id	sid	tid	token	lemma	pos
ejpam-4036	1	1	european	european	PROPN
ejpam-4036	1	2	journal	journal	PROPN
ejpam-4036	1	3	of	of	ADP
ejpam-4036	1	4	pure	pure	ADJ
ejpam-4036	1	5	and	and	CCONJ
ejpam-4036	1	6	applied	apply	VERB
ejpam-4036	1	7	mathematics	mathematic	NOUN
ejpam-4036	1	8	vol	vol	NOUN
ejpam-4036	1	9	.	.	PUNCT
ejpam-4036	2	1	14	14	NUM
ejpam-4036	2	2	,	,	PUNCT
ejpam-4036	2	3	no	no	INTJ
ejpam-4036	2	4	.	.	NOUN
ejpam-4036	2	5	3	3	NUM
ejpam-4036	2	6	,	,	PUNCT
ejpam-4036	2	7	2021	2021	NUM
ejpam-4036	2	8	,	,	PUNCT
ejpam-4036	2	9	1002	1002	NUM
ejpam-4036	2	10	-	-	SYM
ejpam-4036	2	11	1014	1014	NUM
ejpam-4036	2	12	issn	issn	PROPN
ejpam-4036	2	13	1307	1307	NUM
ejpam-4036	2	14	-	-	SYM
ejpam-4036	2	15	5543	5543	NUM
ejpam-4036	2	16	–	–	PUNCT
ejpam-4036	2	17	ejpam.com	ejpam.com	X
ejpam-4036	2	18	published	publish	VERB
ejpam-4036	2	19	by	by	ADP
ejpam-4036	2	20	new	new	PROPN
ejpam-4036	2	21	york	york	PROPN
ejpam-4036	2	22	business	business	PROPN
ejpam-4036	2	23	global	global	ADJ
ejpam-4036	2	24	finite	finite	ADJ
ejpam-4036	2	25	groups	group	NOUN
ejpam-4036	2	26	with	with	ADP
ejpam-4036	2	27	minimal	minimal	ADJ
ejpam-4036	2	28	css	css	PROPN
ejpam-4036	2	29	-	-	PUNCT
ejpam-4036	2	30	subgroups	subgroup	NOUN
ejpam-4036	2	31	abd	abd	PROPN
ejpam-4036	2	32	el	el	PROPN
ejpam-4036	2	33	-	-	PROPN
ejpam-4036	2	34	rahman	rahman	PROPN
ejpam-4036	2	35	heliel1,2,∗	heliel1,2,∗	PROPN
ejpam-4036	2	36	,	,	PUNCT
ejpam-4036	2	37	rola	rola	PROPN
ejpam-4036	2	38	hijazi1	hijazi1	PROPN
ejpam-4036	2	39	,	,	PUNCT
ejpam-4036	2	40	shorouq	shorouq	NOUN
ejpam-4036	2	41	al	al	PROPN
ejpam-4036	2	42	-	-	PUNCT
ejpam-4036	2	43	shammari1,3	shammari1,3	PROPN
ejpam-4036	2	44	1	1	NUM
ejpam-4036	2	45	department	department	NOUN
ejpam-4036	2	46	of	of	ADP
ejpam-4036	2	47	mathematics	mathematic	NOUN
ejpam-4036	2	48	,	,	PUNCT
ejpam-4036	2	49	faculty	faculty	NOUN
ejpam-4036	2	50	of	of	ADP
ejpam-4036	2	51	science	science	NOUN
ejpam-4036	2	52	,	,	PUNCT
ejpam-4036	2	53	king	king	PROPN
ejpam-4036	2	54	abdulaziz	abdulaziz	PROPN
ejpam-4036	2	55	university	university	PROPN
ejpam-4036	2	56	,	,	PUNCT
ejpam-4036	2	57	jeddah	jeddah	PROPN
ejpam-4036	2	58	21589	21589	NUM
ejpam-4036	2	59	,	,	PUNCT
ejpam-4036	2	60	saudi	saudi	PROPN
ejpam-4036	2	61	arabia	arabia	PROPN
ejpam-4036	2	62	2	2	NUM
ejpam-4036	2	63	department	department	NOUN
ejpam-4036	2	64	of	of	ADP
ejpam-4036	2	65	mathematics	mathematic	NOUN
ejpam-4036	2	66	and	and	CCONJ
ejpam-4036	2	67	computer	computer	NOUN
ejpam-4036	2	68	science	science	NOUN
ejpam-4036	2	69	,	,	PUNCT
ejpam-4036	2	70	faculty	faculty	NOUN
ejpam-4036	2	71	of	of	ADP
ejpam-4036	2	72	science	science	NOUN
ejpam-4036	2	73	,	,	PUNCT
ejpam-4036	2	74	beni	beni	ADJ
ejpam-4036	2	75	-	-	ADJ
ejpam-4036	2	76	suef	suef	ADJ
ejpam-4036	2	77	university	university	NOUN
ejpam-4036	2	78	,	,	PUNCT
ejpam-4036	2	79	beni	beni	NOUN
ejpam-4036	2	80	-	-	NOUN
ejpam-4036	2	81	suef	suef	NOUN
ejpam-4036	2	82	62511	62511	NUM
ejpam-4036	2	83	,	,	PUNCT
ejpam-4036	2	84	egypt	egypt	PROPN
ejpam-4036	2	85	3	3	NUM
ejpam-4036	2	86	department	department	PROPN
ejpam-4036	2	87	of	of	ADP
ejpam-4036	2	88	science	science	NOUN
ejpam-4036	2	89	and	and	CCONJ
ejpam-4036	2	90	technology	technology	NOUN
ejpam-4036	2	91	,	,	PUNCT
ejpam-4036	2	92	the	the	DET
ejpam-4036	2	93	university	university	NOUN
ejpam-4036	2	94	college	college	NOUN
ejpam-4036	2	95	in	in	ADP
ejpam-4036	2	96	al	al	PROPN
ejpam-4036	2	97	khafji	khafji	PROPN
ejpam-4036	2	98	,	,	PUNCT
ejpam-4036	2	99	university	university	NOUN
ejpam-4036	2	100	of	of	ADP
ejpam-4036	2	101	hafr	hafr	PROPN
ejpam-4036	2	102	al	al	PROPN
ejpam-4036	2	103	batin	batin	PROPN
ejpam-4036	2	104	,	,	PUNCT
ejpam-4036	2	105	al	al	PROPN
ejpam-4036	2	106	khafji	khafji	PROPN
ejpam-4036	2	107	,	,	PUNCT
ejpam-4036	2	108	saudi	saudi	PROPN
ejpam-4036	2	109	arabia	arabia	PROPN
ejpam-4036	2	110	abstract	abstract	NOUN
ejpam-4036	2	111	.	.	PUNCT
ejpam-4036	3	1	let	let	VERB
ejpam-4036	3	2	g	g	PRON
ejpam-4036	3	3	be	be	AUX
ejpam-4036	3	4	a	a	DET
ejpam-4036	3	5	finite	finite	ADJ
ejpam-4036	3	6	group	group	NOUN
ejpam-4036	3	7	.	.	PUNCT
ejpam-4036	4	1	a	a	DET
ejpam-4036	4	2	subgroup	subgroup	NOUN
ejpam-4036	4	3	h	h	NOUN
ejpam-4036	4	4	of	of	ADP
ejpam-4036	4	5	g	g	PROPN
ejpam-4036	4	6	is	be	AUX
ejpam-4036	4	7	called	call	VERB
ejpam-4036	4	8	ss	ss	NOUN
ejpam-4036	4	9	-	-	ADJ
ejpam-4036	4	10	quasinormal	quasinormal	ADJ
ejpam-4036	4	11	in	in	ADP
ejpam-4036	4	12	g	g	PROPN
ejpam-4036	4	13	if	if	SCONJ
ejpam-4036	4	14	there	there	PRON
ejpam-4036	4	15	is	be	VERB
ejpam-4036	4	16	a	a	DET
ejpam-4036	4	17	supplement	supplement	NOUN
ejpam-4036	4	18	b	b	NOUN
ejpam-4036	4	19	of	of	ADP
ejpam-4036	4	20	h	h	NOUN
ejpam-4036	4	21	to	to	ADP
ejpam-4036	4	22	g	g	NOUN
ejpam-4036	4	23	such	such	ADJ
ejpam-4036	4	24	that	that	SCONJ
ejpam-4036	4	25	h	h	NOUN
ejpam-4036	4	26	permutes	permute	NOUN
ejpam-4036	4	27	with	with	ADP
ejpam-4036	4	28	every	every	DET
ejpam-4036	4	29	sylow	sylow	NOUN
ejpam-4036	4	30	subgroup	subgroup	NOUN
ejpam-4036	4	31	of	of	ADP
ejpam-4036	4	32	b.	b.	PROPN
ejpam-4036	4	33	a	a	DET
ejpam-4036	4	34	subgroup	subgroup	NOUN
ejpam-4036	4	35	h	h	NOUN
ejpam-4036	4	36	of	of	ADP
ejpam-4036	4	37	g	g	PROPN
ejpam-4036	4	38	is	be	AUX
ejpam-4036	4	39	called	call	VERB
ejpam-4036	4	40	css	css	PROPN
ejpam-4036	4	41	-	-	NOUN
ejpam-4036	4	42	subgroup	subgroup	NOUN
ejpam-4036	4	43	in	in	ADP
ejpam-4036	4	44	g	g	PROPN
ejpam-4036	4	45	if	if	SCONJ
ejpam-4036	4	46	there	there	PRON
ejpam-4036	4	47	exists	exist	VERB
ejpam-4036	4	48	a	a	DET
ejpam-4036	4	49	normal	normal	ADJ
ejpam-4036	4	50	subgroup	subgroup	NOUN
ejpam-4036	4	51	k	k	PROPN
ejpam-4036	4	52	of	of	ADP
ejpam-4036	4	53	g	g	PROPN
ejpam-4036	4	54	such	such	ADJ
ejpam-4036	4	55	that	that	SCONJ
ejpam-4036	4	56	g	g	PROPN
ejpam-4036	4	57	=	=	PUNCT
ejpam-4036	4	58	hk	hk	PROPN
ejpam-4036	4	59	and	and	CCONJ
ejpam-4036	4	60	h	h	NOUN
ejpam-4036	4	61	∩k	∩k	PROPN
ejpam-4036	4	62	is	be	AUX
ejpam-4036	4	63	ss	ss	NOUN
ejpam-4036	4	64	-	-	ADJ
ejpam-4036	4	65	quasinormal	quasinormal	ADJ
ejpam-4036	4	66	in	in	ADP
ejpam-4036	4	67	g.	g.	PROPN
ejpam-4036	4	68	in	in	ADP
ejpam-4036	4	69	this	this	DET
ejpam-4036	4	70	paper	paper	NOUN
ejpam-4036	4	71	,	,	PUNCT
ejpam-4036	4	72	we	we	PRON
ejpam-4036	4	73	investigate	investigate	VERB
ejpam-4036	4	74	the	the	DET
ejpam-4036	4	75	influence	influence	NOUN
ejpam-4036	4	76	of	of	ADP
ejpam-4036	4	77	minimal	minimal	ADJ
ejpam-4036	4	78	csssubgroups	csssubgroup	NOUN
ejpam-4036	4	79	of	of	ADP
ejpam-4036	4	80	g	g	NOUN
ejpam-4036	4	81	on	on	ADP
ejpam-4036	4	82	its	its	PRON
ejpam-4036	4	83	structure	structure	NOUN
ejpam-4036	4	84	.	.	PUNCT
ejpam-4036	5	1	our	our	PRON
ejpam-4036	5	2	results	result	NOUN
ejpam-4036	5	3	improve	improve	VERB
ejpam-4036	5	4	and	and	CCONJ
ejpam-4036	5	5	generalize	generalize	VERB
ejpam-4036	5	6	several	several	ADJ
ejpam-4036	5	7	recent	recent	ADJ
ejpam-4036	5	8	results	result	NOUN
ejpam-4036	5	9	in	in	ADP
ejpam-4036	5	10	the	the	DET
ejpam-4036	5	11	literature	literature	NOUN
ejpam-4036	5	12	.	.	PUNCT
ejpam-4036	6	1	2020	2020	NUM
ejpam-4036	6	2	mathematics	mathematics	PROPN
ejpam-4036	6	3	subject	subject	NOUN
ejpam-4036	6	4	classifications	classification	NOUN
ejpam-4036	6	5	:	:	PUNCT
ejpam-4036	6	6	20d10	20d10	NUM
ejpam-4036	6	7	,	,	PUNCT
ejpam-4036	6	8	20d15	20d15	NUM
ejpam-4036	6	9	,	,	PUNCT
ejpam-4036	6	10	20d20	20d20	NUM
ejpam-4036	6	11	key	key	ADJ
ejpam-4036	6	12	words	word	NOUN
ejpam-4036	6	13	and	and	CCONJ
ejpam-4036	6	14	phrases	phrase	NOUN
ejpam-4036	6	15	:	:	PUNCT
ejpam-4036	6	16	css	css	PROPN
ejpam-4036	6	17	-	-	PUNCT
ejpam-4036	6	18	subgroup	subgroup	PROPN
ejpam-4036	6	19	,	,	PUNCT
ejpam-4036	6	20	c	c	NOUN
ejpam-4036	6	21	-	-	PUNCT
ejpam-4036	6	22	normal	normal	ADJ
ejpam-4036	6	23	subgroup	subgroup	NOUN
ejpam-4036	6	24	,	,	PUNCT
ejpam-4036	6	25	ss	ss	ADJ
ejpam-4036	6	26	-	-	ADJ
ejpam-4036	6	27	quasinormal	quasinormal	ADJ
ejpam-4036	6	28	subgroup	subgroup	NOUN
ejpam-4036	6	29	,	,	PUNCT
ejpam-4036	6	30	pnilpotent	pnilpotent	NOUN
ejpam-4036	6	31	group	group	NOUN
ejpam-4036	6	32	,	,	PUNCT
ejpam-4036	6	33	saturated	saturate	VERB
ejpam-4036	6	34	formation	formation	NOUN
ejpam-4036	6	35	.	.	PUNCT
ejpam-4036	7	1	1	1	X
ejpam-4036	7	2	.	.	X
ejpam-4036	7	3	introduction	introduction	NOUN
ejpam-4036	7	4	all	all	DET
ejpam-4036	7	5	groups	group	NOUN
ejpam-4036	7	6	considered	consider	VERB
ejpam-4036	7	7	in	in	ADP
ejpam-4036	7	8	this	this	DET
ejpam-4036	7	9	paper	paper	NOUN
ejpam-4036	7	10	are	be	AUX
ejpam-4036	7	11	finite	finite	ADJ
ejpam-4036	7	12	.	.	PUNCT
ejpam-4036	8	1	the	the	DET
ejpam-4036	8	2	terminology	terminology	NOUN
ejpam-4036	8	3	and	and	CCONJ
ejpam-4036	8	4	notions	notion	NOUN
ejpam-4036	8	5	employed	employ	VERB
ejpam-4036	8	6	agree	agree	VERB
ejpam-4036	8	7	with	with	ADP
ejpam-4036	8	8	standard	standard	ADJ
ejpam-4036	8	9	usage	usage	NOUN
ejpam-4036	8	10	,	,	PUNCT
ejpam-4036	8	11	as	as	ADP
ejpam-4036	8	12	in	in	ADP
ejpam-4036	8	13	[	[	X
ejpam-4036	8	14	2	2	NUM
ejpam-4036	8	15	,	,	PUNCT
ejpam-4036	8	16	5	5	NUM
ejpam-4036	8	17	]	]	PUNCT
ejpam-4036	8	18	,	,	PUNCT
ejpam-4036	8	19	and	and	CCONJ
ejpam-4036	8	20	g	g	NOUN
ejpam-4036	8	21	always	always	ADV
ejpam-4036	8	22	denotes	denote	VERB
ejpam-4036	8	23	a	a	DET
ejpam-4036	8	24	finite	finite	ADJ
ejpam-4036	8	25	group	group	NOUN
ejpam-4036	8	26	.	.	PUNCT
ejpam-4036	9	1	following	follow	VERB
ejpam-4036	9	2	kegel	kegel	PROPN
ejpam-4036	9	3	[	[	X
ejpam-4036	9	4	9	9	NUM
ejpam-4036	9	5	]	]	PUNCT
ejpam-4036	9	6	,	,	PUNCT
ejpam-4036	9	7	a	a	DET
ejpam-4036	9	8	subgroup	subgroup	NOUN
ejpam-4036	9	9	h	h	NOUN
ejpam-4036	9	10	of	of	ADP
ejpam-4036	9	11	g	g	PROPN
ejpam-4036	9	12	is	be	AUX
ejpam-4036	9	13	said	say	VERB
ejpam-4036	9	14	to	to	PART
ejpam-4036	9	15	be	be	AUX
ejpam-4036	9	16	s	s	NOUN
ejpam-4036	9	17	-	-	ADJ
ejpam-4036	9	18	quasinormal	quasinormal	ADJ
ejpam-4036	9	19	in	in	ADP
ejpam-4036	9	20	g	g	PROPN
ejpam-4036	9	21	if	if	SCONJ
ejpam-4036	9	22	h	h	NOUN
ejpam-4036	9	23	permutes	permute	VERB
ejpam-4036	9	24	with	with	ADP
ejpam-4036	9	25	every	every	DET
ejpam-4036	9	26	sylow	sylow	NOUN
ejpam-4036	9	27	subgroup	subgroup	NOUN
ejpam-4036	9	28	of	of	ADP
ejpam-4036	9	29	g	g	PROPN
ejpam-4036	9	30	,	,	PUNCT
ejpam-4036	9	31	i.e	i.e	PRON
ejpam-4036	9	32	,	,	PUNCT
ejpam-4036	9	33	hp	hp	NOUN
ejpam-4036	9	34	=	=	PUNCT
ejpam-4036	9	35	ph	ph	PROPN
ejpam-4036	9	36	for	for	ADP
ejpam-4036	9	37	any	any	DET
ejpam-4036	9	38	sylow	sylow	NOUN
ejpam-4036	9	39	subgroup	subgroup	NOUN
ejpam-4036	9	40	p	p	PROPN
ejpam-4036	9	41	of	of	ADP
ejpam-4036	9	42	g.	g.	PROPN
ejpam-4036	9	43	a	a	DET
ejpam-4036	9	44	subgroup	subgroup	NOUN
ejpam-4036	9	45	h	h	NOUN
ejpam-4036	9	46	of	of	ADP
ejpam-4036	9	47	g	g	PROPN
ejpam-4036	9	48	is	be	AUX
ejpam-4036	9	49	said	say	VERB
ejpam-4036	9	50	to	to	PART
ejpam-4036	9	51	be	be	AUX
ejpam-4036	9	52	c	c	NOUN
ejpam-4036	9	53	-	-	ADJ
ejpam-4036	9	54	normal	normal	ADJ
ejpam-4036	9	55	in	in	ADP
ejpam-4036	9	56	g	g	PROPN
ejpam-4036	9	57	if	if	SCONJ
ejpam-4036	9	58	g	g	PROPN
ejpam-4036	9	59	has	have	VERB
ejpam-4036	9	60	a	a	DET
ejpam-4036	9	61	normal	normal	ADJ
ejpam-4036	9	62	subgroup	subgroup	NOUN
ejpam-4036	9	63	k	k	PROPN
ejpam-4036	10	1	such	such	ADJ
ejpam-4036	10	2	that	that	SCONJ
ejpam-4036	10	3	g	g	PROPN
ejpam-4036	10	4	=	=	PUNCT
ejpam-4036	10	5	hk	hk	PROPN
ejpam-4036	10	6	and	and	CCONJ
ejpam-4036	10	7	h	h	PROPN
ejpam-4036	10	8	∩	∩	NOUN
ejpam-4036	10	9	k	k	PROPN
ejpam-4036	10	10	6	6	NUM
ejpam-4036	10	11	hg	hg	NOUN
ejpam-4036	10	12	,	,	PUNCT
ejpam-4036	10	13	where	where	SCONJ
ejpam-4036	10	14	hg	hg	PROPN
ejpam-4036	10	15	=	=	PROPN
ejpam-4036	10	16	coreg(h	coreg(h	PROPN
ejpam-4036	10	17	)	)	PUNCT
ejpam-4036	10	18	is	be	AUX
ejpam-4036	10	19	the	the	DET
ejpam-4036	10	20	largest	large	ADJ
ejpam-4036	10	21	normal	normal	ADJ
ejpam-4036	10	22	subgroup	subgroup	NOUN
ejpam-4036	10	23	of	of	ADP
ejpam-4036	10	24	g	g	PROPN
ejpam-4036	10	25	contained	contain	VERB
ejpam-4036	10	26	in	in	ADP
ejpam-4036	10	27	h	h	PROPN
ejpam-4036	10	28	(	(	PUNCT
ejpam-4036	10	29	see	see	VERB
ejpam-4036	10	30	wang	wang	PROPN
ejpam-4036	11	1	[	[	X
ejpam-4036	11	2	18	18	NUM
ejpam-4036	11	3	]	]	PUNCT
ejpam-4036	11	4	)	)	PUNCT
ejpam-4036	11	5	.	.	PUNCT
ejpam-4036	12	1	recently	recently	ADV
ejpam-4036	12	2	,	,	PUNCT
ejpam-4036	12	3	in	in	ADP
ejpam-4036	12	4	2008	2008	NUM
ejpam-4036	12	5	,	,	PUNCT
ejpam-4036	12	6	li	li	PROPN
ejpam-4036	12	7	et	et	PROPN
ejpam-4036	12	8	al	al	PROPN
ejpam-4036	12	9	.	.	PUNCT
ejpam-4036	13	1	[	[	X
ejpam-4036	13	2	12	12	NUM
ejpam-4036	13	3	]	]	PUNCT
ejpam-4036	13	4	extended	extend	VERB
ejpam-4036	13	5	squasinormal	squasinormal	ADJ
ejpam-4036	13	6	subgroups	subgroup	NOUN
ejpam-4036	13	7	of	of	ADP
ejpam-4036	13	8	a	a	DET
ejpam-4036	13	9	group	group	NOUN
ejpam-4036	13	10	g	g	NOUN
ejpam-4036	13	11	to	to	ADP
ejpam-4036	13	12	ss	ss	ADJ
ejpam-4036	13	13	-	-	ADJ
ejpam-4036	13	14	quasinormal	quasinormal	ADJ
ejpam-4036	13	15	subgroups	subgroup	NOUN
ejpam-4036	13	16	and	and	CCONJ
ejpam-4036	13	17	they	they	PRON
ejpam-4036	13	18	gave	give	VERB
ejpam-4036	13	19	the	the	DET
ejpam-4036	13	20	following	follow	VERB
ejpam-4036	13	21	definition	definition	NOUN
ejpam-4036	13	22	:	:	PUNCT
ejpam-4036	13	23	a	a	DET
ejpam-4036	13	24	subgroup	subgroup	NOUN
ejpam-4036	13	25	h	h	NOUN
ejpam-4036	13	26	of	of	ADP
ejpam-4036	13	27	g	g	PROPN
ejpam-4036	13	28	is	be	AUX
ejpam-4036	13	29	said	say	VERB
ejpam-4036	13	30	to	to	PART
ejpam-4036	13	31	be	be	AUX
ejpam-4036	13	32	ss	ss	NOUN
ejpam-4036	13	33	-	-	ADJ
ejpam-4036	13	34	quasinormal	quasinormal	ADJ
ejpam-4036	13	35	in	in	ADP
ejpam-4036	13	36	g	g	PROPN
ejpam-4036	13	37	if	if	SCONJ
ejpam-4036	13	38	there	there	PRON
ejpam-4036	13	39	is	be	VERB
ejpam-4036	13	40	a	a	DET
ejpam-4036	13	41	supplement	supplement	NOUN
ejpam-4036	13	42	b	b	NOUN
ejpam-4036	13	43	of	of	ADP
ejpam-4036	13	44	h	h	NOUN
ejpam-4036	13	45	to	to	ADP
ejpam-4036	13	46	g	g	NOUN
ejpam-4036	13	47	such	such	ADJ
ejpam-4036	13	48	that	that	SCONJ
ejpam-4036	13	49	h	h	NOUN
ejpam-4036	13	50	permutes	permute	NOUN
ejpam-4036	13	51	with	with	ADP
ejpam-4036	13	52	every	every	DET
ejpam-4036	13	53	sylow	sylow	NOUN
ejpam-4036	13	54	subgroup	subgroup	NOUN
ejpam-4036	13	55	of	of	ADP
ejpam-4036	13	56	b.	b.	PROPN
ejpam-4036	13	57	obviously	obviously	ADV
ejpam-4036	13	58	,	,	PUNCT
ejpam-4036	13	59	every	every	DET
ejpam-4036	13	60	s	s	ADJ
ejpam-4036	13	61	-	-	ADJ
ejpam-4036	13	62	quasinormal	quasinormal	ADJ
ejpam-4036	13	63	subgroup	subgroup	NOUN
ejpam-4036	13	64	is	be	AUX
ejpam-4036	13	65	ss	ss	NOUN
ejpam-4036	13	66	-	-	ADJ
ejpam-4036	13	67	quasinormal	quasinormal	ADJ
ejpam-4036	13	68	.	.	PUNCT
ejpam-4036	14	1	the	the	DET
ejpam-4036	14	2	converse	converse	NOUN
ejpam-4036	14	3	is	be	AUX
ejpam-4036	14	4	not	not	PART
ejpam-4036	14	5	true	true	ADJ
ejpam-4036	14	6	in	in	ADP
ejpam-4036	14	7	general	general	ADJ
ejpam-4036	14	8	.	.	PUNCT
ejpam-4036	15	1	for	for	ADP
ejpam-4036	15	2	instance	instance	NOUN
ejpam-4036	15	3	,	,	PUNCT
ejpam-4036	15	4	s3	s3	PROPN
ejpam-4036	15	5	is	be	AUX
ejpam-4036	15	6	ss	ss	ADJ
ejpam-4036	15	7	-	-	ADJ
ejpam-4036	15	8	quasinormal	quasinormal	ADJ
ejpam-4036	15	9	subgroup	subgroup	NOUN
ejpam-4036	15	10	of	of	ADP
ejpam-4036	15	11	the	the	DET
ejpam-4036	15	12	symmetric	symmetric	ADJ
ejpam-4036	15	13	group	group	NOUN
ejpam-4036	15	14	s4	s4	NOUN
ejpam-4036	15	15	but	but	CCONJ
ejpam-4036	15	16	∗corresponding	∗corresponde	VERB
ejpam-4036	15	17	author	author	NOUN
ejpam-4036	15	18	.	.	PUNCT
ejpam-4036	16	1	doi	doi	NOUN
ejpam-4036	16	2	:	:	PUNCT
ejpam-4036	16	3	https://doi.org/10.29020/nybg.ejpam.v14i3.4036	https://doi.org/10.29020/nybg.ejpam.v14i3.4036	PROPN
ejpam-4036	16	4	email	email	NOUN
ejpam-4036	16	5	addresses	address	NOUN
ejpam-4036	16	6	:	:	PUNCT
ejpam-4036	16	7	heliel9@yahoo.com	heliel9@yahoo.com	X
ejpam-4036	16	8	;	;	PUNCT
ejpam-4036	16	9	aahsalem1@kau.edu.sa	aahsalem1@kau.edu.sa	PROPN
ejpam-4036	16	10	(	(	PUNCT
ejpam-4036	16	11	a.	a.	NOUN
ejpam-4036	16	12	heliel	heliel	PROPN
ejpam-4036	16	13	)	)	PUNCT
ejpam-4036	16	14	,	,	PUNCT
ejpam-4036	16	15	rhijazi@kau.edu.sa	rhijazi@kau.edu.sa	NOUN
ejpam-4036	16	16	(	(	PUNCT
ejpam-4036	16	17	r.	r.	PROPN
ejpam-4036	16	18	hijazi	hijazi	PROPN
ejpam-4036	16	19	)	)	PUNCT
ejpam-4036	16	20	,	,	PUNCT
ejpam-4036	16	21	salshammari0054@stu.kau.edu.sa	salshammari0054@stu.kau.edu.sa	PROPN
ejpam-4036	16	22	(	(	PUNCT
ejpam-4036	16	23	s.	s.	PROPN
ejpam-4036	16	24	al	al	PROPN
ejpam-4036	16	25	-	-	PUNCT
ejpam-4036	16	26	shammari	shammari	PROPN
ejpam-4036	16	27	)	)	PUNCT
ejpam-4036	16	28	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4036	17	1	1002	1002	NUM
ejpam-4036	17	2	c	c	AUX
ejpam-4036	17	3	©	©	PROPN
ejpam-4036	17	4	2021	2021	NUM
ejpam-4036	17	5	ejpam	ejpam	VERB
ejpam-4036	17	6	all	all	DET
ejpam-4036	17	7	rights	right	NOUN
ejpam-4036	17	8	reserved	reserve	VERB
ejpam-4036	17	9	.	.	PUNCT
ejpam-4036	18	1	a.	a.	NOUN
ejpam-4036	18	2	heliel	heliel	PROPN
ejpam-4036	18	3	,	,	PUNCT
ejpam-4036	18	4	r.	r.	PROPN
ejpam-4036	18	5	hijazi	hijazi	PROPN
ejpam-4036	18	6	,	,	PUNCT
ejpam-4036	18	7	s.	s.	PROPN
ejpam-4036	18	8	al	al	PROPN
ejpam-4036	18	9	-	-	PUNCT
ejpam-4036	18	10	shammari	shammari	PROPN
ejpam-4036	18	11	/	/	SYM
ejpam-4036	18	12	eur	eur	PROPN
ejpam-4036	18	13	.	.	PUNCT
ejpam-4036	19	1	j.	j.	PROPN
ejpam-4036	19	2	pure	pure	PROPN
ejpam-4036	19	3	appl	appl	PROPN
ejpam-4036	19	4	.	.	PROPN
ejpam-4036	19	5	math	math	PROPN
ejpam-4036	19	6	,	,	PUNCT
ejpam-4036	19	7	14	14	NUM
ejpam-4036	19	8	(	(	PUNCT
ejpam-4036	19	9	3	3	NUM
ejpam-4036	19	10	)	)	PUNCT
ejpam-4036	19	11	(	(	PUNCT
ejpam-4036	19	12	2021	2021	NUM
ejpam-4036	19	13	)	)	PUNCT
ejpam-4036	19	14	,	,	PUNCT
ejpam-4036	19	15	1002	1002	NUM
ejpam-4036	19	16	-	-	SYM
ejpam-4036	19	17	1014	1014	NUM
ejpam-4036	19	18	1003	1003	NUM
ejpam-4036	19	19	not	not	PART
ejpam-4036	19	20	s	s	NOUN
ejpam-4036	19	21	-	-	ADJ
ejpam-4036	19	22	quasinormal	quasinormal	ADJ
ejpam-4036	19	23	.	.	PUNCT
ejpam-4036	20	1	more	more	ADV
ejpam-4036	20	2	recently	recently	ADV
ejpam-4036	20	3	,	,	PUNCT
ejpam-4036	20	4	in	in	ADP
ejpam-4036	20	5	2019	2019	NUM
ejpam-4036	20	6	,	,	PUNCT
ejpam-4036	20	7	zhao	zhao	PROPN
ejpam-4036	20	8	et	et	PROPN
ejpam-4036	20	9	al	al	PROPN
ejpam-4036	20	10	.	.	PUNCT
ejpam-4036	21	1	[	[	X
ejpam-4036	21	2	26	26	NUM
ejpam-4036	21	3	]	]	PUNCT
ejpam-4036	21	4	introduced	introduce	VERB
ejpam-4036	21	5	a	a	DET
ejpam-4036	21	6	new	new	ADJ
ejpam-4036	21	7	subgroup	subgroup	NOUN
ejpam-4036	21	8	embedding	embed	VERB
ejpam-4036	21	9	property	property	NOUN
ejpam-4036	21	10	of	of	ADP
ejpam-4036	21	11	a	a	DET
ejpam-4036	21	12	finite	finite	ADJ
ejpam-4036	21	13	group	group	NOUN
ejpam-4036	21	14	,	,	PUNCT
ejpam-4036	21	15	called	call	VERB
ejpam-4036	21	16	css	css	PROPN
ejpam-4036	21	17	-	-	PUNCT
ejpam-4036	21	18	subgroup	subgroup	PROPN
ejpam-4036	21	19	,	,	PUNCT
ejpam-4036	21	20	which	which	PRON
ejpam-4036	21	21	generalize	generalize	VERB
ejpam-4036	21	22	and	and	CCONJ
ejpam-4036	21	23	unify	unify	VERB
ejpam-4036	21	24	both	both	PRON
ejpam-4036	21	25	of	of	ADP
ejpam-4036	21	26	c	c	NOUN
ejpam-4036	21	27	-	-	PUNCT
ejpam-4036	21	28	normality	normality	NOUN
ejpam-4036	21	29	and	and	CCONJ
ejpam-4036	21	30	ss	ss	NOUN
ejpam-4036	21	31	-	-	PUNCT
ejpam-4036	21	32	quasinormality	quasinormality	NOUN
ejpam-4036	21	33	as	as	SCONJ
ejpam-4036	21	34	follows	follow	VERB
ejpam-4036	21	35	:	:	PUNCT
ejpam-4036	21	36	a	a	DET
ejpam-4036	21	37	subgroup	subgroup	NOUN
ejpam-4036	21	38	h	h	NOUN
ejpam-4036	21	39	of	of	ADP
ejpam-4036	21	40	g	g	PROPN
ejpam-4036	21	41	is	be	AUX
ejpam-4036	21	42	called	call	VERB
ejpam-4036	21	43	csssubgroup	csssubgroup	NOUN
ejpam-4036	21	44	of	of	ADP
ejpam-4036	21	45	g	g	PROPN
ejpam-4036	21	46	if	if	SCONJ
ejpam-4036	21	47	there	there	PRON
ejpam-4036	21	48	exists	exist	VERB
ejpam-4036	21	49	a	a	DET
ejpam-4036	21	50	normal	normal	ADJ
ejpam-4036	21	51	subgroup	subgroup	NOUN
ejpam-4036	21	52	k	k	PROPN
ejpam-4036	21	53	of	of	ADP
ejpam-4036	21	54	g	g	PROPN
ejpam-4036	21	55	such	such	ADJ
ejpam-4036	21	56	that	that	SCONJ
ejpam-4036	21	57	g	g	PROPN
ejpam-4036	21	58	=	=	PUNCT
ejpam-4036	21	59	hk	hk	PROPN
ejpam-4036	21	60	and	and	CCONJ
ejpam-4036	21	61	h	h	NOUN
ejpam-4036	21	62	∩k	∩k	PROPN
ejpam-4036	21	63	is	be	AUX
ejpam-4036	21	64	ss	ss	NOUN
ejpam-4036	21	65	-	-	ADJ
ejpam-4036	21	66	quasinormal	quasinormal	ADJ
ejpam-4036	21	67	in	in	ADP
ejpam-4036	21	68	g.	g.	PROPN
ejpam-4036	22	1	it	it	PRON
ejpam-4036	22	2	is	be	AUX
ejpam-4036	22	3	clear	clear	ADJ
ejpam-4036	22	4	that	that	SCONJ
ejpam-4036	22	5	each	each	PRON
ejpam-4036	22	6	of	of	ADP
ejpam-4036	22	7	c	c	NOUN
ejpam-4036	22	8	-	-	PUNCT
ejpam-4036	22	9	normality	normality	NOUN
ejpam-4036	22	10	and	and	CCONJ
ejpam-4036	22	11	ss	ss	NOUN
ejpam-4036	22	12	-	-	PUNCT
ejpam-4036	22	13	quasinormality	quasinormality	NOUN
ejpam-4036	22	14	concepts	concept	NOUN
ejpam-4036	22	15	implies	imply	VERB
ejpam-4036	22	16	css	css	PROPN
ejpam-4036	22	17	-	-	PUNCT
ejpam-4036	22	18	subgroup	subgroup	NOUN
ejpam-4036	22	19	.	.	PUNCT
ejpam-4036	23	1	the	the	DET
ejpam-4036	23	2	converse	converse	NOUN
ejpam-4036	23	3	does	do	AUX
ejpam-4036	23	4	not	not	PART
ejpam-4036	23	5	hold	hold	VERB
ejpam-4036	23	6	in	in	ADP
ejpam-4036	23	7	general	general	ADJ
ejpam-4036	23	8	(	(	PUNCT
ejpam-4036	23	9	see	see	VERB
ejpam-4036	23	10	[	[	X
ejpam-4036	23	11	26	26	NUM
ejpam-4036	23	12	,	,	PUNCT
ejpam-4036	23	13	examples	example	NOUN
ejpam-4036	23	14	1	1	NUM
ejpam-4036	23	15	and	and	CCONJ
ejpam-4036	23	16	2	2	NUM
ejpam-4036	23	17	]	]	NUM
ejpam-4036	23	18	)	)	PUNCT
ejpam-4036	23	19	.	.	PUNCT
ejpam-4036	24	1	over	over	ADP
ejpam-4036	24	2	years	year	NOUN
ejpam-4036	24	3	,	,	PUNCT
ejpam-4036	24	4	many	many	ADJ
ejpam-4036	24	5	authors	author	NOUN
ejpam-4036	24	6	studied	study	VERB
ejpam-4036	24	7	the	the	DET
ejpam-4036	24	8	influence	influence	NOUN
ejpam-4036	24	9	of	of	ADP
ejpam-4036	24	10	minimal	minimal	ADJ
ejpam-4036	24	11	subgroups	subgroup	NOUN
ejpam-4036	24	12	of	of	ADP
ejpam-4036	24	13	a	a	DET
ejpam-4036	24	14	finite	finite	ADJ
ejpam-4036	24	15	group	group	NOUN
ejpam-4036	24	16	on	on	ADP
ejpam-4036	24	17	its	its	PRON
ejpam-4036	24	18	structure	structure	NOUN
ejpam-4036	24	19	(	(	PUNCT
ejpam-4036	24	20	a	a	DET
ejpam-4036	24	21	subgroup	subgroup	NOUN
ejpam-4036	24	22	of	of	ADP
ejpam-4036	24	23	prime	prime	ADJ
ejpam-4036	24	24	order	order	NOUN
ejpam-4036	24	25	is	be	AUX
ejpam-4036	24	26	called	call	VERB
ejpam-4036	24	27	a	a	DET
ejpam-4036	24	28	minimal	minimal	ADJ
ejpam-4036	24	29	subgroup	subgroup	NOUN
ejpam-4036	24	30	)	)	PUNCT
ejpam-4036	24	31	.	.	PUNCT
ejpam-4036	25	1	in	in	ADP
ejpam-4036	25	2	this	this	DET
ejpam-4036	25	3	context	context	NOUN
ejpam-4036	25	4	,	,	PUNCT
ejpam-4036	25	5	buckley	buckley	NOUN
ejpam-4036	25	6	[	[	X
ejpam-4036	25	7	3	3	X
ejpam-4036	25	8	]	]	PUNCT
ejpam-4036	25	9	got	get	VERB
ejpam-4036	25	10	the	the	DET
ejpam-4036	25	11	supersolvability	supersolvability	NOUN
ejpam-4036	25	12	of	of	ADP
ejpam-4036	25	13	a	a	DET
ejpam-4036	25	14	group	group	NOUN
ejpam-4036	25	15	of	of	ADP
ejpam-4036	25	16	odd	odd	ADJ
ejpam-4036	25	17	order	order	NOUN
ejpam-4036	25	18	when	when	SCONJ
ejpam-4036	25	19	all	all	DET
ejpam-4036	25	20	its	its	PRON
ejpam-4036	25	21	minimal	minimal	ADJ
ejpam-4036	25	22	subgroups	subgroup	NOUN
ejpam-4036	25	23	are	be	AUX
ejpam-4036	25	24	normal	normal	ADJ
ejpam-4036	25	25	.	.	PUNCT
ejpam-4036	26	1	in	in	ADP
ejpam-4036	26	2	[	[	X
ejpam-4036	26	3	17	17	NUM
ejpam-4036	26	4	]	]	PUNCT
ejpam-4036	26	5	,	,	PUNCT
ejpam-4036	26	6	shaalan	shaalan	PROPN
ejpam-4036	26	7	proved	prove	VERB
ejpam-4036	26	8	that	that	SCONJ
ejpam-4036	26	9	a	a	DET
ejpam-4036	26	10	group	group	NOUN
ejpam-4036	26	11	g	g	NOUN
ejpam-4036	26	12	is	be	AUX
ejpam-4036	26	13	supersolvable	supersolvable	ADJ
ejpam-4036	26	14	if	if	SCONJ
ejpam-4036	26	15	all	all	DET
ejpam-4036	26	16	subgroups	subgroup	NOUN
ejpam-4036	26	17	of	of	ADP
ejpam-4036	26	18	prime	prime	ADJ
ejpam-4036	26	19	order	order	NOUN
ejpam-4036	26	20	p	p	NOUN
ejpam-4036	26	21	or	or	CCONJ
ejpam-4036	26	22	of	of	ADP
ejpam-4036	26	23	order	order	NOUN
ejpam-4036	26	24	4	4	NUM
ejpam-4036	26	25	(	(	PUNCT
ejpam-4036	26	26	if	if	SCONJ
ejpam-4036	26	27	p	p	X
ejpam-4036	26	28	=	=	NOUN
ejpam-4036	26	29	2	2	NUM
ejpam-4036	26	30	)	)	PUNCT
ejpam-4036	26	31	of	of	ADP
ejpam-4036	26	32	g	g	PROPN
ejpam-4036	26	33	are	be	AUX
ejpam-4036	26	34	s	s	NOUN
ejpam-4036	26	35	-	-	ADJ
ejpam-4036	26	36	quasinormal	quasinormal	ADJ
ejpam-4036	26	37	in	in	ADP
ejpam-4036	26	38	g.	g.	PROPN
ejpam-4036	26	39	later	later	ADV
ejpam-4036	26	40	on	on	ADV
ejpam-4036	26	41	,	,	PUNCT
ejpam-4036	26	42	wang	wang	PROPN
ejpam-4036	27	1	[	[	X
ejpam-4036	27	2	18	18	NUM
ejpam-4036	27	3	]	]	PUNCT
ejpam-4036	27	4	got	get	VERB
ejpam-4036	27	5	the	the	DET
ejpam-4036	27	6	same	same	ADJ
ejpam-4036	27	7	result	result	NOUN
ejpam-4036	27	8	of	of	ADP
ejpam-4036	27	9	shaalan	shaalan	NOUN
ejpam-4036	27	10	[	[	X
ejpam-4036	27	11	17	17	NUM
ejpam-4036	27	12	]	]	PUNCT
ejpam-4036	27	13	just	just	ADV
ejpam-4036	27	14	he	he	PRON
ejpam-4036	27	15	replaced	replace	VERB
ejpam-4036	27	16	s	s	NOUN
ejpam-4036	27	17	-	-	NOUN
ejpam-4036	27	18	quasinormality	quasinormality	NOUN
ejpam-4036	27	19	by	by	ADP
ejpam-4036	27	20	c	c	NOUN
ejpam-4036	27	21	-	-	NOUN
ejpam-4036	27	22	normality	normality	NOUN
ejpam-4036	27	23	.	.	PUNCT
ejpam-4036	28	1	by	by	ADP
ejpam-4036	28	2	using	use	VERB
ejpam-4036	28	3	the	the	DET
ejpam-4036	28	4	ss	ss	ADJ
ejpam-4036	28	5	-	-	PUNCT
ejpam-4036	28	6	quasinormality	quasinormality	NOUN
ejpam-4036	28	7	concept	concept	NOUN
ejpam-4036	28	8	,	,	PUNCT
ejpam-4036	28	9	li	li	PROPN
ejpam-4036	28	10	et	et	PROPN
ejpam-4036	28	11	al	al	PROPN
ejpam-4036	28	12	.	.	PUNCT
ejpam-4036	29	1	[	[	X
ejpam-4036	29	2	11	11	NUM
ejpam-4036	29	3	]	]	PUNCT
ejpam-4036	29	4	extended	extend	VERB
ejpam-4036	29	5	these	these	DET
ejpam-4036	29	6	results	result	NOUN
ejpam-4036	29	7	through	through	ADP
ejpam-4036	29	8	the	the	DET
ejpam-4036	29	9	theory	theory	NOUN
ejpam-4036	29	10	of	of	ADP
ejpam-4036	29	11	formations	formation	NOUN
ejpam-4036	29	12	and	and	CCONJ
ejpam-4036	29	13	proved	prove	VERB
ejpam-4036	29	14	that	that	PRON
ejpam-4036	29	15	:	:	PUNCT
ejpam-4036	29	16	let	let	VERB
ejpam-4036	29	17	f	f	PRON
ejpam-4036	29	18	be	be	AUX
ejpam-4036	29	19	a	a	DET
ejpam-4036	29	20	saturated	saturated	ADJ
ejpam-4036	29	21	formation	formation	NOUN
ejpam-4036	29	22	containing	contain	VERB
ejpam-4036	29	23	u	u	NOUN
ejpam-4036	29	24	and	and	CCONJ
ejpam-4036	29	25	let	let	VERB
ejpam-4036	29	26	g	g	PRON
ejpam-4036	29	27	be	be	AUX
ejpam-4036	29	28	a	a	DET
ejpam-4036	29	29	group	group	NOUN
ejpam-4036	29	30	.	.	PUNCT
ejpam-4036	30	1	then	then	ADV
ejpam-4036	30	2	g	g	PROPN
ejpam-4036	30	3	∈	∈	PROPN
ejpam-4036	30	4	f	f	PROPN
ejpam-4036	31	1	if	if	SCONJ
ejpam-4036	31	2	and	and	CCONJ
ejpam-4036	31	3	only	only	ADV
ejpam-4036	31	4	if	if	SCONJ
ejpam-4036	31	5	g	g	PROPN
ejpam-4036	31	6	has	have	VERB
ejpam-4036	31	7	a	a	DET
ejpam-4036	31	8	normal	normal	ADJ
ejpam-4036	31	9	subgroup	subgroup	NOUN
ejpam-4036	31	10	h	h	NOUN
ejpam-4036	31	11	such	such	ADJ
ejpam-4036	31	12	that	that	SCONJ
ejpam-4036	31	13	g	g	NOUN
ejpam-4036	31	14	/	/	SYM
ejpam-4036	31	15	h	h	NOUN
ejpam-4036	31	16	∈	∈	PROPN
ejpam-4036	31	17	f	f	PROPN
ejpam-4036	31	18	and	and	CCONJ
ejpam-4036	31	19	every	every	DET
ejpam-4036	31	20	subgroup	subgroup	NOUN
ejpam-4036	31	21	of	of	ADP
ejpam-4036	31	22	f	f	PROPN
ejpam-4036	31	23	∗(h	∗(h	PROPN
ejpam-4036	31	24	)	)	PUNCT
ejpam-4036	31	25	of	of	ADP
ejpam-4036	31	26	prime	prime	ADJ
ejpam-4036	31	27	order	order	NOUN
ejpam-4036	31	28	p	p	NOUN
ejpam-4036	31	29	or	or	CCONJ
ejpam-4036	31	30	of	of	ADP
ejpam-4036	31	31	order	order	NOUN
ejpam-4036	31	32	4	4	NUM
ejpam-4036	31	33	(	(	PUNCT
ejpam-4036	31	34	if	if	SCONJ
ejpam-4036	31	35	p	p	X
ejpam-4036	31	36	=	=	NOUN
ejpam-4036	31	37	2	2	NUM
ejpam-4036	31	38	)	)	PUNCT
ejpam-4036	31	39	is	be	AUX
ejpam-4036	31	40	ss	ss	NOUN
ejpam-4036	31	41	-	-	ADJ
ejpam-4036	31	42	quasinormal	quasinormal	ADJ
ejpam-4036	31	43	in	in	ADP
ejpam-4036	31	44	g	g	PROPN
ejpam-4036	31	45	,	,	PUNCT
ejpam-4036	31	46	where	where	SCONJ
ejpam-4036	31	47	f	f	PROPN
ejpam-4036	31	48	∗(h	∗(h	PROPN
ejpam-4036	31	49	)	)	PUNCT
ejpam-4036	31	50	is	be	AUX
ejpam-4036	31	51	the	the	DET
ejpam-4036	31	52	generalized	generalized	ADJ
ejpam-4036	31	53	fitting	fitting	ADJ
ejpam-4036	31	54	subgroup	subgroup	NOUN
ejpam-4036	31	55	of	of	ADP
ejpam-4036	31	56	h.	h.	PROPN
ejpam-4036	31	57	also	also	ADV
ejpam-4036	31	58	,	,	PUNCT
ejpam-4036	31	59	wei	wei	PROPN
ejpam-4036	31	60	et	et	PROPN
ejpam-4036	31	61	al	al	PROPN
ejpam-4036	31	62	.	.	PUNCT
ejpam-4036	32	1	in	in	ADP
ejpam-4036	32	2	[	[	X
ejpam-4036	32	3	21	21	NUM
ejpam-4036	32	4	]	]	PUNCT
ejpam-4036	32	5	used	use	VERB
ejpam-4036	32	6	the	the	DET
ejpam-4036	32	7	c	c	NOUN
ejpam-4036	32	8	-	-	PUNCT
ejpam-4036	32	9	normality	normality	NOUN
ejpam-4036	32	10	concept	concept	NOUN
ejpam-4036	32	11	and	and	CCONJ
ejpam-4036	32	12	obtained	obtain	VERB
ejpam-4036	32	13	the	the	DET
ejpam-4036	32	14	same	same	ADJ
ejpam-4036	32	15	previous	previous	ADJ
ejpam-4036	32	16	result	result	NOUN
ejpam-4036	32	17	.	.	PUNCT
ejpam-4036	33	1	for	for	ADP
ejpam-4036	33	2	more	more	ADJ
ejpam-4036	33	3	results	result	NOUN
ejpam-4036	33	4	in	in	ADP
ejpam-4036	33	5	this	this	DET
ejpam-4036	33	6	direction	direction	NOUN
ejpam-4036	33	7	(	(	PUNCT
ejpam-4036	33	8	see	see	VERB
ejpam-4036	33	9	[	[	X
ejpam-4036	33	10	1	1	NUM
ejpam-4036	33	11	,	,	PUNCT
ejpam-4036	33	12	11	11	NUM
ejpam-4036	33	13	,	,	PUNCT
ejpam-4036	33	14	12	12	NUM
ejpam-4036	33	15	,	,	PUNCT
ejpam-4036	33	16	16–18	16–18	NUM
ejpam-4036	33	17	,	,	PUNCT
ejpam-4036	33	18	20	20	NUM
ejpam-4036	33	19	,	,	PUNCT
ejpam-4036	33	20	21	21	NUM
ejpam-4036	33	21	,	,	PUNCT
ejpam-4036	33	22	24	24	NUM
ejpam-4036	33	23	]	]	PUNCT
ejpam-4036	33	24	)	)	PUNCT
ejpam-4036	33	25	.	.	PUNCT
ejpam-4036	34	1	the	the	DET
ejpam-4036	34	2	main	main	ADJ
ejpam-4036	34	3	purpose	purpose	NOUN
ejpam-4036	34	4	of	of	ADP
ejpam-4036	34	5	this	this	DET
ejpam-4036	34	6	paper	paper	NOUN
ejpam-4036	34	7	is	be	AUX
ejpam-4036	34	8	to	to	PART
ejpam-4036	34	9	improve	improve	VERB
ejpam-4036	34	10	and	and	CCONJ
ejpam-4036	34	11	extend	extend	VERB
ejpam-4036	34	12	the	the	DET
ejpam-4036	34	13	above	above	ADJ
ejpam-4036	34	14	mentioned	mention	VERB
ejpam-4036	34	15	results	result	NOUN
ejpam-4036	34	16	by	by	ADP
ejpam-4036	34	17	using	use	VERB
ejpam-4036	34	18	the	the	DET
ejpam-4036	34	19	recent	recent	ADJ
ejpam-4036	34	20	concept	concept	NOUN
ejpam-4036	34	21	css	css	PROPN
ejpam-4036	34	22	-	-	PUNCT
ejpam-4036	34	23	subgroup	subgroup	NOUN
ejpam-4036	34	24	.	.	PUNCT
ejpam-4036	35	1	more	more	ADV
ejpam-4036	35	2	precisely	precisely	ADV
ejpam-4036	35	3	,	,	PUNCT
ejpam-4036	35	4	we	we	PRON
ejpam-4036	35	5	investigate	investigate	VERB
ejpam-4036	35	6	the	the	DET
ejpam-4036	35	7	structure	structure	NOUN
ejpam-4036	35	8	of	of	ADP
ejpam-4036	35	9	a	a	DET
ejpam-4036	35	10	finite	finite	ADJ
ejpam-4036	35	11	group	group	NOUN
ejpam-4036	35	12	g	g	PROPN
ejpam-4036	35	13	when	when	SCONJ
ejpam-4036	35	14	every	every	DET
ejpam-4036	35	15	subgroup	subgroup	NOUN
ejpam-4036	35	16	of	of	ADP
ejpam-4036	35	17	g	g	PROPN
ejpam-4036	35	18	of	of	ADP
ejpam-4036	35	19	prime	prime	ADJ
ejpam-4036	35	20	order	order	NOUN
ejpam-4036	35	21	p	p	NOUN
ejpam-4036	35	22	or	or	CCONJ
ejpam-4036	35	23	of	of	ADP
ejpam-4036	35	24	order	order	NOUN
ejpam-4036	35	25	4	4	NUM
ejpam-4036	35	26	(	(	PUNCT
ejpam-4036	35	27	if	if	SCONJ
ejpam-4036	35	28	p	p	X
ejpam-4036	35	29	=	=	NOUN
ejpam-4036	35	30	2	2	NUM
ejpam-4036	35	31	)	)	PUNCT
ejpam-4036	35	32	is	be	AUX
ejpam-4036	35	33	css	css	PROPN
ejpam-4036	35	34	-	-	NOUN
ejpam-4036	35	35	subgroup	subgroup	NOUN
ejpam-4036	35	36	in	in	ADP
ejpam-4036	35	37	g.	g.	PROPN
ejpam-4036	35	38	2	2	NUM
ejpam-4036	35	39	.	.	PUNCT
ejpam-4036	35	40	basic	basic	ADJ
ejpam-4036	35	41	definitions	definition	NOUN
ejpam-4036	35	42	and	and	CCONJ
ejpam-4036	35	43	preliminaries	preliminary	NOUN
ejpam-4036	35	44	in	in	ADP
ejpam-4036	35	45	this	this	DET
ejpam-4036	35	46	section	section	NOUN
ejpam-4036	35	47	,	,	PUNCT
ejpam-4036	35	48	we	we	PRON
ejpam-4036	35	49	list	list	VERB
ejpam-4036	35	50	some	some	DET
ejpam-4036	35	51	definitions	definition	NOUN
ejpam-4036	35	52	and	and	CCONJ
ejpam-4036	35	53	state	state	VERB
ejpam-4036	35	54	some	some	DET
ejpam-4036	35	55	known	know	VERB
ejpam-4036	35	56	results	result	NOUN
ejpam-4036	35	57	from	from	ADP
ejpam-4036	35	58	the	the	DET
ejpam-4036	35	59	literature	literature	NOUN
ejpam-4036	35	60	which	which	PRON
ejpam-4036	35	61	will	will	AUX
ejpam-4036	35	62	be	be	AUX
ejpam-4036	35	63	used	use	VERB
ejpam-4036	35	64	in	in	ADP
ejpam-4036	35	65	proving	prove	VERB
ejpam-4036	35	66	our	our	PRON
ejpam-4036	35	67	results	result	NOUN
ejpam-4036	35	68	.	.	PUNCT
ejpam-4036	36	1	a	a	DET
ejpam-4036	36	2	class	class	NOUN
ejpam-4036	36	3	of	of	ADP
ejpam-4036	36	4	groups	group	NOUN
ejpam-4036	36	5	f	f	PROPN
