id	sid	tid	token	lemma	pos
ejpam-5120	1	1	european	european	PROPN
ejpam-5120	1	2	journal	journal	PROPN
ejpam-5120	1	3	of	of	ADP
ejpam-5120	1	4	pure	pure	ADJ
ejpam-5120	1	5	and	and	CCONJ
ejpam-5120	1	6	applied	apply	VERB
ejpam-5120	1	7	mathematics	mathematic	NOUN
ejpam-5120	1	8	vol	vol	NOUN
ejpam-5120	1	9	.	.	PROPN
ejpam-5120	2	1	17	17	NUM
ejpam-5120	2	2	,	,	PUNCT
ejpam-5120	2	3	no	no	INTJ
ejpam-5120	2	4	.	.	NOUN
ejpam-5120	2	5	2	2	NUM
ejpam-5120	2	6	,	,	PUNCT
ejpam-5120	2	7	2024	2024	NUM
ejpam-5120	2	8	,	,	PUNCT
ejpam-5120	2	9	810	810	NUM
ejpam-5120	2	10	-	-	SYM
ejpam-5120	2	11	818	818	NUM
ejpam-5120	2	12	issn	issn	PROPN
ejpam-5120	2	13	1307	1307	NUM
ejpam-5120	2	14	-	-	SYM
ejpam-5120	2	15	5543	5543	NUM
ejpam-5120	2	16	–	–	PUNCT
ejpam-5120	3	1	ejpam.com	ejpam.com	X
ejpam-5120	3	2	published	publish	VERB
ejpam-5120	3	3	by	by	ADP
ejpam-5120	3	4	new	new	PROPN
ejpam-5120	3	5	york	york	PROPN
ejpam-5120	3	6	business	business	PROPN
ejpam-5120	3	7	global	global	ADJ
ejpam-5120	3	8	finite	finite	ADJ
ejpam-5120	3	9	groups	group	NOUN
ejpam-5120	3	10	with	with	ADP
ejpam-5120	3	11	certain	certain	ADJ
ejpam-5120	3	12	weakly	weakly	ADJ
ejpam-5120	3	13	s	s	NOUN
ejpam-5120	3	14	-	-	ADJ
ejpam-5120	3	15	permutable	permutable	ADJ
ejpam-5120	3	16	subgroups	subgroup	NOUN
ejpam-5120	3	17	n.	n.	PROPN
ejpam-5120	3	18	alsowait1	alsowait1	PROPN
ejpam-5120	3	19	,	,	PUNCT
ejpam-5120	3	20	a.	a.	NOUN
ejpam-5120	3	21	a.	a.	NOUN
ejpam-5120	3	22	heliel2,3,∗	heliel2,3,∗	PROPN
ejpam-5120	3	23	,	,	PUNCT
ejpam-5120	3	24	m.	m.	NOUN
ejpam-5120	3	25	m.	m.	PROPN
ejpam-5120	3	26	al	al	PROPN
ejpam-5120	3	27	-	-	PUNCT
ejpam-5120	3	28	shomrani2	shomrani2	PROPN
ejpam-5120	3	29	,	,	PUNCT
ejpam-5120	3	30	a.	a.	PROPN
ejpam-5120	3	31	s.	s.	PROPN
ejpam-5120	3	32	allehyani2	allehyani2	PROPN
ejpam-5120	4	1	1	1	NUM
ejpam-5120	4	2	department	department	NOUN
ejpam-5120	4	3	of	of	ADP
ejpam-5120	4	4	mathematics	mathematic	NOUN
ejpam-5120	4	5	,	,	PUNCT
ejpam-5120	4	6	faculty	faculty	NOUN
ejpam-5120	4	7	of	of	ADP
ejpam-5120	4	8	science	science	NOUN
ejpam-5120	4	9	,	,	PUNCT
ejpam-5120	4	10	northern	northern	ADJ
ejpam-5120	4	11	border	border	NOUN
ejpam-5120	4	12	university	university	PROPN
ejpam-5120	4	13	,	,	PUNCT
ejpam-5120	4	14	arar	arar	PROPN
ejpam-5120	4	15	,	,	PUNCT
ejpam-5120	4	16	saudi	saudi	PROPN
ejpam-5120	4	17	arabia	arabia	PROPN
ejpam-5120	4	18	2	2	NUM
ejpam-5120	4	19	department	department	NOUN
ejpam-5120	4	20	of	of	ADP
ejpam-5120	4	21	mathematics	mathematic	NOUN
ejpam-5120	4	22	,	,	PUNCT
ejpam-5120	4	23	faculty	faculty	NOUN
ejpam-5120	4	24	of	of	ADP
ejpam-5120	4	25	science	science	NOUN
ejpam-5120	4	26	,	,	PUNCT
ejpam-5120	4	27	king	king	PROPN
ejpam-5120	4	28	abdulaziz	abdulaziz	PROPN
ejpam-5120	4	29	university	university	PROPN
ejpam-5120	4	30	,	,	PUNCT
ejpam-5120	4	31	jeddah	jeddah	PROPN
ejpam-5120	4	32	,	,	PUNCT
ejpam-5120	4	33	saudi	saudi	PROPN
ejpam-5120	4	34	arabia	arabia	PROPN
ejpam-5120	4	35	3	3	NUM
ejpam-5120	4	36	department	department	NOUN
ejpam-5120	4	37	of	of	ADP
ejpam-5120	4	38	mathematics	mathematic	NOUN
ejpam-5120	4	39	and	and	CCONJ
ejpam-5120	4	40	computer	computer	NOUN
ejpam-5120	4	41	science	science	NOUN
ejpam-5120	4	42	,	,	PUNCT
ejpam-5120	4	43	faculty	faculty	NOUN
ejpam-5120	4	44	of	of	ADP
ejpam-5120	4	45	science	science	NOUN
ejpam-5120	4	46	,	,	PUNCT
ejpam-5120	4	47	beni	beni	ADJ
ejpam-5120	4	48	-	-	ADJ
ejpam-5120	4	49	suef	suef	ADJ
ejpam-5120	4	50	university	university	NOUN
ejpam-5120	4	51	,	,	PUNCT
ejpam-5120	4	52	beni	beni	NOUN
ejpam-5120	4	53	-	-	ADJ
ejpam-5120	4	54	suef	suef	NOUN
ejpam-5120	4	55	,	,	PUNCT
ejpam-5120	4	56	egypt	egypt	PROPN
ejpam-5120	4	57	abstract	abstract	PROPN
ejpam-5120	4	58	.	.	PUNCT
ejpam-5120	5	1	let	let	VERB
ejpam-5120	5	2	g	g	PRON
ejpam-5120	5	3	be	be	AUX
ejpam-5120	5	4	a	a	DET
ejpam-5120	5	5	finite	finite	ADJ
ejpam-5120	5	6	group	group	NOUN
ejpam-5120	5	7	.	.	PUNCT
ejpam-5120	6	1	a	a	DET
ejpam-5120	6	2	subgroup	subgroup	NOUN
ejpam-5120	6	3	h	h	NOUN
ejpam-5120	6	4	of	of	ADP
ejpam-5120	6	5	g	g	PROPN
ejpam-5120	6	6	is	be	AUX
ejpam-5120	6	7	said	say	VERB
ejpam-5120	6	8	to	to	PART
ejpam-5120	6	9	be	be	AUX
ejpam-5120	6	10	weakly	weakly	ADJ
ejpam-5120	6	11	s	s	NOUN
ejpam-5120	6	12	-	-	NOUN
ejpam-5120	6	13	permutable	permutable	ADJ
ejpam-5120	6	14	in	in	ADP
ejpam-5120	6	15	g	g	PROPN
ejpam-5120	6	16	if	if	SCONJ
ejpam-5120	6	17	g	g	PROPN
ejpam-5120	6	18	has	have	VERB
ejpam-5120	6	19	a	a	DET
ejpam-5120	6	20	subnormal	subnormal	ADJ
ejpam-5120	6	21	subgroup	subgroup	PROPN
ejpam-5120	6	22	t	t	PROPN
ejpam-5120	7	1	such	such	ADJ
ejpam-5120	7	2	that	that	SCONJ
ejpam-5120	7	3	g	g	PROPN
ejpam-5120	7	4	=	=	PUNCT
ejpam-5120	7	5	ht	ht	PROPN
ejpam-5120	7	6	and	and	CCONJ
ejpam-5120	7	7	t	t	PROPN
ejpam-5120	7	8	∩h	∩h	PROPN
ejpam-5120	7	9	≤	≤	PROPN
ejpam-5120	7	10	hsg	hsg	NOUN
ejpam-5120	7	11	,	,	PUNCT
ejpam-5120	7	12	where	where	SCONJ
ejpam-5120	7	13	hsg	hsg	NOUN
ejpam-5120	7	14	is	be	AUX
ejpam-5120	7	15	the	the	DET
ejpam-5120	7	16	subgroup	subgroup	NOUN
ejpam-5120	7	17	of	of	ADP
ejpam-5120	7	18	h	h	PROPN
ejpam-5120	7	19	generated	generate	VERB
ejpam-5120	7	20	by	by	ADP
ejpam-5120	7	21	all	all	DET
ejpam-5120	7	22	those	those	DET
ejpam-5120	7	23	subgroups	subgroup	NOUN
ejpam-5120	7	24	of	of	ADP
ejpam-5120	7	25	h	h	NOUN
ejpam-5120	7	26	which	which	PRON
ejpam-5120	7	27	are	be	AUX
ejpam-5120	7	28	s	s	NOUN
ejpam-5120	7	29	-	-	NOUN
ejpam-5120	7	30	permutable	permutable	ADJ
ejpam-5120	7	31	in	in	ADP
ejpam-5120	7	32	g.	g.	PROPN
ejpam-5120	7	33	in	in	ADP
ejpam-5120	7	34	this	this	DET
ejpam-5120	7	35	paper	paper	NOUN
ejpam-5120	7	36	,	,	PUNCT
ejpam-5120	7	37	we	we	PRON
ejpam-5120	7	38	prove	prove	VERB
ejpam-5120	7	39	the	the	DET
ejpam-5120	7	40	following	following	NOUN
ejpam-5120	7	41	:	:	PUNCT
ejpam-5120	7	42	for	for	ADP
ejpam-5120	7	43	a	a	DET
ejpam-5120	7	44	sylow	sylow	NOUN
ejpam-5120	7	45	p	p	PROPN
ejpam-5120	7	46	-	-	PUNCT
ejpam-5120	7	47	subgroup	subgroup	NOUN
ejpam-5120	7	48	p	p	NOUN
ejpam-5120	7	49	of	of	ADP
ejpam-5120	7	50	g	g	PROPN
ejpam-5120	7	51	(	(	PUNCT
ejpam-5120	7	52	p	p	X
ejpam-5120	7	53	>	>	X
ejpam-5120	7	54	2	2	NUM
ejpam-5120	7	55	)	)	PUNCT
ejpam-5120	7	56	,	,	PUNCT
ejpam-5120	7	57	suppose	suppose	VERB
ejpam-5120	7	58	that	that	SCONJ
ejpam-5120	7	59	p	p	PROPN
ejpam-5120	7	60	has	have	VERB
ejpam-5120	7	61	a	a	DET
ejpam-5120	7	62	subgroup	subgroup	NOUN
ejpam-5120	7	63	d	d	NOUN
ejpam-5120	7	64	such	such	ADJ
ejpam-5120	7	65	that	that	SCONJ
ejpam-5120	7	66	1	1	NUM
ejpam-5120	7	67	<	<	X
ejpam-5120	7	68	|d|	|d|	PROPN
ejpam-5120	7	69	<	<	X
ejpam-5120	7	70	|p	|p	X
ejpam-5120	7	71	|	|	ADV
ejpam-5120	7	72	holds	hold	VERB
ejpam-5120	7	73	and	and	CCONJ
ejpam-5120	7	74	all	all	DET
ejpam-5120	7	75	subgroups	subgroup	NOUN
ejpam-5120	7	76	h	h	NOUN
ejpam-5120	7	77	of	of	ADP
ejpam-5120	7	78	p	p	NOUN
ejpam-5120	7	79	with	with	ADP
ejpam-5120	7	80	|h|	|h|	PROPN
ejpam-5120	7	81	=	=	SYM
ejpam-5120	7	82	|d|	|d|	PROPN
ejpam-5120	7	83	are	be	AUX
ejpam-5120	7	84	weakly	weakly	ADJ
ejpam-5120	7	85	s	s	NOUN
ejpam-5120	7	86	-	-	NOUN
ejpam-5120	7	87	permutable	permutable	ADJ
ejpam-5120	7	88	in	in	ADP
ejpam-5120	7	89	g.	g.	PROPN
ejpam-5120	7	90	then	then	ADV
ejpam-5120	7	91	,	,	PUNCT
ejpam-5120	7	92	the	the	DET
ejpam-5120	7	93	commutator	commutator	NOUN
ejpam-5120	7	94	subgroup	subgroup	PROPN
ejpam-5120	7	95	g	g	PROPN
ejpam-5120	7	96	′	′	NUM
ejpam-5120	7	97	is	be	AUX
ejpam-5120	7	98	p	p	NOUN
ejpam-5120	7	99	-	-	PUNCT
ejpam-5120	7	100	nilpotent	nilpotent	ADJ
ejpam-5120	7	101	.	.	PUNCT
ejpam-5120	8	1	we	we	PRON
ejpam-5120	8	2	certainly	certainly	ADV
ejpam-5120	8	3	believe	believe	VERB
ejpam-5120	8	4	that	that	SCONJ
ejpam-5120	8	5	this	this	DET
ejpam-5120	8	6	result	result	NOUN
