≤	ADJ
ejpam-5993	20	90	g	g	NOUN
ejpam-5993	20	91	:	:	PUNCT
ejpam-5993	20	92	h	h	NOUN
ejpam-5993	20	93	⩽46	⩽46	X
ejpam-5993	20	94	l	l	PROPN
ejpam-5993	20	95	and	and	CCONJ
ejpam-5993	20	96	l	l	NOUN
ejpam-5993	20	97	is	be	AUX
ejpam-5993	20	98	an	an	DET
ejpam-5993	20	99	s	s	NOUN
ejpam-5993	20	100	-	-	PUNCT
ejpam-5993	20	101	permutable	permutable	ADJ
ejpam-5993	20	102	subgroup	subgroup	NOUN
ejpam-5993	20	103	in	in	ADP
ejpam-5993	20	104	g	g	PROPN
ejpam-5993	20	105	}	}	PUNCT
ejpam-5993	20	106	.	.	PUNCT
ejpam-5993	21	1	clearly	clearly	ADV
ejpam-5993	21	2	,	,	PUNCT
ejpam-5993	21	3	every	every	DET
ejpam-5993	21	4	weakly	weakly	ADJ
ejpam-5993	21	5	hc	hc	ADV
ejpam-5993	21	6	-	-	PUNCT
ejpam-5993	21	7	embedded	embed	VERB
ejpam-5993	21	8	in	in	ADP
ejpam-5993	21	9	g47	g47	PROPN
ejpam-5993	21	10	is	be	AUX
ejpam-5993	21	11	an	an	DET
ejpam-5993	21	12	ssh	ssh	NOUN
ejpam-5993	21	13	-	-	PUNCT
ejpam-5993	21	14	subgroup	subgroup	NOUN
ejpam-5993	21	15	in	in	ADP
ejpam-5993	21	16	g	g	PROPN
ejpam-5993	21	17	;	;	PUNCT
ejpam-5993	21	18	to	to	PART
ejpam-5993	21	19	see	see	VERB
ejpam-5993	21	20	that	that	PRON
ejpam-5993	21	21	,	,	PUNCT
ejpam-5993	21	22	assume	assume	VERB
ejpam-5993	21	23	that	that	SCONJ
ejpam-5993	21	24	h	h	NOUN
ejpam-5993	21	25	is	be	AUX
ejpam-5993	21	26	weakly	weakly	ADJ
ejpam-5993	21	27	hc	hc	ADV
ejpam-5993	21	28	-	-	PUNCT
ejpam-5993	21	29	embedded	embed	VERB
ejpam-5993	21	30	in	in	ADP
ejpam-5993	21	31	g.48	g.48	PROPN
ejpam-5993	21	32	then	then	ADV
ejpam-5993	21	33	there	there	PRON
ejpam-5993	21	34	exists	exist	VERB
ejpam-5993	21	35	a	a	DET
ejpam-5993	21	36	normal	normal	ADJ
ejpam-5993	21	37	subgroup	subgroup	NOUN
ejpam-5993	21	38	t	t	PROPN
ejpam-5993	21	39	of	of	ADP
ejpam-5993	21	40	g	g	PROPN
ejpam-5993	22	1	such	such	ADJ
ejpam-5993	22	2	that	that	PRON
ejpam-5993	22	3	hg	hg	NOUN
ejpam-5993	22	4	=	=	PUNCT
ejpam-5993	22	5	ht	ht	PROPN
ejpam-5993	22	6	and	and	CCONJ
ejpam-5993	22	7	hg	hg	NOUN
ejpam-5993	22	8	∩nt	∩nt	PROPN
ejpam-5993	22	9	(	(	PUNCT
ejpam-5993	22	10	h	h	NOUN
ejpam-5993	22	11	)	)	PUNCT
ejpam-5993	22	12	⩽	⩽	NOUN
ejpam-5993	22	13	h,49	h,49	PROPN
ejpam-5993	22	14	for	for	ADP
ejpam-5993	22	15	all	all	DET
ejpam-5993	22	16	g	g	PROPN
ejpam-5993	22	17	∈	∈	PROPN
ejpam-5993	22	18	g.	g.	PROPN
ejpam-5993	22	19	note	note	VERB
ejpam-5993	22	20	that	that	DET
ejpam-5993	22	21	hsg	hsg	NOUN
ejpam-5993	22	22	is	be	AUX
ejpam-5993	22	23	s	s	NOUN
ejpam-5993	22	24	-	-	NOUN
ejpam-5993	22	25	permutable	permutable	ADJ
ejpam-5993	22	26	in	in	ADP
ejpam-5993	22	27	g	g	NOUN
ejpam-5993	22	28	and	and	CCONJ
ejpam-5993	22	29	hsg	hsg	VERB
ejpam-5993	22	30	⩽	⩽	ADJ
ejpam-5993	22	31	hg	hg	NOUN
ejpam-5993	22	32	by	by	ADP
ejpam-5993	22	33	lemma	lemma	PROPN
ejpam-5993	22	34	6	6	NUM
ejpam-5993	22	35	.	.	PUNCT
ejpam-5993	22	36	so,50	so,50	PRON
ejpam-5993	22	37	hsg	hsg	NOUN
ejpam-5993	22	38	=	=	SYM
ejpam-5993	22	39	hsg	hsg	NOUN
ejpam-5993	22	40	∩	∩	NOUN
ejpam-5993	22	41	ht	ht	PROPN
ejpam-5993	22	42	=	=	PUNCT
ejpam-5993	22	43	h	h	PROPN
ejpam-5993	22	44	(	(	PUNCT
ejpam-5993	22	45	hsg	hsg	NOUN
ejpam-5993	22	46	∩	∩	NOUN
ejpam-5993	22	47	t	t	NOUN
ejpam-5993	22	48	)	)	PUNCT
ejpam-5993	23	1	=	=	SYM
ejpam-5993	23	2	hk	hk	PROPN
ejpam-5993	23	3	,	,	PUNCT
ejpam-5993	23	4	where	where	SCONJ
ejpam-5993	23	5	k	k	PROPN
ejpam-5993	23	6	=	=	PRON
ejpam-5993	23	7	hsg	hsg	PROPN
ejpam-5993	23	8	∩	∩	PROPN
ejpam-5993	23	9	t	t	PROPN
ejpam-5993	23	10	.	.	PUNCT
ejpam-5993	24	1	moreover	moreover	ADV
ejpam-5993	24	2	,	,	PUNCT
ejpam-5993	24	3	k	k	PROPN
ejpam-5993	24	4	is	be	AUX
ejpam-5993	24	5	s-51	s-51	VERB
ejpam-5993	24	6	permutable	permutable	ADJ
ejpam-5993	24	7	in	in	ADP
ejpam-5993	24	8	g	g	NOUN
ejpam-5993	24	9	by	by	ADP
ejpam-5993	24	10	[	[	X
ejpam-5993	24	11	1	1	NUM
ejpam-5993	24	12	,	,	PUNCT
ejpam-5993	24	13	satz	satz	X
ejpam-5993	24	14	2	2	NUM
ejpam-5993	24	15	]	]	PUNCT
ejpam-5993	24	16	.	.	PUNCT
ejpam-5993	25	1	clearly	clearly	ADV
ejpam-5993	25	2	,	,	PUNCT
ejpam-5993	25	3	hg	hg	PROPN
ejpam-5993	25	4	∩	∩	NOUN
ejpam-5993	25	5	nk(h	nk(h	X
ejpam-5993	25	6	)	)	PUNCT
ejpam-5993	25	7	=	=	SYM
ejpam-5993	25	8	hg	hg	PROPN
ejpam-5993	25	9	∩	∩	X
ejpam-5993	25	10	ng(h	ng(h	NUM
ejpam-5993	25	11	)	)	PUNCT
ejpam-5993	25	12	∩	∩	NOUN
ejpam-5993	25	13	t	t	PROPN
ejpam-5993	25	14	∩	∩	NOUN
ejpam-5993	25	15	hsg	hsg	NOUN
ejpam-5993	25	16	=	=	SYM
ejpam-5993	25	17	52	52	NUM
ejpam-5993	25	18	hg	hg	NOUN
ejpam-5993	25	19	∩nt	∩nt	PROPN
ejpam-5993	25	20	(	(	PUNCT
ejpam-5993	25	21	h	h	NOUN
ejpam-5993	25	22	)	)	PUNCT
ejpam-5993	25	23	∩hsg	∩hsg	ADJ
ejpam-5993	25	24	⩽	⩽	PROPN
ejpam-5993	25	25	h	h	PROPN
ejpam-5993	26	1	∩hsg	∩hsg	ADJ
ejpam-5993	27	1	=	=	SYM
ejpam-5993	27	2	h	h	NOUN
ejpam-5993	27	3	,	,	PUNCT
ejpam-5993	27	4	for	for	ADP
ejpam-5993	27	5	all	all	DET
ejpam-5993	27	6	g	g	PROPN
ejpam-5993	27	7	∈	∈	PROPN
ejpam-5993	27	8	g.	g.	NOUN
ejpam-5993	27	9	thus	thus	ADV
ejpam-5993	27	10	h	h	PROPN
ejpam-5993	27	11	is	be	AUX
ejpam-5993	27	12	an	an	DET
ejpam-5993	27	13	ssh	ssh	NOUN
ejpam-5993	27	14	-	-	PUNCT
ejpam-5993	27	15	subgroup	subgroup	NOUN
ejpam-5993	27	16	in	in	ADP
ejpam-5993	27	17	g.53	g.53	NOUN
ejpam-5993	27	18	but	but	CCONJ
ejpam-5993	27	19	the	the	DET
ejpam-5993	27	20	converse	converse	NOUN
ejpam-5993	27	21	is	be	AUX
ejpam-5993	27	22	not	not	PART
ejpam-5993	27	23	true	true	ADJ
ejpam-5993	27	24	in	in	ADP
ejpam-5993	27	25	general	general	ADJ
ejpam-5993	27	26	(	(	PUNCT
ejpam-5993	27	27	see	see	VERB
ejpam-5993	27	28	[	[	X
ejpam-5993	27	29	6	6	NUM
ejpam-5993	27	30	,	,	PUNCT
ejpam-5993	27	31	example	example	NOUN
ejpam-5993	27	32	1.5]).54	1.5]).54	NUM
ejpam-5993	27	33	55	55	NUM
ejpam-5993	27	34	several	several	ADJ
ejpam-5993	27	35	researchers	researcher	NOUN
ejpam-5993	27	36	have	have	AUX
ejpam-5993	27	37	studied	study	VERB
ejpam-5993	27	38	the	the	DET
ejpam-5993	27	39	structure	structure	NOUN
ejpam-5993	27	40	of	of	ADP
ejpam-5993	27	41	finite	finite	ADJ
ejpam-5993	27	42	groups	group	NOUN
ejpam-5993	27	43	by	by	ADP
ejpam-5993	27	44	using	use	VERB
ejpam-5993	27	45	the	the	DET
ejpam-5993	27	46	above	above	ADJ
ejpam-5993	27	47	men-56	men-56	PRON
ejpam-5993	27	48	tioned	tione	VERB
ejpam-5993	27	49	concepts	concept	NOUN
ejpam-5993	27	50	.	.	PUNCT
ejpam-5993	28	1	for	for	ADP
ejpam-5993	28	2	example	example	NOUN
ejpam-5993	28	3	,	,	PUNCT
ejpam-5993	28	4	in	in	ADP
ejpam-5993	28	5	1980	1980	NUM
ejpam-5993	28	6	,	,	PUNCT
ejpam-5993	28	7	srinivasan	srinivasan	NOUN
ejpam-5993	28	8	[	[	X
ejpam-5993	28	9	7	7	NUM
ejpam-5993	28	10	]	]	PUNCT
ejpam-5993	28	11	proved	prove	VERB
ejpam-5993	28	12	that	that	SCONJ
ejpam-5993	28	13	if	if	SCONJ
ejpam-5993	28	14	all	all	DET
ejpam-5993	28	15	maximal	maximal	ADJ
ejpam-5993	28	16	subgroups57	subgroups57	NOUN
ejpam-5993	28	17	of	of	ADP
ejpam-5993	28	18	every	every	DET
ejpam-5993	28	19	sylow	sylow	NOUN
ejpam-5993	28	20	subgroup	subgroup	NOUN
ejpam-5993	28	21	of	of	ADP
ejpam-5993	28	22	a	a	DET
ejpam-5993	28	23	group	group	NOUN
ejpam-5993	28	24	g	g	NOUN
ejpam-5993	28	25	are	be	AUX
ejpam-5993	28	26	normal	normal	ADJ
ejpam-5993	28	27	in	in	ADP
ejpam-5993	28	28	g	g	PROPN
ejpam-5993	28	29	,	,	PUNCT
ejpam-5993	28	30	then	then	ADV
ejpam-5993	28	31	g	g	PROPN
ejpam-5993	28	32	is	be	AUX
ejpam-5993	28	33	supersolvable	supersolvable	ADJ
ejpam-5993	28	34	.	.	PUNCT
ejpam-5993	28	35	wang58	wang58	VERB
ejpam-5993	29	1	[	[	X
ejpam-5993	29	2	2	2	X
ejpam-5993	29	3	]	]	PUNCT
ejpam-5993	29	4	got	get	VERB
ejpam-5993	29	5	the	the	DET
ejpam-5993	29	6	supersolvability	supersolvability	NOUN
ejpam-5993	29	7	of	of	ADP
ejpam-5993	29	8	the	the	DET
ejpam-5993	29	9	group	group	NOUN
ejpam-5993	29	10	g	g	NOUN
ejpam-5993	29	11	when	when	SCONJ
ejpam-5993	29	12	all	all	DET
ejpam-5993	29	13	maximal	maximal	ADJ
ejpam-5993	29	14	subgroups	subgroup	NOUN
ejpam-5993	29	15	of	of	ADP
ejpam-5993	29	16	every	every	DET
ejpam-5993	29	17	sylow59	sylow59	NOUN
ejpam-5993	29	18	subgroup	subgroup	NOUN
ejpam-5993	29	19	of	of	ADP
ejpam-5993	29	20	g	g	PROPN
ejpam-5993	29	21	are	be	AUX
ejpam-5993	29	22	c	c	NOUN
ejpam-5993	29	23	-	-	ADJ
ejpam-5993	29	24	normal	normal	ADJ
ejpam-5993	29	25	in	in	ADP
ejpam-5993	29	26	g.	g.	PROPN
ejpam-5993	29	27	moreover	moreover	ADV
ejpam-5993	29	28	,	,	PUNCT
ejpam-5993	29	29	asaad	asaad	VERB
ejpam-5993	29	30	in	in	ADP
ejpam-5993	29	31	[	[	X
ejpam-5993	29	32	8	8	NUM
ejpam-5993	29	33	]	]	PUNCT
ejpam-5993	29	34	proved	prove	VERB
ejpam-5993	29	35	that	that	SCONJ
ejpam-5993	29	36	if	if	SCONJ
ejpam-5993	29	37	all	all	DET
ejpam-5993	29	38	maximal	maximal	ADJ
ejpam-5993	29	39	sub-60	sub-60	NOUN
ejpam-5993	29	40	groups	group	NOUN
ejpam-5993	29	41	of	of	ADP
ejpam-5993	29	42	every	every	DET
ejpam-5993	29	43	sylow	sylow	NOUN
ejpam-5993	29	44	subgroup	subgroup	NOUN
ejpam-5993	29	45	of	of	ADP
ejpam-5993	29	46	g	g	PROPN
ejpam-5993	29	47	are	be	AUX
ejpam-5993	29	48	h	h	NOUN
ejpam-5993	29	49	-	-	PUNCT
ejpam-5993	29	50	subgroups	subgroup	NOUN
ejpam-5993	29	51	in	in	ADP
ejpam-5993	29	52	g	g	NOUN
ejpam-5993	29	53	,	,	PUNCT
ejpam-5993	29	54	then	then	ADV
ejpam-5993	29	55	g	g	PROPN
ejpam-5993	29	56	is	be	AUX
ejpam-5993	29	57	supersolvable	supersolvable	ADJ
ejpam-5993	29	58	.	.	PUNCT
ejpam-5993	30	1	in61	in61	PROPN
ejpam-5993	30	2	addition	addition	NOUN
ejpam-5993	30	3	,	,	PUNCT
ejpam-5993	30	4	in	in	ADP
ejpam-5993	30	5	[	[	PUNCT
ejpam-5993	30	6	4	4	NUM
ejpam-5993	30	7	]	]	PUNCT
ejpam-5993	30	8	,	,	PUNCT
ejpam-5993	30	9	wei	wei	PROPN
ejpam-5993	30	10	and	and	CCONJ
ejpam-5993	30	11	guo	guo	PROPN
ejpam-5993	30	12	obtained	obtain	VERB
ejpam-5993	30	13	the	the	DET
ejpam-5993	30	14	same	same	ADJ
ejpam-5993	30	15	previous	previous	ADJ
ejpam-5993	30	16	result	result	NOUN
ejpam-5993	30	17	by	by	ADP
ejpam-5993	30	18	replacing	replace	VERB
ejpam-5993	30	19	h	h	NOUN
ejpam-5993	30	20	-	-	PUNCT
ejpam-5993	30	21	subgroup62	subgroup62	NOUN
ejpam-5993	30	22	with	with	ADP
ejpam-5993	30	23	hc	hc	PROPN
ejpam-5993	30	24	-	-	PUNCT
ejpam-5993	30	25	subgroup	subgroup	NOUN
ejpam-5993	30	26	.	.	PUNCT
ejpam-5993	31	1	asaad	asaad	PROPN
ejpam-5993	31	2	and	and	CCONJ
ejpam-5993	31	3	ramadan	ramadan	PROPN
ejpam-5993	32	1	[	[	X
ejpam-5993	32	2	5	5	NUM
ejpam-5993	32	3	]	]	PUNCT
ejpam-5993	32	4	,	,	PUNCT
ejpam-5993	32	5	studied	study	VERB
ejpam-5993	32	6	extensively	extensively	ADV
ejpam-5993	32	7	the	the	DET
ejpam-5993	32	8	structure	structure	NOUN
ejpam-5993	32	9	of	of	ADP
ejpam-5993	32	10	a	a	DET
ejpam-5993	32	11	finite63	finite63	NOUN
ejpam-5993	32	12	group	group	NOUN
ejpam-5993	32	13	by	by	ADP
ejpam-5993	32	14	using	use	VERB
ejpam-5993	32	15	the	the	DET
ejpam-5993	32	16	weakly	weakly	ADJ
ejpam-5993	32	17	hc	hc	ADV
ejpam-5993	32	18	-	-	PUNCT
ejpam-5993	32	19	embedded	embed	VERB
ejpam-5993	32	20	subgroup	subgroup	NOUN
ejpam-5993	32	21	concept	concept	NOUN
ejpam-5993	32	22	and	and	CCONJ
ejpam-5993	32	23	proved	prove	VERB
ejpam-5993	32	24	that	that	PRON
ejpam-5993	32	25	:	:	PUNCT
ejpam-5993	32	26	let	let	VERB
ejpam-5993	32	27	g	g	PROPN
ejpam-5993	32	28	be64	be64	PROPN
ejpam-5993	32	29	a	a	DET
ejpam-5993	32	30	group	group	NOUN
ejpam-5993	32	31	and	and	CCONJ
ejpam-5993	32	32	p	p	X
ejpam-5993	32	33	a	a	DET
ejpam-5993	32	34	sylow	sylow	NOUN
ejpam-5993	32	35	p	p	NOUN
ejpam-5993	32	36	-	-	PUNCT
ejpam-5993	32	37	subgroup	subgroup	NOUN
ejpam-5993	32	38	of	of	ADP
ejpam-5993	32	39	g.	g.	PROPN
ejpam-5993	32	40	then	then	ADV
ejpam-5993	32	41	g	g	PROPN
ejpam-5993	32	42	is	be	AUX
ejpam-5993	32	43	p	p	NOUN
ejpam-5993	32	44	-	-	PUNCT
ejpam-5993	32	45	nilpotent	nilpotent	ADJ
ejpam-5993	32	46	if	if	SCONJ
ejpam-5993	32	47	and	and	CCONJ
ejpam-5993	32	48	only	only	ADV
ejpam-5993	32	49	if	if	SCONJ
ejpam-5993	32	50	ng(p	ng(p	NOUN
ejpam-5993	32	51	)	)	PUNCT
ejpam-5993	33	1	is65	is65	PROPN
ejpam-5993	33	2	p	p	NOUN
ejpam-5993	33	3	-	-	PUNCT
ejpam-5993	33	4	nilpotent	nilpotent	NOUN
ejpam-5993	33	5	and	and	CCONJ
ejpam-5993	33	6	every	every	DET
ejpam-5993	33	7	maximal	maximal	ADJ
ejpam-5993	33	8	subgroup	subgroup	NOUN
ejpam-5993	33	9	of	of	ADP
ejpam-5993	33	10	p	p	PROPN
ejpam-5993	33	11	is	be	AUX
ejpam-5993	33	12	weakly	weakly	ADJ
ejpam-5993	33	13	hc	hc	ADV
ejpam-5993	33	14	-	-	PUNCT
ejpam-5993	33	15	embedded	embed	VERB
ejpam-5993	33	16	in	in	ADP
ejpam-5993	33	17	g.	g.	PROPN
ejpam-5993	33	18	in	in	ADP
ejpam-5993	33	19	the	the	DET
ejpam-5993	33	20	same66	same66	NOUN
ejpam-5993	33	21	line	line	NOUN
ejpam-5993	33	22	of	of	ADP
ejpam-5993	33	23	these	these	DET
ejpam-5993	33	24	studies	study	NOUN
ejpam-5993	33	25	,	,	PUNCT
ejpam-5993	33	26	al	al	PROPN
ejpam-5993	33	27	-	-	PUNCT
ejpam-5993	33	28	gafri	gafri	PROPN
ejpam-5993	33	29	and	and	CCONJ
ejpam-5993	33	30	nauman	nauman	NOUN
ejpam-5993	34	1	[	[	X
ejpam-5993	34	2	6	6	NUM
ejpam-5993	34	3	]	]	PUNCT
ejpam-5993	34	4	used	use	VERB
ejpam-5993	34	5	the	the	DET
ejpam-5993	34	6	ssh	ssh	PROPN
ejpam-5993	34	7	-	-	PUNCT
ejpam-5993	34	8	subgroup	subgroup	NOUN
ejpam-5993	34	9	concept	concept	NOUN
ejpam-5993	34	10	to	to	PART
ejpam-5993	34	11	get	get	VERB
ejpam-5993	34	12	a67	a67	NOUN
ejpam-5993	34	13	new	new	ADJ
ejpam-5993	34	14	structure	structure	NOUN
ejpam-5993	34	15	of	of	ADP
ejpam-5993	34	16	the	the	DET
ejpam-5993	34	17	group	group	NOUN
ejpam-5993	34	18	g.	g.	PROPN
ejpam-5993	34	19	in	in	ADP
ejpam-5993	34	20	fact	fact	NOUN
ejpam-5993	34	21	,	,	PUNCT
ejpam-5993	34	22	they	they	PRON
ejpam-5993	34	23	proved	prove	VERB
ejpam-5993	34	24	that	that	PRON
ejpam-5993	34	25	let	let	VERB
ejpam-5993	34	26	p	p	PRON
ejpam-5993	34	27	be	be	AUX
ejpam-5993	34	28	a	a	DET
ejpam-5993	34	29	sylow	sylow	NOUN
ejpam-5993	34	30	p	p	NOUN
ejpam-5993	34	31	-	-	PUNCT
ejpam-5993	34	32	subgroup	subgroup	NOUN
ejpam-5993	34	33	of	of	ADP
ejpam-5993	34	34	a68	a68	PROPN
ejpam-5993	34	35	group	group	NOUN
ejpam-5993	34	36	g	g	PROPN
ejpam-5993	34	37	,	,	PUNCT
ejpam-5993	34	38	for	for	ADP
ejpam-5993	34	39	some	some	DET
ejpam-5993	34	40	prime	prime	ADJ
ejpam-5993	34	41	p.	p.	NOUN
ejpam-5993	34	42	then	then	ADV
ejpam-5993	34	43	g	g	PROPN
ejpam-5993	34	44	is	be	AUX
ejpam-5993	34	45	p	p	NOUN
ejpam-5993	34	46	-	-	PUNCT
ejpam-5993	34	47	nilpotent	nilpotent	ADJ
ejpam-5993	34	48	if	if	SCONJ
ejpam-5993	34	49	and	and	CCONJ
ejpam-5993	34	50	only	only	ADV
ejpam-5993	34	51	if	if	SCONJ
ejpam-5993	34	52	ng(p	ng(p	NOUN
ejpam-5993	34	53	)	)	PUNCT
ejpam-5993	34	54	is	be	AUX
ejpam-5993	34	55	p	p	ADJ
ejpam-5993	34	56	-	-	PUNCT
ejpam-5993	34	57	nilpotent	nilpotent	ADJ
ejpam-5993	34	58	and69	and69	NOUN
ejpam-5993	34	59	every	every	DET
ejpam-5993	34	60	maximal	maximal	ADJ
ejpam-5993	34	61	subgroup	subgroup	NOUN
ejpam-5993	34	62	of	of	ADP
ejpam-5993	34	63	p	p	PROPN
ejpam-5993	34	64	is	be	AUX
ejpam-5993	34	65	an	an	DET
ejpam-5993	34	66	ssh	ssh	NOUN
ejpam-5993	34	67	-	-	PUNCT
ejpam-5993	34	68	subgroup	subgroup	NOUN
ejpam-5993	34	69	in	in	ADP
ejpam-5993	34	70	g.	g.	PROPN
ejpam-5993	34	71	also	also	ADV
ejpam-5993	34	72	,	,	PUNCT
ejpam-5993	34	73	they	they	PRON
ejpam-5993	34	74	proved	prove	VERB
ejpam-5993	34	75	that	that	SCONJ
ejpam-5993	34	76	a	a	DET
ejpam-5993	34	77	group70	group70	NOUN
ejpam-5993	34	78	a.	a.	PROPN
ejpam-5993	34	79	s.	s.	PROPN
ejpam-5993	34	80	allehyani	allehyani	PROPN
ejpam-5993	34	81	/	/	SYM
ejpam-5993	34	82	eur	eur	PROPN
ejpam-5993	34	83	.	.	PUNCT
ejpam-5993	35	1	j.	j.	PROPN
ejpam-5993	35	2	pure	pure	PROPN
ejpam-5993	35	3	appl	appl	PROPN
ejpam-5993	35	4	.	.	PROPN
ejpam-5993	35	5	math	math	PROPN
ejpam-5993	35	6	,	,	PUNCT
ejpam-5993	35	7	18	18	NUM
ejpam-5993	35	8	(	(	PUNCT
ejpam-5993	35	9	2	2	NUM
ejpam-5993	35	10	)	)	PUNCT
ejpam-5993	35	11	(	(	PUNCT
ejpam-5993	35	12	2025	2025	NUM
ejpam-5993	35	13	)	)	PUNCT
ejpam-5993	35	14	,	,	PUNCT
ejpam-5993	35	15	5993	5993	NUM
ejpam-5993	35	16	3	3	NUM
ejpam-5993	35	17	of	of	ADP
ejpam-5993	35	18	13	13	NUM
ejpam-5993	35	19	g	g	NOUN
ejpam-5993	35	20	is	be	AUX
ejpam-5993	35	21	supersolvable	supersolvable	ADJ
ejpam-5993	35	22	if	if	SCONJ
ejpam-5993	35	23	and	and	CCONJ
ejpam-5993	35	24	only	only	ADV
ejpam-5993	35	25	if	if	SCONJ
ejpam-5993	35	26	the	the	DET
ejpam-5993	35	27	maximal	maximal	ADJ
ejpam-5993	35	28	subgroups	subgroup	NOUN
ejpam-5993	35	29	of	of	ADP
ejpam-5993	35	30	the	the	DET
ejpam-5993	35	31	non	non	ADJ
ejpam-5993	35	32	-	-	ADJ
ejpam-5993	35	33	cyclic	cyclic	ADJ
ejpam-5993	35	34	sylow	sylow	NOUN
ejpam-5993	35	35	subgroups71	subgroups71	NOUN
ejpam-5993	35	36	of	of	ADP
ejpam-5993	35	37	g′	g′	NOUN
ejpam-5993	35	38	are	be	AUX
ejpam-5993	35	39	ssh	ssh	NOUN
ejpam-5993	35	40	-	-	PUNCT
ejpam-5993	35	41	subgroup	subgroup	NOUN
ejpam-5993	35	42	in	in	ADP
ejpam-5993	35	43	g.	g.	PROPN
ejpam-5993	35	44	for	for	ADP
ejpam-5993	35	45	more	more	ADJ
ejpam-5993	35	46	results	result	NOUN
ejpam-5993	35	47	along	along	ADP
ejpam-5993	35	48	these	these	DET
ejpam-5993	35	49	same	same	ADJ
ejpam-5993	35	50	lines	line	NOUN
ejpam-5993	35	51	;	;	PUNCT
ejpam-5993	35	52	see	see	VERB
ejpam-5993	35	53	[	[	X
ejpam-5993	35	54	9–12].72	9–12].72	NUM
ejpam-5993	35	55	73	73	NUM
ejpam-5993	35	56	the	the	DET
ejpam-5993	35	57	main	main	ADJ
ejpam-5993	35	58	aim	aim	NOUN
ejpam-5993	35	59	of	of	ADP
ejpam-5993	35	60	this	this	DET
ejpam-5993	35	61	paper	paper	NOUN
ejpam-5993	35	62	is	be	AUX
ejpam-5993	35	63	to	to	PART
ejpam-5993	35	64	continue	continue	VERB
ejpam-5993	35	65	the	the	DET
ejpam-5993	35	66	above	above	ADJ
ejpam-5993	35	67	mentioned	mention	VERB
ejpam-5993	35	68	investigations	investigation	NOUN
ejpam-5993	35	69	.	.	PUNCT
ejpam-5993	36	1	more74	more74	VERB
ejpam-5993	36	2	precisely	precisely	ADV
ejpam-5993	36	3	,	,	PUNCT
ejpam-5993	36	4	we	we	PRON
ejpam-5993	36	5	study	study	VERB
ejpam-5993	36	6	the	the	DET
ejpam-5993	36	7	structure	structure	NOUN
ejpam-5993	36	8	of	of	ADP
ejpam-5993	36	9	a	a	DET
ejpam-5993	36	10	finite	finite	ADJ
ejpam-5993	36	11	group	group	NOUN
ejpam-5993	36	12	g	g	PROPN
ejpam-5993	36	13	under	under	ADP
ejpam-5993	36	14	the	the	DET
ejpam-5993	36	15	assumption	assumption	NOUN
ejpam-5993	36	16	that	that	SCONJ
ejpam-5993	36	17	certain75	certain75	PROPN
ejpam-5993	36	18	subgroups	subgroup	NOUN
ejpam-5993	36	19	of	of	ADP
ejpam-5993	36	20	prime	prime	ADJ
ejpam-5993	36	21	power	power	NOUN
ejpam-5993	36	22	orders	order	NOUN
ejpam-5993	36	23	are	be	AUX
ejpam-5993	36	24	ssh	ssh	NOUN
ejpam-5993	36	25	-	-	PUNCT
ejpam-5993	36	26	subgroups	subgroup	NOUN
ejpam-5993	36	27	in	in	ADP
ejpam-5993	36	28	g	g	PROPN
ejpam-5993	36	29	itself.76	itself.76	PROPN
ejpam-5993	36	30	77	77	NUM
ejpam-5993	36	31	recall	recall	NOUN
ejpam-5993	36	32	that	that	SCONJ
ejpam-5993	36	33	a	a	DET
ejpam-5993	36	34	class	class	NOUN
ejpam-5993	36	35	of	of	ADP
ejpam-5993	36	36	group	group	NOUN
ejpam-5993	36	37	f	f	PROPN
ejpam-5993	36	38	is	be	AUX
ejpam-5993	36	39	said	say	VERB
ejpam-5993	36	40	to	to	PART
ejpam-5993	36	41	be	be	AUX
ejpam-5993	36	42	a	a	DET
ejpam-5993	36	43	formation	formation	NOUN
ejpam-5993	36	44	if	if	SCONJ
ejpam-5993	36	45	f	f	PROPN
ejpam-5993	36	46	is	be	AUX
ejpam-5993	36	47	closed	close	VERB
ejpam-5993	36	48	under	under	ADP
ejpam-5993	36	49	taking78	taking78	NOUN
ejpam-5993	36	50	epimorphic	epimorphic	ADJ
ejpam-5993	36	51	images	image	NOUN
ejpam-5993	36	52	and	and	CCONJ
ejpam-5993	36	53	every	every	DET
ejpam-5993	36	54	groupg	groupg	NOUN
ejpam-5993	36	55	has	have	VERB
ejpam-5993	36	56	a	a	DET
ejpam-5993	36	57	unique	unique	ADJ
ejpam-5993	36	58	smallest	small	ADJ
ejpam-5993	36	59	normal	normal	ADJ
ejpam-5993	36	60	subgroup	subgroup	NOUN
ejpam-5993	36	61	with	with	ADP
ejpam-5993	36	62	quotient79	quotient79	NOUN
ejpam-5993	36	63	in	in	ADP
ejpam-5993	36	64	f.	f.	PROPN
ejpam-5993	37	1	a	a	DET
ejpam-5993	37	2	formation	formation	NOUN
ejpam-5993	37	3	f	f	NOUN
ejpam-5993	37	4	is	be	AUX
ejpam-5993	37	5	called	call	VERB
ejpam-5993	37	6	saturated	saturated	ADJ
ejpam-5993	37	7	if	if	SCONJ
ejpam-5993	37	8	it	it	PRON
ejpam-5993	37	9	is	be	AUX
ejpam-5993	37	10	closed	close	VERB
ejpam-5993	37	11	under	under	ADP
ejpam-5993	37	12	taking	take	VERB
ejpam-5993	37	13	frattini	frattini	ADJ
ejpam-5993	37	14	extensions	extension	NOUN
ejpam-5993	37	15	.	.	PUNCT
ejpam-5993	38	1	u80	u80	NOUN
ejpam-5993	38	2	denotes	denote	VERB
ejpam-5993	38	3	the	the	DET
ejpam-5993	38	4	class	class	NOUN
ejpam-5993	38	5	of	of	ADP
ejpam-5993	38	6	all	all	DET
ejpam-5993	38	7	supersolvable	supersolvable	ADJ
ejpam-5993	38	8	groups	group	NOUN
ejpam-5993	38	9	.	.	PUNCT
ejpam-5993	39	1	clearly	clearly	ADV
ejpam-5993	39	2	,	,	PUNCT
ejpam-5993	39	3	u	u	NOUN
ejpam-5993	39	4	is	be	AUX
ejpam-5993	39	5	a	a	DET
ejpam-5993	39	6	saturated	saturated	ADJ
ejpam-5993	39	7	formation	formation	NOUN
ejpam-5993	39	8	(	(	PUNCT
ejpam-5993	39	9	see	see	VERB
ejpam-5993	39	10	[	[	X
ejpam-5993	39	11	13,81	13,81	NUM
ejpam-5993	39	12	p.	p.	NOUN
ejpam-5993	39	13	713	713	NUM
ejpam-5993	39	14	,	,	PUNCT
ejpam-5993	39	15	satz	satz	PROPN
ejpam-5993	39	16	8.6]).82	8.6]).82	PROPN
ejpam-5993	39	17	most	most	ADJ
ejpam-5993	39	18	of	of	ADP
ejpam-5993	39	19	the	the	DET
ejpam-5993	39	20	notation	notation	NOUN
ejpam-5993	39	21	is	be	AUX
ejpam-5993	39	22	standard	standard	ADJ
ejpam-5993	39	23	and	and	CCONJ
ejpam-5993	39	24	can	can	AUX
ejpam-5993	39	25	be	be	AUX
ejpam-5993	39	26	found	find	VERB
ejpam-5993	39	27	in	in	ADP
ejpam-5993	39	28	[	[	X
ejpam-5993	39	29	14	14	NUM
ejpam-5993	39	30	]	]	PUNCT
ejpam-5993	39	31	and	and	CCONJ
ejpam-5993	39	32	[	[	X
ejpam-5993	39	33	15	15	NUM
ejpam-5993	39	34	]	]	PUNCT
ejpam-5993	39	35	.	.	PUNCT
ejpam-5993	40	1	in	in	ADP
ejpam-5993	40	2	particular	particular	ADJ
ejpam-5993	40	3	,	,	PUNCT
ejpam-5993	40	4	|g|83	|g|83	PROPN
ejpam-5993	40	5	denotes	denote	VERB
ejpam-5993	40	6	the	the	DET
ejpam-5993	40	7	order	order	NOUN
ejpam-5993	40	8	of	of	ADP
ejpam-5993	40	9	g.	g.	PROPN
ejpam-5993	40	10	moreover	moreover	ADV
ejpam-5993	40	11	,	,	PUNCT
ejpam-5993	40	12	φ(g	φ(g	PROPN
ejpam-5993	40	13	)	)	PUNCT
ejpam-5993	40	14	,	,	PUNCT
ejpam-5993	40	15	f	f	PROPN
ejpam-5993	40	16	(	(	PUNCT
ejpam-5993	40	17	g	g	NOUN
ejpam-5993	40	18	)	)	PUNCT
ejpam-5993	40	19	and	and	CCONJ
ejpam-5993	40	20	f	f	PROPN
ejpam-5993	40	21	⋆(g	⋆(g	X
ejpam-5993	40	22	)	)	PUNCT
ejpam-5993	40	23	denote	denote	VERB
ejpam-5993	40	24	the	the	DET
ejpam-5993	40	25	frattini	frattini	NOUN
ejpam-5993	40	26	subgroup,84	subgroup,84	NOUN
ejpam-5993	40	27	the	the	DET
ejpam-5993	40	28	fitting	fitting	ADJ
ejpam-5993	40	29	subgroup	subgroup	NOUN
ejpam-5993	40	30	and	and	CCONJ
ejpam-5993	40	31	the	the	DET
ejpam-5993	40	32	generalized	generalized	ADJ
ejpam-5993	40	33	fitting	fitting	ADJ
ejpam-5993	40	34	subgroup	subgroup	NOUN
ejpam-5993	40	35	of	of	ADP
ejpam-5993	40	36	g.85	g.85	PROPN
ejpam-5993	40	37	2	2	PROPN
ejpam-5993	40	38	.	.	PUNCT
ejpam-5993	40	39	preliminaries86	preliminaries86	PROPN
ejpam-5993	40	40	in	in	ADP
ejpam-5993	40	41	this	this	DET
ejpam-5993	40	42	section	section	NOUN
ejpam-5993	40	43	,	,	PUNCT
ejpam-5993	40	44	we	we	PRON
ejpam-5993	40	45	state	state	VERB
ejpam-5993	40	46	some	some	DET
ejpam-5993	40	47	known	know	VERB
ejpam-5993	40	48	results	result	NOUN
ejpam-5993	40	49	from	from	ADP
ejpam-5993	40	50	the	the	DET
ejpam-5993	40	51	literature	literature	NOUN
ejpam-5993	40	52	which	which	PRON
ejpam-5993	40	53	will	will	AUX
ejpam-5993	40	54	be	be	AUX
ejpam-5993	40	55	used	use	VERB
ejpam-5993	40	56	in87	in87	PROPN
ejpam-5993	40	57	proving	prove	VERB
ejpam-5993	40	58	our	our	PRON
ejpam-5993	40	59	results.88	results.88	NOUN
ejpam-5993	40	60	lemma	lemma	PROPN
ejpam-5993	40	61	1	1	X
ejpam-5993	40	62	.	.	PUNCT
ejpam-5993	41	1	let	let	VERB
ejpam-5993	41	2	h	h	NOUN
ejpam-5993	41	3	and	and	CCONJ
ejpam-5993	41	4	l	l	NOUN
ejpam-5993	41	5	be	be	AUX
ejpam-5993	41	6	normal	normal	ADJ
ejpam-5993	41	7	subgroups	subgroup	NOUN
ejpam-5993	41	8	of	of	ADP
ejpam-5993	41	9	g	g	NOUN
ejpam-5993	41	10	and	and	CCONJ
ejpam-5993	41	11	let	let	VERB
ejpam-5993	41	12	p	p	NOUN
ejpam-5993	41	13	∈	∈	PROPN
ejpam-5993	41	14	π(g	π(g	PROPN
ejpam-5993	41	15	)	)	PUNCT
ejpam-5993	41	16	.	.	PUNCT
ejpam-5993	42	1	then	then	ADV
ejpam-5993	42	2	,	,	PUNCT
ejpam-5993	42	3	the	the	DET
ejpam-5993	42	4	following89	following89	ADJ
ejpam-5993	42	5	hold:90	hold:90	X
ejpam-5993	42	6	(	(	PUNCT
ejpam-5993	42	7	i	i	NOUN
ejpam-5993	42	8	)	)	PUNCT
ejpam-5993	42	9	φ(h	φ(h	PROPN
ejpam-5993	42	10	)	)	PUNCT
ejpam-5993	42	11	⩽	⩽	ADJ
ejpam-5993	42	12	φ(g).91	φ(g).91	NOUN
ejpam-5993	42	13	(	(	PUNCT
ejpam-5993	42	14	ii	ii	PROPN
ejpam-5993	42	15	)	)	PUNCT
ejpam-5993	42	16	if	if	SCONJ
ejpam-5993	42	17	l	l	PROPN
ejpam-5993	42	18	⩽	⩽	ADJ
ejpam-5993	42	19	φ(g	φ(g	PROPN
ejpam-5993	42	20	)	)	PUNCT
ejpam-5993	42	21	,	,	PUNCT
ejpam-5993	42	22	then	then	ADV
ejpam-5993	42	23	f	f	X
ejpam-5993	42	24	(	(	PUNCT
ejpam-5993	42	25	g	g	PROPN
ejpam-5993	42	26	/	/	SYM
ejpam-5993	42	27	l	l	NOUN
ejpam-5993	42	28	)	)	PUNCT
ejpam-5993	42	29	=	=	SYM
ejpam-5993	43	1	f	f	PROPN
ejpam-5993	43	2	(	(	PUNCT
ejpam-5993	43	3	g)/l.92	g)/l.92	NOUN
ejpam-5993	43	4	(	(	PUNCT
ejpam-5993	43	5	iii	iii	NOUN
ejpam-5993	43	6	)	)	PUNCT
ejpam-5993	43	7	if	if	SCONJ
ejpam-5993	43	8	l	l	PROPN
ejpam-5993	43	9	⩽	⩽	ADJ
ejpam-5993	43	10	h	h	NOUN
ejpam-5993	43	11	∩	∩	NOUN
ejpam-5993	43	12	φ(g	φ(g	PROPN
ejpam-5993	43	13	)	)	PUNCT
ejpam-5993	43	14	,	,	PUNCT
ejpam-5993	43	15	then	then	ADV
ejpam-5993	43	16	f	f	X
ejpam-5993	43	17	(	(	PUNCT
ejpam-5993	43	18	h	h	NOUN
ejpam-5993	43	19	/	/	SYM
ejpam-5993	43	20	l	l	NOUN
ejpam-5993	43	21	)	)	PUNCT
ejpam-5993	44	1	=	=	SYM
ejpam-5993	44	2	f	f	PROPN
ejpam-5993	44	3	(	(	PUNCT
ejpam-5993	44	4	h)/l.93	h)/l.93	NOUN
ejpam-5993	44	5	proof	proof	NOUN
ejpam-5993	44	6	.	.	PUNCT
ejpam-5993	45	1	for	for	ADP
ejpam-5993	45	2	(	(	PUNCT
ejpam-5993	45	3	i	i	NOUN
ejpam-5993	45	4	)	)	PUNCT
ejpam-5993	45	5	,	,	PUNCT
ejpam-5993	45	6	see	see	VERB
ejpam-5993	45	7	[	[	X
ejpam-5993	45	8	13	13	NUM
ejpam-5993	45	9	,	,	PUNCT
ejpam-5993	45	10	iii	iii	NOUN
ejpam-5993	45	11	,	,	PUNCT
ejpam-5993	45	12	hilfssatz	hilfssatz	X
ejpam-5993	45	13	3.3	3.3	NUM
ejpam-5993	45	14	]	]	PUNCT
ejpam-5993	45	15	.	.	PUNCT
ejpam-5993	46	1	for	for	ADP
ejpam-5993	46	2	(	(	PUNCT
ejpam-5993	46	3	ii	ii	NOUN
ejpam-5993	46	4	)	)	PUNCT
ejpam-5993	46	5	,	,	PUNCT
ejpam-5993	46	6	and	and	CCONJ
ejpam-5993	46	7	(	(	PUNCT
ejpam-5993	46	8	iii	iii	NOUN
ejpam-5993	46	9	)	)	PUNCT
ejpam-5993	46	10	,	,	PUNCT
ejpam-5993	46	11	see	see	VERB
ejpam-5993	46	12	[	[	X
ejpam-5993	46	13	16	16	NUM
ejpam-5993	46	14	,	,	PUNCT
ejpam-5993	46	15	lemma	lemma	PROPN
ejpam-5993	46	16	2.7].94	2.7].94	PROPN
ejpam-5993	46	17	lemma	lemma	PROPN
ejpam-5993	46	18	2	2	NUM
ejpam-5993	46	19	.	.	PUNCT
ejpam-5993	47	1	let	let	VERB
ejpam-5993	47	2	h	h	NOUN
ejpam-5993	47	3	,	,	PUNCT
ejpam-5993	47	4	m	m	PRON
ejpam-5993	47	5	and	and	CCONJ
ejpam-5993	47	6	l	l	PROPN
ejpam-5993	47	7	be	be	AUX
ejpam-5993	47	8	subgroups	subgroup	NOUN
ejpam-5993	47	9	of	of	ADP
ejpam-5993	47	10	a	a	DET
ejpam-5993	47	11	group	group	NOUN
ejpam-5993	47	12	g	g	NOUN
ejpam-5993	47	13	such	such	ADJ
ejpam-5993	47	14	that	that	SCONJ
ejpam-5993	47	15	h	h	NOUN
ejpam-5993	47	16	is	be	AUX
ejpam-5993	47	17	an	an	DET
ejpam-5993	47	18	sshsubgroup95	sshsubgroup95	NOUN
ejpam-5993	47	19	in	in	ADP
ejpam-5993	47	20	g	g	PROPN
ejpam-5993	47	21	and	and	CCONJ
ejpam-5993	47	22	l	l	NOUN
ejpam-5993	48	1	◁	◁	X
ejpam-5993	49	1	g.	g.	NOUN
ejpam-5993	49	2	then	then	ADV
ejpam-5993	49	3	the	the	DET
ejpam-5993	49	4	following	follow	VERB
ejpam-5993	49	5	statements	statement	NOUN
ejpam-5993	49	6	hold:96	hold:96	X
ejpam-5993	49	7	(	(	PUNCT
ejpam-5993	49	8	i	i	NOUN
ejpam-5993	49	9	)	)	PUNCT
ejpam-5993	49	10	if	if	SCONJ
ejpam-5993	49	11	h	h	PROPN
ejpam-5993	49	12	⩽	⩽	PROPN
ejpam-5993	49	13	m	m	VERB
ejpam-5993	49	14	,	,	PUNCT
ejpam-5993	49	15	then	then	ADV
ejpam-5993	49	16	h	h	NOUN
ejpam-5993	49	17	is	be	AUX
ejpam-5993	49	18	an	an	DET
ejpam-5993	49	19	ssh	ssh	NOUN
ejpam-5993	49	20	-	-	PUNCT
ejpam-5993	49	21	subgroup	subgroup	NOUN
ejpam-5993	49	22	in	in	ADP
ejpam-5993	49	23	m	m	PROPN
ejpam-5993	49	24	.97	.97	NUM
ejpam-5993	49	25	(	(	PUNCT
ejpam-5993	49	26	ii	ii	NOUN
ejpam-5993	49	27	)	)	PUNCT
ejpam-5993	49	28	assume	assume	VERB
ejpam-5993	49	29	that	that	SCONJ
ejpam-5993	49	30	l	l	PROPN
ejpam-5993	49	31	⩽	⩽	ADJ
ejpam-5993	49	32	m	m	PROPN
ejpam-5993	49	33	.	.	PUNCT
ejpam-5993	50	1	then	then	ADV
ejpam-5993	50	2	m	m	PROPN
ejpam-5993	50	3	is	be	AUX
ejpam-5993	50	4	an	an	DET
ejpam-5993	50	5	ssh	ssh	NOUN
ejpam-5993	50	6	-	-	PUNCT
ejpam-5993	50	7	subgroup	subgroup	NOUN
ejpam-5993	50	8	in	in	ADP
ejpam-5993	50	9	g	g	PROPN
ejpam-5993	50	10	if	if	SCONJ
ejpam-5993	51	1	and	and	CCONJ
ejpam-5993	51	2	only	only	ADV
ejpam-5993	51	3	if	if	SCONJ
ejpam-5993	51	4	m	m	NOUN
ejpam-5993	51	5	/	/	SYM
ejpam-5993	51	6	l	l	NOUN
ejpam-5993	51	7	is	be	AUX
ejpam-5993	51	8	an98	an98	PROPN
ejpam-5993	51	9	ssh	ssh	NOUN
ejpam-5993	51	10	-	-	PUNCT
ejpam-5993	51	11	subgroup	subgroup	NOUN
ejpam-5993	51	12	in	in	ADP
ejpam-5993	51	13	g	g	PROPN
ejpam-5993	51	14	/	/	SYM
ejpam-5993	51	15	l.99	l.99	PROPN
ejpam-5993	51	16	(	(	PUNCT
ejpam-5993	51	17	iii	iii	NOUN
ejpam-5993	51	18	)	)	PUNCT
ejpam-5993	51	19	assume	assume	VERB
ejpam-5993	51	20	that	that	SCONJ
ejpam-5993	51	21	h	h	NOUN
ejpam-5993	51	22	is	be	AUX
ejpam-5993	51	23	a	a	DET
ejpam-5993	51	24	p	p	NOUN
ejpam-5993	51	25	-	-	PUNCT
ejpam-5993	51	26	subgroup	subgroup	NOUN
ejpam-5993	51	27	of	of	ADP
ejpam-5993	51	28	g	g	PROPN
ejpam-5993	51	29	and	and	CCONJ
ejpam-5993	51	30	l	l	NOUN
ejpam-5993	51	31	is	be	AUX
ejpam-5993	51	32	a	a	DET
ejpam-5993	51	33	p′-subgroup	p′-subgroup	NUM
ejpam-5993	51	34	of	of	ADP
ejpam-5993	51	35	g	g	PROPN
ejpam-5993	51	36	,	,	PUNCT
ejpam-5993	51	37	for	for	ADP
ejpam-5993	51	38	some	some	DET
ejpam-5993	51	39	prime	prime	ADJ
ejpam-5993	51	40	p.100	p.100	NOUN
ejpam-5993	51	41	then	then	ADV
ejpam-5993	51	42	hl	hl	NOUN
ejpam-5993	51	43	and	and	CCONJ
ejpam-5993	51	44	hl	hl	NOUN
ejpam-5993	51	45	/	/	SYM
ejpam-5993	51	46	l	l	NOUN
ejpam-5993	51	47	are	be	AUX
ejpam-5993	51	48	ssh	ssh	NOUN
ejpam-5993	51	49	-	-	PUNCT
ejpam-5993	51	50	subgroups	subgroup	NOUN
ejpam-5993	51	51	in	in	ADP
ejpam-5993	51	52	g	g	PROPN
ejpam-5993	51	53	and	and	CCONJ
ejpam-5993	51	54	g	g	NOUN
ejpam-5993	51	55	/	/	SYM
ejpam-5993	51	56	l	l	NOUN
ejpam-5993	51	57	,	,	PUNCT
ejpam-5993	51	58	respectively.101	respectively.101	NOUN
ejpam-5993	51	59	proof	proof	NOUN
ejpam-5993	51	60	.	.	PUNCT
ejpam-5993	52	1	see	see	VERB
ejpam-5993	52	2	[	[	X
ejpam-5993	52	3	6	6	NUM
ejpam-5993	52	4	,	,	PUNCT
ejpam-5993	52	5	lemma	lemma	PROPN
ejpam-5993	52	6	2.4].102	2.4].102	NUM
ejpam-5993	52	7	a.	a.	NOUN
ejpam-5993	52	8	s.	s.	PROPN
ejpam-5993	52	9	allehyani	allehyani	PROPN
ejpam-5993	52	10	/	/	SYM
ejpam-5993	52	11	eur	eur	PROPN
ejpam-5993	52	12	.	.	PUNCT
ejpam-5993	53	1	j.	j.	PROPN
ejpam-5993	53	2	pure	pure	PROPN
ejpam-5993	53	3	appl	appl	PROPN
ejpam-5993	53	4	.	.	PROPN
ejpam-5993	53	5	math	math	PROPN
ejpam-5993	53	6	,	,	PUNCT
ejpam-5993	53	7	18	18	NUM
ejpam-5993	53	8	(	(	PUNCT
ejpam-5993	53	9	2	2	NUM
ejpam-5993	53	10	)	)	PUNCT
ejpam-5993	53	11	(	(	PUNCT
ejpam-5993	53	12	2025	2025	NUM
ejpam-5993	53	13	)	)	PUNCT
ejpam-5993	53	14	,	,	PUNCT
ejpam-5993	53	15	5993	5993	NUM
ejpam-5993	53	16	4	4	NUM
ejpam-5993	53	17	of	of	ADP
ejpam-5993	53	18	13	13	NUM
ejpam-5993	53	19	lemma	lemma	PROPN
ejpam-5993	53	20	3	3	X
ejpam-5993	53	21	.	.	PUNCT
ejpam-5993	54	1	let	let	VERB
ejpam-5993	54	2	g	g	PRON
ejpam-5993	54	3	be	be	AUX
ejpam-5993	54	4	a	a	DET
ejpam-5993	54	5	group	group	NOUN
ejpam-5993	54	6	and	and	CCONJ
ejpam-5993	54	7	let	let	VERB
ejpam-5993	54	8	n	n	PRON
ejpam-5993	54	9	be	be	AUX
ejpam-5993	54	10	a	a	DET
ejpam-5993	54	11	nontrivial	nontrivial	ADJ
ejpam-5993	54	12	normal	normal	ADJ
ejpam-5993	54	13	subgroup	subgroup	NOUN
ejpam-5993	54	14	of	of	ADP