ejpam-4036	36	6	is	be	AUX
ejpam-4036	36	7	said	say	VERB
ejpam-4036	36	8	to	to	PART
ejpam-4036	36	9	be	be	AUX
ejpam-4036	36	10	a	a	DET
ejpam-4036	36	11	formation	formation	NOUN
ejpam-4036	36	12	if	if	SCONJ
ejpam-4036	36	13	f	f	PROPN
ejpam-4036	36	14	is	be	AUX
ejpam-4036	36	15	closed	close	VERB
ejpam-4036	36	16	under	under	ADP
ejpam-4036	36	17	taking	take	VERB
ejpam-4036	36	18	epimorphic	epimorphic	ADJ
ejpam-4036	36	19	images	image	NOUN
ejpam-4036	36	20	and	and	CCONJ
ejpam-4036	36	21	every	every	DET
ejpam-4036	36	22	group	group	NOUN
ejpam-4036	36	23	g	g	PROPN
ejpam-4036	36	24	has	have	VERB
ejpam-4036	36	25	a	a	DET
ejpam-4036	36	26	smallest	small	ADJ
ejpam-4036	36	27	normal	normal	ADJ
ejpam-4036	36	28	subgroup	subgroup	NOUN
ejpam-4036	36	29	with	with	ADP
ejpam-4036	36	30	quotient	quotient	NOUN
ejpam-4036	36	31	in	in	ADP
ejpam-4036	36	32	f.	f.	PROPN
ejpam-4036	36	33	this	this	DET
ejpam-4036	36	34	subgroup	subgroup	NOUN
ejpam-4036	36	35	is	be	AUX
ejpam-4036	36	36	called	call	VERB
ejpam-4036	36	37	the	the	DET
ejpam-4036	36	38	f	f	NOUN
ejpam-4036	36	39	-	-	PUNCT
ejpam-4036	36	40	residual	residual	ADJ
ejpam-4036	36	41	of	of	ADP
ejpam-4036	36	42	g	g	PROPN
ejpam-4036	36	43	and	and	CCONJ
ejpam-4036	36	44	it	it	PRON
ejpam-4036	36	45	is	be	AUX
ejpam-4036	36	46	denoted	denote	VERB
ejpam-4036	36	47	by	by	ADP
ejpam-4036	36	48	gf	gf	X
ejpam-4036	36	49	.	.	PUNCT
ejpam-4036	37	1	a	a	DET
ejpam-4036	37	2	formation	formation	NOUN
ejpam-4036	37	3	f	f	NOUN
ejpam-4036	37	4	is	be	AUX
ejpam-4036	37	5	called	call	VERB
ejpam-4036	37	6	saturated	saturated	ADJ
ejpam-4036	37	7	if	if	SCONJ
ejpam-4036	37	8	it	it	PRON
ejpam-4036	37	9	is	be	AUX
ejpam-4036	37	10	closed	close	VERB
ejpam-4036	37	11	under	under	ADP
ejpam-4036	37	12	taking	take	VERB
ejpam-4036	37	13	frattini	frattini	ADJ
ejpam-4036	37	14	extensions	extension	NOUN
ejpam-4036	37	15	.	.	PUNCT
ejpam-4036	38	1	throughout	throughout	ADP
ejpam-4036	38	2	this	this	DET
ejpam-4036	38	3	paper	paper	NOUN
ejpam-4036	38	4	,	,	PUNCT
ejpam-4036	38	5	u	u	NOUN
ejpam-4036	38	6	and	and	CCONJ
ejpam-4036	38	7	n	n	PROPN
ejpam-4036	38	8	will	will	AUX
ejpam-4036	38	9	denote	denote	VERB
ejpam-4036	38	10	the	the	DET
ejpam-4036	38	11	classes	class	NOUN
ejpam-4036	38	12	of	of	ADP
ejpam-4036	38	13	supersolvable	supersolvable	ADJ
ejpam-4036	38	14	groups	group	NOUN
ejpam-4036	38	15	and	and	CCONJ
ejpam-4036	38	16	nilpotent	nilpotent	ADJ
ejpam-4036	38	17	groups	group	NOUN
ejpam-4036	38	18	,	,	PUNCT
ejpam-4036	38	19	respectively	respectively	ADV
ejpam-4036	38	20	.	.	PUNCT
ejpam-4036	39	1	it	it	PRON
ejpam-4036	39	2	is	be	AUX
ejpam-4036	39	3	known	know	VERB
ejpam-4036	39	4	that	that	SCONJ
ejpam-4036	39	5	u	u	PROPN
ejpam-4036	39	6	and	and	CCONJ
ejpam-4036	39	7	n	n	NUM
ejpam-4036	39	8	are	be	AUX
ejpam-4036	39	9	saturated	saturate	VERB
ejpam-4036	39	10	formations	formation	NOUN
ejpam-4036	39	11	(	(	PUNCT
ejpam-4036	39	12	see	see	VERB
ejpam-4036	39	13	[	[	X
ejpam-4036	39	14	7	7	NUM
ejpam-4036	39	15	,	,	PUNCT
ejpam-4036	39	16	satz	satz	PROPN
ejpam-4036	39	17	8.6	8.6	NUM
ejpam-4036	39	18	,	,	PUNCT
ejpam-4036	39	19	p.	p.	NOUN
ejpam-4036	39	20	713	713	NUM
ejpam-4036	39	21	and	and	CCONJ
ejpam-4036	39	22	satz	satz	X
ejpam-4036	39	23	3.7	3.7	NUM
ejpam-4036	39	24	,	,	PUNCT
ejpam-4036	39	25	p.	p.	NOUN
ejpam-4036	39	26	270	270	NUM
ejpam-4036	39	27	]	]	PUNCT
ejpam-4036	39	28	)	)	PUNCT
ejpam-4036	39	29	.	.	PUNCT
ejpam-4036	40	1	a	a	DET
ejpam-4036	40	2	normal	normal	ADJ
ejpam-4036	40	3	subgroup	subgroup	NOUN
ejpam-4036	40	4	n	n	PROPN
ejpam-4036	40	5	of	of	ADP
ejpam-4036	40	6	a	a	DET
ejpam-4036	40	7	group	group	NOUN
ejpam-4036	40	8	g	g	NOUN
ejpam-4036	40	9	is	be	AUX
ejpam-4036	40	10	an	an	DET
ejpam-4036	40	11	f	f	ADJ
ejpam-4036	40	12	-	-	PUNCT
ejpam-4036	40	13	hypercentral	hypercentral	ADJ
ejpam-4036	40	14	subgroup	subgroup	NOUN
ejpam-4036	40	15	of	of	ADP
ejpam-4036	40	16	g	g	PROPN
ejpam-4036	40	17	provided	provide	VERB
ejpam-4036	40	18	n	n	PROPN
ejpam-4036	40	19	possesses	possess	VERB
ejpam-4036	40	20	a	a	DET
ejpam-4036	40	21	chain	chain	NOUN
ejpam-4036	40	22	of	of	ADP
ejpam-4036	40	23	subgroups	subgroup	NOUN
ejpam-4036	40	24	1	1	NUM
ejpam-4036	40	25	=	=	SYM
ejpam-4036	40	26	n0en1e	n0en1e	NUM
ejpam-4036	40	27	...	...	PUNCT
ejpam-4036	40	28	ens	ens	PROPN
ejpam-4036	40	29	=	=	PUNCT
ejpam-4036	40	30	n	n	PRON
ejpam-4036	40	31	such	such	ADJ
ejpam-4036	40	32	that	that	SCONJ
ejpam-4036	40	33	ni+1	ni+1	PROPN
ejpam-4036	40	34	/	/	SYM
ejpam-4036	40	35	ni	ni	PROPN
ejpam-4036	40	36	is	be	AUX
ejpam-4036	40	37	an	an	DET
ejpam-4036	40	38	f	f	ADJ
ejpam-4036	40	39	-	-	ADJ
ejpam-4036	40	40	central	central	ADJ
ejpam-4036	40	41	chief	chief	ADJ
ejpam-4036	40	42	factor	factor	NOUN
ejpam-4036	40	43	of	of	ADP
ejpam-4036	40	44	g	g	PROPN
ejpam-4036	40	45	(	(	PUNCT
ejpam-4036	40	46	see	see	VERB
ejpam-4036	40	47	[	[	X
ejpam-4036	40	48	5	5	NUM
ejpam-4036	40	49	,	,	PUNCT
ejpam-4036	40	50	p.	p.	NOUN
ejpam-4036	40	51	387	387	NUM
ejpam-4036	40	52	]	]	NOUN
ejpam-4036	40	53	)	)	PUNCT
ejpam-4036	40	54	.	.	PUNCT
ejpam-4036	41	1	the	the	DET
ejpam-4036	41	2	product	product	NOUN
ejpam-4036	41	3	of	of	ADP
ejpam-4036	41	4	all	all	DET
ejpam-4036	41	5	f	f	ADJ
ejpam-4036	41	6	-	-	PUNCT
ejpam-4036	41	7	hypercentral	hypercentral	ADJ
ejpam-4036	41	8	subgroups	subgroup	NOUN
ejpam-4036	41	9	of	of	ADP
ejpam-4036	41	10	g	g	PROPN
ejpam-4036	41	11	is	be	AUX
ejpam-4036	41	12	again	again	ADV
ejpam-4036	41	13	an	an	DET
ejpam-4036	41	14	f	f	X
ejpam-4036	41	15	-	-	PUNCT
ejpam-4036	41	16	hypercentral	hypercentral	ADJ
ejpam-4036	41	17	subgroup	subgroup	NOUN
ejpam-4036	41	18	,	,	PUNCT
ejpam-4036	41	19	denoted	denote	VERB
ejpam-4036	41	20	by	by	ADP
ejpam-4036	41	21	zf(g	zf(g	NUM
ejpam-4036	41	22	)	)	PUNCT
ejpam-4036	41	23	,	,	PUNCT
ejpam-4036	41	24	and	and	CCONJ
ejpam-4036	41	25	it	it	PRON
ejpam-4036	41	26	is	be	AUX
ejpam-4036	41	27	called	call	VERB
ejpam-4036	41	28	the	the	DET
ejpam-4036	41	29	f	f	NOUN
ejpam-4036	41	30	-	-	PUNCT
ejpam-4036	41	31	hypercenter	hypercenter	NOUN
ejpam-4036	41	32	of	of	ADP
ejpam-4036	41	33	g	g	NOUN
ejpam-4036	41	34	(	(	PUNCT
ejpam-4036	41	35	see	see	VERB
ejpam-4036	41	36	[	[	X
ejpam-4036	41	37	5	5	NUM
ejpam-4036	41	38	,	,	PUNCT
ejpam-4036	41	39	iv	iv	NUM
ejpam-4036	41	40	6.8	6.8	NUM
ejpam-4036	41	41	]	]	PUNCT
ejpam-4036	41	42	)	)	PUNCT
ejpam-4036	41	43	.	.	PUNCT
ejpam-4036	42	1	for	for	ADP
ejpam-4036	42	2	the	the	DET
ejpam-4036	42	3	formation	formation	NOUN
ejpam-4036	42	4	u	u	NOUN
ejpam-4036	42	5	,	,	PUNCT
ejpam-4036	42	6	the	the	DET
ejpam-4036	42	7	u	u	NOUN
ejpam-4036	42	8	-	-	NOUN
ejpam-4036	42	9	hypercenter	hypercenter	NOUN
ejpam-4036	42	10	of	of	ADP
ejpam-4036	42	11	a	a	DET
ejpam-4036	42	12	group	group	NOUN
ejpam-4036	42	13	g	g	NOUN
ejpam-4036	42	14	will	will	AUX
ejpam-4036	42	15	be	be	AUX
ejpam-4036	42	16	denoted	denote	VERB
ejpam-4036	42	17	by	by	ADP
ejpam-4036	42	18	zu(g	zu(g	NOUN
ejpam-4036	42	19	)	)	PUNCT
ejpam-4036	42	20	,	,	PUNCT
ejpam-4036	42	21	that	that	ADV
ejpam-4036	42	22	is	is	ADV
ejpam-4036	42	23	,	,	PUNCT
ejpam-4036	42	24	zu(g	zu(g	NUM
ejpam-4036	42	25	)	)	PUNCT
ejpam-4036	42	26	is	be	AUX
ejpam-4036	42	27	the	the	DET
ejpam-4036	42	28	product	product	NOUN
ejpam-4036	42	29	of	of	ADP
ejpam-4036	42	30	all	all	DET
ejpam-4036	42	31	normal	normal	ADJ
ejpam-4036	42	32	subgroups	subgroup	NOUN
ejpam-4036	42	33	n	n	CCONJ
ejpam-4036	42	34	of	of	ADP
ejpam-4036	42	35	g	g	NOUN
ejpam-4036	42	36	such	such	ADJ
ejpam-4036	42	37	that	that	SCONJ
ejpam-4036	42	38	each	each	DET
ejpam-4036	42	39	chief	chief	ADJ
ejpam-4036	42	40	factor	factor	NOUN
ejpam-4036	42	41	of	of	ADP
ejpam-4036	42	42	g	g	NOUN
ejpam-4036	42	43	below	below	ADP
ejpam-4036	42	44	n	n	PRON
ejpam-4036	42	45	has	have	VERB
ejpam-4036	42	46	prime	prime	ADJ
ejpam-4036	42	47	order	order	NOUN
ejpam-4036	42	48	and	and	CCONJ
ejpam-4036	42	49	for	for	ADP
ejpam-4036	42	50	the	the	DET
ejpam-4036	42	51	formation	formation	NOUN
ejpam-4036	42	52	n	n	CCONJ
ejpam-4036	42	53	,	,	PUNCT
ejpam-4036	42	54	the	the	DET
ejpam-4036	42	55	n	n	NOUN
ejpam-4036	42	56	-	-	PUNCT
ejpam-4036	42	57	hypercenter	hypercenter	NOUN
ejpam-4036	42	58	of	of	ADP
ejpam-4036	42	59	a.	a.	NOUN
ejpam-4036	42	60	heliel	heliel	PROPN
ejpam-4036	42	61	,	,	PUNCT
ejpam-4036	42	62	r.	r.	PROPN
ejpam-4036	42	63	hijazi	hijazi	PROPN
ejpam-4036	42	64	,	,	PUNCT
ejpam-4036	42	65	s.	s.	PROPN
ejpam-4036	42	66	al	al	PROPN
ejpam-4036	42	67	-	-	PUNCT
ejpam-4036	42	68	shammari	shammari	PROPN
ejpam-4036	42	69	/	/	SYM
ejpam-4036	42	70	eur	eur	PROPN
ejpam-4036	42	71	.	.	PUNCT
ejpam-4036	43	1	j.	j.	PROPN
ejpam-4036	43	2	pure	pure	PROPN
ejpam-4036	43	3	appl	appl	PROPN
ejpam-4036	43	4	.	.	PROPN
ejpam-4036	43	5	math	math	PROPN
ejpam-4036	43	6	,	,	PUNCT
ejpam-4036	43	7	14	14	NUM
ejpam-4036	43	8	(	(	PUNCT
ejpam-4036	43	9	3	3	NUM
ejpam-4036	43	10	)	)	PUNCT
ejpam-4036	43	11	(	(	PUNCT
ejpam-4036	43	12	2021	2021	NUM
ejpam-4036	43	13	)	)	PUNCT
ejpam-4036	43	14	,	,	PUNCT
ejpam-4036	43	15	1002	1002	NUM
ejpam-4036	43	16	-	-	SYM
ejpam-4036	43	17	1014	1014	NUM
ejpam-4036	43	18	1004	1004	NUM
ejpam-4036	43	19	a	a	DET
ejpam-4036	43	20	group	group	NOUN
ejpam-4036	43	21	g	g	NOUN
ejpam-4036	43	22	is	be	AUX
ejpam-4036	43	23	simply	simply	ADV
ejpam-4036	43	24	the	the	DET
ejpam-4036	43	25	terminal	terminal	ADJ
ejpam-4036	43	26	member	member	NOUN
ejpam-4036	43	27	z∞(g	z∞(g	PROPN
ejpam-4036	43	28	)	)	PUNCT
ejpam-4036	43	29	of	of	ADP
ejpam-4036	43	30	the	the	DET
ejpam-4036	43	31	ascending	ascend	VERB
ejpam-4036	43	32	central	central	ADJ
ejpam-4036	43	33	series	series	NOUN
ejpam-4036	43	34	of	of	ADP
ejpam-4036	43	35	g.	g.	PROPN
ejpam-4036	43	36	for	for	ADP
ejpam-4036	43	37	more	more	ADJ
ejpam-4036	43	38	details	detail	NOUN
ejpam-4036	43	39	about	about	ADP
ejpam-4036	43	40	saturated	saturate	VERB
ejpam-4036	43	41	formations	formation	NOUN
ejpam-4036	43	42	,	,	PUNCT
ejpam-4036	43	43	see	see	VERB
ejpam-4036	43	44	[	[	X
ejpam-4036	43	45	5	5	NUM
ejpam-4036	43	46	,	,	PUNCT
ejpam-4036	43	47	iv	iv	ADP
ejpam-4036	43	48	]	]	PUNCT
ejpam-4036	43	49	.	.	PUNCT
ejpam-4036	44	1	for	for	ADP
ejpam-4036	44	2	any	any	DET
ejpam-4036	44	3	group	group	NOUN
ejpam-4036	44	4	g	g	NOUN
ejpam-4036	44	5	,	,	PUNCT
ejpam-4036	44	6	the	the	DET
ejpam-4036	44	7	generalized	generalized	ADJ
ejpam-4036	44	8	fitting	fitting	ADJ
ejpam-4036	44	9	subgroup	subgroup	NOUN
ejpam-4036	44	10	f	f	PROPN
ejpam-4036	44	11	∗(g	∗(g	PROPN
ejpam-4036	44	12	)	)	PUNCT
ejpam-4036	44	13	is	be	AUX
ejpam-4036	44	14	the	the	DET
ejpam-4036	44	15	set	set	NOUN
ejpam-4036	44	16	of	of	ADP
ejpam-4036	44	17	all	all	DET
ejpam-4036	44	18	elements	element	NOUN
ejpam-4036	44	19	x	x	PUNCT
ejpam-4036	44	20	of	of	ADP
ejpam-4036	44	21	g	g	NOUN
ejpam-4036	44	22	which	which	PRON
ejpam-4036	44	23	induce	induce	VERB
ejpam-4036	44	24	an	an	DET
ejpam-4036	44	25	inner	inner	ADJ
ejpam-4036	44	26	automorphism	automorphism	NOUN
ejpam-4036	44	27	on	on	ADP
ejpam-4036	44	28	every	every	DET
ejpam-4036	44	29	chief	chief	ADJ
ejpam-4036	44	30	factor	factor	NOUN
ejpam-4036	44	31	of	of	ADP
ejpam-4036	44	32	g.	g.	PROPN
ejpam-4036	44	33	lemma	lemma	PROPN
ejpam-4036	44	34	1	1	X
ejpam-4036	44	35	.	.	PUNCT
ejpam-4036	45	1	(	(	PUNCT
ejpam-4036	45	2	see	see	VERB
ejpam-4036	45	3	[	[	X
ejpam-4036	45	4	26	26	NUM
ejpam-4036	45	5	,	,	PUNCT
ejpam-4036	45	6	lemma	lemma	PROPN
ejpam-4036	45	7	2.3	2.3	NUM
ejpam-4036	45	8	]	]	PUNCT
ejpam-4036	45	9	)	)	PUNCT
ejpam-4036	45	10	let	let	VERB
ejpam-4036	45	11	h	h	NOUN
ejpam-4036	45	12	be	be	AUX
ejpam-4036	45	13	css	css	PROPN
ejpam-4036	45	14	-	-	PROPN
ejpam-4036	45	15	subgroup	subgroup	NOUN
ejpam-4036	45	16	of	of	ADP
ejpam-4036	45	17	g.	g.	PROPN
ejpam-4036	45	18	(	(	PUNCT
ejpam-4036	45	19	1	1	X
ejpam-4036	45	20	)	)	PUNCT
ejpam-4036	45	21	if	if	SCONJ
ejpam-4036	45	22	h	h	PROPN
ejpam-4036	45	23	6	6	NUM
ejpam-4036	45	24	m	m	NOUN
ejpam-4036	45	25	6	6	NUM
ejpam-4036	45	26	g	g	NOUN
ejpam-4036	45	27	,	,	PUNCT
ejpam-4036	45	28	then	then	ADV
ejpam-4036	45	29	h	h	PROPN
ejpam-4036	45	30	is	be	AUX
ejpam-4036	45	31	css	css	PROPN
ejpam-4036	45	32	-	-	PROPN
ejpam-4036	45	33	subgroup	subgroup	NOUN
ejpam-4036	45	34	of	of	ADP
ejpam-4036	45	35	m	m	PROPN
ejpam-4036	45	36	.	.	PUNCT
ejpam-4036	46	1	(	(	PUNCT
ejpam-4036	46	2	2	2	X
ejpam-4036	46	3	)	)	PUNCT
ejpam-4036	46	4	let	let	VERB
ejpam-4036	46	5	n	n	PRON
ejpam-4036	46	6	e	e	VERB
ejpam-4036	46	7	g	g	NOUN
ejpam-4036	46	8	and	and	CCONJ
ejpam-4036	46	9	n	n	PROPN
ejpam-4036	46	10	6	6	NUM
ejpam-4036	46	11	h.	h.	NOUN
ejpam-4036	46	12	then	then	ADV
ejpam-4036	46	13	h	h	PROPN
ejpam-4036	46	14	is	be	AUX
ejpam-4036	46	15	css	css	PROPN
ejpam-4036	46	16	-	-	NOUN
ejpam-4036	46	17	subgroup	subgroup	NOUN
ejpam-4036	46	18	of	of	ADP
ejpam-4036	46	19	g	g	PROPN
ejpam-4036	46	20	if	if	SCONJ
ejpam-4036	47	1	and	and	CCONJ
ejpam-4036	47	2	only	only	ADV
ejpam-4036	47	3	if	if	SCONJ
ejpam-4036	47	4	h	h	NOUN
ejpam-4036	47	5	/	/	SYM
ejpam-4036	47	6	n	n	PROPN
ejpam-4036	47	7	is	be	AUX
ejpam-4036	47	8	css	css	PROPN
ejpam-4036	47	9	-	-	NOUN
ejpam-4036	47	10	subgroup	subgroup	NOUN
ejpam-4036	47	11	of	of	ADP
ejpam-4036	47	12	g	g	PROPN
ejpam-4036	47	13	/	/	SYM
ejpam-4036	47	14	n	n	PROPN
ejpam-4036	47	15	.	.	PUNCT
ejpam-4036	48	1	(	(	PUNCT
ejpam-4036	48	2	3	3	X
ejpam-4036	48	3	)	)	PUNCT
ejpam-4036	48	4	let	let	VERB
ejpam-4036	48	5	π	π	NOUN
ejpam-4036	48	6	be	be	AUX
ejpam-4036	48	7	a	a	DET
ejpam-4036	48	8	set	set	NOUN
ejpam-4036	48	9	of	of	ADP
ejpam-4036	48	10	some	some	DET
ejpam-4036	48	11	primes	prime	NOUN
ejpam-4036	48	12	and	and	CCONJ
ejpam-4036	48	13	n	n	DET
ejpam-4036	48	14	a	a	DET
ejpam-4036	48	15	normal	normal	ADJ
ejpam-4036	48	16	π′-subgroup	π′-subgroup	PROPN
ejpam-4036	48	17	of	of	ADP
ejpam-4036	48	18	g.	g.	PROPN
ejpam-4036	48	19	if	if	SCONJ
ejpam-4036	48	20	h	h	NOUN
ejpam-4036	48	21	is	be	AUX
ejpam-4036	48	22	a	a	DET
ejpam-4036	48	23	π	π	PROPN
ejpam-4036	48	24	-	-	NOUN
ejpam-4036	48	25	subgroup	subgroup	NOUN
ejpam-4036	48	26	of	of	ADP
ejpam-4036	48	27	g	g	PROPN
ejpam-4036	48	28	,	,	PUNCT
ejpam-4036	48	29	then	then	ADV
ejpam-4036	48	30	hn	hn	PROPN
ejpam-4036	48	31	/	/	SYM
ejpam-4036	48	32	n	n	PROPN
ejpam-4036	48	33	is	be	AUX
ejpam-4036	48	34	css	css	PROPN
ejpam-4036	48	35	-	-	NOUN
ejpam-4036	48	36	subgroup	subgroup	NOUN
ejpam-4036	48	37	of	of	ADP
ejpam-4036	48	38	g	g	PROPN
ejpam-4036	48	39	/	/	SYM
ejpam-4036	48	40	n	n	PROPN
ejpam-4036	48	41	.	.	PUNCT
ejpam-4036	49	1	lemma	lemma	PROPN
ejpam-4036	49	2	2	2	X
ejpam-4036	49	3	.	.	PUNCT
ejpam-4036	50	1	(	(	PUNCT
ejpam-4036	50	2	see	see	VERB
ejpam-4036	50	3	[	[	X
ejpam-4036	50	4	7	7	NUM
ejpam-4036	50	5	,	,	PUNCT
ejpam-4036	50	6	satz	satz	X
ejpam-4036	50	7	5.4	5.4	NUM
ejpam-4036	50	8	,	,	PUNCT
ejpam-4036	50	9	p.	p.	NOUN
ejpam-4036	50	10	434	434	NUM
ejpam-4036	50	11	and	and	CCONJ
ejpam-4036	50	12	satz	satz	PROPN
ejpam-4036	50	13	5.2	5.2	NUM
ejpam-4036	50	14	,	,	PUNCT
ejpam-4036	50	15	p.	p.	NOUN
ejpam-4036	50	16	281	281	NUM
ejpam-4036	50	17	]	]	PUNCT
ejpam-4036	50	18	)	)	PUNCT
ejpam-4036	50	19	let	let	VERB
ejpam-4036	50	20	g	g	PRON
ejpam-4036	50	21	be	be	AUX
ejpam-4036	50	22	a	a	DET
ejpam-4036	50	23	minimal	minimal	ADJ
ejpam-4036	50	24	non	non	ADJ
ejpam-4036	50	25	pnilpotent	pnilpotent	NOUN
ejpam-4036	50	26	group	group	NOUN
ejpam-4036	50	27	(	(	PUNCT
ejpam-4036	50	28	a	a	DET
ejpam-4036	50	29	non	non	ADJ
ejpam-4036	50	30	p	p	ADJ
ejpam-4036	50	31	-	-	PUNCT
ejpam-4036	50	32	nilpotent	nilpotent	ADJ
ejpam-4036	50	33	group	group	NOUN
ejpam-4036	50	34	all	all	PRON
ejpam-4036	50	35	of	of	ADP
ejpam-4036	50	36	its	its	PRON
ejpam-4036	50	37	proper	proper	ADJ
ejpam-4036	50	38	subgroups	subgroup	NOUN
ejpam-4036	50	39	are	be	AUX
ejpam-4036	50	40	p	p	NOUN
ejpam-4036	50	41	-	-	PUNCT
ejpam-4036	50	42	nilpotent	nilpotent	ADJ
ejpam-4036	50	43	)	)	PUNCT
ejpam-4036	50	44	,	,	PUNCT
ejpam-4036	50	45	where	where	SCONJ
ejpam-4036	50	46	p	p	NOUN
ejpam-4036	50	47	is	be	AUX
ejpam-4036	50	48	a	a	DET
ejpam-4036	50	49	prime	prime	NOUN
ejpam-4036	50	50	.	.	PUNCT
ejpam-4036	51	1	(	(	PUNCT
ejpam-4036	51	2	1	1	X
ejpam-4036	51	3	)	)	PUNCT
ejpam-4036	51	4	g	g	NOUN
ejpam-4036	51	5	is	be	AUX
ejpam-4036	51	6	a	a	DET
ejpam-4036	51	7	minimal	minimal	ADJ
ejpam-4036	51	8	non	non	ADJ
ejpam-4036	51	9	-	-	ADJ
ejpam-4036	51	10	nilpotent	nilpotent	ADJ
ejpam-4036	51	11	group	group	NOUN
ejpam-4036	51	12	.	.	PUNCT
ejpam-4036	52	1	(	(	PUNCT
ejpam-4036	52	2	2	2	X
ejpam-4036	52	3	)	)	PUNCT
ejpam-4036	52	4	g	g	NOUN
ejpam-4036	52	5	=	=	SYM
ejpam-4036	52	6	pq	pq	PROPN
ejpam-4036	52	7	,	,	PUNCT
ejpam-4036	52	8	where	where	SCONJ
ejpam-4036	52	9	p	p	NOUN
ejpam-4036	52	10	is	be	AUX
ejpam-4036	52	11	a	a	DET
ejpam-4036	52	12	normal	normal	ADJ
ejpam-4036	52	13	sylow	sylow	NOUN
ejpam-4036	52	14	p	p	NOUN
ejpam-4036	52	15	-	-	PUNCT
ejpam-4036	52	16	subgroup	subgroup	NOUN
ejpam-4036	52	17	of	of	ADP
ejpam-4036	52	18	g	g	PROPN
ejpam-4036	52	19	and	and	CCONJ
ejpam-4036	52	20	q	q	PROPN
ejpam-4036	52	21	is	be	AUX
ejpam-4036	52	22	a	a	DET
ejpam-4036	52	23	non	non	X
ejpam-4036	52	24	normal	normal	ADJ
ejpam-4036	52	25	cyclic	cyclic	ADJ
ejpam-4036	52	26	sylow	sylow	NOUN
ejpam-4036	52	27	q	q	NOUN
ejpam-4036	52	28	-	-	NOUN
ejpam-4036	52	29	subgroup	subgroup	NOUN
ejpam-4036	52	30	of	of	ADP
ejpam-4036	52	31	g.	g.	PROPN
ejpam-4036	52	32	(	(	PUNCT
ejpam-4036	52	33	3	3	X
ejpam-4036	52	34	)	)	PUNCT
ejpam-4036	52	35	p	p	X
ejpam-4036	52	36	/	/	SYM
ejpam-4036	52	37	φ(p	φ(p	PROPN
ejpam-4036	52	38	)	)	PUNCT
ejpam-4036	52	39	is	be	AUX
ejpam-4036	52	40	a	a	DET
ejpam-4036	52	41	minimal	minimal	ADJ
ejpam-4036	52	42	normal	normal	ADJ
ejpam-4036	52	43	subgroup	subgroup	NOUN
ejpam-4036	52	44	of	of	ADP
ejpam-4036	52	45	g	g	PROPN
ejpam-4036	52	46	/	/	SYM
ejpam-4036	52	47	φ(p	φ(p	PROPN
ejpam-4036	52	48	)	)	PUNCT
ejpam-4036	52	49	.	.	PUNCT
ejpam-4036	53	1	(	(	PUNCT
ejpam-4036	53	2	4	4	X
ejpam-4036	53	3	)	)	PUNCT
ejpam-4036	53	4	if	if	SCONJ
ejpam-4036	53	5	p	p	PROPN
ejpam-4036	53	6	>	>	X
ejpam-4036	53	7	2	2	NUM
ejpam-4036	53	8	,	,	PUNCT
ejpam-4036	53	9	then	then	ADV
ejpam-4036	53	10	the	the	DET
ejpam-4036	53	11	exponent	exponent	NOUN
ejpam-4036	53	12	of	of	ADP
ejpam-4036	53	13	p	p	PROPN
ejpam-4036	53	14	is	be	AUX
ejpam-4036	53	15	p	p	NOUN
ejpam-4036	53	16	and	and	CCONJ
ejpam-4036	53	17	when	when	SCONJ
ejpam-4036	53	18	p	p	NOUN
ejpam-4036	53	19	=	=	NOUN
ejpam-4036	53	20	2	2	NUM
ejpam-4036	53	21	,	,	PUNCT
ejpam-4036	53	22	the	the	DET
ejpam-4036	53	23	exponent	exponent	NOUN
ejpam-4036	53	24	of	of	ADP
ejpam-4036	53	25	p	p	PROPN
ejpam-4036	53	26	is	be	AUX
ejpam-4036	53	27	at	at	ADP
ejpam-4036	53	28	most	most	ADV
ejpam-4036	53	29	4	4	NUM
ejpam-4036	53	30	.	.	PUNCT
ejpam-4036	54	1	lemma	lemma	PROPN
ejpam-4036	54	2	3	3	X
ejpam-4036	54	3	.	.	PUNCT
ejpam-4036	55	1	(	(	PUNCT
ejpam-4036	55	2	see	see	VERB
ejpam-4036	55	3	[	[	X
ejpam-4036	55	4	17	17	NUM
ejpam-4036	55	5	,	,	PUNCT
ejpam-4036	55	6	theorem	theorem	VERB
ejpam-4036	55	7	3.2	3.2	NUM
ejpam-4036	55	8	]	]	PUNCT
ejpam-4036	55	9	)	)	PUNCT
ejpam-4036	55	10	let	let	VERB
ejpam-4036	55	11	p	p	PRON
ejpam-4036	55	12	be	be	AUX
ejpam-4036	55	13	the	the	DET
ejpam-4036	55	14	smallest	small	ADJ
ejpam-4036	55	15	prime	prime	ADJ
ejpam-4036	55	16	dividing	dividing	NOUN
ejpam-4036	55	17	|g|	|g|	PROPN
ejpam-4036	55	18	and	and	CCONJ
ejpam-4036	55	19	p	p	X
ejpam-4036	55	20	a	a	DET
ejpam-4036	55	21	sylow	sylow	NOUN
ejpam-4036	55	22	p	p	NOUN
ejpam-4036	55	23	-	-	PUNCT
ejpam-4036	55	24	subgroup	subgroup	NOUN
ejpam-4036	55	25	of	of	ADP
ejpam-4036	55	26	g.	g.	PROPN
ejpam-4036	55	27	if	if	SCONJ
ejpam-4036	55	28	every	every	DET
ejpam-4036	55	29	subgroup	subgroup	NOUN
ejpam-4036	55	30	of	of	ADP
ejpam-4036	55	31	p	p	NOUN
ejpam-4036	55	32	of	of	ADP
ejpam-4036	55	33	order	order	NOUN
ejpam-4036	55	34	p	p	X
ejpam-4036	55	35	or	or	CCONJ
ejpam-4036	55	36	of	of	ADP
ejpam-4036	55	37	order	order	NOUN
ejpam-4036	55	38	4	4	NUM
ejpam-4036	55	39	(	(	PUNCT
ejpam-4036	55	40	if	if	SCONJ
ejpam-4036	55	41	p	p	X
ejpam-4036	55	42	=	=	NOUN
ejpam-4036	55	43	2	2	NUM
ejpam-4036	55	44	)	)	PUNCT
ejpam-4036	55	45	is	be	AUX
ejpam-4036	55	46	s	s	NOUN
ejpam-4036	55	47	-	-	ADJ
ejpam-4036	55	48	quasinormal	quasinormal	ADJ
ejpam-4036	55	49	in	in	ADP
ejpam-4036	55	50	g	g	PROPN
ejpam-4036	55	51	,	,	PUNCT
ejpam-4036	55	52	then	then	ADV
ejpam-4036	55	53	g	g	PROPN
ejpam-4036	55	54	is	be	AUX
ejpam-4036	55	55	p	p	NOUN
ejpam-4036	55	56	-	-	PUNCT
ejpam-4036	55	57	nilpotent	nilpotent	ADJ
ejpam-4036	55	58	.	.	PUNCT
ejpam-4036	56	1	lemma	lemma	PROPN
ejpam-4036	56	2	4	4	NUM
ejpam-4036	56	3	.	.	PUNCT
ejpam-4036	57	1	(	(	PUNCT
ejpam-4036	57	2	see	see	VERB
ejpam-4036	57	3	[	[	X
ejpam-4036	57	4	23	23	NUM
ejpam-4036	57	5	]	]	PUNCT
ejpam-4036	57	6	)	)	PUNCT
ejpam-4036	57	7	let	let	VERB
ejpam-4036	57	8	h	h	PRON
ejpam-4036	57	9	be	be	AUX
ejpam-4036	57	10	a	a	DET
ejpam-4036	57	11	subnormal	subnormal	ADJ
ejpam-4036	57	12	subgroup	subgroup	NOUN
ejpam-4036	57	13	of	of	ADP
ejpam-4036	57	14	g.	g.	PROPN
ejpam-4036	57	15	(	(	PUNCT
ejpam-4036	57	16	1	1	X
ejpam-4036	57	17	)	)	PUNCT
ejpam-4036	57	18	if	if	SCONJ
ejpam-4036	57	19	h	h	NOUN
ejpam-4036	57	20	is	be	AUX
ejpam-4036	57	21	a	a	DET
ejpam-4036	57	22	hall	hall	NOUN
ejpam-4036	57	23	-	-	PUNCT
ejpam-4036	57	24	subgroup	subgroup	NOUN
ejpam-4036	57	25	of	of	ADP
ejpam-4036	57	26	g	g	PROPN
ejpam-4036	57	27	,	,	PUNCT
ejpam-4036	57	28	then	then	ADV
ejpam-4036	57	29	h	h	NOUN
ejpam-4036	57	30	is	be	AUX
ejpam-4036	57	31	normal	normal	ADJ
ejpam-4036	57	32	in	in	ADP
ejpam-4036	57	33	g.	g.	PROPN
ejpam-4036	57	34	(	(	PUNCT
ejpam-4036	57	35	2	2	X
ejpam-4036	57	36	)	)	PUNCT
ejpam-4036	57	37	if	if	SCONJ
ejpam-4036	57	38	h	h	NOUN
ejpam-4036	57	39	is	be	AUX
ejpam-4036	57	40	a	a	DET
ejpam-4036	57	41	π	π	PROPN
ejpam-4036	57	42	-	-	NOUN
ejpam-4036	57	43	subgroup	subgroup	NOUN
ejpam-4036	57	44	of	of	ADP
ejpam-4036	57	45	g	g	PROPN
ejpam-4036	57	46	,	,	PUNCT
ejpam-4036	57	47	then	then	ADV
ejpam-4036	57	48	h	h	PROPN
ejpam-4036	57	49	6	6	NUM
ejpam-4036	57	50	oπ(g	oπ(g	NUM
ejpam-4036	57	51	)	)	PUNCT
ejpam-4036	57	52	.	.	PUNCT
ejpam-4036	58	1	lemma	lemma	PROPN
ejpam-4036	58	2	5	5	NUM
ejpam-4036	58	3	.	.	PUNCT
ejpam-4036	59	1	(	(	PUNCT
ejpam-4036	59	2	see	see	VERB
ejpam-4036	59	3	[	[	X
ejpam-4036	59	4	11	11	NUM
ejpam-4036	59	5	,	,	PUNCT
ejpam-4036	59	6	lemma	lemma	PROPN
ejpam-4036	59	7	2.2	2.2	NUM
ejpam-4036	59	8	]	]	PUNCT
ejpam-4036	59	9	)	)	PUNCT
ejpam-4036	59	10	suppose	suppose	VERB
ejpam-4036	59	11	that	that	SCONJ
ejpam-4036	59	12	p	p	PROPN
ejpam-4036	59	13	is	be	AUX
ejpam-4036	59	14	a	a	DET
ejpam-4036	59	15	p	p	NOUN
ejpam-4036	59	16	-	-	PUNCT
ejpam-4036	59	17	subgroup	subgroup	NOUN
ejpam-4036	59	18	of	of	ADP
ejpam-4036	59	19	g.	g.	PROPN
ejpam-4036	59	20	then	then	ADV
ejpam-4036	59	21	p	p	PROPN
ejpam-4036	59	22	is	be	AUX
ejpam-4036	59	23	s	s	NOUN
ejpam-4036	59	24	-	-	ADJ
ejpam-4036	59	25	quasinormal	quasinormal	ADJ
ejpam-4036	59	26	in	in	ADP
ejpam-4036	59	27	g	g	PROPN
ejpam-4036	59	28	if	if	SCONJ
ejpam-4036	60	1	and	and	CCONJ
ejpam-4036	60	2	only	only	ADV
ejpam-4036	60	3	if	if	SCONJ
ejpam-4036	60	4	p	p	PROPN
ejpam-4036	60	5	6	6	NUM
ejpam-4036	60	6	op(g	op(g	NUM
ejpam-4036	60	7	)	)	PUNCT
ejpam-4036	60	8	and	and	CCONJ
ejpam-4036	60	9	p	p	NOUN
ejpam-4036	60	10	is	be	AUX
ejpam-4036	60	11	ss	ss	NOUN
ejpam-4036	60	12	-	-	ADJ
ejpam-4036	60	13	quasinormal	quasinormal	ADJ
ejpam-4036	60	14	in	in	ADP
ejpam-4036	60	15	g.	g.	PROPN
ejpam-4036	60	16	lemma	lemma	PROPN
ejpam-4036	60	17	6	6	NUM
ejpam-4036	60	18	.	.	PUNCT
ejpam-4036	61	1	(	(	PUNCT
ejpam-4036	61	2	see	see	VERB
ejpam-4036	61	3	[	[	X
ejpam-4036	61	4	13	13	NUM
ejpam-4036	61	5	,	,	PUNCT
ejpam-4036	61	6	theorem	theorem	VERB
ejpam-4036	61	7	3.3	3.3	NUM
ejpam-4036	61	8	]	]	PUNCT
ejpam-4036	61	9	)	)	PUNCT
ejpam-4036	61	10	suppose	suppose	VERB
ejpam-4036	61	11	that	that	SCONJ
ejpam-4036	61	12	p	p	PROPN
ejpam-4036	61	13	is	be	AUX
ejpam-4036	61	14	a	a	DET
ejpam-4036	61	15	normal	normal	ADJ
ejpam-4036	61	16	p	p	NOUN
ejpam-4036	61	17	-	-	PUNCT
ejpam-4036	61	18	subgroup	subgroup	NOUN
ejpam-4036	61	19	of	of	ADP
ejpam-4036	61	20	g	g	PROPN
ejpam-4036	61	21	,	,	PUNCT
ejpam-4036	61	22	where	where	SCONJ
ejpam-4036	61	23	p	p	X
ejpam-4036	61	24	>	>	X
ejpam-4036	61	25	2	2	NUM
ejpam-4036	61	26	.	.	PUNCT
ejpam-4036	61	27	if	if	SCONJ
ejpam-4036	61	28	every	every	DET
ejpam-4036	61	29	subgroup	subgroup	NOUN
ejpam-4036	61	30	of	of	ADP
ejpam-4036	61	31	p	p	NOUN
ejpam-4036	61	32	of	of	ADP
ejpam-4036	61	33	order	order	NOUN
ejpam-4036	61	34	p	p	NOUN
ejpam-4036	61	35	is	be	AUX
ejpam-4036	61	36	s	s	NOUN
ejpam-4036	61	37	-	-	ADJ
ejpam-4036	61	38	quasinormal	quasinormal	ADJ
ejpam-4036	61	39	in	in	ADP
ejpam-4036	61	40	g	g	PROPN
ejpam-4036	61	41	,	,	PUNCT
ejpam-4036	61	42	then	then	ADV
ejpam-4036	61	43	p	p	X
ejpam-4036	61	44	6	6	NUM
ejpam-4036	61	45	zu(g	zu(g	NUM
ejpam-4036	61	46	)	)	PUNCT
ejpam-4036	61	47	.	.	PUNCT
ejpam-4036	62	1	lemma	lemma	PROPN
ejpam-4036	62	2	7	7	NUM
ejpam-4036	62	3	.	.	PUNCT
ejpam-4036	63	1	(	(	PUNCT
ejpam-4036	63	2	see	see	VERB
ejpam-4036	63	3	[	[	X
ejpam-4036	63	4	22	22	NUM
ejpam-4036	63	5	,	,	PUNCT
ejpam-4036	63	6	theorem	theorem	VERB
ejpam-4036	63	7	7.7	7.7	NUM
ejpam-4036	63	8	,	,	PUNCT
ejpam-4036	63	9	p.	p.	NOUN
ejpam-4036	63	10	31	31	NUM
ejpam-4036	63	11	]	]	PUNCT
ejpam-4036	63	12	)	)	PUNCT
ejpam-4036	63	13	let	let	VERB
ejpam-4036	63	14	n	n	PRON
ejpam-4036	63	15	be	be	AUX
ejpam-4036	63	16	a	a	DET
ejpam-4036	63	17	normal	normal	ADJ
ejpam-4036	63	18	subgroup	subgroup	NOUN
ejpam-4036	63	19	of	of	ADP
ejpam-4036	63	20	g	g	PROPN
ejpam-4036	64	1	such	such	ADJ
ejpam-4036	64	2	that	that	SCONJ
ejpam-4036	64	3	n	n	PROPN
ejpam-4036	64	4	6	6	NUM
ejpam-4036	64	5	zu(g	zu(g	NUM
ejpam-4036	64	6	)	)	PUNCT
ejpam-4036	65	1	.	.	PUNCT
ejpam-4036	66	1	then	then	ADV
ejpam-4036	66	2	zu(g	zu(g	NUM
ejpam-4036	66	3	/	/	SYM
ejpam-4036	66	4	n	n	CCONJ
ejpam-4036	66	5	)	)	PUNCT
ejpam-4036	66	6	=	=	SYM
ejpam-4036	67	1	zu(g)/n	zu(g)/n	PROPN
ejpam-4036	67	2	.	.	PUNCT
ejpam-4036	68	1	lemma	lemma	PROPN
ejpam-4036	68	2	8	8	NUM
ejpam-4036	68	3	.	.	PUNCT
ejpam-4036	69	1	(	(	PUNCT
ejpam-4036	69	2	see	see	VERB
ejpam-4036	69	3	[	[	X
ejpam-4036	69	4	22	22	NUM
ejpam-4036	69	5	,	,	PUNCT
ejpam-4036	69	6	theorem	theorem	VERB
ejpam-4036	69	7	6.3	6.3	NUM
ejpam-4036	69	8	,	,	PUNCT
ejpam-4036	69	9	p.	p.	NOUN
ejpam-4036	69	10	220	220	NUM
ejpam-4036	69	11	and	and	CCONJ
ejpam-4036	69	12	corollary	corollary	ADJ
ejpam-4036	69	13	7.8	7.8	NUM
ejpam-4036	69	14	,	,	PUNCT
ejpam-4036	69	15	p.	p.	NOUN
ejpam-4036	69	16	33	33	NUM
ejpam-4036	69	17	]	]	PUNCT
ejpam-4036	69	18	)	)	PUNCT
ejpam-4036	69	19	let	let	VERB
ejpam-4036	69	20	p	p	PRON
ejpam-4036	69	21	be	be	AUX
ejpam-4036	69	22	a	a	DET
ejpam-4036	69	23	normal	normal	ADJ
ejpam-4036	69	24	p	p	NOUN
ejpam-4036	69	25	-	-	PUNCT
ejpam-4036	69	26	subgroup	subgroup	NOUN
ejpam-4036	69	27	of	of	ADP
ejpam-4036	69	28	g	g	PROPN
ejpam-4036	69	29	such	such	ADJ
ejpam-4036	69	30	that	that	SCONJ
ejpam-4036	69	31	|g	|g	NOUN
ejpam-4036	69	32	/	/	SYM
ejpam-4036	69	33	cg(p	cg(p	NUM
ejpam-4036	69	34	)	)	PUNCT
ejpam-4036	69	35	|	|	ADV
ejpam-4036	69	36	is	be	AUX
ejpam-4036	69	37	a	a	DET
ejpam-4036	69	38	power	power	NOUN
ejpam-4036	69	39	of	of	ADP
ejpam-4036	69	40	p.	p.	NOUN
ejpam-4036	70	1	then	then	ADV
ejpam-4036	70	2	p	p	PROPN
ejpam-4036	70	3	6	6	NUM
ejpam-4036	70	4	zu(g	zu(g	NUM
ejpam-4036	70	5	)	)	PUNCT
ejpam-4036	70	6	.	.	PUNCT
ejpam-4036	71	1	a.	a.	NOUN
ejpam-4036	71	2	heliel	heliel	PROPN
ejpam-4036	71	3	,	,	PUNCT
ejpam-4036	71	4	r.	r.	PROPN
ejpam-4036	71	5	hijazi	hijazi	PROPN
ejpam-4036	71	6	,	,	PUNCT
ejpam-4036	71	7	s.	s.	PROPN
ejpam-4036	71	8	al	al	PROPN
ejpam-4036	71	9	-	-	PUNCT
ejpam-4036	71	10	shammari	shammari	PROPN
ejpam-4036	71	11	/	/	SYM
ejpam-4036	71	12	eur	eur	PROPN
ejpam-4036	71	13	.	.	PUNCT
ejpam-4036	72	1	j.	j.	PROPN
ejpam-4036	72	2	pure	pure	PROPN
ejpam-4036	72	3	appl	appl	PROPN
ejpam-4036	72	4	.	.	PROPN
ejpam-4036	72	5	math	math	PROPN
ejpam-4036	72	6	,	,	PUNCT
ejpam-4036	72	7	14	14	NUM
ejpam-4036	72	8	(	(	PUNCT
ejpam-4036	72	9	3	3	NUM
ejpam-4036	72	10	)	)	PUNCT
ejpam-4036	72	11	(	(	PUNCT
ejpam-4036	72	12	2021	2021	NUM
ejpam-4036	72	13	)	)	PUNCT
ejpam-4036	72	14	,	,	PUNCT
ejpam-4036	72	15	1002	1002	NUM
ejpam-4036	72	16	-	-	SYM
ejpam-4036	72	17	1014	1014	NUM
ejpam-4036	72	18	1005	1005	NUM
ejpam-4036	72	19	lemma	lemma	PROPN
ejpam-4036	72	20	9	9	NUM
ejpam-4036	72	21	.	.	PUNCT
ejpam-4036	72	22	(	(	PUNCT
ejpam-4036	72	23	see	see	VERB
ejpam-4036	72	24	[	[	X
ejpam-4036	72	25	5	5	NUM
ejpam-4036	72	26	,	,	PUNCT
ejpam-4036	72	27	propositin	propositin	NOUN
ejpam-4036	72	28	3.11	3.11	NUM
ejpam-4036	72	29	,	,	PUNCT
ejpam-4036	72	30	p.	p.	NOUN
ejpam-4036	72	31	362	362	NUM
ejpam-4036	72	32	]	]	PUNCT
ejpam-4036	72	33	)	)	PUNCT
ejpam-4036	72	34	if	if	SCONJ
ejpam-4036	72	35	f1	f1	PROPN
ejpam-4036	72	36	and	and	CCONJ
ejpam-4036	72	37	f2	f2	PROPN
ejpam-4036	72	38	are	be	AUX
ejpam-4036	72	39	two	two	NUM
ejpam-4036	72	40	saturated	saturated	ADJ
ejpam-4036	72	41	formations	formation	NOUN
ejpam-4036	72	42	such	such	ADJ
ejpam-4036	72	43	that	that	DET
ejpam-4036	72	44	f1	f1	PROPN
ejpam-4036	72	45	⊆	⊆	NUM
ejpam-4036	72	46	f2	f2	PROPN
ejpam-4036	72	47	,	,	PUNCT
ejpam-4036	72	48	then	then	ADV
ejpam-4036	72	49	zf1(g	zf1(g	NUM
ejpam-4036	72	50	)	)	PUNCT
ejpam-4036	72	51	⊆	⊆	NUM
ejpam-4036	72	52	zf2(g	zf2(g	NUM
ejpam-4036	72	53	)	)	PUNCT
ejpam-4036	72	54	.	.	PUNCT
ejpam-4036	73	1	lemma	lemma	PROPN
ejpam-4036	73	2	10	10	NUM
ejpam-4036	73	3	.	.	PUNCT
ejpam-4036	74	1	(	(	PUNCT
ejpam-4036	74	2	see	see	VERB
ejpam-4036	74	3	[	[	X
ejpam-4036	74	4	4	4	NUM
ejpam-4036	74	5	]	]	PUNCT
ejpam-4036	74	6	)	)	PUNCT
ejpam-4036	74	7	let	let	VERB
ejpam-4036	74	8	k	k	PRON
ejpam-4036	74	9	be	be	AUX
ejpam-4036	74	10	a	a	DET
ejpam-4036	74	11	normal	normal	ADJ
ejpam-4036	74	12	subgroup	subgroup	NOUN
ejpam-4036	74	13	of	of	ADP
ejpam-4036	74	14	g	g	PROPN
ejpam-4036	74	15	such	such	ADJ
ejpam-4036	74	16	that	that	SCONJ
ejpam-4036	74	17	g	g	PROPN
ejpam-4036	74	18	/	/	SYM
ejpam-4036	74	19	k	k	PROPN
ejpam-4036	74	20	∈	∈	PROPN
ejpam-4036	74	21	f	f	X
ejpam-4036	74	22	,	,	PUNCT
ejpam-4036	74	23	where	where	SCONJ
ejpam-4036	74	24	f	f	PROPN
ejpam-4036	74	25	is	be	AUX
ejpam-4036	74	26	a	a	DET
ejpam-4036	74	27	saturated	saturated	ADJ
ejpam-4036	74	28	formation	formation	NOUN
ejpam-4036	74	29	.	.	PUNCT
ejpam-4036	75	1	if	if	SCONJ
ejpam-4036	75	2	ω(p	ω(p	NOUN
ejpam-4036	75	3	)	)	PUNCT
ejpam-4036	75	4	6	6	NUM
ejpam-4036	75	5	zf(g	zf(g	NUM
ejpam-4036	75	6	)	)	PUNCT
ejpam-4036	75	7	,	,	PUNCT
ejpam-4036	75	8	where	where	SCONJ
ejpam-4036	75	9	p	p	NOUN
ejpam-4036	75	10	is	be	AUX
ejpam-4036	75	11	a	a	DET
ejpam-4036	75	12	sylow	sylow	NOUN
ejpam-4036	75	13	p	p	NOUN
ejpam-4036	75	14	-	-	PUNCT
ejpam-4036	75	15	subgroup	subgroup	NOUN
ejpam-4036	75	16	of	of	ADP
ejpam-4036	75	17	k	k	PROPN
ejpam-4036	75	18	,	,	PUNCT
ejpam-4036	75	19	then	then	ADV
ejpam-4036	75	20	g	g	PROPN
ejpam-4036	75	21	/	/	SYM
ejpam-4036	75	22	op′(k	op′(k	PROPN
ejpam-4036	75	23	)	)	PUNCT
ejpam-4036	75	24	∈	∈	PROPN
ejpam-4036	75	25	f.	f.	PROPN
ejpam-4036	75	26	lemma	lemma	PROPN
ejpam-4036	75	27	11	11	NUM
ejpam-4036	75	28	.	.	PUNCT
ejpam-4036	76	1	(	(	PUNCT
ejpam-4036	76	2	see	see	VERB
ejpam-4036	76	3	[	[	X
ejpam-4036	76	4	8	8	NUM
ejpam-4036	76	5	,	,	PUNCT
ejpam-4036	76	6	x	x	NOUN
ejpam-4036	76	7	13	13	NUM
ejpam-4036	76	8	]	]	PUNCT
ejpam-4036	76	9	and	and	CCONJ
ejpam-4036	76	10	[	[	X
ejpam-4036	76	11	14	14	NUM
ejpam-4036	76	12	,	,	PUNCT
ejpam-4036	76	13	lemma	lemma	PROPN
ejpam-4036	76	14	2.3(4	2.3(4	NUM
ejpam-4036	76	15	)	)	PUNCT
ejpam-4036	76	16	]	]	PUNCT
ejpam-4036	76	17	)	)	PUNCT
ejpam-4036	76	18	let	let	VERB
ejpam-4036	76	19	m	m	PRON
ejpam-4036	76	20	be	be	AUX
ejpam-4036	76	21	a	a	DET
ejpam-4036	76	22	subgroup	subgroup	NOUN
ejpam-4036	76	23	of	of	ADP
ejpam-4036	76	24	g.	g.	PROPN
ejpam-4036	76	25	(	(	PUNCT
ejpam-4036	76	26	1	1	X
ejpam-4036	76	27	)	)	PUNCT
ejpam-4036	76	28	if	if	SCONJ
ejpam-4036	76	29	m	m	NOUN
ejpam-4036	76	30	is	be	AUX
ejpam-4036	76	31	normal	normal	ADJ
ejpam-4036	76	32	in	in	ADP
ejpam-4036	76	33	g	g	PROPN
ejpam-4036	76	34	,	,	PUNCT
ejpam-4036	76	35	then	then	ADV
ejpam-4036	76	36	f	f	PROPN
ejpam-4036	76	37	∗(m	∗(m	PROPN
ejpam-4036	76	38	)	)	PUNCT
ejpam-4036	76	39	6	6	NUM
ejpam-4036	76	40	f	f	NOUN
ejpam-4036	76	41	∗(g	∗(g	PROPN
ejpam-4036	76	42	)	)	PUNCT
ejpam-4036	76	43	.	.	PUNCT
ejpam-4036	77	1	(	(	PUNCT
ejpam-4036	77	2	2	2	X
ejpam-4036	77	3	)	)	PUNCT
ejpam-4036	77	4	f	f	NOUN
ejpam-4036	77	5	∗(g	∗(g	PROPN
ejpam-4036	77	6	)	)	PUNCT
ejpam-4036	77	7	6=	6=	ADP
ejpam-4036	77	8	1	1	NUM
ejpam-4036	77	9	if	if	SCONJ
ejpam-4036	77	10	g	g	PROPN
ejpam-4036	77	11	6=	6=	PROPN
ejpam-4036	77	12	1	1	NUM
ejpam-4036	77	13	.	.	PUNCT
ejpam-4036	78	1	(	(	PUNCT
ejpam-4036	78	2	3	3	X
ejpam-4036	78	3	)	)	PUNCT
ejpam-4036	78	4	if	if	SCONJ
ejpam-4036	78	5	f	f	PROPN
ejpam-4036	78	6	∗(g	∗(g	PROPN
ejpam-4036	78	7	)	)	PUNCT
ejpam-4036	78	8	is	be	AUX
ejpam-4036	78	9	solvable	solvable	ADJ
ejpam-4036	78	10	,	,	PUNCT
ejpam-4036	78	11	then	then	ADV
ejpam-4036	78	12	f	f	PROPN
ejpam-4036	78	13	∗(g	∗(g	PROPN
ejpam-4036	78	14	)	)	PUNCT