ejpam-5120	8	7	will	will	AUX
ejpam-5120	8	8	improve	improve	VERB
ejpam-5120	8	9	and	and	CCONJ
ejpam-5120	8	10	extend	extend	VERB
ejpam-5120	8	11	a	a	DET
ejpam-5120	8	12	current	current	ADJ
ejpam-5120	8	13	and	and	CCONJ
ejpam-5120	8	14	classical	classical	ADJ
ejpam-5120	8	15	theories	theory	NOUN
ejpam-5120	8	16	in	in	ADP
ejpam-5120	8	17	the	the	DET
ejpam-5120	8	18	literature	literature	NOUN
ejpam-5120	8	19	.	.	PUNCT
ejpam-5120	9	1	2020	2020	NUM
ejpam-5120	9	2	mathematics	mathematics	PROPN
ejpam-5120	9	3	subject	subject	NOUN
ejpam-5120	9	4	classifications	classification	NOUN
ejpam-5120	9	5	:	:	PUNCT
ejpam-5120	9	6	20d10	20d10	NUM
ejpam-5120	9	7	,	,	PUNCT
ejpam-5120	9	8	20d10	20d10	NUM
ejpam-5120	9	9	,	,	PUNCT
ejpam-5120	9	10	20d20	20d20	NUM
ejpam-5120	9	11	.	.	PUNCT
ejpam-5120	10	1	key	key	ADJ
ejpam-5120	10	2	words	word	NOUN
ejpam-5120	10	3	and	and	CCONJ
ejpam-5120	10	4	phrases	phrase	NOUN
ejpam-5120	10	5	:	:	PUNCT
ejpam-5120	10	6	sylow	sylow	NOUN
ejpam-5120	10	7	subgroups	subgroup	NOUN
ejpam-5120	10	8	,	,	PUNCT
ejpam-5120	10	9	s	s	NOUN
ejpam-5120	10	10	-	-	PUNCT
ejpam-5120	10	11	permutable	permutable	ADJ
ejpam-5120	10	12	subgroups	subgroup	NOUN
ejpam-5120	10	13	,	,	PUNCT
ejpam-5120	10	14	weakly	weakly	ADJ
ejpam-5120	10	15	s	s	NOUN
ejpam-5120	10	16	-	-	ADJ
ejpam-5120	10	17	permutable	permutable	ADJ
ejpam-5120	10	18	subgroups	subgroup	NOUN
ejpam-5120	10	19	,	,	PUNCT
ejpam-5120	10	20	p	p	ADJ
ejpam-5120	10	21	-	-	PUNCT
ejpam-5120	10	22	nilpotent	nilpotent	ADJ
ejpam-5120	10	23	groups	group	NOUN
ejpam-5120	10	24	1	1	NUM
ejpam-5120	10	25	.	.	PUNCT
ejpam-5120	10	26	introduction	introduction	NOUN
ejpam-5120	10	27	all	all	DET
ejpam-5120	10	28	groups	group	NOUN
ejpam-5120	10	29	considered	consider	VERB
ejpam-5120	10	30	in	in	ADP
ejpam-5120	10	31	this	this	DET
ejpam-5120	10	32	paper	paper	NOUN
ejpam-5120	10	33	will	will	AUX
ejpam-5120	10	34	be	be	AUX
ejpam-5120	10	35	finite	finite	VERB
ejpam-5120	10	36	.	.	PUNCT
ejpam-5120	11	1	a	a	DET
ejpam-5120	11	2	subgroup	subgroup	NOUN
ejpam-5120	11	3	h	h	NOUN
ejpam-5120	11	4	of	of	ADP
ejpam-5120	11	5	a	a	DET
ejpam-5120	11	6	group	group	NOUN
ejpam-5120	11	7	g	g	NOUN
ejpam-5120	11	8	is	be	AUX
ejpam-5120	11	9	said	say	VERB
ejpam-5120	11	10	to	to	PART
ejpam-5120	11	11	be	be	AUX
ejpam-5120	11	12	permutable	permutable	ADJ
ejpam-5120	11	13	in	in	ADP
ejpam-5120	11	14	g	g	PROPN
ejpam-5120	11	15	if	if	SCONJ
ejpam-5120	11	16	h	h	NOUN
ejpam-5120	11	17	permutes	permute	VERB
ejpam-5120	11	18	with	with	ADP
ejpam-5120	11	19	every	every	DET
ejpam-5120	11	20	subgroup	subgroup	NOUN
ejpam-5120	11	21	of	of	ADP
ejpam-5120	11	22	g	g	PROPN
ejpam-5120	11	23	,	,	PUNCT
ejpam-5120	11	24	that	that	ADV
ejpam-5120	11	25	is	is	ADV
ejpam-5120	11	26	,	,	PUNCT
ejpam-5120	11	27	hk	hk	PROPN
ejpam-5120	11	28	⩽	⩽	PROPN
ejpam-5120	11	29	g	g	PROPN
ejpam-5120	11	30	for	for	ADP
ejpam-5120	11	31	all	all	DET
ejpam-5120	11	32	k	k	PROPN
ejpam-5120	11	33	⩽	⩽	PROPN
ejpam-5120	11	34	g.	g.	PROPN
ejpam-5120	12	1	a	a	DET
ejpam-5120	12	2	subgroup	subgroup	NOUN
ejpam-5120	12	3	h	h	NOUN
ejpam-5120	12	4	of	of	ADP
ejpam-5120	12	5	g	g	PROPN
ejpam-5120	12	6	is	be	AUX
ejpam-5120	12	7	called	call	VERB
ejpam-5120	12	8	s	s	ADJ
ejpam-5120	12	9	-	-	NOUN
ejpam-5120	12	10	permutable	permutable	ADJ
ejpam-5120	12	11	in	in	ADP
ejpam-5120	12	12	g	g	NOUN
ejpam-5120	12	13	provided	provide	VERB
ejpam-5120	12	14	h	h	NOUN
ejpam-5120	12	15	permutes	permute	NOUN
ejpam-5120	12	16	with	with	ADP
ejpam-5120	12	17	all	all	DET
ejpam-5120	12	18	sylow	sylow	NOUN
ejpam-5120	12	19	subgroups	subgroup	NOUN
ejpam-5120	12	20	of	of	ADP
ejpam-5120	12	21	g	g	NOUN
ejpam-5120	12	22	,	,	PUNCT
ejpam-5120	12	23	i.e.	i.e.	X
ejpam-5120	12	24	,	,	PUNCT
ejpam-5120	12	25	hp	hp	ADJ
ejpam-5120	12	26	=	=	PUNCT
ejpam-5120	12	27	ph	ph	PROPN
ejpam-5120	12	28	for	for	ADP
ejpam-5120	12	29	any	any	DET
ejpam-5120	12	30	sylow	sylow	NOUN
ejpam-5120	12	31	subgroup	subgroup	NOUN
ejpam-5120	12	32	p	p	PROPN
ejpam-5120	12	33	of	of	ADP
ejpam-5120	12	34	g.	g.	PROPN
ejpam-5120	12	35	this	this	DET
ejpam-5120	12	36	concept	concept	NOUN
ejpam-5120	12	37	was	be	AUX
ejpam-5120	12	38	proposed	propose	VERB
ejpam-5120	12	39	by	by	ADP
ejpam-5120	12	40	kegel	kegel	PROPN
ejpam-5120	12	41	in	in	ADP
ejpam-5120	12	42	[	[	X
ejpam-5120	12	43	8	8	NUM
ejpam-5120	12	44	]	]	PUNCT
ejpam-5120	12	45	.	.	PUNCT
ejpam-5120	13	1	in	in	ADP
ejpam-5120	13	2	1996	1996	NUM
ejpam-5120	13	3	,	,	PUNCT
ejpam-5120	13	4	wang	wang	PROPN
ejpam-5120	13	5	[	[	X
ejpam-5120	13	6	10	10	NUM
ejpam-5120	13	7	]	]	PUNCT
ejpam-5120	13	8	,	,	PUNCT
ejpam-5120	13	9	defined	define	VERB
ejpam-5120	13	10	the	the	DET
ejpam-5120	13	11	concept	concept	NOUN
ejpam-5120	13	12	of	of	ADP
ejpam-5120	13	13	c	c	NOUN
ejpam-5120	13	14	-	-	PUNCT
ejpam-5120	13	15	normality	normality	NOUN
ejpam-5120	13	16	as	as	SCONJ
ejpam-5120	13	17	follows	follow	VERB
ejpam-5120	13	18	:	:	PUNCT
ejpam-5120	13	19	a	a	DET
ejpam-5120	13	20	subgroup	subgroup	NOUN
ejpam-5120	13	21	h	h	NOUN
ejpam-5120	13	22	of	of	ADP
ejpam-5120	13	23	a	a	DET
ejpam-5120	13	24	group	group	NOUN
ejpam-5120	13	25	g	g	NOUN
ejpam-5120	13	26	is	be	AUX
ejpam-5120	13	27	said	say	VERB
ejpam-5120	13	28	to	to	PART
ejpam-5120	13	29	be	be	AUX
ejpam-5120	13	30	c	c	NOUN
ejpam-5120	13	31	-	-	ADJ
ejpam-5120	13	32	normal	normal	ADJ
ejpam-5120	13	33	in	in	ADP
ejpam-5120	13	34	g	g	PROPN
ejpam-5120	13	35	if	if	SCONJ
ejpam-5120	13	36	g	g	PROPN
ejpam-5120	13	37	has	have	VERB
ejpam-5120	13	38	a	a	DET
ejpam-5120	13	39	normal	normal	ADJ
ejpam-5120	13	40	subgroup	subgroup	NOUN
ejpam-5120	13	41	k	k	PROPN
ejpam-5120	14	1	such	such	ADJ
ejpam-5120	14	2	that	that	SCONJ
ejpam-5120	14	3	g	g	PROPN
ejpam-5120	14	4	=	=	PUNCT
ejpam-5120	14	5	hk	hk	PROPN
ejpam-5120	14	6	and	and	CCONJ
ejpam-5120	14	7	h	h	PROPN
ejpam-5120	14	8	∩	∩	PROPN
ejpam-5120	14	9	k	k	PROPN
ejpam-5120	14	10	⩽	⩽	PROPN
ejpam-5120	14	11	hg	hg	PROPN
ejpam-5120	14	12	,	,	PUNCT
ejpam-5120	14	13	where	where	SCONJ
ejpam-5120	14	14	hg	hg	PROPN
ejpam-5120	14	15	=	=	PROPN
ejpam-5120	14	16	coreg(h	coreg(h	PROPN
ejpam-5120	14	17	)	)	PUNCT
ejpam-5120	14	18	is	be	AUX
ejpam-5120	14	19	the	the	DET
ejpam-5120	14	20	largest	large	ADJ
ejpam-5120	14	21	normal	normal	ADJ
ejpam-5120	14	22	subgroup	subgroup	NOUN
ejpam-5120	14	23	of	of	ADP
ejpam-5120	14	24	g	g	PROPN
ejpam-5120	14	25	contained	contain	VERB
ejpam-5120	14	26	in	in	ADP
ejpam-5120	14	27	h.	h.	PROPN
ejpam-5120	14	28	as	as	ADP
ejpam-5120	14	29	a	a	DET
ejpam-5120	14	30	generalization	generalization	NOUN
ejpam-5120	14	31	of	of	ADP
ejpam-5120	14	32	c	c	NOUN
ejpam-5120	14	33	-	-	NOUN
ejpam-5120	14	34	normality	normality	NOUN
ejpam-5120	14	35	,	,	PUNCT
ejpam-5120	14	36	a	a	DET
ejpam-5120	14	37	subgroup	subgroup	NOUN
ejpam-5120	14	38	h	h	NOUN
ejpam-5120	14	39	of	of	ADP
ejpam-5120	14	40	g	g	PROPN
ejpam-5120	14	41	is	be	AUX
ejpam-5120	14	42	said	say	VERB
ejpam-5120	14	43	to	to	PART
ejpam-5120	14	44	be	be	AUX
ejpam-5120	14	45	c	c	NOUN
ejpam-5120	14	46	-	-	PUNCT
ejpam-5120	14	47	supplemented	supplement	VERB
ejpam-5120	14	48	in	in	ADP
ejpam-5120	14	49	g	g	PROPN
ejpam-5120	14	50	if	if	SCONJ
ejpam-5120	14	51	there	there	PRON
ejpam-5120	14	52	exists	exist	VERB
ejpam-5120	14	53	a	a	DET
ejpam-5120	14	54	subgroup	subgroup	NOUN
ejpam-5120	14	55	k	k	PROPN
ejpam-5120	14	56	of	of	ADP
ejpam-5120	14	57	g	g	PROPN
ejpam-5120	15	1	such	such	ADJ
ejpam-5120	15	2	that	that	SCONJ
ejpam-5120	15	3	g	g	PROPN
ejpam-5120	15	4	=	=	PUNCT
ejpam-5120	15	5	hk	hk	PROPN
ejpam-5120	15	6	and	and	CCONJ
ejpam-5120	15	7	∗corresponding	∗corresponde	VERB
ejpam-5120	15	8	author	author	NOUN
ejpam-5120	15	9	.	.	PUNCT
ejpam-5120	16	1	doi	doi	NOUN
ejpam-5120	16	2	:	:	PUNCT