ejpam-5993	54	15	g.	g.	PROPN
ejpam-5993	55	1	if	if	SCONJ
ejpam-5993	55	2	n∩φ(g	n∩φ(g	NOUN
ejpam-5993	55	3	)	)	PUNCT
ejpam-5993	56	1	=	=	NOUN
ejpam-5993	56	2	103	103	NUM
ejpam-5993	56	3	1	1	NUM
ejpam-5993	56	4	,	,	PUNCT
ejpam-5993	56	5	then	then	ADV
ejpam-5993	56	6	f	f	PROPN
ejpam-5993	56	7	(	(	PUNCT
ejpam-5993	56	8	n	n	CCONJ
ejpam-5993	56	9	)	)	PUNCT
ejpam-5993	56	10	,	,	PUNCT
ejpam-5993	56	11	the	the	DET
ejpam-5993	56	12	fitting	fitting	ADJ
ejpam-5993	56	13	subgroup	subgroup	NOUN
ejpam-5993	56	14	of	of	ADP
ejpam-5993	56	15	n	n	PROPN
ejpam-5993	56	16	,	,	PUNCT
ejpam-5993	56	17	is	be	AUX
ejpam-5993	56	18	the	the	DET
ejpam-5993	56	19	direct	direct	ADJ
ejpam-5993	56	20	product	product	NOUN
ejpam-5993	56	21	of	of	ADP
ejpam-5993	56	22	the	the	DET
ejpam-5993	56	23	minimal	minimal	ADJ
ejpam-5993	56	24	normal104	normal104	PROPN
ejpam-5993	56	25	subgroups	subgroup	NOUN
ejpam-5993	56	26	of	of	ADP
ejpam-5993	56	27	g	g	NOUN
ejpam-5993	56	28	which	which	PRON
ejpam-5993	56	29	are	be	AUX
ejpam-5993	56	30	contained	contain	VERB
ejpam-5993	56	31	in	in	ADP
ejpam-5993	56	32	f	f	PROPN
ejpam-5993	56	33	(	(	PUNCT
ejpam-5993	56	34	n).105	n).105	ADP
ejpam-5993	56	35	proof	proof	NOUN
ejpam-5993	56	36	.	.	PUNCT
ejpam-5993	57	1	see	see	VERB
ejpam-5993	57	2	[	[	X
ejpam-5993	57	3	17	17	NUM
ejpam-5993	57	4	,	,	PUNCT
ejpam-5993	57	5	lemma	lemma	PROPN
ejpam-5993	57	6	2.6].106	2.6].106	NUM
ejpam-5993	57	7	lemma	lemma	PROPN
ejpam-5993	57	8	4	4	X
ejpam-5993	57	9	.	.	PUNCT
ejpam-5993	58	1	let	let	VERB
ejpam-5993	58	2	g	g	PRON
ejpam-5993	58	3	be	be	AUX
ejpam-5993	58	4	a	a	DET
ejpam-5993	58	5	group	group	NOUN
ejpam-5993	58	6	and	and	CCONJ
ejpam-5993	58	7	let	let	VERB
ejpam-5993	58	8	h	h	PRON
ejpam-5993	58	9	be	be	AUX
ejpam-5993	58	10	an	an	DET
ejpam-5993	58	11	h	h	NOUN
ejpam-5993	58	12	-	-	PUNCT
ejpam-5993	58	13	subgroup	subgroup	NOUN
ejpam-5993	58	14	in	in	ADP
ejpam-5993	58	15	g.	g.	PROPN
ejpam-5993	58	16	if	if	SCONJ
ejpam-5993	58	17	h	h	NOUN
ejpam-5993	58	18	is	be	AUX
ejpam-5993	58	19	subnormal	subnormal	ADJ
ejpam-5993	58	20	in	in	ADP
ejpam-5993	58	21	g,107	g,107	PROPN
ejpam-5993	58	22	then	then	ADV
ejpam-5993	58	23	h	h	PROPN
ejpam-5993	58	24	is	be	AUX
ejpam-5993	58	25	normal	normal	ADJ
ejpam-5993	58	26	in	in	ADP
ejpam-5993	58	27	g.108	g.108	NOUN
ejpam-5993	58	28	proof	proof	NOUN
ejpam-5993	58	29	.	.	PUNCT
ejpam-5993	59	1	see	see	VERB
ejpam-5993	59	2	[	[	X
ejpam-5993	59	3	3	3	NUM
ejpam-5993	59	4	,	,	PUNCT
ejpam-5993	59	5	theorem	theorem	VERB
ejpam-5993	59	6	6.2].109	6.2].109	VERB
ejpam-5993	59	7	lemma	lemma	PROPN
ejpam-5993	59	8	5	5	NUM
ejpam-5993	59	9	.	.	PUNCT
ejpam-5993	60	1	let	let	VERB
ejpam-5993	60	2	g	g	PRON
ejpam-5993	60	3	be	be	AUX
ejpam-5993	60	4	a	a	DET
ejpam-5993	60	5	solvable	solvable	ADJ
ejpam-5993	60	6	group	group	NOUN
ejpam-5993	60	7	.	.	PUNCT
ejpam-5993	61	1	suppose	suppose	VERB
ejpam-5993	61	2	that	that	SCONJ
ejpam-5993	61	3	f	f	PROPN
ejpam-5993	61	4	(	(	PUNCT
ejpam-5993	61	5	g	g	NOUN
ejpam-5993	61	6	)	)	PUNCT
ejpam-5993	61	7	possesses	possess	VERB
ejpam-5993	61	8	a	a	DET
ejpam-5993	61	9	normal	normal	ADJ
ejpam-5993	61	10	series110	series110	PROPN
ejpam-5993	61	11	φ(g	φ(g	PROPN
ejpam-5993	61	12	)	)	PUNCT
ejpam-5993	61	13	=	=	SYM
ejpam-5993	61	14	k0	k0	PROPN
ejpam-5993	61	15	⩽	⩽	PROPN
ejpam-5993	61	16	ki	ki	PROPN
ejpam-5993	61	17	⩽	⩽	PROPN
ejpam-5993	61	18	k2	k2	PROPN
ejpam-5993	61	19	⩽	⩽	PROPN
ejpam-5993	61	20	.	.	PUNCT
ejpam-5993	61	21	.	.	PUNCT
ejpam-5993	61	22	.	.	PUNCT
ejpam-5993	62	1	⩽	⩽	ADJ
ejpam-5993	62	2	kn	kn	PROPN
ejpam-5993	62	3	=	=	PUNCT
ejpam-5993	62	4	f	f	PROPN
ejpam-5993	62	5	(	(	PUNCT
ejpam-5993	62	6	g),111	g),111	VERB
ejpam-5993	62	7	such	such	ADJ
ejpam-5993	62	8	that	that	SCONJ
ejpam-5993	62	9	ki	ki	PROPN
ejpam-5993	62	10	,	,	PUNCT
ejpam-5993	62	11	s	s	VERB
ejpam-5993	62	12	are	be	AUX
ejpam-5993	62	13	normal	normal	ADJ
ejpam-5993	62	14	subgroups	subgroup	NOUN
ejpam-5993	62	15	of	of	ADP
ejpam-5993	62	16	g	g	PROPN
ejpam-5993	62	17	and	and	CCONJ
ejpam-5993	62	18	|ki	|ki	NUM
ejpam-5993	62	19	/	/	SYM
ejpam-5993	62	20	ki−1|	ki−1|	NOUN
ejpam-5993	62	21	=	=	NOUN
ejpam-5993	62	22	prime	prime	ADJ
ejpam-5993	62	23	(	(	PUNCT
ejpam-5993	62	24	1	1	NUM
ejpam-5993	62	25	≤	≤	NUM
ejpam-5993	62	26	i	i	NOUN
ejpam-5993	62	27	≤	≤	NOUN
ejpam-5993	62	28	n	n	CCONJ
ejpam-5993	62	29	)	)	PUNCT
ejpam-5993	62	30	.	.	PUNCT
ejpam-5993	63	1	then	then	ADV
ejpam-5993	63	2	g	g	PROPN
ejpam-5993	63	3	is112	is112	PROPN
ejpam-5993	63	4	supersolvable.113	supersolvable.113	PROPN
ejpam-5993	63	5	proof	proof	NOUN
ejpam-5993	63	6	.	.	PUNCT
ejpam-5993	64	1	see	see	VERB
ejpam-5993	64	2	[	[	X
ejpam-5993	64	3	13	13	NUM
ejpam-5993	64	4	,	,	PUNCT
ejpam-5993	64	5	p.	p.	NOUN
ejpam-5993	64	6	720	720	NUM
ejpam-5993	64	7	,	,	PUNCT
ejpam-5993	64	8	satz	satz	PROPN
ejpam-5993	64	9	9.9].114	9.9].114	PROPN
ejpam-5993	65	1	lemma	lemma	PROPN
ejpam-5993	65	2	6	6	NUM
ejpam-5993	65	3	.	.	PUNCT
ejpam-5993	66	1	let	let	VERB
ejpam-5993	66	2	g	g	PRON
ejpam-5993	66	3	be	be	AUX
ejpam-5993	66	4	a	a	DET
ejpam-5993	66	5	group	group	NOUN
ejpam-5993	66	6	and	and	CCONJ
ejpam-5993	66	7	h	h	NOUN
ejpam-5993	66	8	⩽	⩽	PROPN
ejpam-5993	67	1	k	k	PROPN
ejpam-5993	67	2	⩽	⩽	PROPN
ejpam-5993	67	3	g.	g.	PROPN
ejpam-5993	67	4	then	then	ADV
ejpam-5993	67	5	hsg	hsg	VERB
ejpam-5993	67	6	is	be	AUX
ejpam-5993	67	7	s	s	NOUN
ejpam-5993	67	8	-	-	NOUN
ejpam-5993	67	9	permutable	permutable	ADJ
ejpam-5993	67	10	in	in	ADP
ejpam-5993	67	11	g	g	PROPN
ejpam-5993	67	12	and115	and115	PROPN
ejpam-5993	67	13	hsg	hsg	VERB
ejpam-5993	67	14	⩽	⩽	ADJ
ejpam-5993	67	15	hg.116	hg.116	ADP
ejpam-5993	67	16	proof	proof	NOUN
ejpam-5993	67	17	.	.	PUNCT
ejpam-5993	68	1	see	see	VERB
ejpam-5993	68	2	[	[	X
ejpam-5993	68	3	18	18	NUM
ejpam-5993	68	4	,	,	PUNCT
ejpam-5993	68	5	lemma	lemma	PROPN
ejpam-5993	68	6	2.5(1)].117	2.5(1)].117	PROPN
ejpam-5993	68	7	lemma	lemma	PROPN
ejpam-5993	68	8	7	7	X
ejpam-5993	68	9	.	.	PUNCT
ejpam-5993	69	1	let	let	VERB
ejpam-5993	69	2	p	p	PRON
ejpam-5993	69	3	be	be	AUX
ejpam-5993	69	4	an	an	DET
ejpam-5993	69	5	elementary	elementary	ADJ
ejpam-5993	69	6	abelian	abelian	NOUN
ejpam-5993	69	7	p	p	PROPN
ejpam-5993	69	8	-	-	PUNCT
ejpam-5993	69	9	subgroup	subgroup	NOUN
ejpam-5993	69	10	of	of	ADP
ejpam-5993	69	11	g	g	PROPN
ejpam-5993	69	12	such	such	ADJ
ejpam-5993	69	13	that	that	SCONJ
ejpam-5993	69	14	p	p	NOUN
ejpam-5993	69	15	is	be	AUX
ejpam-5993	69	16	not	not	PART
ejpam-5993	69	17	cyclic.118	cyclic.118	VERB
ejpam-5993	69	18	then	then	ADV
ejpam-5993	69	19	the	the	DET
ejpam-5993	69	20	following	follow	VERB
ejpam-5993	69	21	statements	statement	NOUN
ejpam-5993	69	22	are	be	AUX
ejpam-5993	69	23	equivalent:119	equivalent:119	PROPN
ejpam-5993	69	24	(	(	PUNCT
ejpam-5993	69	25	i	i	NOUN
ejpam-5993	69	26	)	)	PUNCT
ejpam-5993	69	27	the	the	DET
ejpam-5993	69	28	subgroups	subgroup	NOUN
ejpam-5993	69	29	of	of	ADP
ejpam-5993	69	30	order	order	NOUN
ejpam-5993	69	31	p	p	NOUN
ejpam-5993	69	32	in	in	ADP
ejpam-5993	69	33	p	p	NOUN
ejpam-5993	69	34	are	be	AUX
ejpam-5993	69	35	normal	normal	ADJ
ejpam-5993	69	36	in	in	ADP
ejpam-5993	69	37	g.120	g.120	ADJ
ejpam-5993	69	38	(	(	PUNCT
ejpam-5993	69	39	ii	ii	NOUN
ejpam-5993	69	40	)	)	PUNCT
ejpam-5993	69	41	the	the	DET
ejpam-5993	69	42	maximal	maximal	ADJ
ejpam-5993	69	43	subgroups	subgroup	NOUN
ejpam-5993	69	44	of	of	ADP
ejpam-5993	69	45	p	p	NOUN
ejpam-5993	69	46	are	be	AUX
ejpam-5993	69	47	normal	normal	ADJ
ejpam-5993	69	48	in	in	ADP
ejpam-5993	69	49	g.121	g.121	PROPN
ejpam-5993	69	50	proof	proof	NOUN
ejpam-5993	69	51	.	.	PUNCT
ejpam-5993	70	1	see	see	VERB
ejpam-5993	70	2	[	[	X
ejpam-5993	70	3	19	19	NUM
ejpam-5993	70	4	,	,	PUNCT
ejpam-5993	70	5	lemma	lemma	PROPN
ejpam-5993	70	6	2.6].122	2.6].122	PROPN
ejpam-5993	70	7	lemma	lemma	PROPN
ejpam-5993	70	8	8	8	NUM
ejpam-5993	70	9	.	.	PUNCT
ejpam-5993	71	1	let	let	VERB
ejpam-5993	71	2	g	g	PRON
ejpam-5993	71	3	be	be	AUX
ejpam-5993	71	4	a	a	DET
ejpam-5993	71	5	group	group	NOUN
ejpam-5993	71	6	and	and	CCONJ
ejpam-5993	71	7	let	let	VERB
ejpam-5993	71	8	l	l	NOUN
ejpam-5993	71	9	be	be	AUX
ejpam-5993	71	10	a	a	DET
ejpam-5993	71	11	subgroup	subgroup	NOUN
ejpam-5993	71	12	of	of	ADP
ejpam-5993	71	13	g:123	g:123	NOUN
ejpam-5993	71	14	(	(	PUNCT
ejpam-5993	71	15	i	i	NOUN
ejpam-5993	71	16	)	)	PUNCT
ejpam-5993	71	17	if	if	SCONJ
ejpam-5993	71	18	l	l	NOUN
ejpam-5993	71	19	⊴	⊴	ADP
ejpam-5993	71	20	g	g	PROPN
ejpam-5993	71	21	,	,	PUNCT
ejpam-5993	71	22	then	then	ADV
ejpam-5993	71	23	f	f	PROPN
ejpam-5993	71	24	∗(l	∗(l	PROPN
ejpam-5993	71	25	)	)	PUNCT
ejpam-5993	71	26	⩽	⩽	NOUN
ejpam-5993	72	1	f	f	X
ejpam-5993	72	2	∗(g).124	∗(g).124	PROPN
ejpam-5993	72	3	(	(	PUNCT
ejpam-5993	72	4	ii	ii	NOUN
ejpam-5993	72	5	)	)	PUNCT
ejpam-5993	72	6	f	f	PROPN
ejpam-5993	72	7	∗(f	∗(f	PROPN
ejpam-5993	72	8	∗(g	∗(g	PROPN
ejpam-5993	72	9	)	)	PUNCT
ejpam-5993	72	10	)	)	PUNCT
ejpam-5993	73	1	=	=	PUNCT
ejpam-5993	73	2	f	f	X
ejpam-5993	73	3	∗(g	∗(g	PROPN
ejpam-5993	73	4	)	)	PUNCT
ejpam-5993	73	5	≥	≥	PROPN
ejpam-5993	73	6	f	f	X
ejpam-5993	73	7	(	(	PUNCT
ejpam-5993	73	8	g	g	NOUN
ejpam-5993	73	9	)	)	PUNCT
ejpam-5993	73	10	.	.	PUNCT
ejpam-5993	74	1	if	if	SCONJ
ejpam-5993	74	2	f	f	PROPN
ejpam-5993	74	3	∗(g	∗(g	PROPN
ejpam-5993	74	4	)	)	PUNCT
ejpam-5993	74	5	is	be	AUX
ejpam-5993	74	6	solvable	solvable	ADJ
ejpam-5993	74	7	,	,	PUNCT
ejpam-5993	74	8	then	then	ADV
ejpam-5993	74	9	f	f	PROPN
ejpam-5993	74	10	∗(g	∗(g	PROPN
ejpam-5993	74	11	)	)	PUNCT
ejpam-5993	75	1	=	=	SYM
ejpam-5993	75	2	f	f	X
ejpam-5993	75	3	(	(	PUNCT
ejpam-5993	75	4	g)125	g)125	PROPN
ejpam-5993	75	5	(	(	PUNCT
ejpam-5993	75	6	iii	iii	NOUN
ejpam-5993	75	7	)	)	PUNCT
ejpam-5993	75	8	suppose	suppose	VERB
ejpam-5993	75	9	that	that	SCONJ
ejpam-5993	75	10	p	p	PROPN
ejpam-5993	75	11	is	be	AUX
ejpam-5993	75	12	a	a	DET
ejpam-5993	75	13	normal	normal	ADJ
ejpam-5993	75	14	p	p	NOUN
ejpam-5993	75	15	-	-	PUNCT
ejpam-5993	75	16	subgroup	subgroup	NOUN
ejpam-5993	75	17	,	,	PUNCT
ejpam-5993	75	18	then	then	ADV
ejpam-5993	75	19	f	f	PROPN
ejpam-5993	75	20	∗(g	∗(g	PROPN
ejpam-5993	75	21	/	/	SYM
ejpam-5993	75	22	φ(p	φ(p	PROPN
ejpam-5993	75	23	)	)	PUNCT
ejpam-5993	75	24	)	)	PUNCT
ejpam-5993	76	1	=	=	PUNCT
ejpam-5993	76	2	f	f	X
ejpam-5993	77	1	∗(g)/φ(p	∗(g)/φ(p	NOUN
ejpam-5993	77	2	)	)	PUNCT
ejpam-5993	77	3	126	126	NUM
ejpam-5993	77	4	proof	proof	NOUN
ejpam-5993	77	5	.	.	PUNCT
ejpam-5993	78	1	see	see	VERB
ejpam-5993	78	2	[	[	X
ejpam-5993	78	3	20	20	NUM
ejpam-5993	78	4	,	,	PUNCT
ejpam-5993	78	5	p.	p.	NOUN
ejpam-5993	78	6	123	123	NUM
ejpam-5993	78	7	,	,	PUNCT
ejpam-5993	78	8	x.	x.	PROPN
ejpam-5993	78	9	13].127	13].127	PROPN
ejpam-5993	78	10	lemma	lemma	PROPN
ejpam-5993	78	11	9	9	X
ejpam-5993	78	12	.	.	PUNCT
ejpam-5993	79	1	let	let	VERB
ejpam-5993	79	2	g	g	PRON
ejpam-5993	79	3	be	be	AUX
ejpam-5993	79	4	a	a	DET
ejpam-5993	79	5	group	group	NOUN
ejpam-5993	79	6	and	and	CCONJ
ejpam-5993	79	7	let	let	VERB
ejpam-5993	79	8	h	h	PRON
ejpam-5993	79	9	be	be	AUX
ejpam-5993	79	10	a	a	DET
ejpam-5993	79	11	normal	normal	ADJ
ejpam-5993	79	12	cyclic	cyclic	ADJ
ejpam-5993	79	13	subgroup	subgroup	NOUN
ejpam-5993	79	14	with	with	ADP
ejpam-5993	79	15	g	g	PROPN
ejpam-5993	79	16	/	/	SYM
ejpam-5993	79	17	h	h	PROPN
ejpam-5993	79	18	supersolv-128	supersolv-128	NOUN
ejpam-5993	79	19	able	able	ADJ
ejpam-5993	79	20	.	.	PUNCT
ejpam-5993	80	1	then	then	ADV
ejpam-5993	80	2	g	g	PROPN
ejpam-5993	80	3	is	be	AUX
ejpam-5993	80	4	supersolvable.129	supersolvable.129	PROPN
ejpam-5993	80	5	proof	proof	NOUN
ejpam-5993	80	6	.	.	PUNCT
ejpam-5993	81	1	see	see	VERB
ejpam-5993	81	2	[	[	X
ejpam-5993	81	3	21	21	NUM
ejpam-5993	81	4	,	,	PUNCT
ejpam-5993	81	5	theorm	theorm	NOUN
ejpam-5993	81	6	1.2].130	1.2].130	NUM
ejpam-5993	81	7	a.	a.	PROPN
ejpam-5993	81	8	s.	s.	PROPN
ejpam-5993	81	9	allehyani	allehyani	PROPN
ejpam-5993	81	10	/	/	SYM
ejpam-5993	81	11	eur	eur	PROPN
ejpam-5993	81	12	.	.	PUNCT
ejpam-5993	82	1	j.	j.	PROPN
ejpam-5993	82	2	pure	pure	PROPN
ejpam-5993	82	3	appl	appl	PROPN
ejpam-5993	82	4	.	.	PROPN
ejpam-5993	82	5	math	math	PROPN
ejpam-5993	82	6	,	,	PUNCT
ejpam-5993	82	7	18	18	NUM
ejpam-5993	82	8	(	(	PUNCT
ejpam-5993	82	9	2	2	NUM
ejpam-5993	82	10	)	)	PUNCT
ejpam-5993	82	11	(	(	PUNCT
ejpam-5993	82	12	2025	2025	NUM
ejpam-5993	82	13	)	)	PUNCT
ejpam-5993	82	14	,	,	PUNCT
ejpam-5993	82	15	5993	5993	NUM
ejpam-5993	82	16	5	5	NUM
ejpam-5993	82	17	of	of	ADP
ejpam-5993	82	18	13	13	NUM
ejpam-5993	82	19	3	3	NUM
ejpam-5993	82	20	.	.	PUNCT
ejpam-5993	82	21	main	main	ADJ
ejpam-5993	82	22	results131	results131	PROPN
ejpam-5993	82	23	in	in	ADP
ejpam-5993	82	24	the	the	DET
ejpam-5993	82	25	present	present	ADJ
ejpam-5993	82	26	section	section	NOUN
ejpam-5993	83	1	,	,	PUNCT
ejpam-5993	83	2	we	we	PRON
ejpam-5993	83	3	will	will	AUX
ejpam-5993	83	4	prove	prove	VERB
ejpam-5993	83	5	some	some	DET
ejpam-5993	83	6	theorems	theorem	NOUN
ejpam-5993	83	7	,	,	PUNCT
ejpam-5993	83	8	also	also	ADV
ejpam-5993	83	9	we	we	PRON
ejpam-5993	83	10	will	will	AUX
ejpam-5993	83	11	give	give	VERB
ejpam-5993	83	12	some	some	DET
ejpam-5993	83	13	illustrative132	illustrative132	PROPN
ejpam-5993	83	14	examples	example	NOUN
ejpam-5993	83	15	and	and	CCONJ
ejpam-5993	83	16	counterexamples.133	counterexamples.133	NOUN
ejpam-5993	83	17	134	134	NUM
ejpam-5993	83	18	we	we	PRON
ejpam-5993	83	19	will	will	AUX
ejpam-5993	83	20	begin	begin	VERB
ejpam-5993	83	21	our	our	PRON
ejpam-5993	83	22	study	study	NOUN
ejpam-5993	83	23	with	with	ADP
ejpam-5993	83	24	the	the	DET
ejpam-5993	83	25	following	follow	VERB
ejpam-5993	83	26	theorem:135	theorem:135	X
ejpam-5993	83	27	theorem	theorem	ADJ
ejpam-5993	83	28	1	1	NUM
ejpam-5993	83	29	.	.	PUNCT
ejpam-5993	83	30	assume	assume	VERB
ejpam-5993	83	31	that	that	SCONJ
ejpam-5993	83	32	g	g	PROPN
ejpam-5993	83	33	is	be	AUX
ejpam-5993	83	34	a	a	DET
ejpam-5993	83	35	solvable	solvable	ADJ
ejpam-5993	83	36	group	group	NOUN
ejpam-5993	83	37	and	and	CCONJ
ejpam-5993	83	38	all	all	DET
ejpam-5993	83	39	maximal	maximal	ADJ
ejpam-5993	83	40	subgroups	subgroup	NOUN
ejpam-5993	83	41	of	of	ADP
ejpam-5993	83	42	the	the	DET
ejpam-5993	83	43	non-136	non-136	ADJ
ejpam-5993	83	44	cyclic	cyclic	ADJ
ejpam-5993	83	45	sylow	sylow	NOUN
ejpam-5993	83	46	subgroups	subgroup	NOUN
ejpam-5993	83	47	of	of	ADP
ejpam-5993	83	48	f	f	PROPN
ejpam-5993	83	49	(	(	PUNCT
ejpam-5993	83	50	g	g	NOUN
ejpam-5993	83	51	)	)	PUNCT
ejpam-5993	83	52	are	be	AUX
ejpam-5993	83	53	ssh	ssh	NOUN
ejpam-5993	83	54	-	-	PUNCT
ejpam-5993	83	55	subgroups	subgroup	NOUN
ejpam-5993	83	56	of	of	ADP
ejpam-5993	83	57	g.	g.	PROPN
ejpam-5993	84	1	then	then	ADV
ejpam-5993	84	2	g	g	PROPN
ejpam-5993	84	3	is	be	AUX
ejpam-5993	84	4	supersolvable.137	supersolvable.137	NOUN
ejpam-5993	84	5	proof	proof	NOUN
ejpam-5993	84	6	.	.	PUNCT
ejpam-5993	85	1	assume	assume	VERB
ejpam-5993	85	2	that	that	SCONJ
ejpam-5993	85	3	the	the	DET
ejpam-5993	85	4	result	result	NOUN
ejpam-5993	85	5	is	be	AUX
ejpam-5993	85	6	false	false	ADJ
ejpam-5993	85	7	and	and	CCONJ
ejpam-5993	85	8	let	let	VERB
ejpam-5993	85	9	g	g	PRON
ejpam-5993	85	10	be	be	AUX
ejpam-5993	85	11	a	a	DET
ejpam-5993	85	12	counterexample	counterexample	NOUN
ejpam-5993	85	13	of	of	ADP
ejpam-5993	85	14	minimal	minimal	ADJ
ejpam-5993	85	15	order.138	order.138	NOUN
ejpam-5993	85	16	we	we	PRON
ejpam-5993	85	17	distinguish	distinguish	VERB
ejpam-5993	85	18	the	the	DET
ejpam-5993	85	19	following	follow	VERB
ejpam-5993	85	20	two	two	NUM
ejpam-5993	85	21	cases:139	cases:139	SYM
ejpam-5993	85	22	140	140	NUM
ejpam-5993	85	23	case	case	NOUN
ejpam-5993	85	24	1	1	NUM
ejpam-5993	85	25	:	:	PUNCT
ejpam-5993	85	26	φ(g	φ(g	ADJ
ejpam-5993	85	27	)	)	PUNCT
ejpam-5993	85	28	̸=	̸=	PROPN
ejpam-5993	85	29	1.141	1.141	NUM
ejpam-5993	85	30	142	142	NUM
ejpam-5993	85	31	then	then	ADV
ejpam-5993	85	32	there	there	PRON
ejpam-5993	85	33	exists	exist	VERB
ejpam-5993	85	34	a	a	DET
ejpam-5993	85	35	prime	prime	NOUN
ejpam-5993	85	36	p	p	NOUN
ejpam-5993	85	37	such	such	ADJ
ejpam-5993	85	38	that	that	DET
ejpam-5993	85	39	p||φ(g)|	p||φ(g)|	PROPN
ejpam-5993	85	40	.	.	PUNCT
ejpam-5993	86	1	since	since	SCONJ
ejpam-5993	86	2	φ(g	φ(g	PROPN
ejpam-5993	86	3	)	)	PUNCT
ejpam-5993	86	4	⩽	⩽	NOUN
ejpam-5993	86	5	f	f	PROPN
ejpam-5993	86	6	(	(	PUNCT
ejpam-5993	86	7	g	g	NOUN
ejpam-5993	86	8	)	)	PUNCT
ejpam-5993	86	9	,	,	PUNCT
ejpam-5993	86	10	it	it	PRON
ejpam-5993	86	11	follows	follow	VERB
ejpam-5993	86	12	that143	that143	PROPN
ejpam-5993	87	1	p||f	p||f	PROPN
ejpam-5993	87	2	(	(	PUNCT
ejpam-5993	87	3	g)|	g)|	PROPN
ejpam-5993	87	4	.	.	PUNCT
ejpam-5993	88	1	let	let	VERB
ejpam-5993	88	2	p1	p1	PROPN
ejpam-5993	88	3	be	be	AUX
ejpam-5993	88	4	a	a	DET
ejpam-5993	88	5	non	non	ADJ
ejpam-5993	88	6	-	-	ADJ
ejpam-5993	88	7	cyclic	cyclic	ADJ
ejpam-5993	88	8	sylow	sylow	NOUN
ejpam-5993	88	9	p	p	NOUN
ejpam-5993	88	10	-	-	PUNCT
ejpam-5993	88	11	subgroup	subgroup	NOUN
ejpam-5993	88	12	of	of	ADP
ejpam-5993	88	13	φ(g	φ(g	PROPN
ejpam-5993	88	14	)	)	PUNCT
ejpam-5993	88	15	.	.	PUNCT
ejpam-5993	89	1	since	since	SCONJ
ejpam-5993	89	2	p1	p1	PROPN
ejpam-5993	89	3	is	be	AUX
ejpam-5993	89	4	characteristic	characteristic	ADJ
ejpam-5993	89	5	in144	in144	PROPN
ejpam-5993	89	6	φ(g	φ(g	PROPN
ejpam-5993	89	7	)	)	PUNCT
ejpam-5993	89	8	⊴	⊴	ADP
ejpam-5993	89	9	g	g	PROPN
ejpam-5993	89	10	,	,	PUNCT
ejpam-5993	89	11	we	we	PRON
ejpam-5993	89	12	have	have	VERB
ejpam-5993	89	13	that	that	DET
ejpam-5993	89	14	p1	p1	PROPN
ejpam-5993	89	15	⊴	⊴	ADP
ejpam-5993	89	16	g.	g.	PROPN
ejpam-5993	89	17	by	by	ADP
ejpam-5993	89	18	lemma	lemma	PROPN
ejpam-5993	89	19	1(ii	1(ii	NUM
ejpam-5993	89	20	)	)	PUNCT
ejpam-5993	89	21	,	,	PUNCT
ejpam-5993	89	22	we	we	PRON
ejpam-5993	89	23	have	have	VERB
ejpam-5993	89	24	that	that	PRON
ejpam-5993	89	25	f	f	PROPN
ejpam-5993	89	26	(	(	PUNCT
ejpam-5993	89	27	g	g	NOUN
ejpam-5993	89	28	/	/	SYM
ejpam-5993	89	29	p1	p1	NOUN
ejpam-5993	89	30	)	)	PUNCT
ejpam-5993	90	1	=	=	SYM
ejpam-5993	90	2	f	f	PROPN
ejpam-5993	90	3	(	(	PUNCT
ejpam-5993	90	4	g)/p1.145	g)/p1.145	PROPN
ejpam-5993	90	5	let	let	VERB
ejpam-5993	90	6	p2	p2	NOUN
ejpam-5993	90	7	/	/	SYM
ejpam-5993	90	8	p1	p1	NOUN
ejpam-5993	90	9	be	be	VERB
ejpam-5993	90	10	a	a	DET
ejpam-5993	90	11	maximal	maximal	ADJ
ejpam-5993	90	12	subgroup	subgroup	NOUN
ejpam-5993	90	13	of	of	ADP
ejpam-5993	90	14	the	the	DET
ejpam-5993	90	15	non	non	ADJ
ejpam-5993	90	16	-	-	ADJ
ejpam-5993	90	17	cyclic	cyclic	ADJ
ejpam-5993	90	18	sylow	sylow	NOUN
ejpam-5993	90	19	p	p	PROPN
ejpam-5993	90	20	-	-	PUNCT
ejpam-5993	90	21	subgroup	subgroup	NOUN
ejpam-5993	90	22	of	of	ADP
ejpam-5993	90	23	f	f	PROPN
ejpam-5993	90	24	(	(	PUNCT
ejpam-5993	90	25	g)/p1	g)/p1	NOUN
ejpam-5993	90	26	.	.	PUNCT
ejpam-5993	91	1	then146	then146	NOUN
ejpam-5993	91	2	p2	p2	PROPN
ejpam-5993	91	3	/	/	SYM
ejpam-5993	91	4	p1	p1	NOUN
ejpam-5993	91	5	is	be	AUX
ejpam-5993	91	6	an	an	DET
ejpam-5993	91	7	ssh	ssh	NOUN
ejpam-5993	91	8	-	-	PUNCT
ejpam-5993	91	9	subgroup	subgroup	NOUN
ejpam-5993	91	10	in	in	ADP
ejpam-5993	91	11	g	g	PROPN
ejpam-5993	91	12	/	/	SYM
ejpam-5993	91	13	p1	p1	NOUN
ejpam-5993	91	14	.	.	PUNCT
ejpam-5993	92	1	by	by	ADP
ejpam-5993	92	2	lemma	lemma	PROPN
ejpam-5993	92	3	2(ii	2(ii	NUM
ejpam-5993	92	4	)	)	PUNCT
ejpam-5993	92	5	,	,	PUNCT
ejpam-5993	92	6	p2	p2	PROPN
ejpam-5993	92	7	is	be	AUX
ejpam-5993	92	8	an	an	DET
ejpam-5993	92	9	ssh	ssh	NOUN
ejpam-5993	92	10	-	-	PUNCT
ejpam-5993	92	11	subgroup	subgroup	NOUN
ejpam-5993	92	12	in	in	ADP
ejpam-5993	92	13	g.147	g.147	PROPN
ejpam-5993	92	14	also	also	ADV
ejpam-5993	92	15	,	,	PUNCT
ejpam-5993	92	16	if	if	SCONJ
ejpam-5993	92	17	q	q	ADJ
ejpam-5993	92	18	is	be	AUX
ejpam-5993	92	19	the	the	DET
ejpam-5993	92	20	non	non	ADJ
ejpam-5993	92	21	-	-	ADJ
ejpam-5993	92	22	cyclic	cyclic	ADJ
ejpam-5993	92	23	sylow	sylow	NOUN
ejpam-5993	92	24	q	q	NOUN
ejpam-5993	92	25	-	-	NOUN
ejpam-5993	92	26	subgroup	subgroup	NOUN
ejpam-5993	92	27	of	of	ADP
ejpam-5993	92	28	f	f	PROPN
ejpam-5993	92	29	(	(	PUNCT
ejpam-5993	92	30	g)/p1	g)/p1	NOUN
ejpam-5993	92	31	,	,	PUNCT
ejpam-5993	92	32	then	then	ADV
ejpam-5993	92	33	q	q	NOUN
ejpam-5993	92	34	=	=	NOUN
ejpam-5993	92	35	fqp1	fqp1	PROPN
ejpam-5993	92	36	/	/	SYM
ejpam-5993	92	37	p1	p1	PROPN
ejpam-5993	92	38	,	,	PUNCT
ejpam-5993	92	39	where148	where148	PROPN
ejpam-5993	92	40	fq	fq	PROPN
ejpam-5993	92	41	is	be	AUX
ejpam-5993	92	42	the	the	DET
ejpam-5993	92	43	non	non	ADJ
ejpam-5993	92	44	-	-	ADJ
ejpam-5993	92	45	cyclic	cyclic	ADJ
ejpam-5993	92	46	sylow	sylow	NOUN
ejpam-5993	92	47	q	q	NOUN
ejpam-5993	92	48	-	-	NOUN
ejpam-5993	92	49	subgroup	subgroup	NOUN
ejpam-5993	92	50	of	of	ADP
ejpam-5993	92	51	f	f	PROPN
ejpam-5993	92	52	(	(	PUNCT
ejpam-5993	92	53	g)(q	g)(q	ADJ
ejpam-5993	92	54	̸=	̸=	PROPN
ejpam-5993	92	55	p	p	NOUN
ejpam-5993	92	56	)	)	PUNCT
ejpam-5993	92	57	.	.	PUNCT
ejpam-5993	93	1	let	let	VERB
ejpam-5993	93	2	m	m	PRON
ejpam-5993	93	3	/	/	SYM
ejpam-5993	93	4	p1	p1	PROPN
ejpam-5993	93	5	be	be	AUX
ejpam-5993	93	6	a	a	DET
ejpam-5993	93	7	maximal	maximal	ADJ
ejpam-5993	93	8	subgroup149	subgroup149	NOUN
ejpam-5993	93	9	of	of	ADP
ejpam-5993	93	10	fqp1	fqp1	PROPN
ejpam-5993	93	11	/	/	SYM
ejpam-5993	93	12	p1	p1	PROPN
ejpam-5993	93	13	.	.	PUNCT
ejpam-5993	94	1	then	then	ADV
ejpam-5993	94	2	m	m	VERB
ejpam-5993	94	3	=	=	SYM
ejpam-5993	94	4	(	(	PUNCT
ejpam-5993	94	5	m	m	PROPN
ejpam-5993	94	6	∩	∩	ADJ
ejpam-5993	94	7	fq)p1	fq)p1	NOUN
ejpam-5993	94	8	,	,	PUNCT
ejpam-5993	94	9	where	where	SCONJ
ejpam-5993	94	10	m	m	PROPN
ejpam-5993	94	11	∩	∩	ADJ
ejpam-5993	94	12	fq	fq	PROPN
ejpam-5993	94	13	is	be	AUX
ejpam-5993	94	14	a	a	DET
ejpam-5993	94	15	maximal	maximal	ADJ
ejpam-5993	94	16	subgroup	subgroup	NOUN
ejpam-5993	94	17	of	of	ADP
ejpam-5993	94	18	fq	fq	PROPN
ejpam-5993	94	19	.	.	PROPN
ejpam-5993	94	20	by150	by150	PROPN
ejpam-5993	94	21	hypothesis	hypothesis	NOUN
ejpam-5993	94	22	of	of	ADP
ejpam-5993	94	23	the	the	DET
ejpam-5993	94	24	theorem	theorem	PROPN
ejpam-5993	94	25	,	,	PUNCT
ejpam-5993	94	26	m	m	PROPN
ejpam-5993	94	27	∩	∩	NOUN
ejpam-5993	94	28	fq	fq	PROPN
ejpam-5993	94	29	an	an	DET
ejpam-5993	94	30	ssh	ssh	NOUN
ejpam-5993	94	31	-	-	PUNCT
ejpam-5993	94	32	subgroup	subgroup	NOUN
ejpam-5993	94	33	in	in	ADP
ejpam-5993	94	34	g	g	PROPN
ejpam-5993	94	35	,	,	PUNCT
ejpam-5993	94	36	which	which	PRON
ejpam-5993	94	37	implies	imply	VERB
ejpam-5993	94	38	that	that	SCONJ
ejpam-5993	94	39	m	m	PROPN
ejpam-5993	94	40	/	/	SYM
ejpam-5993	94	41	p1	p1	PROPN
ejpam-5993	94	42	is151	is151	PROPN
ejpam-5993	94	43	an	an	DET
ejpam-5993	94	44	ssh	ssh	NOUN
ejpam-5993	94	45	-	-	PUNCT
ejpam-5993	94	46	subgroup	subgroup	NOUN
ejpam-5993	94	47	in	in	ADP
ejpam-5993	94	48	g	g	PROPN
ejpam-5993	94	49	/	/	SYM
ejpam-5993	94	50	p1	p1	PROPN
ejpam-5993	94	51	by	by	ADP
ejpam-5993	94	52	lemma	lemma	PROPN
ejpam-5993	94	53	2(iii	2(iii	NUM
ejpam-5993	94	54	)	)	PUNCT
ejpam-5993	94	55	.	.	PUNCT
ejpam-5993	95	1	therefore	therefore	ADV
ejpam-5993	95	2	,	,	PUNCT
ejpam-5993	95	3	every	every	DET
ejpam-5993	95	4	maximal	maximal	ADJ
ejpam-5993	95	5	subgroups	subgroup	NOUN
ejpam-5993	95	6	of	of	ADP
ejpam-5993	95	7	the152	the152	PROPN
ejpam-5993	95	8	non	non	ADJ
ejpam-5993	95	9	-	-	ADJ
ejpam-5993	95	10	cyclic	cyclic	ADJ
ejpam-5993	95	11	sylow	sylow	NOUN
ejpam-5993	95	12	subgroup	subgroup	NOUN
ejpam-5993	95	13	of	of	ADP
ejpam-5993	95	14	f	f	PROPN
ejpam-5993	95	15	(	(	PUNCT
ejpam-5993	95	16	g)/p1	g)/p1	NOUN
ejpam-5993	95	17	are	be	AUX
ejpam-5993	95	18	ssh	ssh	NOUN
ejpam-5993	95	19	-	-	PUNCT
ejpam-5993	95	20	subgroups	subgroup	NOUN
ejpam-5993	95	21	in	in	ADP
ejpam-5993	95	22	g	g	PROPN
ejpam-5993	95	23	/	/	SYM
ejpam-5993	95	24	p1	p1	PROPN
ejpam-5993	95	25	.	.	PUNCT
ejpam-5993	96	1	then	then	ADV
ejpam-5993	96	2	,	,	PUNCT
ejpam-5993	96	3	by	by	ADP
ejpam-5993	96	4	minimal-153	minimal-153	NOUN
ejpam-5993	96	5	ity	ity	PROPN
ejpam-5993	96	6	choice	choice	NOUN
ejpam-5993	96	7	of	of	ADP
ejpam-5993	96	8	|g|	|g|	ADJ
ejpam-5993	96	9	,	,	PUNCT
ejpam-5993	96	10	g	g	NOUN
ejpam-5993	96	11	/	/	SYM
ejpam-5993	96	12	p1	p1	NOUN
ejpam-5993	96	13	is	be	AUX
ejpam-5993	96	14	supersolvable	supersolvable	ADJ
ejpam-5993	96	15	.	.	PUNCT
ejpam-5993	97	1	since	since	SCONJ
ejpam-5993	97	2	(	(	PUNCT
ejpam-5993	97	3	g	g	NOUN
ejpam-5993	97	4	/	/	SYM
ejpam-5993	97	5	p1)/(φ(g)/p1	p1)/(φ(g)/p1	ADJ
ejpam-5993	97	6	)	)	PUNCT
ejpam-5993	97	7	∼=	∼=	ADP
ejpam-5993	97	8	g	g	NOUN
ejpam-5993	97	9	/	/	SYM
ejpam-5993	97	10	φ(g	φ(g	PROPN
ejpam-5993	97	11	)	)	PUNCT
ejpam-5993	97	12	,	,	PUNCT
ejpam-5993	97	13	we	we	PRON
ejpam-5993	97	14	have154	have154	VERB
ejpam-5993	97	15	g	g	NOUN
ejpam-5993	97	16	/	/	SYM
ejpam-5993	97	17	φ(g	φ(g	PROPN
ejpam-5993	97	18	)	)	PUNCT
ejpam-5993	97	19	is	be	AUX
ejpam-5993	97	20	supersolvable	supersolvable	ADJ
ejpam-5993	97	21	.	.	PUNCT
ejpam-5993	98	1	by	by	ADP
ejpam-5993	98	2	a	a	DET
ejpam-5993	98	3	well	well	ADV
ejpam-5993	98	4	-	-	PUNCT
ejpam-5993	98	5	known	know	VERB
ejpam-5993	98	6	theorem	theorem	NOUN
ejpam-5993	98	7	of	of	ADP
ejpam-5993	98	8	huppert	huppert	NOUN
ejpam-5993	98	9	[	[	X
ejpam-5993	98	10	13	13	NUM
ejpam-5993	98	11	,	,	PUNCT
ejpam-5993	98	12	p.	p.	NOUN
ejpam-5993	98	13	713	713	NUM
ejpam-5993	98	14	,	,	PUNCT
ejpam-5993	98	15	satz	satz	PROPN
ejpam-5993	98	16	8.6	8.6	NUM
ejpam-5993	98	17	]	]	PUNCT
ejpam-5993	98	18	,	,	PUNCT
ejpam-5993	98	19	g155	g155	PROPN
ejpam-5993	98	20	is	be	AUX
ejpam-5993	98	21	supersolvable	supersolvable	ADJ
ejpam-5993	98	22	,	,	PUNCT
ejpam-5993	98	23	a	a	DET
ejpam-5993	98	24	contradiction.156	contradiction.156	NOUN
ejpam-5993	98	25	157	157	NUM
ejpam-5993	98	26	case	case	NOUN
ejpam-5993	98	27	2	2	NUM
ejpam-5993	98	28	:	:	PUNCT
ejpam-5993	98	29	φ(g	φ(g	X
ejpam-5993	98	30	)	)	PUNCT
ejpam-5993	98	31	=	=	PUNCT
ejpam-5993	99	1	1.158	1.158	NUM
ejpam-5993	99	2	159	159	NUM
ejpam-5993	99	3	let	let	VERB
ejpam-5993	99	4	p	p	PRON
ejpam-5993	99	5	be	be	AUX
ejpam-5993	99	6	a	a	DET
ejpam-5993	99	7	non	non	ADJ
ejpam-5993	99	8	-	-	ADJ
ejpam-5993	99	9	cyclic	cyclic	ADJ
ejpam-5993	99	10	sylow	sylow	NOUN
ejpam-5993	99	11	p	p	PROPN
ejpam-5993	99	12	-	-	PUNCT
ejpam-5993	99	13	subgroup	subgroup	NOUN
ejpam-5993	99	14	of	of	ADP
ejpam-5993	99	15	f	f	PROPN
ejpam-5993	99	16	(	(	PUNCT
ejpam-5993	99	17	g	g	NOUN
ejpam-5993	99	18	)	)	PUNCT
ejpam-5993	99	19	.	.	PUNCT
ejpam-5993	100	1	since	since	SCONJ
ejpam-5993	100	2	p	p	NOUN
ejpam-5993	100	3	is	be	AUX
ejpam-5993	100	4	characteristic	characteristic	ADJ
ejpam-5993	100	5	in	in	ADP
ejpam-5993	100	6	f	f	PROPN
ejpam-5993	100	7	(	(	PUNCT
ejpam-5993	100	8	g	g	NOUN
ejpam-5993	100	9	)	)	PUNCT
ejpam-5993	100	10	⊴	⊴	ADP
ejpam-5993	100	11	g,160	g,160	PROPN
ejpam-5993	100	12	it	it	PRON
ejpam-5993	100	13	follows	follow	VERB
ejpam-5993	100	14	that	that	SCONJ
ejpam-5993	100	15	p	p	NOUN
ejpam-5993	100	16	⊴	⊴	ADP
ejpam-5993	100	17	g.	g.	PROPN
ejpam-5993	100	18	by	by	ADP
ejpam-5993	100	19	lemma	lemma	PROPN
ejpam-5993	100	20	1(i	1(i	NUM
ejpam-5993	100	21	)	)	PUNCT
ejpam-5993	100	22	,	,	PUNCT
ejpam-5993	100	23	φ(p	φ(p	PROPN
ejpam-5993	100	24	)	)	PUNCT
ejpam-5993	100	25	⩽	⩽	ADJ
ejpam-5993	100	26	φ(g	φ(g	PROPN
ejpam-5993	100	27	)	)	PUNCT
ejpam-5993	100	28	and	and	CCONJ
ejpam-5993	100	29	since	since	SCONJ
ejpam-5993	100	30	φ(g	φ(g	PROPN
ejpam-5993	100	31	)	)	PUNCT
ejpam-5993	100	32	=	=	SYM
ejpam-5993	101	1	1	1	NUM
ejpam-5993	101	2	,	,	PUNCT
ejpam-5993	101	3	then	then	ADV
ejpam-5993	101	4	φ(p	φ(p	PROPN
ejpam-5993	101	5	)	)	PUNCT
ejpam-5993	102	1	=	=	PUNCT
ejpam-5993	102	2	1,161	1,161	NUM
ejpam-5993	102	3	for	for	ADP
ejpam-5993	102	4	every	every	DET
ejpam-5993	102	5	sylow	sylow	NOUN
ejpam-5993	102	6	subgroup	subgroup	NOUN
ejpam-5993	102	7	of	of	ADP
ejpam-5993	102	8	f	f	PROPN
ejpam-5993	102	9	(	(	PUNCT
ejpam-5993	102	10	g	g	NOUN
ejpam-5993	102	11	)	)	PUNCT
ejpam-5993	102	12	.	.	PUNCT
ejpam-5993	103	1	since	since	SCONJ
ejpam-5993	103	2	g	g	PROPN
ejpam-5993	103	3	is	be	AUX
ejpam-5993	103	4	solvable	solvable	ADJ
ejpam-5993	103	5	and	and	CCONJ
ejpam-5993	103	6	φ(g	φ(g	ADJ
ejpam-5993	103	7	)	)	PUNCT
ejpam-5993	103	8	=	=	SYM
ejpam-5993	103	9	1	1	NUM
ejpam-5993	103	10	,	,	PUNCT
ejpam-5993	103	11	then	then	ADV
ejpam-5993	103	12	by	by	ADP
ejpam-5993	103	13	[	[	X
ejpam-5993	103	14	13	13	NUM
ejpam-5993	103	15	,	,	PUNCT
ejpam-5993	103	16	p.	p.	NOUN
ejpam-5993	103	17	279,162	279,162	NUM
ejpam-5993	104	1	staz	staz	NOUN
ejpam-5993	104	2	4.5	4.5	NUM
ejpam-5993	104	3	]	]	PUNCT
ejpam-5993	104	4	,	,	PUNCT
ejpam-5993	104	5	we	we	PRON
ejpam-5993	104	6	have	have	VERB
ejpam-5993	104	7	f	f	PROPN
ejpam-5993	104	8	(	(	PUNCT
ejpam-5993	104	9	g	g	NOUN
ejpam-5993	104	10	)	)	PUNCT
ejpam-5993	104	11	=	=	SYM
ejpam-5993	104	12	r1	r1	PROPN
ejpam-5993	104	13	×r2	×r2	PROPN
ejpam-5993	104	14	×r3	×r3	PROPN
ejpam-5993	104	15	×	×	NOUN
ejpam-5993	104	16	·	·	PUNCT
ejpam-5993	104	17	·	·	PUNCT
ejpam-5993	104	18	·	·	PUNCT
ejpam-5993	104	19	×rm	×rm	NOUN
ejpam-5993	104	20	,	,	PUNCT
ejpam-5993	104	21	where	where	SCONJ
ejpam-5993	104	22	ri(i	ri(i	PUNCT
ejpam-5993	104	23	=	=	SYM
ejpam-5993	104	24	1	1	NUM
ejpam-5993	104	25	,	,	PUNCT
ejpam-5993	104	26	.	.	PUNCT
ejpam-5993	104	27	.	.	PUNCT
ejpam-5993	104	28	.	.	PUNCT
ejpam-5993	105	1	,	,	PUNCT
ejpam-5993	105	2	m	m	PROPN
ejpam-5993	105	3	)	)	PUNCT
ejpam-5993	105	4	is	be	AUX
ejpam-5993	105	5	a	a	DET
ejpam-5993	105	6	minimal163	minimal163	PROPN
ejpam-5993	105	7	normal	normal	ADJ
ejpam-5993	105	8	subgroup	subgroup	NOUN
ejpam-5993	105	9	of	of	ADP
ejpam-5993	105	10	g.	g.	PROPN
ejpam-5993	105	11	clearly	clearly	ADV
ejpam-5993	105	12	,	,	PUNCT
ejpam-5993	105	13	r1	r1	VERB
ejpam-5993	105	14	≤	≤	ADJ
ejpam-5993	105	15	p	p	NOUN
ejpam-5993	105	16	.	.	PUNCT
ejpam-5993	106	1	if	if	SCONJ
ejpam-5993	106	2	r1	r1	PROPN
ejpam-5993	106	3	=	=	PROPN
ejpam-5993	106	4	p	p	X
ejpam-5993	106	5	,	,	PUNCT
ejpam-5993	106	6	then	then	ADV
ejpam-5993	106	7	p	p	NOUN
ejpam-5993	106	8	is	be	AUX
ejpam-5993	106	9	a	a	DET
ejpam-5993	106	10	minimal	minimal	ADJ
ejpam-5993	106	11	normal	normal	ADJ
ejpam-5993	106	12	subgroup164	subgroup164	NOUN
ejpam-5993	106	13	of	of	ADP
ejpam-5993	106	14	g.	g.	PROPN
ejpam-5993	106	15	if	if	SCONJ
ejpam-5993	106	16	|r1|	|r1|	PROPN
ejpam-5993	106	17	=	=	SYM
ejpam-5993	106	18	pe	pe	PROPN
ejpam-5993	106	19	,	,	PUNCT
ejpam-5993	106	20	e	e	X
ejpam-5993	106	21	>	>	X
ejpam-5993	106	22	1	1	NUM
ejpam-5993	106	23	,	,	PUNCT
ejpam-5993	106	24	let	let	VERB
ejpam-5993	106	25	p1	p1	NOUN
ejpam-5993	106	26	be	be	AUX
ejpam-5993	106	27	a	a	DET
ejpam-5993	106	28	maximal	maximal	ADJ
ejpam-5993	106	29	subgroup	subgroup	NOUN
ejpam-5993	106	30	of	of	ADP
ejpam-5993	106	31	r1	r1	PROPN
ejpam-5993	106	32	=	=	PROPN
ejpam-5993	106	33	p	p	PROPN
ejpam-5993	106	34	.	.	PUNCT
ejpam-5993	107	1	by	by	ADP
ejpam-5993	107	2	hypothesis	hypothesis	NOUN
ejpam-5993	107	3	,	,	PUNCT
ejpam-5993	107	4	p1	p1	NOUN
ejpam-5993	107	5	is165	is165	PROPN
ejpam-5993	107	6	an	an	DET
ejpam-5993	107	7	ssh	ssh	NOUN
ejpam-5993	107	8	-	-	PUNCT
ejpam-5993	107	9	subgroup	subgroup	NOUN
ejpam-5993	107	10	of	of	ADP
ejpam-5993	107	11	g.	g.	PROPN
ejpam-5993	107	12	then	then	ADV
ejpam-5993	107	13	g	g	PROPN
ejpam-5993	107	14	has	have	VERB
ejpam-5993	107	15	an	an	DET
ejpam-5993	107	16	s	s	NOUN
ejpam-5993	107	17	-	-	PUNCT
ejpam-5993	107	18	permutable	permutable	ADJ
ejpam-5993	107	19	subgroup	subgroup	NOUN
ejpam-5993	107	20	t	t	PROPN
ejpam-5993	107	21	such	such	ADJ
ejpam-5993	107	22	that	that	SCONJ
ejpam-5993	107	23	psg	psg	PROPN
ejpam-5993	107	24	=	=	SYM
ejpam-5993	107	25	p1t166	p1t166	PROPN
ejpam-5993	107	26	and	and	CCONJ
ejpam-5993	107	27	p	p	DET
ejpam-5993	107	28	g	g	PROPN
ejpam-5993	107	29	1	1	NUM
ejpam-5993	107	30	∩nt	∩nt	NOUN
ejpam-5993	107	31	(	(	PUNCT