ejpam-4036	79	1	=	=	SYM
ejpam-4036	79	2	f	f	X
ejpam-4036	79	3	(	(	PUNCT
ejpam-4036	79	4	g	g	NOUN
ejpam-4036	79	5	)	)	PUNCT
ejpam-4036	79	6	.	.	PUNCT
ejpam-4036	80	1	(	(	PUNCT
ejpam-4036	80	2	4	4	X
ejpam-4036	80	3	)	)	PUNCT
ejpam-4036	80	4	suppose	suppose	VERB
ejpam-4036	80	5	k	k	PROPN
ejpam-4036	80	6	is	be	AUX
ejpam-4036	80	7	a	a	DET
ejpam-4036	80	8	subgroup	subgroup	NOUN
ejpam-4036	80	9	of	of	ADP
ejpam-4036	80	10	g	g	PROPN
ejpam-4036	80	11	contained	contain	VERB
ejpam-4036	80	12	in	in	ADP
ejpam-4036	80	13	z(g	z(g	NOUN
ejpam-4036	80	14	)	)	PUNCT
ejpam-4036	80	15	.	.	PUNCT
ejpam-4036	81	1	then	then	ADV
ejpam-4036	81	2	f	f	PROPN
ejpam-4036	81	3	∗(g	∗(g	PROPN
ejpam-4036	81	4	/	/	SYM
ejpam-4036	81	5	k	k	NOUN
ejpam-4036	81	6	)	)	PUNCT
ejpam-4036	81	7	=	=	SYM
ejpam-4036	81	8	f	f	PROPN
ejpam-4036	81	9	∗(g)/k	∗(g)/k	PROPN
ejpam-4036	81	10	.	.	PUNCT
ejpam-4036	82	1	lemma	lemma	PROPN
ejpam-4036	82	2	12	12	NUM
ejpam-4036	82	3	.	.	PUNCT
ejpam-4036	83	1	(	(	PUNCT
ejpam-4036	83	2	see	see	VERB
ejpam-4036	83	3	[	[	X
ejpam-4036	83	4	10	10	NUM
ejpam-4036	83	5	,	,	PUNCT
ejpam-4036	83	6	corollary	corollary	ADJ
ejpam-4036	83	7	3	3	NUM
ejpam-4036	83	8	]	]	PUNCT
ejpam-4036	83	9	)	)	PUNCT
ejpam-4036	83	10	let	let	VERB
ejpam-4036	83	11	f	f	PRON
ejpam-4036	83	12	be	be	AUX
ejpam-4036	83	13	a	a	DET
ejpam-4036	83	14	saturated	saturated	ADJ
ejpam-4036	83	15	formation	formation	NOUN
ejpam-4036	83	16	and	and	CCONJ
ejpam-4036	83	17	g	g	ADP
ejpam-4036	83	18	a	a	DET
ejpam-4036	83	19	group	group	NOUN
ejpam-4036	83	20	.	.	PUNCT
ejpam-4036	84	1	suppose	suppose	VERB
ejpam-4036	84	2	that	that	SCONJ
ejpam-4036	84	3	cg(n	cg(n	NOUN
ejpam-4036	84	4	)	)	PUNCT
ejpam-4036	84	5	6	6	NUM
ejpam-4036	84	6	n	n	PROPN
ejpam-4036	84	7	e	e	PROPN
ejpam-4036	84	8	g.	g.	NOUN
ejpam-4036	84	9	then	then	ADV
ejpam-4036	84	10	g	g	PROPN
ejpam-4036	84	11	∈	∈	PROPN
ejpam-4036	85	1	f	f	PROPN
ejpam-4036	86	1	if	if	SCONJ
ejpam-4036	86	2	every	every	DET
ejpam-4036	86	3	cyclic	cyclic	ADJ
ejpam-4036	86	4	subgroup	subgroup	NOUN
ejpam-4036	86	5	of	of	ADP
ejpam-4036	86	6	n	n	PROPN
ejpam-4036	86	7	of	of	ADP
ejpam-4036	86	8	prime	prime	ADJ
ejpam-4036	86	9	order	order	NOUN
ejpam-4036	86	10	or	or	CCONJ
ejpam-4036	86	11	of	of	ADP
ejpam-4036	86	12	order	order	NOUN
ejpam-4036	86	13	4	4	NUM
ejpam-4036	86	14	is	be	AUX
ejpam-4036	86	15	contained	contain	VERB
ejpam-4036	86	16	in	in	ADP
ejpam-4036	86	17	zf(g	zf(g	NUM
ejpam-4036	86	18	)	)	PUNCT
ejpam-4036	86	19	.	.	PUNCT
ejpam-4036	87	1	lemma	lemma	PROPN
ejpam-4036	87	2	13	13	NUM
ejpam-4036	87	3	.	.	PUNCT
ejpam-4036	88	1	(	(	PUNCT
ejpam-4036	88	2	see	see	VERB
ejpam-4036	88	3	[	[	X
ejpam-4036	88	4	15	15	NUM
ejpam-4036	88	5	,	,	PUNCT
ejpam-4036	88	6	lemma	lemma	PROPN
ejpam-4036	88	7	2.8	2.8	NUM
ejpam-4036	88	8	]	]	PUNCT
ejpam-4036	88	9	)	)	PUNCT
ejpam-4036	88	10	suppose	suppose	VERB
ejpam-4036	88	11	that	that	SCONJ
ejpam-4036	88	12	g	g	PROPN
ejpam-4036	88	13	is	be	AUX
ejpam-4036	88	14	a	a	DET
ejpam-4036	88	15	group	group	NOUN
ejpam-4036	88	16	and	and	CCONJ
ejpam-4036	88	17	p	p	NOUN
ejpam-4036	88	18	is	be	AUX
ejpam-4036	88	19	a	a	DET
ejpam-4036	88	20	normal	normal	ADJ
ejpam-4036	88	21	p	p	NOUN
ejpam-4036	88	22	-	-	PUNCT
ejpam-4036	88	23	subgroup	subgroup	NOUN
ejpam-4036	88	24	of	of	ADP
ejpam-4036	88	25	g	g	PROPN
ejpam-4036	88	26	contained	contain	VERB
ejpam-4036	88	27	in	in	ADP
ejpam-4036	88	28	z∞(g	z∞(g	NUM
ejpam-4036	88	29	)	)	PUNCT
ejpam-4036	88	30	.	.	PUNCT
ejpam-4036	89	1	then	then	ADV
ejpam-4036	89	2	cg(p	cg(p	PUNCT
ejpam-4036	89	3	)	)	PUNCT
ejpam-4036	89	4	>	>	X
ejpam-4036	89	5	op(g	op(g	NUM
ejpam-4036	89	6	)	)	PUNCT
ejpam-4036	89	7	.	.	PUNCT
ejpam-4036	90	1	lemma	lemma	PROPN
ejpam-4036	90	2	14	14	NUM
ejpam-4036	90	3	.	.	PUNCT
ejpam-4036	91	1	(	(	PUNCT
ejpam-4036	91	2	see	see	VERB
ejpam-4036	91	3	[	[	X
ejpam-4036	91	4	7	7	NUM
ejpam-4036	91	5	,	,	PUNCT
ejpam-4036	91	6	satz	satz	X
ejpam-4036	91	7	2.8	2.8	NUM
ejpam-4036	91	8	,	,	PUNCT
ejpam-4036	91	9	p.	p.	NOUN
ejpam-4036	91	10	420	420	NUM
ejpam-4036	91	11	]	]	PUNCT
ejpam-4036	91	12	)	)	PUNCT
ejpam-4036	91	13	if	if	SCONJ
ejpam-4036	91	14	p	p	NOUN
ejpam-4036	91	15	is	be	AUX
ejpam-4036	91	16	a	a	DET
ejpam-4036	91	17	cyclic	cyclic	ADJ
ejpam-4036	91	18	sylow	sylow	NOUN
ejpam-4036	91	19	p	p	NOUN
ejpam-4036	91	20	-	-	PUNCT
ejpam-4036	91	21	subgroup	subgroup	NOUN
ejpam-4036	91	22	of	of	ADP
ejpam-4036	91	23	g	g	PROPN
ejpam-4036	91	24	,	,	PUNCT
ejpam-4036	91	25	where	where	SCONJ
ejpam-4036	91	26	p	p	NOUN
ejpam-4036	91	27	is	be	AUX
ejpam-4036	91	28	the	the	DET
ejpam-4036	91	29	smallest	small	ADJ
ejpam-4036	91	30	prime	prime	ADJ
ejpam-4036	91	31	dividing	dividing	NOUN
ejpam-4036	91	32	|g|	|g|	PROPN
ejpam-4036	91	33	,	,	PUNCT
ejpam-4036	91	34	then	then	ADV
ejpam-4036	91	35	g	g	PROPN
ejpam-4036	91	36	is	be	AUX
ejpam-4036	91	37	p	p	NOUN
ejpam-4036	91	38	-	-	PUNCT
ejpam-4036	91	39	nilpotent	nilpotent	ADJ
ejpam-4036	91	40	.	.	PUNCT
ejpam-4036	92	1	lemma	lemma	PROPN
ejpam-4036	92	2	15	15	NUM
ejpam-4036	92	3	.	.	PUNCT
ejpam-4036	93	1	(	(	PUNCT
ejpam-4036	93	2	see	see	VERB
ejpam-4036	93	3	[	[	X
ejpam-4036	93	4	6	6	NUM
ejpam-4036	93	5	,	,	PUNCT
ejpam-4036	93	6	theorem	theorem	VERB
ejpam-4036	93	7	3.10	3.10	NUM
ejpam-4036	93	8	,	,	PUNCT
ejpam-4036	93	9	p.	p.	NOUN
ejpam-4036	93	10	184	184	NUM
ejpam-4036	93	11	]	]	SYM
ejpam-4036	93	12	)	)	PUNCT
ejpam-4036	93	13	if	if	SCONJ
ejpam-4036	93	14	h	h	NOUN
ejpam-4036	93	15	is	be	AUX
ejpam-4036	93	16	a	a	DET
ejpam-4036	93	17	p′-group	p′-group	PROPN
ejpam-4036	93	18	of	of	ADP
ejpam-4036	93	19	automorphisms	automorphism	NOUN
ejpam-4036	93	20	of	of	ADP
ejpam-4036	93	21	the	the	DET
ejpam-4036	93	22	p	p	NOUN
ejpam-4036	93	23	-	-	PUNCT
ejpam-4036	93	24	group	group	NOUN
ejpam-4036	93	25	p	p	NOUN
ejpam-4036	93	26	with	with	ADP
ejpam-4036	93	27	p	p	PRON
ejpam-4036	93	28	odd	odd	ADJ
ejpam-4036	93	29	which	which	PRON
ejpam-4036	93	30	acts	act	VERB
ejpam-4036	93	31	trivially	trivially	ADV
ejpam-4036	93	32	on	on	ADP
ejpam-4036	93	33	ω1(p	ω1(p	NOUN
ejpam-4036	93	34	)	)	PUNCT
ejpam-4036	93	35	,	,	PUNCT
ejpam-4036	93	36	then	then	ADV
ejpam-4036	93	37	h	h	NOUN
ejpam-4036	93	38	=	=	NOUN
ejpam-4036	93	39	1	1	X
ejpam-4036	93	40	.	.	PUNCT
ejpam-4036	94	1	lemma	lemma	PROPN
ejpam-4036	94	2	16	16	NUM
ejpam-4036	94	3	.	.	PUNCT
ejpam-4036	95	1	(	(	PUNCT
ejpam-4036	95	2	see	see	VERB
ejpam-4036	95	3	[	[	X
ejpam-4036	95	4	6	6	NUM
ejpam-4036	95	5	,	,	PUNCT
ejpam-4036	95	6	theorem	theorem	VERB
ejpam-4036	95	7	2.4	2.4	NUM
ejpam-4036	95	8	,	,	PUNCT
ejpam-4036	95	9	p.	p.	NOUN
ejpam-4036	95	10	178	178	NUM
ejpam-4036	95	11	]	]	PUNCT
ejpam-4036	95	12	)	)	PUNCT
ejpam-4036	95	13	if	if	SCONJ
ejpam-4036	95	14	h	h	NOUN
ejpam-4036	95	15	is	be	AUX
ejpam-4036	95	16	a	a	DET
ejpam-4036	95	17	p′-group	p′-group	PROPN
ejpam-4036	95	18	of	of	ADP
ejpam-4036	95	19	automorphisms	automorphism	NOUN
ejpam-4036	95	20	of	of	ADP
ejpam-4036	95	21	the	the	DET
ejpam-4036	95	22	abelian	abelian	ADJ
ejpam-4036	95	23	p	p	PROPN
ejpam-4036	95	24	-	-	PUNCT
ejpam-4036	95	25	group	group	NOUN
ejpam-4036	95	26	p	p	NOUN
ejpam-4036	95	27	which	which	PRON
ejpam-4036	95	28	acts	act	VERB
ejpam-4036	95	29	trivially	trivially	ADV
ejpam-4036	95	30	on	on	ADP
ejpam-4036	95	31	ω1(p	ω1(p	NOUN
ejpam-4036	95	32	)	)	PUNCT
ejpam-4036	95	33	,	,	PUNCT
ejpam-4036	95	34	then	then	ADV
ejpam-4036	95	35	h	h	NOUN
ejpam-4036	95	36	=	=	NOUN
ejpam-4036	95	37	1	1	NUM
ejpam-4036	95	38	.	.	NOUN
ejpam-4036	95	39	3	3	NUM
ejpam-4036	95	40	.	.	X
ejpam-4036	95	41	main	main	ADJ
ejpam-4036	95	42	results	result	NOUN
ejpam-4036	95	43	first	first	ADV
ejpam-4036	95	44	we	we	PRON
ejpam-4036	95	45	prove	prove	VERB
ejpam-4036	95	46	:	:	PUNCT
ejpam-4036	95	47	theorem	theorem	NOUN
ejpam-4036	95	48	1	1	NUM
ejpam-4036	95	49	.	.	PUNCT
ejpam-4036	96	1	let	let	VERB
ejpam-4036	96	2	p	p	PRON
ejpam-4036	96	3	be	be	AUX
ejpam-4036	96	4	the	the	DET
ejpam-4036	96	5	smallest	small	ADJ
ejpam-4036	96	6	prime	prime	ADJ
ejpam-4036	96	7	dividing	dividing	NOUN
ejpam-4036	96	8	|g|	|g|	PROPN
ejpam-4036	96	9	and	and	CCONJ
ejpam-4036	96	10	p	p	X
ejpam-4036	96	11	a	a	DET
ejpam-4036	96	12	sylow	sylow	NOUN
ejpam-4036	96	13	p	p	NOUN
ejpam-4036	96	14	-	-	PUNCT
ejpam-4036	96	15	subgroup	subgroup	NOUN
ejpam-4036	96	16	of	of	ADP
ejpam-4036	96	17	g.	g.	PROPN
ejpam-4036	96	18	if	if	SCONJ
ejpam-4036	96	19	every	every	DET
ejpam-4036	96	20	subgroup	subgroup	NOUN
ejpam-4036	96	21	of	of	ADP
ejpam-4036	96	22	p	p	NOUN
ejpam-4036	96	23	of	of	ADP
ejpam-4036	96	24	prime	prime	ADJ
ejpam-4036	96	25	order	order	NOUN
ejpam-4036	96	26	p	p	NOUN
ejpam-4036	96	27	or	or	CCONJ
ejpam-4036	96	28	of	of	ADP
ejpam-4036	96	29	order	order	NOUN
ejpam-4036	96	30	4	4	NUM
ejpam-4036	96	31	(	(	PUNCT
ejpam-4036	96	32	if	if	SCONJ
ejpam-4036	96	33	p	p	X
ejpam-4036	96	34	=	=	NOUN
ejpam-4036	96	35	2	2	NUM
ejpam-4036	96	36	)	)	PUNCT
ejpam-4036	96	37	is	be	AUX
ejpam-4036	96	38	css	css	PROPN
ejpam-4036	96	39	-	-	NOUN
ejpam-4036	96	40	subgroup	subgroup	NOUN
ejpam-4036	96	41	of	of	ADP
ejpam-4036	96	42	g	g	PROPN
ejpam-4036	96	43	,	,	PUNCT
ejpam-4036	96	44	then	then	ADV
ejpam-4036	96	45	g	g	PROPN
ejpam-4036	96	46	is	be	AUX
ejpam-4036	96	47	p	p	NOUN
ejpam-4036	96	48	-	-	PUNCT
ejpam-4036	96	49	nilpotent	nilpotent	ADJ
ejpam-4036	96	50	.	.	PUNCT
ejpam-4036	97	1	proof	proof	NOUN
ejpam-4036	97	2	.	.	PUNCT
ejpam-4036	98	1	assume	assume	VERB
ejpam-4036	98	2	that	that	SCONJ
ejpam-4036	98	3	the	the	DET
ejpam-4036	98	4	result	result	NOUN
ejpam-4036	98	5	is	be	AUX
ejpam-4036	98	6	false	false	ADJ
ejpam-4036	98	7	and	and	CCONJ
ejpam-4036	98	8	let	let	VERB
ejpam-4036	98	9	g	g	PRON
ejpam-4036	98	10	be	be	AUX
ejpam-4036	98	11	a	a	DET
ejpam-4036	98	12	counterexample	counterexample	NOUN
ejpam-4036	98	13	of	of	ADP
ejpam-4036	98	14	minimal	minimal	ADJ
ejpam-4036	98	15	order	order	NOUN
ejpam-4036	98	16	.	.	PUNCT
ejpam-4036	99	1	let	let	VERB
ejpam-4036	99	2	l	l	NOUN
ejpam-4036	99	3	be	be	AUX
ejpam-4036	99	4	an	an	DET
ejpam-4036	99	5	arbitrary	arbitrary	ADJ
ejpam-4036	99	6	proper	proper	ADJ
ejpam-4036	99	7	subgroup	subgroup	NOUN
ejpam-4036	99	8	of	of	ADP
ejpam-4036	99	9	g.	g.	PROPN
ejpam-4036	99	10	then	then	ADV
ejpam-4036	99	11	every	every	DET
ejpam-4036	99	12	subgroup	subgroup	NOUN
ejpam-4036	99	13	of	of	ADP
ejpam-4036	99	14	l	l	NOUN
ejpam-4036	99	15	of	of	ADP
ejpam-4036	99	16	prime	prime	ADJ
ejpam-4036	99	17	order	order	NOUN
ejpam-4036	99	18	p	p	NOUN
ejpam-4036	99	19	or	or	CCONJ
ejpam-4036	99	20	of	of	ADP
ejpam-4036	99	21	order	order	NOUN
ejpam-4036	99	22	4	4	NUM
ejpam-4036	99	23	(	(	PUNCT
ejpam-4036	99	24	if	if	SCONJ
ejpam-4036	99	25	p	p	X
ejpam-4036	99	26	=	=	NOUN
ejpam-4036	99	27	2	2	NUM
ejpam-4036	99	28	)	)	PUNCT
ejpam-4036	99	29	is	be	AUX
ejpam-4036	99	30	css	css	PROPN
ejpam-4036	99	31	-	-	NOUN
ejpam-4036	99	32	subgroup	subgroup	NOUN
ejpam-4036	99	33	of	of	ADP
ejpam-4036	99	34	g	g	NOUN
ejpam-4036	99	35	by	by	ADP
ejpam-4036	99	36	the	the	DET
ejpam-4036	99	37	hypothesis	hypothesis	NOUN
ejpam-4036	99	38	.	.	PUNCT
ejpam-4036	100	1	thus	thus	ADV
ejpam-4036	100	2	,	,	PUNCT
ejpam-4036	100	3	by	by	ADP
ejpam-4036	100	4	lemma	lemma	PROPN
ejpam-4036	100	5	11	11	NUM
ejpam-4036	100	6	,	,	PUNCT
ejpam-4036	100	7	every	every	DET
ejpam-4036	100	8	subgroup	subgroup	NOUN
ejpam-4036	100	9	of	of	ADP
ejpam-4036	100	10	l	l	NOUN
ejpam-4036	100	11	of	of	ADP
ejpam-4036	100	12	prime	prime	ADJ
ejpam-4036	100	13	order	order	NOUN
ejpam-4036	100	14	p	p	NOUN
ejpam-4036	100	15	or	or	CCONJ
ejpam-4036	100	16	of	of	ADP
ejpam-4036	100	17	order	order	NOUN
ejpam-4036	100	18	4	4	NUM
ejpam-4036	100	19	(	(	PUNCT
ejpam-4036	100	20	if	if	SCONJ
ejpam-4036	100	21	p	p	X
ejpam-4036	100	22	=	=	NOUN
ejpam-4036	100	23	2	2	NUM
ejpam-4036	100	24	)	)	PUNCT
ejpam-4036	100	25	is	be	AUX
ejpam-4036	100	26	css	css	PROPN
ejpam-4036	100	27	-	-	PROPN
ejpam-4036	100	28	subgroup	subgroup	NOUN
ejpam-4036	100	29	of	of	ADP
ejpam-4036	100	30	l.	l.	PROPN
ejpam-4036	100	31	that	that	PRON
ejpam-4036	100	32	means	mean	VERB
ejpam-4036	100	33	l	l	NOUN
ejpam-4036	100	34	satisfies	satisfie	NOUN
ejpam-4036	100	35	the	the	DET
ejpam-4036	100	36	hypothesis	hypothesis	NOUN
ejpam-4036	100	37	of	of	ADP
ejpam-4036	100	38	the	the	DET
ejpam-4036	100	39	theorem	theorem	NOUN
ejpam-4036	100	40	and	and	CCONJ
ejpam-4036	100	41	so	so	ADV
ejpam-4036	100	42	l	l	NOUN
ejpam-4036	100	43	is	be	AUX
ejpam-4036	100	44	p	p	NOUN
ejpam-4036	100	45	-	-	PUNCT
ejpam-4036	100	46	nilpotent	nilpotent	ADJ
ejpam-4036	100	47	by	by	ADP
ejpam-4036	100	48	the	the	DET
ejpam-4036	100	49	minimal	minimal	ADJ
ejpam-4036	100	50	choice	choice	NOUN
ejpam-4036	100	51	of	of	ADP
ejpam-4036	100	52	g.	g.	PROPN
ejpam-4036	100	53	hence	hence	ADV
ejpam-4036	100	54	,	,	PUNCT
ejpam-4036	100	55	g	g	PROPN
ejpam-4036	100	56	is	be	AUX
ejpam-4036	100	57	not	not	PART
ejpam-4036	100	58	p	p	NOUN
ejpam-4036	100	59	-	-	PUNCT
ejpam-4036	100	60	nilpotent	nilpotent	ADJ
ejpam-4036	100	61	but	but	CCONJ
ejpam-4036	100	62	all	all	PRON
ejpam-4036	100	63	of	of	ADP
ejpam-4036	100	64	its	its	PRON
ejpam-4036	100	65	proper	proper	ADJ
ejpam-4036	100	66	subgroups	subgroup	NOUN
ejpam-4036	100	67	are	be	AUX
ejpam-4036	100	68	p	p	NOUN
ejpam-4036	100	69	-	-	PUNCT
ejpam-4036	100	70	nilpotent	nilpotent	ADJ
ejpam-4036	100	71	.	.	PUNCT
ejpam-4036	101	1	a.	a.	NOUN
ejpam-4036	101	2	heliel	heliel	PROPN
ejpam-4036	101	3	,	,	PUNCT
ejpam-4036	101	4	r.	r.	PROPN
ejpam-4036	101	5	hijazi	hijazi	PROPN
ejpam-4036	101	6	,	,	PUNCT
ejpam-4036	101	7	s.	s.	PROPN
ejpam-4036	101	8	al	al	PROPN
ejpam-4036	101	9	-	-	PUNCT
ejpam-4036	101	10	shammari	shammari	PROPN
ejpam-4036	101	11	/	/	SYM
ejpam-4036	101	12	eur	eur	PROPN
ejpam-4036	101	13	.	.	PUNCT
ejpam-4036	102	1	j.	j.	PROPN
ejpam-4036	102	2	pure	pure	PROPN
ejpam-4036	102	3	appl	appl	PROPN
ejpam-4036	102	4	.	.	PROPN
ejpam-4036	102	5	math	math	PROPN
ejpam-4036	102	6	,	,	PUNCT
ejpam-4036	102	7	14	14	NUM
ejpam-4036	102	8	(	(	PUNCT
ejpam-4036	102	9	3	3	NUM
ejpam-4036	102	10	)	)	PUNCT
ejpam-4036	102	11	(	(	PUNCT
ejpam-4036	102	12	2021	2021	NUM
ejpam-4036	102	13	)	)	PUNCT
ejpam-4036	102	14	,	,	PUNCT
ejpam-4036	102	15	1002	1002	NUM
ejpam-4036	102	16	-	-	SYM
ejpam-4036	102	17	1014	1014	NUM
ejpam-4036	102	18	1006	1006	NUM
ejpam-4036	102	19	by	by	ADP
ejpam-4036	102	20	lemma	lemma	PROPN
ejpam-4036	102	21	2	2	NUM
ejpam-4036	102	22	,	,	PUNCT
ejpam-4036	102	23	g	g	PROPN
ejpam-4036	102	24	is	be	AUX
ejpam-4036	102	25	a	a	DET
ejpam-4036	102	26	minimal	minimal	ADJ
ejpam-4036	102	27	non	non	ADJ
ejpam-4036	102	28	-	-	ADJ
ejpam-4036	102	29	nilpotent	nilpotent	ADJ
ejpam-4036	102	30	group	group	NOUN
ejpam-4036	102	31	and	and	CCONJ
ejpam-4036	102	32	so	so	ADV
ejpam-4036	102	33	g	g	PROPN
ejpam-4036	102	34	=	=	SYM
ejpam-4036	102	35	pq	pq	PROPN
ejpam-4036	102	36	,	,	PUNCT
ejpam-4036	102	37	where	where	SCONJ
ejpam-4036	102	38	p	p	NOUN
ejpam-4036	102	39	is	be	AUX
ejpam-4036	102	40	a	a	DET
ejpam-4036	102	41	normal	normal	ADJ
ejpam-4036	102	42	sylow	sylow	NOUN
ejpam-4036	102	43	p	p	NOUN
ejpam-4036	102	44	-	-	PUNCT
ejpam-4036	102	45	subgroup	subgroup	NOUN
ejpam-4036	102	46	of	of	ADP
ejpam-4036	102	47	g	g	PROPN
ejpam-4036	102	48	and	and	CCONJ
ejpam-4036	102	49	q	q	PROPN
ejpam-4036	102	50	is	be	AUX
ejpam-4036	102	51	a	a	DET
ejpam-4036	102	52	non	non	ADJ
ejpam-4036	102	53	-	-	ADJ
ejpam-4036	102	54	normal	normal	ADJ
ejpam-4036	102	55	cyclic	cyclic	ADJ
ejpam-4036	102	56	sylow	sylow	NOUN
ejpam-4036	102	57	q	q	NOUN
ejpam-4036	102	58	-	-	NOUN
ejpam-4036	102	59	subgroup	subgroup	NOUN
ejpam-4036	102	60	of	of	ADP
ejpam-4036	102	61	g	g	PROPN
ejpam-4036	102	62	,	,	PUNCT
ejpam-4036	102	63	for	for	ADP
ejpam-4036	102	64	some	some	DET
ejpam-4036	102	65	prime	prime	ADJ
ejpam-4036	102	66	q	q	NOUN
ejpam-4036	103	1	6=	6=	PROPN
ejpam-4036	104	1	p.	p.	NOUN
ejpam-4036	104	2	furthermore	furthermore	ADV
ejpam-4036	104	3	,	,	PUNCT
ejpam-4036	104	4	if	if	SCONJ
ejpam-4036	104	5	p	p	X
ejpam-4036	104	6	>	>	X
ejpam-4036	104	7	2	2	NUM
ejpam-4036	104	8	,	,	PUNCT
ejpam-4036	104	9	then	then	ADV
ejpam-4036	104	10	p	p	NOUN
ejpam-4036	104	11	is	be	AUX
ejpam-4036	104	12	of	of	ADP
ejpam-4036	104	13	exponent	exponent	NOUN
ejpam-4036	104	14	p	p	NOUN
ejpam-4036	104	15	and	and	CCONJ
ejpam-4036	104	16	if	if	SCONJ
ejpam-4036	104	17	p	p	X
ejpam-4036	104	18	=	=	NOUN
ejpam-4036	104	19	2	2	NUM
ejpam-4036	104	20	,	,	PUNCT
ejpam-4036	104	21	p	p	NOUN
ejpam-4036	104	22	is	be	AUX
ejpam-4036	104	23	of	of	ADP
ejpam-4036	104	24	exponent	exponent	NOUN
ejpam-4036	104	25	at	at	ADP
ejpam-4036	104	26	most	most	ADV
ejpam-4036	104	27	4	4	NUM
ejpam-4036	104	28	.	.	PUNCT
ejpam-4036	105	1	if	if	SCONJ
ejpam-4036	105	2	every	every	DET
ejpam-4036	105	3	subgroup	subgroup	NOUN
ejpam-4036	105	4	of	of	ADP
ejpam-4036	105	5	p	p	NOUN
ejpam-4036	105	6	with	with	ADP
ejpam-4036	105	7	order	order	NOUN
ejpam-4036	105	8	p	p	NOUN
ejpam-4036	105	9	or	or	CCONJ
ejpam-4036	105	10	4	4	NUM
ejpam-4036	105	11	(	(	PUNCT
ejpam-4036	105	12	if	if	SCONJ
ejpam-4036	105	13	p	p	X
ejpam-4036	105	14	=	=	NOUN
ejpam-4036	105	15	2	2	NUM
ejpam-4036	105	16	)	)	PUNCT
ejpam-4036	105	17	is	be	AUX
ejpam-4036	105	18	s	s	NOUN
ejpam-4036	105	19	-	-	ADJ
ejpam-4036	105	20	quasinormal	quasinormal	ADJ
ejpam-4036	105	21	in	in	ADP
ejpam-4036	105	22	g	g	PROPN
ejpam-4036	105	23	,	,	PUNCT
ejpam-4036	105	24	then	then	ADV
ejpam-4036	105	25	,	,	PUNCT
ejpam-4036	105	26	by	by	ADP
ejpam-4036	105	27	lemma	lemma	PROPN
ejpam-4036	105	28	3	3	NUM
ejpam-4036	105	29	,	,	PUNCT
ejpam-4036	105	30	we	we	PRON
ejpam-4036	105	31	get	get	VERB
ejpam-4036	105	32	the	the	DET
ejpam-4036	105	33	p	p	NOUN
ejpam-4036	105	34	-	-	PUNCT
ejpam-4036	105	35	nilpotency	nilpotency	NOUN
ejpam-4036	105	36	of	of	ADP
ejpam-4036	105	37	g	g	PROPN
ejpam-4036	105	38	,	,	PUNCT
ejpam-4036	105	39	a	a	DET
ejpam-4036	105	40	contradiction	contradiction	NOUN
ejpam-4036	105	41	.	.	PUNCT
ejpam-4036	106	1	therefore	therefore	ADV
ejpam-4036	106	2	,	,	PUNCT
ejpam-4036	106	3	there	there	PRON
ejpam-4036	106	4	exists	exist	VERB
ejpam-4036	106	5	a	a	DET
ejpam-4036	106	6	subgroup	subgroup	NOUN
ejpam-4036	106	7	s	s	PROPN
ejpam-4036	106	8	of	of	ADP
ejpam-4036	106	9	p	p	NOUN
ejpam-4036	106	10	of	of	ADP
ejpam-4036	106	11	prime	prime	ADJ
ejpam-4036	106	12	order	order	NOUN
ejpam-4036	106	13	p	p	NOUN
ejpam-4036	106	14	or	or	CCONJ
ejpam-4036	106	15	of	of	ADP
ejpam-4036	106	16	order	order	NOUN
ejpam-4036	106	17	4	4	NUM
ejpam-4036	106	18	(	(	PUNCT
ejpam-4036	106	19	if	if	SCONJ
ejpam-4036	106	20	p	p	X
ejpam-4036	106	21	=	=	NOUN
ejpam-4036	106	22	2	2	NUM
ejpam-4036	106	23	)	)	PUNCT
ejpam-4036	106	24	such	such	ADJ
ejpam-4036	106	25	that	that	SCONJ
ejpam-4036	106	26	s	s	VERB
ejpam-4036	106	27	is	be	AUX
ejpam-4036	106	28	not	not	PART
ejpam-4036	106	29	s	s	ADJ
ejpam-4036	106	30	-	-	ADJ
ejpam-4036	106	31	quasinormal	quasinormal	ADJ
ejpam-4036	106	32	in	in	ADP
ejpam-4036	106	33	g.	g.	PROPN
ejpam-4036	106	34	by	by	ADP
ejpam-4036	106	35	hypothesis	hypothesis	NOUN
ejpam-4036	106	36	,	,	PUNCT
ejpam-4036	106	37	s	s	X
ejpam-4036	106	38	is	be	AUX
ejpam-4036	106	39	css	css	ADJ
ejpam-4036	106	40	-	-	NOUN
ejpam-4036	106	41	subgroup	subgroup	NOUN
ejpam-4036	106	42	of	of	ADP
ejpam-4036	106	43	g.	g.	PROPN
ejpam-4036	106	44	then	then	ADV
ejpam-4036	106	45	there	there	PRON
ejpam-4036	106	46	exists	exist	VERB
ejpam-4036	106	47	a	a	DET
ejpam-4036	106	48	normal	normal	ADJ
ejpam-4036	106	49	subgroup	subgroup	NOUN
ejpam-4036	106	50	k	k	PROPN
ejpam-4036	106	51	of	of	ADP
ejpam-4036	106	52	g	g	PROPN
ejpam-4036	106	53	such	such	ADJ
ejpam-4036	106	54	that	that	SCONJ
ejpam-4036	106	55	g	g	NOUN
ejpam-4036	106	56	=	=	PUNCT
ejpam-4036	106	57	sk	sk	PROPN
ejpam-4036	106	58	and	and	CCONJ
ejpam-4036	106	59	s	s	X
ejpam-4036	106	60	∩	∩	X
ejpam-4036	106	61	k	k	PROPN
ejpam-4036	106	62	is	be	AUX
ejpam-4036	106	63	ss	ss	NOUN
ejpam-4036	106	64	-	-	ADJ
ejpam-4036	106	65	quasinormal	quasinormal	ADJ
ejpam-4036	106	66	in	in	ADP
ejpam-4036	106	67	g.	g.	PROPN
ejpam-4036	106	68	assume	assume	VERB
ejpam-4036	106	69	that	that	SCONJ
ejpam-4036	107	1	k	k	PROPN
ejpam-4036	107	2	=	=	PUNCT
ejpam-4036	107	3	g.	g.	PROPN
ejpam-4036	108	1	it	it	PRON
ejpam-4036	108	2	follows	follow	VERB
ejpam-4036	108	3	that	that	SCONJ
ejpam-4036	108	4	s	s	VERB
ejpam-4036	108	5	is	be	AUX
ejpam-4036	108	6	ss	ss	NOUN
ejpam-4036	108	7	-	-	ADJ
ejpam-4036	108	8	quasinormal	quasinormal	ADJ
ejpam-4036	108	9	in	in	ADP
ejpam-4036	108	10	g.	g.	PROPN
ejpam-4036	108	11	since	since	SCONJ
ejpam-4036	108	12	p	p	NOUN
ejpam-4036	108	13	is	be	AUX
ejpam-4036	108	14	normal	normal	ADJ
ejpam-4036	108	15	in	in	ADP
ejpam-4036	108	16	g	g	PROPN
ejpam-4036	108	17	,	,	PUNCT
ejpam-4036	108	18	then	then	ADV
ejpam-4036	108	19	s	s	VERB
ejpam-4036	108	20	is	be	AUX
ejpam-4036	108	21	subnormal	subnormal	ADJ
ejpam-4036	108	22	in	in	ADP
ejpam-4036	108	23	g.	g.	PROPN
ejpam-4036	108	24	thus	thus	ADV
ejpam-4036	108	25	,	,	PUNCT
ejpam-4036	108	26	by	by	ADP
ejpam-4036	108	27	lemma	lemma	PROPN
ejpam-4036	108	28	4	4	NUM
ejpam-4036	108	29	,	,	PUNCT
ejpam-4036	108	30	s	s	VERB
ejpam-4036	108	31	6	6	NUM
ejpam-4036	108	32	op(g	op(g	NUM
ejpam-4036	108	33	)	)	PUNCT
ejpam-4036	108	34	.	.	PUNCT
ejpam-4036	109	1	applying	apply	VERB
ejpam-4036	109	2	lemma	lemma	PROPN
ejpam-4036	109	3	5	5	NUM
ejpam-4036	109	4	,	,	PUNCT
ejpam-4036	109	5	we	we	PRON
ejpam-4036	109	6	get	get	VERB
ejpam-4036	109	7	s	s	NOUN
ejpam-4036	109	8	is	be	AUX
ejpam-4036	109	9	s	s	NOUN
ejpam-4036	109	10	-	-	ADJ
ejpam-4036	109	11	quasinormal	quasinormal	ADJ
ejpam-4036	109	12	in	in	ADP
ejpam-4036	109	13	g	g	PROPN
ejpam-4036	109	14	,	,	PUNCT
ejpam-4036	109	15	a	a	DET
ejpam-4036	109	16	contradiction	contradiction	NOUN
ejpam-4036	109	17	.	.	PUNCT
ejpam-4036	110	1	hence	hence	ADV
ejpam-4036	110	2	,	,	PUNCT
ejpam-4036	110	3	k	k	PROPN
ejpam-4036	110	4	is	be	AUX
ejpam-4036	110	5	a	a	DET
ejpam-4036	110	6	proper	proper	ADJ
ejpam-4036	110	7	normal	normal	ADJ
ejpam-4036	110	8	nilpotent	nilpotent	ADJ
ejpam-4036	110	9	subgroup	subgroup	NOUN
ejpam-4036	110	10	of	of	ADP
ejpam-4036	110	11	g	g	PROPN
ejpam-4036	110	12	which	which	PRON
ejpam-4036	110	13	implies	imply	VERB
ejpam-4036	110	14	that	that	SCONJ
ejpam-4036	110	15	q	q	NOUN
ejpam-4036	110	16	is	be	AUX
ejpam-4036	110	17	characteristic	characteristic	ADJ
ejpam-4036	110	18	in	in	ADP
ejpam-4036	110	19	k.	k.	PROPN
ejpam-4036	110	20	therefore	therefore	ADV
ejpam-4036	110	21	q	q	PROPN
ejpam-4036	110	22	is	be	AUX
ejpam-4036	110	23	a	a	DET
ejpam-4036	110	24	normal	normal	ADJ
ejpam-4036	110	25	subgroup	subgroup	NOUN
ejpam-4036	110	26	in	in	ADP
ejpam-4036	110	27	g	g	PROPN
ejpam-4036	110	28	,	,	PUNCT
ejpam-4036	110	29	a	a	DET
ejpam-4036	110	30	final	final	ADJ
ejpam-4036	110	31	contradiction	contradiction	NOUN
ejpam-4036	110	32	completing	complete	VERB
ejpam-4036	110	33	the	the	DET
ejpam-4036	110	34	proof	proof	NOUN
ejpam-4036	110	35	.	.	PUNCT
ejpam-4036	111	1	lemma	lemma	PROPN
ejpam-4036	111	2	17	17	NUM
ejpam-4036	111	3	.	.	PUNCT
ejpam-4036	112	1	let	let	VERB
ejpam-4036	112	2	p	p	PRON
ejpam-4036	112	3	be	be	AUX
ejpam-4036	112	4	a	a	DET
ejpam-4036	112	5	non	non	ADJ
ejpam-4036	112	6	-	-	ADJ
ejpam-4036	112	7	trivial	trivial	ADJ
ejpam-4036	112	8	normal	normal	ADJ
ejpam-4036	112	9	p	p	NOUN
ejpam-4036	112	10	-	-	PUNCT
ejpam-4036	112	11	subgroup	subgroup	NOUN
ejpam-4036	112	12	of	of	ADP
ejpam-4036	112	13	g	g	PROPN
ejpam-4036	112	14	(	(	PUNCT
ejpam-4036	112	15	where	where	SCONJ
ejpam-4036	112	16	p	p	X
ejpam-4036	112	17	>	>	X
ejpam-4036	112	18	2	2	NUM
ejpam-4036	112	19	)	)	PUNCT
ejpam-4036	112	20	.	.	PUNCT
ejpam-4036	113	1	if	if	SCONJ
ejpam-4036	113	2	every	every	DET
ejpam-4036	113	3	minimal	minimal	ADJ
ejpam-4036	113	4	subgroup	subgroup	NOUN
ejpam-4036	113	5	of	of	ADP
ejpam-4036	113	6	p	p	PROPN
ejpam-4036	113	7	is	be	AUX
ejpam-4036	113	8	css	css	NOUN
ejpam-4036	113	9	-	-	NOUN
ejpam-4036	113	10	subgroup	subgroup	NOUN
ejpam-4036	113	11	of	of	ADP
ejpam-4036	113	12	g	g	PROPN
ejpam-4036	113	13	,	,	PUNCT
ejpam-4036	113	14	then	then	ADV
ejpam-4036	113	15	p	p	X
ejpam-4036	113	16	6	6	NUM
ejpam-4036	113	17	zu(g	zu(g	NUM
ejpam-4036	113	18	)	)	PUNCT
ejpam-4036	113	19	.	.	PUNCT
ejpam-4036	114	1	proof	proof	NOUN
ejpam-4036	114	2	.	.	PUNCT
ejpam-4036	115	1	we	we	PRON
ejpam-4036	115	2	prove	prove	VERB
ejpam-4036	115	3	the	the	DET
ejpam-4036	115	4	theorem	theorem	NOUN
ejpam-4036	115	5	by	by	ADP
ejpam-4036	115	6	induction	induction	NOUN
ejpam-4036	115	7	on	on	ADP
ejpam-4036	115	8	|g|	|g|	PROPN
ejpam-4036	115	9	+	+	CCONJ
ejpam-4036	115	10	|p	|p	NOUN
ejpam-4036	115	11	|	|	ADV
ejpam-4036	115	12	.	.	PUNCT
ejpam-4036	116	1	if	if	SCONJ
ejpam-4036	116	2	every	every	DET
ejpam-4036	116	3	minimal	minimal	ADJ
ejpam-4036	116	4	subgroup	subgroup	NOUN
ejpam-4036	116	5	of	of	ADP
ejpam-4036	116	6	p	p	PROPN
ejpam-4036	116	7	is	be	AUX
ejpam-4036	116	8	s	s	NOUN
ejpam-4036	116	9	-	-	ADJ
ejpam-4036	116	10	quasinormal	quasinormal	ADJ
ejpam-4036	116	11	in	in	ADP
ejpam-4036	116	12	g	g	PROPN
ejpam-4036	116	13	,	,	PUNCT
ejpam-4036	116	14	then	then	ADV
ejpam-4036	116	15	by	by	ADP
ejpam-4036	116	16	lemma	lemma	PROPN
ejpam-4036	116	17	6	6	NUM
ejpam-4036	116	18	,	,	PUNCT
ejpam-4036	116	19	we	we	PRON
ejpam-4036	116	20	get	get	VERB
ejpam-4036	116	21	p	p	NOUN
ejpam-4036	116	22	6	6	NUM
ejpam-4036	116	23	zu(g	zu(g	NUM
ejpam-4036	116	24	)	)	PUNCT
ejpam-4036	116	25	and	and	CCONJ
ejpam-4036	116	26	we	we	PRON
ejpam-4036	116	27	are	be	AUX
ejpam-4036	116	28	done	do	VERB
ejpam-4036	116	29	.	.	PUNCT
ejpam-4036	117	1	thus	thus	ADV
ejpam-4036	117	2	,	,	PUNCT
ejpam-4036	117	3	we	we	PRON
ejpam-4036	117	4	may	may	AUX
ejpam-4036	117	5	assume	assume	VERB
ejpam-4036	117	6	that	that	SCONJ
ejpam-4036	117	7	p	p	PROPN
ejpam-4036	117	8	has	have	VERB
ejpam-4036	117	9	a	a	DET
ejpam-4036	117	10	minimal	minimal	ADJ
ejpam-4036	117	11	subgroup	subgroup	NOUN
ejpam-4036	117	12	l	l	NOUN
ejpam-4036	117	13	such	such	ADJ
ejpam-4036	117	14	that	that	SCONJ
ejpam-4036	117	15	l	l	NOUN
ejpam-4036	117	16	is	be	AUX
ejpam-4036	117	17	not	not	PART
ejpam-4036	117	18	s	s	ADJ
ejpam-4036	117	19	-	-	ADJ
ejpam-4036	117	20	quasinormal	quasinormal	ADJ
ejpam-4036	117	21	in	in	ADP
ejpam-4036	117	22	g.	g.	PROPN
ejpam-4036	117	23	by	by	ADP
ejpam-4036	117	24	the	the	DET
ejpam-4036	117	25	hypothesis	hypothesis	NOUN
ejpam-4036	117	26	of	of	ADP
ejpam-4036	117	27	the	the	DET
ejpam-4036	117	28	lemma	lemma	PROPN
ejpam-4036	117	29	,	,	PUNCT
ejpam-4036	117	30	l	l	PROPN
ejpam-4036	117	31	is	be	AUX
ejpam-4036	117	32	css	css	PROPN
ejpam-4036	117	33	-	-	NOUN
ejpam-4036	117	34	subgroup	subgroup	NOUN
ejpam-4036	117	35	of	of	ADP
ejpam-4036	117	36	g	g	PROPN
ejpam-4036	117	37	,	,	PUNCT
ejpam-4036	117	38	i.e.	i.e.	X
ejpam-4036	117	39	,	,	PUNCT
ejpam-4036	117	40	g	g	PROPN
ejpam-4036	117	41	has	have	VERB
ejpam-4036	117	42	a	a	DET
ejpam-4036	117	43	normal	normal	ADJ
ejpam-4036	117	44	subgroup	subgroup	NOUN
ejpam-4036	117	45	k	k	PROPN
ejpam-4036	117	46	such	such	ADJ
ejpam-4036	117	47	that	that	SCONJ
ejpam-4036	117	48	g	g	NOUN
ejpam-4036	117	49	=	=	PUNCT
ejpam-4036	117	50	lk	lk	NOUN
ejpam-4036	117	51	and	and	CCONJ
ejpam-4036	117	52	l	l	NOUN
ejpam-4036	117	53	∩	∩	X
ejpam-4036	117	54	k	k	PROPN
ejpam-4036	117	55	is	be	AUX
ejpam-4036	117	56	ss	ss	NOUN
ejpam-4036	117	57	-	-	ADJ
ejpam-4036	117	58	quasinormal	quasinormal	ADJ
ejpam-4036	117	59	in	in	ADP
ejpam-4036	117	60	g.	g.	PROPN
ejpam-4036	117	61	if	if	SCONJ
ejpam-4036	117	62	l	l	PROPN
ejpam-4036	117	63	∩	∩	X
ejpam-4036	117	64	k	k	PROPN
ejpam-4036	117	65	6=	6=	PROPN
ejpam-4036	117	66	1	1	NUM
ejpam-4036	117	67	,	,	PUNCT
ejpam-4036	117	68	we	we	PRON
ejpam-4036	117	69	have	have	VERB
ejpam-4036	117	70	l	l	NOUN
ejpam-4036	117	71	∩	∩	ADJ
ejpam-4036	117	72	k	k	PROPN
ejpam-4036	117	73	=	=	SYM
ejpam-4036	117	74	l.	l.	PROPN
ejpam-4036	117	75	hence	hence	ADV
ejpam-4036	117	76	,	,	PUNCT
ejpam-4036	117	77	l	l	PROPN
ejpam-4036	117	78	is	be	AUX
ejpam-4036	117	79	ss	ss	NOUN
ejpam-4036	117	80	-	-	ADJ
ejpam-4036	117	81	quasinormal	quasinormal	ADJ
ejpam-4036	117	82	in	in	ADP
ejpam-4036	117	83	g.	g.	PROPN
ejpam-4036	117	84	since	since	SCONJ
ejpam-4036	117	85	p	p	NOUN
ejpam-4036	117	86	is	be	AUX
ejpam-4036	117	87	normal	normal	ADJ
ejpam-4036	117	88	in	in	ADP
ejpam-4036	117	89	g	g	PROPN
ejpam-4036	117	90	,	,	PUNCT
ejpam-4036	117	91	then	then	ADV
ejpam-4036	117	92	l	l	NOUN
ejpam-4036	117	93	is	be	AUX
ejpam-4036	117	94	subnormal	subnormal	ADJ
ejpam-4036	117	95	in	in	ADP
ejpam-4036	117	96	g.	g.	PROPN
ejpam-4036	117	97	lemma	lemma	PROPN
ejpam-4036	117	98	4	4	NUM
ejpam-4036	117	99	implies	imply	VERB
ejpam-4036	117	100	that	that	SCONJ
ejpam-4036	117	101	l	l	PROPN
ejpam-4036	117	102	6	6	NUM
ejpam-4036	117	103	op(g	op(g	NUM
ejpam-4036	117	104	)	)	PUNCT
ejpam-4036	117	105	.	.	PUNCT
ejpam-4036	118	1	applying	apply	VERB
ejpam-4036	118	2	lemma	lemma	PROPN
ejpam-4036	118	3	5	5	NUM
ejpam-4036	118	4	,	,	PUNCT
ejpam-4036	118	5	l	l	NOUN
ejpam-4036	118	6	is	be	AUX
ejpam-4036	118	7	s	s	NOUN
ejpam-4036	118	8	-	-	ADJ
ejpam-4036	118	9	quasinormal	quasinormal	ADJ
ejpam-4036	118	10	in	in	ADP
ejpam-4036	118	11	g	g	PROPN
ejpam-4036	118	12	,	,	PUNCT
ejpam-4036	118	13	a	a	DET
ejpam-4036	118	14	contradiction	contradiction	NOUN
ejpam-4036	118	15	.	.	PUNCT
ejpam-4036	119	1	therefore	therefore	ADV
ejpam-4036	119	2	,	,	PUNCT
ejpam-4036	119	3	we	we	PRON
ejpam-4036	119	4	may	may	AUX
ejpam-4036	119	5	assume	assume	VERB
ejpam-4036	119	6	l	l	NOUN
ejpam-4036	119	7	∩	∩	X
ejpam-4036	119	8	k	k	PROPN
ejpam-4036	119	9	=	=	SYM
ejpam-4036	119	10	1	1	X
ejpam-4036	119	11	.	.	PUNCT
ejpam-4036	120	1	then	then	ADV
ejpam-4036	120	2	,	,	PUNCT
ejpam-4036	120	3	p	p	X
ejpam-4036	120	4	=	=	PUNCT
ejpam-4036	120	5	p	p	NOUN
ejpam-4036	120	6	∩	∩	NOUN
ejpam-4036	120	7	g	g	NOUN
ejpam-4036	120	8	=	=	SYM
ejpam-4036	120	9	p	p	NOUN
ejpam-4036	120	10	∩	∩	ADJ
ejpam-4036	120	11	lk	lk	NOUN
ejpam-4036	120	12	=	=	PUNCT
ejpam-4036	120	13	l(p	l(p	PROPN
ejpam-4036	120	14	∩	∩	ADJ
ejpam-4036	120	15	k	k	NOUN
ejpam-4036	120	16	)	)	PUNCT
ejpam-4036	120	17	and	and	CCONJ
ejpam-4036	120	18	p	p	PROPN
ejpam-4036	120	19	∩	∩	PROPN
ejpam-4036	120	20	k	k	PROPN
ejpam-4036	120	21	e	e	X
ejpam-4036	120	22	g.	g.	NOUN
ejpam-4036	120	23	by	by	ADP
ejpam-4036	120	24	the	the	DET
ejpam-4036	120	25	hypothesis	hypothesis	NOUN
ejpam-4036	120	26	,	,	PUNCT
ejpam-4036	120	27	every	every	DET
ejpam-4036	120	28	minimal	minimal	ADJ
ejpam-4036	120	29	subgroup	subgroup	NOUN
ejpam-4036	120	30	of	of	ADP
ejpam-4036	120	31	the	the	DET
ejpam-4036	120	32	non	non	ADJ
ejpam-4036	120	33	-	-	ADJ
ejpam-4036	120	34	trivial	trivial	ADJ
ejpam-4036	120	35	normal	normal	ADJ
ejpam-4036	120	36	p	p	NOUN
ejpam-4036	120	37	-	-	PUNCT
ejpam-4036	120	38	subgroup	subgroup	NOUN
ejpam-4036	120	39	p	p	NOUN
ejpam-4036	120	40	∩	∩	PROPN
ejpam-4036	120	41	k	k	PROPN
ejpam-4036	120	42	is	be	AUX
ejpam-4036	120	43	css	css	PROPN
ejpam-4036	120	44	-	-	NOUN
ejpam-4036	120	45	subgroup	subgroup	NOUN
ejpam-4036	120	46	of	of	ADP
ejpam-4036	120	47	g.	g.	PROPN
ejpam-4036	120	48	this	this	PRON
ejpam-4036	120	49	leads	lead	VERB
ejpam-4036	120	50	to	to	ADP
ejpam-4036	120	51	p	p	NOUN
ejpam-4036	120	52	∩	∩	ADJ
ejpam-4036	120	53	k	k	PROPN
ejpam-4036	120	54	6	6	NUM
ejpam-4036	120	55	zu(g	zu(g	NUM
ejpam-4036	120	56	)	)	PUNCT
ejpam-4036	120	57	by	by	ADP
ejpam-4036	120	58	induction	induction	NOUN
ejpam-4036	120	59	on	on	ADP
ejpam-4036	120	60	|g|	|g|	PROPN
ejpam-4036	120	61	+	+	CCONJ
ejpam-4036	120	62	|p	|p	NOUN
ejpam-4036	120	63	|	|	ADV
ejpam-4036	120	64	.	.	PUNCT
ejpam-4036	121	1	hence	hence	ADV
ejpam-4036	121	2	,	,	PUNCT
ejpam-4036	121	3	p/(p	p/(p	PROPN
ejpam-4036	121	4	∩	∩	ADJ
ejpam-4036	121	5	k	k	PROPN
ejpam-4036	121	6	)	)	PUNCT
ejpam-4036	121	7	6	6	NUM
ejpam-4036	121	8	zu(g/(p	zu(g/(p	PROPN
ejpam-4036	121	9	∩	∩	PROPN
ejpam-4036	121	10	k	k	NOUN
ejpam-4036	121	11	)	)	PUNCT
ejpam-4036	121	12	)	)	PUNCT
ejpam-4036	121	13	as	as	ADP
ejpam-4036	121	14	p/(p	p/(p	PROPN
ejpam-4036	121	15	∩	∩	ADJ
ejpam-4036	121	16	k	k	NOUN
ejpam-4036	121	17	)	)	PUNCT
ejpam-4036	121	18	is	be	AUX
ejpam-4036	121	19	a	a	DET
ejpam-4036	121	20	normal	normal	ADJ
ejpam-4036	121	21	subgroup	subgroup	NOUN
ejpam-4036	121	22	of	of	ADP
ejpam-4036	121	23	g/(p	g/(p	PROPN
ejpam-4036	121	24	∩	∩	PROPN
ejpam-4036	121	25	k	k	NOUN
ejpam-4036	121	26	)	)	PUNCT
ejpam-4036	121	27	of	of	ADP
ejpam-4036	121	28	order	order	NOUN
ejpam-4036	122	1	p.	p.	NOUN
ejpam-4036	123	1	but	but	CCONJ
ejpam-4036	123	2	p	p	PROPN
ejpam-4036	123	3	∩	∩	PROPN
ejpam-4036	123	4	k	k	PROPN
ejpam-4036	123	5	6	6	NUM
ejpam-4036	123	6	zu(g	zu(g	NUM
ejpam-4036	123	7	)	)	PUNCT
ejpam-4036	123	8	,	,	PUNCT
ejpam-4036	123	9	then	then	ADV
ejpam-4036	123	10	zu(g/(p	zu(g/(p	PROPN
ejpam-4036	123	11	∩	∩	PROPN
ejpam-4036	123	12	k	k	PROPN
ejpam-4036	123	13	)	)	PUNCT
ejpam-4036	123	14	)	)	PUNCT
ejpam-4036	124	1	=	=	SYM
ejpam-4036	124	2	zu(g)/(p	zu(g)/(p	PROPN
ejpam-4036	124	3	∩	∩	X
ejpam-4036	124	4	k	k	PROPN
ejpam-4036	124	5	)	)	PUNCT
ejpam-4036	124	6	by	by	ADP
ejpam-4036	124	7	lemma	lemma	PROPN
ejpam-4036	124	8	7	7	NUM
ejpam-4036	124	9	.	.	PUNCT
ejpam-4036	124	10	thus	thus	ADV
ejpam-4036	124	11	,	,	PUNCT
ejpam-4036	124	12	p/(p	p/(p	PROPN