ejpam-5120	16	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5120	https://doi.org/10.29020/nybg.ejpam.v17i2.5120	ADJ
ejpam-5120	16	4	email	email	NOUN
ejpam-5120	16	5	addresses	address	NOUN
ejpam-5120	16	6	:	:	PUNCT
ejpam-5120	16	7	nawaf.lazzam@nbu.edu.sa	nawaf.lazzam@nbu.edu.sa	PROPN
ejpam-5120	16	8	(	(	PUNCT
ejpam-5120	16	9	n.	n.	PROPN
ejpam-5120	16	10	alsowait	alsowait	PROPN
ejpam-5120	16	11	)	)	PUNCT
ejpam-5120	16	12	,	,	PUNCT
ejpam-5120	16	13	aahsalem1@kau.edu.sa	aahsalem1@kau.edu.sa	PROPN
ejpam-5120	16	14	(	(	PUNCT
ejpam-5120	16	15	a.	a.	NOUN
ejpam-5120	16	16	a.	a.	NOUN
ejpam-5120	16	17	heliel	heliel	PROPN
ejpam-5120	16	18	)	)	PUNCT
ejpam-5120	16	19	,	,	PUNCT
ejpam-5120	16	20	malshomrani@hotmail.com	malshomrani@hotmail.com	X
ejpam-5120	16	21	(	(	PUNCT
ejpam-5120	16	22	m.	m.	NOUN
ejpam-5120	16	23	m.	m.	PROPN
ejpam-5120	16	24	al	al	PROPN
ejpam-5120	16	25	-	-	PUNCT
ejpam-5120	16	26	shomrani	shomrani	PROPN
ejpam-5120	16	27	)	)	PUNCT
ejpam-5120	16	28	,	,	PUNCT
ejpam-5120	16	29	asaeedallehyani@stu.kau.edu.sa	asaeedallehyani@stu.kau.edu.sa	PROPN
ejpam-5120	16	30	(	(	PUNCT
ejpam-5120	16	31	a.	a.	PROPN
ejpam-5120	16	32	s.	s.	PROPN
ejpam-5120	16	33	allehyani	allehyani	PROPN
ejpam-5120	16	34	)	)	PUNCT
ejpam-5120	16	35	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5120	16	36	810	810	NUM
ejpam-5120	17	1	©	©	ADP
ejpam-5120	17	2	2024	2024	NUM
ejpam-5120	17	3	ejpam	ejpam	NOUN
ejpam-5120	17	4	all	all	DET
ejpam-5120	17	5	rights	right	NOUN
ejpam-5120	17	6	reserved	reserve	VERB
ejpam-5120	17	7	.	.	PUNCT
ejpam-5120	18	1	a.	a.	NOUN
ejpam-5120	18	2	a.	a.	PROPN
ejpam-5120	18	3	heliel	heliel	PROPN
ejpam-5120	18	4	et	et	PROPN
ejpam-5120	18	5	al	al	PROPN
ejpam-5120	18	6	.	.	PUNCT
ejpam-5120	18	7	/	/	SYM
ejpam-5120	18	8	eur	eur	PROPN
ejpam-5120	18	9	.	.	PUNCT
ejpam-5120	19	1	j.	j.	PROPN
ejpam-5120	19	2	pure	pure	PROPN
ejpam-5120	19	3	appl	appl	PROPN
ejpam-5120	19	4	.	.	PROPN
ejpam-5120	19	5	math	math	PROPN
ejpam-5120	19	6	,	,	PUNCT
ejpam-5120	19	7	17	17	NUM
ejpam-5120	19	8	(	(	PUNCT
ejpam-5120	19	9	2	2	NUM
ejpam-5120	19	10	)	)	PUNCT
ejpam-5120	19	11	(	(	PUNCT
ejpam-5120	19	12	2024	2024	NUM
ejpam-5120	19	13	)	)	PUNCT
ejpam-5120	19	14	,	,	PUNCT
ejpam-5120	19	15	810	810	NUM
ejpam-5120	19	16	-	-	SYM
ejpam-5120	19	17	818	818	NUM
ejpam-5120	19	18	811	811	NUM
ejpam-5120	19	19	h	h	NOUN
ejpam-5120	19	20	∩k	∩k	ADJ
ejpam-5120	19	21	⩽	⩽	ADJ
ejpam-5120	19	22	hg	hg	NOUN
ejpam-5120	19	23	,	,	PUNCT
ejpam-5120	19	24	where	where	SCONJ
ejpam-5120	19	25	hg	hg	PROPN
ejpam-5120	19	26	=	=	PROPN
ejpam-5120	19	27	coreg(h	coreg(h	PROPN
ejpam-5120	19	28	)	)	PUNCT
ejpam-5120	19	29	is	be	AUX
ejpam-5120	19	30	the	the	DET
ejpam-5120	19	31	largest	large	ADJ
ejpam-5120	19	32	normal	normal	ADJ
ejpam-5120	19	33	subgroup	subgroup	NOUN
ejpam-5120	19	34	of	of	ADP
ejpam-5120	19	35	g	g	PROPN
ejpam-5120	19	36	contained	contain	VERB
ejpam-5120	19	37	in	in	ADP
ejpam-5120	19	38	h	h	PROPN
ejpam-5120	19	39	(	(	PUNCT
ejpam-5120	19	40	see	see	VERB
ejpam-5120	19	41	[	[	X
ejpam-5120	19	42	1	1	NUM
ejpam-5120	19	43	]	]	NUM
ejpam-5120	19	44	)	)	PUNCT
ejpam-5120	19	45	.	.	PUNCT
ejpam-5120	20	1	a	a	DET
ejpam-5120	20	2	number	number	NOUN
ejpam-5120	20	3	of	of	ADP
ejpam-5120	20	4	scholars	scholar	NOUN
ejpam-5120	20	5	have	have	AUX
ejpam-5120	20	6	studied	study	VERB
ejpam-5120	20	7	influence	influence	NOUN
ejpam-5120	20	8	of	of	ADP
ejpam-5120	20	9	special	special	ADJ
ejpam-5120	20	10	types	type	NOUN
ejpam-5120	20	11	of	of	ADP
ejpam-5120	20	12	subgroups	subgroup	NOUN
ejpam-5120	20	13	behavior	behavior	NOUN
ejpam-5120	20	14	on	on	ADP
ejpam-5120	20	15	the	the	DET
ejpam-5120	20	16	group	group	NOUN
ejpam-5120	20	17	structure	structure	NOUN
ejpam-5120	20	18	.	.	PUNCT
ejpam-5120	21	1	for	for	ADP
ejpam-5120	21	2	instance	instance	NOUN
ejpam-5120	21	3	,	,	PUNCT
ejpam-5120	21	4	gaschütz	gaschütz	NOUN
ejpam-5120	21	5	and	and	CCONJ
ejpam-5120	21	6	itö	itö	ADJ
ejpam-5120	21	7	(	(	PUNCT
ejpam-5120	21	8	[	[	X
ejpam-5120	21	9	7	7	NUM
ejpam-5120	21	10	]	]	PUNCT
ejpam-5120	21	11	,	,	PUNCT
ejpam-5120	21	12	satz	satz	PROPN
ejpam-5120	21	13	5.7	5.7	NUM
ejpam-5120	21	14	,	,	PUNCT
ejpam-5120	21	15	p.	p.	NOUN
ejpam-5120	21	16	436	436	NUM
ejpam-5120	21	17	)	)	PUNCT
ejpam-5120	21	18	proved	prove	VERB
ejpam-5120	21	19	that	that	SCONJ
ejpam-5120	21	20	a	a	DET
ejpam-5120	21	21	group	group	NOUN
ejpam-5120	21	22	g	g	NOUN
ejpam-5120	21	23	is	be	AUX
ejpam-5120	21	24	solvable	solvable	ADJ
ejpam-5120	21	25	if	if	SCONJ
ejpam-5120	21	26	all	all	DET
ejpam-5120	21	27	its	its	PRON
ejpam-5120	21	28	minimal	minimal	ADJ
ejpam-5120	21	29	subgroups	subgroup	NOUN
ejpam-5120	21	30	are	be	AUX
ejpam-5120	21	31	normal	normal	ADJ
ejpam-5120	21	32	(	(	PUNCT
ejpam-5120	21	33	a	a	DET
ejpam-5120	21	34	minimal	minimal	ADJ
ejpam-5120	21	35	subgroup	subgroup	NOUN
ejpam-5120	21	36	is	be	AUX
ejpam-5120	21	37	a	a	DET
ejpam-5120	21	38	subgroup	subgroup	NOUN
ejpam-5120	21	39	of	of	ADP
ejpam-5120	21	40	prime	prime	ADJ
ejpam-5120	21	41	order	order	NOUN
ejpam-5120	21	42	)	)	PUNCT
ejpam-5120	21	43	.	.	PUNCT
ejpam-5120	22	1	in	in	ADP
ejpam-5120	22	2	[	[	X
ejpam-5120	22	3	4	4	NUM
ejpam-5120	22	4	]	]	PUNCT
ejpam-5120	22	5	,	,	PUNCT
ejpam-5120	22	6	heliel	heliel	PROPN
ejpam-5120	22	7	proved	prove	VERB
ejpam-5120	22	8	a	a	DET
ejpam-5120	22	9	group	group	NOUN
ejpam-5120	22	10	g	g	NOUN
ejpam-5120	22	11	is	be	AUX
ejpam-5120	22	12	solvable	solvable	ADJ
ejpam-5120	22	13	if	if	SCONJ
ejpam-5120	22	14	each	each	DET
ejpam-5120	22	15	subgroup	subgroup	NOUN
ejpam-5120	22	16	of	of	ADP
ejpam-5120	22	17	prime	prime	ADJ
ejpam-5120	22	18	odd	odd	ADJ
ejpam-5120	22	19	order	order	NOUN
ejpam-5120	22	20	of	of	ADP
ejpam-5120	22	21	g	g	PROPN
ejpam-5120	22	22	is	be	AUX
ejpam-5120	22	23	c	c	NOUN
ejpam-5120	22	24	-	-	PUNCT
ejpam-5120	22	25	supplemented	supplement	VERB
ejpam-5120	22	26	in	in	ADP
ejpam-5120	22	27	g.	g.	PROPN
ejpam-5120	22	28	in	in	ADP
ejpam-5120	22	29	2015	2015	NUM
ejpam-5120	22	30	,	,	PUNCT
ejpam-5120	22	31	hijazi	hijazi	PROPN
ejpam-5120	23	1	[	[	X
ejpam-5120	23	2	5	5	X
ejpam-5120	23	3	]	]	PUNCT
ejpam-5120	23	4	proved	prove	VERB
ejpam-5120	23	5	that	that	SCONJ
ejpam-5120	23	6	if	if	SCONJ
ejpam-5120	23	7	each	each	DET
ejpam-5120	23	8	sylow	sylow	NOUN
ejpam-5120	23	9	subgroup	subgroup	NOUN
ejpam-5120	23	10	p	p	PROPN
ejpam-5120	23	11	of	of	ADP
ejpam-5120	23	12	g	g	PROPN
ejpam-5120	23	13	has	have	VERB
ejpam-5120	23	14	a	a	DET
ejpam-5120	23	15	subgroup	subgroup	NOUN
ejpam-5120	23	16	d	d	NOUN
ejpam-5120	23	17	such	such	ADJ
ejpam-5120	23	18	that	that	SCONJ
ejpam-5120	23	19	1	1	NUM
ejpam-5120	23	20	<	<	X
ejpam-5120	23	21	|d|	|d|	PROPN
ejpam-5120	23	22	<	<	X
ejpam-5120	23	23	|p	|p	PROPN
ejpam-5120	24	1	|	|	ADV
ejpam-5120	24	2	and	and	CCONJ
ejpam-5120	24	3	all	all	DET
ejpam-5120	24	4	subgroups	subgroup	NOUN
ejpam-5120	24	5	h	h	VERB
ejpam-5120	24	6	of	of	ADP
ejpam-5120	24	7	p	p	NOUN
ejpam-5120	24	8	with	with	ADP
ejpam-5120	24	9	|h|	|h|	PROPN
ejpam-5120	24	10	=	=	SYM
ejpam-5120	24	11	|d|	|d|	PROPN
ejpam-5120	24	12	are	be	AUX
ejpam-5120	24	13	s	s	NOUN
ejpam-5120	24	14	-	-	ADJ
ejpam-5120	24	15	permutable	permutable	ADJ
ejpam-5120	24	16	(	(	PUNCT
ejpam-5120	24	17	or	or	CCONJ
ejpam-5120	24	18	c	c	NOUN
ejpam-5120	24	19	-	-	ADJ
ejpam-5120	24	20	normal	normal	ADJ
ejpam-5120	24	21	)	)	PUNCT
ejpam-5120	24	22	in	in	ADP
ejpam-5120	24	23	g	g	PROPN
ejpam-5120	24	24	,	,	PUNCT
ejpam-5120	24	25	then	then	ADV
ejpam-5120	24	26	g	g	PROPN
ejpam-5120	24	27	is	be	AUX
ejpam-5120	24	28	solvable	solvable	ADJ
ejpam-5120	24	29	.	.	PUNCT
ejpam-5120	25	1	it	it	PRON
ejpam-5120	25	2	is	be	AUX
ejpam-5120	25	3	remarkable	remarkable	ADJ
ejpam-5120	25	4	to	to	PART
ejpam-5120	25	5	mention	mention	VERB
ejpam-5120	25	6	that	that	SCONJ
ejpam-5120	25	7	the	the	DET