ejpam-5993	107	32	p1	p1	NOUN
ejpam-5993	107	33	)	)	PUNCT
ejpam-5993	107	34	≤	≤	NOUN
ejpam-5993	107	35	p1	p1	NOUN
ejpam-5993	107	36	,	,	PUNCT
ejpam-5993	107	37	for	for	ADP
ejpam-5993	107	38	all	all	DET
ejpam-5993	107	39	g	g	PROPN
ejpam-5993	107	40	∈	∈	PROPN
ejpam-5993	107	41	g.	g.	NOUN
ejpam-5993	107	42	since	since	SCONJ
ejpam-5993	107	43	p	p	PROPN
ejpam-5993	107	44	is	be	AUX
ejpam-5993	107	45	a	a	DET
ejpam-5993	107	46	minimal	minimal	ADJ
ejpam-5993	107	47	s	s	NOUN
ejpam-5993	107	48	-	-	ADJ
ejpam-5993	107	49	permutable	permutable	ADJ
ejpam-5993	107	50	subgroup	subgroup	NOUN
ejpam-5993	107	51	of	of	ADP
ejpam-5993	107	52	g,167	g,167	ADJ
ejpam-5993	107	53	we	we	PRON
ejpam-5993	107	54	have	have	VERB
ejpam-5993	107	55	that	that	DET
ejpam-5993	107	56	psg	psg	PROPN
ejpam-5993	107	57	=	=	SYM
ejpam-5993	107	58	p	p	PROPN
ejpam-5993	107	59	=	=	PROPN
ejpam-5993	107	60	p1	p1	PROPN
ejpam-5993	107	61	t	t	PROPN
ejpam-5993	107	62	and	and	CCONJ
ejpam-5993	107	63	p	p	PRON
ejpam-5993	107	64	g	g	PROPN
ejpam-5993	107	65	1	1	NUM
ejpam-5993	107	66	∩nt	∩nt	NOUN
ejpam-5993	107	67	(	(	PUNCT
ejpam-5993	107	68	p1	p1	NOUN
ejpam-5993	107	69	)	)	PUNCT
ejpam-5993	107	70	≤	≤	NOUN
ejpam-5993	107	71	p1	p1	NOUN
ejpam-5993	107	72	,	,	PUNCT
ejpam-5993	107	73	for	for	ADP
ejpam-5993	107	74	all	all	DET
ejpam-5993	107	75	g	g	PROPN
ejpam-5993	107	76	∈	∈	PROPN
ejpam-5993	107	77	g.	g.	NOUN
ejpam-5993	107	78	since	since	SCONJ
ejpam-5993	107	79	p1	p1	PROPN
ejpam-5993	107	80	<	<	X
ejpam-5993	107	81	p	p	X
ejpam-5993	107	82	,	,	PUNCT
ejpam-5993	107	83	we	we	PRON
ejpam-5993	107	84	see168	see168	VERB
ejpam-5993	107	85	that	that	DET
ejpam-5993	107	86	t	t	NOUN
ejpam-5993	107	87	̸=	̸=	PROPN
ejpam-5993	107	88	1	1	NUM
ejpam-5993	107	89	and	and	CCONJ
ejpam-5993	107	90	so	so	ADV
ejpam-5993	107	91	p	p	X
ejpam-5993	107	92	=	=	X
ejpam-5993	107	93	t	t	PROPN
ejpam-5993	107	94	as	as	SCONJ
ejpam-5993	107	95	p	p	PRON
ejpam-5993	107	96	is	be	AUX
ejpam-5993	107	97	abelian	abelian	ADJ
ejpam-5993	107	98	and	and	CCONJ
ejpam-5993	107	99	so	so	ADV
ejpam-5993	107	100	p	p	DET
ejpam-5993	107	101	g	g	PROPN
ejpam-5993	107	102	1	1	NUM
ejpam-5993	107	103	∩nt	∩nt	NOUN
ejpam-5993	107	104	(	(	PUNCT
ejpam-5993	107	105	p1	p1	NOUN
ejpam-5993	107	106	)	)	PUNCT
ejpam-5993	107	107	=	=	NOUN
ejpam-5993	108	1	p	p	NOUN
ejpam-5993	108	2	g	g	PROPN
ejpam-5993	108	3	1	1	NUM
ejpam-5993	108	4	≤	≤	NOUN
ejpam-5993	108	5	p1	p1	NOUN
ejpam-5993	108	6	,	,	PUNCT
ejpam-5993	108	7	for	for	ADP
ejpam-5993	108	8	all	all	DET
ejpam-5993	108	9	g	g	PROPN
ejpam-5993	108	10	∈	∈	PROPN
ejpam-5993	108	11	g.169	g.169	NOUN
ejpam-5993	108	12	this	this	PRON
ejpam-5993	108	13	means	mean	VERB
ejpam-5993	108	14	that	that	SCONJ
ejpam-5993	108	15	p1	p1	NOUN
ejpam-5993	108	16	is	be	AUX
ejpam-5993	108	17	normal	normal	ADJ
ejpam-5993	108	18	in	in	ADP
ejpam-5993	108	19	g	g	PROPN
ejpam-5993	108	20	,	,	PUNCT
ejpam-5993	108	21	a	a	DET
ejpam-5993	108	22	contradiction	contradiction	NOUN
ejpam-5993	108	23	.	.	PUNCT
ejpam-5993	109	1	thus	thus	ADV
ejpam-5993	109	2	we	we	PRON
ejpam-5993	109	3	may	may	AUX
ejpam-5993	109	4	assume	assume	VERB
ejpam-5993	109	5	that	that	SCONJ
ejpam-5993	109	6	r1	r1	PROPN
ejpam-5993	109	7	is	be	AUX
ejpam-5993	109	8	a170	a170	PROPN
ejpam-5993	109	9	proper	proper	ADJ
ejpam-5993	109	10	subgroup	subgroup	NOUN
ejpam-5993	109	11	of	of	ADP
ejpam-5993	109	12	p	p	NOUN
ejpam-5993	109	13	,	,	PUNCT
ejpam-5993	109	14	where	where	SCONJ
ejpam-5993	109	15	p	p	NOUN
ejpam-5993	109	16	is	be	AUX
ejpam-5993	109	17	a	a	DET
ejpam-5993	109	18	non	non	ADJ
ejpam-5993	109	19	-	-	ADJ
ejpam-5993	109	20	cyclic	cyclic	ADJ
ejpam-5993	109	21	sylow	sylow	NOUN
ejpam-5993	109	22	p	p	PROPN
ejpam-5993	109	23	-	-	PUNCT
ejpam-5993	109	24	subgroup	subgroup	NOUN
ejpam-5993	109	25	of	of	ADP
ejpam-5993	109	26	f	f	PROPN
ejpam-5993	109	27	(	(	PUNCT
ejpam-5993	109	28	g	g	NOUN
ejpam-5993	109	29	)	)	PUNCT
ejpam-5993	109	30	.	.	PUNCT
ejpam-5993	110	1	since	since	SCONJ
ejpam-5993	110	2	φ(p	φ(p	PROPN
ejpam-5993	110	3	)	)	PUNCT
ejpam-5993	110	4	=	=	PUNCT
ejpam-5993	110	5	1,171	1,171	NUM
ejpam-5993	110	6	a.	a.	NOUN
ejpam-5993	110	7	s.	s.	PROPN
ejpam-5993	110	8	allehyani	allehyani	PROPN
ejpam-5993	110	9	/	/	SYM
ejpam-5993	110	10	eur	eur	PROPN
ejpam-5993	110	11	.	.	PUNCT
ejpam-5993	111	1	j.	j.	PROPN
ejpam-5993	111	2	pure	pure	PROPN
ejpam-5993	111	3	appl	appl	PROPN
ejpam-5993	111	4	.	.	PROPN
ejpam-5993	111	5	math	math	PROPN
ejpam-5993	111	6	,	,	PUNCT
ejpam-5993	111	7	18	18	NUM
ejpam-5993	111	8	(	(	PUNCT
ejpam-5993	111	9	2	2	NUM
ejpam-5993	111	10	)	)	PUNCT
ejpam-5993	111	11	(	(	PUNCT
ejpam-5993	111	12	2025	2025	NUM
ejpam-5993	111	13	)	)	PUNCT
ejpam-5993	111	14	,	,	PUNCT
ejpam-5993	111	15	5993	5993	NUM
ejpam-5993	111	16	6	6	NUM
ejpam-5993	111	17	of	of	ADP
ejpam-5993	111	18	13	13	NUM
ejpam-5993	111	19	then	then	ADV
ejpam-5993	111	20	there	there	PRON
ejpam-5993	111	21	exists	exist	VERB
ejpam-5993	111	22	a	a	DET
ejpam-5993	111	23	maximal	maximal	ADJ
ejpam-5993	111	24	subgroup	subgroup	NOUN
ejpam-5993	111	25	p1	p1	NOUN
ejpam-5993	111	26	of	of	ADP
ejpam-5993	111	27	p	p	PRON
ejpam-5993	111	28	such	such	ADJ
ejpam-5993	111	29	that	that	SCONJ
ejpam-5993	111	30	r1≮	r1≮	PROPN
ejpam-5993	111	31	p1	p1	PROPN
ejpam-5993	111	32	.	.	PUNCT
ejpam-5993	112	1	by	by	ADP
ejpam-5993	112	2	hypothesis	hypothesis	NOUN
ejpam-5993	112	3	,	,	PUNCT
ejpam-5993	112	4	p1	p1	PROPN
ejpam-5993	112	5	is172	is172	PROPN
ejpam-5993	112	6	an	an	DET
ejpam-5993	112	7	ssh	ssh	NOUN
ejpam-5993	112	8	-	-	PUNCT
ejpam-5993	112	9	subgroup	subgroup	NOUN
ejpam-5993	112	10	in	in	ADP
ejpam-5993	112	11	g	g	PROPN
ejpam-5993	112	12	,	,	PUNCT
ejpam-5993	112	13	then	then	ADV
ejpam-5993	112	14	there	there	PRON
ejpam-5993	112	15	exists	exist	VERB
ejpam-5993	112	16	an	an	DET
ejpam-5993	112	17	s	s	NOUN
ejpam-5993	112	18	-	-	PUNCT
ejpam-5993	112	19	permutable	permutable	ADJ
ejpam-5993	112	20	subgroup	subgroup	NOUN
ejpam-5993	112	21	k	k	PROPN
ejpam-5993	112	22	of	of	ADP
ejpam-5993	112	23	g	g	PROPN
ejpam-5993	112	24	such	such	ADJ
ejpam-5993	112	25	that173	that173	PROPN
ejpam-5993	112	26	(	(	PUNCT
ejpam-5993	112	27	p1	p1	PROPN
ejpam-5993	112	28	)	)	PUNCT
ejpam-5993	112	29	sg	sg	PROPN
ejpam-5993	112	30	=	=	SYM
ejpam-5993	112	31	p1k	p1k	PROPN
ejpam-5993	112	32	and	and	CCONJ
ejpam-5993	112	33	(	(	PUNCT
ejpam-5993	112	34	p1	p1	PROPN
ejpam-5993	112	35	)	)	PUNCT
ejpam-5993	112	36	g	g	ADP
ejpam-5993	112	37	∩nk(p1	∩nk(p1	PROPN
ejpam-5993	112	38	)	)	PUNCT
ejpam-5993	112	39	⩽	⩽	PROPN
ejpam-5993	112	40	p1	p1	PROPN
ejpam-5993	112	41	,	,	PUNCT
ejpam-5993	112	42	for	for	ADP
ejpam-5993	112	43	all	all	DET
ejpam-5993	112	44	g	g	PROPN
ejpam-5993	112	45	∈	∈	PROPN
ejpam-5993	112	46	g.	g.	NOUN
ejpam-5993	112	47	assuming	assume	VERB
ejpam-5993	112	48	that	that	SCONJ
ejpam-5993	112	49	k	k	PROPN
ejpam-5993	112	50	=	=	PUNCT
ejpam-5993	112	51	p	p	X
ejpam-5993	112	52	,	,	PUNCT
ejpam-5993	112	53	then	then	ADV
ejpam-5993	112	54	we174	we174	PROPN
ejpam-5993	112	55	have	have	VERB
ejpam-5993	112	56	(	(	PUNCT
ejpam-5993	112	57	p1	p1	NOUN
ejpam-5993	112	58	)	)	PUNCT
ejpam-5993	112	59	g	g	PROPN
ejpam-5993	112	60	∩ng(p1	∩ng(p1	NOUN
ejpam-5993	112	61	)	)	PUNCT
ejpam-5993	113	1	=	=	PUNCT
ejpam-5993	113	2	(	(	PUNCT
ejpam-5993	113	3	p1	p1	PROPN
ejpam-5993	113	4	)	)	PUNCT
ejpam-5993	113	5	g	g	ADP
ejpam-5993	113	6	∩k	∩k	ADJ
ejpam-5993	113	7	∩ng(p1	∩ng(p1	NOUN
ejpam-5993	113	8	)	)	PUNCT
ejpam-5993	114	1	=	=	SYM
ejpam-5993	114	2	(	(	PUNCT
ejpam-5993	114	3	p1	p1	PROPN
ejpam-5993	114	4	)	)	PUNCT
ejpam-5993	114	5	g	g	ADP
ejpam-5993	114	6	∩nk(p1	∩nk(p1	PROPN
ejpam-5993	114	7	)	)	PUNCT
ejpam-5993	114	8	⩽	⩽	PROPN
ejpam-5993	114	9	p1	p1	PROPN
ejpam-5993	114	10	.	.	PUNCT
ejpam-5993	115	1	then	then	ADV
ejpam-5993	115	2	we	we	PRON
ejpam-5993	115	3	get	get	VERB
ejpam-5993	115	4	p1	p1	PROPN
ejpam-5993	115	5	is	be	AUX
ejpam-5993	115	6	an175	an175	PROPN
ejpam-5993	115	7	h	h	NOUN
ejpam-5993	115	8	-	-	PUNCT
ejpam-5993	115	9	subgroup	subgroup	NOUN
ejpam-5993	115	10	in	in	ADP
ejpam-5993	115	11	g	g	PROPN
ejpam-5993	115	12	and	and	CCONJ
ejpam-5993	115	13	p1	p1	PROPN
ejpam-5993	115	14	⊴	⊴	ADP
ejpam-5993	115	15	p	p	PROPN
ejpam-5993	115	16	.	.	PUNCT
ejpam-5993	116	1	by	by	ADP
ejpam-5993	116	2	lemma	lemma	PROPN
ejpam-5993	116	3	4	4	NUM
ejpam-5993	116	4	,	,	PUNCT
ejpam-5993	116	5	we	we	PRON
ejpam-5993	116	6	get	get	VERB
ejpam-5993	116	7	p1	p1	PROPN
ejpam-5993	116	8	⊴	⊴	ADP
ejpam-5993	116	9	g.	g.	PROPN
ejpam-5993	116	10	now	now	ADV
ejpam-5993	116	11	,	,	PUNCT
ejpam-5993	116	12	p1	p1	PROPN
ejpam-5993	116	13	∩r1	∩r1	PROPN
ejpam-5993	116	14	⊴	⊴	ADP
ejpam-5993	116	15	g	g	PROPN
ejpam-5993	116	16	and	and	CCONJ
ejpam-5993	116	17	r1	r1	PROPN
ejpam-5993	116	18	is176	is176	PROPN
ejpam-5993	116	19	a	a	DET
ejpam-5993	116	20	minimal	minimal	ADJ
ejpam-5993	116	21	normal	normal	ADJ
ejpam-5993	116	22	subgroup	subgroup	NOUN
ejpam-5993	116	23	of	of	ADP
ejpam-5993	116	24	g	g	PROPN
ejpam-5993	116	25	,	,	PUNCT
ejpam-5993	116	26	means	mean	VERB
ejpam-5993	117	1	that	that	SCONJ
ejpam-5993	117	2	p1	p1	NOUN
ejpam-5993	117	3	∩r1	∩r1	PUNCT
ejpam-5993	118	1	=	=	NOUN
ejpam-5993	118	2	1	1	NUM
ejpam-5993	118	3	and	and	CCONJ
ejpam-5993	118	4	since	since	SCONJ
ejpam-5993	118	5	p	p	NOUN
ejpam-5993	119	1	=	=	NOUN
ejpam-5993	119	2	p1r1	p1r1	INTJ
ejpam-5993	119	3	we	we	PRON
ejpam-5993	119	4	have:177	have:177	VERB
ejpam-5993	119	5	p	p	NOUN
ejpam-5993	119	6	=	=	X
ejpam-5993	119	7	|p	|p	X
ejpam-5993	119	8	:	:	PUNCT
ejpam-5993	119	9	p1|	p1|	NOUN
ejpam-5993	119	10	=	=	SYM
ejpam-5993	119	11	|r1	|r1	NOUN
ejpam-5993	119	12	:	:	PUNCT
ejpam-5993	119	13	p1	p1	PROPN
ejpam-5993	119	14	∩r1|	∩r1|	PROPN
ejpam-5993	119	15	=	=	PUNCT
ejpam-5993	119	16	|r1|.178	|r1|.178	NOUN
ejpam-5993	119	17	thus	thus	ADV
ejpam-5993	119	18	,	,	PUNCT
ejpam-5993	119	19	r1	r1	PROPN
ejpam-5993	119	20	is	be	AUX
ejpam-5993	119	21	a	a	DET
ejpam-5993	119	22	cyclic	cyclic	ADJ
ejpam-5993	119	23	subgroup	subgroup	NOUN
ejpam-5993	119	24	of	of	ADP
ejpam-5993	119	25	prime	prime	ADJ
ejpam-5993	119	26	order.179	order.179	NOUN
ejpam-5993	119	27	set	set	VERB
ejpam-5993	120	1	ki	ki	PROPN
ejpam-5993	120	2	=	=	PROPN
ejpam-5993	120	3	r1	r1	PROPN
ejpam-5993	120	4	×r2	×r2	PROPN
ejpam-5993	120	5	×r3	×r3	PROPN
ejpam-5993	120	6	×	×	NOUN
ejpam-5993	120	7	·	·	PUNCT
ejpam-5993	120	8	·	·	PUNCT
ejpam-5993	120	9	·	·	PUNCT
ejpam-5993	121	1	×ri	×ri	ADJ
ejpam-5993	121	2	,	,	PUNCT
ejpam-5993	121	3	where	where	SCONJ
ejpam-5993	121	4	i	i	PRON
ejpam-5993	121	5	=	=	NOUN
ejpam-5993	121	6	1	1	NUM
ejpam-5993	121	7	,	,	PUNCT
ejpam-5993	121	8	.	.	PUNCT
ejpam-5993	121	9	.	.	PUNCT
ejpam-5993	121	10	.	.	PUNCT
ejpam-5993	122	1	,	,	PUNCT
ejpam-5993	122	2	m	m	VERB
ejpam-5993	122	3	and	and	CCONJ
ejpam-5993	122	4	consider	consider	VERB
ejpam-5993	122	5	the	the	DET
ejpam-5993	122	6	chain180	chain180	PROPN
ejpam-5993	122	7	1	1	NUM
ejpam-5993	122	8	=	=	SYM
ejpam-5993	122	9	φ(g	φ(g	X
ejpam-5993	122	10	)	)	PUNCT
ejpam-5993	122	11	=	=	SYM
ejpam-5993	122	12	k0	k0	PROPN
ejpam-5993	122	13	⩽	⩽	PROPN
ejpam-5993	122	14	k1	k1	PROPN
ejpam-5993	122	15	⩽	⩽	PROPN
ejpam-5993	122	16	k2	k2	PROPN
ejpam-5993	122	17	⩽	⩽	PROPN
ejpam-5993	122	18	.	.	PUNCT
ejpam-5993	122	19	.	.	PUNCT
ejpam-5993	123	1	.	.	PUNCT
ejpam-5993	124	1	⩽	⩽	ADJ
ejpam-5993	124	2	km	km	PROPN
ejpam-5993	124	3	=	=	SYM
ejpam-5993	124	4	f	f	PROPN
ejpam-5993	124	5	(	(	PUNCT
ejpam-5993	124	6	g).181	g).181	X
ejpam-5993	124	7	clearly	clearly	ADV
ejpam-5993	124	8	,	,	PUNCT
ejpam-5993	124	9	ki	ki	PROPN
ejpam-5993	124	10	are	be	AUX
ejpam-5993	124	11	normal	normal	ADJ
ejpam-5993	124	12	subgroups	subgroup	NOUN
ejpam-5993	124	13	of	of	ADP
ejpam-5993	124	14	g	g	PROPN
ejpam-5993	124	15	and	and	CCONJ
ejpam-5993	124	16	|ki	|ki	NUM
ejpam-5993	124	17	/	/	SYM
ejpam-5993	124	18	ki−1|	ki−1|	NOUN
ejpam-5993	124	19	=	=	NOUN
ejpam-5993	124	20	prime	prime	ADJ
ejpam-5993	124	21	(	(	PUNCT
ejpam-5993	124	22	1	1	NUM
ejpam-5993	124	23	≤	≤	NUM
ejpam-5993	124	24	i	i	PRON
ejpam-5993	124	25	≤	≤	NOUN
ejpam-5993	124	26	m	m	PROPN
ejpam-5993	124	27	)	)	PUNCT
ejpam-5993	124	28	.	.	PUNCT
ejpam-5993	125	1	applying182	applying182	PROPN
ejpam-5993	125	2	lemma	lemma	PROPN
ejpam-5993	125	3	5	5	NUM
ejpam-5993	125	4	,	,	PUNCT
ejpam-5993	125	5	g	g	PROPN
ejpam-5993	125	6	is	be	AUX
ejpam-5993	125	7	supersolvable	supersolvable	ADJ
ejpam-5993	125	8	,	,	PUNCT
ejpam-5993	125	9	a	a	DET
ejpam-5993	125	10	contradiction.183	contradiction.183	NOUN
ejpam-5993	125	11	the	the	DET
ejpam-5993	125	12	following	follow	VERB
ejpam-5993	125	13	example	example	NOUN
ejpam-5993	125	14	shows	show	VERB
ejpam-5993	125	15	that	that	SCONJ
ejpam-5993	125	16	the	the	DET
ejpam-5993	125	17	solvability	solvability	NOUN
ejpam-5993	125	18	of	of	ADP
ejpam-5993	125	19	g	g	PROPN
ejpam-5993	125	20	in	in	ADP
ejpam-5993	125	21	theorem	theorem	NOUN
ejpam-5993	125	22	1	1	NUM
ejpam-5993	125	23	can	can	AUX
ejpam-5993	125	24	not	not	PART
ejpam-5993	125	25	be	be	AUX
ejpam-5993	125	26	omitted.184	omitted.184	VERB
ejpam-5993	125	27	example	example	NOUN
ejpam-5993	125	28	1	1	NUM
ejpam-5993	125	29	.	.	PUNCT
ejpam-5993	125	30	consider	consider	VERB
ejpam-5993	125	31	the	the	DET
ejpam-5993	125	32	group	group	NOUN
ejpam-5993	125	33	g	g	PROPN
ejpam-5993	125	34	=	=	SYM
ejpam-5993	125	35	n×m	n×m	PROPN
ejpam-5993	125	36	,	,	PUNCT
ejpam-5993	125	37	where	where	SCONJ
ejpam-5993	125	38	n	n	PRON
ejpam-5993	125	39	is	be	AUX
ejpam-5993	125	40	nilpotent	nilpotent	ADJ
ejpam-5993	125	41	and	and	CCONJ
ejpam-5993	125	42	m	m	NOUN
ejpam-5993	125	43	is	be	AUX
ejpam-5993	125	44	a	a	DET
ejpam-5993	125	45	non	non	ADJ
ejpam-5993	125	46	-	-	ADJ
ejpam-5993	125	47	abelian185	abelian185	ADJ
ejpam-5993	125	48	simple	simple	ADJ
ejpam-5993	125	49	group	group	NOUN
ejpam-5993	125	50	.	.	PUNCT
ejpam-5993	126	1	clearly	clearly	ADV
ejpam-5993	126	2	,	,	PUNCT
ejpam-5993	126	3	g	g	PROPN
ejpam-5993	126	4	is	be	AUX
ejpam-5993	126	5	not	not	PART
ejpam-5993	126	6	solvable	solvable	ADJ
ejpam-5993	126	7	.	.	PUNCT
ejpam-5993	127	1	we	we	PRON
ejpam-5993	127	2	notice	notice	VERB
ejpam-5993	127	3	that	that	SCONJ
ejpam-5993	127	4	f	f	PROPN
ejpam-5993	127	5	(	(	PUNCT
ejpam-5993	127	6	g	g	NOUN
ejpam-5993	127	7	)	)	PUNCT
ejpam-5993	127	8	=	=	SYM
ejpam-5993	127	9	f	f	X
ejpam-5993	127	10	(	(	PUNCT
ejpam-5993	127	11	n	n	CCONJ
ejpam-5993	127	12	)	)	PUNCT
ejpam-5993	127	13	=	=	SYM
ejpam-5993	127	14	n	n	PROPN
ejpam-5993	127	15	and	and	CCONJ
ejpam-5993	127	16	every186	every186	PROPN
ejpam-5993	127	17	maximal	maximal	ADJ
ejpam-5993	127	18	subgroup	subgroup	NOUN
ejpam-5993	127	19	of	of	ADP
ejpam-5993	127	20	the	the	DET
ejpam-5993	127	21	non	non	ADJ
ejpam-5993	127	22	-	-	ADJ
ejpam-5993	127	23	cyclic	cyclic	ADJ
ejpam-5993	127	24	sylow	sylow	NOUN
ejpam-5993	127	25	subgroups	subgroup	NOUN
ejpam-5993	127	26	of	of	ADP
ejpam-5993	127	27	f	f	PROPN
ejpam-5993	127	28	(	(	PUNCT
ejpam-5993	127	29	g	g	NOUN
ejpam-5993	127	30	)	)	PUNCT
ejpam-5993	127	31	is	be	AUX
ejpam-5993	127	32	ssh	ssh	NOUN
ejpam-5993	127	33	-	-	PUNCT
ejpam-5993	127	34	subgroup	subgroup	NOUN
ejpam-5993	127	35	of	of	ADP
ejpam-5993	127	36	g.187	g.187	DET
ejpam-5993	127	37	the	the	DET
ejpam-5993	127	38	converse	converse	NOUN
ejpam-5993	127	39	of	of	ADP
ejpam-5993	127	40	theorem	theorem	NOUN
ejpam-5993	127	41	1	1	NUM
ejpam-5993	127	42	is	be	AUX
ejpam-5993	127	43	not	not	PART
ejpam-5993	127	44	necessary	necessary	ADJ
ejpam-5993	127	45	true	true	ADJ
ejpam-5993	127	46	as	as	ADP
ejpam-5993	127	47	the	the	DET
ejpam-5993	127	48	following	follow	VERB
ejpam-5993	127	49	example188	example188	PROPN
ejpam-5993	127	50	example	example	NOUN
ejpam-5993	128	1	2	2	X
ejpam-5993	128	2	.	.	PUNCT
ejpam-5993	128	3	let	let	VERB
ejpam-5993	128	4	g	g	NOUN
ejpam-5993	128	5	=	=	PUNCT
ejpam-5993	128	6	z/3z	z/3z	PROPN
ejpam-5993	128	7	×	×	PROPN
ejpam-5993	128	8	s3	s3	PROPN
ejpam-5993	128	9	.	.	PUNCT
ejpam-5993	129	1	then	then	ADV
ejpam-5993	129	2	g	g	PROPN
ejpam-5993	129	3	is	be	AUX
ejpam-5993	129	4	supersolvable	supersolvable	ADJ
ejpam-5993	129	5	,	,	PUNCT
ejpam-5993	129	6	but	but	CCONJ
ejpam-5993	129	7	there	there	PRON
ejpam-5993	129	8	exists	exist	VERB
ejpam-5993	129	9	a	a	DET
ejpam-5993	129	10	maximal189	maximal189	PROPN
ejpam-5993	129	11	subgroup	subgroup	NOUN
ejpam-5993	129	12	of	of	ADP
ejpam-5993	129	13	the	the	DET
ejpam-5993	129	14	non	non	ADJ
ejpam-5993	129	15	-	-	ADJ
ejpam-5993	129	16	cyclic	cyclic	ADJ
ejpam-5993	129	17	sylow	sylow	NOUN
ejpam-5993	129	18	subgroups	subgroup	NOUN
ejpam-5993	129	19	of	of	ADP
ejpam-5993	129	20	f	f	PROPN
ejpam-5993	129	21	(	(	PUNCT
ejpam-5993	129	22	g	g	NOUN
ejpam-5993	129	23	)	)	PUNCT
ejpam-5993	129	24	which	which	PRON
ejpam-5993	129	25	is	be	AUX
ejpam-5993	129	26	not	not	PART
ejpam-5993	129	27	ssh	ssh	NOUN
ejpam-5993	129	28	-	-	PUNCT
ejpam-5993	129	29	subgroup	subgroup	NOUN
ejpam-5993	129	30	of	of	ADP
ejpam-5993	129	31	g.190	g.190	NOUN
ejpam-5993	129	32	theorem	theorem	NOUN
ejpam-5993	129	33	2	2	X
ejpam-5993	129	34	.	.	PUNCT
ejpam-5993	130	1	let	let	VERB
ejpam-5993	130	2	g	g	PRON
ejpam-5993	130	3	be	be	AUX
ejpam-5993	130	4	a	a	DET
ejpam-5993	130	5	group	group	NOUN
ejpam-5993	130	6	with	with	ADP
ejpam-5993	130	7	a	a	DET
ejpam-5993	130	8	normal	normal	ADJ
ejpam-5993	130	9	solvable	solvable	ADJ
ejpam-5993	130	10	subgroup	subgroup	NOUN
ejpam-5993	130	11	h	h	NOUN
ejpam-5993	130	12	such	such	ADJ
ejpam-5993	130	13	that	that	SCONJ
ejpam-5993	130	14	g	g	PROPN
ejpam-5993	130	15	/	/	SYM
ejpam-5993	130	16	h	h	NOUN
ejpam-5993	130	17	is191	is191	PROPN
ejpam-5993	130	18	supersolvable	supersolvable	ADJ
ejpam-5993	130	19	.	.	PUNCT
ejpam-5993	131	1	if	if	SCONJ
ejpam-5993	131	2	all	all	DET
ejpam-5993	131	3	maximal	maximal	ADJ
ejpam-5993	131	4	subgroups	subgroup	NOUN
ejpam-5993	131	5	of	of	ADP
ejpam-5993	131	6	the	the	DET
ejpam-5993	131	7	non	non	ADJ
ejpam-5993	131	8	-	-	ADJ
ejpam-5993	131	9	cyclic	cyclic	ADJ
ejpam-5993	131	10	sylow	sylow	NOUN
ejpam-5993	131	11	subgroup	subgroup	NOUN
ejpam-5993	131	12	of	of	ADP
ejpam-5993	131	13	f	f	PROPN
ejpam-5993	131	14	(	(	PUNCT
ejpam-5993	131	15	h	h	NOUN
ejpam-5993	131	16	)	)	PUNCT
ejpam-5993	131	17	are192	are192	PROPN
ejpam-5993	131	18	ssh	ssh	NOUN
ejpam-5993	131	19	-	-	PUNCT
ejpam-5993	131	20	subgroups	subgroup	NOUN
ejpam-5993	131	21	of	of	ADP
ejpam-5993	131	22	g	g	NOUN
ejpam-5993	131	23	,	,	PUNCT
ejpam-5993	131	24	then	then	ADV
ejpam-5993	131	25	g	g	PROPN
ejpam-5993	131	26	is	be	AUX
ejpam-5993	131	27	supersolvable.193	supersolvable.193	NUM
ejpam-5993	131	28	proof	proof	NOUN
ejpam-5993	131	29	.	.	PUNCT
ejpam-5993	132	1	assume	assume	VERB
ejpam-5993	132	2	that	that	SCONJ
ejpam-5993	132	3	the	the	DET
ejpam-5993	132	4	claim	claim	NOUN
ejpam-5993	132	5	is	be	AUX
ejpam-5993	132	6	false	false	ADJ
ejpam-5993	132	7	and	and	CCONJ
ejpam-5993	132	8	choose	choose	VERB
ejpam-5993	132	9	g	g	NOUN
ejpam-5993	132	10	to	to	PART
ejpam-5993	132	11	be	be	AUX
ejpam-5993	132	12	a	a	DET
ejpam-5993	132	13	counterexample	counterexample	NOUN
ejpam-5993	132	14	of	of	ADP
ejpam-5993	132	15	minimal194	minimal194	PROPN
ejpam-5993	132	16	order	order	NOUN
ejpam-5993	132	17	.	.	PUNCT
ejpam-5993	133	1	we	we	PRON
ejpam-5993	133	2	distinguish	distinguish	VERB
ejpam-5993	133	3	the	the	DET
ejpam-5993	133	4	following	follow	VERB
ejpam-5993	133	5	two	two	NUM
ejpam-5993	133	6	cases:195	cases:195	PROPN
ejpam-5993	133	7	196	196	NUM
ejpam-5993	133	8	case	case	NOUN
ejpam-5993	133	9	1	1	NUM
ejpam-5993	133	10	:	:	PUNCT
ejpam-5993	133	11	φ(g	φ(g	ADJ
ejpam-5993	133	12	)	)	PUNCT
ejpam-5993	133	13	∩h	∩h	PROPN
ejpam-5993	133	14	̸=	̸=	PROPN
ejpam-5993	133	15	1.197	1.197	NUM
ejpam-5993	133	16	198	198	NUM
ejpam-5993	133	17	then	then	ADV
ejpam-5993	133	18	there	there	PRON
ejpam-5993	133	19	exists	exist	VERB
ejpam-5993	133	20	a	a	DET
ejpam-5993	133	21	prime	prime	NOUN
ejpam-5993	133	22	p	p	NOUN
ejpam-5993	133	23	such	such	ADJ
ejpam-5993	133	24	that	that	DET
ejpam-5993	133	25	p||φ(g	p||φ(g	NOUN
ejpam-5993	133	26	)	)	PUNCT
ejpam-5993	133	27	∩	∩	NOUN
ejpam-5993	133	28	h|	h|	PROPN
ejpam-5993	133	29	.	.	PUNCT
ejpam-5993	134	1	let	let	VERB
ejpam-5993	134	2	p1	p1	PROPN
ejpam-5993	134	3	be	be	AUX
ejpam-5993	134	4	a	a	DET
ejpam-5993	134	5	non	non	ADJ
ejpam-5993	134	6	-	-	ADJ
ejpam-5993	134	7	cyclic	cyclic	ADJ
ejpam-5993	134	8	sylow199	sylow199	PROPN
ejpam-5993	134	9	p	p	PROPN
ejpam-5993	134	10	-	-	PUNCT
ejpam-5993	134	11	subgroup	subgroup	NOUN
ejpam-5993	134	12	of	of	ADP
ejpam-5993	134	13	(	(	PUNCT
ejpam-5993	134	14	φ(g	φ(g	PROPN
ejpam-5993	134	15	)	)	PUNCT
ejpam-5993	134	16	∩	∩	ADJ
ejpam-5993	134	17	h	h	NOUN
ejpam-5993	134	18	)	)	PUNCT
ejpam-5993	134	19	.	.	PUNCT
ejpam-5993	135	1	since	since	SCONJ
ejpam-5993	135	2	(	(	PUNCT
ejpam-5993	135	3	φ(g	φ(g	PROPN
ejpam-5993	135	4	)	)	PUNCT
ejpam-5993	135	5	∩	∩	ADJ
ejpam-5993	135	6	h	h	NOUN
ejpam-5993	135	7	)	)	PUNCT
ejpam-5993	135	8	is	be	AUX
ejpam-5993	135	9	a	a	DET
ejpam-5993	135	10	nilpotent	nilpotent	NOUN
ejpam-5993	135	11	,	,	PUNCT
ejpam-5993	135	12	then	then	ADV
ejpam-5993	135	13	p1	p1	PROPN
ejpam-5993	135	14	⊴	⊴	PROPN
ejpam-5993	135	15	(	(	PUNCT
ejpam-5993	135	16	φ(g	φ(g	PROPN
ejpam-5993	135	17	)	)	PUNCT
ejpam-5993	135	18	∩	∩	NOUN
ejpam-5993	135	19	h).200	h).200	X
ejpam-5993	135	20	now	now	ADV
ejpam-5993	135	21	,	,	PUNCT
ejpam-5993	135	22	p1	p1	PROPN
ejpam-5993	135	23	is	be	AUX
ejpam-5993	135	24	a	a	DET
ejpam-5993	135	25	normal	normal	ADJ
ejpam-5993	135	26	hall	hall	NOUN
ejpam-5993	135	27	subgroup	subgroup	NOUN
ejpam-5993	135	28	of	of	ADP
ejpam-5993	135	29	(	(	PUNCT
ejpam-5993	135	30	φ(g	φ(g	PROPN
ejpam-5993	135	31	)	)	PUNCT
ejpam-5993	135	32	∩	∩	ADJ
ejpam-5993	135	33	h	h	NOUN
ejpam-5993	135	34	)	)	PUNCT
ejpam-5993	135	35	implies	imply	VERB
ejpam-5993	135	36	that	that	SCONJ
ejpam-5993	135	37	p1	p1	NOUN
ejpam-5993	135	38	is	be	AUX
ejpam-5993	135	39	characteristic	characteristic	ADJ
ejpam-5993	135	40	in201	in201	PROPN
ejpam-5993	135	41	(	(	PUNCT
ejpam-5993	135	42	φ(g	φ(g	PROPN
ejpam-5993	135	43	)	)	PUNCT
ejpam-5993	135	44	∩h	∩h	NOUN
ejpam-5993	135	45	)	)	PUNCT
ejpam-5993	135	46	⊴	⊴	ADP
ejpam-5993	135	47	g	g	PROPN
ejpam-5993	135	48	,	,	PUNCT
ejpam-5993	135	49	hence	hence	ADV
ejpam-5993	135	50	p1	p1	PROPN
ejpam-5993	135	51	⊴	⊴	PROPN
ejpam-5993	135	52	g.	g.	PROPN
ejpam-5993	136	1	so	so	ADV
ejpam-5993	136	2	,	,	PUNCT
ejpam-5993	136	3	(	(	PUNCT
ejpam-5993	136	4	g	g	NOUN
ejpam-5993	136	5	/	/	SYM
ejpam-5993	136	6	p1)/(h	p1)/(h	NOUN
ejpam-5993	136	7	/	/	SYM
ejpam-5993	136	8	p1	p1	NOUN
ejpam-5993	136	9	)	)	PUNCT
ejpam-5993	136	10	∼=	∼=	PROPN
ejpam-5993	136	11	g	g	NOUN
ejpam-5993	136	12	/	/	SYM
ejpam-5993	136	13	h	h	NOUN
ejpam-5993	136	14	is	be	AUX
ejpam-5993	136	15	supersolvable.202	supersolvable.202	PROPN
ejpam-5993	136	16	now	now	ADV
ejpam-5993	136	17	,	,	PUNCT
ejpam-5993	136	18	we	we	PRON
ejpam-5993	136	19	show	show	VERB
ejpam-5993	136	20	that	that	SCONJ
ejpam-5993	137	1	f	f	PROPN
ejpam-5993	137	2	(	(	PUNCT
ejpam-5993	137	3	h	h	NOUN
ejpam-5993	137	4	/	/	SYM
ejpam-5993	137	5	p1	p1	NOUN
ejpam-5993	137	6	)	)	PUNCT
ejpam-5993	137	7	=	=	SYM
ejpam-5993	138	1	f	f	PROPN
ejpam-5993	138	2	(	(	PUNCT
ejpam-5993	138	3	h)/p1	h)/p1	PROPN
ejpam-5993	138	4	.	.	PUNCT
ejpam-5993	139	1	it	it	PRON
ejpam-5993	139	2	is	be	AUX
ejpam-5993	139	3	clear	clear	ADJ
ejpam-5993	139	4	f	f	X
ejpam-5993	139	5	(	(	PUNCT
ejpam-5993	139	6	h)/p1	h)/p1	ADV
ejpam-5993	139	7	is	be	AUX
ejpam-5993	139	8	a	a	DET
ejpam-5993	139	9	normal	normal	ADJ
ejpam-5993	139	10	nilpo-203	nilpo-203	ADJ
ejpam-5993	139	11	tent	tent	NOUN
ejpam-5993	139	12	subgroup	subgroup	NOUN
ejpam-5993	139	13	of	of	ADP
ejpam-5993	139	14	h	h	NOUN
ejpam-5993	139	15	/	/	SYM
ejpam-5993	139	16	p1	p1	PROPN
ejpam-5993	139	17	and	and	CCONJ
ejpam-5993	139	18	f	f	PROPN
ejpam-5993	139	19	(	(	PUNCT
ejpam-5993	139	20	h	h	NOUN
ejpam-5993	139	21	/	/	SYM
ejpam-5993	139	22	p1	p1	NOUN
ejpam-5993	139	23	)	)	PUNCT
ejpam-5993	139	24	is	be	AUX
ejpam-5993	139	25	a	a	DET
ejpam-5993	139	26	largest	large	ADJ
ejpam-5993	139	27	normal	normal	ADJ
ejpam-5993	139	28	nilpotent	nilpotent	ADJ
ejpam-5993	139	29	subgroup	subgroup	NOUN
ejpam-5993	139	30	of	of	ADP
ejpam-5993	139	31	h	h	NOUN
ejpam-5993	139	32	/	/	SYM
ejpam-5993	139	33	p1	p1	PROPN
ejpam-5993	139	34	so,204	so,204	PROPN
ejpam-5993	139	35	f	f	PROPN
ejpam-5993	139	36	(	(	PUNCT
ejpam-5993	139	37	h)/p1	h)/p1	PROPN
ejpam-5993	139	38	⩽	⩽	ADJ
ejpam-5993	139	39	f	f	PROPN
ejpam-5993	139	40	(	(	PUNCT
ejpam-5993	139	41	h	h	NOUN
ejpam-5993	139	42	/	/	SYM
ejpam-5993	139	43	p1	p1	NOUN
ejpam-5993	139	44	)	)	PUNCT
ejpam-5993	139	45	.	.	PUNCT
ejpam-5993	140	1	set	set	VERB
ejpam-5993	140	2	f	f	PROPN
ejpam-5993	140	3	(	(	PUNCT
ejpam-5993	140	4	h	h	NOUN
ejpam-5993	140	5	/	/	SYM
ejpam-5993	140	6	p1	p1	NOUN
ejpam-5993	140	7	)	)	PUNCT
ejpam-5993	140	8	=	=	SYM
ejpam-5993	140	9	l	l	X
ejpam-5993	140	10	/	/	SYM
ejpam-5993	140	11	p1	p1	NOUN
ejpam-5993	140	12	.	.	PUNCT
ejpam-5993	141	1	since	since	SCONJ
ejpam-5993	141	2	l	l	NOUN
ejpam-5993	141	3	/	/	SYM
ejpam-5993	141	4	p1	p1	NOUN
ejpam-5993	141	5	is	be	AUX
ejpam-5993	141	6	characteristic	characteristic	ADJ
ejpam-5993	141	7	in	in	ADP
ejpam-5993	141	8	h	h	NOUN
ejpam-5993	141	9	/	/	SYM
ejpam-5993	141	10	p1	p1	NOUN
ejpam-5993	141	11	⊴205	⊴205	X
ejpam-5993	141	12	g	g	PROPN
ejpam-5993	141	13	/	/	SYM
ejpam-5993	141	14	p1	p1	NOUN
ejpam-5993	141	15	,	,	PUNCT
ejpam-5993	141	16	then	then	ADV
ejpam-5993	141	17	l	l	PROPN
ejpam-5993	141	18	/	/	SYM
ejpam-5993	141	19	p1	p1	NOUN
ejpam-5993	141	20	⊴	⊴	ADP
ejpam-5993	141	21	g	g	PROPN
ejpam-5993	141	22	/	/	SYM
ejpam-5993	141	23	p1	p1	NOUN
ejpam-5993	141	24	.	.	PUNCT
ejpam-5993	142	1	but	but	CCONJ
ejpam-5993	142	2	l	l	NOUN
ejpam-5993	142	3	is	be	AUX
ejpam-5993	142	4	a	a	DET
ejpam-5993	142	5	normal	normal	ADJ
ejpam-5993	142	6	nilpotent	nilpotent	ADJ
ejpam-5993	142	7	subgroup	subgroup	NOUN
ejpam-5993	142	8	of	of	ADP
ejpam-5993	142	9	h	h	NOUN
ejpam-5993	142	10	holds	hold	NOUN
ejpam-5993	142	11	by	by	ADP
ejpam-5993	142	12	the206	the206	NOUN
ejpam-5993	142	13	fact	fact	NOUN
ejpam-5993	142	14	that	that	SCONJ
ejpam-5993	142	15	p1	p1	PROPN
ejpam-5993	142	16	⩽	⩽	NOUN
ejpam-5993	142	17	φ(g	φ(g	PROPN
ejpam-5993	142	18	)	)	PUNCT
ejpam-5993	142	19	,	,	PUNCT
ejpam-5993	143	1	then	then	ADV
ejpam-5993	143	2	l	l	PROPN
ejpam-5993	143	3	⩽	⩽	PROPN
ejpam-5993	143	4	f	f	PROPN
ejpam-5993	143	5	(	(	PUNCT
ejpam-5993	143	6	h	h	NOUN
ejpam-5993	143	7	)	)	PUNCT
ejpam-5993	143	8	,	,	PUNCT
ejpam-5993	143	9	and	and	CCONJ
ejpam-5993	143	10	so	so	ADV
ejpam-5993	143	11	l	l	NOUN
ejpam-5993	143	12	/	/	SYM
ejpam-5993	143	13	p1	p1	NOUN
ejpam-5993	143	14	=	=	SYM
ejpam-5993	143	15	f	f	PROPN
ejpam-5993	143	16	(	(	PUNCT
ejpam-5993	143	17	h	h	NOUN
ejpam-5993	143	18	/	/	SYM
ejpam-5993	143	19	p1	p1	NOUN
ejpam-5993	143	20	)	)	PUNCT
ejpam-5993	143	21	⩽	⩽	NOUN
ejpam-5993	144	1	f	f	PROPN
ejpam-5993	144	2	(	(	PUNCT
ejpam-5993	144	3	h)/p1	h)/p1	PROPN
ejpam-5993	144	4	.	.	PUNCT
ejpam-5993	145	1	there-207	there-207	VERB
ejpam-5993	145	2	fore	fore	PROPN
ejpam-5993	145	3	,	,	PUNCT
ejpam-5993	145	4	f	f	PROPN
ejpam-5993	145	5	(	(	PUNCT
ejpam-5993	145	6	h)/p1	h)/p1	NOUN
ejpam-5993	145	7	=	=	SYM
ejpam-5993	145	8	f	f	PROPN
ejpam-5993	145	9	(	(	PUNCT
ejpam-5993	145	10	h	h	NOUN
ejpam-5993	145	11	/	/	SYM
ejpam-5993	145	12	p1	p1	NOUN
ejpam-5993	145	13	)	)	PUNCT
ejpam-5993	145	14	.	.	PUNCT
ejpam-5993	146	1	let	let	VERB
ejpam-5993	146	2	p2	p2	PROPN
ejpam-5993	146	3	/	/	SYM
ejpam-5993	146	4	p1	p1	NOUN
ejpam-5993	146	5	be	be	VERB
ejpam-5993	146	6	a	a	DET
ejpam-5993	146	7	maximal	maximal	ADJ
ejpam-5993	146	8	subgroup	subgroup	NOUN
ejpam-5993	146	9	of	of	ADP
ejpam-5993	146	10	the	the	DET
ejpam-5993	146	11	non	non	ADJ
ejpam-5993	146	12	-	-	ADJ
ejpam-5993	146	13	cyclic	cyclic	ADJ
ejpam-5993	146	14	sylow208	sylow208	PROPN
ejpam-5993	146	15	a.	a.	NOUN
ejpam-5993	146	16	s.	s.	PROPN
ejpam-5993	146	17	allehyani	allehyani	PROPN
ejpam-5993	146	18	/	/	SYM
ejpam-5993	146	19	eur	eur	PROPN
ejpam-5993	146	20	.	.	PUNCT
ejpam-5993	147	1	j.	j.	PROPN
ejpam-5993	147	2	pure	pure	PROPN
ejpam-5993	147	3	appl	appl	PROPN
ejpam-5993	147	4	.	.	PROPN
ejpam-5993	147	5	math	math	PROPN
ejpam-5993	147	6	,	,	PUNCT
ejpam-5993	147	7	18	18	NUM
ejpam-5993	147	8	(	(	PUNCT
ejpam-5993	147	9	2	2	NUM
ejpam-5993	147	10	)	)	PUNCT
ejpam-5993	147	11	(	(	PUNCT
ejpam-5993	147	12	2025	2025	NUM
ejpam-5993	147	13	)	)	PUNCT
ejpam-5993	147	14	,	,	PUNCT
ejpam-5993	147	15	5993	5993	NUM
ejpam-5993	147	16	7	7	NUM
ejpam-5993	147	17	of	of	ADP
ejpam-5993	147	18	13	13	NUM
ejpam-5993	147	19	p	p	NOUN
ejpam-5993	147	20	-	-	PUNCT
ejpam-5993	147	21	subgroup	subgroup	NOUN
ejpam-5993	147	22	of	of	ADP
ejpam-5993	147	23	f	f	PROPN
ejpam-5993	147	24	(	(	PUNCT
ejpam-5993	147	25	h)/p1	h)/p1	PROPN
ejpam-5993	147	26	.	.	PUNCT
ejpam-5993	148	1	then	then	ADV
ejpam-5993	148	2	,	,	PUNCT
ejpam-5993	148	3	by	by	ADP
ejpam-5993	148	4	hypothesis	hypothesis	NOUN
ejpam-5993	148	5	,	,	PUNCT
ejpam-5993	148	6	p2	p2	PROPN
ejpam-5993	148	7	/	/	SYM
ejpam-5993	148	8	p1	p1	NOUN
ejpam-5993	148	9	is	be	AUX
ejpam-5993	148	10	an	an	DET
ejpam-5993	148	11	ssh	ssh	NOUN
ejpam-5993	148	12	-	-	PUNCT
ejpam-5993	148	13	subgroup	subgroup	NOUN
ejpam-5993	148	14	in	in	ADP
ejpam-5993	148	15	g	g	PROPN
ejpam-5993	148	16	/	/	SYM
ejpam-5993	148	17	p1	p1	NOUN
ejpam-5993	148	18	.	.	PUNCT
ejpam-5993	149	1	thus,209	thus,209	NOUN
ejpam-5993	149	2	by	by	ADP
ejpam-5993	149	3	minimalty	minimalty	ADJ
ejpam-5993	149	4	choice	choice	NOUN
ejpam-5993	149	5	of	of	ADP
ejpam-5993	149	6	|g|	|g|	ADJ
ejpam-5993	149	7	,	,	PUNCT
ejpam-5993	149	8	g	g	NOUN
ejpam-5993	149	9	/	/	SYM
ejpam-5993	149	10	p1	p1	NOUN
ejpam-5993	149	11	is	be	AUX
ejpam-5993	149	12	supersolvable	supersolvable	ADJ
ejpam-5993	149	13	and	and	CCONJ
ejpam-5993	149	14	since	since	SCONJ
ejpam-5993	149	15	p1	p1	PROPN
ejpam-5993	149	16	⩽	⩽	PROPN
ejpam-5993	149	17	φ(g	φ(g	PROPN
ejpam-5993	149	18	)	)	PUNCT
ejpam-5993	149	19	,	,	PUNCT
ejpam-5993	149	20	we	we	PRON
ejpam-5993	149	21	get	get	VERB
ejpam-5993	149	22	g	g	NOUN
ejpam-5993	149	23	/	/	SYM
ejpam-5993	149	24	φ(g)210	φ(g)210	NOUN
ejpam-5993	149	25	is	be	AUX
ejpam-5993	149	26	supersolvable	supersolvable	ADJ
ejpam-5993	149	27	.	.	PUNCT
ejpam-5993	150	1	by	by	ADP
ejpam-5993	150	2	huppert	huppert	PROPN
ejpam-5993	150	3	’s	’s	PART
ejpam-5993	150	4	theorem	theorem	NOUN
ejpam-5993	150	5	[	[	PUNCT
ejpam-5993	150	6	13	13	NUM
ejpam-5993	150	7	,	,	PUNCT
ejpam-5993	150	8	p.	p.	NOUN
ejpam-5993	150	9	713	713	NUM
ejpam-5993	150	10	,	,	PUNCT
ejpam-5993	150	11	satz	satz	PROPN
ejpam-5993	150	12	8.6	8.6	NUM
ejpam-5993	150	13	]	]	PUNCT
ejpam-5993	150	14	,	,	PUNCT
ejpam-5993	150	15	g	g	PROPN
ejpam-5993	150	16	is	be	AUX
ejpam-5993	150	17	supersolvable	supersolvable	ADJ
ejpam-5993	150	18	,	,	PUNCT
ejpam-5993	150	19	a211	a211	PROPN
ejpam-5993	150	20	contradiction.212	contradiction.212	VERB
ejpam-5993	150	21	213	213	NUM
ejpam-5993	150	22	case	case	NOUN
ejpam-5993	150	23	2	2	NUM
ejpam-5993	150	24	:	:	PUNCT
ejpam-5993	150	25	φ(g	φ(g	ADJ
ejpam-5993	150	26	)	)	PUNCT
ejpam-5993	150	27	∩h	∩h	NOUN
ejpam-5993	150	28	=	=	PUNCT
ejpam-5993	151	1	1214	1214	NUM
ejpam-5993	151	2	215	215	NUM
ejpam-5993	151	3	ifh	ifh	ADJ
ejpam-5993	151	4	=	=	SYM
ejpam-5993	151	5	1	1	NUM
ejpam-5993	151	6	,	,	PUNCT
ejpam-5993	151	7	nothing	nothing	PRON
ejpam-5993	151	8	need	need	VERB
ejpam-5993	151	9	to	to	PART
ejpam-5993	151	10	prove	prove	VERB
ejpam-5993	151	11	.	.	PUNCT
ejpam-5993	152	1	so	so	ADV
ejpam-5993	152	2	,	,	PUNCT
ejpam-5993	152	3	assume	assume	VERB
ejpam-5993	152	4	thath	thath	VERB
ejpam-5993	152	5	̸=	̸=	PROPN
ejpam-5993	152	6	1	1	NUM
ejpam-5993	152	7	.	.	PUNCT
ejpam-5993	153	1	by	by	ADP