ejpam-4036	124	13	∩	∩	ADJ
ejpam-4036	124	14	k	k	X
ejpam-4036	124	15	)	)	PUNCT
ejpam-4036	124	16	6	6	NUM
ejpam-4036	124	17	zu(g)/(p	zu(g)/(p	PROPN
ejpam-4036	124	18	∩	∩	PROPN
ejpam-4036	124	19	k	k	PROPN
ejpam-4036	124	20	)	)	PUNCT
ejpam-4036	124	21	.	.	PUNCT
ejpam-4036	125	1	now	now	ADV
ejpam-4036	125	2	it	it	PRON
ejpam-4036	125	3	follows	follow	VERB
ejpam-4036	125	4	easily	easily	ADV
ejpam-4036	125	5	that	that	SCONJ
ejpam-4036	125	6	p	p	PROPN
ejpam-4036	125	7	6	6	NUM
ejpam-4036	125	8	zu(g	zu(g	NUM
ejpam-4036	125	9	)	)	PUNCT
ejpam-4036	125	10	.	.	PUNCT
ejpam-4036	126	1	immediate	immediate	ADJ
ejpam-4036	126	2	consequence	consequence	NOUN
ejpam-4036	126	3	of	of	ADP
ejpam-4036	126	4	lemma	lemma	PROPN
ejpam-4036	126	5	17	17	NUM
ejpam-4036	126	6	and	and	CCONJ
ejpam-4036	126	7	theorem	theorem	VERB
ejpam-4036	126	8	1	1	NUM
ejpam-4036	126	9	,	,	PUNCT
ejpam-4036	126	10	we	we	PRON
ejpam-4036	126	11	have	have	VERB
ejpam-4036	126	12	the	the	DET
ejpam-4036	126	13	following	follow	VERB
ejpam-4036	126	14	corollary	corollary	ADJ
ejpam-4036	126	15	:	:	PUNCT
ejpam-4036	126	16	corollary	corollary	ADJ
ejpam-4036	126	17	1	1	NUM
ejpam-4036	126	18	.	.	PUNCT
ejpam-4036	127	1	let	let	VERB
ejpam-4036	127	2	p	p	PRON
ejpam-4036	127	3	be	be	AUX
ejpam-4036	127	4	a	a	DET
ejpam-4036	127	5	normal	normal	ADJ
ejpam-4036	127	6	p	p	NOUN
ejpam-4036	127	7	-	-	PUNCT
ejpam-4036	127	8	subgroup	subgroup	NOUN
ejpam-4036	127	9	of	of	ADP
ejpam-4036	127	10	g.	g.	PROPN
ejpam-4036	127	11	if	if	SCONJ
ejpam-4036	127	12	every	every	DET
ejpam-4036	127	13	subgroup	subgroup	NOUN
ejpam-4036	127	14	of	of	ADP
ejpam-4036	127	15	p	p	NOUN
ejpam-4036	127	16	of	of	ADP
ejpam-4036	127	17	prime	prime	ADJ
ejpam-4036	127	18	order	order	NOUN
ejpam-4036	127	19	p	p	NOUN
ejpam-4036	127	20	or	or	CCONJ
ejpam-4036	127	21	of	of	ADP
ejpam-4036	127	22	order	order	NOUN
ejpam-4036	127	23	4	4	NUM
ejpam-4036	127	24	(	(	PUNCT
ejpam-4036	127	25	if	if	SCONJ
ejpam-4036	127	26	p	p	X
ejpam-4036	127	27	=	=	NOUN
ejpam-4036	127	28	2	2	NUM
ejpam-4036	127	29	)	)	PUNCT
ejpam-4036	127	30	is	be	AUX
ejpam-4036	127	31	css	css	PROPN
ejpam-4036	127	32	-	-	NOUN
ejpam-4036	127	33	subgroup	subgroup	NOUN
ejpam-4036	127	34	of	of	ADP
ejpam-4036	127	35	g	g	PROPN
ejpam-4036	127	36	,	,	PUNCT
ejpam-4036	127	37	then	then	ADV
ejpam-4036	127	38	p	p	X
ejpam-4036	127	39	6	6	NUM
ejpam-4036	127	40	zu(g	zu(g	NUM
ejpam-4036	127	41	)	)	PUNCT
ejpam-4036	127	42	.	.	PUNCT
ejpam-4036	128	1	proof	proof	NOUN
ejpam-4036	128	2	.	.	PUNCT
ejpam-4036	129	1	assume	assume	VERB
ejpam-4036	129	2	that	that	SCONJ
ejpam-4036	129	3	p	p	X
ejpam-4036	129	4	>	>	X
ejpam-4036	129	5	2	2	NUM
ejpam-4036	129	6	.	.	PUNCT
ejpam-4036	129	7	then	then	ADV
ejpam-4036	129	8	,	,	PUNCT
ejpam-4036	129	9	by	by	ADP
ejpam-4036	129	10	lemma	lemma	PROPN
ejpam-4036	129	11	17	17	NUM
ejpam-4036	129	12	,	,	PUNCT
ejpam-4036	129	13	p	p	ADJ
ejpam-4036	129	14	6	6	NUM
ejpam-4036	129	15	zu(g	zu(g	NUM
ejpam-4036	129	16	)	)	PUNCT
ejpam-4036	129	17	and	and	CCONJ
ejpam-4036	129	18	we	we	PRON
ejpam-4036	129	19	are	be	AUX
ejpam-4036	129	20	done	do	VERB
ejpam-4036	129	21	.	.	PUNCT
ejpam-4036	130	1	hence	hence	ADV
ejpam-4036	130	2	,	,	PUNCT
ejpam-4036	130	3	consider	consider	VERB
ejpam-4036	130	4	p	p	NOUN
ejpam-4036	130	5	=	=	NOUN
ejpam-4036	130	6	2	2	X
ejpam-4036	130	7	.	.	PUNCT
ejpam-4036	130	8	let	let	VERB
ejpam-4036	130	9	q	q	NOUN
ejpam-4036	130	10	be	be	AUX
ejpam-4036	130	11	any	any	DET
ejpam-4036	130	12	sylow	sylow	NOUN
ejpam-4036	130	13	q	q	NOUN
ejpam-4036	130	14	-	-	NOUN
ejpam-4036	130	15	subgroup	subgroup	NOUN
ejpam-4036	130	16	of	of	ADP
ejpam-4036	130	17	g	g	PROPN
ejpam-4036	130	18	,	,	PUNCT
ejpam-4036	130	19	where	where	SCONJ
ejpam-4036	130	20	q	q	X
ejpam-4036	130	21	6=	6=	NUM
ejpam-4036	130	22	2	2	NUM
ejpam-4036	130	23	.	.	PUNCT
ejpam-4036	131	1	it	it	PRON
ejpam-4036	131	2	is	be	AUX
ejpam-4036	131	3	clear	clear	ADJ
ejpam-4036	131	4	that	that	SCONJ
ejpam-4036	131	5	pq	pq	PROPN
ejpam-4036	131	6	is	be	AUX
ejpam-4036	131	7	a	a	DET
ejpam-4036	131	8	subgroup	subgroup	NOUN
ejpam-4036	131	9	of	of	ADP
ejpam-4036	131	10	g.	g.	PROPN
ejpam-4036	131	11	since	since	SCONJ
ejpam-4036	131	12	every	every	DET
ejpam-4036	131	13	subgroup	subgroup	NOUN
ejpam-4036	131	14	of	of	ADP
ejpam-4036	131	15	p	p	NOUN
ejpam-4036	131	16	of	of	ADP
ejpam-4036	131	17	prime	prime	ADJ
ejpam-4036	131	18	order	order	NOUN
ejpam-4036	131	19	p	p	NOUN
ejpam-4036	131	20	or	or	CCONJ
ejpam-4036	131	21	of	of	ADP
ejpam-4036	131	22	order	order	NOUN
ejpam-4036	131	23	4	4	NUM
ejpam-4036	131	24	(	(	PUNCT
ejpam-4036	131	25	if	if	SCONJ
ejpam-4036	131	26	p	p	X
ejpam-4036	131	27	=	=	NOUN
ejpam-4036	131	28	2	2	NUM
ejpam-4036	131	29	)	)	PUNCT
ejpam-4036	131	30	is	be	AUX
ejpam-4036	131	31	css	css	PROPN
ejpam-4036	131	32	-	-	NOUN
ejpam-4036	131	33	subgroup	subgroup	NOUN
ejpam-4036	131	34	of	of	ADP
ejpam-4036	131	35	g	g	PROPN
ejpam-4036	131	36	,	,	PUNCT
ejpam-4036	131	37	then	then	ADV
ejpam-4036	131	38	by	by	ADP
ejpam-4036	131	39	lemma	lemma	PROPN
ejpam-4036	131	40	11	11	NUM
ejpam-4036	131	41	,	,	PUNCT
ejpam-4036	131	42	every	every	DET
ejpam-4036	131	43	subgroup	subgroup	NOUN
ejpam-4036	131	44	of	of	ADP
ejpam-4036	131	45	p	p	NOUN
ejpam-4036	131	46	of	of	ADP
ejpam-4036	131	47	prime	prime	ADJ
ejpam-4036	131	48	order	order	NOUN
ejpam-4036	131	49	p	p	NOUN
ejpam-4036	131	50	or	or	CCONJ
ejpam-4036	131	51	of	of	ADP
ejpam-4036	131	52	order	order	NOUN
ejpam-4036	131	53	4	4	NUM
ejpam-4036	131	54	(	(	PUNCT
ejpam-4036	131	55	if	if	SCONJ
ejpam-4036	131	56	p	p	X
ejpam-4036	131	57	=	=	NOUN
ejpam-4036	131	58	2	2	NUM
ejpam-4036	131	59	)	)	PUNCT
ejpam-4036	131	60	is	be	AUX
ejpam-4036	131	61	css	css	PROPN
ejpam-4036	131	62	-	-	PROPN
ejpam-4036	131	63	subgroup	subgroup	NOUN
ejpam-4036	131	64	of	of	ADP
ejpam-4036	131	65	pq	pq	PROPN
ejpam-4036	131	66	.	.	PUNCT
ejpam-4036	132	1	by	by	ADP
ejpam-4036	132	2	applying	apply	VERB
ejpam-4036	132	3	theorem	theorem	NOUN
ejpam-4036	132	4	1	1	NUM
ejpam-4036	132	5	,	,	PUNCT
ejpam-4036	132	6	we	we	PRON
ejpam-4036	132	7	have	have	VERB
ejpam-4036	132	8	pq	pq	PROPN
ejpam-4036	132	9	is	be	AUX
ejpam-4036	132	10	2	2	NUM
ejpam-4036	132	11	-	-	PUNCT
ejpam-4036	132	12	nilpotent	nilpotent	ADJ
ejpam-4036	132	13	.	.	PUNCT
ejpam-4036	133	1	this	this	PRON
ejpam-4036	133	2	implies	imply	VERB
ejpam-4036	133	3	that	that	PRON
ejpam-4036	133	4	pq	pq	NOUN
ejpam-4036	134	1	=	=	SYM
ejpam-4036	135	1	p	p	X
ejpam-4036	135	2	×	×	PROPN
ejpam-4036	135	3	q	q	NOUN
ejpam-4036	136	1	and	and	CCONJ
ejpam-4036	136	2	so	so	ADV
ejpam-4036	136	3	q	q	X
ejpam-4036	136	4	centralizes	centralize	VERB
ejpam-4036	136	5	p	p	NOUN
ejpam-4036	136	6	.	.	PUNCT
ejpam-4036	137	1	thus	thus	ADV
ejpam-4036	137	2	,	,	PUNCT
ejpam-4036	137	3	op(g	op(g	X
ejpam-4036	137	4	)	)	PUNCT
ejpam-4036	137	5	6	6	NUM
ejpam-4036	137	6	cg(p	cg(p	NUM
ejpam-4036	137	7	)	)	PUNCT
ejpam-4036	138	1	and	and	CCONJ
ejpam-4036	138	2	it	it	PRON
ejpam-4036	138	3	follows	follow	VERB
ejpam-4036	138	4	that	that	SCONJ
ejpam-4036	138	5	|g	|g	NOUN
ejpam-4036	138	6	/	/	SYM
ejpam-4036	138	7	cg(p	cg(p	NUM
ejpam-4036	138	8	)	)	PUNCT
ejpam-4036	138	9	|	|	ADV
ejpam-4036	138	10	is	be	AUX
ejpam-4036	138	11	a	a	DET
ejpam-4036	138	12	power	power	NOUN
ejpam-4036	138	13	of	of	ADP
ejpam-4036	138	14	2	2	NUM
ejpam-4036	138	15	.	.	PUNCT
ejpam-4036	138	16	by	by	ADP
ejpam-4036	138	17	lemma	lemma	PROPN
ejpam-4036	138	18	8	8	NUM
ejpam-4036	138	19	,	,	PUNCT
ejpam-4036	138	20	we	we	PRON
ejpam-4036	138	21	conclude	conclude	VERB
ejpam-4036	138	22	p	p	PROPN
ejpam-4036	138	23	6	6	NUM
ejpam-4036	138	24	zu(g	zu(g	NUM
ejpam-4036	138	25	)	)	PUNCT
ejpam-4036	138	26	.	.	PUNCT
ejpam-4036	139	1	a.	a.	NOUN
ejpam-4036	139	2	heliel	heliel	PROPN
ejpam-4036	139	3	,	,	PUNCT
ejpam-4036	139	4	r.	r.	PROPN
ejpam-4036	139	5	hijazi	hijazi	PROPN
ejpam-4036	139	6	,	,	PUNCT
ejpam-4036	139	7	s.	s.	PROPN
ejpam-4036	139	8	al	al	PROPN
ejpam-4036	139	9	-	-	PUNCT
ejpam-4036	139	10	shammari	shammari	PROPN
ejpam-4036	139	11	/	/	SYM
ejpam-4036	139	12	eur	eur	PROPN
ejpam-4036	139	13	.	.	PUNCT
ejpam-4036	140	1	j.	j.	PROPN
ejpam-4036	140	2	pure	pure	PROPN
ejpam-4036	140	3	appl	appl	PROPN
ejpam-4036	140	4	.	.	PROPN
ejpam-4036	140	5	math	math	PROPN
ejpam-4036	140	6	,	,	PUNCT
ejpam-4036	140	7	14	14	NUM
ejpam-4036	140	8	(	(	PUNCT
ejpam-4036	140	9	3	3	NUM
ejpam-4036	140	10	)	)	PUNCT
ejpam-4036	140	11	(	(	PUNCT
ejpam-4036	140	12	2021	2021	NUM
ejpam-4036	140	13	)	)	PUNCT
ejpam-4036	140	14	,	,	PUNCT
ejpam-4036	140	15	1002	1002	NUM
ejpam-4036	140	16	-	-	SYM
ejpam-4036	140	17	1014	1014	NUM
ejpam-4036	140	18	1007	1007	NUM
ejpam-4036	140	19	we	we	PRON
ejpam-4036	140	20	now	now	ADV
ejpam-4036	140	21	prove	prove	VERB
ejpam-4036	140	22	:	:	PUNCT
ejpam-4036	140	23	theorem	theorem	NOUN
ejpam-4036	140	24	2	2	NUM
ejpam-4036	140	25	.	.	PUNCT
ejpam-4036	141	1	let	let	VERB
ejpam-4036	141	2	f	f	PRON
ejpam-4036	141	3	be	be	AUX
ejpam-4036	141	4	a	a	DET
ejpam-4036	141	5	saturated	saturated	ADJ
ejpam-4036	141	6	formation	formation	NOUN
ejpam-4036	141	7	containing	contain	VERB
ejpam-4036	141	8	u	u	NOUN
ejpam-4036	141	9	and	and	CCONJ
ejpam-4036	141	10	g	g	ADP
ejpam-4036	141	11	a	a	DET
ejpam-4036	141	12	group	group	NOUN
ejpam-4036	141	13	.	.	PUNCT
ejpam-4036	142	1	then	then	ADV
ejpam-4036	142	2	g	g	PROPN
ejpam-4036	142	3	∈	∈	PROPN
ejpam-4036	142	4	f	f	PROPN
ejpam-4036	143	1	if	if	SCONJ
ejpam-4036	143	2	and	and	CCONJ
ejpam-4036	143	3	only	only	ADV
ejpam-4036	143	4	if	if	SCONJ
ejpam-4036	143	5	there	there	PRON
ejpam-4036	143	6	exists	exist	VERB
ejpam-4036	143	7	a	a	DET
ejpam-4036	143	8	normal	normal	ADJ
ejpam-4036	143	9	subgroup	subgroup	NOUN
ejpam-4036	143	10	h	h	NOUN
ejpam-4036	143	11	in	in	ADP
ejpam-4036	143	12	g	g	PROPN
ejpam-4036	143	13	such	such	ADJ
ejpam-4036	143	14	that	that	SCONJ
ejpam-4036	143	15	g	g	NOUN
ejpam-4036	143	16	/	/	SYM
ejpam-4036	143	17	h	h	NOUN
ejpam-4036	143	18	∈	∈	PROPN
ejpam-4036	143	19	f	f	PROPN
ejpam-4036	143	20	and	and	CCONJ
ejpam-4036	143	21	every	every	DET
ejpam-4036	143	22	subgroup	subgroup	NOUN
ejpam-4036	143	23	of	of	ADP
ejpam-4036	143	24	h	h	NOUN
ejpam-4036	143	25	of	of	ADP
ejpam-4036	143	26	prime	prime	ADJ
ejpam-4036	143	27	order	order	NOUN
ejpam-4036	143	28	p	p	NOUN
ejpam-4036	143	29	or	or	CCONJ
ejpam-4036	143	30	of	of	ADP
ejpam-4036	143	31	order	order	NOUN
ejpam-4036	143	32	4	4	NUM
ejpam-4036	143	33	(	(	PUNCT
ejpam-4036	143	34	if	if	SCONJ
ejpam-4036	143	35	p	p	X
ejpam-4036	143	36	=	=	NOUN
ejpam-4036	143	37	2	2	NUM
ejpam-4036	143	38	)	)	PUNCT
ejpam-4036	143	39	is	be	AUX
ejpam-4036	143	40	css	css	PROPN
ejpam-4036	143	41	-	-	NOUN
ejpam-4036	143	42	subgroup	subgroup	NOUN
ejpam-4036	143	43	of	of	ADP
ejpam-4036	143	44	g.	g.	PROPN
ejpam-4036	143	45	proof	proof	NOUN
ejpam-4036	143	46	.	.	PUNCT
ejpam-4036	144	1	if	if	SCONJ
ejpam-4036	144	2	g	g	PROPN
ejpam-4036	144	3	∈	∈	PROPN
ejpam-4036	144	4	f	f	X
ejpam-4036	144	5	,	,	PUNCT
ejpam-4036	144	6	then	then	ADV
ejpam-4036	144	7	we	we	PRON
ejpam-4036	144	8	set	set	VERB
ejpam-4036	144	9	h	h	NOUN
ejpam-4036	144	10	=	=	SYM
ejpam-4036	144	11	1	1	NUM
ejpam-4036	144	12	and	and	CCONJ
ejpam-4036	144	13	the	the	DET
ejpam-4036	144	14	result	result	NOUN
ejpam-4036	144	15	follows	follow	VERB
ejpam-4036	144	16	.	.	PUNCT
ejpam-4036	145	1	conversely	conversely	ADV
ejpam-4036	145	2	,	,	PUNCT
ejpam-4036	145	3	assume	assume	VERB
ejpam-4036	145	4	that	that	SCONJ
ejpam-4036	145	5	the	the	DET
ejpam-4036	145	6	result	result	NOUN
ejpam-4036	145	7	is	be	AUX
ejpam-4036	145	8	false	false	ADJ
ejpam-4036	145	9	and	and	CCONJ
ejpam-4036	145	10	let	let	VERB
ejpam-4036	145	11	g	g	PRON
ejpam-4036	145	12	be	be	AUX
ejpam-4036	145	13	a	a	DET
ejpam-4036	145	14	counterexample	counterexample	NOUN
ejpam-4036	145	15	of	of	ADP
ejpam-4036	145	16	minimal	minimal	ADJ
ejpam-4036	145	17	order	order	NOUN
ejpam-4036	145	18	.	.	PUNCT
ejpam-4036	146	1	by	by	ADP
ejpam-4036	146	2	using	use	VERB
ejpam-4036	146	3	lemma	lemma	PROPN
ejpam-4036	146	4	11	11	NUM
ejpam-4036	146	5	and	and	CCONJ
ejpam-4036	146	6	repeated	repeat	VERB
ejpam-4036	146	7	applications	application	NOUN
ejpam-4036	146	8	of	of	ADP
ejpam-4036	146	9	theorem	theorem	NOUN
ejpam-4036	146	10	1	1	NUM
ejpam-4036	146	11	,	,	PUNCT
ejpam-4036	146	12	the	the	DET
ejpam-4036	146	13	group	group	NOUN
ejpam-4036	146	14	h	h	NOUN
ejpam-4036	146	15	has	have	VERB
ejpam-4036	146	16	a	a	DET
ejpam-4036	146	17	sylow	sylow	NOUN
ejpam-4036	146	18	tower	tower	NOUN
ejpam-4036	146	19	of	of	ADP
ejpam-4036	146	20	supersolvable	supersolvable	ADJ
ejpam-4036	146	21	type	type	NOUN
ejpam-4036	146	22	which	which	PRON
ejpam-4036	146	23	means	mean	VERB
ejpam-4036	146	24	that	that	SCONJ
ejpam-4036	146	25	h	h	NOUN
ejpam-4036	146	26	has	have	VERB
ejpam-4036	146	27	a	a	DET
ejpam-4036	146	28	normal	normal	ADJ
ejpam-4036	146	29	sylow	sylow	NOUN
ejpam-4036	146	30	p	p	PROPN
ejpam-4036	146	31	-	-	PUNCT
ejpam-4036	146	32	subgroup	subgroup	NOUN
ejpam-4036	146	33	p	p	NOUN
ejpam-4036	146	34	,	,	PUNCT
ejpam-4036	146	35	where	where	SCONJ
ejpam-4036	146	36	p	p	NOUN
ejpam-4036	146	37	is	be	AUX
ejpam-4036	146	38	the	the	DET
ejpam-4036	146	39	largest	large	ADJ
ejpam-4036	146	40	prime	prime	ADJ
ejpam-4036	146	41	dividing	dividing	NOUN
ejpam-4036	146	42	|h|	|h|	NOUN
ejpam-4036	146	43	.	.	PUNCT
ejpam-4036	147	1	clearly	clearly	ADV
ejpam-4036	147	2	,	,	PUNCT
ejpam-4036	147	3	p	p	NOUN
ejpam-4036	147	4	is	be	AUX
ejpam-4036	147	5	normal	normal	ADJ
ejpam-4036	147	6	in	in	ADP
ejpam-4036	147	7	g	g	NOUN
ejpam-4036	147	8	and	and	CCONJ
ejpam-4036	147	9	hence	hence	ADV
ejpam-4036	147	10	(	(	PUNCT
ejpam-4036	147	11	g	g	NOUN
ejpam-4036	147	12	/	/	SYM
ejpam-4036	147	13	p	p	NOUN
ejpam-4036	147	14	)	)	PUNCT
ejpam-4036	147	15	/(h	/(h	NOUN
ejpam-4036	147	16	/	/	SYM
ejpam-4036	147	17	p	p	NOUN
ejpam-4036	147	18	)	)	PUNCT
ejpam-4036	147	19	∼=	∼=	PROPN
ejpam-4036	147	20	g	g	NOUN
ejpam-4036	147	21	/	/	SYM
ejpam-4036	147	22	h	h	NOUN
ejpam-4036	147	23	∈	∈	PROPN
ejpam-4036	147	24	f.	f.	PROPN
ejpam-4036	147	25	by	by	ADP
ejpam-4036	147	26	lemma	lemma	PROPN
ejpam-4036	147	27	12	12	NUM
ejpam-4036	147	28	,	,	PUNCT
ejpam-4036	147	29	every	every	DET
ejpam-4036	147	30	subgroup	subgroup	NOUN
ejpam-4036	147	31	of	of	ADP
ejpam-4036	147	32	h	h	PROPN
ejpam-4036	147	33	/	/	SYM
ejpam-4036	147	34	p	p	NOUN
ejpam-4036	147	35	of	of	ADP
ejpam-4036	147	36	prime	prime	ADJ
ejpam-4036	147	37	order	order	NOUN
ejpam-4036	147	38	or	or	CCONJ
ejpam-4036	147	39	of	of	ADP
ejpam-4036	147	40	order	order	NOUN
ejpam-4036	147	41	4	4	NUM
ejpam-4036	147	42	(	(	PUNCT
ejpam-4036	147	43	if	if	SCONJ
ejpam-4036	147	44	p	p	X
ejpam-4036	147	45	=	=	NOUN
ejpam-4036	147	46	2	2	NUM
ejpam-4036	147	47	)	)	PUNCT
ejpam-4036	147	48	is	be	AUX
ejpam-4036	147	49	css	css	PROPN
ejpam-4036	147	50	-	-	NOUN
ejpam-4036	147	51	subgroup	subgroup	NOUN
ejpam-4036	147	52	of	of	ADP
ejpam-4036	147	53	g	g	PROPN
ejpam-4036	147	54	/	/	SYM
ejpam-4036	147	55	p	p	NOUN
ejpam-4036	147	56	.	.	PUNCT
ejpam-4036	148	1	then	then	ADV
ejpam-4036	148	2	,	,	PUNCT
ejpam-4036	148	3	by	by	ADP
ejpam-4036	148	4	the	the	DET
ejpam-4036	148	5	minimal	minimal	ADJ
ejpam-4036	148	6	choice	choice	NOUN
ejpam-4036	148	7	of	of	ADP
ejpam-4036	148	8	g	g	NOUN
ejpam-4036	148	9	,	,	PUNCT
ejpam-4036	148	10	we	we	PRON
ejpam-4036	148	11	have	have	VERB
ejpam-4036	148	12	g	g	NOUN
ejpam-4036	148	13	/	/	SYM
ejpam-4036	148	14	p	p	NOUN
ejpam-4036	148	15	∈	∈	PROPN
ejpam-4036	148	16	f	f	NOUN
ejpam-4036	148	17	and	and	CCONJ
ejpam-4036	148	18	so	so	ADV
ejpam-4036	148	19	1	1	X
ejpam-4036	148	20	6=	6=	NUM
ejpam-4036	148	21	gf	gf	X
ejpam-4036	148	22	6	6	NUM
ejpam-4036	148	23	p	p	NOUN
ejpam-4036	148	24	.	.	PUNCT
ejpam-4036	149	1	by	by	ADP
ejpam-4036	149	2	the	the	DET
ejpam-4036	149	3	hypothesis	hypothesis	NOUN
ejpam-4036	149	4	,	,	PUNCT
ejpam-4036	149	5	every	every	DET
ejpam-4036	149	6	subgroup	subgroup	NOUN
ejpam-4036	149	7	of	of	ADP
ejpam-4036	149	8	gf	gf	PROPN
ejpam-4036	149	9	of	of	ADP
ejpam-4036	149	10	prime	prime	ADJ
ejpam-4036	149	11	order	order	NOUN
ejpam-4036	149	12	p	p	NOUN
ejpam-4036	149	13	or	or	CCONJ
ejpam-4036	149	14	of	of	ADP
ejpam-4036	149	15	order	order	NOUN
ejpam-4036	149	16	4	4	NUM
ejpam-4036	149	17	(	(	PUNCT
ejpam-4036	149	18	if	if	SCONJ
ejpam-4036	149	19	p	p	X
ejpam-4036	149	20	=	=	NOUN
ejpam-4036	149	21	2	2	NUM
ejpam-4036	149	22	)	)	PUNCT
ejpam-4036	149	23	is	be	AUX
ejpam-4036	149	24	css	css	PROPN
ejpam-4036	149	25	-	-	PROPN
ejpam-4036	149	26	subgroup	subgroup	NOUN
ejpam-4036	149	27	of	of	ADP
ejpam-4036	149	28	g.	g.	PROPN
ejpam-4036	149	29	then	then	ADV
ejpam-4036	149	30	,	,	PUNCT
ejpam-4036	149	31	by	by	ADP
ejpam-4036	149	32	corollary	corollary	ADJ
ejpam-4036	149	33	1	1	NUM
ejpam-4036	149	34	,	,	PUNCT
ejpam-4036	149	35	gf	gf	X
ejpam-4036	149	36	6	6	NUM
ejpam-4036	149	37	zu(g	zu(g	NUM
ejpam-4036	149	38	)	)	PUNCT
ejpam-4036	149	39	.	.	PUNCT
ejpam-4036	150	1	since	since	SCONJ
ejpam-4036	150	2	ω(gf	ω(gf	NUM
ejpam-4036	150	3	)	)	PUNCT
ejpam-4036	150	4	6	6	NUM
ejpam-4036	150	5	gf	gf	NOUN
ejpam-4036	150	6	and	and	CCONJ
ejpam-4036	150	7	zu(g	zu(g	NUM
ejpam-4036	150	8	)	)	PUNCT
ejpam-4036	150	9	6	6	NUM
ejpam-4036	150	10	zf(g	zf(g	NUM
ejpam-4036	150	11	)	)	PUNCT
ejpam-4036	150	12	,	,	PUNCT
ejpam-4036	150	13	by	by	ADP
ejpam-4036	150	14	lemma	lemma	PROPN
ejpam-4036	150	15	9	9	NUM
ejpam-4036	150	16	,	,	PUNCT
ejpam-4036	150	17	we	we	PRON
ejpam-4036	150	18	have	have	VERB
ejpam-4036	150	19	ω(gf	ω(gf	NUM
ejpam-4036	150	20	)	)	PUNCT
ejpam-4036	150	21	6	6	NUM
ejpam-4036	150	22	gf	gf	NOUN
ejpam-4036	150	23	6	6	NUM
ejpam-4036	150	24	zu(g	zu(g	NOUN
ejpam-4036	150	25	)	)	PUNCT
ejpam-4036	150	26	6	6	NUM
ejpam-4036	150	27	zf(g	zf(g	NUM
ejpam-4036	150	28	)	)	PUNCT
ejpam-4036	150	29	.	.	PUNCT
ejpam-4036	151	1	hence	hence	ADV
ejpam-4036	151	2	,	,	PUNCT
ejpam-4036	151	3	ω(gf	ω(gf	NOUN
ejpam-4036	151	4	)	)	PUNCT
ejpam-4036	151	5	6	6	NUM
ejpam-4036	151	6	zf(g	zf(g	NUM
ejpam-4036	151	7	)	)	PUNCT
ejpam-4036	151	8	.	.	PUNCT
ejpam-4036	152	1	therefore	therefore	ADV
ejpam-4036	152	2	,	,	PUNCT
ejpam-4036	152	3	by	by	ADP
ejpam-4036	152	4	lemma	lemma	PROPN
ejpam-4036	152	5	10	10	NUM
ejpam-4036	152	6	,	,	PUNCT
ejpam-4036	152	7	g	g	PROPN
ejpam-4036	152	8	∈	∈	PROPN
ejpam-4036	152	9	f	f	NOUN
ejpam-4036	152	10	,	,	PUNCT
ejpam-4036	152	11	a	a	DET
ejpam-4036	152	12	contradiction	contradiction	NOUN
ejpam-4036	152	13	.	.	PUNCT
ejpam-4036	153	1	the	the	DET
ejpam-4036	153	2	following	follow	VERB
ejpam-4036	153	3	corollaries	corollary	NOUN
ejpam-4036	153	4	are	be	AUX
ejpam-4036	153	5	immediate	immediate	ADJ
ejpam-4036	153	6	consequences	consequence	NOUN
ejpam-4036	153	7	of	of	ADP
ejpam-4036	153	8	theorem	theorem	ADJ
ejpam-4036	153	9	2	2	NUM
ejpam-4036	153	10	:	:	PUNCT
ejpam-4036	153	11	corollary	corollary	ADJ
ejpam-4036	153	12	2	2	X
ejpam-4036	153	13	.	.	PUNCT
ejpam-4036	154	1	let	let	VERB
ejpam-4036	154	2	h	h	PRON
ejpam-4036	154	3	be	be	AUX
ejpam-4036	154	4	a	a	DET
ejpam-4036	154	5	normal	normal	ADJ
ejpam-4036	154	6	subgroup	subgroup	NOUN
ejpam-4036	154	7	of	of	ADP
ejpam-4036	154	8	g	g	PROPN
ejpam-4036	154	9	such	such	ADJ
ejpam-4036	154	10	that	that	SCONJ
ejpam-4036	154	11	g	g	NOUN
ejpam-4036	154	12	/	/	SYM
ejpam-4036	154	13	h	h	NOUN
ejpam-4036	154	14	is	be	AUX
ejpam-4036	154	15	supersolvable	supersolvable	ADJ
ejpam-4036	154	16	.	.	PUNCT
ejpam-4036	155	1	if	if	SCONJ
ejpam-4036	155	2	every	every	DET
ejpam-4036	155	3	subgroup	subgroup	NOUN
ejpam-4036	155	4	of	of	ADP
ejpam-4036	155	5	h	h	NOUN
ejpam-4036	155	6	of	of	ADP
ejpam-4036	155	7	prime	prime	ADJ
ejpam-4036	155	8	order	order	NOUN
ejpam-4036	155	9	p	p	NOUN
ejpam-4036	155	10	or	or	CCONJ
ejpam-4036	155	11	of	of	ADP
ejpam-4036	155	12	order	order	NOUN
ejpam-4036	155	13	4	4	NUM
ejpam-4036	155	14	(	(	PUNCT
ejpam-4036	155	15	if	if	SCONJ
ejpam-4036	155	16	p	p	X
ejpam-4036	155	17	=	=	NOUN
ejpam-4036	155	18	2	2	NUM
ejpam-4036	155	19	)	)	PUNCT
ejpam-4036	155	20	is	be	AUX
ejpam-4036	155	21	css	css	PROPN
ejpam-4036	155	22	-	-	NOUN
ejpam-4036	155	23	subgroup	subgroup	NOUN
ejpam-4036	155	24	of	of	ADP
ejpam-4036	155	25	g	g	PROPN
ejpam-4036	155	26	,	,	PUNCT
ejpam-4036	155	27	then	then	ADV
ejpam-4036	155	28	g	g	PROPN
ejpam-4036	155	29	is	be	AUX
ejpam-4036	155	30	supersolvable	supersolvable	ADJ
ejpam-4036	155	31	.	.	PUNCT
ejpam-4036	156	1	corollary	corollary	ADJ
ejpam-4036	156	2	3	3	NUM
ejpam-4036	156	3	.	.	PUNCT
ejpam-4036	157	1	let	let	VERB
ejpam-4036	157	2	h	h	PRON
ejpam-4036	157	3	be	be	AUX
ejpam-4036	157	4	a	a	DET
ejpam-4036	157	5	normal	normal	ADJ
ejpam-4036	157	6	subgroup	subgroup	NOUN
ejpam-4036	157	7	of	of	ADP
ejpam-4036	157	8	g	g	PROPN
ejpam-4036	157	9	such	such	ADJ
ejpam-4036	157	10	that	that	SCONJ
ejpam-4036	157	11	(	(	PUNCT
ejpam-4036	157	12	g	g	NOUN
ejpam-4036	157	13	/	/	SYM
ejpam-4036	157	14	h)′	h)′	PROPN
ejpam-4036	157	15	is	be	AUX
ejpam-4036	157	16	nilpotent	nilpotent	ADJ
ejpam-4036	157	17	.	.	PUNCT
ejpam-4036	158	1	if	if	SCONJ
ejpam-4036	158	2	every	every	DET
ejpam-4036	158	3	subgroup	subgroup	NOUN
ejpam-4036	158	4	of	of	ADP
ejpam-4036	158	5	h	h	NOUN
ejpam-4036	158	6	of	of	ADP
ejpam-4036	158	7	prime	prime	ADJ
ejpam-4036	158	8	order	order	NOUN
ejpam-4036	158	9	p	p	NOUN
ejpam-4036	158	10	or	or	CCONJ
ejpam-4036	158	11	of	of	ADP
ejpam-4036	158	12	order	order	NOUN
ejpam-4036	158	13	4	4	NUM
ejpam-4036	158	14	(	(	PUNCT
ejpam-4036	158	15	if	if	SCONJ
ejpam-4036	158	16	p	p	X
ejpam-4036	158	17	=	=	NOUN
ejpam-4036	158	18	2	2	NUM
ejpam-4036	158	19	)	)	PUNCT
ejpam-4036	158	20	is	be	AUX
ejpam-4036	158	21	css	css	PROPN
ejpam-4036	158	22	-	-	NOUN
ejpam-4036	158	23	subgroup	subgroup	NOUN
ejpam-4036	158	24	of	of	ADP
ejpam-4036	158	25	g	g	PROPN
ejpam-4036	158	26	,	,	PUNCT
ejpam-4036	158	27	then	then	ADV
ejpam-4036	158	28	g′	g′	NOUN
ejpam-4036	158	29	is	be	AUX
ejpam-4036	158	30	nilpotent	nilpotent	ADJ
ejpam-4036	158	31	.	.	PUNCT
ejpam-4036	159	1	corollary	corollary	ADJ
ejpam-4036	159	2	4	4	NUM
ejpam-4036	159	3	.	.	PUNCT
ejpam-4036	160	1	let	let	VERB
ejpam-4036	160	2	g	g	PRON
ejpam-4036	160	3	be	be	AUX
ejpam-4036	160	4	a	a	DET
ejpam-4036	160	5	group	group	NOUN
ejpam-4036	160	6	such	such	ADJ
ejpam-4036	160	7	that	that	SCONJ
ejpam-4036	160	8	every	every	DET
ejpam-4036	160	9	subgroup	subgroup	NOUN
ejpam-4036	160	10	of	of	ADP
ejpam-4036	160	11	g	g	PROPN
ejpam-4036	160	12	of	of	ADP
ejpam-4036	160	13	prime	prime	ADJ
ejpam-4036	160	14	order	order	NOUN
ejpam-4036	160	15	p	p	NOUN
ejpam-4036	160	16	or	or	CCONJ
ejpam-4036	160	17	of	of	ADP
ejpam-4036	160	18	order	order	NOUN
ejpam-4036	160	19	4	4	NUM
ejpam-4036	160	20	(	(	PUNCT
ejpam-4036	160	21	if	if	SCONJ
ejpam-4036	160	22	p	p	X
ejpam-4036	160	23	=	=	NOUN
ejpam-4036	160	24	2	2	NUM
ejpam-4036	160	25	)	)	PUNCT
ejpam-4036	160	26	is	be	AUX
ejpam-4036	160	27	css	css	PROPN
ejpam-4036	160	28	-	-	NOUN
ejpam-4036	160	29	subgroup	subgroup	NOUN
ejpam-4036	160	30	of	of	ADP
ejpam-4036	160	31	g	g	PROPN
ejpam-4036	160	32	,	,	PUNCT
ejpam-4036	160	33	then	then	ADV
ejpam-4036	160	34	g	g	PROPN
ejpam-4036	160	35	is	be	AUX
ejpam-4036	160	36	supersolvable	supersolvable	ADJ
ejpam-4036	160	37	.	.	PUNCT
ejpam-4036	161	1	now	now	ADV
ejpam-4036	161	2	we	we	PRON
ejpam-4036	161	3	can	can	AUX
ejpam-4036	161	4	prove	prove	VERB
ejpam-4036	161	5	:	:	PUNCT
ejpam-4036	161	6	theorem	theorem	NOUN
ejpam-4036	161	7	3	3	X
ejpam-4036	161	8	.	.	PUNCT
ejpam-4036	162	1	let	let	VERB
ejpam-4036	162	2	f	f	PRON
ejpam-4036	162	3	be	be	AUX
ejpam-4036	162	4	a	a	DET
ejpam-4036	162	5	saturated	saturated	ADJ
ejpam-4036	162	6	formation	formation	NOUN
ejpam-4036	162	7	containing	contain	VERB
ejpam-4036	162	8	u	u	NOUN
ejpam-4036	162	9	and	and	CCONJ
ejpam-4036	162	10	g	g	ADP
ejpam-4036	162	11	a	a	DET
ejpam-4036	162	12	group	group	NOUN
ejpam-4036	162	13	.	.	PUNCT
ejpam-4036	163	1	then	then	ADV
ejpam-4036	163	2	g	g	PROPN
ejpam-4036	163	3	∈	∈	PROPN
ejpam-4036	163	4	f	f	PROPN
ejpam-4036	164	1	if	if	SCONJ
ejpam-4036	164	2	and	and	CCONJ
ejpam-4036	164	3	only	only	ADV
ejpam-4036	164	4	if	if	SCONJ
ejpam-4036	164	5	g	g	PROPN
ejpam-4036	164	6	has	have	VERB
ejpam-4036	164	7	a	a	DET
ejpam-4036	164	8	normal	normal	ADJ
ejpam-4036	164	9	subgroup	subgroup	NOUN
ejpam-4036	164	10	h	h	NOUN
ejpam-4036	164	11	such	such	ADJ
ejpam-4036	164	12	that	that	SCONJ
ejpam-4036	164	13	g	g	NOUN
ejpam-4036	164	14	/	/	SYM
ejpam-4036	164	15	h	h	NOUN
ejpam-4036	164	16	∈	∈	PROPN
ejpam-4036	164	17	f	f	PROPN
ejpam-4036	164	18	and	and	CCONJ
ejpam-4036	164	19	every	every	DET
ejpam-4036	164	20	subgroup	subgroup	NOUN
ejpam-4036	164	21	of	of	ADP
ejpam-4036	164	22	f	f	PROPN
ejpam-4036	164	23	∗(h	∗(h	PROPN
ejpam-4036	164	24	)	)	PUNCT
ejpam-4036	164	25	of	of	ADP
ejpam-4036	164	26	prime	prime	ADJ
ejpam-4036	164	27	order	order	NOUN
ejpam-4036	164	28	p	p	NOUN
ejpam-4036	164	29	or	or	CCONJ
ejpam-4036	164	30	of	of	ADP
ejpam-4036	164	31	order	order	NOUN
ejpam-4036	164	32	4	4	NUM
ejpam-4036	164	33	(	(	PUNCT
ejpam-4036	164	34	if	if	SCONJ
ejpam-4036	164	35	p	p	X
ejpam-4036	164	36	=	=	NOUN
ejpam-4036	164	37	2	2	NUM
ejpam-4036	164	38	)	)	PUNCT
ejpam-4036	164	39	is	be	AUX
ejpam-4036	164	40	css	css	PROPN
ejpam-4036	164	41	-	-	NOUN
ejpam-4036	164	42	subgroup	subgroup	NOUN
ejpam-4036	164	43	of	of	ADP
ejpam-4036	164	44	g.	g.	PROPN
ejpam-4036	164	45	proof	proof	NOUN
ejpam-4036	164	46	.	.	PUNCT
ejpam-4036	165	1	if	if	SCONJ
ejpam-4036	165	2	g	g	PROPN
ejpam-4036	165	3	∈	∈	PROPN
ejpam-4036	165	4	f	f	X
ejpam-4036	165	5	,	,	PUNCT
ejpam-4036	165	6	then	then	ADV
ejpam-4036	165	7	we	we	PRON
ejpam-4036	165	8	set	set	VERB
ejpam-4036	165	9	h	h	NOUN
ejpam-4036	165	10	=	=	SYM
ejpam-4036	165	11	1	1	NUM
ejpam-4036	165	12	and	and	CCONJ
ejpam-4036	165	13	the	the	DET
ejpam-4036	165	14	theorem	theorem	NOUN
ejpam-4036	165	15	follows	follow	VERB
ejpam-4036	165	16	.	.	PUNCT
ejpam-4036	166	1	now	now	ADV
ejpam-4036	166	2	we	we	PRON
ejpam-4036	166	3	prove	prove	VERB
ejpam-4036	166	4	the	the	DET
ejpam-4036	166	5	converse	converse	NOUN
ejpam-4036	166	6	.	.	PUNCT
ejpam-4036	167	1	by	by	ADP
ejpam-4036	167	2	the	the	DET
ejpam-4036	167	3	hypothesis	hypothesis	NOUN
ejpam-4036	167	4	and	and	CCONJ
ejpam-4036	167	5	lemma	lemma	PROPN
ejpam-4036	167	6	11	11	NUM
ejpam-4036	167	7	,	,	PUNCT
ejpam-4036	167	8	every	every	DET
ejpam-4036	167	9	subgroup	subgroup	NOUN
ejpam-4036	167	10	of	of	ADP
ejpam-4036	167	11	f	f	PROPN
ejpam-4036	167	12	∗(h	∗(h	PROPN
ejpam-4036	167	13	)	)	PUNCT
ejpam-4036	167	14	of	of	ADP
ejpam-4036	167	15	prime	prime	ADJ
ejpam-4036	167	16	order	order	NOUN
ejpam-4036	167	17	p	p	NOUN
ejpam-4036	167	18	or	or	CCONJ
ejpam-4036	167	19	of	of	ADP
ejpam-4036	167	20	order	order	NOUN
ejpam-4036	167	21	4	4	NUM
ejpam-4036	167	22	(	(	PUNCT
ejpam-4036	167	23	if	if	SCONJ
ejpam-4036	167	24	p	p	X
ejpam-4036	167	25	=	=	NOUN
ejpam-4036	167	26	2	2	NUM
ejpam-4036	167	27	)	)	PUNCT
ejpam-4036	167	28	is	be	AUX
ejpam-4036	167	29	css	css	PROPN
ejpam-4036	167	30	-	-	NOUN
ejpam-4036	167	31	subgroup	subgroup	NOUN
ejpam-4036	167	32	of	of	ADP
ejpam-4036	167	33	f	f	PROPN
ejpam-4036	167	34	∗(h	∗(h	PROPN
ejpam-4036	167	35	)	)	PUNCT
ejpam-4036	167	36	.	.	PUNCT
ejpam-4036	168	1	corollary	corollary	ADJ
ejpam-4036	168	2	4	4	NUM
ejpam-4036	168	3	implies	imply	VERB
ejpam-4036	168	4	that	that	SCONJ
ejpam-4036	168	5	f	f	PROPN
ejpam-4036	168	6	∗(h	∗(h	PROPN
ejpam-4036	168	7	)	)	PUNCT
ejpam-4036	168	8	is	be	AUX
ejpam-4036	168	9	supersolvable	supersolvable	ADJ
ejpam-4036	168	10	.	.	PUNCT
ejpam-4036	169	1	hence	hence	ADV
ejpam-4036	169	2	,	,	PUNCT
ejpam-4036	169	3	by	by	ADP
ejpam-4036	169	4	lemma	lemma	PROPN
ejpam-4036	169	5	11	11	NUM
ejpam-4036	169	6	,	,	PUNCT
ejpam-4036	169	7	f	f	PROPN
ejpam-4036	169	8	∗(h	∗(h	PROPN
ejpam-4036	169	9	)	)	PUNCT
ejpam-4036	170	1	=	=	SYM
ejpam-4036	170	2	f	f	PROPN
ejpam-4036	170	3	(	(	PUNCT
ejpam-4036	170	4	h	h	NOUN
ejpam-4036	170	5	)	)	PUNCT
ejpam-4036	170	6	.	.	PUNCT
ejpam-4036	171	1	then	then	ADV
ejpam-4036	171	2	,	,	PUNCT
ejpam-4036	171	3	by	by	ADP
ejpam-4036	171	4	corollary	corollary	ADJ
ejpam-4036	171	5	1	1	NUM
ejpam-4036	171	6	,	,	PUNCT
ejpam-4036	171	7	op(h	op(h	NUM
ejpam-4036	171	8	)	)	PUNCT
ejpam-4036	171	9	6	6	NUM
ejpam-4036	171	10	zu(g	zu(g	NUM
ejpam-4036	171	11	)	)	PUNCT
ejpam-4036	171	12	.	.	PUNCT
ejpam-4036	172	1	since	since	SCONJ
ejpam-4036	172	2	zu(g	zu(g	NUM
ejpam-4036	172	3	)	)	PUNCT
ejpam-4036	172	4	6	6	NUM
ejpam-4036	172	5	zf(g	zf(g	NUM
ejpam-4036	172	6	)	)	PUNCT
ejpam-4036	172	7	,	,	PUNCT
ejpam-4036	172	8	by	by	ADP
ejpam-4036	172	9	lemma	lemma	PROPN
ejpam-4036	172	10	9	9	NUM
ejpam-4036	172	11	,	,	PUNCT
ejpam-4036	172	12	it	it	PRON
ejpam-4036	172	13	follows	follow	VERB
ejpam-4036	172	14	that	that	SCONJ
ejpam-4036	172	15	op(h	op(h	X
ejpam-4036	172	16	)	)	PUNCT
ejpam-4036	172	17	6	6	NUM
ejpam-4036	172	18	zf(g	zf(g	NUM
ejpam-4036	172	19	)	)	PUNCT
ejpam-4036	172	20	and	and	CCONJ
ejpam-4036	172	21	so	so	ADV
ejpam-4036	172	22	f	f	PROPN
ejpam-4036	172	23	∗(h	∗(h	PROPN
ejpam-4036	172	24	)	)	PUNCT
ejpam-4036	173	1	=	=	SYM
ejpam-4036	173	2	f	f	PROPN
ejpam-4036	173	3	(	(	PUNCT
ejpam-4036	173	4	h	h	NOUN
ejpam-4036	173	5	)	)	PUNCT
ejpam-4036	173	6	6	6	NUM
ejpam-4036	173	7	zf(g	zf(g	NUM
ejpam-4036	173	8	)	)	PUNCT
ejpam-4036	173	9	.	.	PUNCT
ejpam-4036	174	1	applying	apply	VERB
ejpam-4036	174	2	lemma	lemma	PROPN
ejpam-4036	174	3	12	12	NUM
ejpam-4036	174	4	,	,	PUNCT
ejpam-4036	174	5	we	we	PRON
ejpam-4036	174	6	get	get	VERB
ejpam-4036	174	7	g	g	PROPN
ejpam-4036	174	8	∈	∈	PROPN
ejpam-4036	174	9	f.	f.	NOUN
ejpam-4036	174	10	immediately	immediately	ADV
ejpam-4036	174	11	from	from	ADP
ejpam-4036	174	12	theorem	theorem	ADJ
ejpam-4036	174	13	3	3	NUM
ejpam-4036	174	14	,	,	PUNCT
ejpam-4036	174	15	we	we	PRON
ejpam-4036	174	16	have	have	VERB
ejpam-4036	174	17	the	the	DET
ejpam-4036	174	18	following	follow	VERB
ejpam-4036	174	19	corollaries	corollary	NOUN
ejpam-4036	174	20	:	:	PUNCT
ejpam-4036	175	1	corollary	corollary	ADJ
ejpam-4036	175	2	5	5	X
ejpam-4036	175	3	.	.	PUNCT
ejpam-4036	176	1	let	let	VERB
ejpam-4036	176	2	h	h	PRON
ejpam-4036	176	3	be	be	AUX
ejpam-4036	176	4	a	a	DET
ejpam-4036	176	5	normal	normal	ADJ
ejpam-4036	176	6	subgroup	subgroup	NOUN
ejpam-4036	176	7	g	g	PROPN
ejpam-4036	176	8	such	such	ADJ
ejpam-4036	176	9	that	that	SCONJ
ejpam-4036	176	10	g	g	NOUN
ejpam-4036	176	11	/	/	SYM
ejpam-4036	176	12	h	h	NOUN
ejpam-4036	176	13	is	be	AUX
ejpam-4036	176	14	supersolvable	supersolvable	ADJ
ejpam-4036	176	15	.	.	PUNCT
ejpam-4036	177	1	if	if	SCONJ
ejpam-4036	177	2	every	every	DET
ejpam-4036	177	3	subgroup	subgroup	NOUN
ejpam-4036	177	4	of	of	ADP
ejpam-4036	177	5	f	f	PROPN
ejpam-4036	177	6	∗(h	∗(h	PROPN
ejpam-4036	177	7	)	)	PUNCT
ejpam-4036	177	8	of	of	ADP
ejpam-4036	177	9	prime	prime	ADJ
ejpam-4036	177	10	order	order	NOUN
ejpam-4036	177	11	p	p	NOUN
ejpam-4036	177	12	or	or	CCONJ
ejpam-4036	177	13	of	of	ADP
ejpam-4036	177	14	order	order	NOUN
ejpam-4036	177	15	4	4	NUM
ejpam-4036	177	16	(	(	PUNCT
ejpam-4036	177	17	if	if	SCONJ
ejpam-4036	177	18	p	p	X
ejpam-4036	177	19	=	=	NOUN
ejpam-4036	177	20	2	2	NUM
ejpam-4036	177	21	)	)	PUNCT
ejpam-4036	177	22	is	be	AUX
ejpam-4036	177	23	css	css	PROPN
ejpam-4036	177	24	-	-	NOUN
ejpam-4036	177	25	subgroup	subgroup	NOUN
ejpam-4036	177	26	of	of	ADP
ejpam-4036	177	27	g	g	PROPN
ejpam-4036	177	28	,	,	PUNCT
ejpam-4036	177	29	then	then	ADV
ejpam-4036	177	30	g	g	PROPN
ejpam-4036	177	31	is	be	AUX
ejpam-4036	177	32	supersolvable	supersolvable	ADJ
ejpam-4036	177	33	.	.	PUNCT
ejpam-4036	178	1	a.	a.	NOUN
ejpam-4036	178	2	heliel	heliel	PROPN
ejpam-4036	178	3	,	,	PUNCT
ejpam-4036	178	4	r.	r.	PROPN
ejpam-4036	178	5	hijazi	hijazi	PROPN
ejpam-4036	178	6	,	,	PUNCT
ejpam-4036	178	7	s.	s.	PROPN
ejpam-4036	178	8	al	al	PROPN
ejpam-4036	178	9	-	-	PUNCT
ejpam-4036	178	10	shammari	shammari	PROPN
ejpam-4036	178	11	/	/	SYM
ejpam-4036	178	12	eur	eur	PROPN
ejpam-4036	178	13	.	.	PUNCT
ejpam-4036	179	1	j.	j.	PROPN
ejpam-4036	179	2	pure	pure	PROPN
ejpam-4036	179	3	appl	appl	PROPN
ejpam-4036	179	4	.	.	PROPN
ejpam-4036	179	5	math	math	PROPN
ejpam-4036	179	6	,	,	PUNCT
ejpam-4036	179	7	14	14	NUM
ejpam-4036	179	8	(	(	PUNCT
ejpam-4036	179	9	3	3	NUM
ejpam-4036	179	10	)	)	PUNCT
ejpam-4036	179	11	(	(	PUNCT
ejpam-4036	179	12	2021	2021	NUM
ejpam-4036	179	13	)	)	PUNCT
ejpam-4036	179	14	,	,	PUNCT
ejpam-4036	179	15	1002	1002	NUM
ejpam-4036	179	16	-	-	SYM
ejpam-4036	179	17	1014	1014	NUM
ejpam-4036	179	18	1008	1008	NUM
ejpam-4036	179	19	corollary	corollary	NOUN
ejpam-4036	179	20	6	6	NUM
ejpam-4036	179	21	.	.	PUNCT
ejpam-4036	180	1	if	if	SCONJ
ejpam-4036	180	2	every	every	DET
ejpam-4036	180	3	subgroup	subgroup	NOUN
ejpam-4036	180	4	of	of	ADP
ejpam-4036	180	5	f	f	PROPN
ejpam-4036	180	6	∗(g	∗(g	PROPN
ejpam-4036	180	7	)	)	PUNCT
ejpam-4036	180	8	of	of	ADP
ejpam-4036	180	9	prime	prime	ADJ
ejpam-4036	180	10	order	order	NOUN
ejpam-4036	180	11	p	p	NOUN
ejpam-4036	180	12	or	or	CCONJ
ejpam-4036	180	13	of	of	ADP
ejpam-4036	180	14	order	order	NOUN
ejpam-4036	180	15	4	4	NUM
ejpam-4036	180	16	(	(	PUNCT
ejpam-4036	180	17	if	if	SCONJ
ejpam-4036	180	18	p	p	X
ejpam-4036	180	19	=	=	NOUN
ejpam-4036	180	20	2	2	NUM
ejpam-4036	180	21	)	)	PUNCT