ejpam-5120	25	8	research	research	NOUN
ejpam-5120	25	9	on	on	ADP
ejpam-5120	25	10	c	c	NOUN
ejpam-5120	25	11	-normal	-normal	ADJ
ejpam-5120	25	12	subgroups	subgroup	NOUN
ejpam-5120	25	13	has	have	AUX
ejpam-5120	25	14	formed	form	VERB
ejpam-5120	25	15	a	a	DET
ejpam-5120	25	16	series	series	NOUN
ejpam-5120	25	17	,	,	PUNCT
ejpam-5120	25	18	which	which	PRON
ejpam-5120	25	19	is	be	AUX
ejpam-5120	25	20	similar	similar	ADJ
ejpam-5120	25	21	to	to	ADP
ejpam-5120	25	22	the	the	DET
ejpam-5120	25	23	series	series	NOUN
ejpam-5120	25	24	of	of	ADP
ejpam-5120	25	25	s	s	NOUN
ejpam-5120	25	26	-	-	ADJ
ejpam-5120	25	27	permutable	permutable	ADJ
ejpam-5120	25	28	subgroups	subgroup	NOUN
ejpam-5120	25	29	,	,	PUNCT
ejpam-5120	25	30	however	however	ADV
ejpam-5120	25	31	the	the	DET
ejpam-5120	25	32	two	two	NUM
ejpam-5120	25	33	series	series	NOUN
ejpam-5120	25	34	are	be	AUX
ejpam-5120	25	35	independent	independent	ADJ
ejpam-5120	25	36	of	of	ADP
ejpam-5120	25	37	each	each	DET
ejpam-5120	25	38	other	other	ADJ
ejpam-5120	25	39	.	.	PUNCT
ejpam-5120	26	1	in	in	ADP
ejpam-5120	26	2	2019	2019	NUM
ejpam-5120	26	3	,	,	PUNCT
ejpam-5120	26	4	hijazi	hijazi	PROPN
ejpam-5120	26	5	and	and	CCONJ
ejpam-5120	26	6	charaf	charaf	VERB
ejpam-5120	26	7	[	[	X
ejpam-5120	26	8	6	6	NUM
ejpam-5120	26	9	]	]	PUNCT
ejpam-5120	26	10	continued	continue	VERB
ejpam-5120	26	11	the	the	DET
ejpam-5120	26	12	above	above	ADV
ejpam-5120	26	13	mentioned	mention	VERB
ejpam-5120	26	14	studies	study	NOUN
ejpam-5120	26	15	and	and	CCONJ
ejpam-5120	26	16	proved	prove	VERB
ejpam-5120	26	17	:	:	PUNCT
ejpam-5120	26	18	let	let	VERB
ejpam-5120	26	19	p	p	PRON
ejpam-5120	26	20	be	be	AUX
ejpam-5120	26	21	a	a	DET
ejpam-5120	26	22	sylow	sylow	NOUN
ejpam-5120	26	23	p	p	NOUN
ejpam-5120	26	24	-	-	PUNCT
ejpam-5120	26	25	subgroup	subgroup	NOUN
ejpam-5120	26	26	of	of	ADP
ejpam-5120	26	27	a	a	DET
ejpam-5120	26	28	group	group	NOUN
ejpam-5120	26	29	g	g	NOUN
ejpam-5120	26	30	,	,	PUNCT
ejpam-5120	26	31	where	where	SCONJ
ejpam-5120	26	32	p	p	NOUN
ejpam-5120	26	33	is	be	AUX
ejpam-5120	26	34	an	an	DET
ejpam-5120	26	35	odd	odd	ADJ
ejpam-5120	26	36	prime	prime	NOUN
ejpam-5120	26	37	,	,	PUNCT
ejpam-5120	26	38	and	and	CCONJ
ejpam-5120	26	39	suppose	suppose	VERB
ejpam-5120	26	40	p	p	NOUN
ejpam-5120	26	41	has	have	VERB
ejpam-5120	26	42	a	a	DET
ejpam-5120	26	43	subgroup	subgroup	NOUN
ejpam-5120	26	44	d	d	NOUN
ejpam-5120	26	45	such	such	ADJ
ejpam-5120	26	46	that	that	SCONJ
ejpam-5120	26	47	1	1	NUM
ejpam-5120	26	48	<	<	X
ejpam-5120	26	49	|d|	|d|	PROPN
ejpam-5120	26	50	<	<	X
ejpam-5120	26	51	|p	|p	PROPN
ejpam-5120	27	1	|	|	ADV
ejpam-5120	27	2	and	and	CCONJ
ejpam-5120	27	3	all	all	DET
ejpam-5120	27	4	subgroups	subgroup	NOUN
ejpam-5120	27	5	h	h	VERB
ejpam-5120	27	6	of	of	ADP
ejpam-5120	27	7	p	p	NOUN
ejpam-5120	27	8	with	with	ADP
ejpam-5120	27	9	|h|	|h|	PROPN
ejpam-5120	27	10	=	=	SYM
ejpam-5120	27	11	|d|	|d|	PROPN
ejpam-5120	27	12	are	be	AUX
ejpam-5120	27	13	s	s	NOUN
ejpam-5120	27	14	-	-	NOUN
ejpam-5120	27	15	permutable	permutable	ADJ
ejpam-5120	27	16	in	in	ADP
ejpam-5120	27	17	g.	g.	PROPN
ejpam-5120	27	18	then	then	ADV
ejpam-5120	27	19	g	g	PROPN
ejpam-5120	27	20	′	′	NUM
ejpam-5120	27	21	is	be	AUX
ejpam-5120	27	22	p	p	NOUN
ejpam-5120	27	23	-	-	PUNCT
ejpam-5120	27	24	nilpotent	nilpotent	ADJ
ejpam-5120	27	25	.	.	PUNCT
ejpam-5120	28	1	in	in	ADP
ejpam-5120	28	2	[	[	X
ejpam-5120	28	3	9	9	NUM
ejpam-5120	28	4	]	]	PUNCT
ejpam-5120	28	5	,	,	PUNCT
ejpam-5120	28	6	skiba	skiba	PROPN
ejpam-5120	28	7	generalized	generalize	VERB
ejpam-5120	28	8	both	both	PRON
ejpam-5120	28	9	of	of	ADP
ejpam-5120	28	10	the	the	DET
ejpam-5120	28	11	concepts	concept	NOUN
ejpam-5120	28	12	s	s	NOUN
ejpam-5120	28	13	-	-	PUNCT
ejpam-5120	28	14	permutability	permutability	NOUN
ejpam-5120	28	15	and	and	CCONJ
ejpam-5120	28	16	c	c	NOUN
ejpam-5120	28	17	-	-	PUNCT
ejpam-5120	28	18	normality	normality	NOUN
ejpam-5120	28	19	as	as	SCONJ
ejpam-5120	28	20	follows	follow	VERB
ejpam-5120	28	21	:	:	PUNCT
ejpam-5120	28	22	a	a	DET
ejpam-5120	28	23	subgroup	subgroup	NOUN
ejpam-5120	28	24	h	h	NOUN
ejpam-5120	28	25	of	of	ADP
ejpam-5120	28	26	g	g	PROPN
ejpam-5120	28	27	is	be	AUX
ejpam-5120	28	28	said	say	VERB
ejpam-5120	28	29	to	to	PART
ejpam-5120	28	30	be	be	AUX
ejpam-5120	28	31	weakly	weakly	ADJ
ejpam-5120	28	32	s	s	NOUN
ejpam-5120	28	33	-	-	NOUN
ejpam-5120	28	34	permutable	permutable	ADJ
ejpam-5120	28	35	in	in	ADP
ejpam-5120	28	36	g	g	PROPN
ejpam-5120	28	37	if	if	SCONJ
ejpam-5120	28	38	there	there	PRON
ejpam-5120	28	39	is	be	VERB
ejpam-5120	28	40	a	a	DET
ejpam-5120	28	41	subnormal	subnormal	ADJ
ejpam-5120	28	42	subgroup	subgroup	PROPN
ejpam-5120	28	43	t	t	PROPN
ejpam-5120	28	44	of	of	ADP
ejpam-5120	28	45	g	g	PROPN
ejpam-5120	28	46	such	such	ADJ
ejpam-5120	28	47	that	that	SCONJ
ejpam-5120	28	48	g	g	NOUN
ejpam-5120	28	49	=	=	PUNCT
ejpam-5120	28	50	ht	ht	PROPN
ejpam-5120	28	51	and	and	CCONJ
ejpam-5120	28	52	h	h	PROPN
ejpam-5120	28	53	∩	∩	PROPN
ejpam-5120	28	54	t	t	PROPN
ejpam-5120	28	55	⩽	⩽	PROPN
ejpam-5120	28	56	hsg	hsg	PROPN
ejpam-5120	28	57	,	,	PUNCT
ejpam-5120	28	58	where	where	SCONJ
ejpam-5120	28	59	hsg	hsg	NOUN
ejpam-5120	28	60	is	be	AUX
ejpam-5120	28	61	the	the	DET
ejpam-5120	28	62	subgroup	subgroup	NOUN
ejpam-5120	28	63	of	of	ADP
ejpam-5120	28	64	h	h	PROPN
ejpam-5120	28	65	generated	generate	VERB
ejpam-5120	28	66	by	by	ADP
ejpam-5120	28	67	all	all	DET
ejpam-5120	28	68	those	those	DET
ejpam-5120	28	69	subgroups	subgroup	NOUN
ejpam-5120	28	70	of	of	ADP
ejpam-5120	28	71	h	h	NOUN
ejpam-5120	28	72	which	which	PRON
ejpam-5120	28	73	are	be	AUX
ejpam-5120	28	74	s	s	NOUN
ejpam-5120	28	75	-	-	NOUN
ejpam-5120	28	76	permutable	permutable	ADJ
ejpam-5120	28	77	in	in	ADP
ejpam-5120	28	78	g.	g.	PROPN
ejpam-5120	28	79	our	our	PRON
ejpam-5120	28	80	main	main	ADJ
ejpam-5120	28	81	purpose	purpose	NOUN
ejpam-5120	28	82	here	here	ADV
ejpam-5120	28	83	is	be	AUX
ejpam-5120	28	84	to	to	PART
ejpam-5120	28	85	use	use	VERB
ejpam-5120	28	86	this	this	DET
ejpam-5120	28	87	more	more	ADV
ejpam-5120	28	88	general	general	ADJ
ejpam-5120	28	89	concept	concept	NOUN
ejpam-5120	28	90	,	,	PUNCT
ejpam-5120	28	91	weakly	weakly	ADJ
ejpam-5120	28	92	s	s	NOUN
ejpam-5120	28	93	-	-	NOUN
ejpam-5120	28	94	permutable	permutable	ADJ
ejpam-5120	28	95	,	,	PUNCT
ejpam-5120	28	96	to	to	PART
ejpam-5120	28	97	take	take	VERB
ejpam-5120	28	98	the	the	DET
ejpam-5120	28	99	above	above	ADJ
ejpam-5120	28	100	mentianed	mentiane	VERB
ejpam-5120	28	101	investigations	investigation	NOUN
ejpam-5120	28	102	further	far	ADV
ejpam-5120	28	103	.	.	PUNCT
ejpam-5120	29	1	more	more	ADV
ejpam-5120	29	2	precisely	precisely	ADV
ejpam-5120	29	3	,	,	PUNCT
ejpam-5120	29	4	we	we	PRON
ejpam-5120	29	5	prove	prove	VERB
ejpam-5120	29	6	:	:	PUNCT
ejpam-5120	29	7	main	main	ADJ
ejpam-5120	29	8	theorem	theorem	NOUN
ejpam-5120	29	9	.	.	PUNCT
ejpam-5120	30	1	let	let	VERB
ejpam-5120	30	2	p	p	PRON
ejpam-5120	30	3	be	be	AUX
ejpam-5120	30	4	an	an	DET
ejpam-5120	30	5	odd	odd	ADJ
ejpam-5120	30	6	prime	prime	NOUN
ejpam-5120	30	7	and	and	CCONJ
ejpam-5120	30	8	let	let	VERB
ejpam-5120	30	9	p	p	PRON
ejpam-5120	30	10	be	be	AUX
ejpam-5120	30	11	a	a	DET
ejpam-5120	30	12	sylow	sylow	NOUN
ejpam-5120	30	13	p	p	NOUN
ejpam-5120	30	14	-	-	PUNCT
ejpam-5120	30	15	subgroup	subgroup	NOUN
ejpam-5120	30	16	of	of	ADP
ejpam-5120	30	17	g.	g.	PROPN
ejpam-5120	30	18	suppose	suppose	VERB
ejpam-5120	30	19	that	that	SCONJ
ejpam-5120	30	20	p	p	PROPN
ejpam-5120	30	21	has	have	VERB
ejpam-5120	30	22	a	a	DET
ejpam-5120	30	23	subgroup	subgroup	NOUN
ejpam-5120	30	24	d	d	NOUN
ejpam-5120	30	25	such	such	ADJ
ejpam-5120	30	26	that	that	SCONJ
ejpam-5120	30	27	1	1	NUM
ejpam-5120	30	28	<	<	X
ejpam-5120	30	29	|d|	|d|	PROPN