ejpam-5993	153	2	lemma	lemma	PROPN
ejpam-5993	153	3	3	3	NUM
ejpam-5993	153	4	,	,	PUNCT
ejpam-5993	153	5	f	f	PROPN
ejpam-5993	153	6	(	(	PUNCT
ejpam-5993	153	7	h	h	NOUN
ejpam-5993	153	8	)	)	PUNCT
ejpam-5993	153	9	is	be	AUX
ejpam-5993	153	10	a	a	DET
ejpam-5993	153	11	direct216	direct216	PROPN
ejpam-5993	153	12	product	product	NOUN
ejpam-5993	153	13	of	of	ADP
ejpam-5993	153	14	minimal	minimal	ADJ
ejpam-5993	153	15	normal	normal	ADJ
ejpam-5993	153	16	subgroups	subgroup	NOUN
ejpam-5993	153	17	of	of	ADP
ejpam-5993	153	18	g	g	NOUN
ejpam-5993	153	19	which	which	PRON
ejpam-5993	153	20	are	be	AUX
ejpam-5993	153	21	contained	contain	VERB
ejpam-5993	153	22	in	in	ADP
ejpam-5993	153	23	f	f	PROPN
ejpam-5993	153	24	(	(	PUNCT
ejpam-5993	153	25	h	h	NOUN
ejpam-5993	153	26	)	)	PUNCT
ejpam-5993	153	27	.	.	PUNCT
ejpam-5993	154	1	let	let	VERB
ejpam-5993	154	2	p	p	PRON
ejpam-5993	154	3	be	be	AUX
ejpam-5993	154	4	a	a	DET
ejpam-5993	154	5	non-217	non-217	ADJ
ejpam-5993	154	6	cyclic	cyclic	ADJ
ejpam-5993	154	7	sylow	sylow	NOUN
ejpam-5993	154	8	p	p	PROPN
ejpam-5993	154	9	-	-	PUNCT
ejpam-5993	154	10	subgroup	subgroup	NOUN
ejpam-5993	154	11	of	of	ADP
ejpam-5993	154	12	f	f	PROPN
ejpam-5993	154	13	(	(	PUNCT
ejpam-5993	154	14	h	h	NOUN
ejpam-5993	154	15	)	)	PUNCT
ejpam-5993	154	16	.	.	PUNCT
ejpam-5993	155	1	then	then	ADV
ejpam-5993	155	2	p	p	X
ejpam-5993	155	3	=	=	PUNCT
ejpam-5993	155	4	r1×r2×r3×	r1×r2×r3×	PROPN
ejpam-5993	155	5	·	·	PUNCT
ejpam-5993	155	6	·	·	PUNCT
ejpam-5993	155	7	·	·	PUNCT
ejpam-5993	155	8	×rt	×rt	ADJ
ejpam-5993	155	9	,	,	PUNCT
ejpam-5993	155	10	where	where	SCONJ
ejpam-5993	155	11	ri(i	ri(i	PUNCT
ejpam-5993	155	12	=	=	SYM
ejpam-5993	155	13	1	1	NUM
ejpam-5993	155	14	,	,	PUNCT
ejpam-5993	155	15	.	.	PUNCT
ejpam-5993	155	16	.	.	PUNCT
ejpam-5993	155	17	.	.	PUNCT
ejpam-5993	156	1	,	,	PUNCT
ejpam-5993	156	2	t)218	t)218	PROPN
ejpam-5993	156	3	is	be	AUX
ejpam-5993	156	4	a	a	DET
ejpam-5993	156	5	minimal	minimal	ADJ
ejpam-5993	156	6	normal	normal	ADJ
ejpam-5993	156	7	subgroup	subgroup	NOUN
ejpam-5993	156	8	of	of	ADP
ejpam-5993	156	9	g.	g.	PROPN
ejpam-5993	156	10	then	then	ADV
ejpam-5993	156	11	there	there	PRON
ejpam-5993	156	12	exists	exist	VERB
ejpam-5993	156	13	a	a	DET
ejpam-5993	156	14	maximal	maximal	ADJ
ejpam-5993	156	15	subgroup	subgroup	NOUN
ejpam-5993	156	16	p1	p1	NOUN
ejpam-5993	156	17	of	of	ADP
ejpam-5993	156	18	p	p	PROPN
ejpam-5993	156	19	,	,	PUNCT
ejpam-5993	156	20	and219	and219	NOUN
ejpam-5993	156	21	by	by	ADP
ejpam-5993	156	22	hypothesis	hypothesis	NOUN
ejpam-5993	156	23	,	,	PUNCT
ejpam-5993	156	24	p1	p1	PROPN
ejpam-5993	156	25	is	be	AUX
ejpam-5993	156	26	an	an	DET
ejpam-5993	156	27	ssh	ssh	NOUN
ejpam-5993	156	28	-	-	PUNCT
ejpam-5993	156	29	subgroup	subgroup	NOUN
ejpam-5993	156	30	in	in	ADP
ejpam-5993	156	31	g.	g.	PROPN
ejpam-5993	156	32	then	then	ADV
ejpam-5993	156	33	there	there	PRON
ejpam-5993	156	34	exists	exist	VERB
ejpam-5993	156	35	an	an	DET
ejpam-5993	156	36	s	s	NOUN
ejpam-5993	156	37	-	-	ADJ
ejpam-5993	156	38	permutable	permutable	ADJ
ejpam-5993	156	39	subgroup220	subgroup220	PROPN
ejpam-5993	156	40	k	k	NOUN
ejpam-5993	156	41	of	of	ADP
ejpam-5993	156	42	g	g	PROPN
ejpam-5993	156	43	such	such	ADJ
ejpam-5993	156	44	that	that	SCONJ
ejpam-5993	156	45	(	(	PUNCT
ejpam-5993	156	46	p1	p1	NOUN
ejpam-5993	156	47	)	)	PUNCT
ejpam-5993	156	48	sg	sg	PROPN
ejpam-5993	157	1	=	=	SYM
ejpam-5993	157	2	p1k	p1k	PROPN
ejpam-5993	157	3	and	and	CCONJ
ejpam-5993	157	4	(	(	PUNCT
ejpam-5993	157	5	p1	p1	PROPN
ejpam-5993	157	6	)	)	PUNCT
ejpam-5993	157	7	g	g	ADP
ejpam-5993	157	8	∩nk(p1	∩nk(p1	PROPN
ejpam-5993	157	9	)	)	PUNCT
ejpam-5993	157	10	⩽	⩽	PROPN
ejpam-5993	157	11	p1	p1	PROPN
ejpam-5993	157	12	,	,	PUNCT
ejpam-5993	157	13	for	for	ADP
ejpam-5993	157	14	all	all	DET
ejpam-5993	157	15	g	g	PROPN
ejpam-5993	157	16	∈	∈	PROPN
ejpam-5993	157	17	g.	g.	NOUN
ejpam-5993	157	18	assuming	assume	VERB
ejpam-5993	157	19	that221	that221	PROPN
ejpam-5993	157	20	k	k	NOUN
ejpam-5993	157	21	=	=	PUNCT
ejpam-5993	157	22	p	p	X
ejpam-5993	157	23	,	,	PUNCT
ejpam-5993	157	24	then	then	ADV
ejpam-5993	157	25	we	we	PRON
ejpam-5993	157	26	have	have	VERB
ejpam-5993	157	27	(	(	PUNCT
ejpam-5993	157	28	p1	p1	NOUN
ejpam-5993	157	29	)	)	PUNCT
ejpam-5993	157	30	g∩ng(p1	g∩ng(p1	NOUN
ejpam-5993	157	31	)	)	PUNCT
ejpam-5993	158	1	=	=	PUNCT
ejpam-5993	158	2	(	(	PUNCT
ejpam-5993	158	3	p1	p1	NOUN
ejpam-5993	158	4	)	)	PUNCT
ejpam-5993	158	5	g∩k∩ng(p1	g∩k∩ng(p1	NOUN
ejpam-5993	158	6	)	)	PUNCT
ejpam-5993	158	7	=	=	SYM
ejpam-5993	158	8	(	(	PUNCT
ejpam-5993	158	9	p1	p1	PROPN
ejpam-5993	158	10	)	)	PUNCT
ejpam-5993	158	11	g∩nk(p1	g∩nk(p1	PROPN
ejpam-5993	158	12	)	)	PUNCT
ejpam-5993	158	13	⩽	⩽	PROPN
ejpam-5993	158	14	p1	p1	PROPN
ejpam-5993	158	15	.	.	PUNCT
ejpam-5993	159	1	then222	then222	PROPN
ejpam-5993	159	2	we	we	PRON
ejpam-5993	159	3	get	get	VERB
ejpam-5993	159	4	p1	p1	PROPN
ejpam-5993	159	5	is	be	AUX
ejpam-5993	159	6	an	an	DET
ejpam-5993	159	7	h	h	NOUN
ejpam-5993	159	8	-	-	PUNCT
ejpam-5993	159	9	subgroup	subgroup	NOUN
ejpam-5993	159	10	in	in	ADP
ejpam-5993	159	11	g	g	PROPN
ejpam-5993	159	12	and	and	CCONJ
ejpam-5993	159	13	p1	p1	PROPN
ejpam-5993	159	14	⊴	⊴	ADP
ejpam-5993	159	15	p	p	X
ejpam-5993	159	16	.	.	PUNCT
ejpam-5993	160	1	applying	apply	VERB
ejpam-5993	160	2	lemma	lemma	PROPN
ejpam-5993	160	3	4	4	NUM
ejpam-5993	160	4	,	,	PUNCT
ejpam-5993	160	5	we	we	PRON
ejpam-5993	160	6	get	get	VERB
ejpam-5993	160	7	p1	p1	PROPN
ejpam-5993	160	8	⊴	⊴	ADP
ejpam-5993	160	9	g.	g.	PROPN
ejpam-5993	160	10	let223	let223	PROPN
ejpam-5993	160	11	q	q	PROPN
ejpam-5993	160	12	be	be	AUX
ejpam-5993	160	13	a	a	DET
ejpam-5993	160	14	non	non	ADJ
ejpam-5993	160	15	-	-	ADJ
ejpam-5993	160	16	cyclic	cyclic	ADJ
ejpam-5993	160	17	sylow	sylow	NOUN
ejpam-5993	160	18	q	q	NOUN
ejpam-5993	160	19	-	-	NOUN
ejpam-5993	160	20	subgroup	subgroup	NOUN
ejpam-5993	160	21	of	of	ADP
ejpam-5993	160	22	f	f	PROPN
ejpam-5993	160	23	(	(	PUNCT
ejpam-5993	160	24	h	h	NOUN
ejpam-5993	160	25	)	)	PUNCT
ejpam-5993	160	26	such	such	ADJ
ejpam-5993	160	27	that	that	SCONJ
ejpam-5993	160	28	(	(	PUNCT
ejpam-5993	160	29	p	p	X
ejpam-5993	160	30	,	,	PUNCT
ejpam-5993	160	31	|q|	|q|	NUM
ejpam-5993	160	32	)	)	PUNCT
ejpam-5993	160	33	=	=	SYM
ejpam-5993	160	34	1	1	X
ejpam-5993	160	35	.	.	PUNCT
ejpam-5993	161	1	now	now	ADV
ejpam-5993	161	2	,	,	PUNCT
ejpam-5993	161	3	p1q	p1q	PROPN
ejpam-5993	161	4	⩽	⩽	NOUN
ejpam-5993	161	5	g	g	PROPN
ejpam-5993	161	6	and224	and224	PROPN
ejpam-5993	161	7	since	since	SCONJ
ejpam-5993	161	8	p1	p1	PROPN
ejpam-5993	161	9	is	be	AUX
ejpam-5993	161	10	a	a	DET
ejpam-5993	161	11	normal	normal	ADJ
ejpam-5993	161	12	hall	hall	NOUN
ejpam-5993	161	13	subgroup	subgroup	NOUN
ejpam-5993	161	14	of	of	ADP
ejpam-5993	161	15	p1q	p1q	PROPN
ejpam-5993	161	16	,	,	PUNCT
ejpam-5993	161	17	it	it	PRON
ejpam-5993	161	18	follows	follow	VERB
ejpam-5993	161	19	that	that	SCONJ
ejpam-5993	161	20	p1	p1	PROPN
ejpam-5993	161	21	is	be	AUX
ejpam-5993	161	22	a	a	DET
ejpam-5993	161	23	characteristic	characteristic	ADJ
ejpam-5993	161	24	subgroup225	subgroup225	PROPN
ejpam-5993	161	25	of	of	ADP
ejpam-5993	161	26	p1q	p1q	PROPN
ejpam-5993	161	27	.	.	PUNCT
ejpam-5993	162	1	in	in	ADP
ejpam-5993	162	2	particular	particular	ADJ
ejpam-5993	162	3	,	,	PUNCT
ejpam-5993	162	4	p1	p1	PROPN
ejpam-5993	162	5	is	be	AUX
ejpam-5993	162	6	a	a	DET
ejpam-5993	162	7	normal	normal	ADJ
ejpam-5993	162	8	subgroup	subgroup	NOUN
ejpam-5993	162	9	of	of	ADP
ejpam-5993	162	10	p1q	p1q	PROPN
ejpam-5993	162	11	.	.	PUNCT
ejpam-5993	163	1	hence	hence	ADV
ejpam-5993	163	2	q	q	PROPN
ejpam-5993	163	3	⩽	⩽	PROPN
ejpam-5993	163	4	ng(p1	ng(p1	PROPN
ejpam-5993	163	5	)	)	PUNCT
ejpam-5993	163	6	for	for	ADP
ejpam-5993	163	7	all	all	DET
ejpam-5993	163	8	sylow226	sylow226	PROPN
ejpam-5993	163	9	q	q	ADJ
ejpam-5993	163	10	-	-	PUNCT
ejpam-5993	163	11	subgroup	subgroup	NOUN
ejpam-5993	163	12	q	q	NOUN
ejpam-5993	163	13	of	of	ADP
ejpam-5993	163	14	f	f	PROPN
ejpam-5993	163	15	(	(	PUNCT
ejpam-5993	163	16	h	h	NOUN
ejpam-5993	163	17	)	)	PUNCT
ejpam-5993	163	18	,	,	PUNCT
ejpam-5993	164	1	where	where	SCONJ
ejpam-5993	164	2	(	(	PUNCT
ejpam-5993	164	3	p	p	X
ejpam-5993	164	4	,	,	PUNCT
ejpam-5993	164	5	|q|	|q|	NUM
ejpam-5993	164	6	)	)	PUNCT
ejpam-5993	164	7	=	=	SYM
ejpam-5993	164	8	1	1	X
ejpam-5993	164	9	.	.	PUNCT
ejpam-5993	164	10	since	since	SCONJ
ejpam-5993	164	11	p1	p1	PROPN
ejpam-5993	164	12	is	be	AUX
ejpam-5993	164	13	a	a	DET
ejpam-5993	164	14	normal	normal	ADJ
ejpam-5993	164	15	subgroup	subgroup	NOUN
ejpam-5993	164	16	of	of	ADP
ejpam-5993	164	17	p	p	PROPN
ejpam-5993	164	18	and	and	CCONJ
ejpam-5993	164	19	p1	p1	PROPN
ejpam-5993	164	20	is	be	AUX
ejpam-5993	164	21	a227	a227	PROPN
ejpam-5993	164	22	normal	normal	ADJ
ejpam-5993	164	23	subgroup	subgroup	NOUN
ejpam-5993	164	24	of	of	ADP
ejpam-5993	164	25	p1q	p1q	PROPN
ejpam-5993	164	26	,	,	PUNCT
ejpam-5993	164	27	we	we	PRON
ejpam-5993	164	28	get	get	VERB
ejpam-5993	164	29	p1	p1	PROPN
ejpam-5993	164	30	is	be	AUX
ejpam-5993	164	31	a	a	DET
ejpam-5993	164	32	normal	normal	ADJ
ejpam-5993	164	33	subgroup	subgroup	NOUN
ejpam-5993	164	34	of	of	ADP
ejpam-5993	164	35	pq	pq	PROPN
ejpam-5993	164	36	.	.	PUNCT
ejpam-5993	165	1	thus	thus	ADV
ejpam-5993	165	2	we	we	PRON
ejpam-5993	165	3	have	have	VERB
ejpam-5993	165	4	that	that	DET
ejpam-5993	165	5	every228	every228	PROPN
ejpam-5993	165	6	maximal	maximal	ADJ
ejpam-5993	165	7	subgroup	subgroup	NOUN
ejpam-5993	165	8	of	of	ADP
ejpam-5993	165	9	p	p	PROPN
ejpam-5993	165	10	is	be	AUX
ejpam-5993	165	11	a	a	DET
ejpam-5993	165	12	normal	normal	ADJ
ejpam-5993	165	13	subgroup	subgroup	NOUN
ejpam-5993	165	14	of	of	ADP
ejpam-5993	165	15	pq	pq	PROPN
ejpam-5993	165	16	.	.	PUNCT
ejpam-5993	166	1	since	since	SCONJ
ejpam-5993	166	2	p	p	NOUN
ejpam-5993	166	3	is	be	AUX
ejpam-5993	166	4	an	an	DET
ejpam-5993	166	5	elementary	elementary	ADJ
ejpam-5993	166	6	abelian229	abelian229	PROPN
ejpam-5993	166	7	p	p	PROPN
ejpam-5993	166	8	-	-	PUNCT
ejpam-5993	166	9	group	group	NOUN
ejpam-5993	166	10	and	and	CCONJ
ejpam-5993	166	11	p	p	NOUN
ejpam-5993	166	12	is	be	AUX
ejpam-5993	166	13	a	a	DET
ejpam-5993	166	14	non	non	ADJ
ejpam-5993	166	15	-	-	ADJ
ejpam-5993	166	16	cyclic	cyclic	ADJ
ejpam-5993	166	17	sylow	sylow	NOUN
ejpam-5993	166	18	p	p	NOUN
ejpam-5993	166	19	-	-	PUNCT
ejpam-5993	166	20	subgroup	subgroup	NOUN
ejpam-5993	166	21	,	,	PUNCT
ejpam-5993	166	22	so	so	CCONJ
ejpam-5993	166	23	every	every	DET
ejpam-5993	166	24	subgroup	subgroup	NOUN
ejpam-5993	166	25	of	of	ADP
ejpam-5993	166	26	order	order	NOUN
ejpam-5993	166	27	p	p	NOUN
ejpam-5993	166	28	is	be	AUX
ejpam-5993	166	29	a	a	DET
ejpam-5993	166	30	normal230	normal230	PROPN
ejpam-5993	166	31	subgroup	subgroup	NOUN
ejpam-5993	166	32	in	in	ADP
ejpam-5993	166	33	pq	pq	PROPN
ejpam-5993	166	34	,	,	PUNCT
ejpam-5993	166	35	where	where	SCONJ
ejpam-5993	166	36	(	(	PUNCT
ejpam-5993	166	37	p	p	X
ejpam-5993	166	38	,	,	PUNCT
ejpam-5993	166	39	|q|	|q|	NUM
ejpam-5993	166	40	)	)	PUNCT
ejpam-5993	166	41	=	=	SYM
ejpam-5993	166	42	1	1	NUM
ejpam-5993	166	43	,	,	PUNCT
ejpam-5993	166	44	by	by	ADP
ejpam-5993	166	45	lemma	lemma	PROPN
ejpam-5993	166	46	7(i	7(i	NUM
ejpam-5993	166	47	)	)	PUNCT
ejpam-5993	166	48	.	.	PUNCT
ejpam-5993	167	1	on	on	ADP
ejpam-5993	167	2	the	the	DET
ejpam-5993	167	3	other	other	ADJ
ejpam-5993	167	4	hand	hand	NOUN
ejpam-5993	167	5	,	,	PUNCT
ejpam-5993	167	6	we	we	PRON
ejpam-5993	167	7	know	know	VERB
ejpam-5993	167	8	that231	that231	PROPN
ejpam-5993	167	9	ri	ri	PROPN
ejpam-5993	167	10	∩	∩	NOUN
ejpam-5993	167	11	z(p	z(p	NOUN
ejpam-5993	167	12	)	)	PUNCT
ejpam-5993	167	13	̸=	̸=	PROPN
ejpam-5993	167	14	1	1	NUM
ejpam-5993	167	15	,	,	PUNCT
ejpam-5993	167	16	where	where	SCONJ
ejpam-5993	167	17	(	(	PUNCT
ejpam-5993	167	18	i	i	NOUN
ejpam-5993	167	19	=	=	NOUN
ejpam-5993	167	20	1	1	NUM
ejpam-5993	167	21	,	,	PUNCT
ejpam-5993	167	22	...	...	PUNCT
ejpam-5993	167	23	,	,	PUNCT
ejpam-5993	167	24	t	t	PROPN
ejpam-5993	167	25	)	)	PUNCT
ejpam-5993	167	26	.	.	PUNCT
ejpam-5993	168	1	let	let	VERB
ejpam-5993	168	2	li	li	PROPN
ejpam-5993	168	3	be	be	AUX
ejpam-5993	168	4	subgroup	subgroup	NOUN
ejpam-5993	168	5	of	of	ADP
ejpam-5993	168	6	ri	ri	NOUN
ejpam-5993	168	7	∩	∩	NOUN
ejpam-5993	168	8	z(p	z(p	NUM
ejpam-5993	168	9	)	)	PUNCT
ejpam-5993	168	10	of	of	ADP
ejpam-5993	168	11	order	order	NOUN
ejpam-5993	168	12	p	p	X
ejpam-5993	168	13	,	,	PUNCT
ejpam-5993	168	14	where232	where232	PROPN
ejpam-5993	168	15	(	(	PUNCT
ejpam-5993	168	16	i	i	NOUN
ejpam-5993	168	17	=	=	NOUN
ejpam-5993	168	18	1	1	NUM
ejpam-5993	168	19	,	,	PUNCT
ejpam-5993	168	20	...	...	PUNCT
ejpam-5993	168	21	,	,	PUNCT
ejpam-5993	168	22	t	t	PROPN
ejpam-5993	168	23	)	)	PUNCT
ejpam-5993	168	24	.	.	PUNCT
ejpam-5993	169	1	then	then	ADV
ejpam-5993	169	2	li	li	PROPN
ejpam-5993	169	3	is	be	AUX
ejpam-5993	169	4	normal	normal	ADJ
ejpam-5993	169	5	in	in	ADP
ejpam-5993	169	6	p	p	NOUN
ejpam-5993	170	1	and	and	CCONJ
ejpam-5993	170	2	we	we	PRON
ejpam-5993	170	3	have	have	VERB
ejpam-5993	170	4	li	li	PROPN
ejpam-5993	170	5	is	be	AUX
ejpam-5993	170	6	subnormal	subnormal	ADJ
ejpam-5993	170	7	in	in	ADP
ejpam-5993	170	8	g.	g.	PROPN
ejpam-5993	171	1	now	now	ADV
ejpam-5993	171	2	,	,	PUNCT
ejpam-5993	171	3	if	if	SCONJ
ejpam-5993	171	4	li	li	PROPN
ejpam-5993	171	5	=	=	SYM
ejpam-5993	171	6	p1,233	p1,233	PROPN
ejpam-5993	171	7	then	then	ADV
ejpam-5993	171	8	li	li	PROPN
ejpam-5993	171	9	is	be	AUX
ejpam-5993	171	10	normal	normal	ADJ
ejpam-5993	171	11	in	in	ADP
ejpam-5993	171	12	g.	g.	PROPN
ejpam-5993	171	13	also	also	ADV
ejpam-5993	171	14	,	,	PUNCT
ejpam-5993	171	15	if	if	SCONJ
ejpam-5993	171	16	li	li	PROPN
ejpam-5993	171	17	is	be	AUX
ejpam-5993	171	18	a	a	DET
ejpam-5993	171	19	proper	proper	ADJ
ejpam-5993	171	20	subgroup	subgroup	NOUN
ejpam-5993	171	21	of	of	ADP
ejpam-5993	171	22	p1	p1	PROPN
ejpam-5993	171	23	,	,	PUNCT
ejpam-5993	171	24	then	then	ADV
ejpam-5993	171	25	li	li	PROPN
ejpam-5993	171	26	is	be	AUX
ejpam-5993	171	27	an	an	DET
ejpam-5993	171	28	h	h	NOUN
ejpam-5993	171	29	-	-	PUNCT
ejpam-5993	171	30	subgroup234	subgroup234	PROPN
ejpam-5993	171	31	in	in	ADP
ejpam-5993	171	32	g.	g.	NOUN
ejpam-5993	171	33	applying	apply	VERB
ejpam-5993	171	34	lemma	lemma	PROPN
ejpam-5993	171	35	4	4	NUM
ejpam-5993	171	36	,	,	PUNCT
ejpam-5993	171	37	we	we	PRON
ejpam-5993	171	38	get	get	VERB
ejpam-5993	171	39	li	li	PROPN
ejpam-5993	171	40	⊴	⊴	PROPN
ejpam-5993	171	41	g.	g.	PROPN
ejpam-5993	171	42	since	since	SCONJ
ejpam-5993	171	43	ri	ri	PROPN
ejpam-5993	171	44	is	be	AUX
ejpam-5993	171	45	a	a	DET
ejpam-5993	171	46	minimal	minimal	ADJ
ejpam-5993	171	47	normal	normal	ADJ
ejpam-5993	171	48	subgroup	subgroup	NOUN
ejpam-5993	171	49	of	of	ADP
ejpam-5993	171	50	g,235	g,235	NUM
ejpam-5993	171	51	it	it	PRON
ejpam-5993	171	52	follows	follow	VERB
ejpam-5993	171	53	that	that	SCONJ
ejpam-5993	171	54	li	li	PROPN
ejpam-5993	171	55	=	=	PUNCT
ejpam-5993	171	56	ri	ri	PROPN
ejpam-5993	171	57	is	be	AUX
ejpam-5993	171	58	a	a	DET
ejpam-5993	171	59	cyclic	cyclic	ADJ
ejpam-5993	171	60	group	group	NOUN
ejpam-5993	171	61	of	of	ADP
ejpam-5993	171	62	order	order	NOUN
ejpam-5993	171	63	p	p	X
ejpam-5993	171	64	,	,	PUNCT
ejpam-5993	171	65	for	for	ADP
ejpam-5993	171	66	any	any	DET
ejpam-5993	171	67	i.	i.	NOUN
ejpam-5993	171	68	therefore	therefore	ADV
ejpam-5993	171	69	,	,	PUNCT
ejpam-5993	171	70	we	we	PRON
ejpam-5993	171	71	can	can	AUX
ejpam-5993	171	72	write236	write236	PROPN
ejpam-5993	171	73	f	f	PROPN
ejpam-5993	171	74	(	(	PUNCT
ejpam-5993	171	75	h	h	NOUN
ejpam-5993	171	76	)	)	PUNCT
ejpam-5993	171	77	=	=	SYM
ejpam-5993	171	78	r1×r2×r3×	r1×r2×r3×	PROPN
ejpam-5993	171	79	·	·	PUNCT
ejpam-5993	171	80	·	·	PUNCT
ejpam-5993	171	81	·	·	PUNCT
ejpam-5993	171	82	×rm	×rm	ADJ
ejpam-5993	171	83	,	,	PUNCT
ejpam-5993	171	84	where	where	SCONJ
ejpam-5993	171	85	ri(i	ri(i	PUNCT
ejpam-5993	171	86	=	=	SYM
ejpam-5993	171	87	1	1	NUM
ejpam-5993	171	88	,	,	PUNCT
ejpam-5993	171	89	.	.	PUNCT
ejpam-5993	171	90	.	.	PUNCT
ejpam-5993	171	91	.	.	PUNCT
ejpam-5993	172	1	,	,	PUNCT
ejpam-5993	172	2	m	m	PROPN
ejpam-5993	172	3	)	)	PUNCT
ejpam-5993	172	4	is	be	AUX
ejpam-5993	172	5	a	a	DET
ejpam-5993	172	6	normal	normal	ADJ
ejpam-5993	172	7	subgroup	subgroup	NOUN
ejpam-5993	172	8	of	of	ADP
ejpam-5993	172	9	g	g	PROPN
ejpam-5993	172	10	of	of	ADP
ejpam-5993	172	11	prime237	prime237	PROPN
ejpam-5993	172	12	order	order	NOUN
ejpam-5993	172	13	.	.	PUNCT
ejpam-5993	173	1	we	we	PRON
ejpam-5993	173	2	have	have	VERB
ejpam-5993	173	3	g	g	NOUN
ejpam-5993	173	4	/	/	SYM
ejpam-5993	173	5	cg(ri	cg(ri	ADJ
ejpam-5993	173	6	)	)	PUNCT
ejpam-5993	173	7	is	be	AUX
ejpam-5993	173	8	isomorphic	isomorphic	ADJ
ejpam-5993	173	9	to	to	ADP
ejpam-5993	173	10	a	a	DET
ejpam-5993	173	11	subgroup	subgroup	NOUN
ejpam-5993	173	12	of	of	ADP
ejpam-5993	173	13	aut(ri	aut(ri	NOUN
ejpam-5993	173	14	)	)	PUNCT
ejpam-5993	173	15	,	,	PUNCT
ejpam-5993	173	16	g	g	NOUN
ejpam-5993	173	17	/	/	SYM
ejpam-5993	173	18	cg(ri	cg(ri	ADJ
ejpam-5993	173	19	)	)	PUNCT
ejpam-5993	173	20	is	be	AUX
ejpam-5993	173	21	cyclic	cyclic	ADJ
ejpam-5993	173	22	,	,	PUNCT
ejpam-5993	173	23	in238	in238	NOUN
ejpam-5993	173	24	particular	particular	ADJ
ejpam-5993	173	25	g	g	NOUN
ejpam-5993	173	26	/	/	SYM
ejpam-5993	173	27	cg(ri	cg(ri	ADJ
ejpam-5993	173	28	)	)	PUNCT
ejpam-5993	173	29	is	be	AUX
ejpam-5993	173	30	supersolvable	supersolvable	ADJ
ejpam-5993	173	31	.	.	PUNCT
ejpam-5993	174	1	hence	hence	ADV
ejpam-5993	174	2	,	,	PUNCT
ejpam-5993	174	3	g/∩m	g/∩m	PROPN
ejpam-5993	174	4	i=1cg(ri	i=1cg(ri	NOUN
ejpam-5993	174	5	)	)	PUNCT
ejpam-5993	174	6	is	be	AUX
ejpam-5993	174	7	supersolvable	supersolvable	ADJ
ejpam-5993	174	8	.	.	PUNCT
ejpam-5993	175	1	notice	notice	VERB
ejpam-5993	175	2	that239	that239	NUM
ejpam-5993	175	3	cg(f	cg(f	NUM
ejpam-5993	175	4	(	(	PUNCT
ejpam-5993	175	5	h	h	NOUN
ejpam-5993	175	6	)	)	PUNCT
ejpam-5993	175	7	)	)	PUNCT
ejpam-5993	176	1	=	=	SYM
ejpam-5993	177	1	∩m	∩m	PROPN
ejpam-5993	177	2	i=1cg(ri	i=1cg(ri	NOUN
ejpam-5993	177	3	)	)	PUNCT
ejpam-5993	177	4	,	,	PUNCT
ejpam-5993	177	5	so	so	ADV
ejpam-5993	177	6	g	g	PROPN
ejpam-5993	177	7	/	/	SYM
ejpam-5993	177	8	cg(f	cg(f	NOUN
ejpam-5993	177	9	(	(	PUNCT
ejpam-5993	177	10	h	h	NOUN
ejpam-5993	177	11	)	)	PUNCT
ejpam-5993	177	12	)	)	PUNCT
ejpam-5993	177	13	is	be	AUX
ejpam-5993	177	14	supersolvable	supersolvable	ADJ
ejpam-5993	177	15	.	.	PUNCT
ejpam-5993	178	1	the	the	DET
ejpam-5993	178	2	supersolvability	supersolvability	NOUN
ejpam-5993	178	3	of	of	ADP
ejpam-5993	178	4	g	g	PROPN
ejpam-5993	178	5	/	/	SYM
ejpam-5993	178	6	h240	h240	PROPN
ejpam-5993	178	7	and	and	CCONJ
ejpam-5993	178	8	g	g	NOUN
ejpam-5993	178	9	/	/	SYM
ejpam-5993	178	10	cg(f	cg(f	NUM
ejpam-5993	178	11	(	(	PUNCT
ejpam-5993	178	12	h	h	NOUN
ejpam-5993	178	13	)	)	PUNCT
ejpam-5993	178	14	)	)	PUNCT
ejpam-5993	178	15	implies	imply	VERB
ejpam-5993	178	16	that	that	SCONJ
ejpam-5993	178	17	g/(h	g/(h	PRON
ejpam-5993	178	18	∩cg(f	∩cg(f	NOUN
ejpam-5993	178	19	(	(	PUNCT
ejpam-5993	178	20	h	h	NOUN
ejpam-5993	178	21	)	)	PUNCT
ejpam-5993	178	22	)	)	PUNCT
ejpam-5993	179	1	=	=	PUNCT
ejpam-5993	179	2	g	g	NOUN
ejpam-5993	179	3	/	/	SYM
ejpam-5993	179	4	ch(f	ch(f	NUM
ejpam-5993	179	5	(	(	PUNCT
ejpam-5993	179	6	h	h	NOUN
ejpam-5993	179	7	)	)	PUNCT
ejpam-5993	179	8	)	)	PUNCT
ejpam-5993	179	9	is	be	AUX
ejpam-5993	179	10	supersolvable	supersolvable	ADJ
ejpam-5993	179	11	.	.	PUNCT
ejpam-5993	180	1	since241	since241	PROPN
ejpam-5993	180	2	h	h	PROPN
ejpam-5993	180	3	is	be	AUX
ejpam-5993	180	4	solvable	solvable	ADJ
ejpam-5993	180	5	,	,	PUNCT
ejpam-5993	180	6	ch(f	ch(f	ADP
ejpam-5993	180	7	(	(	PUNCT
ejpam-5993	180	8	h	h	NOUN
ejpam-5993	180	9	)	)	PUNCT
ejpam-5993	180	10	)	)	PUNCT
ejpam-5993	181	1	⩽	⩽	PROPN
ejpam-5993	181	2	f	f	PROPN
ejpam-5993	181	3	(	(	PUNCT
ejpam-5993	181	4	h	h	NOUN
ejpam-5993	181	5	)	)	PUNCT
ejpam-5993	181	6	.	.	PUNCT
ejpam-5993	182	1	moreover	moreover	ADV
ejpam-5993	182	2	,	,	PUNCT
ejpam-5993	182	3	f	f	PROPN
ejpam-5993	182	4	(	(	PUNCT
ejpam-5993	182	5	h	h	NOUN
ejpam-5993	182	6	)	)	PUNCT
ejpam-5993	182	7	⩽	⩽	NOUN
ejpam-5993	182	8	ch(f	ch(f	ADP
ejpam-5993	182	9	(	(	PUNCT
ejpam-5993	182	10	h	h	NOUN
ejpam-5993	182	11	)	)	PUNCT
ejpam-5993	182	12	)	)	PUNCT
ejpam-5993	183	1	as	as	SCONJ
ejpam-5993	183	2	f	f	PROPN
ejpam-5993	183	3	(	(	PUNCT
ejpam-5993	183	4	h	h	NOUN
ejpam-5993	183	5	)	)	PUNCT
ejpam-5993	183	6	is	be	AUX
ejpam-5993	183	7	abelian.242	abelian.242	NOUN
ejpam-5993	183	8	hence	hence	ADV
ejpam-5993	183	9	,	,	PUNCT
ejpam-5993	183	10	f	f	PROPN
ejpam-5993	183	11	(	(	PUNCT
ejpam-5993	183	12	h	h	NOUN
ejpam-5993	183	13	)	)	PUNCT
ejpam-5993	183	14	=	=	SYM
ejpam-5993	183	15	ch(f	ch(f	X
ejpam-5993	183	16	(	(	PUNCT
ejpam-5993	183	17	h	h	NOUN
ejpam-5993	183	18	)	)	PUNCT
ejpam-5993	183	19	)	)	PUNCT
ejpam-5993	183	20	,	,	PUNCT
ejpam-5993	183	21	and	and	CCONJ
ejpam-5993	183	22	so	so	ADV
ejpam-5993	183	23	g	g	PROPN
ejpam-5993	183	24	/	/	SYM
ejpam-5993	183	25	f	f	PROPN
ejpam-5993	183	26	(	(	PUNCT
ejpam-5993	183	27	h	h	NOUN
ejpam-5993	183	28	)	)	PUNCT
ejpam-5993	183	29	is	be	AUX
ejpam-5993	183	30	supersolvable	supersolvable	ADJ
ejpam-5993	183	31	.	.	PUNCT
ejpam-5993	184	1	then	then	ADV
ejpam-5993	184	2	there	there	PRON
ejpam-5993	184	3	exists	exist	VERB
ejpam-5993	184	4	a	a	DET
ejpam-5993	184	5	chief243	chief243	PROPN
ejpam-5993	184	6	series:244	series:244	NOUN
ejpam-5993	184	7	1̄	1̄	NUM
ejpam-5993	184	8	=	=	SYM
ejpam-5993	184	9	gm	gm	PROPN
ejpam-5993	184	10	/	/	SYM
ejpam-5993	184	11	f	f	PROPN
ejpam-5993	184	12	(	(	PUNCT
ejpam-5993	184	13	h	h	NOUN
ejpam-5993	184	14	)	)	PUNCT
ejpam-5993	184	15	⊴	⊴	ADP
ejpam-5993	184	16	gm−1	gm−1	PROPN
ejpam-5993	184	17	/	/	SYM
ejpam-5993	184	18	f	f	PROPN
ejpam-5993	184	19	(	(	PUNCT
ejpam-5993	184	20	h	h	NOUN
ejpam-5993	184	21	)	)	PUNCT
ejpam-5993	184	22	⊴	⊴	ADP
ejpam-5993	184	23	gm−2	gm−2	PROPN
ejpam-5993	184	24	/	/	SYM
ejpam-5993	184	25	f	f	PROPN
ejpam-5993	184	26	(	(	PUNCT
ejpam-5993	184	27	h	h	NOUN
ejpam-5993	184	28	)	)	PUNCT
ejpam-5993	184	29	⊴	⊴	ADP
ejpam-5993	184	30	·	·	PUNCT
ejpam-5993	184	31	·	·	PUNCT
ejpam-5993	184	32	·	·	PUNCT
ejpam-5993	185	1	⊴	⊴	ADP
ejpam-5993	185	2	g0	g0	PROPN
ejpam-5993	185	3	/	/	SYM
ejpam-5993	185	4	f	f	PROPN
ejpam-5993	185	5	(	(	PUNCT
ejpam-5993	185	6	h	h	NOUN
ejpam-5993	185	7	)	)	PUNCT
ejpam-5993	185	8	=	=	NOUN
ejpam-5993	185	9	g	g	PROPN
ejpam-5993	185	10	/	/	SYM
ejpam-5993	185	11	f	f	PROPN
ejpam-5993	185	12	(	(	PUNCT
ejpam-5993	185	13	h),245	h),245	NOUN
ejpam-5993	185	14	where	where	SCONJ
ejpam-5993	185	15	(	(	PUNCT
ejpam-5993	185	16	(	(	PUNCT
ejpam-5993	185	17	gi−1	gi−1	PROPN
ejpam-5993	185	18	/	/	SYM
ejpam-5993	185	19	f	f	PROPN
ejpam-5993	185	20	(	(	PUNCT
ejpam-5993	185	21	h)/(gi	h)/(gi	PROPN
ejpam-5993	185	22	/	/	SYM
ejpam-5993	185	23	f	f	PROPN
ejpam-5993	185	24	(	(	PUNCT
ejpam-5993	185	25	h))(1	h))(1	PROPN
ejpam-5993	185	26	⩽	⩽	ADJ
ejpam-5993	185	27	i	i	PRON
ejpam-5993	185	28	⩽	⩽	PROPN
ejpam-5993	185	29	m	m	VERB
ejpam-5993	185	30	)	)	PUNCT
ejpam-5993	185	31	are	be	AUX
ejpam-5993	185	32	cyclic	cyclic	ADJ
ejpam-5993	185	33	groups	group	NOUN
ejpam-5993	185	34	of	of	ADP
ejpam-5993	185	35	prime	prime	ADJ
ejpam-5993	185	36	order	order	NOUN
ejpam-5993	185	37	.	.	PUNCT
ejpam-5993	186	1	then246	then246	PROPN
ejpam-5993	187	1	f	f	PROPN
ejpam-5993	187	2	(	(	PUNCT
ejpam-5993	187	3	h	h	NOUN
ejpam-5993	187	4	)	)	PUNCT
ejpam-5993	187	5	=	=	SYM
ejpam-5993	187	6	gm	gm	PROPN
ejpam-5993	187	7	⊴	⊴	ADP
ejpam-5993	187	8	gm−1	gm−1	PROPN
ejpam-5993	187	9	⊴	⊴	ADP
ejpam-5993	187	10	gm−2	gm−2	NOUN
ejpam-5993	187	11	⊴	⊴	ADP
ejpam-5993	187	12	·	·	PUNCT
ejpam-5993	187	13	·	·	PUNCT
ejpam-5993	187	14	·	·	PUNCT
ejpam-5993	188	1	⊴	⊴	NUM
ejpam-5993	188	2	g0	g0	PROPN
ejpam-5993	188	3	=	=	SYM
ejpam-5993	188	4	g	g	PROPN
ejpam-5993	188	5	,	,	PUNCT
ejpam-5993	188	6	(	(	PUNCT
ejpam-5993	188	7	̇∗)247	̇∗)247	X
ejpam-5993	188	8	where	where	SCONJ
ejpam-5993	188	9	gi−1	gi−1	PROPN
ejpam-5993	188	10	/	/	SYM
ejpam-5993	188	11	gi	gi	NOUN
ejpam-5993	188	12	∼=	∼=	PROPN
ejpam-5993	188	13	(	(	PUNCT
ejpam-5993	188	14	(	(	PUNCT
ejpam-5993	188	15	gi−1	gi−1	PROPN
ejpam-5993	188	16	/	/	SYM
ejpam-5993	188	17	f	f	PROPN
ejpam-5993	188	18	(	(	PUNCT
ejpam-5993	188	19	h)/(gi	h)/(gi	PROPN
ejpam-5993	188	20	/	/	SYM
ejpam-5993	188	21	f	f	PROPN
ejpam-5993	188	22	(	(	PUNCT
ejpam-5993	188	23	h))(1	h))(1	PROPN
ejpam-5993	188	24	⩽	⩽	ADJ
ejpam-5993	188	25	i	i	PRON
ejpam-5993	188	26	⩽	⩽	PROPN
ejpam-5993	188	27	m	m	VERB
ejpam-5993	188	28	)	)	PUNCT
ejpam-5993	188	29	are	be	AUX
ejpam-5993	188	30	cyclic	cyclic	ADJ
ejpam-5993	188	31	groups	group	NOUN
ejpam-5993	188	32	of	of	ADP
ejpam-5993	188	33	prime	prime	ADJ
ejpam-5993	188	34	order248	order248	PROPN
ejpam-5993	188	35	and	and	CCONJ
ejpam-5993	188	36	gi	gi	VERB
ejpam-5993	188	37	⊴	⊴	PROPN
ejpam-5993	188	38	g.	g.	PROPN
ejpam-5993	188	39	also	also	ADV
ejpam-5993	188	40	,	,	PUNCT
ejpam-5993	188	41	we	we	PRON
ejpam-5993	188	42	have:249	have:249	VERB
ejpam-5993	188	43	a.	a.	PROPN
ejpam-5993	188	44	s.	s.	PROPN
ejpam-5993	188	45	allehyani	allehyani	PROPN
ejpam-5993	188	46	/	/	SYM
ejpam-5993	188	47	eur	eur	PROPN
ejpam-5993	188	48	.	.	PUNCT
ejpam-5993	189	1	j.	j.	PROPN
ejpam-5993	189	2	pure	pure	PROPN
ejpam-5993	189	3	appl	appl	PROPN
ejpam-5993	189	4	.	.	PROPN
ejpam-5993	189	5	math	math	PROPN
ejpam-5993	189	6	,	,	PUNCT
ejpam-5993	189	7	18	18	NUM
ejpam-5993	189	8	(	(	PUNCT
ejpam-5993	189	9	2	2	NUM
ejpam-5993	189	10	)	)	PUNCT
ejpam-5993	189	11	(	(	PUNCT
ejpam-5993	189	12	2025	2025	NUM
ejpam-5993	189	13	)	)	PUNCT
ejpam-5993	189	14	,	,	PUNCT
ejpam-5993	189	15	5993	5993	NUM
ejpam-5993	189	16	8	8	NUM
ejpam-5993	189	17	of	of	ADP
ejpam-5993	189	18	13	13	NUM
ejpam-5993	189	19	1	1	NUM
ejpam-5993	189	20	=	=	SYM
ejpam-5993	189	21	gn	gn	PROPN
ejpam-5993	189	22	⊴	⊴	PROPN
ejpam-5993	189	23	gn−1	gn−1	PROPN
ejpam-5993	189	24	⊴	⊴	ADP
ejpam-5993	189	25	gn−2	gn−2	PROPN
ejpam-5993	189	26	⊴	⊴	NOUN
ejpam-5993	189	27	·	·	PUNCT
ejpam-5993	189	28	·	·	PUNCT
ejpam-5993	189	29	·	·	PUNCT
ejpam-5993	189	30	gm+1	gm+1	X
ejpam-5993	189	31	⊴	⊴	ADP
ejpam-5993	189	32	gm	gm	PROPN
ejpam-5993	189	33	=	=	SYM
ejpam-5993	189	34	f	f	PROPN
ejpam-5993	189	35	(	(	PUNCT
ejpam-5993	189	36	h	h	NOUN
ejpam-5993	189	37	)	)	PUNCT
ejpam-5993	189	38	,	,	PUNCT
ejpam-5993	189	39	(	(	PUNCT
ejpam-5993	189	40	̇	̇	PROPN
ejpam-5993	189	41	∗	∗	NOUN
ejpam-5993	189	42	∗)250	∗)250	PROPN
ejpam-5993	189	43	where	where	SCONJ
ejpam-5993	189	44	(	(	PUNCT
ejpam-5993	189	45	gi−1	gi−1	PROPN
ejpam-5993	189	46	/	/	SYM
ejpam-5993	189	47	gi)(m+	gi)(m+	PROPN
ejpam-5993	189	48	1	1	NUM
ejpam-5993	189	49	⩽	⩽	NOUN
ejpam-5993	189	50	i	i	PRON
ejpam-5993	189	51	⩽	⩽	NOUN
ejpam-5993	189	52	n	n	CCONJ
ejpam-5993	189	53	)	)	PUNCT
ejpam-5993	189	54	are	be	AUX
ejpam-5993	189	55	cyclic	cyclic	ADJ
ejpam-5993	189	56	groups	group	NOUN
ejpam-5993	189	57	of	of	ADP
ejpam-5993	189	58	prime	prime	ADJ
ejpam-5993	189	59	order	order	NOUN
ejpam-5993	189	60	and	and	CCONJ
ejpam-5993	189	61	gi	gi	INTJ
ejpam-5993	189	62	⊴	⊴	PROPN
ejpam-5993	189	63	g.	g.	PROPN
ejpam-5993	189	64	then	then	ADV
ejpam-5993	189	65	,	,	PUNCT
ejpam-5993	189	66	we251	we251	PROPN
ejpam-5993	189	67	have	have	VERB
ejpam-5993	189	68	from	from	ADP
ejpam-5993	189	69	(	(	PUNCT
ejpam-5993	189	70	∗	∗	NOUN
ejpam-5993	189	71	)	)	PUNCT
ejpam-5993	189	72	and	and	CCONJ
ejpam-5993	189	73	(	(	PUNCT
ejpam-5993	189	74	∗∗):252	∗∗):252	NOUN
ejpam-5993	189	75	1	1	NUM
ejpam-5993	189	76	=	=	SYM
ejpam-5993	189	77	gn	gn	PROPN
ejpam-5993	189	78	⊴	⊴	ADP
ejpam-5993	189	79	·	·	PUNCT
ejpam-5993	189	80	·	·	PUNCT
ejpam-5993	189	81	·	·	PUNCT
ejpam-5993	190	1	⊴	⊴	ADP
ejpam-5993	190	2	gm	gm	PROPN
ejpam-5993	190	3	=	=	SYM
ejpam-5993	190	4	f	f	PROPN
ejpam-5993	190	5	(	(	PUNCT
ejpam-5993	190	6	h	h	NOUN
ejpam-5993	190	7	)	)	PUNCT
ejpam-5993	190	8	⊴	⊴	ADP
ejpam-5993	190	9	·	·	PUNCT
ejpam-5993	190	10	·	·	PUNCT
ejpam-5993	190	11	·	·	PUNCT
ejpam-5993	190	12	⊴	⊴	NUM
ejpam-5993	190	13	g0	g0	PROPN
ejpam-5993	190	14	=	=	SYM
ejpam-5993	190	15	g,253	g,253	NUM
ejpam-5993	190	16	where	where	SCONJ
ejpam-5993	190	17	(	(	PUNCT
ejpam-5993	190	18	gi−1	gi−1	PROPN
ejpam-5993	190	19	/	/	SYM
ejpam-5993	190	20	gi)(1	gi)(1	NOUN
ejpam-5993	190	21	⩽	⩽	ADJ
ejpam-5993	190	22	i	i	PRON
ejpam-5993	190	23	⩽	⩽	NOUN
ejpam-5993	190	24	n	n	CCONJ
ejpam-5993	190	25	)	)	PUNCT
ejpam-5993	190	26	are	be	AUX
ejpam-5993	190	27	cyclic	cyclic	ADJ
ejpam-5993	190	28	groups	group	NOUN
ejpam-5993	190	29	of	of	ADP
ejpam-5993	190	30	prime	prime	ADJ
ejpam-5993	190	31	order	order	NOUN
ejpam-5993	190	32	and	and	CCONJ
ejpam-5993	190	33	gi	gi	INTJ
ejpam-5993	190	34	⊴	⊴	PROPN
ejpam-5993	190	35	g.	g.	PROPN
ejpam-5993	190	36	hence	hence	ADV
ejpam-5993	190	37	,	,	PUNCT
ejpam-5993	190	38	g	g	PROPN
ejpam-5993	190	39	is254	is254	PROPN
ejpam-5993	190	40	supersolvable	supersolvable	PROPN
ejpam-5993	190	41	,	,	PUNCT
ejpam-5993	190	42	a	a	DET
ejpam-5993	190	43	contradiction.255	contradiction.255	PROPN
ejpam-5993	190	44	now	now	ADV
ejpam-5993	190	45	,	,	PUNCT
ejpam-5993	190	46	we	we	PRON
ejpam-5993	190	47	generalize	generalize	VERB
ejpam-5993	190	48	theorem	theorem	VERB
ejpam-5993	190	49	2	2	NUM
ejpam-5993	190	50	to	to	ADP
ejpam-5993	190	51	the	the	DET
ejpam-5993	190	52	class	class	NOUN
ejpam-5993	190	53	of	of	ADP
ejpam-5993	190	54	saturated	saturate	VERB
ejpam-5993	190	55	formation	formation	NOUN
ejpam-5993	190	56	as	as	ADP
ejpam-5993	190	57	follows:256	follows:256	PROPN
ejpam-5993	190	58	theorem	theorem	NOUN
ejpam-5993	190	59	3	3	X
ejpam-5993	190	60	.	.	PUNCT
ejpam-5993	191	1	let	let	AUX
ejpam-5993	191	2	f	f	PRON
ejpam-5993	191	3	be	be	AUX
ejpam-5993	191	4	a	a	DET
ejpam-5993	191	5	saturated	saturated	ADJ
ejpam-5993	191	6	formation	formation	NOUN
ejpam-5993	191	7	containing	contain	VERB
ejpam-5993	191	8	u.	u.	NOUN
ejpam-5993	191	9	suppose	suppose	VERB
ejpam-5993	191	10	that	that	SCONJ
ejpam-5993	191	11	g	g	PROPN
ejpam-5993	191	12	is	be	AUX
ejpam-5993	191	13	a	a	DET
ejpam-5993	191	14	group257	group257	PROPN
ejpam-5993	191	15	with	with	ADP
ejpam-5993	191	16	a	a	DET
ejpam-5993	191	17	solvable	solvable	ADJ
ejpam-5993	191	18	normal	normal	ADJ
ejpam-5993	191	19	subgroup	subgroup	NOUN
ejpam-5993	191	20	h	h	NOUN
ejpam-5993	191	21	such	such	ADJ
ejpam-5993	191	22	that	that	SCONJ
ejpam-5993	191	23	g	g	NOUN
ejpam-5993	191	24	/	/	SYM
ejpam-5993	191	25	h	h	NOUN
ejpam-5993	191	26	∈	∈	PROPN
ejpam-5993	191	27	f.	f.	PROPN
ejpam-5993	191	28	if	if	SCONJ
ejpam-5993	191	29	all	all	DET
ejpam-5993	191	30	maximal	maximal	ADJ
ejpam-5993	191	31	subgroups	subgroup	NOUN
ejpam-5993	191	32	of	of	ADP
ejpam-5993	191	33	the258	the258	PROPN
ejpam-5993	191	34	non	non	ADJ
ejpam-5993	191	35	-	-	ADJ
ejpam-5993	191	36	cyclic	cyclic	ADJ
ejpam-5993	191	37	sylow	sylow	NOUN
ejpam-5993	191	38	subgroups	subgroup	NOUN
ejpam-5993	191	39	of	of	ADP
ejpam-5993	191	40	f	f	PROPN
ejpam-5993	191	41	(	(	PUNCT
ejpam-5993	191	42	h	h	NOUN
ejpam-5993	191	43	)	)	PUNCT
ejpam-5993	191	44	are	be	AUX
ejpam-5993	191	45	ssh	ssh	NOUN
ejpam-5993	191	46	-	-	PUNCT
ejpam-5993	191	47	subgroups	subgroup	NOUN
ejpam-5993	191	48	of	of	ADP
ejpam-5993	191	49	g	g	NOUN
ejpam-5993	191	50	,	,	PUNCT
ejpam-5993	191	51	then	then	ADV
ejpam-5993	191	52	g	g	PROPN
ejpam-5993	191	53	∈	∈	PROPN
ejpam-5993	191	54	f.259	f.259	NOUN
ejpam-5993	191	55	proof	proof	NOUN
ejpam-5993	191	56	.	.	PUNCT
ejpam-5993	192	1	assume	assume	VERB
ejpam-5993	192	2	that	that	SCONJ
ejpam-5993	192	3	the	the	DET
ejpam-5993	192	4	claim	claim	NOUN
ejpam-5993	192	5	is	be	AUX
ejpam-5993	192	6	false	false	ADJ
ejpam-5993	192	7	and	and	CCONJ