ejpam-4036	180	22	is	be	AUX
ejpam-4036	180	23	css	css	PROPN
ejpam-4036	180	24	-	-	NOUN
ejpam-4036	180	25	subgroup	subgroup	NOUN
ejpam-4036	180	26	of	of	ADP
ejpam-4036	180	27	g	g	PROPN
ejpam-4036	180	28	,	,	PUNCT
ejpam-4036	180	29	then	then	ADV
ejpam-4036	180	30	g	g	PROPN
ejpam-4036	180	31	is	be	AUX
ejpam-4036	180	32	supersolvable	supersolvable	ADJ
ejpam-4036	180	33	.	.	PUNCT
ejpam-4036	181	1	corollary	corollary	ADJ
ejpam-4036	181	2	7	7	NUM
ejpam-4036	181	3	.	.	PUNCT
ejpam-4036	182	1	let	let	VERB
ejpam-4036	182	2	f	f	PRON
ejpam-4036	182	3	be	be	AUX
ejpam-4036	182	4	a	a	DET
ejpam-4036	182	5	saturated	saturated	ADJ
ejpam-4036	182	6	formation	formation	NOUN
ejpam-4036	182	7	containing	contain	VERB
ejpam-4036	182	8	u	u	NOUN
ejpam-4036	182	9	and	and	CCONJ
ejpam-4036	182	10	g	g	ADP
ejpam-4036	182	11	a	a	DET
ejpam-4036	182	12	group	group	NOUN
ejpam-4036	182	13	.	.	PUNCT
ejpam-4036	183	1	then	then	ADV
ejpam-4036	183	2	g	g	PROPN
ejpam-4036	183	3	∈	∈	PROPN
ejpam-4036	183	4	f	f	PROPN
ejpam-4036	184	1	if	if	SCONJ
ejpam-4036	184	2	and	and	CCONJ
ejpam-4036	184	3	only	only	ADV
ejpam-4036	184	4	if	if	SCONJ
ejpam-4036	184	5	g	g	PROPN
ejpam-4036	184	6	has	have	VERB
ejpam-4036	184	7	a	a	DET
ejpam-4036	184	8	solvable	solvable	ADJ
ejpam-4036	184	9	normal	normal	ADJ
ejpam-4036	184	10	subgroup	subgroup	NOUN
ejpam-4036	184	11	h	h	NOUN
ejpam-4036	184	12	such	such	ADJ
ejpam-4036	184	13	that	that	SCONJ
ejpam-4036	184	14	g	g	NOUN
ejpam-4036	184	15	/	/	SYM
ejpam-4036	184	16	h	h	NOUN
ejpam-4036	184	17	∈	∈	PROPN
ejpam-4036	184	18	f	f	PROPN
ejpam-4036	184	19	and	and	CCONJ
ejpam-4036	184	20	every	every	DET
ejpam-4036	184	21	subgroup	subgroup	NOUN
ejpam-4036	184	22	of	of	ADP
ejpam-4036	184	23	f	f	PROPN
ejpam-4036	184	24	(	(	PUNCT
ejpam-4036	184	25	h	h	NOUN
ejpam-4036	184	26	)	)	PUNCT
ejpam-4036	184	27	of	of	ADP
ejpam-4036	184	28	prime	prime	ADJ
ejpam-4036	184	29	order	order	NOUN
ejpam-4036	184	30	p	p	NOUN
ejpam-4036	184	31	or	or	CCONJ
ejpam-4036	184	32	of	of	ADP
ejpam-4036	184	33	order	order	NOUN
ejpam-4036	184	34	4	4	NUM
ejpam-4036	184	35	(	(	PUNCT
ejpam-4036	184	36	if	if	SCONJ
ejpam-4036	184	37	p	p	X
ejpam-4036	184	38	=	=	NOUN
ejpam-4036	184	39	2	2	NUM
ejpam-4036	184	40	)	)	PUNCT
ejpam-4036	184	41	is	be	AUX
ejpam-4036	184	42	css	css	PROPN
ejpam-4036	184	43	-	-	NOUN
ejpam-4036	184	44	subgroup	subgroup	NOUN
ejpam-4036	184	45	of	of	ADP
ejpam-4036	184	46	g.	g.	PROPN
ejpam-4036	184	47	we	we	PRON
ejpam-4036	184	48	now	now	ADV
ejpam-4036	184	49	prove	prove	VERB
ejpam-4036	184	50	:	:	PUNCT
ejpam-4036	184	51	theorem	theorem	NOUN
ejpam-4036	184	52	4	4	NUM
ejpam-4036	184	53	.	.	PUNCT
ejpam-4036	185	1	let	let	VERB
ejpam-4036	185	2	g	g	PRON
ejpam-4036	185	3	be	be	AUX
ejpam-4036	185	4	a	a	DET
ejpam-4036	185	5	group	group	NOUN
ejpam-4036	185	6	.	.	PUNCT
ejpam-4036	186	1	if	if	SCONJ
ejpam-4036	186	2	every	every	DET
ejpam-4036	186	3	subgroup	subgroup	NOUN
ejpam-4036	186	4	of	of	ADP
ejpam-4036	186	5	g	g	PROPN
ejpam-4036	186	6	of	of	ADP
ejpam-4036	186	7	prime	prime	ADJ
ejpam-4036	186	8	order	order	NOUN
ejpam-4036	186	9	is	be	AUX
ejpam-4036	186	10	contained	contain	VERB
ejpam-4036	186	11	in	in	ADP
ejpam-4036	186	12	z∞(g	z∞(g	NUM
ejpam-4036	186	13	)	)	PUNCT
ejpam-4036	186	14	and	and	CCONJ
ejpam-4036	186	15	every	every	DET
ejpam-4036	186	16	cyclic	cyclic	ADJ
ejpam-4036	186	17	subgroup	subgroup	NOUN
ejpam-4036	186	18	of	of	ADP
ejpam-4036	186	19	order	order	NOUN
ejpam-4036	186	20	4	4	NUM
ejpam-4036	186	21	of	of	ADP
ejpam-4036	186	22	g	g	PROPN
ejpam-4036	186	23	is	be	AUX
ejpam-4036	186	24	css	css	NOUN
ejpam-4036	186	25	-	-	NOUN
ejpam-4036	186	26	subgroup	subgroup	NOUN
ejpam-4036	186	27	of	of	ADP
ejpam-4036	186	28	g	g	PROPN
ejpam-4036	186	29	or	or	CCONJ
ejpam-4036	186	30	lies	lie	NOUN
ejpam-4036	186	31	in	in	ADP
ejpam-4036	186	32	z∞(g	z∞(g	NUM
ejpam-4036	186	33	)	)	PUNCT
ejpam-4036	186	34	,	,	PUNCT
ejpam-4036	186	35	then	then	ADV
ejpam-4036	186	36	g	g	PROPN
ejpam-4036	186	37	is	be	AUX
ejpam-4036	186	38	nilpotent	nilpotent	ADJ
ejpam-4036	186	39	.	.	PUNCT
ejpam-4036	187	1	proof	proof	NOUN
ejpam-4036	187	2	.	.	PUNCT
ejpam-4036	188	1	assume	assume	VERB
ejpam-4036	188	2	that	that	SCONJ
ejpam-4036	188	3	the	the	DET
ejpam-4036	188	4	result	result	NOUN
ejpam-4036	188	5	is	be	AUX
ejpam-4036	188	6	false	false	ADJ
ejpam-4036	188	7	and	and	CCONJ
ejpam-4036	188	8	let	let	VERB
ejpam-4036	188	9	g	g	PRON
ejpam-4036	188	10	be	be	AUX
ejpam-4036	188	11	a	a	DET
ejpam-4036	188	12	counterexample	counterexample	NOUN
ejpam-4036	188	13	of	of	ADP
ejpam-4036	188	14	minimal	minimal	ADJ
ejpam-4036	188	15	order	order	NOUN
ejpam-4036	188	16	.	.	PUNCT
ejpam-4036	189	1	let	let	VERB
ejpam-4036	189	2	l	l	NOUN
ejpam-4036	189	3	be	be	AUX
ejpam-4036	189	4	an	an	DET
ejpam-4036	189	5	arbitrary	arbitrary	ADJ
ejpam-4036	189	6	proper	proper	ADJ
ejpam-4036	189	7	subgroup	subgroup	NOUN
ejpam-4036	189	8	of	of	ADP
ejpam-4036	189	9	g	g	PROPN
ejpam-4036	189	10	and	and	CCONJ
ejpam-4036	189	11	k	k	PROPN
ejpam-4036	189	12	a	a	DET
ejpam-4036	189	13	cyclic	cyclic	ADJ
ejpam-4036	189	14	subgroup	subgroup	NOUN
ejpam-4036	189	15	of	of	ADP
ejpam-4036	189	16	l	l	NOUN
ejpam-4036	189	17	of	of	ADP
ejpam-4036	189	18	prime	prime	ADJ
ejpam-4036	189	19	order	order	NOUN
ejpam-4036	189	20	or	or	CCONJ
ejpam-4036	189	21	of	of	ADP
ejpam-4036	189	22	order	order	NOUN
ejpam-4036	189	23	4	4	NUM
ejpam-4036	189	24	.	.	PUNCT
ejpam-4036	190	1	then	then	ADV
ejpam-4036	190	2	k	k	PROPN
ejpam-4036	190	3	6	6	NUM
ejpam-4036	190	4	z∞(g	z∞(g	NUM
ejpam-4036	190	5	)	)	PUNCT
ejpam-4036	190	6	∩	∩	NOUN
ejpam-4036	190	7	l	l	NOUN
ejpam-4036	190	8	6	6	NUM
ejpam-4036	190	9	z∞(l	z∞(l	NOUN
ejpam-4036	190	10	)	)	PUNCT
ejpam-4036	190	11	.	.	PUNCT
ejpam-4036	191	1	by	by	ADP
ejpam-4036	191	2	hypotheses	hypothesis	NOUN
ejpam-4036	191	3	and	and	CCONJ
ejpam-4036	191	4	lemma	lemma	PROPN
ejpam-4036	191	5	11	11	NUM
ejpam-4036	191	6	,	,	PUNCT
ejpam-4036	191	7	k	k	PROPN
ejpam-4036	191	8	is	be	AUX
ejpam-4036	191	9	css	css	PROPN
ejpam-4036	191	10	-	-	PROPN
ejpam-4036	191	11	subgroup	subgroup	NOUN
ejpam-4036	191	12	of	of	ADP
ejpam-4036	191	13	l.	l.	PROPN
ejpam-4036	191	14	the	the	DET
ejpam-4036	191	15	minimal	minimal	ADJ
ejpam-4036	191	16	choice	choice	NOUN
ejpam-4036	191	17	of	of	ADP
ejpam-4036	191	18	g	g	PROPN
ejpam-4036	191	19	implies	imply	VERB
ejpam-4036	191	20	that	that	SCONJ
ejpam-4036	191	21	l	l	NOUN
ejpam-4036	191	22	is	be	AUX
ejpam-4036	191	23	nilpotent	nilpotent	ADJ
ejpam-4036	191	24	.	.	PUNCT
ejpam-4036	192	1	since	since	SCONJ
ejpam-4036	192	2	l	l	NOUN
ejpam-4036	192	3	is	be	AUX
ejpam-4036	192	4	an	an	DET
ejpam-4036	192	5	arbitrary	arbitrary	ADJ
ejpam-4036	192	6	proper	proper	ADJ
ejpam-4036	192	7	subgroup	subgroup	NOUN
ejpam-4036	192	8	of	of	ADP
ejpam-4036	192	9	g	g	PROPN
ejpam-4036	192	10	,	,	PUNCT
ejpam-4036	192	11	we	we	PRON
ejpam-4036	192	12	have	have	VERB
ejpam-4036	192	13	that	that	PRON
ejpam-4036	192	14	g	g	PROPN
ejpam-4036	192	15	is	be	AUX
ejpam-4036	192	16	a	a	DET
ejpam-4036	192	17	minimal	minimal	ADJ
ejpam-4036	192	18	non	non	ADJ
ejpam-4036	192	19	-	-	ADJ
ejpam-4036	192	20	nilpotent	nilpotent	ADJ
ejpam-4036	192	21	group	group	NOUN
ejpam-4036	192	22	.	.	PUNCT
ejpam-4036	193	1	hence	hence	ADV
ejpam-4036	193	2	,	,	PUNCT
ejpam-4036	193	3	by	by	ADP
ejpam-4036	193	4	lemma	lemma	PROPN
ejpam-4036	193	5	2	2	NUM
ejpam-4036	193	6	,	,	PUNCT
ejpam-4036	193	7	g	g	PROPN
ejpam-4036	193	8	=	=	SYM
ejpam-4036	193	9	pq	pq	PROPN
ejpam-4036	193	10	,	,	PUNCT
ejpam-4036	193	11	where	where	SCONJ
ejpam-4036	193	12	p	p	NOUN
ejpam-4036	193	13	is	be	AUX
ejpam-4036	193	14	a	a	DET
ejpam-4036	193	15	normal	normal	ADJ
ejpam-4036	193	16	sylow	sylow	NOUN
ejpam-4036	193	17	p	p	NOUN
ejpam-4036	193	18	-	-	PUNCT
ejpam-4036	193	19	subgroup	subgroup	NOUN
ejpam-4036	193	20	of	of	ADP
ejpam-4036	193	21	g	g	PROPN
ejpam-4036	193	22	and	and	CCONJ
ejpam-4036	193	23	q	q	PROPN
ejpam-4036	193	24	is	be	AUX
ejpam-4036	193	25	a	a	DET
ejpam-4036	193	26	non	non	X
ejpam-4036	193	27	normal	normal	ADJ
ejpam-4036	193	28	cyclic	cyclic	ADJ
ejpam-4036	193	29	sylow	sylow	NOUN
ejpam-4036	193	30	q	q	NOUN
ejpam-4036	193	31	-	-	NOUN
ejpam-4036	193	32	subgroup	subgroup	NOUN
ejpam-4036	193	33	of	of	ADP
ejpam-4036	193	34	g	g	PROPN
ejpam-4036	193	35	,	,	PUNCT
ejpam-4036	193	36	p	p	PROPN
ejpam-4036	193	37	6=	6=	PROPN
ejpam-4036	193	38	q.	q.	PROPN
ejpam-4036	193	39	moreover	moreover	ADV
ejpam-4036	193	40	,	,	PUNCT
ejpam-4036	193	41	p	p	X
ejpam-4036	193	42	/	/	SYM
ejpam-4036	193	43	φ(p	φ(p	PROPN
ejpam-4036	193	44	)	)	PUNCT
ejpam-4036	193	45	is	be	AUX
ejpam-4036	193	46	a	a	DET
ejpam-4036	193	47	minimal	minimal	ADJ
ejpam-4036	193	48	normal	normal	ADJ
ejpam-4036	193	49	subgroup	subgroup	NOUN
ejpam-4036	193	50	of	of	ADP
ejpam-4036	193	51	g	g	PROPN
ejpam-4036	193	52	/	/	SYM
ejpam-4036	193	53	φ(p	φ(p	PROPN
ejpam-4036	193	54	)	)	PUNCT
ejpam-4036	193	55	.	.	PUNCT
ejpam-4036	194	1	now	now	ADV
ejpam-4036	194	2	we	we	PRON
ejpam-4036	194	3	have	have	VERB
ejpam-4036	194	4	:	:	PUNCT
ejpam-4036	194	5	(	(	PUNCT
ejpam-4036	194	6	1	1	X
ejpam-4036	194	7	)	)	PUNCT
ejpam-4036	194	8	p	p	NOUN
ejpam-4036	194	9	=	=	SYM
ejpam-4036	194	10	2	2	NUM
ejpam-4036	194	11	and	and	CCONJ
ejpam-4036	194	12	every	every	DET
ejpam-4036	194	13	element	element	NOUN
ejpam-4036	194	14	of	of	ADP
ejpam-4036	194	15	order	order	NOUN
ejpam-4036	194	16	4	4	NUM
ejpam-4036	194	17	is	be	AUX
ejpam-4036	194	18	css	css	NOUN
ejpam-4036	194	19	-	-	NOUN
ejpam-4036	194	20	subgroup	subgroup	NOUN
ejpam-4036	194	21	of	of	ADP
ejpam-4036	194	22	g.	g.	PROPN
ejpam-4036	194	23	assume	assume	VERB
ejpam-4036	194	24	that	that	SCONJ
ejpam-4036	194	25	p	p	X
ejpam-4036	194	26	>	>	X
ejpam-4036	194	27	2	2	NUM
ejpam-4036	194	28	.	.	PUNCT
ejpam-4036	194	29	by	by	ADP
ejpam-4036	194	30	lemma	lemma	PROPN
ejpam-4036	194	31	2	2	NUM
ejpam-4036	194	32	,	,	PUNCT
ejpam-4036	194	33	the	the	DET
ejpam-4036	194	34	exponent	exponent	NOUN
ejpam-4036	194	35	of	of	ADP
ejpam-4036	194	36	p	p	PROPN
ejpam-4036	194	37	is	be	AUX
ejpam-4036	194	38	p.	p.	NOUN
ejpam-4036	194	39	then	then	ADV
ejpam-4036	194	40	,	,	PUNCT
ejpam-4036	194	41	by	by	ADP
ejpam-4036	194	42	the	the	DET
ejpam-4036	194	43	hypotheses	hypothesis	NOUN
ejpam-4036	194	44	,	,	PUNCT
ejpam-4036	194	45	p	p	NOUN
ejpam-4036	194	46	6	6	NUM
ejpam-4036	194	47	z∞(g	z∞(g	NUM
ejpam-4036	194	48	)	)	PUNCT
ejpam-4036	194	49	.	.	PUNCT
ejpam-4036	195	1	applying	apply	VERB
ejpam-4036	195	2	lemma	lemma	PROPN
ejpam-4036	195	3	13	13	NUM
ejpam-4036	195	4	,	,	PUNCT
ejpam-4036	195	5	op(g	op(g	NUM
ejpam-4036	195	6	)	)	PUNCT
ejpam-4036	195	7	6	6	NUM
ejpam-4036	195	8	cg(p	cg(p	NUM
ejpam-4036	195	9	)	)	PUNCT
ejpam-4036	195	10	which	which	PRON
ejpam-4036	195	11	means	mean	VERB
ejpam-4036	195	12	that	that	SCONJ
ejpam-4036	195	13	g	g	PROPN
ejpam-4036	195	14	=	=	PROPN
ejpam-4036	195	15	pq	pq	PROPN
ejpam-4036	196	1	=	=	SYM
ejpam-4036	196	2	p	p	NOUN
ejpam-4036	196	3	×q	×q	NOUN
ejpam-4036	196	4	is	be	AUX
ejpam-4036	196	5	nilpotent	nilpotent	ADJ
ejpam-4036	196	6	,	,	PUNCT
ejpam-4036	196	7	a	a	DET
ejpam-4036	196	8	contradiction	contradiction	NOUN
ejpam-4036	196	9	.	.	PUNCT
ejpam-4036	197	1	if	if	SCONJ
ejpam-4036	197	2	every	every	DET
ejpam-4036	197	3	element	element	NOUN
ejpam-4036	197	4	of	of	ADP
ejpam-4036	197	5	order	order	NOUN
ejpam-4036	197	6	4	4	NUM
ejpam-4036	197	7	of	of	ADP
ejpam-4036	197	8	g	g	PROPN
ejpam-4036	197	9	lies	lie	VERB
ejpam-4036	197	10	in	in	ADP
ejpam-4036	197	11	z∞(g	z∞(g	NUM
ejpam-4036	197	12	)	)	PUNCT
ejpam-4036	197	13	,	,	PUNCT
ejpam-4036	197	14	then	then	ADV
ejpam-4036	197	15	p	p	X
ejpam-4036	197	16	6	6	NUM
ejpam-4036	197	17	z∞(g	z∞(g	NOUN
ejpam-4036	197	18	)	)	PUNCT
ejpam-4036	197	19	which	which	PRON
ejpam-4036	197	20	means	mean	VERB
ejpam-4036	197	21	that	that	SCONJ
ejpam-4036	197	22	g	g	PROPN
ejpam-4036	197	23	=	=	PROPN
ejpam-4036	197	24	pq	pq	PROPN
ejpam-4036	198	1	=	=	SYM
ejpam-4036	198	2	p	p	NOUN
ejpam-4036	198	3	×q	×q	NOUN
ejpam-4036	198	4	is	be	AUX
ejpam-4036	198	5	nilpotent	nilpotent	ADJ
ejpam-4036	198	6	,	,	PUNCT
ejpam-4036	198	7	again	again	ADV
ejpam-4036	198	8	contradiction	contradiction	NOUN
ejpam-4036	198	9	.	.	PUNCT
ejpam-4036	199	1	(	(	PUNCT
ejpam-4036	199	2	2	2	X
ejpam-4036	199	3	)	)	PUNCT
ejpam-4036	199	4	for	for	ADP
ejpam-4036	199	5	every	every	DET
ejpam-4036	199	6	x	x	SYM
ejpam-4036	199	7	∈	∈	PROPN
ejpam-4036	199	8	p	p	NOUN
ejpam-4036	199	9	\	\	PROPN
ejpam-4036	199	10	φ(p	φ(p	PROPN
ejpam-4036	199	11	)	)	PUNCT
ejpam-4036	199	12	,	,	PUNCT
ejpam-4036	199	13	|x|	|x|	PROPN
ejpam-4036	199	14	=	=	SYM
ejpam-4036	199	15	4	4	X
ejpam-4036	199	16	.	.	X
ejpam-4036	199	17	assume	assume	VERB
ejpam-4036	199	18	that	that	SCONJ
ejpam-4036	199	19	|x|	|x|	PROPN
ejpam-4036	199	20	6=	6=	ADP
ejpam-4036	199	21	4	4	NUM
ejpam-4036	199	22	.	.	PUNCT
ejpam-4036	200	1	then	then	ADV
ejpam-4036	200	2	there	there	PRON
ejpam-4036	200	3	exists	exist	VERB
ejpam-4036	200	4	x	x	X
ejpam-4036	200	5	∈	∈	PROPN
ejpam-4036	200	6	p	p	NOUN
ejpam-4036	200	7	\φ(p	\φ(p	VERB
ejpam-4036	200	8	)	)	PUNCT
ejpam-4036	200	9	and	and	CCONJ
ejpam-4036	200	10	|x|	|x|	PROPN
ejpam-4036	200	11	=	=	SYM
ejpam-4036	200	12	2	2	X
ejpam-4036	200	13	.	.	PUNCT
ejpam-4036	201	1	since	since	SCONJ
ejpam-4036	201	2	p	p	NOUN
ejpam-4036	201	3	eg	eg	NOUN
ejpam-4036	201	4	,	,	PUNCT
ejpam-4036	201	5	we	we	PRON
ejpam-4036	201	6	have	have	VERB
ejpam-4036	201	7	that	that	PRON
ejpam-4036	201	8	<	<	X
ejpam-4036	201	9	xg	xg	PROPN
ejpam-4036	201	10	>	>	PROPN
ejpam-4036	201	11	6	6	NUM
ejpam-4036	201	12	p	p	NOUN
ejpam-4036	201	13	.	.	PUNCT
ejpam-4036	202	1	then	then	ADV
ejpam-4036	202	2	<	<	X
ejpam-4036	202	3	xg	xg	X
ejpam-4036	202	4	>	>	X
ejpam-4036	202	5	φ(p	φ(p	PROPN
ejpam-4036	202	6	)	)	PUNCT
ejpam-4036	202	7	/φ(p	/φ(p	SYM
ejpam-4036	202	8	)	)	PUNCT
ejpam-4036	203	1	eg	eg	NOUN
ejpam-4036	203	2	/	/	SYM
ejpam-4036	203	3	φ(p	φ(p	PROPN
ejpam-4036	203	4	)	)	PUNCT
ejpam-4036	203	5	.	.	PUNCT
ejpam-4036	204	1	but	but	CCONJ
ejpam-4036	204	2	as	as	SCONJ
ejpam-4036	204	3	we	we	PRON
ejpam-4036	204	4	mentioned	mention	VERB
ejpam-4036	204	5	above	above	ADP
ejpam-4036	204	6	p	p	X
ejpam-4036	204	7	/	/	SYM
ejpam-4036	204	8	φ(p	φ(p	PROPN
ejpam-4036	204	9	)	)	PUNCT
ejpam-4036	204	10	is	be	AUX
ejpam-4036	204	11	a	a	DET
ejpam-4036	204	12	minimal	minimal	ADJ
ejpam-4036	204	13	normal	normal	ADJ
ejpam-4036	204	14	subgroup	subgroup	NOUN
ejpam-4036	204	15	of	of	ADP
ejpam-4036	204	16	g	g	PROPN
ejpam-4036	204	17	/	/	SYM
ejpam-4036	204	18	φ(p	φ(p	PROPN
ejpam-4036	204	19	)	)	PUNCT
ejpam-4036	204	20	.	.	PUNCT
ejpam-4036	205	1	then	then	ADV
ejpam-4036	205	2	p	p	X
ejpam-4036	205	3	=	=	X
ejpam-4036	205	4	<	<	X
ejpam-4036	205	5	xg	xg	X
ejpam-4036	205	6	>	>	X
ejpam-4036	205	7	φ(p	φ(p	PROPN
ejpam-4036	205	8	)	)	PUNCT
ejpam-4036	206	1	=	=	PUNCT
ejpam-4036	206	2	<	<	X
ejpam-4036	206	3	xg	xg	X
ejpam-4036	206	4	>	>	X
ejpam-4036	206	5	6	6	NUM
ejpam-4036	206	6	z∞(g	z∞(g	NUM
ejpam-4036	206	7	)	)	PUNCT
ejpam-4036	206	8	.	.	PUNCT
ejpam-4036	207	1	in	in	ADP
ejpam-4036	207	2	particular	particular	ADJ
ejpam-4036	207	3	;	;	PUNCT
ejpam-4036	207	4	g	g	PROPN
ejpam-4036	207	5	is	be	AUX
ejpam-4036	207	6	nilpotent	nilpotent	ADJ
ejpam-4036	207	7	,	,	PUNCT
ejpam-4036	207	8	a	a	DET
ejpam-4036	207	9	contradiction	contradiction	NOUN
ejpam-4036	207	10	.	.	PUNCT
ejpam-4036	208	1	(	(	PUNCT
ejpam-4036	208	2	3	3	X
ejpam-4036	208	3	)	)	PUNCT
ejpam-4036	208	4	finishing	finish	VERB
ejpam-4036	208	5	the	the	DET
ejpam-4036	208	6	proof	proof	NOUN
ejpam-4036	208	7	.	.	PUNCT
ejpam-4036	209	1	from	from	ADP
ejpam-4036	209	2	2	2	NUM
ejpam-4036	209	3	,	,	PUNCT
ejpam-4036	209	4	every	every	DET
ejpam-4036	209	5	element	element	NOUN
ejpam-4036	209	6	x	x	PUNCT
ejpam-4036	209	7	in	in	ADP
ejpam-4036	209	8	p	p	NOUN
ejpam-4036	209	9	\	\	PUNCT
ejpam-4036	209	10	φ(p	φ(p	PROPN
ejpam-4036	209	11	)	)	PUNCT
ejpam-4036	209	12	is	be	AUX
ejpam-4036	209	13	of	of	ADP
ejpam-4036	209	14	order	order	NOUN
ejpam-4036	209	15	4	4	NUM
ejpam-4036	209	16	.	.	PUNCT
ejpam-4036	209	17	from	from	ADP
ejpam-4036	209	18	1	1	NUM
ejpam-4036	209	19	,	,	PUNCT
ejpam-4036	209	20	<	<	X
ejpam-4036	209	21	x	x	X
ejpam-4036	209	22	>	>	X
ejpam-4036	209	23	is	be	AUX
ejpam-4036	209	24	csssubgroup	csssubgroup	NOUN
ejpam-4036	209	25	of	of	ADP
ejpam-4036	209	26	g.	g.	PROPN
ejpam-4036	210	1	then	then	ADV
ejpam-4036	210	2	there	there	PRON
ejpam-4036	210	3	exists	exist	VERB
ejpam-4036	210	4	a	a	DET
ejpam-4036	210	5	normal	normal	ADJ
ejpam-4036	210	6	subgroup	subgroup	NOUN
ejpam-4036	210	7	s	s	PROPN
ejpam-4036	210	8	of	of	ADP
ejpam-4036	210	9	g	g	NOUN
ejpam-4036	210	10	such	such	ADJ
ejpam-4036	210	11	that	that	SCONJ
ejpam-4036	210	12	g	g	PROPN
ejpam-4036	210	13	=	=	NOUN
ejpam-4036	210	14	<	<	X
ejpam-4036	210	15	x	x	X
ejpam-4036	210	16	>	>	X
ejpam-4036	210	17	s	s	PROPN
ejpam-4036	210	18	and	and	CCONJ
ejpam-4036	210	19	<	<	X
ejpam-4036	210	20	x	x	X
ejpam-4036	210	21	>	>	X
ejpam-4036	210	22	∩s	∩s	PROPN
ejpam-4036	210	23	is	be	AUX
ejpam-4036	210	24	ss	ss	NOUN
ejpam-4036	210	25	-	-	ADJ
ejpam-4036	210	26	quasinormal	quasinormal	ADJ
ejpam-4036	210	27	in	in	ADP
ejpam-4036	210	28	g.	g.	PROPN
ejpam-4036	210	29	clearly	clearly	ADV
ejpam-4036	210	30	,	,	PUNCT
ejpam-4036	210	31	p	p	PROPN
ejpam-4036	210	32	∩	∩	PROPN
ejpam-4036	210	33	s	s	PART
ejpam-4036	210	34	e	e	NOUN
ejpam-4036	210	35	g.	g.	NOUN
ejpam-4036	210	36	hence	hence	ADV
ejpam-4036	210	37	,	,	PUNCT
ejpam-4036	210	38	(	(	PUNCT
ejpam-4036	210	39	p∩s)φ(p	p∩s)φ(p	ADJ
ejpam-4036	210	40	)	)	PUNCT
ejpam-4036	210	41	/φ(p	/φ(p	SYM
ejpam-4036	210	42	)	)	PUNCT
ejpam-4036	210	43	eg	eg	NOUN
ejpam-4036	210	44	/	/	SYM
ejpam-4036	210	45	φ(p	φ(p	PROPN
ejpam-4036	210	46	)	)	PUNCT
ejpam-4036	210	47	.	.	PUNCT
ejpam-4036	211	1	since	since	SCONJ
ejpam-4036	211	2	p	p	X
ejpam-4036	211	3	/	/	SYM
ejpam-4036	211	4	φ(p	φ(p	PROPN
ejpam-4036	211	5	)	)	PUNCT
ejpam-4036	211	6	is	be	AUX
ejpam-4036	211	7	a	a	DET
ejpam-4036	211	8	minimal	minimal	ADJ
ejpam-4036	211	9	normal	normal	ADJ
ejpam-4036	211	10	subgroup	subgroup	NOUN
ejpam-4036	211	11	g	g	PROPN
ejpam-4036	211	12	/	/	SYM
ejpam-4036	211	13	φ(p	φ(p	PROPN
ejpam-4036	211	14	)	)	PUNCT
ejpam-4036	211	15	,	,	PUNCT
ejpam-4036	211	16	it	it	PRON
ejpam-4036	211	17	follows	follow	VERB
ejpam-4036	211	18	that	that	SCONJ
ejpam-4036	211	19	either	either	CCONJ
ejpam-4036	211	20	p	p	PROPN
ejpam-4036	211	21	∩	∩	X
ejpam-4036	211	22	s	s	PART
ejpam-4036	211	23	6	6	NUM
ejpam-4036	211	24	φ(p	φ(p	PROPN
ejpam-4036	211	25	)	)	PUNCT
ejpam-4036	211	26	or	or	CCONJ
ejpam-4036	211	27	p	p	NOUN
ejpam-4036	211	28	∩	∩	NOUN
ejpam-4036	211	29	s	s	PART
ejpam-4036	211	30	=	=	X
ejpam-4036	211	31	p	p	PROPN
ejpam-4036	211	32	.	.	PUNCT
ejpam-4036	212	1	assume	assume	VERB
ejpam-4036	212	2	first	first	ADV
ejpam-4036	212	3	that	that	SCONJ
ejpam-4036	212	4	p	p	PROPN
ejpam-4036	212	5	∩	∩	X
ejpam-4036	212	6	s	s	PART
ejpam-4036	212	7	6	6	NUM
ejpam-4036	212	8	φ(p	φ(p	PROPN
ejpam-4036	212	9	)	)	PUNCT
ejpam-4036	212	10	.	.	PUNCT
ejpam-4036	213	1	then	then	ADV
ejpam-4036	213	2	p	p	NOUN
ejpam-4036	213	3	=	=	PUNCT
ejpam-4036	213	4	p	p	PROPN
ejpam-4036	213	5	∩	∩	NOUN
ejpam-4036	213	6	g	g	NOUN
ejpam-4036	213	7	=	=	SYM
ejpam-4036	213	8	p	p	PROPN
ejpam-4036	213	9	∩	∩	NOUN
ejpam-4036	213	10	(	(	PUNCT
ejpam-4036	213	11	<	<	X
ejpam-4036	213	12	x	x	X
ejpam-4036	213	13	>	>	X
ejpam-4036	213	14	s	s	X
ejpam-4036	213	15	)	)	PUNCT
ejpam-4036	213	16	=	=	NOUN
ejpam-4036	213	17	<	<	X
ejpam-4036	213	18	x	x	X
ejpam-4036	213	19	>	>	X
ejpam-4036	213	20	(	(	PUNCT
ejpam-4036	213	21	p	p	X
ejpam-4036	213	22	∩	∩	X
ejpam-4036	213	23	s	s	PART
ejpam-4036	213	24	)	)	PUNCT
ejpam-4036	213	25	=	=	NOUN
ejpam-4036	213	26	<	<	X
ejpam-4036	213	27	x	x	X
ejpam-4036	213	28	>	>	X
ejpam-4036	213	29	φ(p	φ(p	PROPN
ejpam-4036	213	30	)	)	PUNCT
ejpam-4036	213	31	.	.	PUNCT
ejpam-4036	214	1	therefore	therefore	ADV
ejpam-4036	214	2	,	,	PUNCT
ejpam-4036	214	3	p	p	NOUN
ejpam-4036	214	4	=	=	X
ejpam-4036	214	5	<	<	X
ejpam-4036	214	6	x	x	X
ejpam-4036	214	7	>	>	X
ejpam-4036	214	8	and	and	CCONJ
ejpam-4036	214	9	this	this	PRON
ejpam-4036	214	10	means	mean	VERB
ejpam-4036	214	11	that	that	SCONJ
ejpam-4036	214	12	p	p	NOUN
ejpam-4036	214	13	is	be	AUX
ejpam-4036	214	14	a	a	DET
ejpam-4036	214	15	cyclic	cyclic	ADJ
ejpam-4036	214	16	normal	normal	ADJ
ejpam-4036	214	17	sylow	sylow	NOUN
ejpam-4036	214	18	2	2	NUM
ejpam-4036	214	19	-	-	PUNCT
ejpam-4036	214	20	subgroup	subgroup	NOUN
ejpam-4036	214	21	of	of	ADP
ejpam-4036	214	22	g	g	NOUN
ejpam-4036	214	23	of	of	ADP
ejpam-4036	214	24	order	order	NOUN
ejpam-4036	214	25	4	4	NUM
ejpam-4036	214	26	.	.	PUNCT
ejpam-4036	214	27	by	by	ADP
ejpam-4036	214	28	lemma	lemma	PROPN
ejpam-4036	214	29	14	14	NUM
ejpam-4036	214	30	,	,	PUNCT
ejpam-4036	214	31	g	g	PROPN
ejpam-4036	214	32	is	be	AUX
ejpam-4036	214	33	2	2	NUM
ejpam-4036	214	34	-	-	PUNCT
ejpam-4036	214	35	nilpotent	nilpotent	NOUN
ejpam-4036	214	36	and	and	CCONJ
ejpam-4036	214	37	so	so	ADV
ejpam-4036	214	38	g	g	PROPN
ejpam-4036	214	39	=	=	PROPN
ejpam-4036	214	40	pq	pq	PROPN
ejpam-4036	214	41	=	=	SYM
ejpam-4036	214	42	p×q	p×q	PROPN
ejpam-4036	214	43	is	be	AUX
ejpam-4036	214	44	nilpotent	nilpotent	ADJ
ejpam-4036	214	45	,	,	PUNCT
ejpam-4036	214	46	a	a	DET
ejpam-4036	214	47	contradiction	contradiction	NOUN
ejpam-4036	214	48	.	.	PUNCT
ejpam-4036	215	1	thus	thus	ADV
ejpam-4036	215	2	,	,	PUNCT
ejpam-4036	215	3	assume	assume	VERB
ejpam-4036	215	4	that	that	SCONJ
ejpam-4036	215	5	p	p	PROPN
ejpam-4036	215	6	∩	∩	NOUN
ejpam-4036	215	7	s	s	PART
ejpam-4036	215	8	=	=	X
ejpam-4036	215	9	p	p	X
ejpam-4036	215	10	.	.	PUNCT
ejpam-4036	216	1	then	then	ADV
ejpam-4036	216	2	<	<	X
ejpam-4036	216	3	x	x	X
ejpam-4036	216	4	>	>	PUNCT
ejpam-4036	216	5	=	=	X
ejpam-4036	216	6	<	<	X
ejpam-4036	216	7	x	x	X
ejpam-4036	216	8	>	>	X
ejpam-4036	216	9	∩p	∩p	X
ejpam-4036	217	1	=	=	SYM
ejpam-4036	217	2	<	<	X
ejpam-4036	217	3	x	x	X
ejpam-4036	217	4	>	>	X
ejpam-4036	217	5	∩(p	∩(p	PROPN
ejpam-4036	217	6	∩	∩	NOUN
ejpam-4036	217	7	s	s	PART
ejpam-4036	217	8	)	)	PUNCT
ejpam-4036	217	9	=	=	PUNCT
ejpam-4036	217	10	(	(	PUNCT
ejpam-4036	217	11	<	<	X
ejpam-4036	217	12	x	x	X
ejpam-4036	217	13	>	>	X
ejpam-4036	217	14	∩p	∩p	NOUN
ejpam-4036	217	15	)	)	PUNCT
ejpam-4036	217	16	∩	∩	PROPN
ejpam-4036	217	17	s	s	PART
ejpam-4036	217	18	=	=	NOUN
ejpam-4036	217	19	<	<	X
ejpam-4036	217	20	x	x	X
ejpam-4036	217	21	>	>	X
ejpam-4036	217	22	∩s	∩s	PROPN
ejpam-4036	217	23	.	.	PUNCT
ejpam-4036	218	1	hence	hence	ADV
ejpam-4036	218	2	,	,	PUNCT
ejpam-4036	218	3	<	<	X
ejpam-4036	218	4	x	x	X
ejpam-4036	218	5	>	>	X
ejpam-4036	218	6	is	be	AUX
ejpam-4036	218	7	ss	ss	NOUN
ejpam-4036	218	8	-	-	ADJ
ejpam-4036	218	9	quasinormal	quasinormal	ADJ
ejpam-4036	218	10	in	in	ADP
ejpam-4036	218	11	g.	g.	PROPN
ejpam-4036	218	12	<	<	X
ejpam-4036	218	13	x	x	X
ejpam-4036	218	14	>	>	X
ejpam-4036	218	15	6	6	NUM
ejpam-4036	218	16	p	p	X
ejpam-4036	218	17	e	e	X
ejpam-4036	218	18	g	g	PROPN
ejpam-4036	218	19	a.	a.	NOUN
ejpam-4036	218	20	heliel	heliel	PROPN
ejpam-4036	218	21	,	,	PUNCT
ejpam-4036	218	22	r.	r.	PROPN
ejpam-4036	218	23	hijazi	hijazi	PROPN
ejpam-4036	218	24	,	,	PUNCT
ejpam-4036	218	25	s.	s.	PROPN
ejpam-4036	218	26	al	al	PROPN
ejpam-4036	218	27	-	-	PUNCT
ejpam-4036	218	28	shammari	shammari	PROPN
ejpam-4036	218	29	/	/	SYM
ejpam-4036	218	30	eur	eur	PROPN
ejpam-4036	218	31	.	.	PUNCT
ejpam-4036	219	1	j.	j.	PROPN
ejpam-4036	219	2	pure	pure	PROPN
ejpam-4036	219	3	appl	appl	PROPN
ejpam-4036	219	4	.	.	PROPN
ejpam-4036	219	5	math	math	PROPN
ejpam-4036	219	6	,	,	PUNCT
ejpam-4036	219	7	14	14	NUM
ejpam-4036	219	8	(	(	PUNCT
ejpam-4036	219	9	3	3	NUM
ejpam-4036	219	10	)	)	PUNCT
ejpam-4036	219	11	(	(	PUNCT
ejpam-4036	219	12	2021	2021	NUM
ejpam-4036	219	13	)	)	PUNCT
ejpam-4036	219	14	,	,	PUNCT
ejpam-4036	219	15	1002	1002	NUM
ejpam-4036	219	16	-	-	SYM
ejpam-4036	219	17	1014	1014	NUM
ejpam-4036	219	18	1009	1009	NUM
ejpam-4036	219	19	implies	imply	VERB
ejpam-4036	219	20	that	that	SCONJ
ejpam-4036	219	21	<	<	X
ejpam-4036	219	22	x	x	X
ejpam-4036	219	23	>	>	X
ejpam-4036	219	24	is	be	AUX
ejpam-4036	219	25	subnormal	subnormal	ADJ
ejpam-4036	219	26	in	in	ADP
ejpam-4036	219	27	g.	g.	PROPN
ejpam-4036	219	28	by	by	ADP
ejpam-4036	219	29	lemma	lemma	PROPN
ejpam-4036	219	30	4	4	NUM
ejpam-4036	219	31	,	,	PUNCT
ejpam-4036	219	32	<	<	X
ejpam-4036	219	33	x	x	X
ejpam-4036	219	34	>	>	X
ejpam-4036	219	35	6	6	NUM
ejpam-4036	219	36	o2(g	o2(g	NUM
ejpam-4036	219	37	)	)	PUNCT
ejpam-4036	219	38	.	.	PUNCT
ejpam-4036	220	1	applying	apply	VERB
ejpam-4036	220	2	lemma	lemma	PROPN
ejpam-4036	220	3	5	5	NUM
ejpam-4036	220	4	,	,	PUNCT
ejpam-4036	220	5	<	<	X
ejpam-4036	220	6	x	x	X
ejpam-4036	220	7	>	>	X
ejpam-4036	220	8	is	be	AUX
ejpam-4036	220	9	s	s	NOUN
ejpam-4036	220	10	-	-	ADJ
ejpam-4036	220	11	quasinormal	quasinormal	ADJ
ejpam-4036	220	12	in	in	ADP
ejpam-4036	220	13	g.	g.	PROPN
ejpam-4036	220	14	thus	thus	ADV
ejpam-4036	220	15	,	,	PUNCT
ejpam-4036	220	16	<	<	X
ejpam-4036	220	17	x	x	X
ejpam-4036	220	18	>	>	X
ejpam-4036	220	19	q	q	PROPN
ejpam-4036	220	20	6	6	NUM
ejpam-4036	220	21	g.	g.	NOUN
ejpam-4036	220	22	if	if	SCONJ
ejpam-4036	220	23	<	<	X
ejpam-4036	220	24	x	x	X
ejpam-4036	220	25	>	>	X
ejpam-4036	220	26	q	q	PROPN
ejpam-4036	221	1	=	=	SYM
ejpam-4036	221	2	g	g	NOUN
ejpam-4036	221	3	,	,	PUNCT
ejpam-4036	221	4	then	then	ADV
ejpam-4036	221	5	<	<	X
ejpam-4036	221	6	x	x	X
ejpam-4036	221	7	>	>	PUNCT
ejpam-4036	221	8	=	=	PUNCT
ejpam-4036	221	9	p	p	X
ejpam-4036	221	10	which	which	PRON
ejpam-4036	221	11	implies	imply	VERB
ejpam-4036	221	12	g	g	PROPN
ejpam-4036	221	13	is	be	AUX
ejpam-4036	221	14	nilpotent	nilpotent	ADJ
ejpam-4036	221	15	,	,	PUNCT
ejpam-4036	221	16	a	a	DET
ejpam-4036	221	17	contradiction	contradiction	NOUN
ejpam-4036	221	18	.	.	PUNCT
ejpam-4036	222	1	therefore	therefore	ADV
ejpam-4036	222	2	,	,	PUNCT
ejpam-4036	222	3	<	<	X
ejpam-4036	222	4	x	x	X
ejpam-4036	222	5	>	>	X
ejpam-4036	222	6	q	q	X
ejpam-4036	222	7	<	<	X
ejpam-4036	222	8	g	g	NOUN
ejpam-4036	222	9	and	and	CCONJ
ejpam-4036	222	10	it	it	PRON
ejpam-4036	222	11	follows	follow	VERB
ejpam-4036	222	12	that	that	SCONJ
ejpam-4036	222	13	<	<	X
ejpam-4036	222	14	x	x	X
ejpam-4036	222	15	>	>	X
ejpam-4036	222	16	q	q	X
ejpam-4036	222	17	is	be	AUX
ejpam-4036	222	18	nilpotent	nilpotent	ADJ
ejpam-4036	222	19	.	.	PUNCT
ejpam-4036	223	1	then	then	ADV
ejpam-4036	223	2	<	<	X
ejpam-4036	223	3	x	x	X
ejpam-4036	223	4	>	>	X
ejpam-4036	223	5	q	q	PROPN
ejpam-4036	224	1	=	=	X
ejpam-4036	224	2	<	<	X
ejpam-4036	224	3	x	x	X
ejpam-4036	224	4	>	>	X
ejpam-4036	224	5	×q	×q	PROPN
ejpam-4036	224	6	.	.	PUNCT
ejpam-4036	225	1	thus	thus	ADV
ejpam-4036	225	2	,	,	PUNCT
ejpam-4036	225	3	<	<	X
ejpam-4036	225	4	x	x	X
ejpam-4036	225	5	>	>	X
ejpam-4036	225	6	6	6	NUM
ejpam-4036	225	7	ng(q	ng(q	NOUN
ejpam-4036	225	8	)	)	PUNCT
ejpam-4036	225	9	implies	imply	VERB
ejpam-4036	225	10	that	that	SCONJ
ejpam-4036	225	11	p	p	PROPN
ejpam-4036	225	12	6	6	NUM
ejpam-4036	225	13	ng(q	ng(q	NOUN
ejpam-4036	225	14	)	)	PUNCT
ejpam-4036	225	15	and	and	CCONJ
ejpam-4036	226	1	so	so	ADV
ejpam-4036	226	2	g	g	PROPN
ejpam-4036	226	3	=	=	PROPN
ejpam-4036	226	4	pq	pq	PROPN
ejpam-4036	227	1	=	=	SYM
ejpam-4036	228	1	p	p	NOUN
ejpam-4036	228	2	×	×	NOUN
ejpam-4036	228	3	q	q	NOUN
ejpam-4036	228	4	is	be	AUX
ejpam-4036	228	5	nilpotent	nilpotent	ADJ
ejpam-4036	228	6	,	,	PUNCT
ejpam-4036	228	7	a	a	DET
ejpam-4036	228	8	final	final	ADJ
ejpam-4036	228	9	contradiction	contradiction	NOUN
ejpam-4036	228	10	completing	complete	VERB
ejpam-4036	228	11	the	the	DET
ejpam-4036	228	12	proof	proof	NOUN
ejpam-4036	228	13	.	.	PUNCT
ejpam-4036	229	1	theorem	theorem	ADJ
ejpam-4036	229	2	5	5	NUM
ejpam-4036	229	3	.	.	PUNCT
ejpam-4036	230	1	let	let	VERB
ejpam-4036	230	2	h	h	PRON
ejpam-4036	230	3	be	be	AUX
ejpam-4036	230	4	a	a	DET
ejpam-4036	230	5	normal	normal	ADJ
ejpam-4036	230	6	subgroup	subgroup	NOUN
ejpam-4036	230	7	of	of	ADP
ejpam-4036	230	8	g	g	PROPN
ejpam-4036	230	9	such	such	ADJ
ejpam-4036	230	10	that	that	SCONJ
ejpam-4036	230	11	g	g	NOUN
ejpam-4036	230	12	/	/	SYM
ejpam-4036	230	13	h	h	NOUN
ejpam-4036	230	14	is	be	AUX
ejpam-4036	230	15	nilpotent	nilpotent	ADJ
ejpam-4036	230	16	.	.	PUNCT
ejpam-4036	231	1	if	if	SCONJ
ejpam-4036	231	2	every	every	DET
ejpam-4036	231	3	subgroup	subgroup	NOUN
ejpam-4036	231	4	of	of	ADP
ejpam-4036	231	5	h	h	PROPN
ejpam-4036	231	6	of	of	ADP
ejpam-4036	231	7	prime	prime	ADJ
ejpam-4036	231	8	order	order	NOUN
ejpam-4036	231	9	is	be	AUX
ejpam-4036	231	10	contained	contain	VERB
ejpam-4036	231	11	in	in	ADP
ejpam-4036	231	12	z∞(g	z∞(g	NUM
ejpam-4036	231	13	)	)	PUNCT
ejpam-4036	231	14	and	and	CCONJ
ejpam-4036	231	15	every	every	DET
ejpam-4036	231	16	cyclic	cyclic	ADJ
ejpam-4036	231	17	subgroup	subgroup	NOUN
ejpam-4036	231	18	of	of	ADP
ejpam-4036	231	19	order	order	NOUN
ejpam-4036	231	20	4	4	NUM
ejpam-4036	231	21	of	of	ADP
ejpam-4036	231	22	h	h	NOUN
ejpam-4036	231	23	is	be	AUX
ejpam-4036	231	24	css	css	PROPN
ejpam-4036	231	25	-	-	NOUN
ejpam-4036	231	26	subgroup	subgroup	NOUN
ejpam-4036	231	27	of	of	ADP
ejpam-4036	231	28	g	g	PROPN
ejpam-4036	231	29	or	or	CCONJ
ejpam-4036	231	30	lies	lie	NOUN
ejpam-4036	231	31	in	in	ADP
ejpam-4036	231	32	z∞(g	z∞(g	NUM
ejpam-4036	231	33	)	)	PUNCT
ejpam-4036	231	34	,	,	PUNCT
ejpam-4036	231	35	then	then	ADV
ejpam-4036	231	36	g	g	PROPN
ejpam-4036	231	37	is	be	AUX
ejpam-4036	231	38	nilpotent	nilpotent	ADJ
ejpam-4036	231	39	.	.	PUNCT
ejpam-4036	232	1	proof	proof	NOUN
ejpam-4036	232	2	.	.	PUNCT
ejpam-4036	233	1	assume	assume	VERB
ejpam-4036	233	2	that	that	SCONJ
ejpam-4036	233	3	the	the	DET
ejpam-4036	233	4	result	result	NOUN
ejpam-4036	233	5	is	be	AUX
ejpam-4036	233	6	false	false	ADJ
ejpam-4036	233	7	and	and	CCONJ
ejpam-4036	233	8	let	let	VERB
ejpam-4036	233	9	g	g	PRON
ejpam-4036	233	10	be	be	AUX
ejpam-4036	233	11	a	a	DET
ejpam-4036	233	12	counterexample	counterexample	NOUN
ejpam-4036	233	13	of	of	ADP
ejpam-4036	233	14	minimal	minimal	ADJ
ejpam-4036	233	15	order	order	NOUN
ejpam-4036	233	16	.	.	PUNCT
ejpam-4036	234	1	let	let	VERB
ejpam-4036	234	2	l	l	NOUN
ejpam-4036	234	3	be	be	AUX
ejpam-4036	234	4	an	an	DET
ejpam-4036	234	5	arbitrary	arbitrary	ADJ
ejpam-4036	234	6	proper	proper	ADJ
ejpam-4036	234	7	subgroup	subgroup	NOUN
ejpam-4036	234	8	of	of	ADP
ejpam-4036	234	9	g.	g.	PROPN
ejpam-4036	234	10	since	since	SCONJ
ejpam-4036	234	11	g	g	PROPN
ejpam-4036	234	12	/	/	SYM
ejpam-4036	234	13	h	h	NOUN
ejpam-4036	234	14	is	be	AUX
ejpam-4036	234	15	nilpotent	nilpotent	ADJ
ejpam-4036	234	16	,	,	PUNCT
ejpam-4036	234	17	we	we	PRON
ejpam-4036	234	18	have	have	VERB
ejpam-4036	234	19	l	l	NOUN
ejpam-4036	234	20	/	/	SYM
ejpam-4036	234	21	l	l	NOUN
ejpam-4036	234	22	∩	∩	ADJ
ejpam-4036	234	23	h	h	NOUN
ejpam-4036	234	24	∼=	∼=	PROPN
ejpam-4036	234	25	lh	lh	PROPN
ejpam-4036	234	26	/	/	SYM
ejpam-4036	234	27	h	h	NOUN
ejpam-4036	234	28	is	be	AUX
ejpam-4036	234	29	nilpotent	nilpotent	ADJ
ejpam-4036	234	30	.	.	PUNCT
ejpam-4036	235	1	the	the	DET
ejpam-4036	235	2	element	element	NOUN
ejpam-4036	235	3	of	of	ADP
ejpam-4036	235	4	prime	prime	ADJ
ejpam-4036	235	5	order	order	NOUN
ejpam-4036	235	6	or	or	CCONJ
ejpam-4036	235	7	of	of	ADP
ejpam-4036	235	8	order	order	NOUN
ejpam-4036	235	9	4	4	NUM
ejpam-4036	235	10	of	of	ADP
ejpam-4036	235	11	l	l	NOUN
ejpam-4036	235	12	∩	∩	ADJ
ejpam-4036	235	13	h	h	NOUN
ejpam-4036	235	14	is	be	AUX
ejpam-4036	235	15	contained	contain	VERB
ejpam-4036	235	16	in	in	ADP
ejpam-4036	235	17	z∞(g)∩l	z∞(g)∩l	NOUN
ejpam-4036	235	18	6	6	NUM
ejpam-4036	235	19	z∞(l	z∞(l	NOUN
ejpam-4036	235	20	)	)	PUNCT
ejpam-4036	235	21	.	.	PUNCT
ejpam-4036	236	1	by	by	ADP
ejpam-4036	236	2	hypotheses	hypothesis	NOUN
ejpam-4036	236	3	and	and	CCONJ
ejpam-4036	236	4	lemma	lemma	PROPN
ejpam-4036	236	5	11	11	NUM
ejpam-4036	236	6	,	,	PUNCT
ejpam-4036	236	7	every	every	DET
ejpam-4036	236	8	cyclic	cyclic	ADJ
ejpam-4036	236	9	subgroup	subgroup	NOUN
ejpam-4036	236	10	of	of	ADP
ejpam-4036	236	11	order	order	NOUN
ejpam-4036	236	12	4	4	NUM
ejpam-4036	236	13	of	of	ADP
ejpam-4036	236	14	l∩h	l∩h	PROPN
ejpam-4036	236	15	is	be	AUX
ejpam-4036	236	16	css	css	NOUN
ejpam-4036	236	17	-	-	NOUN
ejpam-4036	236	18	subgroup	subgroup	NOUN
ejpam-4036	236	19	in	in	ADP
ejpam-4036	236	20	l.	l.	PROPN
ejpam-4036	236	21	thus	thus	ADV
ejpam-4036	236	22	the	the	DET
ejpam-4036	236	23	pair	pair	NOUN
ejpam-4036	236	24	(	(	PUNCT
ejpam-4036	236	25	l	l	NOUN
ejpam-4036	236	26	,	,	PUNCT
ejpam-4036	236	27	l∩h	l∩h	ADJ
ejpam-4036	236	28	)	)	PUNCT
ejpam-4036	236	29	satisfies	satisfy	VERB
ejpam-4036	236	30	the	the	DET
ejpam-4036	236	31	hypotheses	hypothesis	NOUN
ejpam-4036	236	32	of	of	ADP
ejpam-4036	236	33	the	the	DET
ejpam-4036	236	34	theorem	theorem	NOUN
ejpam-4036	236	35	in	in	ADP
ejpam-4036	236	36	any	any	DET
ejpam-4036	236	37	case	case	NOUN
ejpam-4036	236	38	.	.	PUNCT
ejpam-4036	237	1	then	then	ADV
ejpam-4036	237	2	l	l	NOUN
ejpam-4036	237	3	is	be	AUX
ejpam-4036	237	4	nilpotent	nilpotent	ADJ
ejpam-4036	237	5	,	,	PUNCT
ejpam-4036	237	6	that	that	ADV
ejpam-4036	237	7	is	is	ADV
ejpam-4036	237	8	,	,	PUNCT
ejpam-4036	237	9	g	g	PROPN