ejpam-5120	30	30	<	<	X
ejpam-5120	30	31	|p	|p	PROPN
ejpam-5120	31	1	|	|	ADV
ejpam-5120	31	2	and	and	CCONJ
ejpam-5120	31	3	all	all	DET
ejpam-5120	31	4	subgroups	subgroup	NOUN
ejpam-5120	31	5	h	h	VERB
ejpam-5120	31	6	of	of	ADP
ejpam-5120	31	7	p	p	NOUN
ejpam-5120	31	8	with	with	ADP
ejpam-5120	31	9	|h|	|h|	PROPN
ejpam-5120	31	10	=	=	SYM
ejpam-5120	31	11	|d|	|d|	PROPN
ejpam-5120	31	12	are	be	AUX
ejpam-5120	31	13	weakly	weakly	ADJ
ejpam-5120	31	14	s	s	NOUN
ejpam-5120	31	15	-	-	NOUN
ejpam-5120	31	16	permutable	permutable	ADJ
ejpam-5120	31	17	in	in	ADP
ejpam-5120	31	18	g.	g.	PROPN
ejpam-5120	31	19	then	then	ADV
ejpam-5120	31	20	g	g	PROPN
ejpam-5120	31	21	′	′	NUM
ejpam-5120	31	22	is	be	AUX
ejpam-5120	31	23	p	p	NOUN
ejpam-5120	31	24	-	-	PUNCT
ejpam-5120	31	25	nilpotent	nilpotent	ADJ
ejpam-5120	31	26	.	.	PUNCT
ejpam-5120	32	1	2	2	X
ejpam-5120	32	2	.	.	X
ejpam-5120	32	3	preliminaries	preliminary	NOUN
ejpam-5120	32	4	in	in	ADP
ejpam-5120	32	5	this	this	DET
ejpam-5120	32	6	section	section	NOUN
ejpam-5120	32	7	,	,	PUNCT
ejpam-5120	32	8	we	we	PRON
ejpam-5120	32	9	state	state	VERB
ejpam-5120	32	10	some	some	DET
ejpam-5120	32	11	known	know	VERB
ejpam-5120	32	12	results	result	NOUN
ejpam-5120	32	13	from	from	ADP
ejpam-5120	32	14	the	the	DET
ejpam-5120	32	15	literature	literature	NOUN
ejpam-5120	32	16	which	which	PRON
ejpam-5120	32	17	will	will	AUX
ejpam-5120	32	18	be	be	AUX
ejpam-5120	32	19	used	use	VERB
ejpam-5120	32	20	in	in	ADP
ejpam-5120	32	21	proving	prove	VERB
ejpam-5120	32	22	our	our	PRON
ejpam-5120	32	23	results	result	NOUN
ejpam-5120	32	24	.	.	PUNCT
ejpam-5120	33	1	lemma	lemma	PROPN
ejpam-5120	33	2	1	1	NUM
ejpam-5120	33	3	.	.	PUNCT
ejpam-5120	34	1	(	(	PUNCT
ejpam-5120	34	2	see	see	VERB
ejpam-5120	34	3	[	[	X
ejpam-5120	34	4	6	6	NUM
ejpam-5120	34	5	,	,	PUNCT
ejpam-5120	34	6	theorem	theorem	VERB
ejpam-5120	34	7	2	2	NUM
ejpam-5120	34	8	]	]	PUNCT
ejpam-5120	34	9	)	)	PUNCT
ejpam-5120	34	10	let	let	VERB
ejpam-5120	34	11	p	p	PRON
ejpam-5120	34	12	be	be	AUX
ejpam-5120	34	13	a	a	DET
ejpam-5120	34	14	sylow	sylow	NOUN
ejpam-5120	34	15	p	p	NOUN
ejpam-5120	34	16	-	-	PUNCT
ejpam-5120	34	17	subgroup	subgroup	NOUN
ejpam-5120	34	18	of	of	ADP
ejpam-5120	34	19	a	a	DET
ejpam-5120	34	20	group	group	NOUN
ejpam-5120	34	21	g	g	NOUN
ejpam-5120	34	22	,	,	PUNCT
ejpam-5120	34	23	where	where	SCONJ
ejpam-5120	34	24	p	p	NOUN
ejpam-5120	34	25	is	be	AUX
ejpam-5120	34	26	an	an	DET
ejpam-5120	34	27	odd	odd	ADJ
ejpam-5120	34	28	prime	prime	NOUN
ejpam-5120	34	29	.	.	PUNCT
ejpam-5120	35	1	if	if	SCONJ
ejpam-5120	35	2	each	each	DET
ejpam-5120	35	3	subgroup	subgroup	NOUN
ejpam-5120	35	4	of	of	ADP
ejpam-5120	35	5	p	p	NOUN
ejpam-5120	35	6	of	of	ADP
ejpam-5120	35	7	order	order	NOUN
ejpam-5120	35	8	p	p	NOUN
ejpam-5120	35	9	is	be	AUX
ejpam-5120	35	10	s	s	NOUN
ejpam-5120	35	11	-	-	NOUN
ejpam-5120	35	12	permutable	permutable	ADJ
ejpam-5120	35	13	in	in	ADP
ejpam-5120	35	14	g	g	PROPN
ejpam-5120	35	15	,	,	PUNCT
ejpam-5120	35	16	then	then	ADV
ejpam-5120	35	17	g	g	PROPN
ejpam-5120	35	18	′	′	NUM
ejpam-5120	35	19	is	be	AUX
ejpam-5120	35	20	p	p	NOUN
ejpam-5120	35	21	-	-	PUNCT
ejpam-5120	35	22	nilpotent	nilpotent	ADJ
ejpam-5120	35	23	.	.	PUNCT
ejpam-5120	36	1	lemma	lemma	PROPN
ejpam-5120	36	2	2	2	NUM
ejpam-5120	36	3	.	.	PUNCT
ejpam-5120	37	1	(	(	PUNCT
ejpam-5120	37	2	see	see	VERB
ejpam-5120	37	3	[	[	X
ejpam-5120	37	4	9	9	NUM
ejpam-5120	37	5	,	,	PUNCT
ejpam-5120	37	6	theorem	theorem	VERB
ejpam-5120	37	7	1.4	1.4	NUM
ejpam-5120	37	8	]	]	PUNCT
ejpam-5120	37	9	)	)	PUNCT
ejpam-5120	37	10	let	let	VERB
ejpam-5120	37	11	f	f	PRON
ejpam-5120	37	12	be	be	AUX
ejpam-5120	37	13	a	a	DET
ejpam-5120	37	14	saturated	saturated	ADJ
ejpam-5120	37	15	formation	formation	NOUN
ejpam-5120	37	16	containing	contain	VERB
ejpam-5120	37	17	all	all	DET
ejpam-5120	37	18	supersolvable	supersolvable	ADJ
ejpam-5120	37	19	groups	group	NOUN
ejpam-5120	37	20	and	and	CCONJ
ejpam-5120	37	21	g	g	ADP
ejpam-5120	37	22	a	a	DET
ejpam-5120	37	23	group	group	NOUN
ejpam-5120	37	24	with	with	ADP
ejpam-5120	37	25	a	a	DET
ejpam-5120	37	26	normal	normal	ADJ
ejpam-5120	37	27	subgroup	subgroup	NOUN
ejpam-5120	37	28	e	e	NOUN
ejpam-5120	37	29	such	such	ADJ
ejpam-5120	37	30	that	that	SCONJ
ejpam-5120	37	31	g	g	NOUN
ejpam-5120	37	32	/	/	SYM
ejpam-5120	37	33	e	e	PROPN
ejpam-5120	37	34	∈	∈	PROPN
ejpam-5120	37	35	f.	f.	PROPN
ejpam-5120	37	36	suppose	suppose	VERB
ejpam-5120	37	37	that	that	SCONJ
ejpam-5120	37	38	every	every	DET
ejpam-5120	37	39	non	non	ADJ
ejpam-5120	37	40	-	-	ADJ
ejpam-5120	37	41	cyclic	cyclic	ADJ
ejpam-5120	37	42	sylow	sylow	NOUN
ejpam-5120	37	43	subgroup	subgroup	NOUN
ejpam-5120	37	44	p	p	PROPN
ejpam-5120	37	45	of	of	ADP
ejpam-5120	37	46	e	e	PROPN
ejpam-5120	37	47	has	have	VERB
ejpam-5120	37	48	a	a	DET
ejpam-5120	37	49	subgroup	subgroup	NOUN
ejpam-5120	37	50	d	d	NOUN
ejpam-5120	37	51	such	such	ADJ
ejpam-5120	37	52	that	that	SCONJ
ejpam-5120	37	53	1	1	NUM
ejpam-5120	37	54	<	<	X
ejpam-5120	37	55	|d|	|d|	PROPN
ejpam-5120	37	56	<	<	X
ejpam-5120	37	57	|p	|p	PROPN
ejpam-5120	38	1	|	|	ADV
ejpam-5120	38	2	and	and	CCONJ
ejpam-5120	38	3	all	all	DET
ejpam-5120	38	4	subgroups	subgroup	NOUN
ejpam-5120	38	5	h	h	NOUN
ejpam-5120	38	6	of	of	ADP
ejpam-5120	38	7	p	p	NOUN
ejpam-5120	38	8	with	with	ADP
ejpam-5120	38	9	order	order	NOUN
ejpam-5120	38	10	|h|	|h|	X
ejpam-5120	38	11	=	=	SYM
ejpam-5120	38	12	|d|	|d|	PROPN
ejpam-5120	38	13	and	and	CCONJ
ejpam-5120	38	14	with	with	ADP
ejpam-5120	38	15	order	order	NOUN
ejpam-5120	38	16	2|d|	2|d|	NUM
ejpam-5120	38	17	(	(	PUNCT
ejpam-5120	38	18	if	if	SCONJ
ejpam-5120	38	19	p	p	NOUN
ejpam-5120	38	20	is	be	AUX
ejpam-5120	38	21	a	a	DET
ejpam-5120	38	22	non	non	ADJ
ejpam-5120	38	23	-	-	ADJ
ejpam-5120	38	24	abelian	abelian	ADJ
ejpam-5120	38	25	2	2	NUM
ejpam-5120	38	26	-	-	PUNCT
ejpam-5120	38	27	group	group	NOUN
ejpam-5120	38	28	and	and	CCONJ
ejpam-5120	38	29	|p	|p	NOUN
ejpam-5120	38	30	:	:	PUNCT
ejpam-5120	38	31	d|	d|	X
ejpam-5120	38	32	>	>	X
ejpam-5120	38	33	2	2	X
ejpam-5120	38	34	)	)	PUNCT
ejpam-5120	38	35	not	not	PART
ejpam-5120	38	36	having	have	VERB
ejpam-5120	38	37	a	a	DET
ejpam-5120	38	38	supersolvable	supersolvable	ADJ
ejpam-5120	38	39	supplement	supplement	NOUN
ejpam-5120	38	40	in	in	ADP
ejpam-5120	38	41	g	g	PROPN
ejpam-5120	38	42	are	be	AUX
ejpam-5120	38	43	weakly	weakly	ADJ
ejpam-5120	38	44	s	s	NOUN
ejpam-5120	38	45	-	-	NOUN
ejpam-5120	38	46	permutable	permutable	ADJ
ejpam-5120	38	47	in	in	ADP
ejpam-5120	38	48	g.	g.	PROPN
ejpam-5120	38	49	then	then	ADV
ejpam-5120	38	50	g	g	PROPN
ejpam-5120	38	51	∈	∈	PROPN
ejpam-5120	38	52	f	f	PROPN
ejpam-5120	38	53	lemma	lemma	PROPN
ejpam-5120	38	54	3	3	X
ejpam-5120	38	55	.	.	PUNCT
ejpam-5120	39	1	(	(	PUNCT
ejpam-5120	39	2	see	see	VERB
ejpam-5120	39	3	[	[	X
ejpam-5120	39	4	2	2	NUM
ejpam-5120	39	5	,	,	PUNCT
ejpam-5120	39	6	theorem	theorem	VERB
ejpam-5120	39	7	10.6	10.6	NUM
ejpam-5120	39	8	(	(	PUNCT
ejpam-5120	39	9	a	a	NOUN
ejpam-5120	39	10	)	)	PUNCT
ejpam-5120	39	11	,	,	PUNCT
ejpam-5120	39	12	p.	p.	NOUN
ejpam-5120	39	13	36	36	NUM
ejpam-5120	39	14	]	]	PUNCT
ejpam-5120	39	15	)	)	PUNCT
ejpam-5120	39	16	let	let	VERB
ejpam-5120	39	17	g	g	PRON
ejpam-5120	39	18	be	be	AUX
ejpam-5120	39	19	a	a	DET
ejpam-5120	39	20	finite	finite	ADJ
ejpam-5120	39	21	group	group	NOUN
ejpam-5120	39	22	:	:	PUNCT
ejpam-5120	39	23	(	(	PUNCT
ejpam-5120	39	24	i	i	NOUN
ejpam-5120	39	25	)	)	PUNCT
ejpam-5120	39	26	cg(f	cg(f	PUNCT
ejpam-5120	39	27	(	(	PUNCT
ejpam-5120	39	28	g))f	g))f	NOUN
ejpam-5120	39	29	(	(	PUNCT
ejpam-5120	39	30	g)/f	g)/f	X
ejpam-5120	39	31	(	(	PUNCT
ejpam-5120	39	32	g	g	NOUN
ejpam-5120	39	33	)	)	PUNCT
ejpam-5120	39	34	contains	contain	VERB
ejpam-5120	39	35	no	no	DET
ejpam-5120	39	36	non	non	ADJ