ejpam-5993	192	8	choose	choose	VERB
ejpam-5993	192	9	g	g	NOUN
ejpam-5993	192	10	to	to	PART
ejpam-5993	192	11	be	be	AUX
ejpam-5993	192	12	a	a	DET
ejpam-5993	192	13	counterexample	counterexample	NOUN
ejpam-5993	192	14	of	of	ADP
ejpam-5993	192	15	minimal260	minimal260	PROPN
ejpam-5993	192	16	order	order	NOUN
ejpam-5993	192	17	.	.	PUNCT
ejpam-5993	193	1	we	we	PRON
ejpam-5993	193	2	aim	aim	VERB
ejpam-5993	193	3	to	to	PART
ejpam-5993	193	4	obtain	obtain	VERB
ejpam-5993	193	5	that	that	SCONJ
ejpam-5993	193	6	there	there	PRON
ejpam-5993	193	7	is	be	VERB
ejpam-5993	193	8	no	no	DET
ejpam-5993	193	9	such	such	ADJ
ejpam-5993	193	10	counterexample	counterexample	NOUN
ejpam-5993	193	11	of	of	ADP
ejpam-5993	193	12	g	g	NOUN
ejpam-5993	193	13	by	by	ADP
ejpam-5993	193	14	the	the	DET
ejpam-5993	193	15	following	follow	VERB
ejpam-5993	193	16	steps:261	steps:261	PRON
ejpam-5993	193	17	262	262	NUM
ejpam-5993	193	18	(	(	PUNCT
ejpam-5993	193	19	1	1	NUM
ejpam-5993	193	20	)	)	PUNCT
ejpam-5993	193	21	φ(g	φ(g	ADJ
ejpam-5993	193	22	)	)	PUNCT
ejpam-5993	193	23	∩h	∩h	NOUN
ejpam-5993	193	24	=	=	PUNCT
ejpam-5993	193	25	1263	1263	NUM
ejpam-5993	193	26	if	if	SCONJ
ejpam-5993	193	27	not	not	PART
ejpam-5993	193	28	,	,	PUNCT
ejpam-5993	193	29	φ(g	φ(g	ADJ
ejpam-5993	193	30	)	)	PUNCT
ejpam-5993	193	31	∩h	∩h	NOUN
ejpam-5993	193	32	̸=	̸=	PROPN
ejpam-5993	193	33	1	1	NUM
ejpam-5993	193	34	and	and	CCONJ
ejpam-5993	193	35	then	then	ADV
ejpam-5993	193	36	there	there	PRON
ejpam-5993	193	37	exists	exist	VERB
ejpam-5993	193	38	a	a	DET
ejpam-5993	193	39	prime	prime	NOUN
ejpam-5993	193	40	p	p	NOUN
ejpam-5993	193	41	such	such	ADJ
ejpam-5993	193	42	that	that	DET
ejpam-5993	193	43	p||φ(g	p||φ(g	X
ejpam-5993	193	44	)	)	PUNCT
ejpam-5993	193	45	∩h|	∩h|	PROPN
ejpam-5993	193	46	.	.	PUNCT
ejpam-5993	194	1	let	let	AUX
ejpam-5993	194	2	p1264	p1264	VERB
ejpam-5993	194	3	be	be	AUX
ejpam-5993	194	4	a	a	DET
ejpam-5993	194	5	non	non	ADJ
ejpam-5993	194	6	-	-	ADJ
ejpam-5993	194	7	cyclic	cyclic	ADJ
ejpam-5993	194	8	sylow	sylow	NOUN
ejpam-5993	194	9	p	p	NOUN
ejpam-5993	194	10	-	-	PUNCT
ejpam-5993	194	11	subgroup	subgroup	NOUN
ejpam-5993	194	12	of	of	ADP
ejpam-5993	194	13	(	(	PUNCT
ejpam-5993	194	14	φ(g	φ(g	PROPN
ejpam-5993	194	15	)	)	PUNCT
ejpam-5993	194	16	∩h	∩h	NOUN
ejpam-5993	194	17	)	)	PUNCT
ejpam-5993	194	18	.	.	PUNCT
ejpam-5993	195	1	clearly	clearly	ADV
ejpam-5993	195	2	,	,	PUNCT
ejpam-5993	195	3	p1	p1	PROPN
ejpam-5993	195	4	⊴	⊴	ADP
ejpam-5993	195	5	g	g	PROPN
ejpam-5993	195	6	and	and	CCONJ
ejpam-5993	195	7	(	(	PUNCT
ejpam-5993	195	8	g	g	NOUN
ejpam-5993	195	9	/	/	SYM
ejpam-5993	195	10	p1)/(h	p1)/(h	NOUN
ejpam-5993	195	11	/	/	SYM
ejpam-5993	195	12	p1	p1	NOUN
ejpam-5993	195	13	)	)	PUNCT
ejpam-5993	195	14	∼=265	∼=265	NOUN
ejpam-5993	195	15	g	g	NOUN
ejpam-5993	195	16	/	/	SYM
ejpam-5993	195	17	h	h	NOUN
ejpam-5993	195	18	∈	∈	PROPN
ejpam-5993	195	19	f.	f.	PROPN
ejpam-5993	195	20	by	by	ADP
ejpam-5993	195	21	using	use	VERB
ejpam-5993	195	22	similar	similar	ADJ
ejpam-5993	195	23	arguments	argument	NOUN
ejpam-5993	195	24	as	as	ADP
ejpam-5993	195	25	in	in	ADP
ejpam-5993	195	26	the	the	DET
ejpam-5993	195	27	second	second	ADJ
ejpam-5993	195	28	paragraph	paragraph	NOUN
ejpam-5993	195	29	of	of	ADP
ejpam-5993	195	30	(	(	PUNCT
ejpam-5993	195	31	1	1	NUM
ejpam-5993	195	32	)	)	PUNCT
ejpam-5993	195	33	in	in	ADP
ejpam-5993	195	34	theorem	theorem	ADJ
ejpam-5993	195	35	2,266	2,266	NUM
ejpam-5993	195	36	we	we	PRON
ejpam-5993	195	37	can	can	AUX
ejpam-5993	195	38	see	see	VERB
ejpam-5993	195	39	that	that	SCONJ
ejpam-5993	195	40	g	g	PROPN
ejpam-5993	195	41	/	/	SYM
ejpam-5993	195	42	p1	p1	PROPN
ejpam-5993	195	43	∈	∈	PROPN
ejpam-5993	195	44	f.	f.	PROPN
ejpam-5993	195	45	but	but	CCONJ
ejpam-5993	195	46	p1	p1	PROPN
ejpam-5993	195	47	⩽	⩽	PROPN
ejpam-5993	195	48	φ(g	φ(g	PROPN
ejpam-5993	195	49	)	)	PUNCT
ejpam-5993	195	50	,	,	PUNCT
ejpam-5993	195	51	then	then	ADV
ejpam-5993	195	52	g	g	PROPN
ejpam-5993	195	53	/	/	SYM
ejpam-5993	195	54	φ(g	φ(g	ADJ
ejpam-5993	195	55	)	)	PUNCT
ejpam-5993	195	56	∈	∈	PROPN
ejpam-5993	195	57	f	f	PROPN
ejpam-5993	195	58	and	and	CCONJ
ejpam-5993	195	59	,	,	PUNCT
ejpam-5993	195	60	since	since	SCONJ
ejpam-5993	195	61	f	f	PROPN
ejpam-5993	195	62	is	be	AUX
ejpam-5993	195	63	saturated,267	saturated,267	INTJ
ejpam-5993	195	64	we	we	PRON
ejpam-5993	195	65	have	have	VERB
ejpam-5993	195	66	g	g	PROPN
ejpam-5993	195	67	∈	∈	PROPN
ejpam-5993	195	68	f	f	PROPN
ejpam-5993	195	69	,	,	PUNCT
ejpam-5993	195	70	a	a	DET
ejpam-5993	195	71	contradiction	contradiction	NOUN
ejpam-5993	195	72	.	.	PUNCT
ejpam-5993	196	1	thus	thus	ADV
ejpam-5993	196	2	φ(g	φ(g	ADJ
ejpam-5993	196	3	)	)	PUNCT
ejpam-5993	196	4	∩h	∩h	NOUN
ejpam-5993	196	5	=	=	NOUN
ejpam-5993	197	1	1.268	1.268	NUM
ejpam-5993	197	2	269	269	NUM
ejpam-5993	197	3	(	(	PUNCT
ejpam-5993	197	4	2	2	NUM
ejpam-5993	197	5	)	)	PUNCT
ejpam-5993	197	6	let	let	VERB
ejpam-5993	197	7	p	p	PRON
ejpam-5993	197	8	be	be	AUX
ejpam-5993	197	9	a	a	DET
ejpam-5993	197	10	non	non	ADJ
ejpam-5993	197	11	-	-	ADJ
ejpam-5993	197	12	cyclic	cyclic	ADJ
ejpam-5993	197	13	sylow	sylow	NOUN
ejpam-5993	197	14	p	p	PROPN
ejpam-5993	197	15	-	-	PUNCT
ejpam-5993	197	16	subgroup	subgroup	NOUN
ejpam-5993	197	17	of	of	ADP
ejpam-5993	197	18	f	f	PROPN
ejpam-5993	197	19	(	(	PUNCT
ejpam-5993	197	20	h	h	NOUN
ejpam-5993	197	21	)	)	PUNCT
ejpam-5993	197	22	.	.	PUNCT
ejpam-5993	198	1	then	then	ADV
ejpam-5993	198	2	p	p	X
ejpam-5993	198	3	=	=	PROPN
ejpam-5993	198	4	r1	r1	PROPN
ejpam-5993	198	5	×r2	×r2	PROPN
ejpam-5993	198	6	×r3	×r3	PROPN
ejpam-5993	198	7	×	×	NOUN
ejpam-5993	198	8	·	·	PUNCT
ejpam-5993	198	9	·	·	PUNCT
ejpam-5993	198	10	·	·	PUNCT
ejpam-5993	198	11	×rt,270	×rt,270	PUNCT
ejpam-5993	199	1	where	where	SCONJ
ejpam-5993	199	2	ri(i	ri(i	PUNCT
ejpam-5993	199	3	=	=	SYM
ejpam-5993	199	4	1	1	NUM
ejpam-5993	199	5	,	,	PUNCT
ejpam-5993	199	6	.	.	PUNCT
ejpam-5993	199	7	.	.	PUNCT
ejpam-5993	200	1	.	.	PUNCT
ejpam-5993	201	1	,	,	PUNCT
ejpam-5993	201	2	t	t	X
ejpam-5993	201	3	)	)	PUNCT
ejpam-5993	201	4	are	be	AUX
ejpam-5993	201	5	normal	normal	ADJ
ejpam-5993	201	6	subgroups	subgroup	NOUN
ejpam-5993	201	7	of	of	ADP
ejpam-5993	201	8	g	g	NOUN
ejpam-5993	201	9	of	of	ADP
ejpam-5993	201	10	order	order	NOUN
ejpam-5993	201	11	p.271	p.271	NUM
ejpam-5993	201	12	by	by	ADP
ejpam-5993	201	13	(	(	PUNCT
ejpam-5993	201	14	1	1	NUM
ejpam-5993	201	15	)	)	PUNCT
ejpam-5993	201	16	and	and	CCONJ
ejpam-5993	201	17	lemma	lemma	PROPN
ejpam-5993	201	18	3	3	NUM
ejpam-5993	201	19	,	,	PUNCT
ejpam-5993	201	20	we	we	PRON
ejpam-5993	201	21	have	have	VERB
ejpam-5993	201	22	p	p	NOUN
ejpam-5993	201	23	=	=	PUNCT
ejpam-5993	201	24	r1	r1	PROPN
ejpam-5993	202	1	×	×	PROPN
ejpam-5993	202	2	r2	r2	PROPN
ejpam-5993	202	3	×	×	PROPN
ejpam-5993	202	4	r3	r3	PROPN
ejpam-5993	202	5	×	×	NOUN
ejpam-5993	202	6	·	·	PUNCT
ejpam-5993	202	7	·	·	PUNCT
ejpam-5993	202	8	·	·	PUNCT
ejpam-5993	203	1	×	×	X
ejpam-5993	203	2	rt	rt	INTJ
ejpam-5993	203	3	,	,	PUNCT
ejpam-5993	203	4	where	where	SCONJ
ejpam-5993	203	5	ri(i	ri(i	PUNCT
ejpam-5993	203	6	=	=	SYM
ejpam-5993	203	7	1	1	NUM
ejpam-5993	203	8	,	,	PUNCT
ejpam-5993	203	9	.	.	PUNCT
ejpam-5993	203	10	.	.	PUNCT
ejpam-5993	203	11	.	.	PUNCT
ejpam-5993	204	1	,	,	PUNCT
ejpam-5993	204	2	t)272	t)272	PROPN
ejpam-5993	204	3	is	be	AUX
ejpam-5993	204	4	a	a	DET
ejpam-5993	204	5	minimal	minimal	ADJ
ejpam-5993	204	6	normal	normal	ADJ
ejpam-5993	204	7	subgroup	subgroup	NOUN
ejpam-5993	204	8	of	of	ADP
ejpam-5993	204	9	g.	g.	PROPN
ejpam-5993	204	10	it	it	PRON
ejpam-5993	204	11	is	be	AUX
ejpam-5993	204	12	easily	easily	ADV
ejpam-5993	204	13	follows	follow	VERB
ejpam-5993	204	14	,	,	PUNCT
ejpam-5993	204	15	by	by	ADP
ejpam-5993	204	16	a	a	DET
ejpam-5993	204	17	similar	similar	ADJ
ejpam-5993	204	18	argument	argument	NOUN
ejpam-5993	204	19	to	to	ADP
ejpam-5993	204	20	(	(	PUNCT
ejpam-5993	204	21	2	2	NUM
ejpam-5993	204	22	)	)	PUNCT
ejpam-5993	204	23	in273	in273	NOUN
ejpam-5993	204	24	theorem	theorem	NOUN
ejpam-5993	204	25	2	2	NUM
ejpam-5993	204	26	,	,	PUNCT
ejpam-5993	204	27	that	that	DET
ejpam-5993	204	28	|ri|	|ri|	NOUN
ejpam-5993	204	29	=	=	SYM
ejpam-5993	205	1	p.274	p.274	NOUN
ejpam-5993	205	2	275	275	NUM
ejpam-5993	205	3	(	(	PUNCT
ejpam-5993	205	4	3	3	NUM
ejpam-5993	205	5	)	)	PUNCT
ejpam-5993	205	6	g	g	NOUN
ejpam-5993	205	7	/	/	SYM
ejpam-5993	205	8	f	f	PROPN
ejpam-5993	205	9	(	(	PUNCT
ejpam-5993	205	10	h	h	NOUN
ejpam-5993	205	11	)	)	PUNCT
ejpam-5993	205	12	∈	∈	NOUN
ejpam-5993	205	13	f.276	f.276	NOUN
ejpam-5993	205	14	from	from	ADP
ejpam-5993	205	15	(	(	PUNCT
ejpam-5993	205	16	2	2	NUM
ejpam-5993	205	17	)	)	PUNCT
ejpam-5993	205	18	,	,	PUNCT
ejpam-5993	205	19	denote	denote	VERB
ejpam-5993	205	20	f	f	PROPN
ejpam-5993	205	21	(	(	PUNCT
ejpam-5993	205	22	h	h	NOUN
ejpam-5993	205	23	)	)	PUNCT
ejpam-5993	206	1	=	=	SYM
ejpam-5993	206	2	r1	r1	PROPN
ejpam-5993	206	3	×	×	PROPN
ejpam-5993	206	4	r2	r2	PROPN
ejpam-5993	206	5	×	×	PROPN
ejpam-5993	206	6	r3	r3	PROPN
ejpam-5993	206	7	×	×	NOUN
ejpam-5993	206	8	·	·	PUNCT
ejpam-5993	206	9	·	·	PUNCT
ejpam-5993	206	10	·	·	PUNCT
ejpam-5993	207	1	×	×	PROPN
ejpam-5993	207	2	rr	rr	NOUN
ejpam-5993	207	3	,	,	PUNCT
ejpam-5993	207	4	where	where	SCONJ
ejpam-5993	207	5	ri(i	ri(i	PUNCT
ejpam-5993	207	6	=	=	SYM
ejpam-5993	207	7	1	1	NUM
ejpam-5993	207	8	,	,	PUNCT
ejpam-5993	207	9	.	.	PUNCT
ejpam-5993	207	10	.	.	PUNCT
ejpam-5993	207	11	.	.	PUNCT
ejpam-5993	208	1	,	,	PUNCT
ejpam-5993	208	2	r	r	X
ejpam-5993	208	3	)	)	PUNCT
ejpam-5993	208	4	are	be	AUX
ejpam-5993	208	5	minimal277	minimal277	PROPN
ejpam-5993	208	6	normal	normal	ADJ
ejpam-5993	208	7	subgroups	subgroup	NOUN
ejpam-5993	208	8	of	of	ADP
ejpam-5993	208	9	g.	g.	PROPN
ejpam-5993	208	10	we	we	PRON
ejpam-5993	208	11	have	have	VERB
ejpam-5993	208	12	g	g	NOUN
ejpam-5993	208	13	/	/	SYM
ejpam-5993	208	14	cg(ri	cg(ri	ADJ
ejpam-5993	208	15	)	)	PUNCT
ejpam-5993	209	1	is	be	AUX
ejpam-5993	209	2	isomorphic	isomorphic	ADJ
ejpam-5993	209	3	to	to	ADP
ejpam-5993	209	4	a	a	DET
ejpam-5993	209	5	subgroup	subgroup	NOUN
ejpam-5993	209	6	of	of	ADP
ejpam-5993	209	7	aut(ri),278	aut(ri),278	NOUN
ejpam-5993	209	8	which	which	PRON
ejpam-5993	209	9	implies	imply	VERB
ejpam-5993	209	10	that	that	SCONJ
ejpam-5993	209	11	g	g	PROPN
ejpam-5993	209	12	/	/	SYM
ejpam-5993	209	13	cg(ri	cg(ri	ADJ
ejpam-5993	209	14	)	)	PUNCT
ejpam-5993	209	15	is	be	AUX
ejpam-5993	209	16	cyclic	cyclic	ADJ
ejpam-5993	209	17	,	,	PUNCT
ejpam-5993	209	18	and	and	CCONJ
ejpam-5993	210	1	g	g	NOUN
ejpam-5993	210	2	/	/	SYM
ejpam-5993	210	3	cg(ri	cg(ri	ADJ
ejpam-5993	210	4	)	)	PUNCT
ejpam-5993	210	5	∈	∈	PROPN
ejpam-5993	210	6	u.	u.	PROPN
ejpam-5993	211	1	so	so	ADV
ejpam-5993	211	2	g/(∩r	g/(∩r	PROPN
ejpam-5993	211	3	i=1cg(ri	i=1cg(ri	PROPN
ejpam-5993	211	4	)	)	PUNCT
ejpam-5993	211	5	)	)	PUNCT
ejpam-5993	212	1	∈	∈	PROPN
ejpam-5993	212	2	u.279	u.279	NOUN
ejpam-5993	212	3	notice	notice	NOUN
ejpam-5993	212	4	that	that	SCONJ
ejpam-5993	212	5	cg(f	cg(f	PUNCT
ejpam-5993	212	6	(	(	PUNCT
ejpam-5993	212	7	h	h	NOUN
ejpam-5993	212	8	)	)	PUNCT
ejpam-5993	212	9	)	)	PUNCT
ejpam-5993	212	10	=	=	SYM
ejpam-5993	212	11	∩r	∩r	ADJ
ejpam-5993	212	12	i=1cg(ri	i=1cg(ri	NOUN
ejpam-5993	212	13	)	)	PUNCT
ejpam-5993	212	14	,	,	PUNCT
ejpam-5993	212	15	so	so	ADV
ejpam-5993	212	16	g	g	PROPN
ejpam-5993	212	17	/	/	SYM
ejpam-5993	212	18	cg(f	cg(f	NOUN
ejpam-5993	212	19	(	(	PUNCT
ejpam-5993	212	20	h	h	NOUN
ejpam-5993	212	21	)	)	PUNCT
ejpam-5993	212	22	)	)	PUNCT
ejpam-5993	213	1	∈	∈	PROPN
ejpam-5993	213	2	u	u	NOUN
ejpam-5993	213	3	⊆	⊆	NUM
ejpam-5993	213	4	f.	f.	NOUN
ejpam-5993	213	5	since	since	SCONJ
ejpam-5993	213	6	g	g	PROPN
ejpam-5993	213	7	/	/	SYM
ejpam-5993	213	8	h	h	NOUN
ejpam-5993	213	9	∈	∈	PROPN
ejpam-5993	213	10	f	f	PROPN
ejpam-5993	213	11	and280	and280	PROPN
ejpam-5993	213	12	g	g	PROPN
ejpam-5993	213	13	/	/	SYM
ejpam-5993	213	14	cg(f	cg(f	NUM
ejpam-5993	213	15	(	(	PUNCT
ejpam-5993	213	16	h	h	NOUN
ejpam-5993	213	17	)	)	PUNCT
ejpam-5993	213	18	)	)	PUNCT
ejpam-5993	214	1	∈	∈	PROPN
ejpam-5993	215	1	f	f	X
ejpam-5993	215	2	,	,	PUNCT
ejpam-5993	215	3	it	it	PRON
ejpam-5993	215	4	follows	follow	VERB
ejpam-5993	215	5	that	that	SCONJ
ejpam-5993	215	6	g/(h	g/(h	PROPN
ejpam-5993	215	7	∩	∩	NOUN
ejpam-5993	215	8	cg(f	cg(f	PUNCT
ejpam-5993	215	9	(	(	PUNCT
ejpam-5993	215	10	h	h	NOUN
ejpam-5993	215	11	)	)	PUNCT
ejpam-5993	215	12	)	)	PUNCT
ejpam-5993	216	1	=	=	PUNCT
ejpam-5993	216	2	g	g	NOUN
ejpam-5993	216	3	/	/	SYM
ejpam-5993	216	4	ch(f	ch(f	NUM
ejpam-5993	216	5	(	(	PUNCT
ejpam-5993	216	6	h	h	NOUN
ejpam-5993	216	7	)	)	PUNCT
ejpam-5993	216	8	)	)	PUNCT
ejpam-5993	217	1	∈	∈	PROPN
ejpam-5993	217	2	f.	f.	PROPN
ejpam-5993	217	3	as	as	ADP
ejpam-5993	217	4	h	h	NOUN
ejpam-5993	217	5	is281	is281	PROPN
ejpam-5993	217	6	solvable	solvable	ADJ
ejpam-5993	217	7	,	,	PUNCT
ejpam-5993	217	8	ch(f	ch(f	ADP
ejpam-5993	217	9	(	(	PUNCT
ejpam-5993	217	10	h	h	NOUN
ejpam-5993	217	11	)	)	PUNCT
ejpam-5993	217	12	)	)	PUNCT
ejpam-5993	218	1	⩽	⩽	PROPN
ejpam-5993	218	2	f	f	PROPN
ejpam-5993	218	3	(	(	PUNCT
ejpam-5993	218	4	h	h	NOUN
ejpam-5993	218	5	)	)	PUNCT
ejpam-5993	218	6	.	.	PUNCT
ejpam-5993	219	1	moreover	moreover	ADV
ejpam-5993	219	2	,	,	PUNCT
ejpam-5993	219	3	f	f	PROPN
ejpam-5993	219	4	(	(	PUNCT
ejpam-5993	219	5	h	h	NOUN
ejpam-5993	219	6	)	)	PUNCT
ejpam-5993	219	7	⩽	⩽	NOUN
ejpam-5993	219	8	ch(f	ch(f	ADP
ejpam-5993	219	9	(	(	PUNCT
ejpam-5993	219	10	h	h	NOUN
ejpam-5993	219	11	)	)	PUNCT
ejpam-5993	219	12	)	)	PUNCT
ejpam-5993	220	1	as	as	SCONJ
ejpam-5993	220	2	f	f	PROPN
ejpam-5993	220	3	(	(	PUNCT
ejpam-5993	220	4	h	h	NOUN
ejpam-5993	220	5	)	)	PUNCT
ejpam-5993	220	6	is	be	AUX
ejpam-5993	220	7	abelian	abelian	ADJ
ejpam-5993	220	8	.	.	PUNCT
ejpam-5993	221	1	hence,282	hence,282	PROPN
ejpam-5993	222	1	f	f	PROPN
ejpam-5993	222	2	(	(	PUNCT
ejpam-5993	222	3	h	h	NOUN
ejpam-5993	222	4	)	)	PUNCT
ejpam-5993	222	5	=	=	SYM
ejpam-5993	222	6	ch(f	ch(f	X
ejpam-5993	222	7	(	(	PUNCT
ejpam-5993	222	8	h	h	NOUN
ejpam-5993	222	9	)	)	PUNCT
ejpam-5993	222	10	)	)	PUNCT
ejpam-5993	222	11	,	,	PUNCT
ejpam-5993	222	12	and	and	CCONJ
ejpam-5993	222	13	so	so	ADV
ejpam-5993	222	14	g	g	PROPN
ejpam-5993	222	15	/	/	SYM
ejpam-5993	222	16	f	f	PROPN
ejpam-5993	222	17	(	(	PUNCT
ejpam-5993	222	18	h	h	NOUN
ejpam-5993	222	19	)	)	PUNCT
ejpam-5993	222	20	∈	∈	PROPN
ejpam-5993	222	21	f.283	f.283	NOUN
ejpam-5993	222	22	284	284	NUM
ejpam-5993	222	23	(	(	PUNCT
ejpam-5993	222	24	4	4	NUM
ejpam-5993	222	25	)	)	PUNCT
ejpam-5993	222	26	if	if	SCONJ
ejpam-5993	222	27	n	n	PRON
ejpam-5993	222	28	is	be	AUX
ejpam-5993	222	29	a	a	DET
ejpam-5993	222	30	minimal	minimal	ADJ
ejpam-5993	222	31	normal	normal	ADJ
ejpam-5993	222	32	subgroup	subgroup	NOUN
ejpam-5993	222	33	of	of	ADP
ejpam-5993	222	34	g	g	PROPN
ejpam-5993	222	35	contained	contain	VERB
ejpam-5993	222	36	in	in	ADP
ejpam-5993	222	37	h	h	NOUN
ejpam-5993	222	38	,	,	PUNCT
ejpam-5993	222	39	then	then	ADV
ejpam-5993	222	40	g	g	PROPN
ejpam-5993	222	41	/	/	SYM
ejpam-5993	222	42	n	n	CCONJ
ejpam-5993	222	43	∈	∈	PROPN
ejpam-5993	222	44	f.285	f.285	ADV
ejpam-5993	222	45	let	let	VERB
ejpam-5993	222	46	n	n	PRON
ejpam-5993	222	47	be	be	AUX
ejpam-5993	222	48	an	an	DET
ejpam-5993	222	49	arbitrary	arbitrary	ADJ
ejpam-5993	222	50	minimal	minimal	ADJ
ejpam-5993	222	51	normal	normal	ADJ
ejpam-5993	222	52	subgroup	subgroup	NOUN
ejpam-5993	222	53	of	of	ADP
ejpam-5993	222	54	g	g	PROPN
ejpam-5993	222	55	contained	contain	VERB
ejpam-5993	222	56	in	in	ADP
ejpam-5993	222	57	h.	h.	PROPN
ejpam-5993	222	58	since	since	SCONJ
ejpam-5993	222	59	h	h	PROPN
ejpam-5993	222	60	is286	is286	ADJ
ejpam-5993	222	61	solvable	solvable	ADJ
ejpam-5993	222	62	,	,	PUNCT
ejpam-5993	222	63	we	we	PRON
ejpam-5993	222	64	may	may	AUX
ejpam-5993	222	65	assume	assume	VERB
ejpam-5993	222	66	that	that	SCONJ
ejpam-5993	222	67	n	n	PRON
ejpam-5993	222	68	is	be	AUX
ejpam-5993	222	69	an	an	DET
ejpam-5993	222	70	elementary	elementary	ADJ
ejpam-5993	222	71	abelian	abelian	NOUN
ejpam-5993	222	72	p	p	PROPN
ejpam-5993	222	73	-	-	PUNCT
ejpam-5993	222	74	group	group	NOUN
ejpam-5993	222	75	for	for	ADP
ejpam-5993	222	76	some	some	DET
ejpam-5993	222	77	prime	prime	NOUN
ejpam-5993	222	78	p	p	PROPN
ejpam-5993	222	79	and287	and287	PROPN
ejpam-5993	222	80	n	n	NUM
ejpam-5993	222	81	⩽	⩽	NOUN
ejpam-5993	222	82	f	f	PROPN
ejpam-5993	222	83	(	(	PUNCT
ejpam-5993	222	84	h	h	NOUN
ejpam-5993	222	85	)	)	PUNCT
ejpam-5993	222	86	.	.	PUNCT
ejpam-5993	223	1	now	now	ADV
ejpam-5993	223	2	,	,	PUNCT
ejpam-5993	223	3	we	we	PRON
ejpam-5993	223	4	show	show	VERB
ejpam-5993	223	5	g	g	NOUN
ejpam-5993	223	6	/	/	SYM
ejpam-5993	223	7	n	n	PROPN
ejpam-5993	223	8	and	and	CCONJ
ejpam-5993	223	9	f	f	PROPN
ejpam-5993	223	10	(	(	PUNCT
ejpam-5993	223	11	h)/n	h)/n	PROPN
ejpam-5993	223	12	satisfy	satisfy	VERB
ejpam-5993	223	13	the	the	DET
ejpam-5993	223	14	hypothesis	hypothesis	NOUN
ejpam-5993	223	15	of	of	ADP
ejpam-5993	223	16	the	the	DET
ejpam-5993	223	17	theorem.288	theorem.288	PROPN
ejpam-5993	223	18	consider	consider	VERB
ejpam-5993	223	19	the	the	DET
ejpam-5993	223	20	solvable	solvable	ADJ
ejpam-5993	223	21	normal	normal	ADJ
ejpam-5993	223	22	subgroup	subgroup	NOUN
ejpam-5993	223	23	f	f	PROPN
ejpam-5993	223	24	(	(	PUNCT
ejpam-5993	223	25	h)/n	h)/n	PROPN
ejpam-5993	223	26	.	.	PUNCT
ejpam-5993	224	1	then289	then289	PROPN
ejpam-5993	224	2	a.	a.	NOUN
ejpam-5993	224	3	s.	s.	PROPN
ejpam-5993	224	4	allehyani	allehyani	PROPN
ejpam-5993	224	5	/	/	SYM
ejpam-5993	224	6	eur	eur	PROPN
ejpam-5993	224	7	.	.	PUNCT
ejpam-5993	225	1	j.	j.	PROPN
ejpam-5993	225	2	pure	pure	PROPN
ejpam-5993	225	3	appl	appl	PROPN
ejpam-5993	225	4	.	.	PROPN
ejpam-5993	225	5	math	math	PROPN
ejpam-5993	225	6	,	,	PUNCT
ejpam-5993	225	7	18	18	NUM
ejpam-5993	225	8	(	(	PUNCT
ejpam-5993	225	9	2	2	NUM
ejpam-5993	225	10	)	)	PUNCT
ejpam-5993	225	11	(	(	PUNCT
ejpam-5993	225	12	2025	2025	NUM
ejpam-5993	225	13	)	)	PUNCT
ejpam-5993	225	14	,	,	PUNCT
ejpam-5993	225	15	5993	5993	NUM
ejpam-5993	225	16	9	9	NUM
ejpam-5993	225	17	of	of	ADP
ejpam-5993	225	18	13	13	NUM
ejpam-5993	225	19	(	(	PUNCT
ejpam-5993	225	20	g	g	NOUN
ejpam-5993	225	21	/	/	SYM
ejpam-5993	225	22	n)/(f	n)/(f	NOUN
ejpam-5993	225	23	(	(	PUNCT
ejpam-5993	225	24	h)/n	h)/n	PROPN
ejpam-5993	225	25	)	)	PUNCT
ejpam-5993	225	26	∼=	∼=	PROPN
ejpam-5993	225	27	g	g	NOUN
ejpam-5993	225	28	/	/	SYM
ejpam-5993	225	29	f	f	PROPN
ejpam-5993	225	30	(	(	PUNCT
ejpam-5993	225	31	h	h	NOUN
ejpam-5993	225	32	)	)	PUNCT
ejpam-5993	225	33	∈	∈	PROPN
ejpam-5993	225	34	f.290	f.290	NUM
ejpam-5993	225	35	to	to	PART
ejpam-5993	225	36	prove	prove	VERB
ejpam-5993	225	37	g	g	NOUN
ejpam-5993	225	38	/	/	SYM
ejpam-5993	225	39	n	n	NOUN
ejpam-5993	225	40	∈	∈	NOUN
ejpam-5993	225	41	f	f	X
ejpam-5993	225	42	,	,	PUNCT
ejpam-5993	225	43	we	we	PRON
ejpam-5993	225	44	need	need	AUX
ejpam-5993	225	45	only	only	ADV
ejpam-5993	225	46	show	show	VERB
ejpam-5993	225	47	that	that	SCONJ
ejpam-5993	225	48	all	all	DET
ejpam-5993	225	49	maximal	maximal	ADJ
ejpam-5993	225	50	subgroups	subgroup	NOUN
ejpam-5993	225	51	of	of	ADP
ejpam-5993	225	52	the	the	DET
ejpam-5993	225	53	non	non	ADJ
ejpam-5993	225	54	-	-	ADJ
ejpam-5993	225	55	cyclic291	cyclic291	ADJ
ejpam-5993	225	56	sylow	sylow	NOUN
ejpam-5993	225	57	subgroups	subgroup	NOUN
ejpam-5993	225	58	of	of	ADP
ejpam-5993	225	59	f	f	PROPN
ejpam-5993	225	60	(	(	PUNCT
ejpam-5993	225	61	h)/n	h)/n	X
ejpam-5993	225	62	=	=	SYM
ejpam-5993	225	63	f	f	PROPN
ejpam-5993	225	64	(	(	PUNCT
ejpam-5993	225	65	f	f	PROPN
ejpam-5993	225	66	(	(	PUNCT
ejpam-5993	225	67	h)/n	h)/n	PROPN
ejpam-5993	225	68	)	)	PUNCT
ejpam-5993	225	69	are	be	AUX
ejpam-5993	225	70	ssh	ssh	NOUN
ejpam-5993	225	71	-	-	PUNCT
ejpam-5993	225	72	subgroups	subgroup	NOUN
ejpam-5993	225	73	in	in	ADP
ejpam-5993	225	74	g	g	PROPN
ejpam-5993	225	75	/	/	SYM
ejpam-5993	225	76	n	n	NOUN
ejpam-5993	225	77	.	.	PUNCT
ejpam-5993	226	1	now	now	ADV
ejpam-5993	226	2	p	p	X
ejpam-5993	226	3	/	/	SYM
ejpam-5993	226	4	n	n	PROPN
ejpam-5993	226	5	is292	is292	PROPN
ejpam-5993	226	6	the	the	DET
ejpam-5993	226	7	non	non	ADJ
ejpam-5993	226	8	-	-	ADJ
ejpam-5993	226	9	cyclic	cyclic	ADJ
ejpam-5993	226	10	sylow	sylow	NOUN
ejpam-5993	226	11	p	p	PROPN
ejpam-5993	226	12	-	-	PUNCT
ejpam-5993	226	13	subgroup	subgroup	NOUN
ejpam-5993	226	14	of	of	ADP
ejpam-5993	226	15	f	f	PROPN
ejpam-5993	226	16	(	(	PUNCT
ejpam-5993	226	17	h)/n	h)/n	PROPN
ejpam-5993	226	18	,	,	PUNCT
ejpam-5993	226	19	where	where	SCONJ
ejpam-5993	226	20	p	p	NOUN
ejpam-5993	226	21	is	be	AUX
ejpam-5993	226	22	the	the	DET
ejpam-5993	226	23	non	non	ADJ
ejpam-5993	226	24	-	-	ADJ
ejpam-5993	226	25	cyclic	cyclic	ADJ
ejpam-5993	226	26	sylow	sylow	NOUN
ejpam-5993	226	27	p	p	PROPN
ejpam-5993	226	28	-	-	PUNCT
ejpam-5993	226	29	subgroup293	subgroup293	PROPN
ejpam-5993	226	30	of	of	ADP
ejpam-5993	226	31	f	f	PROPN
ejpam-5993	226	32	(	(	PUNCT
ejpam-5993	226	33	h	h	NOUN
ejpam-5993	226	34	)	)	PUNCT
ejpam-5993	226	35	.	.	PUNCT
ejpam-5993	227	1	thus	thus	ADV
ejpam-5993	227	2	if	if	SCONJ
ejpam-5993	227	3	p1	p1	PROPN
ejpam-5993	227	4	/	/	SYM
ejpam-5993	227	5	n	n	PRON
ejpam-5993	227	6	is	be	AUX
ejpam-5993	227	7	maximal	maximal	ADJ
ejpam-5993	227	8	in	in	ADP
ejpam-5993	227	9	p	p	PROPN
ejpam-5993	227	10	/	/	SYM
ejpam-5993	227	11	n	n	NOUN
ejpam-5993	227	12	,	,	PUNCT
ejpam-5993	227	13	p1	p1	NOUN
ejpam-5993	227	14	is	be	AUX
ejpam-5993	227	15	maximal	maximal	ADJ
ejpam-5993	227	16	in	in	ADP
ejpam-5993	227	17	p	p	NOUN
ejpam-5993	227	18	,	,	PUNCT
ejpam-5993	227	19	so	so	ADV
ejpam-5993	227	20	p1	p1	PROPN
ejpam-5993	227	21	is	be	AUX
ejpam-5993	227	22	an	an	DET
ejpam-5993	227	23	ssh	ssh	NOUN
ejpam-5993	227	24	-	-	PUNCT
ejpam-5993	227	25	subgroup294	subgroup294	NOUN
ejpam-5993	227	26	in	in	ADP
ejpam-5993	227	27	g	g	NOUN
ejpam-5993	227	28	by	by	ADP
ejpam-5993	227	29	hypothesis	hypothesis	NOUN
ejpam-5993	227	30	,	,	PUNCT
ejpam-5993	227	31	and	and	CCONJ
ejpam-5993	227	32	p1	p1	PROPN
ejpam-5993	227	33	/	/	SYM
ejpam-5993	227	34	n	n	PROPN
ejpam-5993	227	35	is	be	AUX
ejpam-5993	227	36	ssh	ssh	NOUN
ejpam-5993	227	37	-	-	PUNCT
ejpam-5993	227	38	subgroup	subgroup	NOUN
ejpam-5993	227	39	in	in	ADP
ejpam-5993	227	40	g	g	PROPN
ejpam-5993	227	41	/	/	SYM
ejpam-5993	227	42	n	n	NOUN
ejpam-5993	227	43	by	by	ADP
ejpam-5993	227	44	lemma	lemma	PROPN
ejpam-5993	227	45	2(ii	2(ii	NUM
ejpam-5993	227	46	)	)	PUNCT
ejpam-5993	227	47	.	.	PUNCT
ejpam-5993	228	1	now	now	ADV
ejpam-5993	228	2	suppose	suppose	VERB
ejpam-5993	228	3	q295	q295	PROPN
ejpam-5993	228	4	is	be	AUX
ejpam-5993	228	5	a	a	DET
ejpam-5993	228	6	prime	prime	NOUN
ejpam-5993	228	7	different	different	ADJ
ejpam-5993	228	8	from	from	ADP
ejpam-5993	228	9	p	p	PRON
ejpam-5993	228	10	,	,	PUNCT
ejpam-5993	228	11	so	so	SCONJ
ejpam-5993	228	12	qn	qn	PROPN
ejpam-5993	228	13	/	/	SYM
ejpam-5993	228	14	n	n	PROPN
ejpam-5993	228	15	is	be	AUX
ejpam-5993	228	16	the	the	DET
ejpam-5993	228	17	sylow	sylow	NOUN
ejpam-5993	228	18	q	q	NOUN
ejpam-5993	228	19	-	-	PUNCT
ejpam-5993	228	20	subgroup	subgroup	NOUN
ejpam-5993	228	21	of	of	ADP
ejpam-5993	228	22	f	f	PROPN
ejpam-5993	228	23	(	(	PUNCT
ejpam-5993	228	24	h)/n	h)/n	PROPN
ejpam-5993	228	25	,	,	PUNCT
ejpam-5993	228	26	where	where	SCONJ
ejpam-5993	228	27	q	q	NOUN
ejpam-5993	228	28	is	be	AUX
ejpam-5993	228	29	the296	the296	NOUN
ejpam-5993	228	30	sylow	sylow	NOUN
ejpam-5993	228	31	q	q	NOUN
ejpam-5993	228	32	-	-	NOUN
ejpam-5993	228	33	subgroup	subgroup	NOUN
ejpam-5993	228	34	of	of	ADP
ejpam-5993	228	35	f	f	PROPN
ejpam-5993	228	36	(	(	PUNCT
ejpam-5993	228	37	h	h	NOUN
ejpam-5993	228	38	)	)	PUNCT
ejpam-5993	228	39	.	.	PUNCT
ejpam-5993	229	1	then	then	ADV
ejpam-5993	229	2	any	any	DET
ejpam-5993	229	3	maximal	maximal	ADJ
ejpam-5993	229	4	subgroup	subgroup	NOUN
ejpam-5993	229	5	of	of	ADP
ejpam-5993	229	6	qn	qn	PROPN
ejpam-5993	229	7	/	/	SYM
ejpam-5993	229	8	n	n	PROPN
ejpam-5993	229	9	is	be	AUX
ejpam-5993	229	10	of	of	ADP
ejpam-5993	229	11	the	the	DET
ejpam-5993	229	12	form	form	NOUN
ejpam-5993	229	13	q1n	q1n	NOUN
ejpam-5993	229	14	/	/	SYM
ejpam-5993	229	15	n	n	PROPN
ejpam-5993	229	16	,	,	PUNCT
ejpam-5993	229	17	297	297	NUM
ejpam-5993	229	18	where	where	SCONJ
ejpam-5993	229	19	q1	q1	PROPN
ejpam-5993	229	20	is	be	AUX
ejpam-5993	229	21	a	a	DET
ejpam-5993	229	22	maximal	maximal	ADJ
ejpam-5993	229	23	subgroup	subgroup	NOUN
ejpam-5993	229	24	of	of	ADP
ejpam-5993	229	25	q.	q.	PROPN
ejpam-5993	229	26	thus	thus	ADV
ejpam-5993	229	27	q1	q1	PROPN
ejpam-5993	229	28	is	be	AUX
ejpam-5993	229	29	an	an	DET
ejpam-5993	229	30	ssh	ssh	NOUN
ejpam-5993	229	31	-	-	PUNCT
ejpam-5993	229	32	subgroup	subgroup	NOUN
ejpam-5993	229	33	in	in	ADP
ejpam-5993	229	34	g	g	PROPN
ejpam-5993	229	35	by	by	ADP
ejpam-5993	229	36	hypothesis,298	hypothesis,298	PUNCT
ejpam-5993	230	1	so	so	ADV
ejpam-5993	230	2	q1n	q1n	PROPN
ejpam-5993	230	3	/	/	SYM
ejpam-5993	230	4	n	n	PROPN
ejpam-5993	230	5	is	be	AUX
ejpam-5993	230	6	an	an	DET
ejpam-5993	230	7	ssh	ssh	NOUN
ejpam-5993	230	8	-	-	PUNCT
ejpam-5993	230	9	subgroup	subgroup	NOUN
ejpam-5993	230	10	in	in	ADP
ejpam-5993	230	11	g	g	PROPN
ejpam-5993	230	12	/	/	SYM
ejpam-5993	230	13	n	n	NOUN
ejpam-5993	230	14	by	by	ADP
ejpam-5993	230	15	lemma	lemma	PROPN
ejpam-5993	230	16	2	2	PROPN
ejpam-5993	230	17	(	(	PUNCT
ejpam-5993	230	18	ii	ii	NOUN
ejpam-5993	230	19	)	)	PUNCT
ejpam-5993	230	20	.	.	PUNCT
ejpam-5993	231	1	so	so	ADV
ejpam-5993	231	2	g	g	PROPN
ejpam-5993	231	3	/	/	SYM
ejpam-5993	231	4	n	n	PROPN
ejpam-5993	231	5	and	and	CCONJ
ejpam-5993	231	6	f	f	PROPN
ejpam-5993	231	7	(	(	PUNCT
ejpam-5993	231	8	h)/n	h)/n	PROPN
ejpam-5993	231	9	satisfy299	satisfy299	PROPN
ejpam-5993	232	1	the	the	DET
ejpam-5993	232	2	hypotheses	hypothesis	NOUN
ejpam-5993	232	3	of	of	ADP
ejpam-5993	232	4	the	the	DET
ejpam-5993	232	5	theorem	theorem	NOUN
ejpam-5993	232	6	.	.	PUNCT
ejpam-5993	233	1	it	it	PRON
ejpam-5993	233	2	follows	follow	VERB
ejpam-5993	233	3	that	that	SCONJ
ejpam-5993	233	4	g	g	PROPN
ejpam-5993	233	5	/	/	SYM
ejpam-5993	233	6	n	n	CCONJ
ejpam-5993	233	7	∈	∈	NOUN
ejpam-5993	233	8	f.300	f.300	X
ejpam-5993	233	9	301	301	NUM
ejpam-5993	233	10	(	(	PUNCT
ejpam-5993	233	11	5	5	NUM
ejpam-5993	233	12	)	)	PUNCT
ejpam-5993	233	13	the	the	DET
ejpam-5993	233	14	final	final	ADJ
ejpam-5993	233	15	contradiction302	contradiction302	NOUN
ejpam-5993	233	16	by	by	ADP
ejpam-5993	233	17	(	(	PUNCT
ejpam-5993	233	18	2	2	NUM
ejpam-5993	233	19	)	)	PUNCT
ejpam-5993	233	20	and	and	CCONJ
ejpam-5993	233	21	(	(	PUNCT
ejpam-5993	233	22	4	4	NUM
ejpam-5993	233	23	)	)	PUNCT
ejpam-5993	233	24	,	,	PUNCT
ejpam-5993	233	25	f	f	PROPN
ejpam-5993	233	26	(	(	PUNCT
ejpam-5993	233	27	h	h	NOUN
ejpam-5993	233	28	)	)	PUNCT
ejpam-5993	234	1	=	=	SYM
ejpam-5993	234	2	⟨x1⟩	⟨x1⟩	PROPN
ejpam-5993	234	3	,	,	PUNCT
ejpam-5993	234	4	is	be	AUX
ejpam-5993	234	5	the	the	DET
ejpam-5993	234	6	unique	unique	ADJ
ejpam-5993	234	7	minimal	minimal	ADJ
ejpam-5993	234	8	normal	normal	ADJ
ejpam-5993	234	9	subgroup	subgroup	NOUN
ejpam-5993	234	10	of	of	ADP
ejpam-5993	234	11	g	g	PROPN
ejpam-5993	234	12	contained	contain	VERB
ejpam-5993	234	13	in303	in303	PROPN
ejpam-5993	234	14	h	h	NOUN
ejpam-5993	234	15	,	,	PUNCT
ejpam-5993	234	16	so	so	SCONJ
ejpam-5993	234	17	f	f	X
ejpam-5993	234	18	(	(	PUNCT
ejpam-5993	234	19	h	h	NOUN
ejpam-5993	234	20	)	)	PUNCT
ejpam-5993	234	21	is	be	AUX
ejpam-5993	234	22	cyclic	cyclic	ADJ
ejpam-5993	234	23	of	of	ADP
ejpam-5993	234	24	prime	prime	ADJ
ejpam-5993	234	25	order	order	NOUN
ejpam-5993	234	26	.	.	PUNCT
ejpam-5993	235	1	let	let	VERB
ejpam-5993	235	2	n	n	NOUN
ejpam-5993	235	3	=	=	SYM
ejpam-5993	235	4	f	f	PROPN
ejpam-5993	235	5	(	(	PUNCT
ejpam-5993	235	6	h	h	NOUN
ejpam-5993	235	7	)	)	PUNCT
ejpam-5993	235	8	,	,	PUNCT
ejpam-5993	235	9	we	we	PRON
ejpam-5993	235	10	show	show	VERB
ejpam-5993	235	11	that	that	SCONJ
ejpam-5993	235	12	n	n	PRON
ejpam-5993	235	13	is	be	AUX
ejpam-5993	235	14	the	the	DET
ejpam-5993	235	15	only	only	ADJ
ejpam-5993	235	16	minimal304	minimal304	PROPN
ejpam-5993	235	17	normal	normal	ADJ
ejpam-5993	235	18	subgroup	subgroup	NOUN
ejpam-5993	235	19	of	of	ADP
ejpam-5993	235	20	g.	g.	PROPN
ejpam-5993	235	21	suppose	suppose	VERB
ejpam-5993	235	22	that	that	SCONJ
ejpam-5993	235	23	l	l	PROPN
ejpam-5993	235	24	̸=	̸=	PROPN
ejpam-5993	235	25	n	n	PART
ejpam-5993	235	26	is	be	AUX
ejpam-5993	235	27	another	another	DET
ejpam-5993	235	28	minimal	minimal	ADJ
ejpam-5993	235	29	normal	normal	ADJ
ejpam-5993	235	30	subgroup	subgroup	NOUN
ejpam-5993	235	31	of	of	ADP
ejpam-5993	235	32	g,305	g,305	NOUN
ejpam-5993	235	33	and	and	CCONJ
ejpam-5993	235	34	consider	consider	VERB
ejpam-5993	235	35	nl	nl	NOUN
ejpam-5993	235	36	/	/	SYM
ejpam-5993	235	37	l	l	NOUN
ejpam-5993	235	38	normal	normal	ADJ
ejpam-5993	235	39	subgroup	subgroup	NOUN
ejpam-5993	235	40	of	of	ADP
ejpam-5993	235	41	g	g	PROPN
ejpam-5993	235	42	/	/	SYM
ejpam-5993	235	43	l.	l.	PROPN
ejpam-5993	236	1	since306	since306	PROPN
ejpam-5993	237	1	(	(	PUNCT
ejpam-5993	237	2	g	g	NOUN
ejpam-5993	237	3	/	/	SYM
ejpam-5993	237	4	l)/(nl	l)/(nl	NOUN
ejpam-5993	237	5	/	/	SYM
ejpam-5993	237	6	l	l	NOUN
ejpam-5993	237	7	)	)	PUNCT
ejpam-5993	237	8	∼=	∼=	ADP
ejpam-5993	237	9	g	g	NOUN
ejpam-5993	237	10	/	/	SYM
ejpam-5993	237	11	nl	nl	NOUN
ejpam-5993	237	12	∼=	∼=	PROPN
ejpam-5993	237	13	(	(	PUNCT
ejpam-5993	237	14	g	g	NOUN
ejpam-5993	237	15	/	/	SYM
ejpam-5993	237	16	n)/(nl	n)/(nl	NOUN
ejpam-5993	237	17	/	/	SYM
ejpam-5993	237	18	n),307	n),307	NOUN
ejpam-5993	237	19	and	and	CCONJ
ejpam-5993	237	20	g	g	NOUN
ejpam-5993	237	21	/	/	SYM
ejpam-5993	237	22	n	n	NOUN
ejpam-5993	237	23	∈	∈	NOUN
ejpam-5993	237	24	f	f	X
ejpam-5993	237	25	,	,	PUNCT
ejpam-5993	237	26	we	we	PRON
ejpam-5993	237	27	have	have	AUX
ejpam-5993	237	28	(	(	PUNCT
ejpam-5993	237	29	g	g	NOUN
ejpam-5993	237	30	/	/	SYM
ejpam-5993	237	31	l)/(nl	l)/(nl	NOUN
ejpam-5993	237	32	/	/	SYM
ejpam-5993	237	33	l	l	NOUN
ejpam-5993	237	34	)	)	PUNCT
ejpam-5993	237	35	∈	∈	PROPN
ejpam-5993	237	36	f.	f.	PROPN
ejpam-5993	237	37	notice	notice	VERB
ejpam-5993	237	38	that	that	SCONJ
ejpam-5993	237	39	n	n	NOUN
ejpam-5993	237	40	∩	∩	ADJ
ejpam-5993	237	41	l	l	NOUN
ejpam-5993	237	42	=	=	SYM
ejpam-5993	237	43	1	1	NUM
ejpam-5993	237	44	,	,	PUNCT
ejpam-5993	237	45	hence	hence	ADV
ejpam-5993	237	46	(	(	PUNCT
ejpam-5993	237	47	nl	nl	PROPN
ejpam-5993	237	48	/	/	SYM
ejpam-5993	237	49	l	l	NOUN
ejpam-5993	237	50	)	)	PUNCT
ejpam-5993	237	51	∼=	∼=	NOUN
ejpam-5993	237	52	n	n	PRON
ejpam-5993	237	53	.308	.308	NUM
ejpam-5993	237	54	and	and	CCONJ
ejpam-5993	237	55	so	so	ADV
ejpam-5993	237	56	,	,	PUNCT
ejpam-5993	237	57	the	the	DET
ejpam-5993	237	58	only	only	ADJ
ejpam-5993	237	59	maximal	maximal	ADJ
ejpam-5993	237	60	subgroup	subgroup	NOUN
ejpam-5993	237	61	of	of	ADP
ejpam-5993	237	62	the	the	DET
ejpam-5993	237	63	non	non	ADJ
ejpam-5993	237	64	-	-	ADJ
ejpam-5993	237	65	cyclic	cyclic	ADJ
ejpam-5993	237	66	sylow	sylow	NOUN
ejpam-5993	237	67	subgroup	subgroup	NOUN
ejpam-5993	237	68	of	of	ADP
ejpam-5993	237	69	f	f	PROPN
ejpam-5993	237	70	(	(	PUNCT
ejpam-5993	237	71	nl	nl	PROPN
ejpam-5993	237	72	/	/	SYM
ejpam-5993	237	73	l	l	NOUN
ejpam-5993	237	74	)	)	PUNCT
ejpam-5993	238	1	=	=	NOUN
ejpam-5993	238	2	309	309	NUM
ejpam-5993	238	3	nl	nl	NOUN
ejpam-5993	238	4	/	/	SYM
ejpam-5993	238	5	l	l	NOUN
ejpam-5993	238	6	is	be	AUX
ejpam-5993	238	7	trivial	trivial	ADJ
ejpam-5993	238	8	subgroup	subgroup	NOUN
ejpam-5993	238	9	,	,	PUNCT
ejpam-5993	238	10	which	which	PRON
ejpam-5993	238	11	is	be	AUX
ejpam-5993	238	12	an	an	DET
ejpam-5993	238	13	ssh	ssh	NOUN
ejpam-5993	238	14	-	-	PUNCT
ejpam-5993	238	15	subgroup	subgroup	NOUN
ejpam-5993	238	16	in	in	ADP