ejpam-4036	237	10	is	be	AUX
ejpam-4036	237	11	a	a	DET
ejpam-4036	237	12	minimal	minimal	ADJ
ejpam-4036	237	13	non	non	ADJ
ejpam-4036	237	14	-	-	ADJ
ejpam-4036	237	15	nilpotent	nilpotent	ADJ
ejpam-4036	237	16	group	group	NOUN
ejpam-4036	237	17	.	.	PUNCT
ejpam-4036	238	1	applying	apply	VERB
ejpam-4036	238	2	lemma	lemma	PROPN
ejpam-4036	238	3	2	2	NUM
ejpam-4036	238	4	,	,	PUNCT
ejpam-4036	238	5	g	g	PROPN
ejpam-4036	238	6	=	=	SYM
ejpam-4036	238	7	pq	pq	PROPN
ejpam-4036	238	8	,	,	PUNCT
ejpam-4036	238	9	where	where	SCONJ
ejpam-4036	238	10	p	p	NOUN
ejpam-4036	238	11	is	be	AUX
ejpam-4036	238	12	normal	normal	ADJ
ejpam-4036	238	13	sylow	sylow	NOUN
ejpam-4036	238	14	p	p	PROPN
ejpam-4036	238	15	-	-	PUNCT
ejpam-4036	238	16	subgroup	subgroup	NOUN
ejpam-4036	238	17	of	of	ADP
ejpam-4036	238	18	g	g	PROPN
ejpam-4036	238	19	and	and	CCONJ
ejpam-4036	238	20	q	q	PROPN
ejpam-4036	238	21	is	be	AUX
ejpam-4036	238	22	non	non	ADJ
ejpam-4036	238	23	normal	normal	ADJ
ejpam-4036	238	24	cyclic	cyclic	ADJ
ejpam-4036	238	25	sylow	sylow	NOUN
ejpam-4036	238	26	q	q	NOUN
ejpam-4036	238	27	-	-	NOUN
ejpam-4036	238	28	subgroup	subgroup	NOUN
ejpam-4036	238	29	of	of	ADP
ejpam-4036	238	30	g	g	PROPN
ejpam-4036	238	31	,	,	PUNCT
ejpam-4036	238	32	p	p	PROPN
ejpam-4036	238	33	6=	6=	NUM
ejpam-4036	238	34	q.	q.	NOUN
ejpam-4036	238	35	since	since	SCONJ
ejpam-4036	238	36	g	g	PROPN
ejpam-4036	238	37	/	/	SYM
ejpam-4036	238	38	h	h	NOUN
ejpam-4036	238	39	and	and	CCONJ
ejpam-4036	238	40	g	g	NOUN
ejpam-4036	238	41	/	/	SYM
ejpam-4036	238	42	p	p	NOUN
ejpam-4036	238	43	are	be	AUX
ejpam-4036	238	44	nilpotent	nilpotent	ADJ
ejpam-4036	238	45	,	,	PUNCT
ejpam-4036	238	46	then	then	ADV
ejpam-4036	238	47	g	g	PROPN
ejpam-4036	238	48	/	/	SYM
ejpam-4036	238	49	p	p	NOUN
ejpam-4036	238	50	∩h	∩h	PROPN
ejpam-4036	238	51	6	6	NUM
ejpam-4036	238	52	g	g	NOUN
ejpam-4036	238	53	/	/	SYM
ejpam-4036	238	54	p	p	NOUN
ejpam-4036	238	55	×	×	NOUN
ejpam-4036	238	56	g	g	NOUN
ejpam-4036	238	57	/	/	SYM
ejpam-4036	238	58	h	h	NOUN
ejpam-4036	238	59	is	be	AUX
ejpam-4036	238	60	nilpotent	nilpotent	ADJ
ejpam-4036	238	61	.	.	PUNCT
ejpam-4036	239	1	now	now	ADV
ejpam-4036	239	2	we	we	PRON
ejpam-4036	239	3	deal	deal	VERB
ejpam-4036	239	4	with	with	ADP
ejpam-4036	239	5	:	:	PUNCT
ejpam-4036	239	6	(	(	PUNCT
ejpam-4036	239	7	1	1	X
ejpam-4036	239	8	)	)	PUNCT
ejpam-4036	239	9	p	p	NOUN
ejpam-4036	239	10	6	6	NUM
ejpam-4036	239	11	h.	h.	NOUN
ejpam-4036	239	12	assume	assume	VERB
ejpam-4036	239	13	that	that	SCONJ
ejpam-4036	239	14	p	p	X
ejpam-4036	239	15	>	>	X
ejpam-4036	239	16	2	2	NUM
ejpam-4036	239	17	.	.	PUNCT
ejpam-4036	239	18	then	then	ADV
ejpam-4036	239	19	,	,	PUNCT
ejpam-4036	239	20	by	by	ADP
ejpam-4036	239	21	lemma	lemma	PROPN
ejpam-4036	239	22	2	2	NUM
ejpam-4036	239	23	,	,	PUNCT
ejpam-4036	239	24	the	the	DET
ejpam-4036	239	25	exponent	exponent	NOUN
ejpam-4036	239	26	of	of	ADP
ejpam-4036	239	27	p	p	PROPN
ejpam-4036	239	28	is	be	AUX
ejpam-4036	239	29	p	p	NOUN
ejpam-4036	240	1	and	and	CCONJ
ejpam-4036	241	1	so	so	ADV
ejpam-4036	241	2	p	p	NOUN
ejpam-4036	241	3	=	=	NOUN
ejpam-4036	241	4	p	p	NOUN
ejpam-4036	241	5	∩	∩	ADJ
ejpam-4036	241	6	h	h	NOUN
ejpam-4036	241	7	6	6	NUM
ejpam-4036	241	8	z∞(g	z∞(g	NUM
ejpam-4036	241	9	)	)	PUNCT
ejpam-4036	241	10	.	.	PUNCT
ejpam-4036	242	1	applying	apply	VERB
ejpam-4036	242	2	lemma	lemma	PROPN
ejpam-4036	242	3	13	13	NUM
ejpam-4036	242	4	,	,	PUNCT
ejpam-4036	242	5	we	we	PRON
ejpam-4036	242	6	have	have	VERB
ejpam-4036	242	7	op(g	op(g	NOUN
ejpam-4036	242	8	)	)	PUNCT
ejpam-4036	242	9	6	6	NUM
ejpam-4036	242	10	cg(p	cg(p	NUM
ejpam-4036	242	11	)	)	PUNCT
ejpam-4036	242	12	.	.	PUNCT
ejpam-4036	243	1	this	this	PRON
ejpam-4036	243	2	implies	imply	VERB
ejpam-4036	243	3	g	g	PROPN
ejpam-4036	243	4	=	=	SYM
ejpam-4036	243	5	pq	pq	PROPN
ejpam-4036	244	1	=	=	SYM
ejpam-4036	244	2	p	p	NOUN
ejpam-4036	244	3	×	×	NOUN
ejpam-4036	244	4	q	q	NOUN
ejpam-4036	244	5	is	be	AUX
ejpam-4036	244	6	nilpotent	nilpotent	ADJ
ejpam-4036	244	7	,	,	PUNCT
ejpam-4036	244	8	a	a	DET
ejpam-4036	244	9	contradiction	contradiction	NOUN
ejpam-4036	244	10	.	.	PUNCT
ejpam-4036	245	1	thus	thus	ADV
ejpam-4036	245	2	,	,	PUNCT
ejpam-4036	245	3	we	we	PRON
ejpam-4036	245	4	may	may	AUX
ejpam-4036	245	5	assume	assume	VERB
ejpam-4036	245	6	that	that	SCONJ
ejpam-4036	245	7	p	p	X
ejpam-4036	245	8	=	=	NOUN
ejpam-4036	245	9	2	2	X
ejpam-4036	245	10	.	.	PUNCT
ejpam-4036	245	11	since	since	SCONJ
ejpam-4036	245	12	p	p	NOUN
ejpam-4036	245	13	e	e	PROPN
ejpam-4036	245	14	g	g	PROPN
ejpam-4036	245	15	,	,	PUNCT
ejpam-4036	245	16	it	it	PRON
ejpam-4036	245	17	follows	follow	VERB
ejpam-4036	245	18	that	that	SCONJ
ejpam-4036	245	19	every	every	DET
ejpam-4036	245	20	element	element	NOUN
ejpam-4036	245	21	of	of	ADP
ejpam-4036	245	22	order	order	NOUN
ejpam-4036	245	23	2	2	NUM
ejpam-4036	245	24	or	or	CCONJ
ejpam-4036	245	25	4	4	NUM
ejpam-4036	245	26	of	of	ADP
ejpam-4036	245	27	g	g	NOUN
ejpam-4036	245	28	is	be	AUX
ejpam-4036	245	29	contained	contain	VERB
ejpam-4036	245	30	in	in	ADP
ejpam-4036	245	31	p	p	NOUN
ejpam-4036	245	32	;	;	PUNCT
ejpam-4036	245	33	in	in	ADP
ejpam-4036	245	34	particular	particular	ADJ
ejpam-4036	245	35	in	in	ADP
ejpam-4036	245	36	h.	h.	PROPN
ejpam-4036	245	37	thus	thus	ADV
ejpam-4036	245	38	,	,	PUNCT
ejpam-4036	245	39	every	every	DET
ejpam-4036	245	40	element	element	NOUN
ejpam-4036	245	41	of	of	ADP
ejpam-4036	245	42	order	order	NOUN
ejpam-4036	245	43	2	2	NUM
ejpam-4036	245	44	of	of	ADP
ejpam-4036	245	45	g	g	PROPN
ejpam-4036	245	46	lies	lie	VERB
ejpam-4036	245	47	in	in	ADP
ejpam-4036	245	48	z∞(g	z∞(g	NUM
ejpam-4036	245	49	)	)	PUNCT
ejpam-4036	245	50	and	and	CCONJ
ejpam-4036	245	51	,	,	PUNCT
ejpam-4036	245	52	by	by	ADP
ejpam-4036	245	53	hypotheses	hypothesis	NOUN
ejpam-4036	245	54	,	,	PUNCT
ejpam-4036	245	55	every	every	DET
ejpam-4036	245	56	cyclic	cyclic	ADJ
ejpam-4036	245	57	subgroup	subgroup	NOUN
ejpam-4036	245	58	of	of	ADP
ejpam-4036	245	59	order	order	NOUN
ejpam-4036	245	60	4	4	NUM
ejpam-4036	245	61	is	be	AUX
ejpam-4036	245	62	css	css	NOUN
ejpam-4036	245	63	-	-	NOUN
ejpam-4036	245	64	subgroup	subgroup	NOUN
ejpam-4036	245	65	of	of	ADP
ejpam-4036	245	66	g	g	PROPN
ejpam-4036	245	67	or	or	CCONJ
ejpam-4036	245	68	lies	lie	VERB
ejpam-4036	245	69	also	also	ADV
ejpam-4036	245	70	in	in	ADP
ejpam-4036	245	71	z∞(g	z∞(g	NUM
ejpam-4036	245	72	)	)	PUNCT
ejpam-4036	245	73	.	.	PUNCT
ejpam-4036	246	1	applying	apply	VERB
ejpam-4036	246	2	similar	similar	ADJ
ejpam-4036	246	3	arguments	argument	NOUN
ejpam-4036	246	4	to	to	ADP
ejpam-4036	246	5	those	those	PRON
ejpam-4036	246	6	in	in	ADP
ejpam-4036	246	7	(	(	PUNCT
ejpam-4036	246	8	2	2	NUM
ejpam-4036	246	9	)	)	PUNCT
ejpam-4036	246	10	and	and	CCONJ
ejpam-4036	246	11	(	(	PUNCT
ejpam-4036	246	12	3	3	X
ejpam-4036	246	13	)	)	PUNCT
ejpam-4036	246	14	of	of	ADP
ejpam-4036	246	15	the	the	DET
ejpam-4036	246	16	proof	proof	NOUN
ejpam-4036	246	17	of	of	ADP
ejpam-4036	246	18	theorem	theorem	ADJ
ejpam-4036	246	19	4	4	NUM
ejpam-4036	246	20	,	,	PUNCT
ejpam-4036	246	21	we	we	PRON
ejpam-4036	246	22	have	have	VERB
ejpam-4036	246	23	that	that	PRON
ejpam-4036	246	24	g	g	PROPN
ejpam-4036	246	25	is	be	AUX
ejpam-4036	246	26	nilpotent	nilpotent	ADJ
ejpam-4036	246	27	,	,	PUNCT
ejpam-4036	246	28	a	a	DET
ejpam-4036	246	29	contradiction	contradiction	NOUN
ejpam-4036	246	30	.	.	PUNCT
ejpam-4036	247	1	(	(	PUNCT
ejpam-4036	247	2	2	2	X
ejpam-4036	247	3	)	)	PUNCT
ejpam-4036	247	4	p	p	NOUN
ejpam-4036	247	5	h.	h.	PROPN
ejpam-4036	247	6	then	then	ADV
ejpam-4036	247	7	p	p	X
ejpam-4036	247	8	∩	∩	ADJ
ejpam-4036	247	9	h	h	NOUN
ejpam-4036	247	10	<	<	X
ejpam-4036	247	11	p	p	NOUN
ejpam-4036	247	12	and	and	CCONJ
ejpam-4036	247	13	hence	hence	ADV
ejpam-4036	247	14	q(p	q(p	PROPN
ejpam-4036	247	15	∩	∩	ADJ
ejpam-4036	247	16	h	h	NOUN
ejpam-4036	247	17	)	)	PUNCT
ejpam-4036	247	18	<	<	X
ejpam-4036	247	19	g.	g.	PROPN
ejpam-4036	247	20	therefore	therefore	ADV
ejpam-4036	247	21	,	,	PUNCT
ejpam-4036	247	22	q(p	q(p	PROPN
ejpam-4036	247	23	∩	∩	ADJ
ejpam-4036	247	24	h	h	NOUN
ejpam-4036	247	25	)	)	PUNCT
ejpam-4036	247	26	is	be	AUX
ejpam-4036	247	27	nilpotent	nilpotent	ADJ
ejpam-4036	247	28	which	which	PRON
ejpam-4036	247	29	implies	imply	VERB
ejpam-4036	247	30	that	that	SCONJ
ejpam-4036	247	31	q(p	q(p	PROPN
ejpam-4036	247	32	∩	∩	ADJ
ejpam-4036	247	33	h	h	NOUN
ejpam-4036	247	34	)	)	PUNCT
ejpam-4036	247	35	=	=	PUNCT
ejpam-4036	248	1	q	q	PUNCT
ejpam-4036	248	2	×	×	NOUN
ejpam-4036	248	3	(	(	PUNCT
ejpam-4036	248	4	p	p	NOUN
ejpam-4036	248	5	∩	∩	ADJ
ejpam-4036	248	6	h	h	NOUN
ejpam-4036	248	7	)	)	PUNCT
ejpam-4036	248	8	.	.	PUNCT
ejpam-4036	249	1	moreover	moreover	ADV
ejpam-4036	249	2	,	,	PUNCT
ejpam-4036	249	3	q	q	PROPN
ejpam-4036	249	4	is	be	AUX
ejpam-4036	249	5	characteristic	characteristic	ADJ
ejpam-4036	249	6	in	in	ADP
ejpam-4036	249	7	q(p	q(p	PROPN
ejpam-4036	249	8	∩h	∩h	NOUN
ejpam-4036	249	9	)	)	PUNCT
ejpam-4036	249	10	.	.	PUNCT
ejpam-4036	250	1	clearly	clearly	ADV
ejpam-4036	250	2	,	,	PUNCT
ejpam-4036	250	3	as	as	SCONJ
ejpam-4036	250	4	g	g	PROPN
ejpam-4036	250	5	/	/	SYM
ejpam-4036	250	6	p	p	NOUN
ejpam-4036	250	7	∩h	∩h	NOUN
ejpam-4036	250	8	=	=	PUNCT
ejpam-4036	250	9	(	(	PUNCT
ejpam-4036	250	10	p	p	X
ejpam-4036	250	11	/	/	X
ejpam-4036	250	12	p	p	X
ejpam-4036	250	13	∩h)(q(p	∩h)(q(p	X
ejpam-4036	250	14	∩h)/p	∩h)/p	NOUN
ejpam-4036	250	15	∩h	∩h	NOUN
ejpam-4036	250	16	)	)	PUNCT
ejpam-4036	250	17	is	be	AUX
ejpam-4036	250	18	nilpotent	nilpotent	ADJ
ejpam-4036	250	19	,	,	PUNCT
ejpam-4036	250	20	then	then	ADV
ejpam-4036	250	21	q(p	q(p	PROPN
ejpam-4036	250	22	∩h)/p	∩h)/p	NUM
ejpam-4036	251	1	∩h	∩h	ADJ
ejpam-4036	251	2	eg	eg	NOUN
ejpam-4036	251	3	/	/	SYM
ejpam-4036	251	4	p	p	NOUN
ejpam-4036	251	5	∩h	∩h	NOUN
ejpam-4036	251	6	.	.	PUNCT
ejpam-4036	252	1	thus	thus	ADV
ejpam-4036	252	2	q(p	q(p	PROPN
ejpam-4036	252	3	∩h	∩h	NOUN
ejpam-4036	252	4	)	)	PUNCT
ejpam-4036	252	5	eg	eg	NOUN
ejpam-4036	252	6	.	.	PUNCT
ejpam-4036	253	1	hence	hence	ADV
ejpam-4036	253	2	qeg	qeg	NOUN
ejpam-4036	253	3	,	,	PUNCT
ejpam-4036	253	4	a	a	DET
ejpam-4036	253	5	contradiction	contradiction	NOUN
ejpam-4036	253	6	.	.	PUNCT
ejpam-4036	254	1	theorem	theorem	NOUN
ejpam-4036	254	2	6	6	NUM
ejpam-4036	254	3	.	.	PUNCT
ejpam-4036	255	1	let	let	VERB
ejpam-4036	255	2	h	h	PRON
ejpam-4036	255	3	be	be	AUX
ejpam-4036	255	4	a	a	DET
ejpam-4036	255	5	normal	normal	ADJ
ejpam-4036	255	6	subgroup	subgroup	NOUN
ejpam-4036	255	7	of	of	ADP
ejpam-4036	255	8	g	g	PROPN
ejpam-4036	255	9	such	such	ADJ
ejpam-4036	255	10	that	that	SCONJ
ejpam-4036	255	11	g	g	NOUN
ejpam-4036	255	12	/	/	SYM
ejpam-4036	255	13	h	h	NOUN
ejpam-4036	255	14	is	be	AUX
ejpam-4036	255	15	nilpotent	nilpotent	ADJ
ejpam-4036	255	16	and	and	CCONJ
ejpam-4036	255	17	every	every	DET
ejpam-4036	255	18	cyclic	cyclic	ADJ
ejpam-4036	255	19	subgroup	subgroup	NOUN
ejpam-4036	255	20	of	of	ADP
ejpam-4036	255	21	order	order	NOUN
ejpam-4036	255	22	4	4	NUM
ejpam-4036	255	23	of	of	ADP
ejpam-4036	255	24	f	f	PROPN
ejpam-4036	255	25	∗(h	∗(h	PROPN
ejpam-4036	255	26	)	)	PUNCT
ejpam-4036	255	27	is	be	AUX
ejpam-4036	255	28	css	css	PROPN
ejpam-4036	255	29	-	-	PROPN
ejpam-4036	255	30	subgroup	subgroup	NOUN
ejpam-4036	255	31	of	of	ADP
ejpam-4036	255	32	g.	g.	PROPN
ejpam-4036	256	1	then	then	ADV
ejpam-4036	256	2	g	g	PROPN
ejpam-4036	256	3	is	be	AUX
ejpam-4036	256	4	nilpotent	nilpotent	ADJ
ejpam-4036	256	5	if	if	SCONJ
ejpam-4036	256	6	and	and	CCONJ
ejpam-4036	256	7	only	only	ADV
ejpam-4036	256	8	if	if	SCONJ
ejpam-4036	256	9	every	every	DET
ejpam-4036	256	10	subgroup	subgroup	NOUN
ejpam-4036	256	11	of	of	ADP
ejpam-4036	256	12	prime	prime	ADJ
ejpam-4036	256	13	order	order	NOUN
ejpam-4036	256	14	of	of	ADP
ejpam-4036	256	15	f	f	PROPN
ejpam-4036	256	16	∗(h	∗(h	PROPN
ejpam-4036	256	17	)	)	PUNCT
ejpam-4036	256	18	is	be	AUX
ejpam-4036	256	19	contained	contain	VERB
ejpam-4036	256	20	in	in	ADP
ejpam-4036	256	21	z∞(g	z∞(g	NUM
ejpam-4036	256	22	)	)	PUNCT
ejpam-4036	256	23	.	.	PUNCT
ejpam-4036	257	1	proof	proof	NOUN
ejpam-4036	257	2	.	.	PUNCT
ejpam-4036	258	1	if	if	SCONJ
ejpam-4036	258	2	g	g	PROPN
ejpam-4036	258	3	is	be	AUX
ejpam-4036	258	4	nilpotent	nilpotent	ADJ
ejpam-4036	258	5	,	,	PUNCT
ejpam-4036	258	6	then	then	ADV
ejpam-4036	258	7	we	we	PRON
ejpam-4036	258	8	set	set	VERB
ejpam-4036	258	9	h	h	NOUN
ejpam-4036	258	10	=	=	SYM
ejpam-4036	258	11	1	1	NUM
ejpam-4036	258	12	and	and	CCONJ
ejpam-4036	258	13	the	the	DET
ejpam-4036	258	14	result	result	NOUN
ejpam-4036	258	15	follows	follow	VERB
ejpam-4036	258	16	.	.	PUNCT
ejpam-4036	259	1	conversely	conversely	ADV
ejpam-4036	259	2	,	,	PUNCT
ejpam-4036	259	3	assume	assume	VERB
ejpam-4036	259	4	that	that	SCONJ
ejpam-4036	259	5	the	the	DET
ejpam-4036	259	6	result	result	NOUN
ejpam-4036	259	7	is	be	AUX
ejpam-4036	259	8	false	false	ADJ
ejpam-4036	259	9	and	and	CCONJ
ejpam-4036	259	10	let	let	VERB
ejpam-4036	259	11	g	g	PRON
ejpam-4036	259	12	be	be	AUX
ejpam-4036	259	13	a	a	DET
ejpam-4036	259	14	counterexample	counterexample	NOUN
ejpam-4036	259	15	of	of	ADP
ejpam-4036	259	16	minimal	minimal	ADJ
ejpam-4036	259	17	order	order	NOUN
ejpam-4036	259	18	.	.	PUNCT
ejpam-4036	260	1	with	with	ADP
ejpam-4036	260	2	the	the	DET
ejpam-4036	260	3	same	same	ADJ
ejpam-4036	260	4	arguments	argument	NOUN
ejpam-4036	260	5	to	to	ADP
ejpam-4036	260	6	those	those	PRON
ejpam-4036	260	7	in	in	ADP
ejpam-4036	260	8	steps	step	NOUN
ejpam-4036	260	9	(	(	PUNCT
ejpam-4036	260	10	1	1	NUM
ejpam-4036	260	11	)	)	PUNCT
ejpam-4036	260	12	and	and	CCONJ
ejpam-4036	260	13	(	(	PUNCT
ejpam-4036	260	14	2	2	X
ejpam-4036	260	15	)	)	PUNCT
ejpam-4036	260	16	of	of	ADP
ejpam-4036	260	17	the	the	DET
ejpam-4036	260	18	proof	proof	NOUN
ejpam-4036	260	19	of	of	ADP
ejpam-4036	260	20	theorem	theorem	NOUN
ejpam-4036	260	21	4.4	4.4	NUM
ejpam-4036	260	22	in	in	ADP
ejpam-4036	260	23	[	[	PUNCT
ejpam-4036	260	24	11	11	NUM
ejpam-4036	260	25	]	]	PUNCT
ejpam-4036	260	26	,	,	PUNCT
ejpam-4036	260	27	we	we	PRON
ejpam-4036	260	28	have	have	VERB
ejpam-4036	260	29	:	:	PUNCT
ejpam-4036	260	30	a.	a.	NOUN
ejpam-4036	260	31	heliel	heliel	PROPN
ejpam-4036	260	32	,	,	PUNCT
ejpam-4036	260	33	r.	r.	PROPN
ejpam-4036	260	34	hijazi	hijazi	PROPN
ejpam-4036	260	35	,	,	PUNCT
ejpam-4036	260	36	s.	s.	PROPN
ejpam-4036	260	37	al	al	PROPN
ejpam-4036	260	38	-	-	PUNCT
ejpam-4036	260	39	shammari	shammari	PROPN
ejpam-4036	260	40	/	/	SYM
ejpam-4036	260	41	eur	eur	PROPN
ejpam-4036	260	42	.	.	PUNCT
ejpam-4036	261	1	j.	j.	PROPN
ejpam-4036	261	2	pure	pure	PROPN
ejpam-4036	261	3	appl	appl	PROPN
ejpam-4036	261	4	.	.	PROPN
ejpam-4036	261	5	math	math	PROPN
ejpam-4036	261	6	,	,	PUNCT
ejpam-4036	261	7	14	14	NUM
ejpam-4036	261	8	(	(	PUNCT
ejpam-4036	261	9	3	3	NUM
ejpam-4036	261	10	)	)	PUNCT
ejpam-4036	261	11	(	(	PUNCT
ejpam-4036	261	12	2021	2021	NUM
ejpam-4036	261	13	)	)	PUNCT
ejpam-4036	261	14	,	,	PUNCT
ejpam-4036	261	15	1002	1002	NUM
ejpam-4036	261	16	-	-	SYM
ejpam-4036	261	17	1014	1014	NUM
ejpam-4036	261	18	1010	1010	NUM
ejpam-4036	261	19	(	(	PUNCT
ejpam-4036	261	20	1	1	X
ejpam-4036	261	21	)	)	PUNCT
ejpam-4036	261	22	every	every	DET
ejpam-4036	261	23	proper	proper	ADJ
ejpam-4036	261	24	normal	normal	ADJ
ejpam-4036	261	25	subgroup	subgroup	NOUN
ejpam-4036	261	26	of	of	ADP
ejpam-4036	261	27	g	g	PROPN
ejpam-4036	261	28	is	be	AUX
ejpam-4036	261	29	nilpotent	nilpotent	ADJ
ejpam-4036	261	30	,	,	PUNCT
ejpam-4036	261	31	and	and	CCONJ
ejpam-4036	261	32	f	f	PROPN
ejpam-4036	261	33	(	(	PUNCT
ejpam-4036	261	34	g	g	NOUN
ejpam-4036	261	35	)	)	PUNCT
ejpam-4036	261	36	is	be	AUX
ejpam-4036	261	37	the	the	DET
ejpam-4036	261	38	unique	unique	ADJ
ejpam-4036	261	39	maximal	maximal	ADJ
ejpam-4036	261	40	normal	normal	ADJ
ejpam-4036	261	41	subgroup	subgroup	NOUN
ejpam-4036	261	42	of	of	ADP
ejpam-4036	261	43	g.	g.	PROPN
ejpam-4036	261	44	(	(	PUNCT
ejpam-4036	261	45	2	2	NUM
ejpam-4036	261	46	)	)	PUNCT
ejpam-4036	261	47	h	h	NOUN
ejpam-4036	261	48	=	=	SYM
ejpam-4036	261	49	g	g	NOUN
ejpam-4036	261	50	,	,	PUNCT
ejpam-4036	261	51	g′	g′	NOUN
ejpam-4036	261	52	=	=	SYM
ejpam-4036	261	53	g	g	PROPN
ejpam-4036	261	54	and	and	CCONJ
ejpam-4036	261	55	f	f	PROPN
ejpam-4036	261	56	∗(g	∗(g	PROPN
ejpam-4036	261	57	)	)	PUNCT
ejpam-4036	262	1	=	=	SYM
ejpam-4036	262	2	f	f	X
ejpam-4036	262	3	(	(	PUNCT
ejpam-4036	262	4	g	g	NOUN
ejpam-4036	262	5	)	)	PUNCT
ejpam-4036	262	6	<	<	X
ejpam-4036	262	7	g.	g.	PROPN
ejpam-4036	262	8	(	(	PUNCT
ejpam-4036	262	9	3	3	X
ejpam-4036	262	10	)	)	PUNCT
ejpam-4036	262	11	let	let	VERB
ejpam-4036	262	12	q	q	NOUN
ejpam-4036	262	13	be	be	AUX
ejpam-4036	262	14	a	a	DET
ejpam-4036	262	15	minimal	minimal	ADJ
ejpam-4036	262	16	prime	prime	ADJ
ejpam-4036	262	17	divisor	divisor	NOUN
ejpam-4036	262	18	of	of	ADP
ejpam-4036	262	19	|f	|f	PROPN
ejpam-4036	262	20	(	(	PUNCT
ejpam-4036	262	21	g)|	g)|	NOUN
ejpam-4036	262	22	and	and	CCONJ
ejpam-4036	262	23	q	q	ADJ
ejpam-4036	262	24	a	a	DET
ejpam-4036	262	25	sylow	sylow	NOUN
ejpam-4036	262	26	q	q	NOUN
ejpam-4036	262	27	-	-	NOUN
ejpam-4036	262	28	subgroup	subgroup	NOUN
ejpam-4036	262	29	of	of	ADP
ejpam-4036	262	30	f	f	PROPN
ejpam-4036	262	31	(	(	PUNCT
ejpam-4036	262	32	g	g	NOUN
ejpam-4036	262	33	)	)	PUNCT
ejpam-4036	262	34	.	.	PUNCT
ejpam-4036	263	1	then	then	ADV
ejpam-4036	263	2	g	g	PROPN
ejpam-4036	263	3	/	/	SYM
ejpam-4036	263	4	cg(q	cg(q	NUM
ejpam-4036	263	5	)	)	PUNCT
ejpam-4036	263	6	is	be	AUX
ejpam-4036	263	7	a	a	DET
ejpam-4036	263	8	q	q	NOUN
ejpam-4036	263	9	-	-	NOUN
ejpam-4036	263	10	group	group	NOUN
ejpam-4036	263	11	.	.	PUNCT
ejpam-4036	264	1	since	since	SCONJ
ejpam-4036	264	2	f	f	PROPN
ejpam-4036	264	3	∗(g	∗(g	PROPN
ejpam-4036	264	4	)	)	PUNCT
ejpam-4036	264	5	6=	6=	ADP
ejpam-4036	264	6	1	1	NUM
ejpam-4036	264	7	,	,	PUNCT
ejpam-4036	264	8	then	then	ADV
ejpam-4036	264	9	we	we	PRON
ejpam-4036	264	10	may	may	AUX
ejpam-4036	264	11	assume	assume	VERB
ejpam-4036	264	12	that	that	SCONJ
ejpam-4036	264	13	q	q	NOUN
ejpam-4036	264	14	is	be	AUX
ejpam-4036	264	15	a	a	DET
ejpam-4036	264	16	minimal	minimal	ADJ
ejpam-4036	264	17	prime	prime	ADJ
ejpam-4036	264	18	divisor	divisor	NOUN
ejpam-4036	264	19	of	of	ADP
ejpam-4036	264	20	|f	|f	PROPN
ejpam-4036	264	21	(	(	PUNCT
ejpam-4036	264	22	g)|	g)|	NOUN
ejpam-4036	264	23	and	and	CCONJ
ejpam-4036	264	24	q	q	NOUN
ejpam-4036	264	25	is	be	AUX
ejpam-4036	264	26	a	a	DET
ejpam-4036	264	27	sylow	sylow	NOUN
ejpam-4036	264	28	q	q	NOUN
ejpam-4036	264	29	-	-	NOUN
ejpam-4036	264	30	subgroup	subgroup	NOUN
ejpam-4036	264	31	of	of	ADP
ejpam-4036	264	32	f	f	PROPN
ejpam-4036	264	33	(	(	PUNCT
ejpam-4036	264	34	g	g	NOUN
ejpam-4036	264	35	)	)	PUNCT
ejpam-4036	264	36	which	which	PRON
ejpam-4036	264	37	is	be	AUX
ejpam-4036	264	38	a	a	DET
ejpam-4036	264	39	non	non	ADJ
ejpam-4036	264	40	-	-	ADJ
ejpam-4036	264	41	trivial	trivial	ADJ
ejpam-4036	264	42	normal	normal	ADJ
ejpam-4036	264	43	subgroup	subgroup	NOUN
ejpam-4036	264	44	of	of	ADP
ejpam-4036	264	45	g.	g.	PROPN
ejpam-4036	264	46	clearly	clearly	ADV
ejpam-4036	264	47	,	,	PUNCT
ejpam-4036	264	48	from	from	ADP
ejpam-4036	264	49	hypotheses	hypothesis	NOUN
ejpam-4036	264	50	,	,	PUNCT
ejpam-4036	264	51	ω1(q	ω1(q	NUM
ejpam-4036	264	52	)	)	PUNCT
ejpam-4036	264	53	6	6	NUM
ejpam-4036	264	54	z∞(g	z∞(g	NUM
ejpam-4036	264	55	)	)	PUNCT
ejpam-4036	264	56	.	.	PUNCT
ejpam-4036	265	1	thus	thus	ADV
ejpam-4036	265	2	,	,	PUNCT
ejpam-4036	265	3	by	by	ADP
ejpam-4036	265	4	lemma	lemma	PROPN
ejpam-4036	265	5	13	13	NUM
ejpam-4036	265	6	,	,	PUNCT
ejpam-4036	265	7	cg(ω1(q	cg(ω1(q	PROPN
ejpam-4036	265	8	)	)	PUNCT
ejpam-4036	265	9	)	)	PUNCT
ejpam-4036	265	10	>	>	X
ejpam-4036	265	11	oq(g	oq(g	NUM
ejpam-4036	265	12	)	)	PUNCT
ejpam-4036	265	13	.	.	PUNCT
ejpam-4036	266	1	if	if	SCONJ
ejpam-4036	266	2	q	q	PROPN
ejpam-4036	266	3	>	>	X
ejpam-4036	266	4	2	2	NUM
ejpam-4036	266	5	,	,	PUNCT
ejpam-4036	266	6	then	then	ADV
ejpam-4036	266	7	,	,	PUNCT
ejpam-4036	266	8	by	by	ADP
ejpam-4036	266	9	lemma	lemma	PROPN
ejpam-4036	266	10	15	15	NUM
ejpam-4036	266	11	,	,	PUNCT
ejpam-4036	266	12	cg(q	cg(q	NOUN
ejpam-4036	266	13	)	)	PUNCT
ejpam-4036	266	14	>	>	X
ejpam-4036	266	15	oq(g	oq(g	NUM
ejpam-4036	266	16	)	)	PUNCT
ejpam-4036	266	17	.	.	PUNCT
ejpam-4036	267	1	this	this	PRON
ejpam-4036	267	2	implies	imply	VERB
ejpam-4036	267	3	that	that	SCONJ
ejpam-4036	267	4	g	g	NOUN
ejpam-4036	267	5	/	/	SYM
ejpam-4036	267	6	cg(q	cg(q	NUM
ejpam-4036	267	7	)	)	PUNCT
ejpam-4036	267	8	is	be	AUX
ejpam-4036	267	9	a	a	DET
ejpam-4036	267	10	q	q	NOUN
ejpam-4036	267	11	-	-	NOUN
ejpam-4036	267	12	group	group	NOUN
ejpam-4036	267	13	.	.	PUNCT
ejpam-4036	268	1	if	if	SCONJ
ejpam-4036	268	2	q	q	NOUN
ejpam-4036	268	3	=	=	NOUN
ejpam-4036	268	4	2	2	NUM
ejpam-4036	268	5	,	,	PUNCT
ejpam-4036	268	6	let	let	VERB
ejpam-4036	268	7	<	<	X
ejpam-4036	268	8	x	x	X
ejpam-4036	268	9	>	>	X
ejpam-4036	268	10	be	be	AUX
ejpam-4036	268	11	an	an	DET
ejpam-4036	268	12	arbitrary	arbitrary	ADJ
ejpam-4036	268	13	cyclic	cyclic	ADJ
ejpam-4036	268	14	subgroup	subgroup	NOUN
ejpam-4036	268	15	of	of	ADP
ejpam-4036	268	16	q	q	NOUN
ejpam-4036	268	17	of	of	ADP
ejpam-4036	268	18	order	order	NOUN
ejpam-4036	268	19	4	4	NUM
ejpam-4036	268	20	.	.	PUNCT
ejpam-4036	268	21	by	by	ADP
ejpam-4036	268	22	hypotheses	hypothesis	NOUN
ejpam-4036	268	23	,	,	PUNCT
ejpam-4036	268	24	<	<	X
ejpam-4036	268	25	x	x	X
ejpam-4036	268	26	>	>	X
ejpam-4036	268	27	is	be	AUX
ejpam-4036	268	28	css	css	PROPN
ejpam-4036	268	29	-	-	PROPN
ejpam-4036	268	30	subgroup	subgroup	NOUN
ejpam-4036	268	31	of	of	ADP
ejpam-4036	268	32	g.	g.	PROPN
ejpam-4036	268	33	then	then	ADV
ejpam-4036	268	34	,	,	PUNCT
ejpam-4036	268	35	there	there	PRON
ejpam-4036	268	36	exists	exist	VERB
ejpam-4036	268	37	a	a	DET
ejpam-4036	268	38	normal	normal	ADJ
ejpam-4036	268	39	subgroup	subgroup	NOUN
ejpam-4036	268	40	l	l	NOUN
ejpam-4036	268	41	of	of	ADP
ejpam-4036	268	42	g	g	PROPN
ejpam-4036	269	1	such	such	ADJ
ejpam-4036	269	2	that	that	SCONJ
ejpam-4036	269	3	g	g	PROPN
ejpam-4036	269	4	=	=	NOUN
ejpam-4036	269	5	<	<	X
ejpam-4036	269	6	x	x	X
ejpam-4036	269	7	>	>	X
ejpam-4036	269	8	l	l	NOUN
ejpam-4036	269	9	and	and	CCONJ
ejpam-4036	269	10	<	<	X
ejpam-4036	269	11	x	x	X
ejpam-4036	269	12	>	>	X
ejpam-4036	269	13	∩l	∩l	NOUN
ejpam-4036	269	14	is	be	AUX
ejpam-4036	269	15	ss	ss	NOUN
ejpam-4036	269	16	-	-	ADJ
ejpam-4036	269	17	quasinormal	quasinormal	ADJ
ejpam-4036	269	18	in	in	ADP
ejpam-4036	269	19	g.	g.	PROPN
ejpam-4036	270	1	if	if	SCONJ
ejpam-4036	270	2	<	<	X
ejpam-4036	270	3	x	x	X
ejpam-4036	270	4	>	>	X
ejpam-4036	270	5	∩l	∩l	NOUN
ejpam-4036	270	6	=	=	SYM
ejpam-4036	270	7	1	1	NUM
ejpam-4036	270	8	,	,	PUNCT
ejpam-4036	270	9	then	then	ADV
ejpam-4036	270	10	l	l	NOUN
ejpam-4036	270	11	is	be	AUX
ejpam-4036	270	12	a	a	DET
ejpam-4036	270	13	proper	proper	ADJ
ejpam-4036	270	14	normal	normal	ADJ
ejpam-4036	270	15	subgroup	subgroup	NOUN
ejpam-4036	270	16	of	of	ADP
ejpam-4036	270	17	g	g	PROPN
ejpam-4036	270	18	and	and	CCONJ
ejpam-4036	270	19	,	,	PUNCT
ejpam-4036	270	20	by	by	ADP
ejpam-4036	270	21	(	(	PUNCT
ejpam-4036	270	22	1	1	NUM
ejpam-4036	270	23	)	)	PUNCT
ejpam-4036	270	24	,	,	PUNCT
ejpam-4036	270	25	l	l	NOUN
ejpam-4036	270	26	is	be	AUX
ejpam-4036	270	27	nilpotent	nilpotent	ADJ
ejpam-4036	270	28	.	.	PUNCT
ejpam-4036	271	1	it	it	PRON
ejpam-4036	271	2	follows	follow	VERB
ejpam-4036	271	3	that	that	SCONJ
ejpam-4036	271	4	any	any	DET
ejpam-4036	271	5	sylow	sylow	NOUN
ejpam-4036	271	6	p	p	NOUN
ejpam-4036	271	7	-	-	PUNCT
ejpam-4036	271	8	subgroup	subgroup	NOUN
ejpam-4036	271	9	of	of	ADP
ejpam-4036	271	10	l	l	NOUN
ejpam-4036	271	11	is	be	AUX
ejpam-4036	271	12	normal	normal	ADJ
ejpam-4036	271	13	in	in	ADP
ejpam-4036	271	14	g	g	PROPN
ejpam-4036	271	15	,	,	PUNCT
ejpam-4036	271	16	where	where	SCONJ
ejpam-4036	271	17	p	p	NOUN
ejpam-4036	271	18	is	be	AUX
ejpam-4036	271	19	any	any	DET
ejpam-4036	271	20	prime	prime	ADJ
ejpam-4036	271	21	number	number	NOUN
ejpam-4036	271	22	such	such	ADJ
ejpam-4036	272	1	that	that	SCONJ
ejpam-4036	272	2	p	p	PROPN
ejpam-4036	272	3	6=	6=	ADP
ejpam-4036	272	4	2	2	NUM
ejpam-4036	272	5	.	.	PUNCT
ejpam-4036	272	6	therefore	therefore	ADV
ejpam-4036	272	7	,	,	PUNCT
ejpam-4036	272	8	g	g	PROPN
ejpam-4036	272	9	is	be	AUX
ejpam-4036	272	10	nilpotent	nilpotent	ADJ
ejpam-4036	272	11	,	,	PUNCT
ejpam-4036	272	12	a	a	DET
ejpam-4036	272	13	contradiction	contradiction	NOUN
ejpam-4036	272	14	.	.	PUNCT
ejpam-4036	273	1	hence	hence	ADV
ejpam-4036	273	2	we	we	PRON
ejpam-4036	273	3	may	may	AUX
ejpam-4036	273	4	assume	assume	VERB
ejpam-4036	273	5	that	that	SCONJ
ejpam-4036	273	6	<	<	X
ejpam-4036	273	7	x	x	X
ejpam-4036	273	8	>	>	X
ejpam-4036	273	9	6	6	NUM
ejpam-4036	273	10	l	l	NOUN
ejpam-4036	273	11	and	and	CCONJ
ejpam-4036	273	12	<	<	X
ejpam-4036	273	13	x	x	X
ejpam-4036	273	14	>	>	X
ejpam-4036	273	15	is	be	AUX
ejpam-4036	273	16	ss	ss	NOUN
ejpam-4036	273	17	-	-	ADJ
ejpam-4036	273	18	quasinormal	quasinormal	ADJ
ejpam-4036	273	19	in	in	ADP
ejpam-4036	273	20	g.	g.	PROPN
ejpam-4036	273	21	since	since	SCONJ
ejpam-4036	273	22	q	q	PROPN
ejpam-4036	273	23	is	be	AUX
ejpam-4036	273	24	a	a	DET
ejpam-4036	273	25	normal	normal	ADJ
ejpam-4036	273	26	subgroup	subgroup	NOUN
ejpam-4036	273	27	of	of	ADP
ejpam-4036	273	28	g	g	PROPN
ejpam-4036	273	29	,	,	PUNCT
ejpam-4036	273	30	it	it	PRON
ejpam-4036	273	31	follows	follow	VERB
ejpam-4036	273	32	that	that	SCONJ
ejpam-4036	273	33	<	<	X
ejpam-4036	273	34	x	x	X
ejpam-4036	273	35	>	>	X
ejpam-4036	273	36	is	be	AUX
ejpam-4036	273	37	subnormal	subnormal	ADJ
ejpam-4036	273	38	in	in	ADP
ejpam-4036	273	39	g.	g.	PROPN
ejpam-4036	273	40	hence	hence	ADV
ejpam-4036	273	41	,	,	PUNCT
ejpam-4036	273	42	by	by	ADP
ejpam-4036	273	43	lemma	lemma	PROPN
ejpam-4036	273	44	4	4	NUM
ejpam-4036	273	45	,	,	PUNCT
ejpam-4036	273	46	<	<	X
ejpam-4036	273	47	x	x	X
ejpam-4036	273	48	>	>	X
ejpam-4036	273	49	6	6	NUM
ejpam-4036	273	50	o2(g	o2(g	NUM
ejpam-4036	273	51	)	)	PUNCT
ejpam-4036	273	52	.	.	PUNCT
ejpam-4036	274	1	applying	apply	VERB
ejpam-4036	274	2	lemma	lemma	PROPN
ejpam-4036	274	3	5	5	NUM
ejpam-4036	274	4	,	,	PUNCT
ejpam-4036	274	5	<	<	X
ejpam-4036	274	6	x	x	X
ejpam-4036	274	7	>	>	X
ejpam-4036	274	8	is	be	AUX
ejpam-4036	274	9	s	s	NOUN
ejpam-4036	274	10	-	-	ADJ
ejpam-4036	274	11	quasinormal	quasinormal	ADJ
ejpam-4036	274	12	in	in	ADP
ejpam-4036	274	13	g.	g.	PROPN
ejpam-4036	274	14	now	now	ADV
ejpam-4036	274	15	,	,	PUNCT
ejpam-4036	274	16	let	let	VERB
ejpam-4036	274	17	p	p	PRON
ejpam-4036	274	18	be	be	AUX
ejpam-4036	274	19	any	any	DET
ejpam-4036	274	20	sylow	sylow	NOUN
ejpam-4036	274	21	p	p	NOUN
ejpam-4036	274	22	-	-	PUNCT
ejpam-4036	274	23	subgroup	subgroup	NOUN
ejpam-4036	274	24	of	of	ADP
ejpam-4036	274	25	g	g	PROPN
ejpam-4036	274	26	,	,	PUNCT
ejpam-4036	274	27	where	where	SCONJ
ejpam-4036	274	28	p	p	NOUN
ejpam-4036	274	29	6=	6=	PROPN
ejpam-4036	274	30	2	2	NUM
ejpam-4036	274	31	.	.	PUNCT
ejpam-4036	274	32	therefore	therefore	ADV
ejpam-4036	274	33	<	<	X
ejpam-4036	274	34	x	x	X
ejpam-4036	274	35	>	>	X
ejpam-4036	275	1	p	p	X
ejpam-4036	275	2	6	6	NUM
ejpam-4036	275	3	g.	g.	NOUN
ejpam-4036	275	4	clearly	clearly	ADV
ejpam-4036	275	5	,	,	PUNCT
ejpam-4036	275	6	as	as	SCONJ
ejpam-4036	275	7	<	<	X
ejpam-4036	275	8	x	x	X
ejpam-4036	275	9	>	>	X
ejpam-4036	275	10	is	be	AUX
ejpam-4036	275	11	subnormal	subnormal	ADJ
ejpam-4036	275	12	in	in	ADP
ejpam-4036	275	13	<	<	X
ejpam-4036	275	14	x	x	X
ejpam-4036	275	15	>	>	X
ejpam-4036	275	16	p	p	NOUN
ejpam-4036	275	17	and	and	CCONJ
ejpam-4036	275	18	<	<	X
ejpam-4036	275	19	x	x	X
ejpam-4036	275	20	>	>	X
ejpam-4036	275	21	is	be	AUX
ejpam-4036	275	22	a	a	DET
ejpam-4036	275	23	sylow	sylow	NOUN
ejpam-4036	275	24	2	2	NUM
ejpam-4036	275	25	-	-	PUNCT
ejpam-4036	275	26	subgroup	subgroup	NOUN
ejpam-4036	275	27	of	of	ADP
ejpam-4036	275	28	<	<	X
ejpam-4036	275	29	x	x	X
ejpam-4036	275	30	>	>	X
ejpam-4036	275	31	p	p	X
ejpam-4036	275	32	,	,	PUNCT
ejpam-4036	275	33	we	we	PRON
ejpam-4036	275	34	have	have	VERB
ejpam-4036	275	35	<	<	X
ejpam-4036	275	36	x	x	X
ejpam-4036	275	37	>	>	X
ejpam-4036	275	38	is	be	AUX
ejpam-4036	275	39	normal	normal	ADJ
ejpam-4036	275	40	in	in	ADP
ejpam-4036	275	41	<	<	X
ejpam-4036	275	42	x	x	X
ejpam-4036	275	43	>	>	X
ejpam-4036	275	44	p	p	X
ejpam-4036	275	45	.	.	PUNCT
ejpam-4036	276	1	hence	hence	ADV
ejpam-4036	276	2	,	,	PUNCT
ejpam-4036	276	3	by	by	ADP
ejpam-4036	276	4	lemma	lemma	PROPN
ejpam-4036	276	5	16	16	NUM
ejpam-4036	276	6	,	,	PUNCT
ejpam-4036	276	7	<	<	X
ejpam-4036	276	8	x	x	X
ejpam-4036	276	9	>	>	X
ejpam-4036	276	10	p	p	X
ejpam-4036	276	11	is	be	AUX
ejpam-4036	276	12	nilpotent	nilpotent	ADJ
ejpam-4036	276	13	.	.	PUNCT
ejpam-4036	277	1	it	it	PRON
ejpam-4036	277	2	follows	follow	VERB
ejpam-4036	277	3	that	that	SCONJ
ejpam-4036	277	4	p	p	PROPN
ejpam-4036	277	5	6	6	NUM
ejpam-4036	277	6	cg	cg	NOUN
ejpam-4036	277	7	(	(	PUNCT
ejpam-4036	277	8	<	<	X
ejpam-4036	277	9	x	x	X
ejpam-4036	277	10	>	>	PUNCT
ejpam-4036	277	11	)	)	PUNCT
ejpam-4036	277	12	and	and	CCONJ
ejpam-4036	277	13	so	so	ADV
ejpam-4036	277	14	o2(g	o2(g	ADJ
ejpam-4036	277	15	)	)	PUNCT
ejpam-4036	277	16	6	6	NUM
ejpam-4036	277	17	cg	cg	NOUN
ejpam-4036	277	18	(	(	PUNCT
ejpam-4036	277	19	<	<	X
ejpam-4036	277	20	x	x	X
ejpam-4036	277	21	>	>	PUNCT
ejpam-4036	277	22	)	)	PUNCT
ejpam-4036	277	23	.	.	PUNCT
ejpam-4036	278	1	this	this	PRON
ejpam-4036	278	2	implies	imply	VERB
ejpam-4036	278	3	that	that	SCONJ
ejpam-4036	278	4	o2(g	o2(g	NUM
ejpam-4036	278	5	)	)	PUNCT
ejpam-4036	278	6	6	6	NUM
ejpam-4036	278	7	cg(q	cg(q	NOUN
ejpam-4036	278	8	)	)	PUNCT
ejpam-4036	278	9	and	and	CCONJ
ejpam-4036	278	10	so	so	ADV
ejpam-4036	278	11	g	g	NOUN
ejpam-4036	278	12	/	/	SYM
ejpam-4036	278	13	cg(q	cg(q	PUNCT
ejpam-4036	278	14	)	)	PUNCT
ejpam-4036	278	15	is	be	AUX
ejpam-4036	278	16	a	a	DET
ejpam-4036	278	17	2	2	NUM
ejpam-4036	278	18	-	-	PUNCT
ejpam-4036	278	19	group	group	NOUN
ejpam-4036	278	20	.	.	PUNCT
ejpam-4036	279	1	(	(	PUNCT
ejpam-4036	279	2	4	4	X
ejpam-4036	279	3	)	)	PUNCT
ejpam-4036	279	4	we	we	PRON
ejpam-4036	279	5	have	have	VERB
ejpam-4036	279	6	a	a	DET
ejpam-4036	279	7	contradiction	contradiction	NOUN
ejpam-4036	279	8	.	.	PUNCT
ejpam-4036	280	1	by	by	ADP
ejpam-4036	280	2	2	2	NUM
ejpam-4036	280	3	,	,	PUNCT
ejpam-4036	280	4	g	g	NOUN
ejpam-4036	280	5	=	=	PUNCT
ejpam-4036	280	6	g′	g′	NOUN
ejpam-4036	280	7	and	and	CCONJ
ejpam-4036	280	8	so	so	ADV
ejpam-4036	280	9	cg(q	cg(q	PUNCT
ejpam-4036	280	10	)	)	PUNCT
ejpam-4036	280	11	=	=	SYM
ejpam-4036	280	12	g	g	NOUN
ejpam-4036	280	13	,	,	PUNCT
ejpam-4036	280	14	q	q	PROPN
ejpam-4036	280	15	6	6	NUM
ejpam-4036	280	16	z(g	z(g	NOUN
ejpam-4036	280	17	)	)	PUNCT
ejpam-4036	280	18	.	.	PUNCT
ejpam-4036	281	1	by	by	ADP
ejpam-4036	281	2	lemma	lemma	PROPN
ejpam-4036	281	3	11	11	NUM
ejpam-4036	281	4	,	,	PUNCT
ejpam-4036	281	5	f	f	PROPN
ejpam-4036	281	6	∗(g	∗(g	PROPN
ejpam-4036	281	7	/	/	SYM
ejpam-4036	281	8	q	q	NOUN
ejpam-4036	281	9	)	)	PUNCT
ejpam-4036	281	10	=	=	SYM
ejpam-4036	281	11	f	f	PROPN
ejpam-4036	281	12	∗(g)/q	∗(g)/q	PROPN
ejpam-4036	281	13	.	.	PUNCT
ejpam-4036	282	1	let	let	VERB
ejpam-4036	282	2	g	g	NOUN
ejpam-4036	282	3	=	=	SYM
ejpam-4036	282	4	g	g	PROPN
ejpam-4036	282	5	/	/	SYM
ejpam-4036	282	6	q.	q.	PROPN
ejpam-4036	282	7	then	then	ADV
ejpam-4036	282	8	,	,	PUNCT
ejpam-4036	282	9	3	3	NUM
ejpam-4036	282	10	imply	imply	VERB
ejpam-4036	282	11	that	that	SCONJ
ejpam-4036	282	12	each	each	DET
ejpam-4036	282	13	element	element	NOUN
ejpam-4036	282	14	y	y	PROPN
ejpam-4036	282	15	of	of	ADP
ejpam-4036	282	16	prime	prime	ADJ
ejpam-4036	282	17	order	order	NOUN
ejpam-4036	282	18	n	n	NOUN
ejpam-4036	282	19	in	in	ADP
ejpam-4036	282	20	f	f	PROPN
ejpam-4036	282	21	∗(g	∗(g	PROPN
ejpam-4036	282	22	)	)	PUNCT
ejpam-4036	282	23	can	can	AUX
ejpam-4036	282	24	be	be	AUX
ejpam-4036	282	25	viewed	view	VERB
ejpam-4036	282	26	as	as	ADP
ejpam-4036	282	27	an	an	DET
ejpam-4036	282	28	image	image	NOUN
ejpam-4036	282	29	in	in	ADP
ejpam-4036	282	30	element	element	NOUN
ejpam-4036	282	31	y	y	PROPN
ejpam-4036	282	32	of	of	ADP
ejpam-4036	282	33	prime	prime	ADJ
ejpam-4036	282	34	order	order	NOUN
ejpam-4036	282	35	n	n	NOUN
ejpam-4036	282	36	in	in	ADP
ejpam-4036	282	37	f	f	PROPN
ejpam-4036	282	38	∗(g	∗(g	PROPN
ejpam-4036	282	39	)	)	PUNCT
ejpam-4036	282	40	,	,	PUNCT
ejpam-4036	282	41	for	for	ADP
ejpam-4036	282	42	each	each	DET
ejpam-4036	282	43	n	n	PROPN
ejpam-4036	282	44	>	>	X
ejpam-4036	282	45	q.	q.	PROPN
ejpam-4036	282	46	thus	thus	ADV
ejpam-4036	282	47	,	,	PUNCT
ejpam-4036	282	48	by	by	ADP
ejpam-4036	282	49	hypotheses	hypothesis	NOUN
ejpam-4036	282	50	,	,	PUNCT
ejpam-4036	282	51	y	y	PROPN
ejpam-4036	282	52	6	6	NUM
ejpam-4036	282	53	z∞(g	z∞(g	NUM
ejpam-4036	282	54	)	)	PUNCT
ejpam-4036	282	55	.	.	PUNCT
ejpam-4036	283	1	since	since	SCONJ
ejpam-4036	283	2	q	q	PROPN
ejpam-4036	283	3	6	6	NUM
ejpam-4036	283	4	z(g	z(g	NOUN
ejpam-4036	283	5	)	)	PUNCT
ejpam-4036	283	6	,	,	PUNCT
ejpam-4036	283	7	then	then	ADV
ejpam-4036	283	8	z∞(g	z∞(g	PROPN
ejpam-4036	283	9	/	/	SYM
ejpam-4036	283	10	q	q	NOUN
ejpam-4036	283	11	)	)	PUNCT
ejpam-4036	283	12	=	=	SYM
ejpam-4036	283	13	z∞(g)/q	z∞(g)/q	NUM
ejpam-4036	283	14	.	.	PUNCT
ejpam-4036	284	1	hence	hence	ADV