ejpam-5120	39	37	-	-	ADJ
ejpam-5120	39	38	trivial	trivial	ADJ
ejpam-5120	39	39	solvable	solvable	ADJ
ejpam-5120	39	40	normal	normal	ADJ
ejpam-5120	39	41	subgroup	subgroup	NOUN
ejpam-5120	39	42	of	of	ADP
ejpam-5120	39	43	g	g	PROPN
ejpam-5120	39	44	/	/	SYM
ejpam-5120	39	45	f	f	PROPN
ejpam-5120	39	46	(	(	PUNCT
ejpam-5120	39	47	g	g	NOUN
ejpam-5120	39	48	)	)	PUNCT
ejpam-5120	39	49	.	.	PUNCT
ejpam-5120	40	1	in	in	ADP
ejpam-5120	40	2	particuler	particuler	NOUN
ejpam-5120	40	3	,	,	PUNCT
ejpam-5120	40	4	cg(f	cg(f	PUNCT
ejpam-5120	40	5	(	(	PUNCT
ejpam-5120	40	6	g	g	NOUN
ejpam-5120	40	7	)	)	PUNCT
ejpam-5120	40	8	)	)	PUNCT
ejpam-5120	40	9	≤	≤	NUM
ejpam-5120	41	1	f	f	X
ejpam-5120	41	2	(	(	PUNCT
ejpam-5120	41	3	g	g	NOUN
ejpam-5120	41	4	)	)	PUNCT
ejpam-5120	41	5	when	when	SCONJ
ejpam-5120	41	6	g	g	PROPN
ejpam-5120	41	7	solvable	solvable	VERB
ejpam-5120	41	8	.	.	PUNCT
ejpam-5120	42	1	a.	a.	NOUN
ejpam-5120	42	2	a.	a.	PROPN
ejpam-5120	42	3	heliel	heliel	PROPN
ejpam-5120	42	4	et	et	PROPN
ejpam-5120	42	5	al	al	PROPN
ejpam-5120	42	6	.	.	PUNCT
ejpam-5120	42	7	/	/	SYM
ejpam-5120	42	8	eur	eur	PROPN
ejpam-5120	42	9	.	.	PUNCT
ejpam-5120	43	1	j.	j.	PROPN
ejpam-5120	43	2	pure	pure	PROPN
ejpam-5120	43	3	appl	appl	PROPN
ejpam-5120	43	4	.	.	PROPN
ejpam-5120	43	5	math	math	PROPN
ejpam-5120	43	6	,	,	PUNCT
ejpam-5120	43	7	17	17	NUM
ejpam-5120	43	8	(	(	PUNCT
ejpam-5120	43	9	2	2	NUM
ejpam-5120	43	10	)	)	PUNCT
ejpam-5120	43	11	(	(	PUNCT
ejpam-5120	43	12	2024	2024	NUM
ejpam-5120	43	13	)	)	PUNCT
ejpam-5120	43	14	,	,	PUNCT
ejpam-5120	43	15	810	810	NUM
ejpam-5120	43	16	-	-	SYM
ejpam-5120	43	17	818	818	NUM
ejpam-5120	43	18	812	812	NUM
ejpam-5120	43	19	(	(	PUNCT
ejpam-5120	43	20	ii	ii	NOUN
ejpam-5120	43	21	)	)	PUNCT
ejpam-5120	43	22	if	if	SCONJ
ejpam-5120	43	23	n	n	PRON
ejpam-5120	43	24	is	be	AUX
ejpam-5120	43	25	a	a	DET
ejpam-5120	43	26	minimal	minimal	ADJ
ejpam-5120	43	27	normal	normal	ADJ
ejpam-5120	43	28	subgroup	subgroup	NOUN
ejpam-5120	43	29	of	of	ADP
ejpam-5120	43	30	g	g	PROPN
ejpam-5120	43	31	,	,	PUNCT
ejpam-5120	43	32	then	then	ADV
ejpam-5120	43	33	f	f	PROPN
ejpam-5120	43	34	(	(	PUNCT
ejpam-5120	43	35	g	g	NOUN
ejpam-5120	43	36	)	)	PUNCT
ejpam-5120	43	37	≤	≤	NOUN
ejpam-5120	43	38	cg(n	cg(n	NOUN
ejpam-5120	43	39	)	)	PUNCT
ejpam-5120	43	40	,	,	PUNCT
ejpam-5120	43	41	furthermore	furthermore	ADV
ejpam-5120	43	42	,	,	PUNCT
ejpam-5120	43	43	if	if	SCONJ
ejpam-5120	43	44	n	n	PRON
ejpam-5120	43	45	is	be	AUX
ejpam-5120	43	46	abelian	abelian	ADJ
ejpam-5120	43	47	,	,	PUNCT
ejpam-5120	43	48	then	then	ADV
ejpam-5120	43	49	n	n	CCONJ
ejpam-5120	43	50	≤	≤	ADJ
ejpam-5120	43	51	z(f	z(f	NOUN
ejpam-5120	43	52	(	(	PUNCT
ejpam-5120	43	53	g	g	NOUN
ejpam-5120	43	54	)	)	PUNCT
ejpam-5120	43	55	.	.	PUNCT
ejpam-5120	44	1	lemma	lemma	PROPN
ejpam-5120	44	2	4	4	NUM
ejpam-5120	44	3	.	.	PUNCT
ejpam-5120	45	1	(	(	PUNCT
ejpam-5120	45	2	see	see	VERB
ejpam-5120	45	3	[	[	X
ejpam-5120	45	4	9	9	NUM
ejpam-5120	45	5	,	,	PUNCT
ejpam-5120	45	6	theorem	theorem	VERB
ejpam-5120	45	7	2.20	2.20	NUM
ejpam-5120	45	8	]	]	PUNCT
ejpam-5120	45	9	)	)	PUNCT
ejpam-5120	45	10	let	let	VERB
ejpam-5120	45	11	a	a	PRON
ejpam-5120	45	12	be	be	AUX
ejpam-5120	45	13	a	a	DET
ejpam-5120	45	14	p	p	NOUN
ejpam-5120	45	15	-	-	PUNCT
ejpam-5120	45	16	group	group	NOUN
ejpam-5120	45	17	of	of	ADP
ejpam-5120	45	18	automorphisms	automorphism	NOUN
ejpam-5120	45	19	of	of	ADP
ejpam-5120	45	20	the	the	DET
ejpam-5120	45	21	p	p	NOUN
ejpam-5120	45	22	-	-	PUNCT
ejpam-5120	45	23	group	group	NOUN
ejpam-5120	45	24	p	p	NOUN
ejpam-5120	45	25	of	of	ADP
ejpam-5120	45	26	odd	odd	ADJ
ejpam-5120	45	27	order	order	NOUN
ejpam-5120	45	28	.	.	PUNCT
ejpam-5120	46	1	assume	assume	VERB
ejpam-5120	46	2	that	that	SCONJ
ejpam-5120	46	3	every	every	DET
ejpam-5120	46	4	subgroup	subgroup	NOUN
ejpam-5120	46	5	of	of	ADP
ejpam-5120	46	6	p	p	NOUN
ejpam-5120	46	7	with	with	ADP
ejpam-5120	46	8	prime	prime	ADJ
ejpam-5120	46	9	order	order	NOUN
ejpam-5120	46	10	is	be	AUX
ejpam-5120	46	11	a	a	DET
ejpam-5120	46	12	-	-	PUNCT
ejpam-5120	46	13	invariant	invariant	ADJ
ejpam-5120	46	14	.	.	PUNCT
ejpam-5120	47	1	then	then	ADV
ejpam-5120	47	2	a	a	PRON
ejpam-5120	47	3	is	be	AUX
ejpam-5120	47	4	cyclic	cyclic	ADJ
ejpam-5120	47	5	.	.	PUNCT
ejpam-5120	48	1	lemma	lemma	PROPN
ejpam-5120	48	2	5	5	NUM
ejpam-5120	48	3	.	.	PUNCT
ejpam-5120	49	1	(	(	PUNCT
ejpam-5120	49	2	see	see	VERB
ejpam-5120	49	3	[	[	X
ejpam-5120	49	4	9	9	NUM
ejpam-5120	49	5	,	,	PUNCT
ejpam-5120	49	6	lemma	lemma	PROPN
ejpam-5120	49	7	2.10	2.10	NUM
ejpam-5120	49	8	]	]	PUNCT
ejpam-5120	49	9	)	)	PUNCT
ejpam-5120	49	10	let	let	VERB
ejpam-5120	49	11	g	g	PRON
ejpam-5120	49	12	be	be	AUX
ejpam-5120	49	13	a	a	DET
ejpam-5120	49	14	group	group	NOUN
ejpam-5120	49	15	and	and	CCONJ
ejpam-5120	49	16	h	h	NOUN
ejpam-5120	49	17	⩽	⩽	PROPN
ejpam-5120	50	1	k	k	PROPN
ejpam-5120	50	2	⩽	⩽	PROPN
ejpam-5120	50	3	g.	g.	PROPN
ejpam-5120	50	4	then	then	ADV
ejpam-5120	50	5	:	:	PUNCT
ejpam-5120	50	6	(	(	PUNCT
ejpam-5120	50	7	i	i	NOUN
ejpam-5120	50	8	)	)	PUNCT
ejpam-5120	50	9	if	if	SCONJ
ejpam-5120	50	10	h	h	NOUN
ejpam-5120	50	11	is	be	AUX
ejpam-5120	50	12	s	s	NOUN
ejpam-5120	50	13	-	-	NOUN
ejpam-5120	50	14	permutable	permutable	ADJ
ejpam-5120	50	15	in	in	ADP
ejpam-5120	50	16	g	g	PROPN
ejpam-5120	50	17	,	,	PUNCT
ejpam-5120	50	18	then	then	ADV
ejpam-5120	50	19	h	h	NOUN
ejpam-5120	50	20	is	be	AUX
ejpam-5120	50	21	weakly	weakly	ADJ
ejpam-5120	50	22	s	s	NOUN
ejpam-5120	50	23	-	-	NOUN
ejpam-5120	50	24	permutable	permutable	ADJ
ejpam-5120	50	25	in	in	ADP
ejpam-5120	50	26	g.	g.	PROPN
ejpam-5120	50	27	(	(	PUNCT
ejpam-5120	50	28	ii	ii	PROPN
ejpam-5120	50	29	)	)	PUNCT
ejpam-5120	50	30	suppose	suppose	VERB
ejpam-5120	50	31	that	that	SCONJ
ejpam-5120	50	32	h	h	NOUN
ejpam-5120	50	33	is	be	AUX
ejpam-5120	50	34	normal	normal	ADJ
ejpam-5120	50	35	in	in	ADP
ejpam-5120	50	36	g.	g.	PROPN
ejpam-5120	50	37	then	then	ADV
ejpam-5120	50	38	k	k	X
ejpam-5120	50	39	/	/	SYM
ejpam-5120	50	40	h	h	NOUN
ejpam-5120	50	41	is	be	AUX
ejpam-5120	50	42	weakly	weakly	ADJ
ejpam-5120	50	43	s	s	NOUN
ejpam-5120	50	44	-	-	NOUN
ejpam-5120	50	45	permutable	permutable	ADJ
ejpam-5120	50	46	in	in	ADP
ejpam-5120	50	47	g	g	PROPN
ejpam-5120	50	48	/	/	SYM
ejpam-5120	50	49	h	h	NOUN
ejpam-5120	50	50	if	if	SCONJ
ejpam-5120	51	1	and	and	CCONJ
ejpam-5120	51	2	only	only	ADV
ejpam-5120	51	3	if	if	SCONJ
ejpam-5120	51	4	k	k	PROPN
ejpam-5120	51	5	is	be	AUX
ejpam-5120	51	6	weakly	weakly	ADJ
ejpam-5120	51	7	s	s	NOUN
ejpam-5120	51	8	-	-	NOUN
ejpam-5120	51	9	permutable	permutable	ADJ
ejpam-5120	51	10	in	in	ADP
ejpam-5120	51	11	g.	g.	PROPN
ejpam-5120	51	12	(	(	PUNCT
ejpam-5120	51	13	iii	iii	X
ejpam-5120	51	14	)	)	PUNCT
ejpam-5120	51	15	if	if	SCONJ
ejpam-5120	51	16	h	h	NOUN
ejpam-5120	51	17	is	be	AUX
ejpam-5120	51	18	weakly	weakly	ADJ
ejpam-5120	51	19	s	s	NOUN
ejpam-5120	51	20	-	-	NOUN
ejpam-5120	51	21	permutable	permutable	ADJ
ejpam-5120	51	22	in	in	ADP
ejpam-5120	51	23	g	g	PROPN
ejpam-5120	51	24	,	,	PUNCT
ejpam-5120	51	25	then	then	ADV
ejpam-5120	51	26	h	h	NOUN
ejpam-5120	51	27	is	be	AUX
ejpam-5120	51	28	weakly	weakly	ADJ
ejpam-5120	51	29	s	s	NOUN
ejpam-5120	51	30	-	-	NOUN
ejpam-5120	51	31	permutable	permutable	ADJ
ejpam-5120	51	32	in	in	ADP
ejpam-5120	51	33	k.	k.	PROPN
ejpam-5120	51	34	(	(	PUNCT
ejpam-5120	51	35	iv	iv	X
ejpam-5120	51	36	)	)	PUNCT
ejpam-5120	51	37	suppose	suppose	VERB
ejpam-5120	51	38	that	that	SCONJ
ejpam-5120	51	39	h	h	NOUN
ejpam-5120	51	40	is	be	AUX
ejpam-5120	51	41	normal	normal	ADJ
ejpam-5120	51	42	in	in	ADP
ejpam-5120	51	43	g.	g.	PROPN
ejpam-5120	51	44	then	then	ADV
ejpam-5120	51	45	the	the	DET
ejpam-5120	51	46	subgroup	subgroup	NOUN
ejpam-5120	51	47	he	he	PRON
ejpam-5120	51	48	/	/	SYM
ejpam-5120	51	49	h	h	PROPN