ejpam-5993	238	17	g	g	PROPN
ejpam-5993	238	18	/	/	SYM
ejpam-5993	238	19	l.	l.	NOUN
ejpam-5993	238	20	by	by	ADP
ejpam-5993	238	21	the	the	DET
ejpam-5993	238	22	minimal	minimal	ADJ
ejpam-5993	238	23	choice	choice	NOUN
ejpam-5993	238	24	of310	of310	PUNCT
ejpam-5993	238	25	g	g	NOUN
ejpam-5993	238	26	,	,	PUNCT
ejpam-5993	238	27	g	g	NOUN
ejpam-5993	238	28	/	/	SYM
ejpam-5993	238	29	l	l	NOUN
ejpam-5993	238	30	∈	∈	PROPN
ejpam-5993	238	31	f.	f.	PROPN
ejpam-5993	239	1	so	so	ADV
ejpam-5993	239	2	,	,	PUNCT
ejpam-5993	239	3	g	g	PROPN
ejpam-5993	239	4	∈	∈	PROPN
ejpam-5993	239	5	f	f	X
ejpam-5993	239	6	,	,	PUNCT
ejpam-5993	239	7	a	a	DET
ejpam-5993	239	8	contradiction	contradiction	NOUN
ejpam-5993	239	9	.	.	PUNCT
ejpam-5993	240	1	thus	thus	ADV
ejpam-5993	240	2	,	,	PUNCT
ejpam-5993	240	3	n	n	PROPN
ejpam-5993	240	4	=	=	SYM
ejpam-5993	240	5	f	f	PROPN
ejpam-5993	240	6	(	(	PUNCT
ejpam-5993	240	7	h	h	NOUN
ejpam-5993	240	8	)	)	PUNCT
ejpam-5993	240	9	=	=	NOUN
ejpam-5993	240	10	⟨x1⟩	⟨x1⟩	NOUN
ejpam-5993	240	11	is	be	AUX
ejpam-5993	240	12	unique	unique	ADJ
ejpam-5993	240	13	minimal311	minimal311	PROPN
ejpam-5993	240	14	normal	normal	ADJ
ejpam-5993	240	15	in	in	ADP
ejpam-5993	240	16	g.	g.	PROPN
ejpam-5993	240	17	by	by	ADP
ejpam-5993	240	18	(	(	PUNCT
ejpam-5993	240	19	1	1	NUM
ejpam-5993	240	20	)	)	PUNCT
ejpam-5993	240	21	,	,	PUNCT
ejpam-5993	240	22	φ(g	φ(g	PROPN
ejpam-5993	240	23	)	)	PUNCT
ejpam-5993	240	24	=	=	SYM
ejpam-5993	241	1	⟨x1⟩	⟨x1⟩	PROPN
ejpam-5993	241	2	∩	∩	NOUN
ejpam-5993	241	3	φ(g	φ(g	NOUN
ejpam-5993	241	4	)	)	PUNCT
ejpam-5993	241	5	=	=	SYM
ejpam-5993	241	6	1	1	X
ejpam-5993	241	7	.	.	PUNCT
ejpam-5993	242	1	let	let	VERB
ejpam-5993	242	2	m	m	PRON
ejpam-5993	242	3	be	be	AUX
ejpam-5993	242	4	maximal	maximal	ADJ
ejpam-5993	242	5	subgroup	subgroup	NOUN
ejpam-5993	242	6	of	of	ADP
ejpam-5993	242	7	g312	g312	PROPN
ejpam-5993	242	8	such	such	ADJ
ejpam-5993	242	9	that	that	DET
ejpam-5993	242	10	⟨x1⟩	⟨x1⟩	PROPN
ejpam-5993	243	1	⊈	⊈	PROPN
ejpam-5993	243	2	m	m	NOUN
ejpam-5993	243	3	.	.	PUNCT
ejpam-5993	244	1	then	then	ADV
ejpam-5993	244	2	g	g	PROPN
ejpam-5993	244	3	=	=	SYM
ejpam-5993	244	4	⟨x1⟩m	⟨x1⟩m	PROPN
ejpam-5993	244	5	and	and	CCONJ
ejpam-5993	244	6	⟨x1⟩	⟨x1⟩	PROPN
ejpam-5993	244	7	∩	∩	NOUN
ejpam-5993	244	8	m	m	NOUN
ejpam-5993	244	9	=	=	NOUN
ejpam-5993	244	10	1	1	X
ejpam-5993	244	11	.	.	PUNCT
ejpam-5993	245	1	if	if	SCONJ
ejpam-5993	245	2	⟨x1⟩	⟨x1⟩	PROPN
ejpam-5993	245	3	<	<	X
ejpam-5993	245	4	cg(⟨x1⟩	cg(⟨x1⟩	NOUN
ejpam-5993	245	5	)	)	PUNCT
ejpam-5993	245	6	,	,	PUNCT
ejpam-5993	245	7	then313	then313	PROPN
ejpam-5993	245	8	1	1	NUM
ejpam-5993	245	9	<	<	X
ejpam-5993	245	10	cg(⟨x1⟩	cg(⟨x1⟩	NOUN
ejpam-5993	245	11	)	)	PUNCT
ejpam-5993	245	12	∩	∩	NOUN
ejpam-5993	245	13	m	m	VERB
ejpam-5993	245	14	⩽	⩽	ADJ
ejpam-5993	245	15	⟨x1⟩m	⟨x1⟩m	PROPN
ejpam-5993	245	16	=	=	PUNCT
ejpam-5993	245	17	g.	g.	NOUN
ejpam-5993	245	18	by	by	ADP
ejpam-5993	245	19	the	the	DET
ejpam-5993	245	20	unique	unique	ADJ
ejpam-5993	245	21	minimal	minimal	ADJ
ejpam-5993	245	22	normality	normality	NOUN
ejpam-5993	245	23	of	of	ADP
ejpam-5993	245	24	⟨x1⟩	⟨x1⟩	PROPN
ejpam-5993	245	25	,	,	PUNCT
ejpam-5993	245	26	⟨x1⟩	⟨x1⟩	PROPN
ejpam-5993	245	27	⩽314	⩽314	NOUN
ejpam-5993	245	28	cg(⟨x1⟩	cg(⟨x1⟩	X
ejpam-5993	245	29	)	)	PUNCT
ejpam-5993	246	1	∩m	∩m	PROPN
ejpam-5993	246	2	⩽	⩽	PROPN
ejpam-5993	246	3	m	m	ADV
ejpam-5993	246	4	,	,	PUNCT
ejpam-5993	246	5	then	then	ADV
ejpam-5993	246	6	g	g	PROPN
ejpam-5993	246	7	=	=	SYM
ejpam-5993	246	8	⟨x1⟩m	⟨x1⟩m	PROPN
ejpam-5993	246	9	=	=	PUNCT
ejpam-5993	246	10	m	m	PROPN
ejpam-5993	246	11	,	,	PUNCT
ejpam-5993	246	12	a	a	DET
ejpam-5993	246	13	contradiction	contradiction	NOUN
ejpam-5993	246	14	.	.	PUNCT
ejpam-5993	247	1	thus	thus	ADV
ejpam-5993	247	2	,	,	PUNCT
ejpam-5993	247	3	⟨x1⟩	⟨x1⟩	PROPN
ejpam-5993	247	4	=	=	NOUN
ejpam-5993	247	5	cg(⟨x1⟩	cg(⟨x1⟩	PRON
ejpam-5993	247	6	)	)	PUNCT
ejpam-5993	247	7	.	.	PUNCT
ejpam-5993	248	1	it315	it315	PROPN
ejpam-5993	248	2	follows	follow	VERB
ejpam-5993	248	3	that	that	PRON
ejpam-5993	248	4	g/⟨x1⟩	g/⟨x1⟩	PROPN
ejpam-5993	248	5	=	=	PUNCT
ejpam-5993	248	6	g	g	NOUN
ejpam-5993	248	7	/	/	SYM
ejpam-5993	248	8	cg(⟨x1⟩	cg(⟨x1⟩	PRON
ejpam-5993	248	9	)	)	PUNCT
ejpam-5993	248	10	⊆	⊆	NUM
ejpam-5993	248	11	aut(⟨x1⟩	aut(⟨x1⟩	PRON
ejpam-5993	248	12	)	)	PUNCT
ejpam-5993	248	13	is	be	AUX
ejpam-5993	248	14	cyclic	cyclic	ADJ
ejpam-5993	248	15	of	of	ADP
ejpam-5993	248	16	order	order	NOUN
ejpam-5993	248	17	dividing	divide	VERB
ejpam-5993	248	18	p	p	NOUN
ejpam-5993	248	19	−	−	PROPN
ejpam-5993	248	20	1	1	NUM
ejpam-5993	248	21	and	and	CCONJ
ejpam-5993	248	22	so316	so316	PROPN
ejpam-5993	248	23	g/⟨x1⟩	g/⟨x1⟩	NOUN
ejpam-5993	248	24	)	)	PUNCT
ejpam-5993	249	1	∈	∈	PROPN
ejpam-5993	249	2	u.	u.	PROPN
ejpam-5993	249	3	hence	hence	ADV
ejpam-5993	249	4	,	,	PUNCT
ejpam-5993	249	5	g	g	PROPN
ejpam-5993	249	6	∈	∈	PROPN
ejpam-5993	249	7	u	u	NOUN
ejpam-5993	249	8	⊆	⊆	NUM
ejpam-5993	249	9	f	f	NUM
ejpam-5993	249	10	,	,	PUNCT
ejpam-5993	249	11	the	the	DET
ejpam-5993	249	12	final	final	ADJ
ejpam-5993	249	13	contradiction.317	contradiction.317	NOUN
ejpam-5993	249	14	in	in	ADP
ejpam-5993	249	15	the	the	DET
ejpam-5993	249	16	following	follow	VERB
ejpam-5993	249	17	remark	remark	NOUN
ejpam-5993	249	18	,	,	PUNCT
ejpam-5993	249	19	we	we	PRON
ejpam-5993	249	20	will	will	AUX
ejpam-5993	249	21	mention	mention	VERB
ejpam-5993	249	22	some	some	DET
ejpam-5993	249	23	cases.318	cases.318	PROPN
ejpam-5993	249	24	remark	remark	VERB
ejpam-5993	249	25	1	1	NUM
ejpam-5993	249	26	.	.	PUNCT
ejpam-5993	250	1	(	(	PUNCT
ejpam-5993	250	2	i	i	NOUN
ejpam-5993	250	3	)	)	PUNCT
ejpam-5993	250	4	theorem	theorem	VERB
ejpam-5993	250	5	3	3	NUM
ejpam-5993	250	6	is	be	AUX
ejpam-5993	250	7	not	not	PART
ejpam-5993	250	8	true	true	ADJ
ejpam-5993	250	9	if	if	SCONJ
ejpam-5993	250	10	we	we	PRON
ejpam-5993	250	11	omit	omit	VERB
ejpam-5993	250	12	the	the	DET
ejpam-5993	250	13	solvability	solvability	NOUN
ejpam-5993	250	14	of	of	ADP
ejpam-5993	250	15	h.	h.	PROPN
ejpam-5993	250	16	set	set	VERB
ejpam-5993	250	17	g	g	PROPN
ejpam-5993	250	18	=	=	PUNCT
ejpam-5993	250	19	n	n	PROPN
ejpam-5993	250	20	×m	×m	NOUN
ejpam-5993	250	21	,	,	PUNCT
ejpam-5993	250	22	319	319	NUM
ejpam-5993	250	23	where	where	SCONJ
ejpam-5993	250	24	n	n	PROPN
ejpam-5993	250	25	=	=	SYM
ejpam-5993	250	26	sl(2	sl(2	PROPN
ejpam-5993	250	27	,	,	PUNCT
ejpam-5993	250	28	5	5	NUM
ejpam-5993	250	29	)	)	PUNCT
ejpam-5993	250	30	,	,	PUNCT
ejpam-5993	250	31	the	the	DET
ejpam-5993	250	32	special	special	ADJ
ejpam-5993	250	33	linear	linear	PROPN
ejpam-5993	250	34	group	group	NOUN
ejpam-5993	250	35	of	of	ADP
ejpam-5993	250	36	degree	degree	NOUN
ejpam-5993	250	37	2	2	NUM
ejpam-5993	250	38	and	and	CCONJ
ejpam-5993	250	39	m	m	PROPN
ejpam-5993	250	40	∈	∈	PROPN
ejpam-5993	251	1	u.	u.	NOUN
ejpam-5993	251	2	then	then	ADV
ejpam-5993	251	3	f	f	PROPN
ejpam-5993	251	4	(	(	PUNCT
ejpam-5993	251	5	n	n	CCONJ
ejpam-5993	251	6	)	)	PUNCT
ejpam-5993	251	7	=	=	NOUN
ejpam-5993	251	8	320	320	NUM
ejpam-5993	251	9	z(n	z(n	NOUN
ejpam-5993	251	10	)	)	PUNCT
ejpam-5993	251	11	∼=	∼=	PROPN
ejpam-5993	251	12	z2	z2	NOUN
ejpam-5993	251	13	and	and	CCONJ
ejpam-5993	251	14	g	g	NOUN
ejpam-5993	251	15	/	/	SYM
ejpam-5993	251	16	n	n	PRON
ejpam-5993	251	17	∼=	∼=	PART
ejpam-5993	251	18	m	m	NOUN
ejpam-5993	251	19	∈	∈	NOUN
ejpam-5993	251	20	u	u	NOUN
ejpam-5993	251	21	,	,	PUNCT
ejpam-5993	251	22	but	but	CCONJ
ejpam-5993	251	23	g	g	NOUN
ejpam-5993	251	24	does	do	AUX
ejpam-5993	251	25	not	not	PART
ejpam-5993	251	26	belong	belong	VERB
ejpam-5993	251	27	to	to	ADP
ejpam-5993	251	28	u.321	u.321	PROPN
ejpam-5993	251	29	(	(	PUNCT
ejpam-5993	251	30	ii	ii	NOUN
ejpam-5993	251	31	)	)	PUNCT
ejpam-5993	251	32	theorem	theorem	NOUN
ejpam-5993	251	33	3	3	NUM
ejpam-5993	251	34	is	be	AUX
ejpam-5993	251	35	not	not	PART
ejpam-5993	251	36	true	true	ADJ
ejpam-5993	251	37	for	for	ADP
ejpam-5993	251	38	saturated	saturated	ADJ
ejpam-5993	251	39	formations	formation	NOUN
ejpam-5993	251	40	f	f	NOUN
ejpam-5993	251	41	which	which	PRON
ejpam-5993	251	42	do	do	AUX
ejpam-5993	251	43	not	not	PART
ejpam-5993	251	44	contain	contain	VERB
ejpam-5993	251	45	u.	u.	ADV
ejpam-5993	251	46	for322	for322	PROPN
ejpam-5993	251	47	example	example	NOUN
ejpam-5993	251	48	,	,	PUNCT
ejpam-5993	251	49	if	if	SCONJ
ejpam-5993	251	50	f	f	PROPN
ejpam-5993	251	51	is	be	AUX
ejpam-5993	251	52	the	the	DET
ejpam-5993	251	53	saturated	saturate	VERB
ejpam-5993	251	54	formation	formation	NOUN
ejpam-5993	251	55	of	of	ADP
ejpam-5993	251	56	all	all	DET
ejpam-5993	251	57	nilpotent	nilpotent	ADJ
ejpam-5993	251	58	groups	group	NOUN
ejpam-5993	251	59	,	,	PUNCT
ejpam-5993	251	60	then	then	ADV
ejpam-5993	251	61	the	the	DET
ejpam-5993	251	62	symmetric323	symmetric323	PROPN
ejpam-5993	251	63	group	group	NOUN
ejpam-5993	251	64	s3	s3	PROPN
ejpam-5993	251	65	of	of	ADP
ejpam-5993	251	66	degree	degree	NOUN
ejpam-5993	251	67	three	three	NUM
ejpam-5993	251	68	is	be	AUX
ejpam-5993	251	69	a	a	DET
ejpam-5993	251	70	counterexample.324	counterexample.324	NOUN
ejpam-5993	251	71	theorem	theorem	NOUN
ejpam-5993	251	72	4	4	X
ejpam-5993	251	73	.	.	PUNCT
ejpam-5993	252	1	let	let	VERB
ejpam-5993	252	2	g	g	PRON
ejpam-5993	252	3	be	be	AUX
ejpam-5993	252	4	a	a	DET
ejpam-5993	252	5	group	group	NOUN
ejpam-5993	252	6	with	with	ADP
ejpam-5993	252	7	a	a	DET
ejpam-5993	252	8	normal	normal	ADJ
ejpam-5993	252	9	subgroup	subgroup	NOUN
ejpam-5993	252	10	h	h	NOUN
ejpam-5993	252	11	such	such	ADJ
ejpam-5993	252	12	that	that	SCONJ
ejpam-5993	252	13	g	g	PROPN
ejpam-5993	252	14	/	/	SYM
ejpam-5993	252	15	h	h	PROPN
ejpam-5993	252	16	is	be	AUX
ejpam-5993	252	17	supersolvable.325	supersolvable.325	PROPN
ejpam-5993	252	18	if	if	SCONJ
ejpam-5993	252	19	all	all	DET
ejpam-5993	252	20	maximal	maximal	ADJ
ejpam-5993	252	21	subgroups	subgroup	NOUN
ejpam-5993	252	22	of	of	ADP
ejpam-5993	252	23	the	the	DET
ejpam-5993	252	24	non	non	ADJ
ejpam-5993	252	25	-	-	ADJ
ejpam-5993	252	26	cyclic	cyclic	ADJ
ejpam-5993	252	27	sylow	sylow	NOUN
ejpam-5993	252	28	subgroups	subgroup	NOUN
ejpam-5993	252	29	of	of	ADP
ejpam-5993	252	30	f	f	PROPN
ejpam-5993	252	31	∗(h	∗(h	PROPN
ejpam-5993	252	32	)	)	PUNCT
ejpam-5993	252	33	are	be	AUX
ejpam-5993	252	34	ssh	ssh	NOUN
ejpam-5993	252	35	-	-	PUNCT
ejpam-5993	252	36	subgroups326	subgroups326	PROPN
ejpam-5993	252	37	of	of	ADP
ejpam-5993	252	38	g	g	NOUN
ejpam-5993	252	39	,	,	PUNCT
ejpam-5993	252	40	then	then	ADV
ejpam-5993	252	41	g	g	PROPN
ejpam-5993	252	42	is	be	AUX
ejpam-5993	252	43	supersolvable.327	supersolvable.327	ADJ
ejpam-5993	252	44	a.	a.	NOUN
ejpam-5993	252	45	s.	s.	PROPN
ejpam-5993	252	46	allehyani	allehyani	PROPN
ejpam-5993	252	47	/	/	SYM
ejpam-5993	252	48	eur	eur	PROPN
ejpam-5993	252	49	.	.	PUNCT
ejpam-5993	253	1	j.	j.	PROPN
ejpam-5993	253	2	pure	pure	PROPN
ejpam-5993	253	3	appl	appl	PROPN
ejpam-5993	253	4	.	.	PROPN
ejpam-5993	253	5	math	math	PROPN
ejpam-5993	253	6	,	,	PUNCT
ejpam-5993	253	7	18	18	NUM
ejpam-5993	253	8	(	(	PUNCT
ejpam-5993	253	9	2	2	NUM
ejpam-5993	253	10	)	)	PUNCT
ejpam-5993	253	11	(	(	PUNCT
ejpam-5993	253	12	2025	2025	NUM
ejpam-5993	253	13	)	)	PUNCT
ejpam-5993	253	14	,	,	PUNCT
ejpam-5993	253	15	5993	5993	NUM
ejpam-5993	253	16	10	10	NUM
ejpam-5993	253	17	of	of	ADP
ejpam-5993	253	18	13	13	NUM
ejpam-5993	253	19	proof	proof	NOUN
ejpam-5993	253	20	.	.	PUNCT
ejpam-5993	253	21	suppose	suppose	VERB
ejpam-5993	253	22	that	that	SCONJ
ejpam-5993	253	23	the	the	DET
ejpam-5993	253	24	theorem	theorem	NOUN
ejpam-5993	253	25	is	be	AUX
ejpam-5993	253	26	false	false	ADJ
ejpam-5993	253	27	and	and	CCONJ
ejpam-5993	253	28	assume	assume	VERB
ejpam-5993	253	29	that	that	SCONJ
ejpam-5993	253	30	g	g	PROPN
ejpam-5993	253	31	is	be	AUX
ejpam-5993	253	32	a	a	DET
ejpam-5993	253	33	counterexample	counterexample	NOUN
ejpam-5993	253	34	of328	of328	ADP
ejpam-5993	253	35	minimal	minimal	ADJ
ejpam-5993	253	36	order	order	NOUN
ejpam-5993	253	37	.	.	PUNCT
ejpam-5993	254	1	then	then	ADV
ejpam-5993	254	2	we	we	PRON
ejpam-5993	254	3	have:329	have:329	X
ejpam-5993	254	4	330	330	NUM
ejpam-5993	254	5	(	(	PUNCT
ejpam-5993	254	6	1	1	NUM
ejpam-5993	254	7	)	)	PUNCT
ejpam-5993	254	8	every	every	DET
ejpam-5993	254	9	proper	proper	ADJ
ejpam-5993	254	10	normal	normal	ADJ
ejpam-5993	254	11	subgroup	subgroup	NOUN
ejpam-5993	254	12	of	of	ADP
ejpam-5993	254	13	g	g	PROPN
ejpam-5993	254	14	containing	contain	VERB
ejpam-5993	254	15	f	f	PROPN
ejpam-5993	254	16	∗(h	∗(h	PROPN
ejpam-5993	254	17	)	)	PUNCT
ejpam-5993	254	18	is	be	AUX
ejpam-5993	254	19	supersolvable.331	supersolvable.331	ADJ
ejpam-5993	254	20	if	if	SCONJ
ejpam-5993	254	21	n	n	PRON
ejpam-5993	254	22	is	be	AUX
ejpam-5993	254	23	a	a	DET
ejpam-5993	254	24	proper	proper	ADJ
ejpam-5993	254	25	normal	normal	ADJ
ejpam-5993	254	26	subgroup	subgroup	NOUN
ejpam-5993	254	27	of	of	ADP
ejpam-5993	254	28	g	g	PROPN
ejpam-5993	254	29	containing	contain	VERB
ejpam-5993	254	30	f	f	PROPN
ejpam-5993	254	31	∗(h	∗(h	PROPN
ejpam-5993	254	32	)	)	PUNCT
ejpam-5993	254	33	,	,	PUNCT
ejpam-5993	254	34	we	we	PRON
ejpam-5993	254	35	have	have	VERB
ejpam-5993	254	36	n	n	NUM
ejpam-5993	254	37	/	/	SYM
ejpam-5993	254	38	n	n	CCONJ
ejpam-5993	254	39	∩h	∩h	NOUN
ejpam-5993	254	40	∼=	∼=	PROPN
ejpam-5993	254	41	nh	nh	PROPN
ejpam-5993	254	42	/	/	SYM
ejpam-5993	254	43	h	h	NOUN
ejpam-5993	254	44	is332	is332	NOUN
ejpam-5993	254	45	supersolvable	supersolvable	ADJ
ejpam-5993	254	46	as	as	ADP
ejpam-5993	254	47	nh	nh	PROPN
ejpam-5993	254	48	/	/	SYM
ejpam-5993	254	49	h	h	NOUN
ejpam-5993	254	50	⩽	⩽	NOUN
ejpam-5993	254	51	g	g	PROPN
ejpam-5993	254	52	/	/	SYM
ejpam-5993	254	53	h	h	NOUN
ejpam-5993	254	54	which	which	PRON
ejpam-5993	254	55	is	be	AUX
ejpam-5993	254	56	supersolvable	supersolvable	ADJ
ejpam-5993	254	57	.	.	PUNCT
ejpam-5993	255	1	by	by	ADP
ejpam-5993	255	2	lemma	lemma	PROPN
ejpam-5993	255	3	8((i	8((i	PROPN
ejpam-5993	255	4	)	)	PUNCT
ejpam-5993	255	5	and	and	CCONJ
ejpam-5993	255	6	(	(	PUNCT
ejpam-5993	255	7	ii)),333	ii)),333	NOUN
ejpam-5993	255	8	f	f	PROPN
ejpam-5993	255	9	∗(h	∗(h	PROPN
ejpam-5993	255	10	)	)	PUNCT
ejpam-5993	256	1	=	=	SYM
ejpam-5993	256	2	f	f	PROPN
ejpam-5993	256	3	∗(f	∗(f	PROPN
ejpam-5993	256	4	∗(h	∗(h	PROPN
ejpam-5993	256	5	)	)	PUNCT
ejpam-5993	256	6	)	)	PUNCT
ejpam-5993	257	1	⩽	⩽	PROPN
ejpam-5993	257	2	f	f	PROPN
ejpam-5993	257	3	∗(h	∗(h	PROPN
ejpam-5993	257	4	∩n	∩n	PROPN
ejpam-5993	257	5	)	)	PUNCT
ejpam-5993	258	1	⩽	⩽	NOUN
ejpam-5993	259	1	f	f	PROPN
ejpam-5993	259	2	∗(h),334	∗(h),334	ADJ
ejpam-5993	260	1	so	so	ADV
ejpam-5993	260	2	,	,	PUNCT
ejpam-5993	260	3	f	f	PROPN
ejpam-5993	260	4	∗(h	∗(h	PROPN
ejpam-5993	260	5	)	)	PUNCT
ejpam-5993	260	6	=	=	SYM
ejpam-5993	261	1	f	f	PROPN
ejpam-5993	261	2	∗(h	∗(h	PROPN
ejpam-5993	261	3	∩n	∩n	PROPN
ejpam-5993	261	4	)	)	PUNCT
ejpam-5993	261	5	.	.	PUNCT
ejpam-5993	262	1	then	then	ADV
ejpam-5993	262	2	all	all	DET
ejpam-5993	262	3	maximal	maximal	ADJ
ejpam-5993	262	4	subgroups	subgroup	NOUN
ejpam-5993	262	5	of	of	ADP
ejpam-5993	262	6	the	the	DET
ejpam-5993	262	7	non	non	ADJ
ejpam-5993	262	8	-	-	ADJ
ejpam-5993	262	9	cyclic	cyclic	ADJ
ejpam-5993	262	10	sylow	sylow	NOUN
ejpam-5993	262	11	subgroups335	subgroups335	PROPN
ejpam-5993	262	12	of	of	ADP
ejpam-5993	262	13	f	f	PROPN
ejpam-5993	262	14	∗(h	∗(h	PROPN
ejpam-5993	262	15	∩	∩	NOUN
ejpam-5993	262	16	n	n	CCONJ
ejpam-5993	262	17	)	)	PUNCT
ejpam-5993	262	18	(	(	PUNCT
ejpam-5993	262	19	i.	i.	PROPN
ejpam-5993	262	20	e.	e.	PROPN
ejpam-5993	262	21	of	of	ADP
ejpam-5993	262	22	f	f	PROPN
ejpam-5993	262	23	∗(h	∗(h	PROPN
ejpam-5993	262	24	)	)	PUNCT
ejpam-5993	262	25	)	)	PUNCT
ejpam-5993	262	26	are	be	AUX
ejpam-5993	262	27	ssh	ssh	NOUN
ejpam-5993	262	28	-	-	PUNCT
ejpam-5993	262	29	subgroups	subgroup	NOUN
ejpam-5993	262	30	in	in	ADP
ejpam-5993	262	31	g.	g.	PROPN
ejpam-5993	262	32	thus	thus	ADV
ejpam-5993	262	33	,	,	PUNCT
ejpam-5993	262	34	all	all	PRON
ejpam-5993	262	35	maximal	maximal	ADJ
ejpam-5993	262	36	subgroups336	subgroups336	PROPN
ejpam-5993	262	37	of	of	ADP
ejpam-5993	262	38	the	the	DET
ejpam-5993	262	39	non	non	ADJ
ejpam-5993	262	40	-	-	ADJ
ejpam-5993	262	41	cyclic	cyclic	ADJ
ejpam-5993	262	42	sylow	sylow	NOUN
ejpam-5993	262	43	subgroups	subgroup	NOUN
ejpam-5993	262	44	of	of	ADP
ejpam-5993	262	45	f	f	PROPN
ejpam-5993	262	46	∗(h	∗(h	PROPN
ejpam-5993	262	47	∩n	∩n	PROPN
ejpam-5993	262	48	)	)	PUNCT
ejpam-5993	262	49	(	(	PUNCT
ejpam-5993	262	50	i.	i.	PROPN
ejpam-5993	262	51	e.	e.	PROPN
ejpam-5993	262	52	of	of	ADP
ejpam-5993	262	53	f	f	PROPN
ejpam-5993	262	54	∗(h	∗(h	PROPN
ejpam-5993	262	55	)	)	PUNCT
ejpam-5993	262	56	)	)	PUNCT
ejpam-5993	263	1	are	be	AUX
ejpam-5993	263	2	ssh	ssh	NOUN
ejpam-5993	263	3	-	-	PUNCT
ejpam-5993	263	4	subgroups	subgroup	NOUN
ejpam-5993	263	5	in337	in337	ADJ
ejpam-5993	263	6	n	n	VERB
ejpam-5993	263	7	by	by	ADP
ejpam-5993	263	8	lemma	lemma	PROPN
ejpam-5993	263	9	2(ii	2(ii	NUM
ejpam-5993	263	10	)	)	PUNCT
ejpam-5993	263	11	.	.	PUNCT
ejpam-5993	264	1	so	so	ADV
ejpam-5993	264	2	,	,	PUNCT
ejpam-5993	264	3	we	we	PRON
ejpam-5993	264	4	have	have	VERB
ejpam-5993	264	5	n	n	PRON
ejpam-5993	264	6	,	,	PUNCT
ejpam-5993	264	7	h	h	NOUN
ejpam-5993	264	8	∩	∩	NOUN
ejpam-5993	264	9	n	n	AUX
ejpam-5993	264	10	satisfy	satisfy	VERB
ejpam-5993	264	11	the	the	DET
ejpam-5993	264	12	hypothesis	hypothesis	NOUN
ejpam-5993	264	13	of	of	ADP
ejpam-5993	264	14	the	the	DET
ejpam-5993	264	15	theorem	theorem	NOUN
ejpam-5993	264	16	.	.	PUNCT
ejpam-5993	265	1	the338	the338	ADJ
ejpam-5993	265	2	minimality	minimality	NOUN
ejpam-5993	265	3	of	of	ADP
ejpam-5993	265	4	g	g	PROPN
ejpam-5993	265	5	implies	imply	VERB
ejpam-5993	265	6	that	that	SCONJ
ejpam-5993	265	7	n	n	X
ejpam-5993	265	8	is	be	AUX
ejpam-5993	265	9	supersolvable.339	supersolvable.339	PRON
ejpam-5993	265	10	340	340	NUM
ejpam-5993	265	11	(	(	PUNCT
ejpam-5993	265	12	2	2	NUM
ejpam-5993	265	13	)	)	PUNCT
ejpam-5993	265	14	h	h	NOUN
ejpam-5993	265	15	=	=	SYM
ejpam-5993	265	16	g	g	NOUN
ejpam-5993	265	17	,	,	PUNCT
ejpam-5993	265	18	and	and	CCONJ
ejpam-5993	265	19	f	f	PROPN
ejpam-5993	265	20	∗(h	∗(h	PROPN
ejpam-5993	265	21	)	)	PUNCT
ejpam-5993	265	22	=	=	SYM
ejpam-5993	265	23	f	f	PROPN
ejpam-5993	265	24	(	(	PUNCT
ejpam-5993	265	25	h	h	NOUN
ejpam-5993	265	26	)	)	PUNCT
ejpam-5993	265	27	<	<	X
ejpam-5993	266	1	g341	g341	PROPN
ejpam-5993	266	2	if	if	SCONJ
ejpam-5993	266	3	h	h	PRON
ejpam-5993	266	4	<	<	X
ejpam-5993	266	5	g	g	PROPN
ejpam-5993	266	6	,	,	PUNCT
ejpam-5993	266	7	then	then	ADV
ejpam-5993	266	8	h	h	NOUN
ejpam-5993	266	9	is	be	AUX
ejpam-5993	266	10	supersolvable	supersolvable	ADJ
ejpam-5993	266	11	by	by	ADP
ejpam-5993	266	12	(	(	PUNCT
ejpam-5993	266	13	1	1	NUM
ejpam-5993	266	14	)	)	PUNCT
ejpam-5993	266	15	.	.	PUNCT
ejpam-5993	267	1	in	in	ADP
ejpam-5993	267	2	particular	particular	ADJ
ejpam-5993	267	3	,	,	PUNCT
ejpam-5993	267	4	h	h	NOUN
ejpam-5993	267	5	is	be	AUX
ejpam-5993	267	6	solvable	solvable	ADJ
ejpam-5993	267	7	,	,	PUNCT
ejpam-5993	267	8	so	so	ADV
ejpam-5993	267	9	by	by	ADP
ejpam-5993	267	10	lemma	lemma	PROPN
ejpam-5993	267	11	9	9	NUM
ejpam-5993	267	12	,	,	PUNCT
ejpam-5993	267	13	g342	g342	PROPN
ejpam-5993	267	14	is	be	AUX
ejpam-5993	267	15	solvable	solvable	ADJ
ejpam-5993	267	16	and	and	CCONJ
ejpam-5993	267	17	f	f	PROPN
ejpam-5993	267	18	∗(h	∗(h	PROPN
ejpam-5993	267	19	)	)	PUNCT
ejpam-5993	268	1	=	=	SYM
ejpam-5993	268	2	f	f	PROPN
ejpam-5993	268	3	(	(	PUNCT
ejpam-5993	268	4	h	h	NOUN
ejpam-5993	268	5	)	)	PUNCT
ejpam-5993	268	6	by	by	ADP
ejpam-5993	268	7	lemma	lemma	PROPN
ejpam-5993	268	8	8(ii	8(ii	PROPN
ejpam-5993	268	9	)	)	PUNCT
ejpam-5993	268	10	,	,	PUNCT
ejpam-5993	268	11	then	then	ADV
ejpam-5993	268	12	g	g	PROPN
ejpam-5993	268	13	is	be	AUX
ejpam-5993	268	14	supersolvable	supersolvable	ADJ
ejpam-5993	268	15	by	by	ADP
ejpam-5993	268	16	theorem	theorem	NOUN
ejpam-5993	268	17	2	2	NUM
ejpam-5993	268	18	,	,	PUNCT
ejpam-5993	268	19	a343	a343	PROPN
ejpam-5993	268	20	contradiction.344	contradiction.344	NOUN
ejpam-5993	268	21	if	if	SCONJ
ejpam-5993	268	22	f	f	PROPN
ejpam-5993	268	23	∗(h	∗(h	PROPN
ejpam-5993	268	24	)	)	PUNCT
ejpam-5993	269	1	=	=	SYM
ejpam-5993	269	2	g	g	NOUN
ejpam-5993	269	3	,	,	PUNCT
ejpam-5993	269	4	then	then	ADV
ejpam-5993	269	5	g	g	PROPN
ejpam-5993	269	6	is	be	AUX
ejpam-5993	269	7	supersolvable	supersolvable	ADJ
ejpam-5993	269	8	by	by	ADP
ejpam-5993	269	9	theorem	theorem	NOUN
ejpam-5993	269	10	3	3	NUM
ejpam-5993	269	11	,	,	PUNCT
ejpam-5993	269	12	a	a	DET
ejpam-5993	269	13	contradiction	contradiction	NOUN
ejpam-5993	269	14	.	.	PUNCT
ejpam-5993	270	1	then	then	ADV
ejpam-5993	270	2	f	f	PROPN
ejpam-5993	270	3	∗(h	∗(h	PROPN
ejpam-5993	270	4	)	)	PUNCT
ejpam-5993	270	5	<	<	X
ejpam-5993	271	1	g345	g345	PROPN
ejpam-5993	272	1	and	and	CCONJ
ejpam-5993	272	2	it	it	PRON
ejpam-5993	272	3	is	be	AUX
ejpam-5993	272	4	supersolvable	supersolvable	ADJ
ejpam-5993	272	5	by	by	ADP
ejpam-5993	272	6	(	(	PUNCT
ejpam-5993	272	7	1	1	NUM
ejpam-5993	272	8	)	)	PUNCT
ejpam-5993	272	9	.	.	PUNCT
ejpam-5993	273	1	so	so	ADV
ejpam-5993	273	2	,	,	PUNCT
ejpam-5993	273	3	f	f	PROPN
ejpam-5993	273	4	∗(h	∗(h	PROPN
ejpam-5993	273	5	)	)	PUNCT
ejpam-5993	274	1	=	=	SYM
ejpam-5993	274	2	f	f	PROPN
ejpam-5993	274	3	(	(	PUNCT
ejpam-5993	274	4	h).346	h).346	NOUN
ejpam-5993	274	5	347	347	NUM
ejpam-5993	274	6	(	(	PUNCT
ejpam-5993	274	7	3	3	NUM
ejpam-5993	274	8	)	)	PUNCT
ejpam-5993	274	9	for	for	ADP
ejpam-5993	274	10	any	any	DET
ejpam-5993	274	11	sylow	sylow	NOUN
ejpam-5993	274	12	p	p	NOUN
ejpam-5993	274	13	-	-	PUNCT
ejpam-5993	274	14	subgroup	subgroup	NOUN
ejpam-5993	274	15	p	p	NOUN
ejpam-5993	274	16	of	of	ADP
ejpam-5993	274	17	f	f	PROPN
ejpam-5993	274	18	(	(	PUNCT
ejpam-5993	274	19	g	g	NOUN
ejpam-5993	274	20	)	)	PUNCT
ejpam-5993	274	21	,	,	PUNCT
ejpam-5993	274	22	φ(p	φ(p	PROPN
ejpam-5993	274	23	)	)	PUNCT
ejpam-5993	274	24	=	=	PUNCT
ejpam-5993	275	1	1	1	NUM
ejpam-5993	275	2	,	,	PUNCT
ejpam-5993	275	3	i.e.	i.e.	X
ejpam-5993	275	4	p	p	NOUN
ejpam-5993	275	5	is	be	AUX
ejpam-5993	275	6	elementary	elementary	ADJ
ejpam-5993	275	7	abelian.348	abelian.348	ADV
ejpam-5993	275	8	if	if	SCONJ
ejpam-5993	275	9	there	there	PRON
ejpam-5993	275	10	exists	exist	VERB
ejpam-5993	275	11	a	a	DET
ejpam-5993	275	12	sylow	sylow	NOUN
ejpam-5993	275	13	p	p	NOUN
ejpam-5993	275	14	-	-	PUNCT
ejpam-5993	275	15	subgroup	subgroup	NOUN
ejpam-5993	275	16	p	p	NOUN
ejpam-5993	275	17	of	of	ADP
ejpam-5993	275	18	f	f	PROPN
ejpam-5993	275	19	(	(	PUNCT
ejpam-5993	275	20	g	g	NOUN
ejpam-5993	275	21	)	)	PUNCT
ejpam-5993	275	22	with	with	ADP
ejpam-5993	275	23	φ(p	φ(p	PROPN
ejpam-5993	275	24	)	)	PUNCT
ejpam-5993	276	1	̸=	̸=	PROPN
ejpam-5993	276	2	1	1	NUM
ejpam-5993	276	3	,	,	PUNCT
ejpam-5993	276	4	then	then	ADV
ejpam-5993	276	5	consider	consider	VERB
ejpam-5993	276	6	the	the	DET
ejpam-5993	276	7	factor349	factor349	PROPN
ejpam-5993	276	8	group	group	NOUN
ejpam-5993	276	9	g	g	PROPN
ejpam-5993	276	10	/	/	SYM
ejpam-5993	276	11	φ(p	φ(p	PROPN
ejpam-5993	276	12	)	)	PUNCT
ejpam-5993	276	13	.	.	PUNCT
ejpam-5993	277	1	by	by	ADP
ejpam-5993	277	2	lemma	lemma	PROPN
ejpam-5993	277	3	8(iii	8(iii	NUM
ejpam-5993	277	4	)	)	PUNCT
ejpam-5993	277	5	,	,	PUNCT
ejpam-5993	277	6	f	f	PROPN
ejpam-5993	277	7	∗(g	∗(g	PROPN
ejpam-5993	277	8	/	/	SYM
ejpam-5993	277	9	φ(p	φ(p	PROPN
ejpam-5993	277	10	)	)	PUNCT
ejpam-5993	277	11	)	)	PUNCT
ejpam-5993	278	1	=	=	PUNCT
ejpam-5993	278	2	f	f	X
ejpam-5993	278	3	∗(g)/φ(p	∗(g)/φ(p	PROPN
ejpam-5993	278	4	)	)	PUNCT
ejpam-5993	279	1	=	=	SYM
ejpam-5993	279	2	f	f	X
ejpam-5993	279	3	(	(	PUNCT
ejpam-5993	279	4	g)/φ(p	g)/φ(p	PROPN
ejpam-5993	279	5	)	)	PUNCT
ejpam-5993	279	6	.	.	PUNCT
ejpam-5993	280	1	if	if	SCONJ
ejpam-5993	280	2	p1	p1	PROPN
ejpam-5993	280	3	/	/	SYM
ejpam-5993	280	4	φ(p	φ(p	PROPN
ejpam-5993	280	5	)	)	PUNCT
ejpam-5993	280	6	350	350	NUM
ejpam-5993	280	7	is	be	AUX
ejpam-5993	280	8	a	a	DET
ejpam-5993	280	9	maximal	maximal	ADJ
ejpam-5993	280	10	subgroup	subgroup	NOUN
ejpam-5993	280	11	of	of	ADP
ejpam-5993	280	12	the	the	DET
ejpam-5993	280	13	non	non	ADJ
ejpam-5993	280	14	-	-	ADJ
ejpam-5993	280	15	cyclic	cyclic	ADJ
ejpam-5993	280	16	sylow	sylow	NOUN
ejpam-5993	280	17	p	p	NOUN
ejpam-5993	280	18	-	-	PUNCT
ejpam-5993	280	19	subgroup	subgroup	NOUN
ejpam-5993	280	20	p	p	NOUN
ejpam-5993	280	21	/	/	SYM
ejpam-5993	280	22	φ(p	φ(p	PROPN
ejpam-5993	280	23	)	)	PUNCT
ejpam-5993	280	24	of	of	ADP
ejpam-5993	280	25	f	f	PROPN
ejpam-5993	280	26	∗(g)/φ(p	∗(g)/φ(p	PROPN
ejpam-5993	280	27	)	)	PUNCT
ejpam-5993	280	28	,	,	PUNCT
ejpam-5993	280	29	then351	then351	PROPN
ejpam-5993	280	30	p1	p1	PROPN
ejpam-5993	280	31	is	be	AUX
ejpam-5993	280	32	a	a	DET
ejpam-5993	280	33	maximal	maximal	ADJ
ejpam-5993	280	34	subgroup	subgroup	NOUN
ejpam-5993	280	35	of	of	ADP
ejpam-5993	280	36	the	the	DET
ejpam-5993	280	37	non	non	ADJ
ejpam-5993	280	38	-	-	ADJ
ejpam-5993	280	39	cyclic	cyclic	ADJ
ejpam-5993	280	40	sylow	sylow	NOUN
ejpam-5993	280	41	p	p	PROPN
ejpam-5993	280	42	-	-	PUNCT
ejpam-5993	280	43	subgroup	subgroup	NOUN
ejpam-5993	280	44	p	p	NOUN
ejpam-5993	280	45	of	of	ADP
ejpam-5993	280	46	f	f	PROPN
ejpam-5993	280	47	∗(g	∗(g	PROPN
ejpam-5993	280	48	)	)	PUNCT
ejpam-5993	280	49	.	.	PUNCT
ejpam-5993	281	1	so	so	ADV
ejpam-5993	281	2	,	,	PUNCT
ejpam-5993	281	3	p1	p1	PROPN
ejpam-5993	281	4	is	be	AUX
ejpam-5993	281	5	an352	an352	PROPN
ejpam-5993	281	6	ssh	ssh	NOUN
ejpam-5993	281	7	-	-	PUNCT
ejpam-5993	281	8	subgroup	subgroup	NOUN
ejpam-5993	281	9	,	,	PUNCT
ejpam-5993	281	10	by	by	ADP
ejpam-5993	281	11	hypothesis	hypothesis	NOUN
ejpam-5993	281	12	.	.	PUNCT
ejpam-5993	282	1	then	then	ADV
ejpam-5993	282	2	p1	p1	PROPN
ejpam-5993	282	3	/	/	SYM
ejpam-5993	282	4	φ(p	φ(p	PROPN
ejpam-5993	282	5	)	)	PUNCT
ejpam-5993	282	6	is	be	AUX
ejpam-5993	282	7	an	an	DET
ejpam-5993	282	8	ssh	ssh	NOUN
ejpam-5993	282	9	-	-	PUNCT
ejpam-5993	282	10	subgroup	subgroup	NOUN
ejpam-5993	282	11	by	by	ADP
ejpam-5993	282	12	lemma	lemma	PROPN
ejpam-5993	282	13	2(iii	2(iii	NUM
ejpam-5993	282	14	)	)	PUNCT
ejpam-5993	282	15	.	.	PUNCT
ejpam-5993	283	1	if353	if353	PROPN
ejpam-5993	283	2	q∗/φ(p	q∗/φ(p	PROPN
ejpam-5993	283	3	)	)	PUNCT
ejpam-5993	283	4	is	be	AUX
ejpam-5993	283	5	a	a	DET
ejpam-5993	283	6	maximal	maximal	ADJ
ejpam-5993	283	7	subgroup	subgroup	NOUN
ejpam-5993	283	8	of	of	ADP
ejpam-5993	283	9	the	the	DET
ejpam-5993	283	10	non	non	ADJ
ejpam-5993	283	11	-	-	ADJ
ejpam-5993	283	12	cyclic	cyclic	ADJ
ejpam-5993	283	13	sylow	sylow	NOUN
ejpam-5993	283	14	q	q	NOUN
ejpam-5993	283	15	-	-	NOUN
ejpam-5993	283	16	subgroup	subgroup	NOUN
ejpam-5993	283	17	of	of	ADP
ejpam-5993	283	18	qφ(p	qφ(p	PROPN
ejpam-5993	283	19	)	)	PUNCT
ejpam-5993	283	20	/φ(p	/φ(p	PUNCT
ejpam-5993	283	21	)	)	PUNCT
ejpam-5993	284	1	of354	of354	PROPN
ejpam-5993	284	2	f	f	X
ejpam-5993	284	3	∗(g)/φ(p	∗(g)/φ(p	PROPN
ejpam-5993	284	4	)	)	PUNCT
ejpam-5993	284	5	,	,	PUNCT
ejpam-5993	284	6	where	where	SCONJ
ejpam-5993	284	7	q	q	NOUN
ejpam-5993	284	8	is	be	AUX
ejpam-5993	284	9	the	the	DET
ejpam-5993	284	10	non	non	ADJ
ejpam-5993	284	11	-	-	ADJ
ejpam-5993	284	12	cyclic	cyclic	ADJ
ejpam-5993	284	13	sylow	sylow	NOUN
ejpam-5993	284	14	q	q	NOUN
ejpam-5993	284	15	-	-	NOUN
ejpam-5993	284	16	subgroup	subgroup	NOUN
ejpam-5993	284	17	of	of	ADP
ejpam-5993	284	18	f	f	PROPN
ejpam-5993	284	19	∗(g	∗(g	PROPN
ejpam-5993	284	20	)	)	PUNCT
ejpam-5993	284	21	and	and	CCONJ
ejpam-5993	284	22	q	q	PROPN
ejpam-5993	284	23	̸=	̸=	PROPN
ejpam-5993	284	24	p	p	NOUN
ejpam-5993	284	25	,	,	PUNCT
ejpam-5993	284	26	then	then	ADV
ejpam-5993	284	27	we355	we355	PROPN
ejpam-5993	284	28	can	can	AUX
ejpam-5993	284	29	denoted	denote	VERB
ejpam-5993	284	30	q∗	q∗	NOUN
ejpam-5993	284	31	=	=	SYM
ejpam-5993	284	32	q1φ(p	q1φ(p	PROPN
ejpam-5993	284	33	)	)	PUNCT
ejpam-5993	284	34	,	,	PUNCT
ejpam-5993	284	35	where	where	SCONJ
ejpam-5993	284	36	q1	q1	PROPN
ejpam-5993	284	37	is	be	AUX
ejpam-5993	284	38	a	a	DET
ejpam-5993	284	39	maximal	maximal	ADJ
ejpam-5993	284	40	subgroup	subgroup	NOUN
ejpam-5993	284	41	of	of	ADP
ejpam-5993	284	42	the	the	DET
ejpam-5993	284	43	non	non	ADJ
ejpam-5993	284	44	-	-	ADJ
ejpam-5993	284	45	cyclic	cyclic	ADJ
ejpam-5993	284	46	sylow356	sylow356	PROPN
ejpam-5993	284	47	q	q	NOUN
ejpam-5993	284	48	-	-	NOUN
ejpam-5993	284	49	subgroup	subgroup	NOUN
ejpam-5993	284	50	of	of	ADP
ejpam-5993	284	51	q	q	PROPN
ejpam-5993	284	52	of	of	ADP
ejpam-5993	284	53	f	f	PROPN
ejpam-5993	284	54	∗(g	∗(g	PROPN
ejpam-5993	284	55	)	)	PUNCT
ejpam-5993	284	56	.	.	PUNCT
ejpam-5993	285	1	now	now	ADV
ejpam-5993	285	2	,	,	PUNCT
ejpam-5993	285	3	q1	q1	PROPN
ejpam-5993	285	4	is	be	AUX
ejpam-5993	285	5	an	an	DET
ejpam-5993	285	6	ssh	ssh	NOUN
ejpam-5993	285	7	-	-	PUNCT
ejpam-5993	285	8	subgroup	subgroup	NOUN
ejpam-5993	285	9	(	(	PUNCT
ejpam-5993	285	10	by	by	ADP
ejpam-5993	285	11	hypothesis	hypothesis	NOUN
ejpam-5993	285	12	and	and	CCONJ
ejpam-5993	285	13	by	by	ADP
ejpam-5993	285	14	lemma357	lemma357	PROPN
ejpam-5993	285	15	2	2	NUM
ejpam-5993	285	16	(	(	PUNCT
ejpam-5993	285	17	iii	iii	NOUN
ejpam-5993	285	18	)	)	PUNCT
ejpam-5993	285	19	)	)	PUNCT
ejpam-5993	285	20	,	,	PUNCT
ejpam-5993	285	21	implies	imply	VERB
ejpam-5993	285	22	that	that	SCONJ
ejpam-5993	285	23	q∗/φ(p	q∗/φ(p	PROPN
ejpam-5993	285	24	)	)	PUNCT
ejpam-5993	285	25	is	be	AUX
ejpam-5993	285	26	an	an	DET
ejpam-5993	285	27	ssh	ssh	NOUN
ejpam-5993	285	28	-	-	PUNCT
ejpam-5993	285	29	subgroup	subgroup	NOUN
ejpam-5993	285	30	in	in	ADP
ejpam-5993	285	31	g	g	PROPN
ejpam-5993	285	32	/	/	SYM
ejpam-5993	285	33	φ(p	φ(p	PROPN
ejpam-5993	285	34	)	)	PUNCT
ejpam-5993	285	35	.	.	PUNCT
ejpam-5993	286	1	by	by	ADP
ejpam-5993	286	2	minimality	minimality	NOUN
ejpam-5993	286	3	of	of	ADP
ejpam-5993	286	4	g,358	g,358	PROPN
ejpam-5993	286	5	g	g	PROPN
ejpam-5993	286	6	/	/	SYM
ejpam-5993	286	7	φ(p	φ(p	PROPN
ejpam-5993	286	8	)	)	PUNCT
ejpam-5993	286	9	is	be	AUX
ejpam-5993	286	10	supersolvable	supersolvable	ADJ
ejpam-5993	286	11	.	.	PUNCT
ejpam-5993	287	1	but	but	CCONJ
ejpam-5993	287	2	p	p	NOUN
ejpam-5993	287	3	⊴	⊴	ADP
ejpam-5993	287	4	g	g	PROPN
ejpam-5993	287	5	,	,	PUNCT
ejpam-5993	287	6	then	then	ADV
ejpam-5993	287	7	φ(p	φ(p	PROPN
ejpam-5993	287	8	)	)	PUNCT
ejpam-5993	287	9	⩽	⩽	ADJ
ejpam-5993	287	10	φ(g	φ(g	PROPN
ejpam-5993	287	11	)	)	PUNCT
ejpam-5993	287	12	,	,	PUNCT
ejpam-5993	287	13	and	and	CCONJ
ejpam-5993	287	14	we	we	PRON
ejpam-5993	287	15	get	get	VERB
ejpam-5993	287	16	g	g	NOUN
ejpam-5993	287	17	/	/	SYM
ejpam-5993	287	18	φ(g	φ(g	NOUN
ejpam-5993	287	19	)	)	PUNCT
ejpam-5993	287	20	is	be	AUX
ejpam-5993	287	21	super-359	super-359	ADV
ejpam-5993	287	22	solvable	solvable	ADJ
ejpam-5993	287	23	.	.	PUNCT
ejpam-5993	288	1	by	by	ADP
ejpam-5993	288	2	huppert	huppert	PROPN
ejpam-5993	288	3	’s	’s	PART
ejpam-5993	288	4	theorem	theorem	NOUN
ejpam-5993	288	5	[	[	PUNCT
ejpam-5993	288	6	13	13	NUM
ejpam-5993	288	7	,	,	PUNCT
ejpam-5993	288	8	p.	p.	NOUN
ejpam-5993	288	9	713	713	NUM
ejpam-5993	288	10	,	,	PUNCT
ejpam-5993	288	11	satz	satz	PROPN
ejpam-5993	288	12	8.6	8.6	NUM
ejpam-5993	288	13	]	]	PUNCT
ejpam-5993	288	14	,	,	PUNCT
ejpam-5993	288	15	g	g	PROPN
ejpam-5993	288	16	is	be	AUX
ejpam-5993	288	17	supersolvable	supersolvable	ADJ
ejpam-5993	288	18	,	,	PUNCT
ejpam-5993	288	19	a	a	DET
ejpam-5993	288	20	contradiction.360	contradiction.360	NOUN
ejpam-5993	288	21	361	361	NUM
ejpam-5993	288	22	(	(	PUNCT
ejpam-5993	288	23	4	4	NUM
ejpam-5993	288	24	)	)	PUNCT
ejpam-5993	288	25	there	there	PRON
ejpam-5993	288	26	is	be	VERB
ejpam-5993	288	27	no	no	DET
ejpam-5993	288	28	subgroup	subgroup	NOUN
ejpam-5993	288	29	of	of	ADP
ejpam-5993	288	30	prime	prime	ADJ
ejpam-5993	288	31	order	order	NOUN