ejpam-4036	284	2	y	y	PROPN
ejpam-4036	284	3	6	6	NUM
ejpam-4036	284	4	z∞(g	z∞(g	SYM
ejpam-4036	284	5	/	/	SYM
ejpam-4036	284	6	q	q	NOUN
ejpam-4036	284	7	)	)	PUNCT
ejpam-4036	284	8	.	.	PUNCT
ejpam-4036	285	1	clearly	clearly	ADV
ejpam-4036	285	2	,	,	PUNCT
ejpam-4036	285	3	f	f	PROPN
ejpam-4036	285	4	∗(g	∗(g	PROPN
ejpam-4036	285	5	/	/	SYM
ejpam-4036	285	6	q	q	NOUN
ejpam-4036	285	7	)	)	PUNCT
ejpam-4036	285	8	does	do	AUX
ejpam-4036	285	9	not	not	PART
ejpam-4036	285	10	have	have	VERB
ejpam-4036	285	11	an	an	DET
ejpam-4036	285	12	element	element	NOUN
ejpam-4036	285	13	of	of	ADP
ejpam-4036	285	14	order	order	NOUN
ejpam-4036	285	15	2	2	X
ejpam-4036	285	16	.	.	PUNCT
ejpam-4036	286	1	this	this	PRON
ejpam-4036	286	2	means	mean	VERB
ejpam-4036	286	3	that	that	SCONJ
ejpam-4036	286	4	g	g	PROPN
ejpam-4036	286	5	satisfies	satisfy	VERB
ejpam-4036	286	6	the	the	DET
ejpam-4036	286	7	hypotheses	hypothesis	NOUN
ejpam-4036	286	8	of	of	ADP
ejpam-4036	286	9	the	the	DET
ejpam-4036	286	10	theorem	theorem	NOUN
ejpam-4036	286	11	.	.	PUNCT
ejpam-4036	287	1	then	then	ADV
ejpam-4036	287	2	g	g	PROPN
ejpam-4036	287	3	=	=	SYM
ejpam-4036	287	4	g	g	PROPN
ejpam-4036	287	5	/	/	SYM
ejpam-4036	287	6	q	q	NOUN
ejpam-4036	287	7	is	be	AUX
ejpam-4036	287	8	nilpotent	nilpotent	ADJ
ejpam-4036	287	9	by	by	ADP
ejpam-4036	287	10	our	our	PRON
ejpam-4036	287	11	choice	choice	NOUN
ejpam-4036	287	12	of	of	ADP
ejpam-4036	287	13	g	g	PROPN
ejpam-4036	288	1	and	and	CCONJ
ejpam-4036	288	2	so	so	ADV
ejpam-4036	288	3	g	g	PROPN
ejpam-4036	288	4	is	be	AUX
ejpam-4036	288	5	nilpotent	nilpotent	ADJ
ejpam-4036	288	6	which	which	PRON
ejpam-4036	288	7	yields	yield	VERB
ejpam-4036	288	8	the	the	DET
ejpam-4036	288	9	desired	desire	VERB
ejpam-4036	288	10	contradiction	contradiction	NOUN
ejpam-4036	288	11	.	.	PUNCT
ejpam-4036	289	1	4	4	X
ejpam-4036	289	2	.	.	X
ejpam-4036	290	1	some	some	DET
ejpam-4036	290	2	applications	application	NOUN
ejpam-4036	290	3	as	as	SCONJ
ejpam-4036	290	4	it	it	PRON
ejpam-4036	290	5	was	be	AUX
ejpam-4036	290	6	mentioned	mention	VERB
ejpam-4036	290	7	in	in	ADP
ejpam-4036	290	8	the	the	DET
ejpam-4036	290	9	introduction	introduction	NOUN
ejpam-4036	290	10	each	each	PRON
ejpam-4036	290	11	of	of	ADP
ejpam-4036	290	12	c	c	NOUN
ejpam-4036	290	13	-	-	PUNCT
ejpam-4036	290	14	normality	normality	NOUN
ejpam-4036	290	15	and	and	CCONJ
ejpam-4036	290	16	ss	ss	NOUN
ejpam-4036	290	17	-	-	PUNCT
ejpam-4036	290	18	quasinormality	quasinormality	NOUN
ejpam-4036	290	19	subgroups	subgroup	NOUN
ejpam-4036	290	20	implies	imply	VERB
ejpam-4036	290	21	css	cs	NOUN
ejpam-4036	290	22	-	-	PUNCT
ejpam-4036	290	23	subgroups	subgroup	NOUN
ejpam-4036	290	24	.	.	PUNCT
ejpam-4036	291	1	therefore	therefore	ADV
ejpam-4036	291	2	the	the	DET
ejpam-4036	291	3	following	follow	VERB
ejpam-4036	291	4	results	result	NOUN
ejpam-4036	291	5	are	be	AUX
ejpam-4036	291	6	direct	direct	ADJ
ejpam-4036	291	7	consequences	consequence	NOUN
ejpam-4036	291	8	of	of	ADP
ejpam-4036	291	9	our	our	PRON
ejpam-4036	291	10	results	result	NOUN
ejpam-4036	291	11	.	.	PUNCT
ejpam-4036	292	1	corollary	corollary	ADJ
ejpam-4036	292	2	8	8	NUM
ejpam-4036	292	3	.	.	PUNCT
ejpam-4036	293	1	(	(	PUNCT
ejpam-4036	293	2	[	[	X
ejpam-4036	293	3	1	1	NUM
ejpam-4036	293	4	,	,	PUNCT
ejpam-4036	293	5	lemma	lemma	PROPN
ejpam-4036	293	6	3.1	3.1	NUM
ejpam-4036	293	7	]	]	PUNCT
ejpam-4036	293	8	)	)	PUNCT
ejpam-4036	293	9	let	let	VERB
ejpam-4036	293	10	p	p	PRON
ejpam-4036	293	11	be	be	AUX
ejpam-4036	293	12	the	the	DET
ejpam-4036	293	13	smallest	small	ADJ
ejpam-4036	293	14	prime	prime	ADJ
ejpam-4036	293	15	dividing	dividing	NOUN
ejpam-4036	293	16	|g|	|g|	PROPN
ejpam-4036	293	17	and	and	CCONJ
ejpam-4036	293	18	p	p	X
ejpam-4036	293	19	a	a	DET
ejpam-4036	293	20	sylow	sylow	NOUN
ejpam-4036	293	21	p	p	NOUN
ejpam-4036	293	22	-	-	PUNCT
ejpam-4036	293	23	subgroup	subgroup	NOUN
ejpam-4036	293	24	of	of	ADP
ejpam-4036	293	25	a	a	DET
ejpam-4036	293	26	group	group	NOUN
ejpam-4036	293	27	g.	g.	NOUN
ejpam-4036	294	1	if	if	SCONJ
ejpam-4036	294	2	every	every	DET
ejpam-4036	294	3	subgroup	subgroup	NOUN
ejpam-4036	294	4	of	of	ADP
ejpam-4036	294	5	p	p	NOUN
ejpam-4036	294	6	of	of	ADP
ejpam-4036	294	7	prime	prime	ADJ
ejpam-4036	294	8	order	order	NOUN
ejpam-4036	294	9	or	or	CCONJ
ejpam-4036	294	10	of	of	ADP
ejpam-4036	294	11	order	order	NOUN
ejpam-4036	294	12	4	4	NUM
ejpam-4036	294	13	(	(	PUNCT
ejpam-4036	294	14	if	if	SCONJ
ejpam-4036	294	15	p	p	X
ejpam-4036	294	16	=	=	NOUN
ejpam-4036	294	17	2	2	NUM
ejpam-4036	294	18	)	)	PUNCT
ejpam-4036	294	19	is	be	AUX
ejpam-4036	294	20	c	c	NOUN
ejpam-4036	294	21	-	-	ADJ
ejpam-4036	294	22	normal	normal	ADJ
ejpam-4036	294	23	in	in	ADP
ejpam-4036	294	24	g	g	PROPN
ejpam-4036	294	25	,	,	PUNCT
ejpam-4036	294	26	then	then	ADV
ejpam-4036	294	27	g	g	PROPN
ejpam-4036	294	28	is	be	AUX
ejpam-4036	294	29	p	p	NOUN
ejpam-4036	294	30	-	-	PUNCT
ejpam-4036	294	31	nilpotent	nilpotent	ADJ
ejpam-4036	294	32	.	.	PUNCT
ejpam-4036	295	1	a.	a.	NOUN
ejpam-4036	295	2	heliel	heliel	PROPN
ejpam-4036	295	3	,	,	PUNCT
ejpam-4036	295	4	r.	r.	PROPN
ejpam-4036	295	5	hijazi	hijazi	PROPN
ejpam-4036	295	6	,	,	PUNCT
ejpam-4036	295	7	s.	s.	PROPN
ejpam-4036	295	8	al	al	PROPN
ejpam-4036	295	9	-	-	PUNCT
ejpam-4036	295	10	shammari	shammari	PROPN
ejpam-4036	295	11	/	/	SYM
ejpam-4036	295	12	eur	eur	PROPN
ejpam-4036	295	13	.	.	PUNCT
ejpam-4036	296	1	j.	j.	PROPN
ejpam-4036	296	2	pure	pure	PROPN
ejpam-4036	296	3	appl	appl	PROPN
ejpam-4036	296	4	.	.	PROPN
ejpam-4036	296	5	math	math	PROPN
ejpam-4036	296	6	,	,	PUNCT
ejpam-4036	296	7	14	14	NUM
ejpam-4036	296	8	(	(	PUNCT
ejpam-4036	296	9	3	3	NUM
ejpam-4036	296	10	)	)	PUNCT
ejpam-4036	296	11	(	(	PUNCT
ejpam-4036	296	12	2021	2021	NUM
ejpam-4036	296	13	)	)	PUNCT
ejpam-4036	296	14	,	,	PUNCT
ejpam-4036	296	15	1002	1002	NUM
ejpam-4036	296	16	-	-	SYM
ejpam-4036	296	17	1014	1014	NUM
ejpam-4036	296	18	1011	1011	NUM
ejpam-4036	296	19	corollary	corollary	NOUN
ejpam-4036	296	20	9	9	NUM
ejpam-4036	296	21	.	.	PUNCT
ejpam-4036	297	1	(	(	PUNCT
ejpam-4036	297	2	[	[	X
ejpam-4036	297	3	18	18	NUM
ejpam-4036	297	4	,	,	PUNCT
ejpam-4036	297	5	theorem	theorem	VERB
ejpam-4036	297	6	4.2	4.2	NUM
ejpam-4036	297	7	]	]	PUNCT
ejpam-4036	297	8	)	)	PUNCT
ejpam-4036	297	9	let	let	VERB
ejpam-4036	297	10	g	g	PRON
ejpam-4036	297	11	be	be	AUX
ejpam-4036	297	12	a	a	DET
ejpam-4036	297	13	group	group	NOUN
ejpam-4036	297	14	such	such	ADJ
ejpam-4036	297	15	that	that	SCONJ
ejpam-4036	297	16	every	every	DET
ejpam-4036	297	17	subgroup	subgroup	NOUN
ejpam-4036	297	18	of	of	ADP
ejpam-4036	297	19	g	g	PROPN
ejpam-4036	297	20	of	of	ADP
ejpam-4036	297	21	prime	prime	ADJ
ejpam-4036	297	22	order	order	NOUN
ejpam-4036	297	23	or	or	CCONJ
ejpam-4036	297	24	of	of	ADP
ejpam-4036	297	25	order	order	NOUN
ejpam-4036	297	26	4	4	NUM
ejpam-4036	297	27	(	(	PUNCT
ejpam-4036	297	28	if	if	SCONJ
ejpam-4036	297	29	p	p	X
ejpam-4036	297	30	=	=	NOUN
ejpam-4036	297	31	2	2	NUM
ejpam-4036	297	32	)	)	PUNCT
ejpam-4036	297	33	is	be	AUX
ejpam-4036	297	34	c	c	NOUN
ejpam-4036	297	35	-	-	ADJ
ejpam-4036	297	36	normal	normal	ADJ
ejpam-4036	297	37	in	in	ADP
ejpam-4036	297	38	g	g	PROPN
ejpam-4036	297	39	,	,	PUNCT
ejpam-4036	297	40	then	then	ADV
ejpam-4036	297	41	g	g	PROPN
ejpam-4036	297	42	is	be	AUX
ejpam-4036	297	43	supersolvable	supersolvable	ADJ
ejpam-4036	297	44	.	.	PUNCT
ejpam-4036	298	1	corollary	corollary	ADJ
ejpam-4036	298	2	10	10	NUM
ejpam-4036	298	3	.	.	PUNCT
ejpam-4036	299	1	(	(	PUNCT
ejpam-4036	299	2	[	[	X
ejpam-4036	299	3	1	1	NUM
ejpam-4036	299	4	,	,	PUNCT
ejpam-4036	299	5	theorem	theorem	VERB
ejpam-4036	299	6	3.2	3.2	NUM
ejpam-4036	299	7	]	]	PUNCT
ejpam-4036	299	8	and	and	CCONJ
ejpam-4036	299	9	[	[	X
ejpam-4036	299	10	16	16	NUM
ejpam-4036	299	11	,	,	PUNCT
ejpam-4036	299	12	theorem	theorem	VERB
ejpam-4036	299	13	3.9	3.9	NUM
ejpam-4036	299	14	]	]	PUNCT
ejpam-4036	299	15	)	)	PUNCT
ejpam-4036	299	16	let	let	VERB
ejpam-4036	299	17	f	f	PRON
ejpam-4036	299	18	be	be	AUX
ejpam-4036	299	19	a	a	DET
ejpam-4036	299	20	saturated	saturated	ADJ
ejpam-4036	299	21	formation	formation	NOUN
ejpam-4036	299	22	containing	contain	VERB
ejpam-4036	299	23	u	u	NOUN
ejpam-4036	299	24	and	and	CCONJ
ejpam-4036	299	25	g	g	ADP
ejpam-4036	299	26	a	a	DET
ejpam-4036	299	27	group	group	NOUN
ejpam-4036	299	28	.	.	PUNCT
ejpam-4036	300	1	g	g	PROPN
ejpam-4036	300	2	∈	∈	PROPN
ejpam-4036	300	3	f	f	PROPN
ejpam-4036	301	1	if	if	SCONJ
ejpam-4036	301	2	and	and	CCONJ
ejpam-4036	301	3	only	only	ADV
ejpam-4036	301	4	if	if	SCONJ
ejpam-4036	301	5	there	there	PRON
ejpam-4036	301	6	exists	exist	VERB
ejpam-4036	301	7	a	a	DET
ejpam-4036	301	8	normal	normal	ADJ
ejpam-4036	301	9	subgroup	subgroup	NOUN
ejpam-4036	301	10	h	h	NOUN
ejpam-4036	301	11	in	in	ADP
ejpam-4036	301	12	g	g	PROPN
ejpam-4036	301	13	such	such	ADJ
ejpam-4036	301	14	that	that	SCONJ
ejpam-4036	301	15	g	g	NOUN
ejpam-4036	301	16	/	/	SYM
ejpam-4036	301	17	h	h	NOUN
ejpam-4036	301	18	∈	∈	PROPN
ejpam-4036	301	19	f	f	PROPN
ejpam-4036	301	20	and	and	CCONJ
ejpam-4036	301	21	every	every	DET
ejpam-4036	301	22	subgroup	subgroup	NOUN
ejpam-4036	301	23	of	of	ADP
ejpam-4036	301	24	h	h	NOUN
ejpam-4036	301	25	of	of	ADP
ejpam-4036	301	26	prime	prime	ADJ
ejpam-4036	301	27	order	order	NOUN
ejpam-4036	301	28	or	or	CCONJ
ejpam-4036	301	29	of	of	ADP
ejpam-4036	301	30	order	order	NOUN
ejpam-4036	301	31	4	4	NUM
ejpam-4036	301	32	(	(	PUNCT
ejpam-4036	301	33	if	if	SCONJ
ejpam-4036	301	34	p	p	X
ejpam-4036	301	35	=	=	NOUN
ejpam-4036	301	36	2	2	NUM
ejpam-4036	301	37	)	)	PUNCT
ejpam-4036	301	38	is	be	AUX
ejpam-4036	301	39	c	c	NOUN
ejpam-4036	301	40	-	-	ADJ
ejpam-4036	301	41	normal	normal	ADJ
ejpam-4036	301	42	in	in	ADP
ejpam-4036	301	43	g.	g.	PROPN
ejpam-4036	301	44	corollary	corollary	PROPN
ejpam-4036	301	45	11	11	NUM
ejpam-4036	301	46	.	.	PUNCT
ejpam-4036	302	1	(	(	PUNCT
ejpam-4036	302	2	[	[	X
ejpam-4036	302	3	1	1	NUM
ejpam-4036	302	4	,	,	PUNCT
ejpam-4036	302	5	theorem	theorem	VERB
ejpam-4036	302	6	3.6	3.6	NUM
ejpam-4036	302	7	]	]	PUNCT
ejpam-4036	302	8	and	and	CCONJ
ejpam-4036	302	9	[	[	X
ejpam-4036	302	10	24	24	NUM
ejpam-4036	302	11	,	,	PUNCT
ejpam-4036	302	12	theorem	theorem	VERB
ejpam-4036	302	13	3	3	NUM
ejpam-4036	302	14	]	]	PUNCT
ejpam-4036	302	15	)	)	PUNCT
ejpam-4036	302	16	let	let	VERB
ejpam-4036	302	17	f	f	PRON
ejpam-4036	302	18	be	be	AUX
ejpam-4036	302	19	a	a	DET
ejpam-4036	302	20	saturated	saturated	ADJ
ejpam-4036	302	21	formation	formation	NOUN
ejpam-4036	302	22	containing	contain	VERB
ejpam-4036	302	23	u	u	NOUN
ejpam-4036	302	24	and	and	CCONJ
ejpam-4036	302	25	g	g	ADP
ejpam-4036	302	26	a	a	DET
ejpam-4036	302	27	group	group	NOUN
ejpam-4036	302	28	.	.	PUNCT
ejpam-4036	303	1	g	g	PROPN
ejpam-4036	303	2	∈	∈	PROPN
ejpam-4036	303	3	f	f	PROPN
ejpam-4036	304	1	if	if	SCONJ
ejpam-4036	304	2	and	and	CCONJ
ejpam-4036	304	3	only	only	ADV
ejpam-4036	304	4	if	if	SCONJ
ejpam-4036	304	5	there	there	PRON
ejpam-4036	304	6	exists	exist	VERB
ejpam-4036	304	7	a	a	DET
ejpam-4036	304	8	normal	normal	ADJ
ejpam-4036	304	9	solvable	solvable	ADJ
ejpam-4036	304	10	subgroup	subgroup	NOUN
ejpam-4036	304	11	h	h	NOUN
ejpam-4036	304	12	in	in	ADP
ejpam-4036	304	13	g	g	PROPN
ejpam-4036	304	14	such	such	ADJ
ejpam-4036	304	15	that	that	SCONJ
ejpam-4036	304	16	g	g	NOUN
ejpam-4036	304	17	/	/	SYM
ejpam-4036	304	18	h	h	NOUN
ejpam-4036	304	19	∈	∈	PROPN
ejpam-4036	304	20	f	f	PROPN
ejpam-4036	304	21	and	and	CCONJ
ejpam-4036	304	22	every	every	DET
ejpam-4036	304	23	subgroup	subgroup	NOUN
ejpam-4036	304	24	of	of	ADP
ejpam-4036	304	25	f	f	PROPN
ejpam-4036	304	26	(	(	PUNCT
ejpam-4036	304	27	h	h	NOUN
ejpam-4036	304	28	)	)	PUNCT
ejpam-4036	304	29	of	of	ADP
ejpam-4036	304	30	prime	prime	ADJ
ejpam-4036	304	31	order	order	NOUN
ejpam-4036	304	32	or	or	CCONJ
ejpam-4036	304	33	of	of	ADP
ejpam-4036	304	34	order	order	NOUN
ejpam-4036	304	35	4	4	NUM
ejpam-4036	304	36	(	(	PUNCT
ejpam-4036	304	37	if	if	SCONJ
ejpam-4036	304	38	p	p	X
ejpam-4036	304	39	=	=	NOUN
ejpam-4036	304	40	2	2	NUM
ejpam-4036	304	41	)	)	PUNCT
ejpam-4036	304	42	is	be	AUX
ejpam-4036	304	43	c	c	NOUN
ejpam-4036	304	44	-	-	ADJ
ejpam-4036	304	45	normal	normal	ADJ
ejpam-4036	304	46	in	in	ADP
ejpam-4036	304	47	g.	g.	PROPN
ejpam-4036	304	48	corollary	corollary	PROPN
ejpam-4036	304	49	12	12	NUM
ejpam-4036	304	50	.	.	PUNCT
ejpam-4036	305	1	(	(	PUNCT
ejpam-4036	305	2	[	[	X
ejpam-4036	305	3	21	21	NUM
ejpam-4036	305	4	,	,	PUNCT
ejpam-4036	305	5	theorem	theorem	VERB
ejpam-4036	305	6	3.2	3.2	NUM
ejpam-4036	305	7	]	]	PUNCT
ejpam-4036	305	8	)	)	PUNCT
ejpam-4036	305	9	let	let	VERB
ejpam-4036	305	10	f	f	PRON
ejpam-4036	305	11	be	be	AUX
ejpam-4036	305	12	a	a	DET
ejpam-4036	305	13	saturated	saturated	ADJ
ejpam-4036	305	14	formation	formation	NOUN
ejpam-4036	305	15	containing	contain	VERB
ejpam-4036	305	16	u	u	NOUN
ejpam-4036	305	17	and	and	CCONJ
ejpam-4036	305	18	g	g	ADP
ejpam-4036	305	19	a	a	DET
ejpam-4036	305	20	group	group	NOUN
ejpam-4036	305	21	.	.	PUNCT
ejpam-4036	306	1	if	if	SCONJ
ejpam-4036	306	2	g	g	PROPN
ejpam-4036	306	3	has	have	VERB
ejpam-4036	306	4	a	a	DET
ejpam-4036	306	5	normal	normal	ADJ
ejpam-4036	306	6	subgroup	subgroup	NOUN
ejpam-4036	306	7	h	h	NOUN
ejpam-4036	306	8	such	such	ADJ
ejpam-4036	306	9	that	that	SCONJ
ejpam-4036	306	10	g	g	NOUN
ejpam-4036	306	11	/	/	SYM
ejpam-4036	306	12	h	h	NOUN
ejpam-4036	306	13	∈	∈	PROPN
ejpam-4036	306	14	f	f	PROPN
ejpam-4036	306	15	and	and	CCONJ
ejpam-4036	306	16	every	every	DET
ejpam-4036	306	17	subgroup	subgroup	NOUN
ejpam-4036	306	18	of	of	ADP
ejpam-4036	306	19	f	f	PROPN
ejpam-4036	306	20	∗(h	∗(h	PROPN
ejpam-4036	306	21	)	)	PUNCT
ejpam-4036	306	22	of	of	ADP
ejpam-4036	306	23	prime	prime	ADJ
ejpam-4036	306	24	order	order	NOUN
ejpam-4036	306	25	or	or	CCONJ
ejpam-4036	306	26	of	of	ADP
ejpam-4036	306	27	order	order	NOUN
ejpam-4036	306	28	4	4	NUM
ejpam-4036	306	29	is	be	AUX
ejpam-4036	306	30	c	c	NOUN
ejpam-4036	306	31	-	-	ADJ
ejpam-4036	306	32	normal	normal	ADJ
ejpam-4036	306	33	in	in	ADP
ejpam-4036	306	34	g	g	PROPN
ejpam-4036	306	35	,	,	PUNCT
ejpam-4036	306	36	then	then	ADV
ejpam-4036	306	37	g	g	PROPN
ejpam-4036	306	38	∈	∈	PROPN
ejpam-4036	306	39	f.	f.	PROPN
ejpam-4036	306	40	corollary	corollary	PROPN
ejpam-4036	306	41	13	13	NUM
ejpam-4036	306	42	.	.	PUNCT
ejpam-4036	307	1	(	(	PUNCT
ejpam-4036	307	2	[	[	X
ejpam-4036	307	3	19	19	NUM
ejpam-4036	307	4	,	,	PUNCT
ejpam-4036	307	5	theorem	theorem	VERB
ejpam-4036	307	6	3.1	3.1	NUM
ejpam-4036	307	7	]	]	PUNCT
ejpam-4036	307	8	)	)	PUNCT
ejpam-4036	307	9	let	let	VERB
ejpam-4036	307	10	h	h	NOUN
ejpam-4036	307	11	be	be	AUX
ejpam-4036	307	12	a	a	DET
ejpam-4036	307	13	normal	normal	ADJ
ejpam-4036	307	14	subgroup	subgroup	NOUN
ejpam-4036	307	15	of	of	ADP
ejpam-4036	307	16	a	a	DET
ejpam-4036	307	17	group	group	NOUN
ejpam-4036	307	18	g	g	NOUN
ejpam-4036	307	19	such	such	DET
ejpam-4036	307	20	that	that	SCONJ
ejpam-4036	307	21	g	g	NOUN
ejpam-4036	307	22	/	/	SYM
ejpam-4036	307	23	h	h	NOUN
ejpam-4036	307	24	is	be	AUX
ejpam-4036	307	25	nilpotent	nilpotent	ADJ
ejpam-4036	307	26	and	and	CCONJ
ejpam-4036	307	27	every	every	DET
ejpam-4036	307	28	cyclic	cyclic	ADJ
ejpam-4036	307	29	subgroup	subgroup	NOUN
ejpam-4036	307	30	of	of	ADP
ejpam-4036	307	31	order	order	NOUN
ejpam-4036	307	32	4	4	NUM
ejpam-4036	307	33	of	of	ADP
ejpam-4036	307	34	f	f	PROPN
ejpam-4036	307	35	∗(h	∗(h	PROPN
ejpam-4036	307	36	)	)	PUNCT
ejpam-4036	307	37	is	be	AUX
ejpam-4036	307	38	c	c	NOUN
ejpam-4036	307	39	-	-	ADJ
ejpam-4036	307	40	normal	normal	ADJ
ejpam-4036	307	41	in	in	ADP
ejpam-4036	307	42	g	g	PROPN
ejpam-4036	307	43	,	,	PUNCT
ejpam-4036	307	44	then	then	ADV
ejpam-4036	307	45	g	g	PROPN
ejpam-4036	307	46	is	be	AUX
ejpam-4036	307	47	nilpotent	nilpotent	ADJ
ejpam-4036	307	48	if	if	SCONJ
ejpam-4036	307	49	and	and	CCONJ
ejpam-4036	307	50	only	only	ADV
ejpam-4036	307	51	if	if	SCONJ
ejpam-4036	307	52	every	every	DET
ejpam-4036	307	53	subgroup	subgroup	NOUN
ejpam-4036	307	54	of	of	ADP
ejpam-4036	307	55	prime	prime	ADJ
ejpam-4036	307	56	order	order	NOUN
ejpam-4036	307	57	of	of	ADP
ejpam-4036	307	58	f	f	PROPN
ejpam-4036	307	59	∗(h	∗(h	PROPN
ejpam-4036	307	60	)	)	PUNCT
ejpam-4036	307	61	is	be	AUX
ejpam-4036	307	62	contained	contain	VERB
ejpam-4036	307	63	in	in	ADP
ejpam-4036	307	64	the	the	DET
ejpam-4036	307	65	hypercenter	hypercenter	NOUN
ejpam-4036	307	66	z∞(g	z∞(g	NOUN
ejpam-4036	307	67	)	)	PUNCT
ejpam-4036	307	68	of	of	ADP
ejpam-4036	307	69	g.	g.	PROPN
ejpam-4036	307	70	corollary	corollary	PROPN
ejpam-4036	307	71	14	14	NUM
ejpam-4036	307	72	.	.	PUNCT
ejpam-4036	308	1	let	let	VERB
ejpam-4036	308	2	p	p	PRON
ejpam-4036	308	3	be	be	AUX
ejpam-4036	308	4	the	the	DET
ejpam-4036	308	5	smallest	small	ADJ
ejpam-4036	308	6	prime	prime	ADJ
ejpam-4036	308	7	dividing	dividing	NOUN
ejpam-4036	308	8	|g|	|g|	PROPN
ejpam-4036	308	9	and	and	CCONJ
ejpam-4036	308	10	p	p	X
ejpam-4036	308	11	a	a	DET
ejpam-4036	308	12	sylow	sylow	NOUN
ejpam-4036	308	13	p	p	NOUN
ejpam-4036	308	14	-	-	PUNCT
ejpam-4036	308	15	subgroup	subgroup	NOUN
ejpam-4036	308	16	of	of	ADP
ejpam-4036	308	17	a	a	DET
ejpam-4036	308	18	group	group	NOUN
ejpam-4036	308	19	g.	g.	NOUN
ejpam-4036	309	1	if	if	SCONJ
ejpam-4036	309	2	every	every	DET
ejpam-4036	309	3	subgroup	subgroup	NOUN
ejpam-4036	309	4	of	of	ADP
ejpam-4036	309	5	p	p	NOUN
ejpam-4036	309	6	of	of	ADP
ejpam-4036	309	7	prime	prime	ADJ
ejpam-4036	309	8	order	order	NOUN
ejpam-4036	309	9	or	or	CCONJ
ejpam-4036	309	10	of	of	ADP
ejpam-4036	309	11	order	order	NOUN
ejpam-4036	309	12	4	4	NUM
ejpam-4036	309	13	(	(	PUNCT
ejpam-4036	309	14	if	if	SCONJ
ejpam-4036	309	15	p	p	X
ejpam-4036	309	16	=	=	NOUN
ejpam-4036	309	17	2	2	NUM
ejpam-4036	309	18	)	)	PUNCT
ejpam-4036	309	19	is	be	AUX
ejpam-4036	309	20	ss	ss	NOUN
ejpam-4036	309	21	-	-	ADJ
ejpam-4036	309	22	quasinormal	quasinormal	ADJ
ejpam-4036	309	23	in	in	ADP
ejpam-4036	309	24	g	g	PROPN
ejpam-4036	309	25	,	,	PUNCT
ejpam-4036	309	26	then	then	ADV
ejpam-4036	309	27	g	g	PROPN
ejpam-4036	309	28	is	be	AUX
ejpam-4036	309	29	p	p	NOUN
ejpam-4036	309	30	-	-	PUNCT
ejpam-4036	309	31	nilpotent	nilpotent	ADJ
ejpam-4036	309	32	.	.	PUNCT
ejpam-4036	310	1	corollary	corollary	ADJ
ejpam-4036	310	2	15	15	NUM
ejpam-4036	310	3	.	.	PUNCT
ejpam-4036	311	1	(	(	PUNCT
ejpam-4036	311	2	[	[	X
ejpam-4036	311	3	11	11	NUM
ejpam-4036	311	4	,	,	PUNCT
ejpam-4036	311	5	theorem	theorem	VERB
ejpam-4036	311	6	3.4	3.4	NUM
ejpam-4036	311	7	]	]	PUNCT
ejpam-4036	311	8	)	)	PUNCT
ejpam-4036	311	9	let	let	VERB
ejpam-4036	311	10	g	g	PRON
ejpam-4036	311	11	be	be	AUX
ejpam-4036	311	12	a	a	DET
ejpam-4036	311	13	group	group	NOUN
ejpam-4036	311	14	such	such	ADJ
ejpam-4036	311	15	that	that	SCONJ
ejpam-4036	311	16	every	every	DET
ejpam-4036	311	17	subgroup	subgroup	NOUN
ejpam-4036	311	18	of	of	ADP
ejpam-4036	311	19	g	g	PROPN
ejpam-4036	311	20	of	of	ADP
ejpam-4036	311	21	prime	prime	ADJ
ejpam-4036	311	22	order	order	NOUN
ejpam-4036	311	23	or	or	CCONJ
ejpam-4036	311	24	of	of	ADP
ejpam-4036	311	25	order	order	NOUN
ejpam-4036	311	26	4	4	NUM
ejpam-4036	311	27	(	(	PUNCT
ejpam-4036	311	28	if	if	SCONJ
ejpam-4036	311	29	p	p	X
ejpam-4036	311	30	=	=	NOUN
ejpam-4036	311	31	2	2	NUM
ejpam-4036	311	32	)	)	PUNCT
ejpam-4036	311	33	is	be	AUX
ejpam-4036	311	34	ss	ss	NOUN
ejpam-4036	311	35	-	-	ADJ
ejpam-4036	311	36	quasinormal	quasinormal	ADJ
ejpam-4036	311	37	in	in	ADP
ejpam-4036	311	38	g	g	PROPN
ejpam-4036	311	39	,	,	PUNCT
ejpam-4036	311	40	then	then	ADV
ejpam-4036	311	41	g	g	PROPN
ejpam-4036	311	42	is	be	AUX
ejpam-4036	311	43	supersolvable	supersolvable	ADJ
ejpam-4036	311	44	.	.	PUNCT
ejpam-4036	312	1	corollary	corollary	ADJ
ejpam-4036	312	2	16	16	NUM
ejpam-4036	312	3	.	.	PUNCT
ejpam-4036	313	1	let	let	VERB
ejpam-4036	313	2	f	f	PRON
ejpam-4036	313	3	be	be	AUX
ejpam-4036	313	4	a	a	DET
ejpam-4036	313	5	saturated	saturated	ADJ
ejpam-4036	313	6	formation	formation	NOUN
ejpam-4036	313	7	containing	contain	VERB
ejpam-4036	313	8	u	u	NOUN
ejpam-4036	313	9	and	and	CCONJ
ejpam-4036	313	10	g	g	ADP
ejpam-4036	313	11	a	a	DET
ejpam-4036	313	12	group	group	NOUN
ejpam-4036	313	13	.	.	PUNCT
ejpam-4036	314	1	g	g	PROPN
ejpam-4036	314	2	∈	∈	PROPN
ejpam-4036	314	3	f	f	PROPN
ejpam-4036	315	1	if	if	SCONJ
ejpam-4036	315	2	and	and	CCONJ
ejpam-4036	315	3	only	only	ADV
ejpam-4036	315	4	if	if	SCONJ
ejpam-4036	315	5	there	there	PRON
ejpam-4036	315	6	exists	exist	VERB
ejpam-4036	315	7	a	a	DET
ejpam-4036	315	8	normal	normal	ADJ
ejpam-4036	315	9	subgroup	subgroup	NOUN
ejpam-4036	315	10	h	h	NOUN
ejpam-4036	315	11	in	in	ADP
ejpam-4036	315	12	g	g	PROPN
ejpam-4036	315	13	such	such	ADJ
ejpam-4036	315	14	that	that	SCONJ
ejpam-4036	315	15	g	g	NOUN
ejpam-4036	315	16	/	/	SYM
ejpam-4036	315	17	h	h	NOUN
ejpam-4036	315	18	∈	∈	PROPN
ejpam-4036	315	19	f	f	PROPN
ejpam-4036	315	20	and	and	CCONJ
ejpam-4036	315	21	every	every	DET
ejpam-4036	315	22	subgroup	subgroup	NOUN
ejpam-4036	315	23	of	of	ADP
ejpam-4036	315	24	h	h	NOUN
ejpam-4036	315	25	of	of	ADP
ejpam-4036	315	26	prime	prime	ADJ
ejpam-4036	315	27	order	order	NOUN
ejpam-4036	315	28	or	or	CCONJ
ejpam-4036	315	29	of	of	ADP
ejpam-4036	315	30	order	order	NOUN
ejpam-4036	315	31	4	4	NUM
ejpam-4036	315	32	(	(	PUNCT
ejpam-4036	315	33	if	if	SCONJ
ejpam-4036	315	34	p	p	X
ejpam-4036	315	35	=	=	NOUN
ejpam-4036	315	36	2	2	NUM
ejpam-4036	315	37	)	)	PUNCT
ejpam-4036	315	38	is	be	AUX
ejpam-4036	315	39	ss	ss	NOUN
ejpam-4036	315	40	-	-	ADJ
ejpam-4036	315	41	quasinormal	quasinormal	ADJ
ejpam-4036	315	42	in	in	ADP
ejpam-4036	315	43	g.	g.	PROPN
ejpam-4036	315	44	corollary	corollary	PROPN
ejpam-4036	315	45	17	17	NUM
ejpam-4036	315	46	.	.	PUNCT
ejpam-4036	316	1	(	(	PUNCT
ejpam-4036	316	2	[	[	X
ejpam-4036	316	3	11	11	NUM
ejpam-4036	316	4	,	,	PUNCT
ejpam-4036	316	5	theorem	theorem	VERB
ejpam-4036	316	6	3.5	3.5	NUM
ejpam-4036	316	7	]	]	PUNCT
ejpam-4036	316	8	)	)	PUNCT
ejpam-4036	316	9	let	let	VERB
ejpam-4036	316	10	f	f	PRON
ejpam-4036	316	11	be	be	AUX
ejpam-4036	316	12	a	a	DET
ejpam-4036	316	13	saturated	saturated	ADJ
ejpam-4036	316	14	formation	formation	NOUN
ejpam-4036	316	15	containing	contain	VERB
ejpam-4036	316	16	u	u	NOUN
ejpam-4036	316	17	and	and	CCONJ
ejpam-4036	316	18	g	g	ADP
ejpam-4036	316	19	a	a	DET
ejpam-4036	316	20	group	group	NOUN
ejpam-4036	316	21	.	.	PUNCT
ejpam-4036	317	1	g	g	PROPN
ejpam-4036	317	2	∈	∈	PROPN
ejpam-4036	317	3	f	f	PROPN
ejpam-4036	318	1	if	if	SCONJ
ejpam-4036	318	2	and	and	CCONJ
ejpam-4036	318	3	only	only	ADV
ejpam-4036	318	4	if	if	SCONJ
ejpam-4036	318	5	there	there	PRON
ejpam-4036	318	6	exists	exist	VERB
ejpam-4036	318	7	a	a	DET
ejpam-4036	318	8	normal	normal	ADJ
ejpam-4036	318	9	solvable	solvable	ADJ
ejpam-4036	318	10	subgroup	subgroup	NOUN
ejpam-4036	318	11	h	h	NOUN
ejpam-4036	318	12	in	in	ADP
ejpam-4036	318	13	g	g	PROPN
ejpam-4036	318	14	such	such	ADJ
ejpam-4036	318	15	that	that	SCONJ
ejpam-4036	318	16	g	g	NOUN
ejpam-4036	318	17	/	/	SYM
ejpam-4036	318	18	h	h	NOUN
ejpam-4036	318	19	∈	∈	PROPN
ejpam-4036	318	20	f	f	PROPN
ejpam-4036	318	21	and	and	CCONJ
ejpam-4036	318	22	every	every	DET
ejpam-4036	318	23	subgroup	subgroup	NOUN
ejpam-4036	318	24	of	of	ADP
ejpam-4036	318	25	f	f	PROPN
ejpam-4036	318	26	(	(	PUNCT
ejpam-4036	318	27	h	h	NOUN
ejpam-4036	318	28	)	)	PUNCT
ejpam-4036	318	29	of	of	ADP
ejpam-4036	318	30	prime	prime	ADJ
ejpam-4036	318	31	order	order	NOUN
ejpam-4036	318	32	or	or	CCONJ
ejpam-4036	318	33	of	of	ADP
ejpam-4036	318	34	order	order	NOUN
ejpam-4036	318	35	4	4	NUM
ejpam-4036	318	36	(	(	PUNCT
ejpam-4036	318	37	if	if	SCONJ
ejpam-4036	318	38	p	p	X
ejpam-4036	318	39	=	=	NOUN
ejpam-4036	318	40	2	2	NUM
ejpam-4036	318	41	)	)	PUNCT
ejpam-4036	318	42	is	be	AUX
ejpam-4036	318	43	ss	ss	NOUN
ejpam-4036	318	44	-	-	ADJ
ejpam-4036	318	45	quasinormal	quasinormal	ADJ
ejpam-4036	318	46	in	in	ADP
ejpam-4036	318	47	g.	g.	PROPN
ejpam-4036	318	48	corollary	corollary	PROPN
ejpam-4036	318	49	18	18	NUM
ejpam-4036	318	50	.	.	PUNCT
ejpam-4036	319	1	(	(	PUNCT
ejpam-4036	319	2	[	[	X
ejpam-4036	319	3	11	11	NUM
ejpam-4036	319	4	,	,	PUNCT
ejpam-4036	319	5	theorem	theorem	VERB
ejpam-4036	319	6	3.6	3.6	NUM
ejpam-4036	319	7	]	]	PUNCT
ejpam-4036	319	8	)	)	PUNCT
ejpam-4036	319	9	let	let	VERB
ejpam-4036	319	10	g	g	PRON
ejpam-4036	319	11	be	be	AUX
ejpam-4036	319	12	a	a	DET
ejpam-4036	319	13	group	group	NOUN
ejpam-4036	319	14	.	.	PUNCT
ejpam-4036	320	1	if	if	SCONJ
ejpam-4036	320	2	g	g	PROPN
ejpam-4036	320	3	has	have	VERB
ejpam-4036	320	4	a	a	DET
ejpam-4036	320	5	normal	normal	ADJ
ejpam-4036	320	6	subgroup	subgroup	NOUN
ejpam-4036	320	7	h	h	NOUN
ejpam-4036	320	8	such	such	ADJ
ejpam-4036	320	9	that	that	SCONJ
ejpam-4036	320	10	g	g	PROPN
ejpam-4036	320	11	/	/	SYM
ejpam-4036	320	12	h	h	NOUN
ejpam-4036	320	13	is	be	AUX
ejpam-4036	320	14	supersolvable	supersolvable	ADJ
ejpam-4036	320	15	and	and	CCONJ
ejpam-4036	320	16	every	every	DET
ejpam-4036	320	17	subgroup	subgroup	NOUN
ejpam-4036	320	18	of	of	ADP
ejpam-4036	320	19	f	f	PROPN
ejpam-4036	320	20	∗(h	∗(h	PROPN
ejpam-4036	320	21	)	)	PUNCT
ejpam-4036	320	22	of	of	ADP
ejpam-4036	320	23	prime	prime	ADJ
ejpam-4036	320	24	order	order	NOUN
ejpam-4036	320	25	or	or	CCONJ
ejpam-4036	320	26	of	of	ADP
ejpam-4036	320	27	order	order	NOUN
ejpam-4036	320	28	4	4	NUM
ejpam-4036	320	29	is	be	AUX
ejpam-4036	320	30	ss	ss	NOUN
ejpam-4036	320	31	-	-	ADJ
ejpam-4036	320	32	quasinormal	quasinormal	ADJ
ejpam-4036	320	33	in	in	ADP
ejpam-4036	320	34	g	g	PROPN
ejpam-4036	320	35	,	,	PUNCT
ejpam-4036	320	36	then	then	ADV
ejpam-4036	320	37	g	g	PROPN
ejpam-4036	320	38	is	be	AUX
ejpam-4036	320	39	supersolvable	supersolvable	ADJ
ejpam-4036	320	40	.	.	PUNCT
ejpam-4036	321	1	corollary	corollary	ADJ
ejpam-4036	321	2	19	19	NUM
ejpam-4036	321	3	.	.	PUNCT
ejpam-4036	322	1	(	(	PUNCT
ejpam-4036	322	2	[	[	X
ejpam-4036	322	3	11	11	NUM
ejpam-4036	322	4	,	,	PUNCT
ejpam-4036	322	5	theorem	theorem	VERB
ejpam-4036	322	6	3.7	3.7	NUM
ejpam-4036	322	7	]	]	PUNCT
ejpam-4036	322	8	)	)	PUNCT
ejpam-4036	322	9	let	let	VERB
ejpam-4036	322	10	f	f	PRON
ejpam-4036	322	11	be	be	AUX
ejpam-4036	322	12	a	a	DET
ejpam-4036	322	13	saturated	saturated	ADJ
ejpam-4036	322	14	formation	formation	NOUN
ejpam-4036	322	15	containing	contain	VERB
ejpam-4036	322	16	u	u	NOUN
ejpam-4036	322	17	and	and	CCONJ
ejpam-4036	322	18	g	g	ADP
ejpam-4036	322	19	a	a	DET
ejpam-4036	322	20	group	group	NOUN
ejpam-4036	322	21	.	.	PUNCT
ejpam-4036	323	1	then	then	ADV
ejpam-4036	323	2	g	g	PROPN
ejpam-4036	323	3	∈	∈	PROPN
ejpam-4036	323	4	f	f	PROPN
ejpam-4036	324	1	if	if	SCONJ
ejpam-4036	324	2	and	and	CCONJ
ejpam-4036	324	3	only	only	ADV
ejpam-4036	324	4	if	if	SCONJ
ejpam-4036	324	5	g	g	PROPN
ejpam-4036	324	6	has	have	VERB
ejpam-4036	324	7	a	a	DET
ejpam-4036	324	8	normal	normal	ADJ
ejpam-4036	324	9	subgroup	subgroup	NOUN
ejpam-4036	324	10	h	h	NOUN
ejpam-4036	324	11	such	such	ADJ
ejpam-4036	324	12	that	that	SCONJ
ejpam-4036	324	13	g	g	NOUN
ejpam-4036	324	14	/	/	SYM
ejpam-4036	324	15	h	h	NOUN
ejpam-4036	324	16	∈	∈	PROPN
ejpam-4036	324	17	f	f	PROPN
ejpam-4036	324	18	and	and	CCONJ
ejpam-4036	324	19	every	every	DET
ejpam-4036	324	20	subgroup	subgroup	NOUN
ejpam-4036	324	21	of	of	ADP
ejpam-4036	324	22	f	f	PROPN
ejpam-4036	324	23	∗(h	∗(h	PROPN
ejpam-4036	324	24	)	)	PUNCT
ejpam-4036	324	25	of	of	ADP
ejpam-4036	324	26	prime	prime	ADJ
ejpam-4036	324	27	order	order	NOUN
ejpam-4036	324	28	or	or	CCONJ
ejpam-4036	324	29	of	of	ADP
ejpam-4036	324	30	order	order	NOUN
ejpam-4036	324	31	4	4	NUM
ejpam-4036	324	32	is	be	AUX
ejpam-4036	324	33	ss	ss	NOUN
ejpam-4036	324	34	-	-	ADJ
ejpam-4036	324	35	quasinormal	quasinormal	ADJ
ejpam-4036	324	36	in	in	ADP
ejpam-4036	324	37	g.	g.	PROPN
ejpam-4036	324	38	corollary	corollary	PROPN
ejpam-4036	324	39	20	20	NUM
ejpam-4036	324	40	.	.	PUNCT
ejpam-4036	325	1	(	(	PUNCT
ejpam-4036	325	2	[	[	X
ejpam-4036	325	3	11	11	NUM
ejpam-4036	325	4	,	,	PUNCT
ejpam-4036	325	5	theorem	theorem	VERB
ejpam-4036	325	6	4.1	4.1	NUM
ejpam-4036	325	7	]	]	PUNCT
ejpam-4036	325	8	)	)	PUNCT
ejpam-4036	325	9	let	let	VERB
ejpam-4036	325	10	g	g	PRON
ejpam-4036	325	11	be	be	AUX
ejpam-4036	325	12	a	a	DET
ejpam-4036	325	13	group	group	NOUN
ejpam-4036	325	14	.	.	PUNCT
ejpam-4036	326	1	if	if	SCONJ
ejpam-4036	326	2	every	every	DET
ejpam-4036	326	3	subgroup	subgroup	NOUN
ejpam-4036	326	4	of	of	ADP
ejpam-4036	326	5	g	g	PROPN
ejpam-4036	326	6	of	of	ADP
ejpam-4036	326	7	prime	prime	ADJ
ejpam-4036	326	8	order	order	NOUN
ejpam-4036	326	9	is	be	AUX
ejpam-4036	326	10	contained	contain	VERB
ejpam-4036	326	11	in	in	ADP
ejpam-4036	326	12	z∞(g	z∞(g	NUM
ejpam-4036	326	13	)	)	PUNCT
ejpam-4036	326	14	and	and	CCONJ
ejpam-4036	326	15	every	every	DET
ejpam-4036	326	16	cyclic	cyclic	ADJ
ejpam-4036	326	17	subgroup	subgroup	NOUN
ejpam-4036	326	18	of	of	ADP
ejpam-4036	326	19	order	order	NOUN
ejpam-4036	326	20	4	4	NUM
ejpam-4036	326	21	of	of	ADP
ejpam-4036	326	22	g	g	PROPN
ejpam-4036	326	23	is	be	AUX
ejpam-4036	326	24	ss	ss	NOUN
ejpam-4036	326	25	-	-	ADJ
ejpam-4036	326	26	quasinormal	quasinormal	ADJ
ejpam-4036	326	27	in	in	ADP
ejpam-4036	326	28	g	g	PROPN
ejpam-4036	326	29	or	or	CCONJ
ejpam-4036	326	30	lies	lie	NOUN
ejpam-4036	326	31	in	in	ADP
ejpam-4036	326	32	z∞(g	z∞(g	NUM
ejpam-4036	326	33	)	)	PUNCT
ejpam-4036	326	34	,	,	PUNCT
ejpam-4036	326	35	then	then	ADV
ejpam-4036	326	36	g	g	PROPN
ejpam-4036	326	37	is	be	AUX
ejpam-4036	326	38	nilpotent	nilpotent	ADJ
ejpam-4036	326	39	.	.	PUNCT
ejpam-4036	327	1	references	reference	NOUN
ejpam-4036	327	2	1012	1012	NUM
ejpam-4036	327	3	corollary	corollary	ADJ
ejpam-4036	327	4	21	21	NUM
ejpam-4036	327	5	.	.	PUNCT
ejpam-4036	328	1	(	(	PUNCT
ejpam-4036	328	2	[	[	X
ejpam-4036	328	3	11	11	NUM
ejpam-4036	328	4	,	,	PUNCT
ejpam-4036	328	5	theorem	theorem	VERB
ejpam-4036	328	6	4.2	4.2	NUM
ejpam-4036	328	7	]	]	PUNCT
ejpam-4036	328	8	)	)	PUNCT
ejpam-4036	328	9	let	let	VERB
ejpam-4036	328	10	h	h	NOUN
ejpam-4036	328	11	be	be	AUX
ejpam-4036	328	12	a	a	DET
ejpam-4036	328	13	normal	normal	ADJ
ejpam-4036	328	14	subgroup	subgroup	NOUN
ejpam-4036	328	15	of	of	ADP
ejpam-4036	328	16	a	a	DET
ejpam-4036	328	17	group	group	NOUN
ejpam-4036	328	18	g	g	NOUN
ejpam-4036	328	19	such	such	DET
ejpam-4036	328	20	that	that	SCONJ
ejpam-4036	328	21	g	g	NOUN
ejpam-4036	328	22	/	/	SYM
ejpam-4036	328	23	h	h	NOUN
ejpam-4036	328	24	is	be	AUX
ejpam-4036	328	25	nilpotent	nilpotent	ADJ
ejpam-4036	328	26	.	.	PUNCT
ejpam-4036	329	1	if	if	SCONJ
ejpam-4036	329	2	every	every	DET
ejpam-4036	329	3	subgroup	subgroup	NOUN
ejpam-4036	329	4	of	of	ADP
ejpam-4036	329	5	h	h	PROPN
ejpam-4036	329	6	of	of	ADP
ejpam-4036	329	7	prime	prime	ADJ
ejpam-4036	329	8	order	order	NOUN
ejpam-4036	329	9	is	be	AUX
ejpam-4036	329	10	contained	contain	VERB
ejpam-4036	329	11	in	in	ADP
ejpam-4036	329	12	z∞(g	z∞(g	NUM
ejpam-4036	329	13	)	)	PUNCT
ejpam-4036	329	14	and	and	CCONJ
ejpam-4036	329	15	every	every	DET
ejpam-4036	329	16	cyclic	cyclic	ADJ
ejpam-4036	329	17	subgroup	subgroup	NOUN
ejpam-4036	329	18	of	of	ADP
ejpam-4036	329	19	order	order	NOUN
ejpam-4036	329	20	4	4	NUM
ejpam-4036	329	21	of	of	ADP
ejpam-4036	329	22	h	h	NOUN
ejpam-4036	329	23	is	be	AUX
ejpam-4036	329	24	ss	ss	NOUN
ejpam-4036	329	25	-	-	ADJ
ejpam-4036	329	26	quasinormal	quasinormal	ADJ
ejpam-4036	329	27	in	in	ADP
ejpam-4036	329	28	g	g	PROPN
ejpam-4036	329	29	or	or	CCONJ
ejpam-4036	329	30	lies	lie	NOUN
ejpam-4036	329	31	in	in	ADP
ejpam-4036	329	32	z∞(g	z∞(g	NUM
ejpam-4036	329	33	)	)	PUNCT
ejpam-4036	329	34	,	,	PUNCT
ejpam-4036	329	35	then	then	ADV
ejpam-4036	329	36	g	g	PROPN
ejpam-4036	329	37	is	be	AUX
ejpam-4036	329	38	nilpotent	nilpotent	ADJ
ejpam-4036	329	39	.	.	PUNCT
ejpam-4036	330	1	corollary	corollary	ADJ
ejpam-4036	330	2	22	22	NUM
ejpam-4036	330	3	.	.	PUNCT
ejpam-4036	331	1	(	(	PUNCT
ejpam-4036	331	2	[	[	X
ejpam-4036	331	3	11	11	NUM
ejpam-4036	331	4	,	,	PUNCT
ejpam-4036	331	5	theorem	theorem	VERB
ejpam-4036	331	6	4.4	4.4	NUM
ejpam-4036	331	7	]	]	PUNCT
ejpam-4036	331	8	)	)	PUNCT
ejpam-4036	331	9	let	let	VERB
ejpam-4036	331	10	h	h	NOUN
ejpam-4036	331	11	be	be	AUX
ejpam-4036	331	12	a	a	DET
ejpam-4036	331	13	normal	normal	ADJ
ejpam-4036	331	14	subgroup	subgroup	NOUN
ejpam-4036	331	15	of	of	ADP
ejpam-4036	331	16	a	a	DET
ejpam-4036	331	17	group	group	NOUN
ejpam-4036	331	18	g	g	NOUN
ejpam-4036	331	19	such	such	DET
ejpam-4036	331	20	that	that	SCONJ
ejpam-4036	331	21	g	g	NOUN
ejpam-4036	331	22	/	/	SYM
ejpam-4036	331	23	h	h	NOUN
ejpam-4036	331	24	is	be	AUX
ejpam-4036	331	25	nilpotent	nilpotent	ADJ
ejpam-4036	331	26	and	and	CCONJ
ejpam-4036	331	27	every	every	DET
ejpam-4036	331	28	cyclic	cyclic	ADJ
ejpam-4036	331	29	subgroup	subgroup	NOUN
ejpam-4036	331	30	of	of	ADP
ejpam-4036	331	31	order	order	NOUN
ejpam-4036	331	32	4	4	NUM
ejpam-4036	331	33	of	of	ADP
ejpam-4036	331	34	f	f	PROPN
ejpam-4036	331	35	∗(h	∗(h	PROPN
ejpam-4036	331	36	)	)	PUNCT
ejpam-4036	331	37	is	be	AUX
ejpam-4036	331	38	ss	ss	NOUN
ejpam-4036	331	39	-	-	ADJ
ejpam-4036	331	40	quasinormal	quasinormal	ADJ
ejpam-4036	331	41	in	in	ADP
ejpam-4036	331	42	g	g	PROPN
ejpam-4036	331	43	,	,	PUNCT
ejpam-4036	331	44	then	then	ADV