ejpam-5120	51	50	is	be	AUX
ejpam-5120	51	51	weakly	weakly	ADJ
ejpam-5120	51	52	s	s	NOUN
ejpam-5120	51	53	-	-	NOUN
ejpam-5120	51	54	permutable	permutable	ADJ
ejpam-5120	51	55	in	in	ADP
ejpam-5120	51	56	g	g	PROPN
ejpam-5120	51	57	/	/	SYM
ejpam-5120	51	58	h	h	NOUN
ejpam-5120	51	59	for	for	ADP
ejpam-5120	51	60	every	every	DET
ejpam-5120	51	61	weakly	weakly	ADJ
ejpam-5120	51	62	s	s	NOUN
ejpam-5120	51	63	-	-	ADJ
ejpam-5120	51	64	permutable	permutable	ADJ
ejpam-5120	51	65	subgroup	subgroup	NOUN
ejpam-5120	51	66	e	e	NOUN
ejpam-5120	51	67	in	in	ADP
ejpam-5120	51	68	g	g	PROPN
ejpam-5120	51	69	satisfying	satisfy	VERB
ejpam-5120	51	70	(	(	PUNCT
ejpam-5120	51	71	|h|	|h|	PROPN
ejpam-5120	51	72	,	,	PUNCT
ejpam-5120	51	73	|e|	|e|	PROPN
ejpam-5120	51	74	)	)	PUNCT
ejpam-5120	51	75	=	=	SYM
ejpam-5120	52	1	1	1	X
ejpam-5120	52	2	.	.	PUNCT
ejpam-5120	52	3	(	(	PUNCT
ejpam-5120	52	4	v	v	NOUN
ejpam-5120	52	5	)	)	PUNCT
ejpam-5120	52	6	suppose	suppose	VERB
ejpam-5120	52	7	that	that	SCONJ
ejpam-5120	52	8	h	h	NOUN
ejpam-5120	52	9	is	be	AUX
ejpam-5120	52	10	a	a	DET
ejpam-5120	52	11	p	p	NOUN
ejpam-5120	52	12	-	-	PUNCT
ejpam-5120	52	13	subgroup	subgroup	NOUN
ejpam-5120	52	14	for	for	ADP
ejpam-5120	52	15	some	some	DET
ejpam-5120	52	16	prime	prime	ADJ
ejpam-5120	52	17	p	p	NOUN
ejpam-5120	52	18	and	and	CCONJ
ejpam-5120	52	19	h	h	NOUN
ejpam-5120	52	20	is	be	AUX
ejpam-5120	52	21	not	not	PART
ejpam-5120	52	22	s	s	NOUN
ejpam-5120	52	23	-	-	NOUN
ejpam-5120	52	24	permutable	permutable	ADJ
ejpam-5120	52	25	in	in	ADP
ejpam-5120	52	26	g.	g.	PROPN
ejpam-5120	52	27	assume	assume	VERB
ejpam-5120	52	28	that	that	SCONJ
ejpam-5120	52	29	h	h	NOUN
ejpam-5120	52	30	is	be	AUX
ejpam-5120	52	31	weakly	weakly	ADJ
ejpam-5120	52	32	s	s	NOUN
ejpam-5120	52	33	-	-	NOUN
ejpam-5120	52	34	permutable	permutable	ADJ
ejpam-5120	52	35	in	in	ADP
ejpam-5120	52	36	g.	g.	PROPN
ejpam-5120	52	37	then	then	ADV
ejpam-5120	52	38	g	g	PROPN
ejpam-5120	52	39	has	have	VERB
ejpam-5120	52	40	a	a	DET
ejpam-5120	52	41	normal	normal	ADJ
ejpam-5120	52	42	subgroup	subgroup	NOUN
ejpam-5120	52	43	m	m	VERB
ejpam-5120	52	44	such	such	ADJ
ejpam-5120	52	45	that	that	SCONJ
ejpam-5120	52	46	|g	|g	VERB
ejpam-5120	52	47	:	:	PUNCT
ejpam-5120	52	48	m	m	VERB
ejpam-5120	52	49	|	|	ADV
ejpam-5120	52	50	=	=	SYM
ejpam-5120	52	51	p	p	PROPN
ejpam-5120	52	52	and	and	CCONJ
ejpam-5120	52	53	g	g	NOUN
ejpam-5120	53	1	=	=	NOUN
ejpam-5120	53	2	hm	hm	INTJ
ejpam-5120	53	3	.	.	PUNCT
ejpam-5120	54	1	lemma	lemma	PROPN
ejpam-5120	54	2	6	6	NUM
ejpam-5120	54	3	.	.	PUNCT
ejpam-5120	55	1	(	(	PUNCT
ejpam-5120	55	2	see	see	VERB
ejpam-5120	55	3	[	[	X
ejpam-5120	55	4	11	11	NUM
ejpam-5120	55	5	,	,	PUNCT
ejpam-5120	55	6	lemma	lemma	PROPN
ejpam-5120	55	7	2.3	2.3	NUM
ejpam-5120	55	8	,	,	PUNCT
ejpam-5120	55	9	p.	p.	NOUN
ejpam-5120	55	10	214	214	NUM
ejpam-5120	55	11	]	]	PUNCT
ejpam-5120	55	12	)	)	PUNCT
ejpam-5120	55	13	if	if	SCONJ
ejpam-5120	55	14	g	g	PROPN
ejpam-5120	55	15	is	be	AUX
ejpam-5120	55	16	solvable	solvable	ADJ
ejpam-5120	55	17	and	and	CCONJ
ejpam-5120	55	18	φ(g	φ(g	ADJ
ejpam-5120	55	19	)	)	PUNCT
ejpam-5120	55	20	=	=	SYM
ejpam-5120	55	21	1	1	NUM
ejpam-5120	55	22	,	,	PUNCT
ejpam-5120	55	23	then	then	ADV
ejpam-5120	55	24	fit(g	fit(g	NOUN
ejpam-5120	55	25	)	)	PUNCT
ejpam-5120	55	26	is	be	AUX
ejpam-5120	55	27	the	the	DET
ejpam-5120	55	28	direct	direct	ADJ
ejpam-5120	55	29	product	product	NOUN
ejpam-5120	55	30	of	of	ADP
ejpam-5120	55	31	(	(	PUNCT
ejpam-5120	55	32	abelian	abelian	PROPN
ejpam-5120	55	33	)	)	PUNCT
ejpam-5120	55	34	minimal	minimal	ADJ
ejpam-5120	55	35	normal	normal	ADJ
ejpam-5120	55	36	subgroups	subgroup	NOUN
ejpam-5120	55	37	of	of	ADP
ejpam-5120	55	38	g.	g.	PROPN
ejpam-5120	55	39	lemma	lemma	PROPN
ejpam-5120	55	40	7	7	X
ejpam-5120	55	41	.	.	PUNCT
ejpam-5120	56	1	(	(	PUNCT
ejpam-5120	56	2	see	see	VERB
ejpam-5120	56	3	[	[	X
ejpam-5120	56	4	9	9	NUM
ejpam-5120	56	5	,	,	PUNCT
ejpam-5120	56	6	theorem	theorem	VERB
ejpam-5120	56	7	2.11	2.11	NUM
ejpam-5120	56	8	]	]	PUNCT
ejpam-5120	56	9	)	)	PUNCT
ejpam-5120	56	10	let	let	VERB
ejpam-5120	56	11	n	n	PRON
ejpam-5120	56	12	be	be	AUX
ejpam-5120	56	13	an	an	DET
ejpam-5120	56	14	elementary	elementary	ADJ
ejpam-5120	56	15	abelian	abelian	ADJ
ejpam-5120	56	16	normal	normal	ADJ
ejpam-5120	56	17	subgroup	subgroup	NOUN
ejpam-5120	56	18	of	of	ADP
ejpam-5120	56	19	a	a	DET
ejpam-5120	56	20	group	group	NOUN
ejpam-5120	56	21	g.	g.	PROPN
ejpam-5120	56	22	assume	assume	VERB
ejpam-5120	56	23	that	that	SCONJ
ejpam-5120	56	24	n	n	PRON
ejpam-5120	56	25	has	have	VERB
ejpam-5120	56	26	a	a	DET
ejpam-5120	56	27	subgroup	subgroup	NOUN
ejpam-5120	56	28	d	d	NOUN
ejpam-5120	57	1	such	such	ADJ
ejpam-5120	57	2	that	that	SCONJ
ejpam-5120	57	3	1	1	NUM
ejpam-5120	57	4	<	<	X
ejpam-5120	57	5	|d|	|d|	X
ejpam-5120	57	6	<	<	X
ejpam-5120	57	7	|n	|n	NOUN
ejpam-5120	58	1	|	|	ADV
ejpam-5120	58	2	and	and	CCONJ
ejpam-5120	58	3	every	every	DET
ejpam-5120	58	4	subgroup	subgroup	NOUN
ejpam-5120	58	5	h	h	NOUN
ejpam-5120	58	6	of	of	ADP
ejpam-5120	58	7	n	n	CCONJ
ejpam-5120	58	8	satisfying	satisfy	VERB
ejpam-5120	58	9	|h|	|h|	PROPN
ejpam-5120	58	10	=	=	SYM
ejpam-5120	58	11	|d|	|d|	PROPN
ejpam-5120	58	12	is	be	AUX
ejpam-5120	58	13	weakly	weakly	ADJ
ejpam-5120	58	14	s	s	NOUN
ejpam-5120	58	15	-	-	NOUN
ejpam-5120	58	16	permutable	permutable	ADJ
ejpam-5120	58	17	in	in	ADP
ejpam-5120	58	18	g.	g.	PROPN
ejpam-5120	58	19	then	then	ADV
ejpam-5120	58	20	some	some	DET
ejpam-5120	58	21	maximal	maximal	ADJ
ejpam-5120	58	22	subgroup	subgroup	NOUN
ejpam-5120	58	23	of	of	ADP
ejpam-5120	58	24	n	n	PROPN
ejpam-5120	58	25	is	be	AUX
ejpam-5120	58	26	normal	normal	ADJ
ejpam-5120	58	27	in	in	ADP
ejpam-5120	58	28	g.	g.	PROPN
ejpam-5120	58	29	lemma	lemma	PROPN
ejpam-5120	58	30	8	8	NUM
ejpam-5120	58	31	.	.	PUNCT
ejpam-5120	59	1	(	(	PUNCT
ejpam-5120	59	2	see	see	VERB
ejpam-5120	59	3	[	[	X
ejpam-5120	59	4	3	3	NUM
ejpam-5120	59	5	,	,	PUNCT
ejpam-5120	59	6	theorem	theorem	VERB
ejpam-5120	59	7	3.2	3.2	NUM
ejpam-5120	59	8	,	,	PUNCT
ejpam-5120	59	9	p.	p.	NOUN
ejpam-5120	59	10	228	228	NUM
ejpam-5120	59	11	]	]	PUNCT
ejpam-5120	59	12	)	)	PUNCT
ejpam-5120	59	13	if	if	SCONJ
ejpam-5120	59	14	op′	op′	X
ejpam-5120	59	15	(	(	PUNCT
ejpam-5120	59	16	g	g	NOUN
ejpam-5120	59	17	)	)	PUNCT
ejpam-5120	59	18	=	=	SYM
ejpam-5120	59	19	1	1	NUM
ejpam-5120	59	20	,	,	PUNCT
ejpam-5120	59	21	then	then	ADV
ejpam-5120	59	22	cg(op(g	cg(op(g	NOUN
ejpam-5120	59	23	)	)	PUNCT
ejpam-5120	59	24	)	)	PUNCT
ejpam-5120	60	1	⊆	⊆	NUM
ejpam-5120	60	2	op(g	op(g	NUM
ejpam-5120	60	3	)	)	PUNCT
ejpam-5120	60	4	.	.	PUNCT
ejpam-5120	61	1	3	3	X
ejpam-5120	61	2	.	.	X
ejpam-5120	61	3	results	result	NOUN
ejpam-5120	61	4	we	we	PRON
ejpam-5120	61	5	first	first	ADV
ejpam-5120	61	6	prove	prove	VERB
ejpam-5120	61	7	the	the	DET
ejpam-5120	61	8	following	follow	VERB
ejpam-5120	61	9	theorem	theorem	NOUN
ejpam-5120	61	10	:	:	PUNCT
ejpam-5120	61	11	theorem	theorem	NOUN
ejpam-5120	61	12	1	1	NUM
ejpam-5120	61	13	.	.	PUNCT
ejpam-5120	62	1	let	let	VERB
ejpam-5120	62	2	p	p	PRON
ejpam-5120	62	3	be	be	AUX
ejpam-5120	62	4	a	a	DET
ejpam-5120	62	5	sylow	sylow	NOUN
ejpam-5120	62	6	p	p	NOUN
ejpam-5120	62	7	-	-	PUNCT
ejpam-5120	62	8	subgroup	subgroup	NOUN
ejpam-5120	62	9	of	of	ADP
ejpam-5120	62	10	a	a	DET
ejpam-5120	62	11	group	group	NOUN
ejpam-5120	62	12	g	g	NOUN
ejpam-5120	62	13	,	,	PUNCT
ejpam-5120	62	14	where	where	SCONJ
ejpam-5120	62	15	p	p	NOUN
ejpam-5120	62	16	is	be	AUX
ejpam-5120	62	17	an	an	DET
ejpam-5120	62	18	odd	odd	ADJ
ejpam-5120	62	19	prime	prime	NOUN
ejpam-5120	62	20	and	and	CCONJ
ejpam-5120	62	21	suppose	suppose	VERB
ejpam-5120	62	22	that	that	SCONJ
ejpam-5120	62	23	each	each	DET
ejpam-5120	62	24	subgroup	subgroup	NOUN
ejpam-5120	62	25	of	of	ADP