ejpam-5993	288	32	normal	normal	ADJ
ejpam-5993	288	33	in	in	ADP
ejpam-5993	288	34	g.362	g.362	PROPN
ejpam-5993	288	35	if	if	SCONJ
ejpam-5993	288	36	not	not	PART
ejpam-5993	288	37	,	,	PUNCT
ejpam-5993	288	38	let	let	VERB
ejpam-5993	288	39	p0	p0	NOUN
ejpam-5993	288	40	be	be	AUX
ejpam-5993	288	41	a	a	DET
ejpam-5993	288	42	normal	normal	ADJ
ejpam-5993	288	43	subgroup	subgroup	NOUN
ejpam-5993	288	44	of	of	ADP
ejpam-5993	288	45	g	g	PROPN
ejpam-5993	288	46	of	of	ADP
ejpam-5993	288	47	prime	prime	ADJ
ejpam-5993	288	48	order	order	NOUN
ejpam-5993	289	1	p.	p.	NOUN
ejpam-5993	289	2	then	then	ADV
ejpam-5993	289	3	p0	p0	PROPN
ejpam-5993	289	4	⩽	⩽	PROPN
ejpam-5993	289	5	p	p	PROPN
ejpam-5993	289	6	as	as	ADP
ejpam-5993	289	7	p	p	NOUN
ejpam-5993	289	8	⊴	⊴	PROPN
ejpam-5993	289	9	g.	g.	PROPN
ejpam-5993	289	10	since363	since363	PROPN
ejpam-5993	289	11	p0	p0	NOUN
ejpam-5993	289	12	⩽	⩽	ADJ
ejpam-5993	289	13	z(p	z(p	ADV
ejpam-5993	289	14	)	)	PUNCT
ejpam-5993	290	1	⩽	⩽	ADJ
ejpam-5993	290	2	z(f	z(f	NOUN
ejpam-5993	290	3	(	(	PUNCT
ejpam-5993	290	4	g	g	NOUN
ejpam-5993	290	5	)	)	PUNCT
ejpam-5993	290	6	)	)	PUNCT
ejpam-5993	290	7	,	,	PUNCT
ejpam-5993	290	8	it	it	PRON
ejpam-5993	290	9	follows	follow	VERB
ejpam-5993	290	10	that	that	SCONJ
ejpam-5993	291	1	f	f	PROPN
ejpam-5993	291	2	(	(	PUNCT
ejpam-5993	291	3	g	g	NOUN
ejpam-5993	291	4	)	)	PUNCT
ejpam-5993	291	5	⩽	⩽	ADJ
ejpam-5993	291	6	cg(p0	cg(p0	NOUN
ejpam-5993	291	7	)	)	PUNCT
ejpam-5993	291	8	⩽	⩽	ADJ
ejpam-5993	291	9	g.	g.	PROPN
ejpam-5993	291	10	by	by	ADP
ejpam-5993	291	11	(	(	PUNCT
ejpam-5993	291	12	2	2	NUM
ejpam-5993	291	13	)	)	PUNCT
ejpam-5993	291	14	and	and	CCONJ
ejpam-5993	291	15	lemma	lemma	PROPN
ejpam-5993	291	16	8((i)364	8((i)364	PROPN
ejpam-5993	291	17	and	and	CCONJ
ejpam-5993	291	18	(	(	PUNCT
ejpam-5993	291	19	ii	ii	NOUN
ejpam-5993	291	20	)	)	PUNCT
ejpam-5993	291	21	)	)	PUNCT
ejpam-5993	291	22	,	,	PUNCT
ejpam-5993	291	23	f	f	PROPN
ejpam-5993	291	24	∗(g	∗(g	PROPN
ejpam-5993	291	25	)	)	PUNCT
ejpam-5993	291	26	⩽	⩽	PROPN
ejpam-5993	291	27	f	f	PROPN
ejpam-5993	291	28	∗(cg(p0	∗(cg(p0	PROPN
ejpam-5993	291	29	)	)	PUNCT
ejpam-5993	291	30	)	)	PUNCT
ejpam-5993	291	31	.	.	PUNCT
ejpam-5993	292	1	but	but	CCONJ
ejpam-5993	292	2	f	f	PROPN
ejpam-5993	292	3	∗(cg(p0	∗(cg(p0	PROPN
ejpam-5993	292	4	)	)	PUNCT
ejpam-5993	292	5	)	)	PUNCT
ejpam-5993	293	1	⩽	⩽	NOUN
ejpam-5993	293	2	f	f	PROPN
ejpam-5993	293	3	∗(g	∗(g	PROPN
ejpam-5993	293	4	)	)	PUNCT
ejpam-5993	293	5	.	.	PUNCT
ejpam-5993	294	1	therefore	therefore	ADV
ejpam-5993	294	2	,	,	PUNCT
ejpam-5993	294	3	by	by	ADP
ejpam-5993	294	4	the	the	DET
ejpam-5993	294	5	fact	fact	NOUN
ejpam-5993	294	6	that365	that365	PROPN
ejpam-5993	294	7	cg(p0	cg(p0	PROPN
ejpam-5993	294	8	)	)	PUNCT
ejpam-5993	294	9	⊴	⊴	ADP
ejpam-5993	294	10	g	g	PROPN
ejpam-5993	294	11	and	and	CCONJ
ejpam-5993	294	12	lemma	lemma	PROPN
ejpam-5993	294	13	8(i	8(i	NUM
ejpam-5993	294	14	)	)	PUNCT
ejpam-5993	294	15	,	,	PUNCT
ejpam-5993	294	16	f	f	PROPN
ejpam-5993	294	17	∗(cg(p0	∗(cg(p0	PROPN
ejpam-5993	294	18	)	)	PUNCT
ejpam-5993	294	19	)	)	PUNCT
ejpam-5993	295	1	=	=	PUNCT
ejpam-5993	295	2	f	f	X
ejpam-5993	295	3	∗(g	∗(g	PROPN
ejpam-5993	295	4	)	)	PUNCT
ejpam-5993	296	1	=	=	SYM
ejpam-5993	296	2	f	f	X
ejpam-5993	296	3	(	(	PUNCT
ejpam-5993	296	4	g	g	NOUN
ejpam-5993	296	5	)	)	PUNCT
ejpam-5993	296	6	.	.	PUNCT
ejpam-5993	297	1	if	if	SCONJ
ejpam-5993	297	2	further	further	ADJ
ejpam-5993	297	3	cg(p0	cg(p0	NOUN
ejpam-5993	297	4	)	)	PUNCT
ejpam-5993	297	5	<	<	X
ejpam-5993	297	6	g	g	PROPN
ejpam-5993	297	7	,	,	PUNCT
ejpam-5993	297	8	then366	then366	PROPN
ejpam-5993	297	9	cg(p0	cg(p0	NOUN
ejpam-5993	297	10	)	)	PUNCT
ejpam-5993	297	11	is	be	AUX
ejpam-5993	297	12	supersolvable	supersolvable	ADJ
ejpam-5993	297	13	by	by	ADP
ejpam-5993	297	14	(	(	PUNCT
ejpam-5993	297	15	1	1	NUM
ejpam-5993	297	16	)	)	PUNCT
ejpam-5993	297	17	.	.	PUNCT
ejpam-5993	298	1	since	since	SCONJ
ejpam-5993	298	2	g	g	PROPN
ejpam-5993	298	3	/	/	SYM
ejpam-5993	298	4	cg(p0	cg(p0	NOUN
ejpam-5993	298	5	)	)	PUNCT
ejpam-5993	298	6	is	be	AUX
ejpam-5993	298	7	isomorphic	isomorphic	ADJ
ejpam-5993	298	8	to	to	ADP
ejpam-5993	298	9	a	a	DET
ejpam-5993	298	10	subgroup	subgroup	NOUN
ejpam-5993	298	11	of	of	ADP
ejpam-5993	298	12	aut(p0),367	aut(p0),367	PROPN
ejpam-5993	298	13	which	which	PRON
ejpam-5993	298	14	is	be	AUX
ejpam-5993	298	15	cyclic	cyclic	ADJ
ejpam-5993	298	16	,	,	PUNCT
ejpam-5993	298	17	we	we	PRON
ejpam-5993	298	18	get	get	VERB
ejpam-5993	298	19	that	that	PRON
ejpam-5993	298	20	g	g	NOUN
ejpam-5993	298	21	/	/	SYM
ejpam-5993	298	22	cg(p0	cg(p0	NOUN
ejpam-5993	298	23	)	)	PUNCT
ejpam-5993	298	24	is	be	AUX
ejpam-5993	298	25	cyclic	cyclic	ADJ
ejpam-5993	298	26	and	and	CCONJ
ejpam-5993	298	27	hence	hence	ADV
ejpam-5993	298	28	solvable	solvable	ADJ
ejpam-5993	298	29	.	.	PUNCT
ejpam-5993	299	1	but	but	CCONJ
ejpam-5993	299	2	g	g	NOUN
ejpam-5993	299	3	/	/	SYM
ejpam-5993	299	4	cg(p0	cg(p0	NOUN
ejpam-5993	299	5	)	)	PUNCT
ejpam-5993	300	1	is368	is368	NOUN
ejpam-5993	300	2	solvable	solvable	ADJ
ejpam-5993	300	3	,	,	PUNCT
ejpam-5993	300	4	then	then	ADV
ejpam-5993	300	5	g	g	PROPN
ejpam-5993	300	6	is	be	AUX
ejpam-5993	300	7	solvable	solvable	ADJ
ejpam-5993	300	8	.	.	PUNCT
ejpam-5993	301	1	applying	apply	VERB
ejpam-5993	301	2	theorem	theorem	ADJ
ejpam-5993	301	3	1	1	NUM
ejpam-5993	301	4	implies	imply	VERB
ejpam-5993	301	5	that	that	SCONJ
ejpam-5993	301	6	g	g	PROPN
ejpam-5993	301	7	is	be	AUX
ejpam-5993	301	8	supersolvable	supersolvable	ADJ
ejpam-5993	301	9	,	,	PUNCT
ejpam-5993	301	10	a	a	DET
ejpam-5993	301	11	con-369	con-369	PROPN
ejpam-5993	301	12	a.	a.	NOUN
ejpam-5993	301	13	s.	s.	PROPN
ejpam-5993	301	14	allehyani	allehyani	PROPN
ejpam-5993	301	15	/	/	SYM
ejpam-5993	301	16	eur	eur	PROPN
ejpam-5993	301	17	.	.	PUNCT
ejpam-5993	302	1	j.	j.	PROPN
ejpam-5993	302	2	pure	pure	PROPN
ejpam-5993	302	3	appl	appl	PROPN
ejpam-5993	302	4	.	.	PROPN
ejpam-5993	302	5	math	math	PROPN
ejpam-5993	302	6	,	,	PUNCT
ejpam-5993	302	7	18	18	NUM
ejpam-5993	302	8	(	(	PUNCT
ejpam-5993	302	9	2	2	NUM
ejpam-5993	302	10	)	)	PUNCT
ejpam-5993	302	11	(	(	PUNCT
ejpam-5993	302	12	2025	2025	NUM
ejpam-5993	302	13	)	)	PUNCT
ejpam-5993	302	14	,	,	PUNCT
ejpam-5993	302	15	5993	5993	NUM
ejpam-5993	302	16	11	11	NUM
ejpam-5993	302	17	of	of	ADP
ejpam-5993	302	18	13	13	NUM
ejpam-5993	302	19	tradiction	tradiction	NOUN
ejpam-5993	302	20	.	.	PUNCT
ejpam-5993	303	1	if	if	SCONJ
ejpam-5993	303	2	cg(p0	cg(p0	NOUN
ejpam-5993	303	3	)	)	PUNCT
ejpam-5993	304	1	=	=	SYM
ejpam-5993	304	2	g	g	NOUN
ejpam-5993	304	3	,	,	PUNCT
ejpam-5993	304	4	then	then	ADV
ejpam-5993	304	5	p0	p0	PROPN
ejpam-5993	304	6	⩽	⩽	PROPN
ejpam-5993	304	7	z(g	z(g	NOUN
ejpam-5993	304	8	)	)	PUNCT
ejpam-5993	304	9	.	.	PUNCT
ejpam-5993	305	1	by	by	ADP
ejpam-5993	305	2	lemma	lemma	PROPN
ejpam-5993	305	3	8(iii	8(iii	NUM
ejpam-5993	305	4	)	)	PUNCT
ejpam-5993	305	5	,	,	PUNCT
ejpam-5993	305	6	f	f	PROPN
ejpam-5993	305	7	∗(g	∗(g	PROPN
ejpam-5993	305	8	/	/	SYM
ejpam-5993	305	9	p0	p0	NOUN
ejpam-5993	305	10	)	)	PUNCT
ejpam-5993	306	1	=	=	SYM
ejpam-5993	306	2	f	f	NUM
ejpam-5993	306	3	∗(g)/p0	∗(g)/p0	NOUN
ejpam-5993	306	4	.	.	PUNCT
ejpam-5993	307	1	by370	by370	NOUN
ejpam-5993	307	2	using	use	VERB
ejpam-5993	307	3	similar	similar	ADJ
ejpam-5993	307	4	argument	argument	NOUN
ejpam-5993	307	5	in	in	ADP
ejpam-5993	307	6	(	(	PUNCT
ejpam-5993	307	7	3	3	NUM
ejpam-5993	307	8	)	)	PUNCT
ejpam-5993	307	9	,	,	PUNCT
ejpam-5993	307	10	we	we	PRON
ejpam-5993	307	11	get	get	VERB
ejpam-5993	307	12	that	that	SCONJ
ejpam-5993	307	13	all	all	DET
ejpam-5993	307	14	maximal	maximal	ADJ
ejpam-5993	307	15	subgroups	subgroup	NOUN
ejpam-5993	307	16	of	of	ADP
ejpam-5993	307	17	the	the	DET
ejpam-5993	307	18	non	non	ADJ
ejpam-5993	307	19	-	-	ADJ
ejpam-5993	307	20	cyclic	cyclic	ADJ
ejpam-5993	307	21	sylow371	sylow371	PROPN
ejpam-5993	307	22	subgroups	subgroup	NOUN
ejpam-5993	307	23	of	of	ADP
ejpam-5993	307	24	f	f	PROPN
ejpam-5993	307	25	∗(g	∗(g	PROPN
ejpam-5993	307	26	/	/	SYM
ejpam-5993	307	27	p0	p0	NOUN
ejpam-5993	307	28	)	)	PUNCT
ejpam-5993	307	29	are	be	AUX
ejpam-5993	307	30	ssh	ssh	NOUN
ejpam-5993	307	31	-	-	PUNCT
ejpam-5993	307	32	subgroups	subgroup	NOUN
ejpam-5993	307	33	in	in	ADP
ejpam-5993	307	34	g	g	NOUN
ejpam-5993	307	35	/	/	SYM
ejpam-5993	307	36	p0	p0	NOUN
ejpam-5993	307	37	.	.	PUNCT
ejpam-5993	308	1	the	the	DET
ejpam-5993	308	2	minimal	minimal	ADJ
ejpam-5993	308	3	choice	choice	NOUN
ejpam-5993	308	4	of	of	ADP
ejpam-5993	308	5	g	g	PROPN
ejpam-5993	308	6	implies372	implies372	PROPN
ejpam-5993	308	7	that	that	SCONJ
ejpam-5993	308	8	g	g	NOUN
ejpam-5993	308	9	/	/	SYM
ejpam-5993	308	10	p0	p0	NOUN
ejpam-5993	308	11	is	be	AUX
ejpam-5993	308	12	supersolvable	supersolvable	ADJ
ejpam-5993	308	13	.	.	PUNCT
ejpam-5993	309	1	therefore	therefore	ADV
ejpam-5993	309	2	,	,	PUNCT
ejpam-5993	309	3	by	by	ADP
ejpam-5993	309	4	lemma	lemma	PROPN
ejpam-5993	309	5	9	9	NUM
ejpam-5993	309	6	,	,	PUNCT
ejpam-5993	309	7	g	g	PROPN
ejpam-5993	309	8	is	be	AUX
ejpam-5993	309	9	supersolvable	supersolvable	ADJ
ejpam-5993	309	10	,	,	PUNCT
ejpam-5993	309	11	a	a	DET
ejpam-5993	309	12	contradiction.373	contradiction.373	NUM
ejpam-5993	309	13	374	374	NUM
ejpam-5993	309	14	(	(	PUNCT
ejpam-5993	309	15	5	5	NUM
ejpam-5993	309	16	)	)	PUNCT
ejpam-5993	309	17	the	the	DET
ejpam-5993	309	18	final	final	ADJ
ejpam-5993	309	19	contradiction.375	contradiction.375	NOUN
ejpam-5993	309	20	from	from	ADP
ejpam-5993	309	21	(	(	PUNCT
ejpam-5993	309	22	3	3	NUM
ejpam-5993	309	23	)	)	PUNCT
ejpam-5993	309	24	,	,	PUNCT
ejpam-5993	309	25	φ(p	φ(p	PROPN
ejpam-5993	309	26	)	)	PUNCT
ejpam-5993	310	1	=	=	PUNCT
ejpam-5993	310	2	1	1	X
ejpam-5993	310	3	.	.	PUNCT
ejpam-5993	310	4	then	then	ADV
ejpam-5993	310	5	by	by	ADP
ejpam-5993	310	6	lemma	lemma	PROPN
ejpam-5993	310	7	3	3	NUM
ejpam-5993	310	8	,	,	PUNCT
ejpam-5993	310	9	f	f	PROPN
ejpam-5993	310	10	(	(	PUNCT
ejpam-5993	310	11	g	g	NOUN
ejpam-5993	310	12	)	)	PUNCT
ejpam-5993	310	13	is	be	AUX
ejpam-5993	310	14	a	a	DET
ejpam-5993	310	15	direct	direct	ADJ
ejpam-5993	310	16	product	product	NOUN
ejpam-5993	310	17	of	of	ADP
ejpam-5993	310	18	minimal	minimal	ADJ
ejpam-5993	310	19	normal376	normal376	PROPN
ejpam-5993	310	20	subgroups	subgroup	NOUN
ejpam-5993	310	21	of	of	ADP
ejpam-5993	310	22	g	g	NOUN
ejpam-5993	310	23	which	which	PRON
ejpam-5993	310	24	are	be	AUX
ejpam-5993	310	25	contained	contain	VERB
ejpam-5993	310	26	in	in	ADP
ejpam-5993	310	27	f	f	PROPN
ejpam-5993	310	28	(	(	PUNCT
ejpam-5993	310	29	g	g	NOUN
ejpam-5993	310	30	)	)	PUNCT
ejpam-5993	310	31	.	.	PUNCT
ejpam-5993	311	1	let	let	VERB
ejpam-5993	311	2	p	p	PRON
ejpam-5993	311	3	be	be	AUX
ejpam-5993	311	4	a	a	DET
ejpam-5993	311	5	non	non	ADJ
ejpam-5993	311	6	-	-	ADJ
ejpam-5993	311	7	cyclic	cyclic	ADJ
ejpam-5993	311	8	sylow	sylow	NOUN
ejpam-5993	311	9	p	p	PROPN
ejpam-5993	311	10	-	-	PUNCT
ejpam-5993	311	11	subgroup	subgroup	NOUN
ejpam-5993	311	12	of377	of377	PROPN
ejpam-5993	311	13	f	f	X
ejpam-5993	311	14	(	(	PUNCT
ejpam-5993	311	15	g	g	NOUN
ejpam-5993	311	16	)	)	PUNCT
ejpam-5993	311	17	.	.	PUNCT
ejpam-5993	312	1	then	then	ADV
ejpam-5993	312	2	p	p	X
ejpam-5993	312	3	=	=	PROPN
ejpam-5993	312	4	r1	r1	PROPN
ejpam-5993	312	5	×	×	PROPN
ejpam-5993	312	6	r2	r2	PROPN
ejpam-5993	312	7	×	×	PROPN
ejpam-5993	312	8	r3	r3	PROPN
ejpam-5993	312	9	×	×	NOUN
ejpam-5993	312	10	·	·	PUNCT
ejpam-5993	312	11	·	·	PUNCT
ejpam-5993	312	12	·	·	PUNCT
ejpam-5993	313	1	×	×	X
ejpam-5993	313	2	rt	rt	INTJ
ejpam-5993	313	3	,	,	PUNCT
ejpam-5993	313	4	where	where	SCONJ
ejpam-5993	313	5	ri(i	ri(i	PUNCT
ejpam-5993	313	6	=	=	SYM
ejpam-5993	313	7	1	1	NUM
ejpam-5993	313	8	,	,	PUNCT
ejpam-5993	313	9	.	.	PUNCT
ejpam-5993	313	10	.	.	PUNCT
ejpam-5993	313	11	.	.	PUNCT
ejpam-5993	314	1	,	,	PUNCT
ejpam-5993	314	2	t	t	X
ejpam-5993	314	3	)	)	PUNCT
ejpam-5993	314	4	is	be	AUX
ejpam-5993	314	5	a	a	DET
ejpam-5993	314	6	minimal	minimal	ADJ
ejpam-5993	314	7	normal378	normal378	PROPN
ejpam-5993	314	8	subgroup	subgroup	NOUN
ejpam-5993	314	9	of	of	ADP
ejpam-5993	314	10	g.	g.	PROPN
ejpam-5993	314	11	let	let	VERB
ejpam-5993	314	12	p	p	PRON
ejpam-5993	314	13	be	be	AUX
ejpam-5993	314	14	a	a	DET
ejpam-5993	314	15	non	non	ADJ
ejpam-5993	314	16	-	-	ADJ
ejpam-5993	314	17	cyclic	cyclic	ADJ
ejpam-5993	314	18	sylow	sylow	NOUN
ejpam-5993	314	19	p	p	PROPN
ejpam-5993	314	20	-	-	PUNCT
ejpam-5993	314	21	subgroup	subgroup	NOUN
ejpam-5993	314	22	of	of	ADP
ejpam-5993	314	23	f	f	PROPN
ejpam-5993	314	24	(	(	PUNCT
ejpam-5993	314	25	g	g	NOUN
ejpam-5993	314	26	)	)	PUNCT
ejpam-5993	314	27	and	and	CCONJ
ejpam-5993	314	28	p	p	PROPN
ejpam-5993	314	29	is	be	AUX
ejpam-5993	314	30	characteristic379	characteristic379	PROPN
ejpam-5993	314	31	in	in	ADP
ejpam-5993	314	32	f	f	PROPN
ejpam-5993	314	33	(	(	PUNCT
ejpam-5993	314	34	g	g	NOUN
ejpam-5993	314	35	)	)	PUNCT
ejpam-5993	314	36	⊴	⊴	ADP
ejpam-5993	314	37	g	g	PROPN
ejpam-5993	314	38	,	,	PUNCT
ejpam-5993	314	39	then	then	ADV
ejpam-5993	314	40	p	p	X
ejpam-5993	314	41	⊴	⊴	PROPN
ejpam-5993	314	42	g.	g.	PROPN
ejpam-5993	314	43	then	then	ADV
ejpam-5993	314	44	there	there	PRON
ejpam-5993	314	45	exists	exist	VERB
ejpam-5993	314	46	a	a	DET
ejpam-5993	314	47	maximal	maximal	ADJ
ejpam-5993	314	48	subgroup	subgroup	NOUN
ejpam-5993	314	49	p1	p1	NOUN
ejpam-5993	314	50	of	of	ADP
ejpam-5993	314	51	p	p	PROPN
ejpam-5993	314	52	,	,	PUNCT
ejpam-5993	314	53	and	and	CCONJ
ejpam-5993	314	54	by380	by380	ADJ
ejpam-5993	314	55	hypothesis	hypothesis	NOUN
ejpam-5993	314	56	,	,	PUNCT
ejpam-5993	314	57	p1	p1	PROPN
ejpam-5993	314	58	is	be	AUX
ejpam-5993	314	59	an	an	DET
ejpam-5993	314	60	ssh	ssh	NOUN
ejpam-5993	314	61	-	-	PUNCT
ejpam-5993	314	62	subgroup	subgroup	NOUN
ejpam-5993	314	63	in	in	ADP
ejpam-5993	314	64	g.	g.	PROPN
ejpam-5993	314	65	then	then	ADV
ejpam-5993	314	66	there	there	PRON
ejpam-5993	314	67	exists	exist	VERB
ejpam-5993	314	68	an	an	DET
ejpam-5993	314	69	s	s	NOUN
ejpam-5993	314	70	-	-	ADJ
ejpam-5993	314	71	permutable	permutable	ADJ
ejpam-5993	314	72	subgroup381	subgroup381	PROPN
ejpam-5993	314	73	k	k	PROPN
ejpam-5993	314	74	of	of	ADP
ejpam-5993	314	75	g	g	PROPN
ejpam-5993	314	76	such	such	ADJ
ejpam-5993	314	77	that	that	SCONJ
ejpam-5993	314	78	(	(	PUNCT
ejpam-5993	314	79	p1	p1	NOUN
ejpam-5993	314	80	)	)	PUNCT
ejpam-5993	314	81	sg	sg	PROPN
ejpam-5993	314	82	=	=	SYM
ejpam-5993	314	83	p1k	p1k	PROPN
ejpam-5993	314	84	and	and	CCONJ
ejpam-5993	314	85	(	(	PUNCT
ejpam-5993	314	86	p1	p1	PROPN
ejpam-5993	314	87	)	)	PUNCT
ejpam-5993	314	88	g	g	ADP
ejpam-5993	314	89	∩nk(p1	∩nk(p1	PROPN
ejpam-5993	314	90	)	)	PUNCT
ejpam-5993	314	91	⩽	⩽	PROPN
ejpam-5993	314	92	p1	p1	PROPN
ejpam-5993	314	93	,	,	PUNCT
ejpam-5993	314	94	for	for	ADP
ejpam-5993	314	95	all	all	DET
ejpam-5993	314	96	g	g	PROPN
ejpam-5993	314	97	∈	∈	PROPN
ejpam-5993	314	98	g.	g.	NOUN
ejpam-5993	314	99	assuming	assume	VERB
ejpam-5993	314	100	that382	that382	PROPN
ejpam-5993	314	101	k	k	PROPN
ejpam-5993	314	102	=	=	PUNCT
ejpam-5993	314	103	p	p	X
ejpam-5993	314	104	,	,	PUNCT
ejpam-5993	314	105	then	then	ADV
ejpam-5993	314	106	we	we	PRON
ejpam-5993	314	107	have	have	VERB
ejpam-5993	314	108	(	(	PUNCT
ejpam-5993	314	109	p1	p1	NOUN
ejpam-5993	314	110	)	)	PUNCT
ejpam-5993	314	111	g∩ng(p1	g∩ng(p1	NOUN
ejpam-5993	314	112	)	)	PUNCT
ejpam-5993	314	113	=	=	PUNCT
ejpam-5993	314	114	(	(	PUNCT
ejpam-5993	314	115	p1	p1	NOUN
ejpam-5993	314	116	)	)	PUNCT
ejpam-5993	314	117	g∩k∩ng(p1	g∩k∩ng(p1	NOUN
ejpam-5993	314	118	)	)	PUNCT
ejpam-5993	314	119	=	=	SYM
ejpam-5993	314	120	(	(	PUNCT
ejpam-5993	314	121	p1	p1	PROPN
ejpam-5993	314	122	)	)	PUNCT
ejpam-5993	314	123	g∩nk(p1	g∩nk(p1	PROPN
ejpam-5993	314	124	)	)	PUNCT
ejpam-5993	314	125	⩽	⩽	PROPN
ejpam-5993	314	126	p1	p1	PROPN
ejpam-5993	314	127	.	.	PUNCT
ejpam-5993	315	1	then383	then383	PROPN
ejpam-5993	315	2	we	we	PRON
ejpam-5993	315	3	get	get	VERB
ejpam-5993	315	4	p1	p1	PROPN
ejpam-5993	315	5	is	be	AUX
ejpam-5993	315	6	an	an	DET
ejpam-5993	315	7	h	h	NOUN
ejpam-5993	315	8	-	-	PUNCT
ejpam-5993	315	9	subgroup	subgroup	NOUN
ejpam-5993	315	10	in	in	ADP
ejpam-5993	315	11	g	g	PROPN
ejpam-5993	315	12	and	and	CCONJ
ejpam-5993	315	13	p1	p1	PROPN
ejpam-5993	315	14	⊴	⊴	ADP
ejpam-5993	315	15	p	p	X
ejpam-5993	315	16	.	.	PUNCT
ejpam-5993	316	1	applying	apply	VERB
ejpam-5993	316	2	lemma	lemma	PROPN
ejpam-5993	316	3	4	4	NUM
ejpam-5993	316	4	,	,	PUNCT
ejpam-5993	316	5	we	we	PRON
ejpam-5993	316	6	get	get	VERB
ejpam-5993	316	7	p1	p1	PROPN
ejpam-5993	316	8	⊴	⊴	PROPN
ejpam-5993	316	9	g.	g.	PROPN
ejpam-5993	316	10	let384	let384	AUX
ejpam-5993	316	11	q	q	PUNCT
ejpam-5993	316	12	be	be	AUX
ejpam-5993	316	13	a	a	DET
ejpam-5993	316	14	non	non	ADJ
ejpam-5993	316	15	-	-	ADJ
ejpam-5993	316	16	cyclic	cyclic	ADJ
ejpam-5993	316	17	sylow	sylow	NOUN
ejpam-5993	316	18	q	q	NOUN
ejpam-5993	316	19	-	-	NOUN
ejpam-5993	316	20	subgroup	subgroup	NOUN
ejpam-5993	316	21	of	of	ADP
ejpam-5993	316	22	f	f	PROPN
ejpam-5993	316	23	(	(	PUNCT
ejpam-5993	316	24	g	g	NOUN
ejpam-5993	316	25	)	)	PUNCT
ejpam-5993	317	1	such	such	ADJ
ejpam-5993	317	2	that	that	SCONJ
ejpam-5993	317	3	(	(	PUNCT
ejpam-5993	317	4	p	p	X
ejpam-5993	317	5	,	,	PUNCT
ejpam-5993	317	6	|q|	|q|	NUM
ejpam-5993	317	7	)	)	PUNCT
ejpam-5993	317	8	=	=	SYM
ejpam-5993	317	9	1	1	X
ejpam-5993	317	10	.	.	PUNCT
ejpam-5993	317	11	now	now	ADV
ejpam-5993	317	12	,	,	PUNCT
ejpam-5993	317	13	p1q	p1q	PROPN
ejpam-5993	317	14	⩽	⩽	NOUN
ejpam-5993	317	15	g	g	PROPN
ejpam-5993	317	16	and385	and385	PROPN
ejpam-5993	317	17	since	since	SCONJ
ejpam-5993	317	18	p1	p1	PROPN
ejpam-5993	317	19	is	be	AUX
ejpam-5993	317	20	a	a	DET
ejpam-5993	317	21	normal	normal	ADJ
ejpam-5993	317	22	hall	hall	NOUN
ejpam-5993	317	23	subgroup	subgroup	NOUN
ejpam-5993	317	24	of	of	ADP
ejpam-5993	317	25	p1q	p1q	PROPN
ejpam-5993	317	26	,	,	PUNCT
ejpam-5993	317	27	it	it	PRON
ejpam-5993	317	28	follows	follow	VERB
ejpam-5993	317	29	that	that	SCONJ
ejpam-5993	317	30	p1	p1	PROPN
ejpam-5993	317	31	is	be	AUX
ejpam-5993	317	32	a	a	DET
ejpam-5993	317	33	characteristic	characteristic	ADJ
ejpam-5993	317	34	subgroup386	subgroup386	PROPN
ejpam-5993	317	35	of	of	ADP
ejpam-5993	317	36	p1q	p1q	PROPN
ejpam-5993	317	37	.	.	PUNCT
ejpam-5993	318	1	in	in	ADP
ejpam-5993	318	2	particular	particular	ADJ
ejpam-5993	318	3	p1	p1	NOUN
ejpam-5993	318	4	is	be	AUX
ejpam-5993	318	5	a	a	DET
ejpam-5993	318	6	normal	normal	ADJ
ejpam-5993	318	7	subgroup	subgroup	NOUN
ejpam-5993	318	8	of	of	ADP
ejpam-5993	318	9	p1q	p1q	PROPN
ejpam-5993	318	10	.	.	PUNCT
ejpam-5993	319	1	hence	hence	ADV
ejpam-5993	319	2	q	q	PROPN
ejpam-5993	319	3	⩽	⩽	PROPN
ejpam-5993	319	4	ng(p1	ng(p1	PROPN
ejpam-5993	319	5	)	)	PUNCT
ejpam-5993	319	6	for	for	ADP
ejpam-5993	319	7	all	all	PRON
ejpam-5993	319	8	sylow387	sylow387	PROPN
ejpam-5993	319	9	q	q	PROPN
ejpam-5993	319	10	-	-	PUNCT
ejpam-5993	319	11	subgroup	subgroup	NOUN
ejpam-5993	319	12	q	q	NOUN
ejpam-5993	319	13	of	of	ADP
ejpam-5993	319	14	f	f	PROPN
ejpam-5993	319	15	(	(	PUNCT
ejpam-5993	319	16	g	g	NOUN
ejpam-5993	319	17	)	)	PUNCT
ejpam-5993	319	18	,	,	PUNCT
ejpam-5993	320	1	where	where	SCONJ
ejpam-5993	320	2	(	(	PUNCT
ejpam-5993	320	3	p	p	X
ejpam-5993	320	4	,	,	PUNCT
ejpam-5993	320	5	|q|	|q|	NUM
ejpam-5993	320	6	)	)	PUNCT
ejpam-5993	320	7	=	=	SYM
ejpam-5993	320	8	1	1	X
ejpam-5993	320	9	.	.	PUNCT
ejpam-5993	320	10	since	since	SCONJ
ejpam-5993	320	11	p1	p1	PROPN
ejpam-5993	320	12	is	be	AUX
ejpam-5993	320	13	a	a	DET
ejpam-5993	320	14	normal	normal	ADJ
ejpam-5993	320	15	subgroup	subgroup	NOUN
ejpam-5993	320	16	of	of	ADP
ejpam-5993	320	17	p	p	PROPN
ejpam-5993	320	18	and	and	CCONJ
ejpam-5993	320	19	p1	p1	PROPN
ejpam-5993	320	20	is388	is388	AUX
ejpam-5993	320	21	a	a	DET
ejpam-5993	320	22	normal	normal	ADJ
ejpam-5993	320	23	subgroup	subgroup	NOUN
ejpam-5993	320	24	of	of	ADP
ejpam-5993	320	25	p1q	p1q	PROPN
ejpam-5993	320	26	,	,	PUNCT
ejpam-5993	320	27	we	we	PRON
ejpam-5993	320	28	get	get	VERB
ejpam-5993	320	29	p1	p1	PROPN
ejpam-5993	320	30	is	be	AUX
ejpam-5993	320	31	a	a	DET
ejpam-5993	320	32	normal	normal	ADJ
ejpam-5993	320	33	subgroup	subgroup	NOUN
ejpam-5993	320	34	of	of	ADP
ejpam-5993	320	35	pq	pq	PROPN
ejpam-5993	320	36	.	.	PUNCT
ejpam-5993	321	1	thus	thus	ADV
ejpam-5993	321	2	we	we	PRON
ejpam-5993	321	3	have	have	VERB
ejpam-5993	321	4	that389	that389	PROPN
ejpam-5993	321	5	every	every	DET
ejpam-5993	321	6	maximal	maximal	ADJ
ejpam-5993	321	7	subgroup	subgroup	NOUN
ejpam-5993	321	8	of	of	ADP
ejpam-5993	321	9	p	p	PROPN
ejpam-5993	321	10	is	be	AUX
ejpam-5993	321	11	a	a	DET
ejpam-5993	321	12	normal	normal	ADJ
ejpam-5993	321	13	subgroup	subgroup	NOUN
ejpam-5993	321	14	of	of	ADP
ejpam-5993	321	15	pq	pq	INTJ
ejpam-5993	321	16	by	by	ADP
ejpam-5993	321	17	lemma	lemma	PROPN
ejpam-5993	321	18	7(ii	7(ii	PROPN
ejpam-5993	321	19	)	)	PUNCT
ejpam-5993	321	20	.	.	PUNCT
ejpam-5993	322	1	since	since	SCONJ
ejpam-5993	322	2	p	p	NOUN
ejpam-5993	322	3	is	be	AUX
ejpam-5993	322	4	an390	an390	PROPN
ejpam-5993	322	5	elementary	elementary	ADJ
ejpam-5993	322	6	abelian	abelian	NOUN
ejpam-5993	322	7	p	p	PROPN
ejpam-5993	322	8	-	-	PUNCT
ejpam-5993	322	9	group	group	NOUN
ejpam-5993	322	10	and	and	CCONJ
ejpam-5993	322	11	p	p	NOUN
ejpam-5993	322	12	is	be	AUX
ejpam-5993	322	13	a	a	DET
ejpam-5993	322	14	non	non	ADJ
ejpam-5993	322	15	-	-	ADJ
ejpam-5993	322	16	cyclic	cyclic	ADJ
ejpam-5993	322	17	sylow	sylow	NOUN
ejpam-5993	322	18	p	p	NOUN
ejpam-5993	322	19	-	-	PUNCT
ejpam-5993	322	20	subgroup	subgroup	NOUN
ejpam-5993	322	21	,	,	PUNCT
ejpam-5993	322	22	so	so	CCONJ
ejpam-5993	322	23	every	every	DET
ejpam-5993	322	24	subgroup	subgroup	NOUN
ejpam-5993	322	25	of391	of391	PROPN
ejpam-5993	322	26	order	order	NOUN
ejpam-5993	322	27	p	p	NOUN
ejpam-5993	322	28	is	be	AUX
ejpam-5993	322	29	a	a	DET
ejpam-5993	322	30	normal	normal	ADJ
ejpam-5993	322	31	subgroup	subgroup	NOUN
ejpam-5993	322	32	in	in	ADP
ejpam-5993	322	33	pq	pq	PROPN
ejpam-5993	322	34	,	,	PUNCT
ejpam-5993	322	35	where	where	SCONJ
ejpam-5993	322	36	(	(	PUNCT
ejpam-5993	322	37	p	p	X
ejpam-5993	322	38	,	,	PUNCT
ejpam-5993	322	39	|q|	|q|	NUM
ejpam-5993	322	40	)	)	PUNCT
ejpam-5993	322	41	=	=	SYM
ejpam-5993	322	42	1	1	X
ejpam-5993	322	43	.	.	PUNCT
ejpam-5993	323	1	on	on	ADP
ejpam-5993	323	2	the	the	DET
ejpam-5993	323	3	other	other	ADJ
ejpam-5993	323	4	hand	hand	NOUN
ejpam-5993	323	5	,	,	PUNCT
ejpam-5993	323	6	we	we	PRON
ejpam-5993	323	7	know	know	VERB
ejpam-5993	323	8	that392	that392	PROPN
ejpam-5993	323	9	ri	ri	PROPN
ejpam-5993	323	10	∩	∩	PROPN
ejpam-5993	323	11	z(p	z(p	X
ejpam-5993	323	12	)	)	PUNCT
ejpam-5993	323	13	̸=	̸=	PROPN
ejpam-5993	323	14	1	1	NUM
ejpam-5993	323	15	,	,	PUNCT
ejpam-5993	323	16	where	where	SCONJ
ejpam-5993	323	17	(	(	PUNCT
ejpam-5993	323	18	i	i	NOUN
ejpam-5993	323	19	=	=	NOUN
ejpam-5993	323	20	1	1	NUM
ejpam-5993	323	21	,	,	PUNCT
ejpam-5993	323	22	...	...	PUNCT
ejpam-5993	323	23	,	,	PUNCT
ejpam-5993	323	24	t	t	PROPN
ejpam-5993	323	25	)	)	PUNCT
ejpam-5993	323	26	.	.	PUNCT
ejpam-5993	324	1	let	let	VERB
ejpam-5993	324	2	li	li	PROPN
ejpam-5993	324	3	be	be	AUX
ejpam-5993	324	4	subgroup	subgroup	NOUN
ejpam-5993	324	5	of	of	ADP
ejpam-5993	324	6	ri	ri	NOUN
ejpam-5993	324	7	∩	∩	NOUN
ejpam-5993	324	8	z(p	z(p	NUM
ejpam-5993	324	9	)	)	PUNCT
ejpam-5993	324	10	of	of	ADP
ejpam-5993	324	11	order	order	NOUN
ejpam-5993	324	12	p	p	X
ejpam-5993	324	13	,	,	PUNCT
ejpam-5993	324	14	,	,	PUNCT
ejpam-5993	324	15	where393	where393	PROPN
ejpam-5993	324	16	(	(	PUNCT
ejpam-5993	324	17	i	i	NOUN
ejpam-5993	324	18	=	=	NOUN
ejpam-5993	324	19	1	1	NUM
ejpam-5993	324	20	,	,	PUNCT
ejpam-5993	324	21	...	...	PUNCT
ejpam-5993	324	22	,	,	PUNCT
ejpam-5993	324	23	t	t	PROPN
ejpam-5993	324	24	)	)	PUNCT
ejpam-5993	324	25	.	.	PUNCT
ejpam-5993	325	1	then	then	ADV
ejpam-5993	325	2	li	li	PROPN
ejpam-5993	325	3	is	be	AUX
ejpam-5993	325	4	normal	normal	ADJ
ejpam-5993	325	5	in	in	ADP
ejpam-5993	325	6	p	p	NOUN
ejpam-5993	326	1	and	and	CCONJ
ejpam-5993	326	2	we	we	PRON
ejpam-5993	326	3	have	have	VERB
ejpam-5993	326	4	li	li	PROPN
ejpam-5993	326	5	is	be	AUX
ejpam-5993	326	6	subnormal	subnormal	ADJ
ejpam-5993	326	7	in	in	ADP
ejpam-5993	326	8	g.	g.	PROPN
ejpam-5993	327	1	now	now	ADV
ejpam-5993	327	2	,	,	PUNCT
ejpam-5993	327	3	if	if	SCONJ
ejpam-5993	327	4	li	li	PROPN
ejpam-5993	327	5	=	=	SYM
ejpam-5993	327	6	p1,394	p1,394	PROPN
ejpam-5993	327	7	then	then	ADV
ejpam-5993	327	8	li	li	PROPN
ejpam-5993	327	9	is	be	AUX
ejpam-5993	327	10	normal	normal	ADJ
ejpam-5993	327	11	in	in	ADP
ejpam-5993	327	12	g.	g.	PROPN
ejpam-5993	327	13	also	also	ADV
ejpam-5993	327	14	,	,	PUNCT
ejpam-5993	327	15	if	if	SCONJ
ejpam-5993	327	16	li	li	PROPN
ejpam-5993	327	17	is	be	AUX
ejpam-5993	327	18	a	a	DET
ejpam-5993	327	19	proper	proper	ADJ
ejpam-5993	327	20	subgroup	subgroup	NOUN
ejpam-5993	327	21	of	of	ADP
ejpam-5993	327	22	p1	p1	PROPN
ejpam-5993	327	23	,	,	PUNCT
ejpam-5993	327	24	then	then	ADV
ejpam-5993	327	25	li	li	PROPN
ejpam-5993	327	26	is	be	AUX
ejpam-5993	327	27	an	an	DET
ejpam-5993	327	28	h	h	NOUN
ejpam-5993	327	29	-	-	PUNCT
ejpam-5993	327	30	subgroup395	subgroup395	PROPN
ejpam-5993	327	31	in	in	ADP
ejpam-5993	327	32	g.	g.	NOUN
ejpam-5993	327	33	applying	apply	VERB
ejpam-5993	327	34	lemma	lemma	PROPN
ejpam-5993	327	35	4	4	NUM
ejpam-5993	327	36	,	,	PUNCT
ejpam-5993	327	37	we	we	PRON
ejpam-5993	327	38	get	get	VERB
ejpam-5993	327	39	li	li	PROPN
ejpam-5993	327	40	⊴	⊴	PROPN
ejpam-5993	327	41	g.	g.	PROPN
ejpam-5993	327	42	since	since	SCONJ
ejpam-5993	327	43	ri	ri	PROPN
ejpam-5993	327	44	is	be	AUX
ejpam-5993	327	45	a	a	DET
ejpam-5993	327	46	minimal	minimal	ADJ
ejpam-5993	327	47	normal	normal	ADJ
ejpam-5993	327	48	subgroup	subgroup	NOUN
ejpam-5993	327	49	of	of	ADP
ejpam-5993	327	50	g,396	g,396	ADV
ejpam-5993	327	51	it	it	PRON
ejpam-5993	327	52	follows	follow	VERB
ejpam-5993	327	53	that	that	SCONJ
ejpam-5993	327	54	|li|	|li|	PROPN
ejpam-5993	327	55	=	=	SYM
ejpam-5993	327	56	|ri|	|ri|	NOUN
ejpam-5993	328	1	=	=	PUNCT
ejpam-5993	328	2	p	p	NOUN
ejpam-5993	328	3	is	be	AUX
ejpam-5993	328	4	a	a	DET
ejpam-5993	328	5	cyclic	cyclic	ADJ
ejpam-5993	328	6	group	group	NOUN
ejpam-5993	328	7	of	of	ADP
ejpam-5993	328	8	order	order	NOUN
ejpam-5993	328	9	p	p	X
ejpam-5993	328	10	,	,	PUNCT
ejpam-5993	328	11	for	for	ADP
ejpam-5993	328	12	any	any	DET
ejpam-5993	328	13	i	i	PROPN
ejpam-5993	328	14	,	,	PUNCT
ejpam-5993	328	15	which	which	PRON
ejpam-5993	328	16	contradict	contradict	VERB
ejpam-5993	328	17	(	(	PUNCT
ejpam-5993	328	18	4)397	4)397	NUM
ejpam-5993	328	19	completing	complete	VERB
ejpam-5993	328	20	the	the	DET
ejpam-5993	328	21	proof	proof	NOUN
ejpam-5993	328	22	of	of	ADP
ejpam-5993	328	23	the	the	DET
ejpam-5993	328	24	theorem.398	theorem.398	PROPN
ejpam-5993	328	25	as	as	ADP
ejpam-5993	328	26	an	an	DET
ejpam-5993	328	27	application	application	NOUN
ejpam-5993	328	28	of	of	ADP
ejpam-5993	328	29	theorem	theorem	NOUN
ejpam-5993	328	30	4	4	NUM
ejpam-5993	328	31	,	,	PUNCT
ejpam-5993	328	32	we	we	PRON
ejpam-5993	328	33	have:399	have:399	VERB
ejpam-5993	328	34	theorem	theorem	VERB
ejpam-5993	328	35	5	5	NUM
ejpam-5993	328	36	.	.	PUNCT
ejpam-5993	329	1	let	let	VERB
ejpam-5993	329	2	f	f	PRON
ejpam-5993	329	3	be	be	AUX
ejpam-5993	329	4	a	a	DET
ejpam-5993	329	5	saturated	saturated	ADJ
ejpam-5993	329	6	formation	formation	NOUN
ejpam-5993	329	7	containing	contain	VERB
ejpam-5993	329	8	u.	u.	NOUN
ejpam-5993	329	9	a	a	DET
ejpam-5993	329	10	group	group	NOUN
ejpam-5993	329	11	g	g	PROPN
ejpam-5993	329	12	lies	lie	VERB
ejpam-5993	329	13	in	in	ADP
ejpam-5993	329	14	f	f	PROPN
ejpam-5993	329	15	if	if	SCONJ
ejpam-5993	329	16	and400	and400	PROPN
ejpam-5993	329	17	only	only	ADV
ejpam-5993	329	18	if	if	SCONJ
ejpam-5993	329	19	it	it	PRON
ejpam-5993	329	20	has	have	VERB
ejpam-5993	329	21	a	a	DET
ejpam-5993	329	22	solvable	solvable	ADJ
ejpam-5993	329	23	normal	normal	ADJ
ejpam-5993	329	24	subgroup	subgroup	NOUN
ejpam-5993	329	25	h	h	NOUN
ejpam-5993	330	1	such	such	ADJ
ejpam-5993	330	2	that	that	SCONJ
ejpam-5993	330	3	g	g	NOUN
ejpam-5993	330	4	/	/	SYM
ejpam-5993	330	5	h	h	NOUN
ejpam-5993	330	6	∈	∈	PROPN
ejpam-5993	330	7	f	f	PROPN
ejpam-5993	330	8	and	and	CCONJ
ejpam-5993	330	9	all	all	PRON
ejpam-5993	330	10	maximal	maximal	ADJ
ejpam-5993	330	11	subgroups401	subgroups401	PROPN
ejpam-5993	330	12	of	of	ADP
ejpam-5993	330	13	the	the	DET
ejpam-5993	330	14	non	non	ADJ
ejpam-5993	330	15	-	-	ADJ
ejpam-5993	330	16	cyclic	cyclic	ADJ
ejpam-5993	330	17	sylow	sylow	NOUN
ejpam-5993	330	18	subgroups	subgroup	NOUN
ejpam-5993	330	19	of	of	ADP
ejpam-5993	330	20	f	f	PROPN
ejpam-5993	330	21	⋆(h	⋆(h	PROPN
ejpam-5993	330	22	)	)	PUNCT
ejpam-5993	330	23	are	be	AUX
ejpam-5993	330	24	ssh	ssh	NOUN
ejpam-5993	330	25	-	-	PUNCT
ejpam-5993	330	26	subgroups	subgroup	NOUN
ejpam-5993	330	27	in	in	ADP
ejpam-5993	330	28	g.402	g.402	NOUN
ejpam-5993	330	29	proof	proof	NOUN
ejpam-5993	330	30	.	.	PUNCT
ejpam-5993	331	1	we	we	PRON
ejpam-5993	331	2	need	need	VERB
ejpam-5993	331	3	only	only	ADV
ejpam-5993	331	4	to	to	PART
ejpam-5993	331	5	prove	prove	VERB
ejpam-5993	331	6	the	the	DET
ejpam-5993	331	7	part	part	NOUN
ejpam-5993	331	8	”	"	PUNCT
ejpam-5993	331	9	if	if	SCONJ
ejpam-5993	331	10	”	"	PUNCT
ejpam-5993	331	11	.	.	PUNCT
ejpam-5993	332	1	we	we	PRON
ejpam-5993	332	2	use	use	VERB
ejpam-5993	332	3	induction	induction	NOUN
ejpam-5993	332	4	on	on	ADP
ejpam-5993	332	5	|g|	|g|	PROPN
ejpam-5993	332	6	.	.	PUNCT
ejpam-5993	333	1	by	by	ADP
ejpam-5993	333	2	hypothesis403	hypothesis403	PROPN
ejpam-5993	333	3	and	and	CCONJ
ejpam-5993	333	4	lemma	lemma	PROPN
ejpam-5993	333	5	2(i	2(i	NUM
ejpam-5993	333	6	)	)	PUNCT
ejpam-5993	333	7	,	,	PUNCT
ejpam-5993	333	8	we	we	PRON
ejpam-5993	333	9	have	have	VERB
ejpam-5993	333	10	that	that	SCONJ
ejpam-5993	333	11	all	all	DET
ejpam-5993	333	12	maximal	maximal	ADJ
ejpam-5993	333	13	subgroups	subgroup	NOUN
ejpam-5993	333	14	of	of	ADP
ejpam-5993	333	15	the	the	DET
ejpam-5993	333	16	non	non	ADJ
ejpam-5993	333	17	-	-	ADJ
ejpam-5993	333	18	cyclic	cyclic	ADJ
ejpam-5993	333	19	sylow	sylow	NOUN
ejpam-5993	333	20	subgroups404	subgroups404	PROPN
ejpam-5993	333	21	of	of	ADP
ejpam-5993	333	22	f	f	PROPN
ejpam-5993	333	23	⋆(h	⋆(h	PROPN
ejpam-5993	333	24	)	)	PUNCT
ejpam-5993	333	25	are	be	AUX
ejpam-5993	333	26	ssh	ssh	NOUN
ejpam-5993	333	27	-	-	PUNCT
ejpam-5993	333	28	subgroups	subgroup	NOUN
ejpam-5993	333	29	of	of	ADP
ejpam-5993	333	30	h.	h.	PROPN
ejpam-5993	334	1	then	then	ADV
ejpam-5993	334	2	f	f	PROPN
ejpam-5993	334	3	⋆(h	⋆(h	PROPN
ejpam-5993	334	4	)	)	PUNCT
ejpam-5993	334	5	=	=	SYM
ejpam-5993	334	6	f	f	PROPN
ejpam-5993	334	7	(	(	PUNCT
ejpam-5993	334	8	h	h	NOUN
ejpam-5993	334	9	)	)	PUNCT
ejpam-5993	334	10	as	as	SCONJ
ejpam-5993	334	11	h	h	NOUN
ejpam-5993	334	12	is	be	AUX
ejpam-5993	334	13	supersolvable	supersolvable	ADJ
ejpam-5993	334	14	by405	by405	PROPN
ejpam-5993	334	15	theorem	theorem	VERB
ejpam-5993	334	16	4	4	NUM
ejpam-5993	334	17	.	.	PUNCT
ejpam-5993	335	1	therefore	therefore	ADV
ejpam-5993	335	2	,	,	PUNCT
ejpam-5993	335	3	h	h	NOUN
ejpam-5993	335	4	is	be	AUX
ejpam-5993	335	5	solvable	solvable	ADJ
ejpam-5993	335	6	normal	normal	ADJ
ejpam-5993	335	7	subgroup	subgroup	NOUN
ejpam-5993	335	8	of	of	ADP
ejpam-5993	335	9	g	g	NOUN
ejpam-5993	335	10	with	with	ADP
ejpam-5993	335	11	g	g	PROPN
ejpam-5993	335	12	/	/	SYM
ejpam-5993	335	13	h	h	NOUN
ejpam-5993	335	14	∈	∈	PROPN
ejpam-5993	335	15	f	f	PROPN
ejpam-5993	335	16	and	and	CCONJ
ejpam-5993	335	17	all406	all406	VERB
ejpam-5993	335	18	maximal	maximal	ADJ
ejpam-5993	335	19	subgroups	subgroup	NOUN
ejpam-5993	335	20	of	of	ADP
ejpam-5993	335	21	the	the	DET