ejpam-4036	331	45	g	g	PROPN
ejpam-4036	331	46	is	be	AUX
ejpam-4036	331	47	nilpotent	nilpotent	ADJ
ejpam-4036	331	48	if	if	SCONJ
ejpam-4036	331	49	and	and	CCONJ
ejpam-4036	331	50	only	only	ADV
ejpam-4036	331	51	if	if	SCONJ
ejpam-4036	331	52	every	every	DET
ejpam-4036	331	53	subgroup	subgroup	NOUN
ejpam-4036	331	54	of	of	ADP
ejpam-4036	331	55	prime	prime	ADJ
ejpam-4036	331	56	order	order	NOUN
ejpam-4036	331	57	of	of	ADP
ejpam-4036	331	58	f	f	PROPN
ejpam-4036	331	59	∗(h	∗(h	PROPN
ejpam-4036	331	60	)	)	PUNCT
ejpam-4036	331	61	is	be	AUX
ejpam-4036	331	62	contained	contain	VERB
ejpam-4036	331	63	in	in	ADP
ejpam-4036	331	64	the	the	DET
ejpam-4036	331	65	hypercenter	hypercenter	NOUN
ejpam-4036	331	66	z∞(g	z∞(g	NOUN
ejpam-4036	331	67	)	)	PUNCT
ejpam-4036	331	68	of	of	ADP
ejpam-4036	331	69	g.	g.	PROPN
ejpam-4036	331	70	based	base	VERB
ejpam-4036	331	71	on	on	ADP
ejpam-4036	331	72	the	the	DET
ejpam-4036	331	73	results	result	NOUN
ejpam-4036	331	74	that	that	PRON
ejpam-4036	331	75	have	have	AUX
ejpam-4036	331	76	been	be	AUX
ejpam-4036	331	77	achieved	achieve	VERB
ejpam-4036	331	78	in	in	ADP
ejpam-4036	331	79	this	this	DET
ejpam-4036	331	80	paper	paper	NOUN
ejpam-4036	331	81	and	and	CCONJ
ejpam-4036	331	82	[	[	X
ejpam-4036	331	83	25	25	NUM
ejpam-4036	331	84	,	,	PUNCT
ejpam-4036	331	85	26	26	NUM
ejpam-4036	331	86	]	]	PUNCT
ejpam-4036	331	87	,	,	PUNCT
ejpam-4036	331	88	the	the	DET
ejpam-4036	331	89	following	follow	VERB
ejpam-4036	331	90	questions	question	NOUN
ejpam-4036	331	91	arise	arise	VERB
ejpam-4036	331	92	:	:	PUNCT
ejpam-4036	331	93	question	question	NOUN
ejpam-4036	331	94	1	1	NUM
ejpam-4036	331	95	.	.	PUNCT
ejpam-4036	332	1	let	let	VERB
ejpam-4036	332	2	p	p	PRON
ejpam-4036	332	3	be	be	AUX
ejpam-4036	332	4	a	a	DET
ejpam-4036	332	5	sylow	sylow	NOUN
ejpam-4036	332	6	p	p	NOUN
ejpam-4036	332	7	-	-	PUNCT
ejpam-4036	332	8	subgroup	subgroup	NOUN
ejpam-4036	332	9	of	of	ADP
ejpam-4036	332	10	a	a	DET
ejpam-4036	332	11	group	group	NOUN
ejpam-4036	332	12	g	g	NOUN
ejpam-4036	332	13	,	,	PUNCT
ejpam-4036	332	14	where	where	SCONJ
ejpam-4036	332	15	p	p	NOUN
ejpam-4036	332	16	is	be	AUX
ejpam-4036	332	17	the	the	DET
ejpam-4036	332	18	smallest	small	ADJ
ejpam-4036	332	19	prime	prime	ADJ
ejpam-4036	332	20	dividing	dividing	NOUN
ejpam-4036	332	21	|g|	|g|	PROPN
ejpam-4036	332	22	.	.	PUNCT
ejpam-4036	333	1	assume	assume	VERB
ejpam-4036	333	2	that	that	SCONJ
ejpam-4036	333	3	all	all	DET
ejpam-4036	333	4	maximal	maximal	ADJ
ejpam-4036	333	5	subgroups	subgroup	NOUN
ejpam-4036	333	6	of	of	ADP
ejpam-4036	333	7	p	p	NOUN
ejpam-4036	333	8	are	be	AUX
ejpam-4036	333	9	css	css	ADJ
ejpam-4036	333	10	-	-	NOUN
ejpam-4036	333	11	subgroups	subgroup	NOUN
ejpam-4036	333	12	of	of	ADP
ejpam-4036	333	13	g.	g.	PROPN
ejpam-4036	333	14	is	be	AUX
ejpam-4036	333	15	g	g	PROPN
ejpam-4036	333	16	p	p	NOUN
ejpam-4036	333	17	-	-	PUNCT
ejpam-4036	333	18	nilpotent	nilpotent	ADJ
ejpam-4036	333	19	?	?	PUNCT
ejpam-4036	334	1	question	question	NOUN
ejpam-4036	334	2	2	2	NUM
ejpam-4036	334	3	.	.	X
ejpam-4036	334	4	assume	assume	VERB
ejpam-4036	334	5	that	that	SCONJ
ejpam-4036	334	6	all	all	DET
ejpam-4036	334	7	maximal	maximal	ADJ
ejpam-4036	334	8	subgroups	subgroup	NOUN
ejpam-4036	334	9	of	of	ADP
ejpam-4036	334	10	every	every	DET
ejpam-4036	334	11	sylow	sylow	NOUN
ejpam-4036	334	12	subgroup	subgroup	NOUN
ejpam-4036	334	13	of	of	ADP
ejpam-4036	334	14	a	a	DET
ejpam-4036	334	15	group	group	NOUN
ejpam-4036	334	16	g	g	PROPN
ejpam-4036	334	17	are	be	AUX
ejpam-4036	334	18	css	cs	NOUN
ejpam-4036	334	19	-	-	NOUN
ejpam-4036	334	20	subgroups	subgroup	NOUN
ejpam-4036	334	21	of	of	ADP
ejpam-4036	334	22	g.	g.	PROPN
ejpam-4036	334	23	is	be	AUX
ejpam-4036	334	24	g	g	NOUN
ejpam-4036	334	25	supersolvable	supersolvable	ADJ
ejpam-4036	334	26	?	?	PUNCT
ejpam-4036	335	1	question	question	NOUN
ejpam-4036	335	2	3	3	NUM
ejpam-4036	335	3	.	.	PUNCT
ejpam-4036	336	1	let	let	VERB
ejpam-4036	336	2	f	f	PRON
ejpam-4036	336	3	be	be	AUX
ejpam-4036	336	4	a	a	DET
ejpam-4036	336	5	saturated	saturated	ADJ
ejpam-4036	336	6	formation	formation	NOUN
ejpam-4036	336	7	containing	contain	VERB
ejpam-4036	336	8	u	u	NOUN
ejpam-4036	336	9	and	and	CCONJ
ejpam-4036	336	10	h	h	NOUN
ejpam-4036	336	11	a	a	DET
ejpam-4036	336	12	normal	normal	ADJ
ejpam-4036	336	13	subgroup	subgroup	NOUN
ejpam-4036	336	14	of	of	ADP
ejpam-4036	336	15	g	g	PROPN
ejpam-4036	336	16	such	such	ADJ
ejpam-4036	336	17	that	that	SCONJ
ejpam-4036	336	18	g	g	NOUN
ejpam-4036	336	19	/	/	SYM
ejpam-4036	336	20	h	h	NOUN
ejpam-4036	336	21	∈	∈	PROPN
ejpam-4036	336	22	f.	f.	PROPN
ejpam-4036	336	23	assume	assume	VERB
ejpam-4036	336	24	that	that	SCONJ
ejpam-4036	336	25	every	every	DET
ejpam-4036	336	26	non	non	ADJ
ejpam-4036	336	27	-	-	ADJ
ejpam-4036	336	28	cyclic	cyclic	ADJ
ejpam-4036	336	29	sylow	sylow	NOUN
ejpam-4036	336	30	subgroup	subgroup	NOUN
ejpam-4036	336	31	p	p	PROPN
ejpam-4036	336	32	of	of	ADP
ejpam-4036	336	33	h	h	NOUN
ejpam-4036	336	34	has	have	VERB
ejpam-4036	336	35	a	a	DET
ejpam-4036	336	36	subgroup	subgroup	NOUN
ejpam-4036	336	37	d	d	NOUN
ejpam-4036	336	38	with	with	ADP
ejpam-4036	336	39	1	1	NUM
ejpam-4036	336	40	<	<	X
ejpam-4036	336	41	|d|	|d|	PROPN
ejpam-4036	336	42	<	<	X
ejpam-4036	336	43	|p	|p	X
ejpam-4036	336	44	|	|	ADV
ejpam-4036	336	45	such	such	ADJ
ejpam-4036	336	46	that	that	SCONJ
ejpam-4036	336	47	every	every	DET
ejpam-4036	336	48	subgroup	subgroup	NOUN
ejpam-4036	336	49	of	of	ADP
ejpam-4036	336	50	p	p	NOUN
ejpam-4036	336	51	of	of	ADP
ejpam-4036	336	52	order	order	NOUN
ejpam-4036	336	53	|d|	|d|	PROPN
ejpam-4036	336	54	(	(	PUNCT
ejpam-4036	336	55	and	and	CCONJ
ejpam-4036	336	56	4	4	NUM
ejpam-4036	336	57	if	if	SCONJ
ejpam-4036	336	58	|d|	|d|	PROPN
ejpam-4036	336	59	=	=	SYM
ejpam-4036	336	60	2	2	X
ejpam-4036	336	61	)	)	PUNCT
ejpam-4036	336	62	is	be	AUX
ejpam-4036	336	63	css	css	PROPN
ejpam-4036	336	64	-	-	PROPN
ejpam-4036	336	65	subgroup	subgroup	NOUN
ejpam-4036	336	66	of	of	ADP
ejpam-4036	336	67	g.	g.	PROPN
ejpam-4036	336	68	is	be	AUX
ejpam-4036	336	69	g	g	PROPN
ejpam-4036	336	70	∈	∈	PROPN
ejpam-4036	336	71	f	f	X
ejpam-4036	336	72	?	?	PUNCT
ejpam-4036	336	73	question	question	NOUN
ejpam-4036	336	74	4	4	NUM
ejpam-4036	336	75	.	.	PUNCT
ejpam-4036	337	1	let	let	VERB
ejpam-4036	337	2	f	f	PRON
ejpam-4036	337	3	be	be	AUX
ejpam-4036	337	4	a	a	DET
ejpam-4036	337	5	saturated	saturated	ADJ
ejpam-4036	337	6	formation	formation	NOUN
ejpam-4036	337	7	containing	contain	VERB
ejpam-4036	337	8	u	u	NOUN
ejpam-4036	337	9	and	and	CCONJ
ejpam-4036	337	10	h	h	NOUN
ejpam-4036	337	11	a	a	DET
ejpam-4036	337	12	normal	normal	ADJ
ejpam-4036	337	13	subgroup	subgroup	NOUN
ejpam-4036	337	14	of	of	ADP
ejpam-4036	337	15	g	g	PROPN
ejpam-4036	337	16	such	such	ADJ
ejpam-4036	337	17	that	that	SCONJ
ejpam-4036	337	18	g	g	NOUN
ejpam-4036	337	19	/	/	SYM
ejpam-4036	337	20	h	h	NOUN
ejpam-4036	337	21	∈	∈	PROPN
ejpam-4036	337	22	f.	f.	PROPN
ejpam-4036	337	23	assume	assume	VERB
ejpam-4036	337	24	that	that	SCONJ
ejpam-4036	337	25	every	every	DET
ejpam-4036	337	26	non	non	ADJ
ejpam-4036	337	27	-	-	ADJ
ejpam-4036	337	28	cyclic	cyclic	ADJ
ejpam-4036	337	29	sylow	sylow	NOUN
ejpam-4036	337	30	subgroup	subgroup	NOUN
ejpam-4036	337	31	p	p	PROPN
ejpam-4036	337	32	of	of	ADP
ejpam-4036	337	33	f	f	PROPN
ejpam-4036	337	34	∗(h	∗(h	PROPN
ejpam-4036	337	35	)	)	PUNCT
ejpam-4036	337	36	has	have	VERB
ejpam-4036	337	37	a	a	DET
ejpam-4036	337	38	subgroup	subgroup	NOUN
ejpam-4036	337	39	d	d	NOUN
ejpam-4036	337	40	with	with	ADP
ejpam-4036	337	41	1	1	NUM
ejpam-4036	337	42	<	<	X
ejpam-4036	337	43	|d|	|d|	PROPN
ejpam-4036	337	44	<	<	X
ejpam-4036	337	45	|p	|p	X
ejpam-4036	337	46	|	|	ADV
ejpam-4036	337	47	such	such	ADJ
ejpam-4036	337	48	that	that	SCONJ
ejpam-4036	337	49	every	every	DET
ejpam-4036	337	50	subgroup	subgroup	NOUN
ejpam-4036	337	51	of	of	ADP
ejpam-4036	337	52	p	p	NOUN
ejpam-4036	337	53	of	of	ADP
ejpam-4036	337	54	order	order	NOUN
ejpam-4036	337	55	|d|	|d|	PROPN
ejpam-4036	337	56	(	(	PUNCT
ejpam-4036	337	57	and	and	CCONJ
ejpam-4036	337	58	4	4	NUM
ejpam-4036	337	59	if	if	SCONJ
ejpam-4036	337	60	|d|	|d|	PROPN
ejpam-4036	337	61	=	=	SYM
ejpam-4036	337	62	2	2	X
ejpam-4036	337	63	)	)	PUNCT
ejpam-4036	337	64	is	be	AUX
ejpam-4036	337	65	css	css	PROPN
ejpam-4036	337	66	-	-	PROPN
ejpam-4036	337	67	subgroup	subgroup	NOUN
ejpam-4036	337	68	of	of	ADP
ejpam-4036	337	69	g.	g.	PROPN
ejpam-4036	337	70	is	be	AUX
ejpam-4036	337	71	g	g	PROPN
ejpam-4036	337	72	∈	∈	PROPN
ejpam-4036	337	73	f	f	X
ejpam-4036	337	74	?	?	PUNCT
ejpam-4036	338	1	references	reference	NOUN
ejpam-4036	338	2	[	[	X
ejpam-4036	338	3	1	1	NUM
ejpam-4036	338	4	]	]	PUNCT
ejpam-4036	338	5	m.	m.	NOUN
ejpam-4036	338	6	asaad	asaad	NOUN
ejpam-4036	338	7	and	and	CCONJ
ejpam-4036	338	8	m.	m.	PROPN
ejpam-4036	338	9	e.	e.	PROPN
ejpam-4036	338	10	mohamed	mohamed	PROPN
ejpam-4036	338	11	.	.	PUNCT
ejpam-4036	339	1	on	on	ADP
ejpam-4036	339	2	c	c	NOUN
ejpam-4036	339	3	-	-	PUNCT
ejpam-4036	339	4	normality	normality	NOUN
ejpam-4036	339	5	of	of	ADP
ejpam-4036	339	6	finite	finite	ADJ
ejpam-4036	339	7	groups	group	NOUN
ejpam-4036	339	8	.	.	PUNCT
ejpam-4036	340	1	j.	j.	PROPN
ejpam-4036	340	2	aust	aust	PROPN
ejpam-4036	340	3	.	.	PUNCT
ejpam-4036	341	1	math	math	PROPN
ejpam-4036	341	2	.	.	PUNCT
ejpam-4036	342	1	soc	soc	PROPN
ejpam-4036	342	2	.	.	PUNCT
ejpam-4036	342	3	,	,	PUNCT
ejpam-4036	342	4	78:297–304	78:297–304	PROPN
ejpam-4036	342	5	,	,	PUNCT
ejpam-4036	342	6	2005	2005	NUM
ejpam-4036	342	7	.	.	PUNCT
ejpam-4036	343	1	[	[	X
ejpam-4036	343	2	2	2	NUM
ejpam-4036	343	3	]	]	PUNCT
ejpam-4036	343	4	a.	a.	NOUN
ejpam-4036	343	5	ballester	ballester	PROPN
ejpam-4036	343	6	-	-	PUNCT
ejpam-4036	343	7	bolinches	bolinches	PROPN
ejpam-4036	343	8	and	and	CCONJ
ejpam-4036	343	9	l.m	l.m	PROPN
ejpam-4036	343	10	.	.	PROPN
ejpam-4036	343	11	ezquerro	ezquerro	PROPN
ejpam-4036	343	12	.	.	PUNCT
ejpam-4036	344	1	classes	class	NOUN
ejpam-4036	344	2	of	of	ADP
ejpam-4036	344	3	finite	finite	ADJ
ejpam-4036	344	4	groups	group	NOUN
ejpam-4036	344	5	,	,	PUNCT
ejpam-4036	344	6	vol	vol	NOUN
ejpam-4036	344	7	.	.	PUNCT
ejpam-4036	345	1	584	584	NUM
ejpam-4036	345	2	of	of	ADP
ejpam-4036	345	3	mathematics	mathematic	NOUN
ejpam-4036	345	4	and	and	CCONJ
ejpam-4036	345	5	its	its	PRON
ejpam-4036	345	6	applications	application	NOUN
ejpam-4036	345	7	.	.	PUNCT
ejpam-4036	346	1	springer	springer	NOUN
ejpam-4036	346	2	,	,	PUNCT
ejpam-4036	346	3	new	new	PROPN
ejpam-4036	346	4	york	york	PROPN
ejpam-4036	346	5	,	,	PUNCT
ejpam-4036	346	6	2006	2006	NUM
ejpam-4036	346	7	.	.	PUNCT
ejpam-4036	347	1	[	[	X
ejpam-4036	347	2	3	3	X
ejpam-4036	347	3	]	]	X
ejpam-4036	347	4	j.	j.	PROPN
ejpam-4036	347	5	buckley	buckley	PROPN
ejpam-4036	347	6	.	.	PUNCT
ejpam-4036	348	1	finite	finite	PROPN
ejpam-4036	348	2	groups	group	NOUN
ejpam-4036	348	3	whose	whose	DET
ejpam-4036	348	4	minimal	minimal	ADJ
ejpam-4036	348	5	subgroups	subgroup	NOUN
ejpam-4036	348	6	are	be	AUX
ejpam-4036	348	7	normal	normal	ADJ
ejpam-4036	348	8	.	.	PUNCT
ejpam-4036	349	1	math	math	NOUN
ejpam-4036	349	2	.	.	PUNCT
ejpam-4036	350	1	z.	z.	PROPN
ejpam-4036	350	2	,	,	PUNCT
ejpam-4036	350	3	116:15–17	116:15–17	NUM
ejpam-4036	350	4	,	,	PUNCT
ejpam-4036	350	5	1970	1970	NUM
ejpam-4036	350	6	.	.	PUNCT
ejpam-4036	351	1	[	[	X
ejpam-4036	351	2	4	4	X
ejpam-4036	351	3	]	]	PUNCT
ejpam-4036	351	4	j.	j.	PROPN
ejpam-4036	351	5	b.	b.	PROPN
ejpam-4036	351	6	derr	derr	PROPN
ejpam-4036	351	7	,	,	PUNCT
ejpam-4036	351	8	w.	w.	PROPN
ejpam-4036	351	9	e.	e.	PROPN
ejpam-4036	351	10	deskins	deskins	PROPN
ejpam-4036	351	11	,	,	PUNCT
ejpam-4036	351	12	and	and	CCONJ
ejpam-4036	351	13	n.	n.	PROPN
ejpam-4036	351	14	p.	p.	PROPN
ejpam-4036	351	15	mukherjee	mukherjee	PROPN
ejpam-4036	351	16	.	.	PUNCT
ejpam-4036	352	1	the	the	DET
ejpam-4036	352	2	influence	influence	NOUN
ejpam-4036	352	3	of	of	ADP
ejpam-4036	352	4	minimal	minimal	ADJ
ejpam-4036	352	5	p	p	NOUN
ejpam-4036	352	6	-	-	PUNCT
ejpam-4036	352	7	subgroups	subgroup	NOUN
ejpam-4036	352	8	on	on	ADP
ejpam-4036	352	9	the	the	DET
ejpam-4036	352	10	structure	structure	NOUN
ejpam-4036	352	11	of	of	ADP
ejpam-4036	352	12	finite	finite	ADJ
ejpam-4036	352	13	groups	group	NOUN
ejpam-4036	352	14	.	.	PUNCT
ejpam-4036	353	1	arch	arch	PROPN
ejpam-4036	353	2	.	.	PUNCT
ejpam-4036	354	1	math	math	NOUN
ejpam-4036	354	2	.	.	PUNCT
ejpam-4036	354	3	,	,	PUNCT
ejpam-4036	354	4	45:1–4	45:1–4	NOUN
ejpam-4036	354	5	,	,	PUNCT
ejpam-4036	354	6	1985	1985	NUM
ejpam-4036	354	7	.	.	PUNCT
ejpam-4036	355	1	[	[	X
ejpam-4036	355	2	5	5	X
ejpam-4036	355	3	]	]	PUNCT
ejpam-4036	355	4	k.	k.	NOUN
ejpam-4036	355	5	doerk	doerk	PROPN
ejpam-4036	355	6	and	and	CCONJ
ejpam-4036	355	7	t.	t.	PROPN
ejpam-4036	355	8	hawkes	hawkes	PROPN
ejpam-4036	355	9	.	.	PUNCT
ejpam-4036	356	1	finite	finite	VERB
ejpam-4036	356	2	soluble	soluble	ADJ
ejpam-4036	356	3	groups	group	NOUN
ejpam-4036	356	4	.	.	PUNCT
ejpam-4036	357	1	walter	walter	PROPN
ejpam-4036	357	2	de	de	PROPN
ejpam-4036	357	3	gruyter	gruyter	PROPN
ejpam-4036	357	4	,	,	PUNCT
ejpam-4036	357	5	berlin	berlin	PROPN
ejpam-4036	357	6	,	,	PUNCT
ejpam-4036	357	7	new	new	PROPN
ejpam-4036	357	8	york	york	PROPN
ejpam-4036	357	9	,	,	PUNCT
ejpam-4036	357	10	1992	1992	NUM
ejpam-4036	357	11	.	.	PUNCT
ejpam-4036	358	1	references	reference	NOUN
ejpam-4036	358	2	1013	1013	NUM
ejpam-4036	358	3	[	[	X
ejpam-4036	358	4	6	6	NUM
ejpam-4036	358	5	]	]	PUNCT
ejpam-4036	358	6	d.	d.	PROPN
ejpam-4036	358	7	gorenstein	gorenstein	PROPN
ejpam-4036	358	8	.	.	PUNCT
ejpam-4036	359	1	finite	finite	PROPN
ejpam-4036	359	2	groups	group	NOUN
ejpam-4036	359	3	.	.	PUNCT
ejpam-4036	360	1	harper	harper	NOUN
ejpam-4036	360	2	and	and	CCONJ
ejpam-4036	360	3	row	row	NOUN
ejpam-4036	360	4	publishers	publisher	NOUN
ejpam-4036	360	5	,	,	PUNCT
ejpam-4036	360	6	new	new	PROPN
ejpam-4036	360	7	york	york	PROPN
ejpam-4036	360	8	,	,	PUNCT
ejpam-4036	360	9	1968	1968	NUM
ejpam-4036	360	10	.	.	PUNCT
ejpam-4036	361	1	[	[	X
ejpam-4036	361	2	7	7	X
ejpam-4036	361	3	]	]	X
ejpam-4036	361	4	b.	b.	PROPN
ejpam-4036	361	5	huppert	huppert	PROPN
ejpam-4036	361	6	.	.	PUNCT
ejpam-4036	362	1	endliche	endliche	PROPN
ejpam-4036	362	2	gruppen	gruppen	PROPN
ejpam-4036	362	3	i.	i.	PROPN
ejpam-4036	362	4	springer	springer	PROPN
ejpam-4036	362	5	-	-	PUNCT
ejpam-4036	362	6	verlag	verlag	PROPN
ejpam-4036	362	7	,	,	PUNCT
ejpam-4036	362	8	berlin	berlin	PROPN
ejpam-4036	362	9	,	,	PUNCT
ejpam-4036	362	10	heidelberg	heidelberg	PROPN
ejpam-4036	362	11	,	,	PUNCT
ejpam-4036	362	12	new	new	PROPN
ejpam-4036	362	13	york	york	PROPN
ejpam-4036	362	14	,	,	PUNCT
ejpam-4036	362	15	1979	1979	NUM
ejpam-4036	362	16	.	.	PUNCT
ejpam-4036	363	1	[	[	X
ejpam-4036	363	2	8	8	NUM
ejpam-4036	363	3	]	]	X
ejpam-4036	363	4	b.	b.	PROPN
ejpam-4036	363	5	huppert	huppert	PROPN
ejpam-4036	363	6	and	and	CCONJ
ejpam-4036	363	7	n.	n.	PROPN
ejpam-4036	363	8	blackburn	blackburn	PROPN
ejpam-4036	363	9	.	.	PUNCT
ejpam-4036	364	1	finite	finite	PROPN
ejpam-4036	364	2	groups	groups	PROPN
ejpam-4036	364	3	iii	iii	PROPN
ejpam-4036	364	4	.	.	PUNCT
ejpam-4036	364	5	springer	springer	NOUN
ejpam-4036	364	6	-	-	PUNCT
ejpam-4036	364	7	verlag	verlag	PROPN
ejpam-4036	364	8	,	,	PUNCT
ejpam-4036	364	9	berlin	berlin	PROPN
ejpam-4036	364	10	,	,	PUNCT
ejpam-4036	364	11	heidelberg	heidelberg	PROPN
ejpam-4036	364	12	,	,	PUNCT
ejpam-4036	364	13	new	new	PROPN
ejpam-4036	364	14	york	york	PROPN
ejpam-4036	364	15	,	,	PUNCT
ejpam-4036	364	16	1982	1982	NUM
ejpam-4036	364	17	.	.	PUNCT
ejpam-4036	365	1	[	[	X
ejpam-4036	365	2	9	9	NUM
ejpam-4036	365	3	]	]	X
ejpam-4036	365	4	o.	o.	PROPN
ejpam-4036	365	5	h.	h.	PROPN
ejpam-4036	365	6	kegel	kegel	PROPN
ejpam-4036	365	7	.	.	PUNCT
ejpam-4036	366	1	sylow	sylow	NOUN
ejpam-4036	366	2	-	-	PUNCT
ejpam-4036	366	3	gruppen	gruppen	NOUN
ejpam-4036	366	4	und	und	NOUN
ejpam-4036	366	5	subnormalteiler	subnormalteiler	NOUN
ejpam-4036	366	6	endlicher	endlicher	PROPN
ejpam-4036	366	7	gruppen	gruppen	PROPN
ejpam-4036	366	8	.	.	PUNCT
ejpam-4036	367	1	math	math	NOUN
ejpam-4036	367	2	.	.	PUNCT
ejpam-4036	368	1	z.	z.	PROPN
ejpam-4036	368	2	,	,	PUNCT
ejpam-4036	368	3	78:205–221	78:205–221	PROPN
ejpam-4036	368	4	,	,	PUNCT
ejpam-4036	368	5	1962	1962	NUM
ejpam-4036	368	6	.	.	PUNCT
ejpam-4036	369	1	[	[	X
ejpam-4036	369	2	10	10	NUM
ejpam-4036	369	3	]	]	X
ejpam-4036	369	4	r.	r.	PROPN
ejpam-4036	369	5	laue	laue	PROPN
ejpam-4036	369	6	.	.	PUNCT
ejpam-4036	369	7	dualization	dualization	NOUN
ejpam-4036	369	8	of	of	ADP
ejpam-4036	369	9	saturation	saturation	NOUN
ejpam-4036	369	10	for	for	ADP
ejpam-4036	369	11	locally	locally	ADV
ejpam-4036	369	12	defined	define	VERB
ejpam-4036	369	13	formations	formation	NOUN
ejpam-4036	369	14	.	.	PUNCT
ejpam-4036	370	1	j.	j.	PROPN
ejpam-4036	370	2	algebra	algebra	PROPN
ejpam-4036	370	3	,	,	PUNCT
ejpam-4036	370	4	52:347	52:347	PROPN
ejpam-4036	370	5	–	–	PUNCT
ejpam-4036	370	6	353	353	NUM
ejpam-4036	370	7	,	,	PUNCT
ejpam-4036	370	8	1978	1978	NUM
ejpam-4036	370	9	.	.	PUNCT
ejpam-4036	371	1	[	[	X
ejpam-4036	371	2	11	11	NUM
ejpam-4036	371	3	]	]	PUNCT
ejpam-4036	371	4	s.	s.	PROPN
ejpam-4036	371	5	li	li	PROPN
ejpam-4036	371	6	,	,	PUNCT
ejpam-4036	371	7	z.	z.	PROPN
ejpam-4036	371	8	shen	shen	PROPN
ejpam-4036	371	9	,	,	PUNCT
ejpam-4036	371	10	and	and	CCONJ
ejpam-4036	371	11	x.	x.	PROPN
ejpam-4036	371	12	kong	kong	PROPN
ejpam-4036	371	13	.	.	PUNCT
ejpam-4036	372	1	on	on	ADP
ejpam-4036	372	2	ss	ss	ADJ
ejpam-4036	372	3	-	-	ADJ
ejpam-4036	372	4	quasinormal	quasinormal	ADJ
ejpam-4036	372	5	subgroup	subgroup	NOUN
ejpam-4036	372	6	of	of	ADP
ejpam-4036	372	7	finite	finite	PROPN
ejpam-4036	372	8	groups	group	NOUN
ejpam-4036	372	9	.	.	PUNCT
ejpam-4036	373	1	comm	comm	NOUN
ejpam-4036	373	2	.	.	PUNCT
ejpam-4036	374	1	algebra	algebra	PROPN
ejpam-4036	374	2	,	,	PUNCT
ejpam-4036	374	3	36(12):4436–4447	36(12):4436–4447	PROPN
ejpam-4036	374	4	,	,	PUNCT
ejpam-4036	374	5	2008	2008	NUM
ejpam-4036	374	6	.	.	PUNCT
ejpam-4036	375	1	[	[	X
ejpam-4036	375	2	12	12	NUM
ejpam-4036	375	3	]	]	X
ejpam-4036	375	4	s.	s.	PROPN
ejpam-4036	375	5	li	li	PROPN
ejpam-4036	375	6	,	,	PUNCT
ejpam-4036	375	7	z.	z.	PROPN
ejpam-4036	375	8	shen	shen	PROPN
ejpam-4036	375	9	,	,	PUNCT
ejpam-4036	375	10	j.	j.	PROPN
ejpam-4036	375	11	liu	liu	PROPN
ejpam-4036	375	12	,	,	PUNCT
ejpam-4036	375	13	and	and	CCONJ
ejpam-4036	375	14	x.	x.	PROPN
ejpam-4036	375	15	liu	liu	PROPN
ejpam-4036	375	16	.	.	PUNCT
ejpam-4036	376	1	the	the	DET
ejpam-4036	376	2	influence	influence	NOUN
ejpam-4036	376	3	of	of	ADP
ejpam-4036	376	4	ss	ss	NOUN
ejpam-4036	376	5	-	-	PUNCT
ejpam-4036	376	6	quasinormality	quasinormality	NOUN
ejpam-4036	376	7	of	of	ADP
ejpam-4036	376	8	some	some	DET
ejpam-4036	376	9	subgroups	subgroup	NOUN
ejpam-4036	376	10	on	on	ADP
ejpam-4036	376	11	the	the	DET
ejpam-4036	376	12	structure	structure	NOUN
ejpam-4036	376	13	of	of	ADP
ejpam-4036	376	14	finite	finite	ADJ
ejpam-4036	376	15	groups	group	NOUN
ejpam-4036	376	16	.	.	PUNCT
ejpam-4036	377	1	j.	j.	PROPN
ejpam-4036	377	2	algebra	algebra	PROPN
ejpam-4036	377	3	,	,	PUNCT
ejpam-4036	377	4	319:4275–4287	319:4275–4287	NUM
ejpam-4036	377	5	,	,	PUNCT
ejpam-4036	377	6	2008	2008	NUM
ejpam-4036	377	7	.	.	PUNCT
ejpam-4036	378	1	[	[	X
ejpam-4036	378	2	13	13	NUM
ejpam-4036	378	3	]	]	X
ejpam-4036	378	4	y.	y.	PROPN
ejpam-4036	378	5	li	li	PROPN
ejpam-4036	378	6	and	and	CCONJ
ejpam-4036	378	7	b.	b.	PROPN
ejpam-4036	378	8	li	li	PROPN
ejpam-4036	378	9	.	.	PROPN
ejpam-4036	379	1	on	on	ADP
ejpam-4036	379	2	minimal	minimal	ADJ
ejpam-4036	379	3	weakly	weakly	ADJ
ejpam-4036	379	4	s	s	NOUN
ejpam-4036	379	5	-	-	PUNCT
ejpam-4036	379	6	supplemented	supplement	VERB
ejpam-4036	379	7	subgroups	subgroup	NOUN
ejpam-4036	379	8	of	of	ADP
ejpam-4036	379	9	finite	finite	ADJ
ejpam-4036	379	10	groups	group	NOUN
ejpam-4036	379	11	.	.	PUNCT
ejpam-4036	380	1	j.	j.	PROPN
ejpam-4036	380	2	algebra	algebra	PROPN
ejpam-4036	380	3	appl	appl	PROPN
ejpam-4036	380	4	.	.	PUNCT
ejpam-4036	381	1	,	,	PUNCT
ejpam-4036	381	2	10(5):811–820	10(5):811–820	PROPN
ejpam-4036	381	3	,	,	PUNCT
ejpam-4036	381	4	2011	2011	NUM
ejpam-4036	381	5	.	.	PUNCT
ejpam-4036	382	1	[	[	X
ejpam-4036	382	2	14	14	NUM
ejpam-4036	382	3	]	]	X
ejpam-4036	382	4	y.	y.	PROPN
ejpam-4036	382	5	li	li	PROPN
ejpam-4036	382	6	and	and	CCONJ
ejpam-4036	382	7	y.	y.	PROPN
ejpam-4036	382	8	wang	wang	PROPN
ejpam-4036	382	9	.	.	PUNCT
ejpam-4036	383	1	the	the	DET
ejpam-4036	383	2	influence	influence	NOUN
ejpam-4036	383	3	of	of	ADP
ejpam-4036	383	4	minimal	minimal	ADJ
ejpam-4036	383	5	subgroups	subgroup	NOUN
ejpam-4036	383	6	on	on	ADP
ejpam-4036	383	7	the	the	DET
ejpam-4036	383	8	structure	structure	NOUN
ejpam-4036	383	9	of	of	ADP
ejpam-4036	383	10	a	a	DET
ejpam-4036	383	11	finite	finite	ADJ
ejpam-4036	383	12	group	group	NOUN
ejpam-4036	383	13	.	.	PUNCT
ejpam-4036	384	1	proc	proc	PROPN
ejpam-4036	384	2	.	.	PUNCT
ejpam-4036	385	1	amer	amer	PROPN
ejpam-4036	385	2	.	.	PUNCT
ejpam-4036	385	3	math	math	PROPN
ejpam-4036	385	4	.	.	PUNCT
ejpam-4036	386	1	soc	soc	PROPN
ejpam-4036	386	2	.	.	PUNCT
ejpam-4036	386	3	,	,	PUNCT
ejpam-4036	386	4	131(2):337–341	131(2):337–341	NUM
ejpam-4036	386	5	,	,	PUNCT
ejpam-4036	386	6	2002	2002	NUM
ejpam-4036	386	7	.	.	PUNCT
ejpam-4036	387	1	[	[	X
ejpam-4036	387	2	15	15	NUM
ejpam-4036	387	3	]	]	X
ejpam-4036	387	4	y.	y.	PROPN
ejpam-4036	387	5	li	li	PROPN
ejpam-4036	387	6	and	and	CCONJ
ejpam-4036	387	7	y.	y.	PROPN
ejpam-4036	387	8	wang	wang	PROPN
ejpam-4036	387	9	.	.	PUNCT
ejpam-4036	388	1	on	on	ADP
ejpam-4036	388	2	π	π	PROPN
ejpam-4036	388	3	-	-	ADJ
ejpam-4036	388	4	quasinormally	quasinormally	ADV
ejpam-4036	388	5	embedded	embed	VERB
ejpam-4036	388	6	subgroups	subgroup	NOUN
ejpam-4036	388	7	of	of	ADP
ejpam-4036	388	8	finite	finite	PROPN
ejpam-4036	388	9	group	group	NOUN
ejpam-4036	388	10	.	.	PUNCT
ejpam-4036	389	1	j.	j.	PROPN
ejpam-4036	389	2	algebra	algebra	PROPN
ejpam-4036	389	3	,	,	PUNCT
ejpam-4036	389	4	281:109–123	281:109–123	NUM
ejpam-4036	389	5	,	,	PUNCT
ejpam-4036	389	6	2004	2004	NUM
ejpam-4036	389	7	.	.	PUNCT
ejpam-4036	390	1	[	[	X
ejpam-4036	390	2	16	16	NUM
ejpam-4036	390	3	]	]	PUNCT
ejpam-4036	390	4	m.	m.	NOUN
ejpam-4036	390	5	ramadan	ramadan	PROPN
ejpam-4036	390	6	,	,	PUNCT
ejpam-4036	390	7	m.	m.	PROPN
ejpam-4036	390	8	e.	e.	PROPN
ejpam-4036	390	9	mohamed	mohamed	PROPN
ejpam-4036	390	10	,	,	PUNCT
ejpam-4036	390	11	and	and	CCONJ
ejpam-4036	390	12	a.	a.	NOUN
ejpam-4036	390	13	a.	a.	NOUN
ejpam-4036	390	14	heliel	heliel	PROPN
ejpam-4036	390	15	.	.	PUNCT
ejpam-4036	391	1	on	on	ADP
ejpam-4036	391	2	c	c	NOUN
ejpam-4036	391	3	-	-	PUNCT
ejpam-4036	391	4	normality	normality	NOUN
ejpam-4036	391	5	of	of	ADP
ejpam-4036	391	6	certain	certain	ADJ
ejpam-4036	391	7	subgroups	subgroup	NOUN
ejpam-4036	391	8	of	of	ADP
ejpam-4036	391	9	prime	prime	ADJ
ejpam-4036	391	10	power	power	NOUN
ejpam-4036	391	11	order	order	NOUN
ejpam-4036	391	12	of	of	ADP
ejpam-4036	391	13	finite	finite	ADJ
ejpam-4036	391	14	groups	group	NOUN
ejpam-4036	391	15	.	.	PUNCT
ejpam-4036	392	1	arch	arch	PROPN
ejpam-4036	392	2	.	.	PUNCT
ejpam-4036	393	1	math	math	NOUN
ejpam-4036	393	2	.	.	PUNCT
ejpam-4036	393	3	,	,	PUNCT
ejpam-4036	393	4	85:203–210	85:203–210	PROPN
ejpam-4036	393	5	,	,	PUNCT
ejpam-4036	393	6	2005	2005	NUM
ejpam-4036	393	7	.	.	PUNCT
ejpam-4036	394	1	[	[	X
ejpam-4036	394	2	17	17	NUM
ejpam-4036	394	3	]	]	PUNCT
ejpam-4036	394	4	a.	a.	NOUN
ejpam-4036	394	5	shaalan	shaalan	PROPN
ejpam-4036	394	6	.	.	PUNCT
ejpam-4036	395	1	the	the	DET
ejpam-4036	395	2	influence	influence	NOUN
ejpam-4036	395	3	of	of	ADP
ejpam-4036	395	4	π	π	PROPN
ejpam-4036	395	5	-	-	NOUN
ejpam-4036	395	6	quasinormality	quasinormality	NOUN
ejpam-4036	395	7	of	of	ADP
ejpam-4036	395	8	some	some	DET
ejpam-4036	395	9	subgroups	subgroup	NOUN
ejpam-4036	395	10	on	on	ADP
ejpam-4036	395	11	the	the	DET
ejpam-4036	395	12	structure	structure	NOUN
ejpam-4036	395	13	of	of	ADP
ejpam-4036	395	14	a	a	DET
ejpam-4036	395	15	finite	finite	ADJ
ejpam-4036	395	16	group	group	NOUN
ejpam-4036	395	17	.	.	PUNCT
ejpam-4036	396	1	acta	acta	PROPN
ejpam-4036	396	2	math	math	PROPN
ejpam-4036	396	3	.	.	PUNCT
ejpam-4036	397	1	hungar	hungar	PROPN
ejpam-4036	397	2	.	.	PUNCT
ejpam-4036	397	3	,	,	PUNCT
ejpam-4036	398	1	56:287–293	56:287–293	NUM
ejpam-4036	398	2	,	,	PUNCT
ejpam-4036	398	3	1990	1990	NUM
ejpam-4036	398	4	.	.	PUNCT
ejpam-4036	399	1	[	[	X
ejpam-4036	399	2	18	18	NUM
ejpam-4036	399	3	]	]	X
ejpam-4036	399	4	y.	y.	PROPN
ejpam-4036	399	5	wang	wang	PROPN
ejpam-4036	399	6	.	.	PUNCT
ejpam-4036	400	1	c	c	X
ejpam-4036	400	2	-	-	PUNCT
ejpam-4036	400	3	normality	normality	NOUN
ejpam-4036	400	4	of	of	ADP
ejpam-4036	400	5	groups	group	NOUN
ejpam-4036	400	6	and	and	CCONJ
ejpam-4036	400	7	its	its	PRON
ejpam-4036	400	8	properties	property	NOUN
ejpam-4036	400	9	.	.	PUNCT
ejpam-4036	401	1	j.	j.	PROPN
ejpam-4036	401	2	algebra	algebra	PROPN
ejpam-4036	401	3	,	,	PUNCT
ejpam-4036	401	4	180:954–965	180:954–965	NUM
ejpam-4036	401	5	,	,	PUNCT
ejpam-4036	401	6	1996	1996	NUM
ejpam-4036	401	7	.	.	PUNCT
ejpam-4036	402	1	[	[	X
ejpam-4036	402	2	19	19	NUM
ejpam-4036	402	3	]	]	X
ejpam-4036	402	4	y.	y.	PROPN
ejpam-4036	402	5	wang	wang	PROPN
ejpam-4036	402	6	.	.	PUNCT
ejpam-4036	403	1	the	the	DET
ejpam-4036	403	2	influence	influence	NOUN
ejpam-4036	403	3	of	of	ADP
ejpam-4036	403	4	minimal	minimal	ADJ
ejpam-4036	403	5	subgroups	subgroup	NOUN
ejpam-4036	403	6	on	on	ADP
ejpam-4036	403	7	the	the	DET
ejpam-4036	403	8	structure	structure	NOUN
ejpam-4036	403	9	of	of	ADP
ejpam-4036	403	10	finite	finite	ADJ
ejpam-4036	403	11	groups	group	NOUN
ejpam-4036	403	12	.	.	PUNCT
ejpam-4036	404	1	acta	acta	PROPN
ejpam-4036	404	2	math	math	PROPN
ejpam-4036	404	3	.	.	PUNCT
ejpam-4036	405	1	sin	sin	NOUN
ejpam-4036	405	2	.	.	PUNCT
ejpam-4036	406	1	(	(	PUNCT
ejpam-4036	406	2	engl	engl	PROPN
ejpam-4036	406	3	.	.	PUNCT
ejpam-4036	406	4	ser	ser	PROPN
ejpam-4036	406	5	.	.	PUNCT
ejpam-4036	406	6	)	)	PUNCT
ejpam-4036	406	7	,	,	PUNCT
ejpam-4036	406	8	16(1):63–70	16(1):63–70	NUM
ejpam-4036	406	9	,	,	PUNCT
ejpam-4036	406	10	2000	2000	NUM
ejpam-4036	406	11	.	.	PUNCT
ejpam-4036	407	1	[	[	X
ejpam-4036	407	2	20	20	NUM
ejpam-4036	407	3	]	]	PUNCT
ejpam-4036	407	4	h.	h.	PROPN
ejpam-4036	407	5	wei	wei	PROPN
ejpam-4036	407	6	.	.	PUNCT
ejpam-4036	408	1	on	on	ADP
ejpam-4036	408	2	c	c	NOUN
ejpam-4036	408	3	-	-	ADJ
ejpam-4036	408	4	normal	normal	ADJ
ejpam-4036	408	5	maximal	maximal	ADJ
ejpam-4036	408	6	and	and	CCONJ
ejpam-4036	408	7	minimal	minimal	ADJ
ejpam-4036	408	8	subgroups	subgroup	NOUN
ejpam-4036	408	9	of	of	ADP
ejpam-4036	408	10	sylow	sylow	NOUN
ejpam-4036	408	11	subgroups	subgroup	NOUN
ejpam-4036	408	12	of	of	ADP
ejpam-4036	408	13	finite	finite	ADJ
ejpam-4036	408	14	groups	group	NOUN
ejpam-4036	408	15	.	.	PUNCT
ejpam-4036	409	1	comm	comm	NOUN
ejpam-4036	409	2	.	.	PUNCT
ejpam-4036	410	1	algebra	algebra	NOUN
ejpam-4036	410	2	,	,	PUNCT
ejpam-4036	410	3	29(5):2193–2200	29(5):2193–2200	NUM
ejpam-4036	410	4	,	,	PUNCT
ejpam-4036	410	5	2001	2001	NUM
ejpam-4036	410	6	.	.	PUNCT
ejpam-4036	411	1	[	[	X
ejpam-4036	411	2	21	21	NUM
ejpam-4036	411	3	]	]	X
ejpam-4036	411	4	h.	h.	PROPN
ejpam-4036	411	5	wei	wei	PROPN
ejpam-4036	411	6	,	,	PUNCT
ejpam-4036	411	7	y.	y.	PROPN
ejpam-4036	411	8	wang	wang	PROPN
ejpam-4036	411	9	,	,	PUNCT
ejpam-4036	411	10	and	and	CCONJ
ejpam-4036	411	11	y.	y.	PROPN
ejpam-4036	411	12	li	li	PROPN
ejpam-4036	411	13	.	.	PUNCT
ejpam-4036	412	1	on	on	ADP
ejpam-4036	412	2	c	c	NOUN
ejpam-4036	412	3	-	-	ADJ
ejpam-4036	412	4	normal	normal	ADJ
ejpam-4036	412	5	maximal	maximal	ADJ
ejpam-4036	412	6	and	and	CCONJ
ejpam-4036	412	7	minimal	minimal	ADJ
ejpam-4036	412	8	subgroups	subgroup	NOUN
ejpam-4036	412	9	of	of	ADP
ejpam-4036	412	10	sylow	sylow	NOUN
ejpam-4036	412	11	subgroups	subgroup	NOUN
ejpam-4036	412	12	of	of	ADP
ejpam-4036	412	13	finite	finite	PROPN
ejpam-4036	412	14	groups	groups	PROPN
ejpam-4036	412	15	ii	ii	PROPN
ejpam-4036	412	16	.	.	PROPN
ejpam-4036	412	17	comm	comm	NOUN
ejpam-4036	412	18	.	.	PUNCT
ejpam-4036	413	1	algebra	algebra	PROPN
ejpam-4036	413	2	,	,	PUNCT
ejpam-4036	413	3	31(10):4807–4816	31(10):4807–4816	NUM
ejpam-4036	413	4	,	,	PUNCT
ejpam-4036	413	5	2003	2003	NUM
ejpam-4036	413	6	.	.	PUNCT
ejpam-4036	414	1	[	[	X
ejpam-4036	414	2	22	22	NUM
ejpam-4036	414	3	]	]	PUNCT
ejpam-4036	414	4	m.	m.	NOUN
ejpam-4036	414	5	weinstein	weinstein	PROPN
ejpam-4036	414	6	,	,	PUNCT
ejpam-4036	414	7	editor	editor	NOUN
ejpam-4036	414	8	.	.	PUNCT
ejpam-4036	415	1	between	between	ADP
ejpam-4036	415	2	nilpotent	nilpotent	NOUN
ejpam-4036	415	3	and	and	CCONJ
ejpam-4036	415	4	solvable	solvable	ADJ
ejpam-4036	415	5	.	.	PUNCT
ejpam-4036	416	1	polygonal	polygonal	ADJ
ejpam-4036	416	2	publishing	publishing	PROPN
ejpam-4036	416	3	house	house	PROPN
ejpam-4036	416	4	,	,	PUNCT
ejpam-4036	416	5	passaic	passaic	PROPN
ejpam-4036	416	6	,	,	PUNCT
ejpam-4036	416	7	1982	1982	NUM
ejpam-4036	416	8	.	.	PUNCT
ejpam-4036	417	1	references	reference	NOUN
ejpam-4036	417	2	1014	1014	NUM
ejpam-4036	418	1	[	[	X
ejpam-4036	418	2	23	23	NUM
ejpam-4036	418	3	]	]	X
ejpam-4036	418	4	h.	h.	NOUN
ejpam-4036	418	5	wielandt	wielandt	PROPN
ejpam-4036	418	6	.	.	PUNCT
ejpam-4036	419	1	subnormal	subnormal	ADJ
ejpam-4036	419	2	subgroups	subgroup	NOUN
ejpam-4036	419	3	and	and	CCONJ
ejpam-4036	419	4	permutation	permutation	NOUN
ejpam-4036	419	5	groups	group	NOUN
ejpam-4036	419	6	.	.	PUNCT
ejpam-4036	420	1	lectures	lecture	NOUN
ejpam-4036	420	2	given	give	VERB
ejpam-4036	420	3	at	at	ADP
ejpam-4036	420	4	the	the	DET
ejpam-4036	420	5	ohio	ohio	PROPN
ejpam-4036	420	6	state	state	PROPN
ejpam-4036	420	7	university	university	PROPN
ejpam-4036	420	8	,	,	PUNCT
ejpam-4036	420	9	columbus	columbus	PROPN
ejpam-4036	420	10	,	,	PUNCT
ejpam-4036	420	11	ohio	ohio	PROPN
ejpam-4036	420	12	,	,	PUNCT
ejpam-4036	420	13	usa	usa	PROPN
ejpam-4036	420	14	,	,	PUNCT
ejpam-4036	420	15	1971	1971	NUM
ejpam-4036	420	16	.	.	PUNCT
ejpam-4036	421	1	[	[	X
ejpam-4036	421	2	24	24	NUM
ejpam-4036	421	3	]	]	X
ejpam-4036	421	4	l.	l.	PROPN
ejpam-4036	421	5	yangming	yangming	PROPN
ejpam-4036	421	6	.	.	PUNCT
ejpam-4036	422	1	some	some	DET
ejpam-4036	422	2	notes	note	NOUN
ejpam-4036	422	3	on	on	ADP
ejpam-4036	422	4	the	the	DET
ejpam-4036	422	5	minimal	minimal	ADJ
ejpam-4036	422	6	subgroups	subgroup	NOUN
ejpam-4036	422	7	of	of	ADP
ejpam-4036	422	8	fitting	fitting	ADJ
ejpam-4036	422	9	subgroups	subgroup	NOUN
ejpam-4036	422	10	of	of	ADP
ejpam-4036	422	11	finite	finite	ADJ
ejpam-4036	422	12	groups	group	NOUN
ejpam-4036	422	13	.	.	PUNCT
ejpam-4036	423	1	j.	j.	PROPN
ejpam-4036	423	2	pure	pure	PROPN
ejpam-4036	423	3	appl	appl	PROPN
ejpam-4036	423	4	.	.	PUNCT
ejpam-4036	424	1	algebra	algebra	NOUN
ejpam-4036	424	2	,	,	PUNCT
ejpam-4036	424	3	171:289–294	171:289–294	NUM
ejpam-4036	424	4	,	,	PUNCT
ejpam-4036	424	5	2002	2002	NUM
ejpam-4036	424	6	.	.	PUNCT
ejpam-4036	425	1	[	[	X
ejpam-4036	425	2	25	25	NUM
ejpam-4036	425	3	]	]	PUNCT
ejpam-4036	425	4	x.	x.	NOUN
ejpam-4036	425	5	zhao	zhao	PROPN
ejpam-4036	425	6	,	,	PUNCT
ejpam-4036	425	7	j.	j.	PROPN
ejpam-4036	425	8	sui	sui	PROPN
ejpam-4036	425	9	,	,	PUNCT
ejpam-4036	425	10	r.	r.	PROPN
ejpam-4036	425	11	chen	chen	PROPN
ejpam-4036	425	12	,	,	PUNCT
ejpam-4036	425	13	and	and	CCONJ
ejpam-4036	425	14	q.	q.	PROPN
ejpam-4036	425	15	huang	huang	PROPN
ejpam-4036	425	16	.	.	PROPN
ejpam-4036	426	1	on	on	ADP
ejpam-4036	426	2	the	the	DET
ejpam-4036	426	3	supersolvablity	supersolvablity	NOUN
ejpam-4036	426	4	of	of	ADP
ejpam-4036	426	5	finite	finite	ADJ
ejpam-4036	426	6	groups	group	NOUN
ejpam-4036	426	7	.	.	PUNCT
ejpam-4036	427	1	bull	bull	NOUN
ejpam-4036	427	2	.	.	PUNCT
ejpam-4036	428	1	iranian	iranian	ADJ
ejpam-4036	428	2	math	math	PROPN
ejpam-4036	428	3	.	.	PUNCT
ejpam-4036	429	1	soc	soc	PROPN
ejpam-4036	429	2	.	.	PUNCT
ejpam-4036	429	3	,	,	PUNCT
ejpam-4036	429	4	46:1485–1491	46:1485–1491	NUM
ejpam-4036	429	5	,	,	PUNCT
ejpam-4036	429	6	2020	2020	NUM
ejpam-4036	429	7	.	.	PUNCT
ejpam-4036	430	1	[	[	X
ejpam-4036	430	2	26	26	NUM
ejpam-4036	430	3	]	]	PUNCT
ejpam-4036	430	4	x.	x.	NOUN
ejpam-4036	430	5	zhao	zhao	PROPN
ejpam-4036	430	6	,	,	PUNCT
ejpam-4036	430	7	l.	l.	PROPN
ejpam-4036	430	8	zhou	zhou	PROPN
ejpam-4036	430	9	,	,	PUNCT
ejpam-4036	430	10	and	and	CCONJ
ejpam-4036	430	11	s.	s.	PROPN
ejpam-4036	430	12	li	li	PROPN
ejpam-4036	430	13	.	.	PROPN
ejpam-4036	431	1	on	on	ADP
ejpam-4036	431	2	the	the	DET
ejpam-4036	431	3	p	p	NOUN
ejpam-4036	431	4	-	-	PUNCT
ejpam-4036	431	5	nilpotence	nilpotence	NOUN
ejpam-4036	431	6	of	of	ADP
ejpam-4036	431	7	finite	finite	ADJ
ejpam-4036	431	8	groups	group	NOUN
ejpam-4036	431	9	.	.	PUNCT
ejpam-4036	432	1	ital	ital	PROPN
ejpam-4036	432	2	.	.	PUNCT
ejpam-4036	433	1	j.	j.	PROPN
ejpam-4036	433	2	pure	pure	PROPN
ejpam-4036	433	3	appl	appl	PROPN
ejpam-4036	433	4	.	.	PUNCT
ejpam-4036	433	5	math	math	PROPN
ejpam-4036	433	6	.	.	PUNCT
ejpam-4036	433	7	,	,	PUNCT
ejpam-4036	433	8	41:97–103	41:97–103	NUM
ejpam-4036	433	9	,	,	PUNCT
ejpam-4036	433	10	2019	2019	NUM
ejpam-4036	433	11	.	.	PUNCT