ejpam-5993	335	22	non	non	ADJ
ejpam-5993	335	23	-	-	ADJ
ejpam-5993	335	24	cyclic	cyclic	ADJ
ejpam-5993	335	25	sylow	sylow	NOUN
ejpam-5993	335	26	subgroups	subgroup	NOUN
ejpam-5993	335	27	of	of	ADP
ejpam-5993	335	28	f	f	PROPN
ejpam-5993	335	29	(	(	PUNCT
ejpam-5993	335	30	h	h	NOUN
ejpam-5993	335	31	)	)	PUNCT
ejpam-5993	335	32	are	be	AUX
ejpam-5993	335	33	ssh	ssh	NOUN
ejpam-5993	335	34	-	-	PUNCT
ejpam-5993	335	35	subgroups	subgroup	NOUN
ejpam-5993	335	36	in	in	ADP
ejpam-5993	335	37	g.407	g.407	NOUN
ejpam-5993	335	38	applying	apply	VERB
ejpam-5993	335	39	theorem	theorem	NOUN
ejpam-5993	335	40	3	3	NUM
ejpam-5993	335	41	yield	yield	NOUN
ejpam-5993	335	42	g	g	PROPN
ejpam-5993	335	43	∈	∈	PROPN
ejpam-5993	335	44	f.	f.	NOUN
ejpam-5993	336	1	this	this	PRON
ejpam-5993	336	2	completes	complete	VERB
ejpam-5993	336	3	the	the	DET
ejpam-5993	336	4	proof	proof	NOUN
ejpam-5993	336	5	of	of	ADP
ejpam-5993	336	6	the	the	DET
ejpam-5993	336	7	theorem.408	theorem.408	NOUN
ejpam-5993	336	8	remark	remark	NOUN
ejpam-5993	336	9	2	2	NUM
ejpam-5993	336	10	.	.	PUNCT
ejpam-5993	337	1	(	(	PUNCT
ejpam-5993	337	2	i	i	NOUN
ejpam-5993	337	3	)	)	PUNCT
ejpam-5993	337	4	theorem	theorem	VERB
ejpam-5993	337	5	5	5	NUM
ejpam-5993	337	6	is	be	AUX
ejpam-5993	337	7	not	not	PART
ejpam-5993	337	8	true	true	ADJ
ejpam-5993	337	9	if	if	SCONJ
ejpam-5993	337	10	we	we	PRON
ejpam-5993	337	11	omit	omit	VERB
ejpam-5993	337	12	the	the	DET
ejpam-5993	337	13	solvability	solvability	NOUN
ejpam-5993	337	14	of	of	ADP
ejpam-5993	337	15	h.	h.	PROPN
ejpam-5993	337	16	set	set	VERB
ejpam-5993	337	17	g	g	PROPN
ejpam-5993	337	18	=	=	PUNCT
ejpam-5993	337	19	n	n	PROPN
ejpam-5993	337	20	×m	×m	NOUN
ejpam-5993	337	21	,	,	PUNCT
ejpam-5993	337	22	409	409	NUM
ejpam-5993	337	23	a.	a.	NOUN
ejpam-5993	337	24	s.	s.	PROPN
ejpam-5993	337	25	allehyani	allehyani	PROPN
ejpam-5993	337	26	/	/	SYM
ejpam-5993	337	27	eur	eur	PROPN
ejpam-5993	337	28	.	.	PUNCT
ejpam-5993	338	1	j.	j.	PROPN
ejpam-5993	338	2	pure	pure	PROPN
ejpam-5993	338	3	appl	appl	PROPN
ejpam-5993	338	4	.	.	PROPN
ejpam-5993	338	5	math	math	PROPN
ejpam-5993	338	6	,	,	PUNCT
ejpam-5993	338	7	18	18	NUM
ejpam-5993	338	8	(	(	PUNCT
ejpam-5993	338	9	2	2	NUM
ejpam-5993	338	10	)	)	PUNCT
ejpam-5993	338	11	(	(	PUNCT
ejpam-5993	338	12	2025	2025	NUM
ejpam-5993	338	13	)	)	PUNCT
ejpam-5993	338	14	,	,	PUNCT
ejpam-5993	338	15	5993	5993	NUM
ejpam-5993	338	16	12	12	NUM
ejpam-5993	338	17	of	of	ADP
ejpam-5993	338	18	13	13	NUM
ejpam-5993	338	19	where	where	SCONJ
ejpam-5993	338	20	n	n	PROPN
ejpam-5993	338	21	=	=	SYM
ejpam-5993	338	22	sl(2	sl(2	PROPN
ejpam-5993	338	23	,	,	PUNCT
ejpam-5993	338	24	5	5	NUM
ejpam-5993	338	25	)	)	PUNCT
ejpam-5993	338	26	,	,	PUNCT
ejpam-5993	338	27	the	the	DET
ejpam-5993	338	28	special	special	ADJ
ejpam-5993	338	29	linear	linear	PROPN
ejpam-5993	338	30	group	group	NOUN
ejpam-5993	338	31	of	of	ADP
ejpam-5993	338	32	degree	degree	NOUN
ejpam-5993	338	33	2	2	NUM
ejpam-5993	338	34	and	and	CCONJ
ejpam-5993	338	35	m	m	PROPN
ejpam-5993	338	36	∈	∈	PROPN
ejpam-5993	338	37	u.	u.	NOUN
ejpam-5993	339	1	then	then	ADV
ejpam-5993	339	2	f	f	PROPN
ejpam-5993	339	3	⋆(n	⋆(n	PROPN
ejpam-5993	339	4	)	)	PUNCT
ejpam-5993	340	1	=	=	NOUN
ejpam-5993	340	2	410	410	NUM
ejpam-5993	340	3	n	n	NOUN
ejpam-5993	340	4	and	and	CCONJ
ejpam-5993	340	5	g	g	NOUN
ejpam-5993	340	6	/	/	SYM
ejpam-5993	340	7	n	n	PRON
ejpam-5993	340	8	∼=	∼=	PART
ejpam-5993	340	9	m	m	NOUN
ejpam-5993	340	10	∈	∈	NOUN
ejpam-5993	340	11	u	u	NOUN
ejpam-5993	340	12	,	,	PUNCT
ejpam-5993	340	13	but	but	CCONJ
ejpam-5993	340	14	g	g	NOUN
ejpam-5993	340	15	does	do	AUX
ejpam-5993	340	16	not	not	PART
ejpam-5993	340	17	belong	belong	VERB
ejpam-5993	340	18	to	to	ADP
ejpam-5993	340	19	u.411	u.411	ADJ
ejpam-5993	340	20	(	(	PUNCT
ejpam-5993	340	21	ii	ii	NOUN
ejpam-5993	340	22	)	)	PUNCT
ejpam-5993	340	23	theorem	theorem	NOUN
ejpam-5993	340	24	5	5	NUM
ejpam-5993	340	25	is	be	AUX
ejpam-5993	340	26	not	not	PART
ejpam-5993	340	27	true	true	ADJ
ejpam-5993	340	28	for	for	ADP
ejpam-5993	340	29	non	non	ADJ
ejpam-5993	340	30	-	-	ADJ
ejpam-5993	340	31	saturated	saturated	ADJ
ejpam-5993	340	32	formation	formation	NOUN
ejpam-5993	340	33	.	.	PUNCT
ejpam-5993	341	1	for	for	ADP
ejpam-5993	341	2	example	example	NOUN
ejpam-5993	341	3	,	,	PUNCT
ejpam-5993	341	4	let	let	VERB
ejpam-5993	341	5	f	f	PRON
ejpam-5993	341	6	be	be	AUX
ejpam-5993	341	7	the	the	DET
ejpam-5993	341	8	forma-412	forma-412	ADJ
ejpam-5993	341	9	tion	tion	NOUN
ejpam-5993	341	10	composed	compose	VERB
ejpam-5993	341	11	of	of	ADP
ejpam-5993	341	12	all	all	DET
ejpam-5993	341	13	groups	group	NOUN
ejpam-5993	341	14	g	g	ADP
ejpam-5993	341	15	such	such	ADJ
ejpam-5993	341	16	that	that	DET
ejpam-5993	341	17	gu	gu	NOUN
ejpam-5993	341	18	,	,	PUNCT
ejpam-5993	341	19	the	the	DET
ejpam-5993	341	20	supersolvable	supersolvable	ADJ
ejpam-5993	341	21	residual	residual	NOUN
ejpam-5993	341	22	,	,	PUNCT
ejpam-5993	341	23	is	be	AUX
ejpam-5993	341	24	elementary413	elementary413	PROPN
ejpam-5993	341	25	abelian	abelian	NOUN
ejpam-5993	341	26	.	.	PUNCT
ejpam-5993	342	1	it	it	PRON
ejpam-5993	342	2	is	be	AUX
ejpam-5993	342	3	clear	clear	ADJ
ejpam-5993	342	4	that	that	SCONJ
ejpam-5993	342	5	u	u	PROPN
ejpam-5993	342	6	⊆	⊆	NUM
ejpam-5993	342	7	f	f	PROPN
ejpam-5993	342	8	and	and	CCONJ
ejpam-5993	342	9	f	f	PROPN
ejpam-5993	342	10	is	be	AUX
ejpam-5993	342	11	not	not	PART
ejpam-5993	342	12	a	a	DET
ejpam-5993	342	13	saturated	saturated	ADJ
ejpam-5993	342	14	formation	formation	NOUN
ejpam-5993	342	15	.	.	PUNCT
ejpam-5993	343	1	let	let	VERB
ejpam-5993	343	2	g	g	PROPN
ejpam-5993	343	3	=	=	PROPN
ejpam-5993	343	4	sl(2	sl(2	PROPN
ejpam-5993	343	5	,	,	PUNCT
ejpam-5993	343	6	3)414	3)414	NUM
ejpam-5993	343	7	and	and	CCONJ
ejpam-5993	343	8	n	n	NOUN
ejpam-5993	343	9	=	=	PUNCT
ejpam-5993	343	10	z(g	z(g	NOUN
ejpam-5993	343	11	)	)	PUNCT
ejpam-5993	343	12	.	.	PUNCT
ejpam-5993	344	1	then	then	ADV
ejpam-5993	344	2	g	g	PROPN
ejpam-5993	344	3	/	/	SYM
ejpam-5993	344	4	n	n	PRON
ejpam-5993	344	5	∼=	∼=	NOUN
ejpam-5993	344	6	a4	a4	NOUN
ejpam-5993	344	7	,	,	PUNCT
ejpam-5993	344	8	so	so	SCONJ
ejpam-5993	344	9	g	g	PROPN
ejpam-5993	344	10	/	/	SYM
ejpam-5993	344	11	n	n	CCONJ
ejpam-5993	344	12	∈	∈	PROPN
ejpam-5993	344	13	f.	f.	NOUN
ejpam-5993	345	1	but	but	CCONJ
ejpam-5993	345	2	g	g	PROPN
ejpam-5993	345	3	does	do	AUX
ejpam-5993	345	4	not	not	PART
ejpam-5993	345	5	belong	belong	VERB
ejpam-5993	345	6	to	to	ADP
ejpam-5993	345	7	u.415	u.415	NOUN
ejpam-5993	345	8	4	4	NUM
ejpam-5993	345	9	.	.	PUNCT
ejpam-5993	346	1	conclusion416	conclusion416	X
ejpam-5993	346	2	due	due	ADP
ejpam-5993	346	3	to	to	ADP
ejpam-5993	346	4	the	the	DET
ejpam-5993	346	5	importance	importance	NOUN
ejpam-5993	346	6	of	of	ADP
ejpam-5993	346	7	finite	finite	ADJ
ejpam-5993	346	8	groups	group	NOUN
ejpam-5993	346	9	theory	theory	NOUN
ejpam-5993	346	10	and	and	CCONJ
ejpam-5993	346	11	its	its	PRON
ejpam-5993	346	12	application	application	NOUN
ejpam-5993	346	13	in	in	ADP
ejpam-5993	346	14	abstract	abstract	ADJ
ejpam-5993	346	15	algebra,417	algebra,417	PROPN
ejpam-5993	347	1	our	our	PRON
ejpam-5993	347	2	study	study	NOUN
ejpam-5993	347	3	in	in	ADP
ejpam-5993	347	4	this	this	DET
ejpam-5993	347	5	article	article	NOUN
ejpam-5993	347	6	focused	focus	VERB
ejpam-5993	347	7	on	on	ADP
ejpam-5993	347	8	the	the	DET
ejpam-5993	347	9	structure	structure	NOUN
ejpam-5993	347	10	of	of	ADP
ejpam-5993	347	11	a	a	DET
ejpam-5993	347	12	finite	finite	ADJ
ejpam-5993	347	13	group	group	NOUN
ejpam-5993	347	14	g	g	NOUN
ejpam-5993	347	15	assuming	assume	VERB
ejpam-5993	347	16	that	that	SCONJ
ejpam-5993	347	17	some418	some418	PROPN
ejpam-5993	347	18	subgroups	subgroup	NOUN
ejpam-5993	347	19	of	of	ADP
ejpam-5993	347	20	prime	prime	ADJ
ejpam-5993	347	21	power	power	NOUN
ejpam-5993	347	22	order	order	NOUN
ejpam-5993	347	23	are	be	AUX
ejpam-5993	347	24	ssh	ssh	NOUN
ejpam-5993	347	25	-	-	PUNCT
ejpam-5993	347	26	subgroups	subgroup	NOUN
ejpam-5993	347	27	.	.	PUNCT
ejpam-5993	348	1	in	in	ADP
ejpam-5993	348	2	the	the	DET
ejpam-5993	348	3	current	current	ADJ
ejpam-5993	348	4	article	article	NOUN
ejpam-5993	348	5	,	,	PUNCT
ejpam-5993	348	6	we	we	PRON
ejpam-5993	348	7	have419	have419	PROPN
ejpam-5993	348	8	reached	reach	VERB
ejpam-5993	348	9	the	the	DET
ejpam-5993	348	10	following	follow	VERB
ejpam-5993	348	11	results	result	NOUN
ejpam-5993	348	12	:	:	PUNCT
ejpam-5993	348	13	if	if	SCONJ
ejpam-5993	348	14	g	g	PROPN
ejpam-5993	348	15	is	be	AUX
ejpam-5993	348	16	solvable	solvable	ADJ
ejpam-5993	348	17	and	and	CCONJ
ejpam-5993	348	18	the	the	DET
ejpam-5993	348	19	maximal	maximal	ADJ
ejpam-5993	348	20	subgroups	subgroup	NOUN
ejpam-5993	348	21	of	of	ADP
ejpam-5993	348	22	the	the	DET
ejpam-5993	348	23	non-420	non-420	PROPN
ejpam-5993	348	24	cyclic	cyclic	PROPN
ejpam-5993	348	25	sylow	sylow	NOUN
ejpam-5993	348	26	subgroups	subgroup	NOUN
ejpam-5993	348	27	of	of	ADP
ejpam-5993	348	28	f	f	PROPN
ejpam-5993	348	29	(	(	PUNCT
ejpam-5993	348	30	g	g	NOUN
ejpam-5993	348	31	)	)	PUNCT
ejpam-5993	348	32	are	be	AUX
ejpam-5993	348	33	ssh	ssh	NOUN
ejpam-5993	348	34	-	-	PUNCT
ejpam-5993	348	35	subgroups	subgroup	NOUN
ejpam-5993	348	36	,	,	PUNCT
ejpam-5993	348	37	then	then	ADV
ejpam-5993	348	38	g	g	PROPN
ejpam-5993	348	39	is	be	AUX
ejpam-5993	348	40	supersolvable	supersolvable	ADJ
ejpam-5993	348	41	.	.	PUNCT
ejpam-5993	349	1	also	also	ADV
ejpam-5993	349	2	,	,	PUNCT
ejpam-5993	349	3	let421	let421	PROPN
ejpam-5993	349	4	g	g	PROPN
ejpam-5993	349	5	be	be	AUX
ejpam-5993	349	6	a	a	DET
ejpam-5993	349	7	group	group	NOUN
ejpam-5993	349	8	with	with	ADP
ejpam-5993	349	9	a	a	DET
ejpam-5993	349	10	normal	normal	ADJ
ejpam-5993	349	11	subgroup	subgroup	NOUN
ejpam-5993	349	12	h	h	NOUN
ejpam-5993	349	13	such	such	ADJ
ejpam-5993	349	14	that	that	SCONJ
ejpam-5993	349	15	g	g	PROPN
ejpam-5993	349	16	/	/	SYM
ejpam-5993	349	17	h	h	NOUN
ejpam-5993	349	18	is	be	AUX
ejpam-5993	349	19	supersolvable	supersolvable	ADJ
ejpam-5993	349	20	.	.	PUNCT
ejpam-5993	350	1	if	if	SCONJ
ejpam-5993	350	2	all	all	DET
ejpam-5993	350	3	maximal422	maximal422	PROPN
ejpam-5993	350	4	subgroups	subgroup	NOUN
ejpam-5993	350	5	of	of	ADP
ejpam-5993	350	6	the	the	DET
ejpam-5993	350	7	non	non	ADJ
ejpam-5993	350	8	-	-	ADJ
ejpam-5993	350	9	cyclic	cyclic	ADJ
ejpam-5993	350	10	sylow	sylow	NOUN
ejpam-5993	350	11	subgroups	subgroup	NOUN
ejpam-5993	350	12	of	of	ADP
ejpam-5993	350	13	f	f	PROPN
ejpam-5993	350	14	⋆(h	⋆(h	PROPN
ejpam-5993	350	15	)	)	PUNCT
ejpam-5993	350	16	are	be	AUX
ejpam-5993	350	17	ssh	ssh	NOUN
ejpam-5993	350	18	-	-	PUNCT
ejpam-5993	350	19	subgroups	subgroup	NOUN
ejpam-5993	350	20	of	of	ADP
ejpam-5993	350	21	g	g	NOUN
ejpam-5993	350	22	,	,	PUNCT
ejpam-5993	350	23	then	then	ADV
ejpam-5993	350	24	g423	g423	PROPN
ejpam-5993	350	25	is	be	AUX
ejpam-5993	350	26	supersolvable	supersolvable	ADJ
ejpam-5993	350	27	.	.	PUNCT
ejpam-5993	351	1	finally	finally	ADV
ejpam-5993	351	2	,	,	PUNCT
ejpam-5993	351	3	several	several	ADJ
ejpam-5993	351	4	recent	recent	ADJ
ejpam-5993	351	5	and	and	CCONJ
ejpam-5993	351	6	classical	classical	ADJ
ejpam-5993	351	7	results	result	NOUN
ejpam-5993	351	8	were	be	AUX
ejpam-5993	351	9	generalized	generalize	VERB
ejpam-5993	351	10	through	through	ADP
ejpam-5993	351	11	the424	the424	PROPN
ejpam-5993	351	12	theory	theory	NOUN
ejpam-5993	351	13	of	of	ADP
ejpam-5993	351	14	formations.425	formations.425	PROPN
ejpam-5993	351	15	acknowledgements426	acknowledgements426	PROPN
ejpam-5993	351	16	the	the	DET
ejpam-5993	351	17	author	author	NOUN
ejpam-5993	351	18	thank	thank	VERB
ejpam-5993	351	19	the	the	DET
ejpam-5993	351	20	reviewers	reviewer	NOUN
ejpam-5993	351	21	for	for	ADP
ejpam-5993	351	22	their	their	PRON
ejpam-5993	351	23	valuable	valuable	ADJ
ejpam-5993	351	24	and	and	CCONJ
ejpam-5993	351	25	helpful	helpful	ADJ
ejpam-5993	351	26	suggestions	suggestion	NOUN
ejpam-5993	351	27	and	and	CCONJ
ejpam-5993	351	28	com-427	com-427	ADJ
ejpam-5993	351	29	ments.428	ments.428	PROPN
ejpam-5993	351	30	references429	references429	PROPN
ejpam-5993	352	1	[	[	X
ejpam-5993	352	2	1	1	X
ejpam-5993	352	3	]	]	X
ejpam-5993	352	4	o.	o.	PROPN
ejpam-5993	352	5	h.	h.	PROPN
ejpam-5993	352	6	kegel	kegel	PROPN
ejpam-5993	352	7	.	.	PUNCT
ejpam-5993	353	1	sylow	sylow	NOUN
ejpam-5993	353	2	-	-	PUNCT
ejpam-5993	353	3	gruppen	gruppen	NOUN
ejpam-5993	353	4	und	und	NOUN
ejpam-5993	353	5	subnormalteiler	subnormalteiler	NOUN
ejpam-5993	353	6	endlicher	endlicher	PROPN
ejpam-5993	353	7	gruppen	gruppen	PROPN
ejpam-5993	353	8	.	.	PUNCT
ejpam-5993	354	1	mathematische430	mathematische430	PROPN
ejpam-5993	354	2	zeitschrift	zeitschrift	NOUN
ejpam-5993	354	3	,	,	PUNCT
ejpam-5993	354	4	78(1):205–221	78(1):205–221	PROPN
ejpam-5993	354	5	,	,	PUNCT
ejpam-5993	354	6	1962.431	1962.431	NUM
ejpam-5993	355	1	[	[	X
ejpam-5993	355	2	2	2	NUM
ejpam-5993	355	3	]	]	X
ejpam-5993	355	4	y.	y.	PROPN
ejpam-5993	355	5	wang	wang	PROPN
ejpam-5993	355	6	.	.	PUNCT
ejpam-5993	356	1	c	c	X
ejpam-5993	356	2	-	-	PUNCT
ejpam-5993	356	3	normality	normality	NOUN
ejpam-5993	356	4	of	of	ADP
ejpam-5993	356	5	groups	group	NOUN
ejpam-5993	356	6	and	and	CCONJ
ejpam-5993	356	7	its	its	PRON
ejpam-5993	356	8	properties	property	NOUN
ejpam-5993	356	9	.	.	PUNCT
ejpam-5993	357	1	journal	journal	NOUN
ejpam-5993	357	2	of	of	ADP
ejpam-5993	357	3	algebra	algebra	PROPN
ejpam-5993	357	4	,	,	PUNCT
ejpam-5993	357	5	180(3):954–432	180(3):954–432	NUM
ejpam-5993	357	6	965	965	NUM
ejpam-5993	357	7	,	,	PUNCT
ejpam-5993	357	8	1996.433	1996.433	NUM
ejpam-5993	358	1	[	[	X
ejpam-5993	358	2	3	3	NUM
ejpam-5993	358	3	]	]	PUNCT
ejpam-5993	358	4	m.	m.	NOUN
ejpam-5993	358	5	bianchi	bianchi	PROPN
ejpam-5993	358	6	,	,	PUNCT
ejpam-5993	358	7	a.	a.	PROPN
ejpam-5993	358	8	g.	g.	PROPN
ejpam-5993	358	9	b.	b.	PROPN
ejpam-5993	358	10	mauri	mauri	PROPN
ejpam-5993	358	11	,	,	PUNCT
ejpam-5993	358	12	m.	m.	NOUN
ejpam-5993	358	13	herzog	herzog	PROPN
ejpam-5993	358	14	,	,	PUNCT
ejpam-5993	358	15	and	and	CCONJ
ejpam-5993	358	16	l.	l.	PROPN
ejpam-5993	358	17	verardi	verardi	PROPN
ejpam-5993	358	18	.	.	PUNCT
ejpam-5993	359	1	on	on	ADP
ejpam-5993	359	2	finite	finite	PROPN
ejpam-5993	359	3	solvable	solvable	ADJ
ejpam-5993	359	4	groups434	groups434	PROPN
ejpam-5993	359	5	in	in	ADP
ejpam-5993	359	6	which	which	PRON
ejpam-5993	359	7	normality	normality	NOUN
ejpam-5993	359	8	is	be	AUX
ejpam-5993	359	9	a	a	DET
ejpam-5993	359	10	transitive	transitive	ADJ
ejpam-5993	359	11	relation	relation	NOUN
ejpam-5993	359	12	.	.	PUNCT
ejpam-5993	360	1	journal	journal	PROPN
ejpam-5993	360	2	of	of	ADP
ejpam-5993	360	3	group	group	PROPN
ejpam-5993	360	4	theory	theory	NOUN
ejpam-5993	360	5	,	,	PUNCT
ejpam-5993	360	6	3(2):147–156,435	3(2):147–156,435	NUM
ejpam-5993	360	7	2000.436	2000.436	NUM
ejpam-5993	361	1	[	[	X
ejpam-5993	361	2	4	4	NUM
ejpam-5993	361	3	]	]	PUNCT
ejpam-5993	361	4	x.	x.	NOUN
ejpam-5993	361	5	wei	wei	PROPN
ejpam-5993	361	6	and	and	CCONJ
ejpam-5993	361	7	x.	x.	PROPN
ejpam-5993	361	8	guo	guo	PROPN
ejpam-5993	361	9	.	.	PUNCT
ejpam-5993	362	1	on	on	ADP
ejpam-5993	362	2	hc	hc	NOUN
ejpam-5993	362	3	-	-	PUNCT
ejpam-5993	362	4	subgroups	subgroup	NOUN
ejpam-5993	362	5	and	and	CCONJ
ejpam-5993	362	6	the	the	DET
ejpam-5993	362	7	structure	structure	NOUN
ejpam-5993	362	8	of	of	ADP
ejpam-5993	362	9	finite	finite	ADJ
ejpam-5993	362	10	groups	group	NOUN
ejpam-5993	362	11	.	.	PUNCT
ejpam-5993	363	1	communi-437	communi-437	ADJ
ejpam-5993	363	2	cations	cation	NOUN
ejpam-5993	363	3	in	in	ADP
ejpam-5993	363	4	algebra	algebra	NOUN
ejpam-5993	363	5	,	,	PUNCT
ejpam-5993	363	6	40(9):3245–3256	40(9):3245–3256	NUM
ejpam-5993	363	7	,	,	PUNCT
ejpam-5993	363	8	2012.438	2012.438	NUM
ejpam-5993	363	9	[	[	X
ejpam-5993	363	10	5	5	NUM
ejpam-5993	363	11	]	]	PUNCT
ejpam-5993	363	12	m.	m.	NOUN
ejpam-5993	363	13	asaad	asaad	NOUN
ejpam-5993	363	14	and	and	CCONJ
ejpam-5993	363	15	m.	m.	PROPN
ejpam-5993	363	16	ramadan	ramadan	PROPN
ejpam-5993	363	17	.	.	PUNCT
ejpam-5993	364	1	on	on	ADP
ejpam-5993	364	2	weakly	weakly	ADJ
ejpam-5993	364	3	hc	hc	ADV
ejpam-5993	364	4	-	-	PUNCT
ejpam-5993	364	5	embedded	embed	VERB
ejpam-5993	364	6	subgroups	subgroup	NOUN
ejpam-5993	364	7	of	of	ADP
ejpam-5993	364	8	finite	finite	ADJ
ejpam-5993	364	9	groups.439	groups.439	ADJ
ejpam-5993	364	10	journal	journal	NOUN
ejpam-5993	364	11	of	of	ADP
ejpam-5993	364	12	algebra	algebra	PROPN
ejpam-5993	364	13	and	and	CCONJ
ejpam-5993	364	14	its	its	PRON
ejpam-5993	364	15	applications	application	NOUN
ejpam-5993	364	16	,	,	PUNCT
ejpam-5993	364	17	15(5):1650091	15(5):1650091	NUM
ejpam-5993	364	18	,	,	PUNCT
ejpam-5993	364	19	2016.440	2016.440	NUM
ejpam-5993	364	20	[	[	X
ejpam-5993	364	21	6	6	NUM
ejpam-5993	364	22	]	]	PUNCT
ejpam-5993	364	23	t.	t.	PROPN
ejpam-5993	364	24	m.	m.	PROPN
ejpam-5993	364	25	al	al	PROPN
ejpam-5993	364	26	-	-	PUNCT
ejpam-5993	364	27	gafri	gafri	PROPN
ejpam-5993	364	28	and	and	CCONJ
ejpam-5993	364	29	s.	s.	PROPN
ejpam-5993	364	30	k.	k.	PROPN
ejpam-5993	364	31	nauman	nauman	PROPN
ejpam-5993	364	32	.	.	PUNCT
ejpam-5993	365	1	on	on	ADP
ejpam-5993	365	2	ssh	ssh	NOUN
ejpam-5993	365	3	-	-	PUNCT
ejpam-5993	365	4	subgroups	subgroup	NOUN
ejpam-5993	365	5	of	of	ADP
ejpam-5993	365	6	finite	finite	ADJ
ejpam-5993	365	7	groups	group	NOUN
ejpam-5993	365	8	.	.	PUNCT
ejpam-5993	366	1	annali441	annali441	NOUN
ejpam-5993	366	2	dell’università	dell’università	X
ejpam-5993	366	3	di	di	NOUN
ejpam-5993	366	4	ferrara	ferrara	NOUN
ejpam-5993	366	5	,	,	PUNCT
ejpam-5993	366	6	64(2):209–225	64(2):209–225	PROPN
ejpam-5993	366	7	,	,	PUNCT
ejpam-5993	366	8	2018.442	2018.442	NUM
ejpam-5993	366	9	[	[	X
ejpam-5993	366	10	7	7	NUM
ejpam-5993	366	11	]	]	PUNCT
ejpam-5993	366	12	s.	s.	PROPN
ejpam-5993	366	13	srinivasan	srinivasan	PROPN
ejpam-5993	366	14	.	.	PUNCT
ejpam-5993	367	1	two	two	NUM
ejpam-5993	367	2	sufficient	sufficient	ADJ
ejpam-5993	367	3	conditions	condition	NOUN
ejpam-5993	367	4	for	for	ADP
ejpam-5993	367	5	supersolvability	supersolvability	NOUN
ejpam-5993	367	6	of	of	ADP
ejpam-5993	367	7	finite	finite	ADJ
ejpam-5993	367	8	groups	group	NOUN
ejpam-5993	367	9	.	.	PUNCT
ejpam-5993	368	1	israel443	israel443	PROPN
ejpam-5993	368	2	journal	journal	PROPN
ejpam-5993	368	3	of	of	ADP
ejpam-5993	368	4	mathematics	mathematic	NOUN
ejpam-5993	368	5	,	,	PUNCT
ejpam-5993	368	6	35(3):210–214	35(3):210–214	NUM
ejpam-5993	368	7	,	,	PUNCT
ejpam-5993	368	8	1980.444	1980.444	NUM
ejpam-5993	368	9	a.	a.	NOUN
ejpam-5993	368	10	s.	s.	PROPN
ejpam-5993	368	11	allehyani	allehyani	PROPN
ejpam-5993	368	12	/	/	SYM
ejpam-5993	368	13	eur	eur	PROPN
ejpam-5993	368	14	.	.	PUNCT
ejpam-5993	369	1	j.	j.	PROPN
ejpam-5993	369	2	pure	pure	PROPN
ejpam-5993	369	3	appl	appl	PROPN
ejpam-5993	369	4	.	.	PROPN
ejpam-5993	369	5	math	math	PROPN
ejpam-5993	369	6	,	,	PUNCT
ejpam-5993	369	7	18	18	NUM
ejpam-5993	369	8	(	(	PUNCT
ejpam-5993	369	9	2	2	NUM
ejpam-5993	369	10	)	)	PUNCT
ejpam-5993	369	11	(	(	PUNCT
ejpam-5993	369	12	2025	2025	NUM
ejpam-5993	369	13	)	)	PUNCT
ejpam-5993	369	14	,	,	PUNCT
ejpam-5993	369	15	5993	5993	NUM
ejpam-5993	369	16	13	13	NUM
ejpam-5993	369	17	of	of	ADP
ejpam-5993	369	18	13	13	NUM
ejpam-5993	369	19	[	[	SYM
ejpam-5993	369	20	8	8	NUM
ejpam-5993	369	21	]	]	PUNCT
ejpam-5993	369	22	m.	m.	NOUN
ejpam-5993	369	23	asaad	asaad	NOUN
ejpam-5993	369	24	.	.	PUNCT
ejpam-5993	370	1	on	on	ADP
ejpam-5993	370	2	p	p	PROPN
ejpam-5993	370	3	-	-	PUNCT
ejpam-5993	370	4	nilpotence	nilpotence	NOUN
ejpam-5993	370	5	and	and	CCONJ
ejpam-5993	370	6	supersolvability	supersolvability	NOUN
ejpam-5993	370	7	of	of	ADP
ejpam-5993	370	8	finite	finite	ADJ
ejpam-5993	370	9	groups	group	NOUN
ejpam-5993	370	10	.	.	PUNCT
ejpam-5993	371	1	communications	communication	NOUN
ejpam-5993	371	2	in445	in445	PROPN
ejpam-5993	371	3	algebra	algebra	PROPN
ejpam-5993	371	4	,	,	PUNCT
ejpam-5993	371	5	34(1):189–195	34(1):189–195	PROPN
ejpam-5993	371	6	,	,	PUNCT
ejpam-5993	371	7	2006.446	2006.446	NUM
ejpam-5993	371	8	[	[	X
ejpam-5993	371	9	9	9	NUM
ejpam-5993	371	10	]	]	PUNCT
ejpam-5993	371	11	m.	m.	NOUN
ejpam-5993	371	12	m.	m.	NOUN
ejpam-5993	371	13	al	al	PROPN
ejpam-5993	371	14	-	-	PUNCT
ejpam-5993	371	15	shomrani	shomrani	PROPN
ejpam-5993	371	16	,	,	PUNCT
ejpam-5993	371	17	m.	m.	NOUN
ejpam-5993	371	18	ramadan	ramadan	PROPN
ejpam-5993	371	19	,	,	PUNCT
ejpam-5993	371	20	and	and	CCONJ
ejpam-5993	371	21	a.	a.	NOUN
ejpam-5993	371	22	a.	a.	NOUN
ejpam-5993	371	23	heliel	heliel	PROPN
ejpam-5993	371	24	.	.	PUNCT
ejpam-5993	372	1	finite	finite	ADJ
ejpam-5993	372	2	groups	group	NOUN
ejpam-5993	372	3	whose	whose	DET
ejpam-5993	372	4	minimal447	minimal447	PROPN
ejpam-5993	372	5	subgroups	subgroup	NOUN
ejpam-5993	372	6	are	be	AUX
ejpam-5993	372	7	weakly	weakly	ADJ
ejpam-5993	372	8	h	h	NOUN
ejpam-5993	372	9	-	-	PUNCT
ejpam-5993	372	10	subgroups	subgroup	NOUN
ejpam-5993	372	11	.	.	PUNCT
ejpam-5993	373	1	acta	acta	PROPN
ejpam-5993	373	2	mathematica	mathematica	PROPN
ejpam-5993	373	3	scientia	scientia	PROPN
ejpam-5993	373	4	,	,	PUNCT
ejpam-5993	373	5	32(6):2295–2301,448	32(6):2295–2301,448	NUM
ejpam-5993	373	6	2012.449	2012.449	PROPN
ejpam-5993	374	1	[	[	X
ejpam-5993	374	2	10	10	NUM
ejpam-5993	374	3	]	]	PUNCT
ejpam-5993	374	4	m.	m.	NOUN
ejpam-5993	374	5	asaad	asaad	NOUN
ejpam-5993	374	6	,	,	PUNCT
ejpam-5993	374	7	m.	m.	NOUN
ejpam-5993	374	8	m.	m.	PROPN
ejpam-5993	374	9	al	al	PROPN
ejpam-5993	374	10	-	-	PUNCT
ejpam-5993	374	11	shomrani	shomrani	PROPN
ejpam-5993	374	12	,	,	PUNCT
ejpam-5993	374	13	and	and	CCONJ
ejpam-5993	374	14	a.	a.	NOUN
ejpam-5993	374	15	a.	a.	NOUN
ejpam-5993	374	16	heliel	heliel	PROPN
ejpam-5993	374	17	.	.	PUNCT
ejpam-5993	375	1	influence	influence	NOUN
ejpam-5993	375	2	of	of	ADP
ejpam-5993	375	3	weakly	weakly	ADJ
ejpam-5993	375	4	h	h	NOUN
ejpam-5993	375	5	-	-	NOUN
ejpam-5993	375	6	subgroups450	subgroups450	PROPN
ejpam-5993	375	7	on	on	ADP
ejpam-5993	375	8	the	the	DET
ejpam-5993	375	9	structure	structure	NOUN
ejpam-5993	375	10	of	of	ADP
ejpam-5993	375	11	finite	finite	ADJ
ejpam-5993	375	12	groups	group	NOUN
ejpam-5993	375	13	.	.	PUNCT
ejpam-5993	376	1	studia	studia	PROPN
ejpam-5993	376	2	scientiarum	scientiarum	PROPN
ejpam-5993	376	3	mathematicarum	mathematicarum	PROPN
ejpam-5993	376	4	hungarica,451	hungarica,451	PROPN
ejpam-5993	376	5	51(1):27–40	51(1):27–40	NUM
ejpam-5993	376	6	,	,	PUNCT
ejpam-5993	376	7	2014.452	2014.452	NUM
ejpam-5993	376	8	[	[	X
ejpam-5993	376	9	11	11	NUM
ejpam-5993	376	10	]	]	PUNCT
ejpam-5993	376	11	m.	m.	NOUN
ejpam-5993	376	12	asaad	asaad	PROPN
ejpam-5993	376	13	,	,	PUNCT
ejpam-5993	376	14	m.	m.	NOUN
ejpam-5993	376	15	ramadan	ramadan	PROPN
ejpam-5993	376	16	,	,	PUNCT
ejpam-5993	376	17	and	and	CCONJ
ejpam-5993	376	18	a.	a.	NOUN
ejpam-5993	376	19	a.	a.	NOUN
ejpam-5993	376	20	heliel	heliel	PROPN
ejpam-5993	376	21	.	.	PUNCT
ejpam-5993	377	1	influence	influence	NOUN
ejpam-5993	377	2	of	of	ADP
ejpam-5993	377	3	weaklyh	weaklyh	NOUN
ejpam-5993	377	4	-	-	PUNCT
ejpam-5993	377	5	embedded	embed	VERB
ejpam-5993	377	6	subgroups453	subgroups453	PROPN
ejpam-5993	377	7	on	on	ADP
ejpam-5993	377	8	the	the	DET
ejpam-5993	377	9	structure	structure	NOUN
ejpam-5993	377	10	of	of	ADP
ejpam-5993	377	11	finite	finite	ADJ
ejpam-5993	377	12	groups	group	NOUN
ejpam-5993	377	13	.	.	PUNCT
ejpam-5993	378	1	publicationes	publicatione	NOUN
ejpam-5993	378	2	mathematicae	mathematicae	PROPN
ejpam-5993	378	3	debrecen	debrecen	PROPN
ejpam-5993	378	4	,	,	PUNCT
ejpam-5993	378	5	91(3	91(3	NOUN
ejpam-5993	378	6	-	-	SYM
ejpam-5993	378	7	4):503–454	4):503–454	NUM
ejpam-5993	378	8	513	513	NUM
ejpam-5993	378	9	,	,	PUNCT
ejpam-5993	378	10	2017.455	2017.455	NUM
ejpam-5993	379	1	[	[	X
ejpam-5993	379	2	12	12	NUM
ejpam-5993	379	3	]	]	PUNCT
ejpam-5993	379	4	m.	m.	NOUN
ejpam-5993	379	5	asaad	asaad	PROPN
ejpam-5993	379	6	,	,	PUNCT
ejpam-5993	379	7	a.	a.	NOUN
ejpam-5993	379	8	a.	a.	NOUN
ejpam-5993	379	9	heliel	heliel	PROPN
ejpam-5993	379	10	,	,	PUNCT
ejpam-5993	379	11	and	and	CCONJ
ejpam-5993	379	12	m.	m.	NOUN
ejpam-5993	379	13	m.	m.	PROPN
ejpam-5993	379	14	al	al	PROPN
ejpam-5993	379	15	-	-	PUNCT
ejpam-5993	379	16	shomrani	shomrani	PROPN
ejpam-5993	379	17	.	.	PUNCT
ejpam-5993	380	1	on	on	ADP
ejpam-5993	380	2	weakly	weakly	ADJ
ejpam-5993	380	3	h	h	NOUN
ejpam-5993	380	4	-	-	PUNCT
ejpam-5993	380	5	subgroups	subgroup	NOUN
ejpam-5993	380	6	of	of	ADP
ejpam-5993	380	7	finite456	finite456	PROPN
ejpam-5993	380	8	groups	group	NOUN
ejpam-5993	380	9	.	.	PUNCT
ejpam-5993	381	1	communications	communication	NOUN
ejpam-5993	381	2	in	in	ADP
ejpam-5993	381	3	algebra	algebra	NOUN
ejpam-5993	381	4	,	,	PUNCT
ejpam-5993	381	5	40(9):3540–3550	40(9):3540–3550	NUM
ejpam-5993	381	6	,	,	PUNCT
ejpam-5993	381	7	2012.457	2012.457	NUM
ejpam-5993	381	8	[	[	SYM
ejpam-5993	381	9	13	13	NUM
ejpam-5993	381	10	]	]	PUNCT
ejpam-5993	381	11	b.	b.	PROPN
ejpam-5993	381	12	huppert	huppert	PROPN
ejpam-5993	381	13	.	.	PUNCT
ejpam-5993	382	1	endliche	endliche	PROPN
ejpam-5993	382	2	gruppen	gruppen	PROPN
ejpam-5993	382	3	i.	i.	PROPN
ejpam-5993	382	4	springer	springer	PROPN
ejpam-5993	382	5	,	,	PUNCT
ejpam-5993	382	6	berlin	berlin	PROPN
ejpam-5993	382	7	,	,	PUNCT
ejpam-5993	382	8	1967.458	1967.458	PROPN
ejpam-5993	382	9	[	[	X
ejpam-5993	382	10	14	14	NUM
ejpam-5993	382	11	]	]	X
ejpam-5993	382	12	w.	w.	PROPN
ejpam-5993	382	13	guo	guo	PROPN
ejpam-5993	382	14	.	.	PUNCT
ejpam-5993	383	1	the	the	DET
ejpam-5993	383	2	theory	theory	NOUN
ejpam-5993	383	3	of	of	ADP
ejpam-5993	383	4	classes	class	NOUN
ejpam-5993	383	5	of	of	ADP
ejpam-5993	383	6	groups	group	NOUN
ejpam-5993	383	7	.	.	PUNCT
ejpam-5993	384	1	kluwer	kluwer	NOUN
ejpam-5993	384	2	academic	academic	ADJ
ejpam-5993	384	3	publishers	publisher	NOUN
ejpam-5993	384	4	,	,	PUNCT
ejpam-5993	384	5	dordrecht,459	dordrecht,459	NOUN
ejpam-5993	384	6	2000.460	2000.460	NUM
ejpam-5993	385	1	[	[	X
ejpam-5993	385	2	15	15	NUM
ejpam-5993	385	3	]	]	X
ejpam-5993	385	4	d.	d.	PROPN
ejpam-5993	385	5	j.	j.	PROPN
ejpam-5993	385	6	s.	s.	PROPN
ejpam-5993	385	7	robinson	robinson	PROPN
ejpam-5993	385	8	.	.	PUNCT
ejpam-5993	386	1	a	a	DET
ejpam-5993	386	2	course	course	NOUN
ejpam-5993	386	3	in	in	ADP
ejpam-5993	386	4	the	the	DET
ejpam-5993	386	5	theory	theory	NOUN
ejpam-5993	386	6	of	of	ADP
ejpam-5993	386	7	groups	group	NOUN
ejpam-5993	386	8	.	.	PUNCT
ejpam-5993	387	1	springer	springer	NOUN
ejpam-5993	387	2	,	,	PUNCT
ejpam-5993	387	3	new	new	PROPN
ejpam-5993	387	4	york	york	PROPN
ejpam-5993	387	5	,	,	PUNCT
ejpam-5993	387	6	1993.461	1993.461	NUM
ejpam-5993	388	1	[	[	X
ejpam-5993	388	2	16	16	NUM
ejpam-5993	388	3	]	]	X
ejpam-5993	388	4	l.	l.	PROPN
ejpam-5993	388	5	miao	miao	PROPN
ejpam-5993	388	6	and	and	CCONJ
ejpam-5993	388	7	w.	w.	PROPN
ejpam-5993	388	8	lempken	lempken	PROPN
ejpam-5993	388	9	.	.	PUNCT
ejpam-5993	389	1	on	on	ADP
ejpam-5993	389	2	m	m	ADJ
ejpam-5993	389	3	-	-	PUNCT
ejpam-5993	389	4	supplemented	supplement	VERB
ejpam-5993	389	5	subgroups	subgroup	NOUN
ejpam-5993	389	6	of	of	ADP
ejpam-5993	389	7	finite	finite	ADJ
ejpam-5993	389	8	groups	group	NOUN
ejpam-5993	389	9	.	.	PUNCT
ejpam-5993	390	1	journal462	journal462	PROPN
ejpam-5993	390	2	of	of	ADP
ejpam-5993	390	3	group	group	PROPN
ejpam-5993	390	4	theory	theory	NOUN
ejpam-5993	390	5	,	,	PUNCT
ejpam-5993	390	6	12(2):271–287	12(2):271–287	NUM
ejpam-5993	390	7	,	,	PUNCT
ejpam-5993	390	8	2009.463	2009.463	PROPN
ejpam-5993	390	9	[	[	X
ejpam-5993	390	10	17	17	NUM
ejpam-5993	390	11	]	]	X
ejpam-5993	390	12	y.	y.	PROPN
ejpam-5993	390	13	wang	wang	PROPN
ejpam-5993	390	14	,	,	PUNCT
ejpam-5993	390	15	y.	y.	PROPN
ejpam-5993	390	16	li	li	PROPN
ejpam-5993	390	17	,	,	PUNCT
ejpam-5993	390	18	and	and	CCONJ
ejpam-5993	390	19	h.	h.	PROPN
ejpam-5993	390	20	wei	wei	PROPN
ejpam-5993	390	21	.	.	PUNCT
ejpam-5993	391	1	the	the	DET
ejpam-5993	391	2	influence	influence	NOUN
ejpam-5993	391	3	of	of	ADP
ejpam-5993	391	4	π	π	PROPN
ejpam-5993	391	5	-	-	NOUN
ejpam-5993	391	6	quasinormality	quasinormality	NOUN
ejpam-5993	391	7	of	of	ADP
ejpam-5993	391	8	some	some	DET
ejpam-5993	391	9	subgroups	subgroup	NOUN
ejpam-5993	391	10	of464	of464	ADP
ejpam-5993	391	11	a	a	DET
ejpam-5993	391	12	finite	finite	ADJ
ejpam-5993	391	13	group	group	NOUN
ejpam-5993	391	14	.	.	PUNCT
ejpam-5993	392	1	archiv	archiv	PROPN
ejpam-5993	392	2	der	der	PROPN
ejpam-5993	392	3	mathematik	mathematik	PROPN
ejpam-5993	392	4	,	,	PUNCT
ejpam-5993	392	5	81(3):245–252	81(3):245–252	PROPN
ejpam-5993	392	6	,	,	PUNCT
ejpam-5993	392	7	2003.465	2003.465	PROPN
ejpam-5993	393	1	[	[	X
ejpam-5993	393	2	18	18	NUM
ejpam-5993	393	3	]	]	X
ejpam-5993	393	4	w.	w.	PROPN
ejpam-5993	393	5	guo	guo	PROPN
ejpam-5993	393	6	and	and	CCONJ
ejpam-5993	393	7	a.	a.	PROPN
ejpam-5993	393	8	n.	n.	PROPN
ejpam-5993	393	9	skiba	skiba	PROPN
ejpam-5993	393	10	.	.	PUNCT
ejpam-5993	394	1	finite	finite	PROPN
ejpam-5993	394	2	groups	group	NOUN
ejpam-5993	394	3	with	with	ADP
ejpam-5993	394	4	given	give	VERB
ejpam-5993	394	5	s	s	PRON
ejpam-5993	394	6	-	-	PUNCT
ejpam-5993	394	7	embedded	embed	VERB
ejpam-5993	394	8	and	and	CCONJ
ejpam-5993	394	9	n	n	CCONJ
ejpam-5993	394	10	-	-	PUNCT
ejpam-5993	394	11	embedded466	embedded466	PROPN
ejpam-5993	394	12	subgroups	subgroup	NOUN
ejpam-5993	394	13	.	.	PUNCT
ejpam-5993	395	1	journal	journal	NOUN
ejpam-5993	395	2	of	of	ADP
ejpam-5993	395	3	algebra	algebra	PROPN
ejpam-5993	395	4	,	,	PUNCT
ejpam-5993	395	5	321(10):2843–2860	321(10):2843–2860	NUM
ejpam-5993	395	6	,	,	PUNCT
ejpam-5993	395	7	2009.467	2009.467	NUM
ejpam-5993	395	8	[	[	X
ejpam-5993	395	9	19	19	NUM
ejpam-5993	395	10	]	]	PUNCT
ejpam-5993	395	11	m.	m.	NOUN
ejpam-5993	395	12	asaad	asaad	NOUN
ejpam-5993	395	13	and	and	CCONJ
ejpam-5993	395	14	a.	a.	NOUN
ejpam-5993	395	15	a.	a.	NOUN
ejpam-5993	395	16	heliel	heliel	PROPN
ejpam-5993	395	17	.	.	PUNCT
ejpam-5993	396	1	on	on	ADP
ejpam-5993	396	2	permutable	permutable	ADJ
ejpam-5993	396	3	subgroups	subgroup	NOUN
ejpam-5993	396	4	of	of	ADP
ejpam-5993	396	5	finite	finite	ADJ
ejpam-5993	396	6	groups	group	NOUN
ejpam-5993	396	7	.	.	PUNCT
ejpam-5993	397	1	archiv	archiv	PROPN
ejpam-5993	397	2	der468	der468	PROPN
ejpam-5993	397	3	mathematik	mathematik	PROPN
ejpam-5993	397	4	,	,	PUNCT
ejpam-5993	397	5	80(2):113–118	80(2):113–118	PROPN
ejpam-5993	397	6	,	,	PUNCT
ejpam-5993	397	7	2003.469	2003.469	NUM
ejpam-5993	397	8	[	[	X
ejpam-5993	397	9	20	20	NUM
ejpam-5993	397	10	]	]	PUNCT
ejpam-5993	397	11	b.	b.	PROPN
ejpam-5993	397	12	huppert	huppert	PROPN
ejpam-5993	397	13	and	and	CCONJ
ejpam-5993	397	14	n.	n.	PROPN
ejpam-5993	397	15	blackburn	blackburn	PROPN
ejpam-5993	397	16	.	.	PUNCT
ejpam-5993	398	1	finite	finite	PROPN
ejpam-5993	398	2	groups	groups	PROPN
ejpam-5993	398	3	iii	iii	PROPN
ejpam-5993	398	4	.	.	PROPN
ejpam-5993	398	5	springer	springer	PROPN
ejpam-5993	398	6	,	,	PUNCT
ejpam-5993	398	7	berlin	berlin	PROPN
ejpam-5993	398	8	,	,	PUNCT
ejpam-5993	398	9	1982.470	1982.470	PROPN
ejpam-5993	399	1	[	[	X
ejpam-5993	399	2	21	21	NUM
ejpam-5993	399	3	]	]	PUNCT
ejpam-5993	399	4	m.	m.	NOUN
ejpam-5993	399	5	weinstein	weinstein	PROPN
ejpam-5993	399	6	.	.	PUNCT
ejpam-5993	400	1	between	between	ADP
ejpam-5993	400	2	nilpotent	nilpotent	NOUN
ejpam-5993	400	3	and	and	CCONJ
ejpam-5993	400	4	solvable	solvable	ADJ
ejpam-5993	400	5	.	.	PUNCT
ejpam-5993	401	1	polygonal	polygonal	ADJ
ejpam-5993	401	2	publishing	publishing	NOUN
ejpam-5993	401	3	house	house	NOUN
ejpam-5993	401	4	,	,	PUNCT
ejpam-5993	401	5	passaic,471	passaic,471	PROPN
ejpam-5993	401	6	nj	nj	PROPN
ejpam-5993	401	7	,	,	PUNCT
ejpam-5993	401	8	1982.472	1982.472	ADJ