ejpam-5120	62	26	p	p	NOUN
ejpam-5120	62	27	of	of	ADP
ejpam-5120	62	28	order	order	NOUN
ejpam-5120	62	29	p	p	NOUN
ejpam-5120	62	30	is	be	AUX
ejpam-5120	62	31	weakly	weakly	ADJ
ejpam-5120	62	32	s	s	NOUN
ejpam-5120	62	33	-	-	NOUN
ejpam-5120	62	34	permutable	permutable	ADJ
ejpam-5120	62	35	in	in	ADP
ejpam-5120	62	36	g.	g.	PROPN
ejpam-5120	62	37	then	then	ADV
ejpam-5120	62	38	g	g	PROPN
ejpam-5120	62	39	′	′	NUM
ejpam-5120	62	40	is	be	AUX
ejpam-5120	62	41	p	p	NOUN
ejpam-5120	62	42	-	-	PUNCT
ejpam-5120	62	43	nilpotent	nilpotent	ADJ
ejpam-5120	62	44	.	.	PUNCT
ejpam-5120	63	1	proof	proof	NOUN
ejpam-5120	63	2	.	.	PUNCT
ejpam-5120	64	1	we	we	PRON
ejpam-5120	64	2	prove	prove	VERB
ejpam-5120	64	3	the	the	DET
ejpam-5120	64	4	theorem	theorem	NOUN
ejpam-5120	64	5	by	by	ADP
ejpam-5120	64	6	induction	induction	NOUN
ejpam-5120	64	7	on	on	ADP
ejpam-5120	64	8	|g|	|g|	PROPN
ejpam-5120	64	9	.	.	PUNCT
ejpam-5120	65	1	if	if	SCONJ
ejpam-5120	65	2	each	each	DET
ejpam-5120	65	3	subgroup	subgroup	NOUN
ejpam-5120	65	4	of	of	ADP
ejpam-5120	65	5	p	p	NOUN
ejpam-5120	65	6	of	of	ADP
ejpam-5120	65	7	order	order	NOUN
ejpam-5120	65	8	p	p	NOUN
ejpam-5120	65	9	is	be	AUX
ejpam-5120	65	10	s	s	NOUN
ejpam-5120	65	11	-	-	NOUN
ejpam-5120	65	12	permutable	permutable	ADJ
ejpam-5120	65	13	in	in	ADP
ejpam-5120	65	14	g	g	PROPN
ejpam-5120	65	15	,	,	PUNCT
ejpam-5120	65	16	then	then	ADV
ejpam-5120	65	17	g	g	PROPN
ejpam-5120	65	18	′	′	NUM
ejpam-5120	65	19	is	be	AUX
ejpam-5120	65	20	p	p	NOUN
ejpam-5120	65	21	-	-	PUNCT
ejpam-5120	65	22	nilpotent	nilpotent	ADJ
ejpam-5120	65	23	by	by	ADP
ejpam-5120	65	24	lemma	lemma	PROPN
ejpam-5120	65	25	1	1	NUM
ejpam-5120	65	26	.	.	PUNCT
ejpam-5120	66	1	thus	thus	ADV
ejpam-5120	66	2	we	we	PRON
ejpam-5120	66	3	may	may	AUX
ejpam-5120	66	4	assume	assume	VERB
ejpam-5120	66	5	that	that	SCONJ
ejpam-5120	66	6	there	there	PRON
ejpam-5120	66	7	exists	exist	VERB
ejpam-5120	66	8	a	a	DET
ejpam-5120	66	9	subgroup	subgroup	NOUN
ejpam-5120	66	10	h	h	NOUN
ejpam-5120	66	11	of	of	ADP
ejpam-5120	66	12	p	p	NOUN
ejpam-5120	66	13	of	of	ADP
ejpam-5120	66	14	order	order	NOUN
ejpam-5120	66	15	p	p	NOUN
ejpam-5120	66	16	such	such	ADJ
ejpam-5120	66	17	that	that	DET
ejpam-5120	66	18	h	h	NOUN
ejpam-5120	66	19	is	be	AUX
ejpam-5120	66	20	not	not	PART
ejpam-5120	66	21	s	s	NOUN
ejpam-5120	66	22	-	-	NOUN
ejpam-5120	66	23	permutable	permutable	ADJ
ejpam-5120	66	24	in	in	ADP
ejpam-5120	66	25	g.	g.	PROPN
ejpam-5120	66	26	by	by	ADP
ejpam-5120	66	27	hypothesis	hypothesis	NOUN
ejpam-5120	66	28	,	,	PUNCT
ejpam-5120	66	29	h	h	PROPN
ejpam-5120	66	30	is	be	AUX
ejpam-5120	66	31	weakly	weakly	ADJ
ejpam-5120	66	32	s	s	NOUN
ejpam-5120	66	33	-	-	NOUN
ejpam-5120	66	34	permutable	permutable	ADJ
ejpam-5120	66	35	in	in	ADP
ejpam-5120	66	36	g.	g.	PROPN
ejpam-5120	67	1	so	so	ADV
ejpam-5120	67	2	,	,	PUNCT
ejpam-5120	67	3	there	there	PRON
ejpam-5120	67	4	exists	exist	VERB
ejpam-5120	67	5	subnormal	subnormal	ADJ
ejpam-5120	67	6	subgroup	subgroup	PROPN
ejpam-5120	67	7	k	k	PROPN
ejpam-5120	67	8	of	of	ADP
ejpam-5120	67	9	g	g	PROPN
ejpam-5120	67	10	such	such	ADJ
ejpam-5120	67	11	that	that	SCONJ
ejpam-5120	67	12	g	g	PROPN
ejpam-5120	67	13	=	=	PUNCT
ejpam-5120	67	14	hk	hk	PROPN
ejpam-5120	67	15	and	and	CCONJ
ejpam-5120	67	16	k	k	PROPN
ejpam-5120	67	17	∩h	∩h	PROPN
ejpam-5120	67	18	≤	≤	PROPN
ejpam-5120	67	19	hsg	hsg	PROPN
ejpam-5120	67	20	.	.	PUNCT
ejpam-5120	68	1	however	however	ADV
ejpam-5120	68	2	,	,	PUNCT
ejpam-5120	68	3	hsg	hsg	NOUN
ejpam-5120	68	4	is	be	AUX
ejpam-5120	68	5	the	the	DET
ejpam-5120	68	6	subgroup	subgroup	NOUN
ejpam-5120	68	7	of	of	ADP
ejpam-5120	68	8	h	h	PROPN
ejpam-5120	68	9	generated	generate	VERB
ejpam-5120	68	10	by	by	ADP
ejpam-5120	68	11	all	all	DET
ejpam-5120	68	12	those	those	DET
ejpam-5120	68	13	subgroups	subgroup	NOUN
ejpam-5120	68	14	of	of	ADP
ejpam-5120	68	15	h	h	NOUN
ejpam-5120	68	16	which	which	PRON
ejpam-5120	68	17	are	be	AUX
ejpam-5120	68	18	s	s	NOUN
ejpam-5120	68	19	-	-	NOUN
ejpam-5120	68	20	permutable	permutable	ADJ
ejpam-5120	68	21	in	in	ADP
ejpam-5120	68	22	g	g	NOUN
ejpam-5120	68	23	,	,	PUNCT
ejpam-5120	68	24	and	and	CCONJ
ejpam-5120	68	25	|h|	|h|	PROPN
ejpam-5120	68	26	=	=	SYM
ejpam-5120	68	27	p	p	NOUN
ejpam-5120	68	28	,	,	PUNCT
ejpam-5120	68	29	then	then	ADV
ejpam-5120	68	30	hsg	hsg	VERB
ejpam-5120	68	31	=	=	SYM
ejpam-5120	68	32	1	1	NUM
ejpam-5120	68	33	and	and	CCONJ
ejpam-5120	68	34	so	so	ADV
ejpam-5120	68	35	a.	a.	NOUN
ejpam-5120	68	36	a.	a.	PROPN
ejpam-5120	68	37	heliel	heliel	PROPN
ejpam-5120	68	38	et	et	PROPN
ejpam-5120	69	1	al	al	PROPN
ejpam-5120	69	2	.	.	PUNCT
ejpam-5120	69	3	/	/	SYM
ejpam-5120	69	4	eur	eur	PROPN
ejpam-5120	69	5	.	.	PUNCT
ejpam-5120	70	1	j.	j.	PROPN
ejpam-5120	70	2	pure	pure	PROPN
ejpam-5120	70	3	appl	appl	PROPN
ejpam-5120	70	4	.	.	PROPN
ejpam-5120	70	5	math	math	PROPN
ejpam-5120	70	6	,	,	PUNCT
ejpam-5120	70	7	17	17	NUM
ejpam-5120	70	8	(	(	PUNCT
ejpam-5120	70	9	2	2	NUM
ejpam-5120	70	10	)	)	PUNCT
ejpam-5120	70	11	(	(	PUNCT
ejpam-5120	70	12	2024	2024	NUM
ejpam-5120	70	13	)	)	PUNCT
ejpam-5120	70	14	,	,	PUNCT
ejpam-5120	70	15	810	810	NUM
ejpam-5120	70	16	-	-	SYM
ejpam-5120	70	17	818	818	NUM
ejpam-5120	70	18	813	813	NUM
ejpam-5120	70	19	k	k	PROPN
ejpam-5120	70	20	∩h	∩h	NOUN
ejpam-5120	70	21	=	=	PUNCT
ejpam-5120	71	1	1	1	X
ejpam-5120	71	2	.	.	PUNCT
ejpam-5120	71	3	clearly	clearly	ADV
ejpam-5120	71	4	,	,	PUNCT
ejpam-5120	71	5	k	k	PROPN
ejpam-5120	71	6	◁g	◁g	PROPN
ejpam-5120	71	7	.	.	PUNCT
ejpam-5120	72	1	by	by	ADP
ejpam-5120	72	2	induction	induction	NOUN
ejpam-5120	72	3	on	on	ADP
ejpam-5120	72	4	|g|	|g|	PROPN
ejpam-5120	72	5	,	,	PUNCT
ejpam-5120	72	6	k	k	PROPN
ejpam-5120	72	7	′	′	NOUN
ejpam-5120	72	8	is	be	AUX
ejpam-5120	72	9	p	p	NOUN
ejpam-5120	72	10	-	-	PUNCT
ejpam-5120	72	11	nilpotent	nilpotent	ADJ
ejpam-5120	72	12	.	.	PUNCT
ejpam-5120	73	1	hence	hence	ADV
ejpam-5120	73	2	,	,	PUNCT
ejpam-5120	73	3	if	if	SCONJ
ejpam-5120	73	4	op	op	NOUN
ejpam-5120	73	5	′	′	NUM
ejpam-5120	73	6	(	(	PUNCT
ejpam-5120	73	7	g	g	NOUN
ejpam-5120	73	8	)	)	PUNCT
ejpam-5120	73	9	̸=	̸=	PROPN
ejpam-5120	73	10	1	1	NUM
ejpam-5120	73	11	,	,	PUNCT
ejpam-5120	73	12	the	the	DET
ejpam-5120	73	13	group	group	NOUN
ejpam-5120	73	14	g	g	PROPN
ejpam-5120	73	15	/	/	SYM
ejpam-5120	73	16	op′	op′	PROPN
ejpam-5120	73	17	(	(	PUNCT
ejpam-5120	73	18	g	g	NOUN
ejpam-5120	73	19	)	)	PUNCT
ejpam-5120	73	20	satisfies	satisfy	VERB
ejpam-5120	73	21	the	the	DET
ejpam-5120	73	22	hypothesis	hypothesis	NOUN
ejpam-5120	73	23	of	of	ADP
ejpam-5120	73	24	theorem	theorem	NOUN
ejpam-5120	73	25	and	and	CCONJ
ejpam-5120	73	26	so	so	ADV
ejpam-5120	73	27	g	g	PROPN
ejpam-5120	73	28	′	′	NUM
ejpam-5120	73	29	/(g	/(g	PUNCT
ejpam-5120	74	1	′	′	NUM
ejpam-5120	74	2	∩	∩	ADJ
ejpam-5120	74	3	op′	op′	X
ejpam-5120	74	4	(	(	PUNCT
ejpam-5120	74	5	g	g	NOUN
ejpam-5120	74	6	)	)	PUNCT
ejpam-5120	74	7	)	)	PUNCT
ejpam-5120	74	8	is	be	AUX
ejpam-5120	74	9	pnilpotent	pnilpotent	NOUN
ejpam-5120	74	10	,	,	PUNCT
ejpam-5120	74	11	by	by	ADP
ejpam-5120	74	12	induction	induction	NOUN
ejpam-5120	74	13	on	on	ADP
ejpam-5120	74	14	|g|	|g|	PROPN
ejpam-5120	74	15	,	,	PUNCT
ejpam-5120	74	16	which	which	PRON
ejpam-5120	74	17	implies	imply	VERB
ejpam-5120	74	18	that	that	SCONJ
ejpam-5120	74	19	g	g	PROPN
ejpam-5120	74	20	′	′	NUM
ejpam-5120	74	21	is	be	AUX
ejpam-5120	74	22	p	p	NOUN
ejpam-5120	74	23	-	-	PUNCT
ejpam-5120	74	24	nilpotent	nilpotent	ADJ
ejpam-5120	74	25	.	.	PUNCT
ejpam-5120	75	1	thus	thus	ADV
ejpam-5120	75	2	we	we	PRON
ejpam-5120	75	3	may	may	AUX
ejpam-5120	75	4	assume	assume	VERB
ejpam-5120	75	5	that	that	SCONJ
ejpam-5120	75	6	op′	op′	PROPN
ejpam-5120	75	7	(	(	PUNCT
ejpam-5120	75	8	g	g	NOUN
ejpam-5120	75	9	)	)	PUNCT
ejpam-5120	75	10	=	=	SYM
ejpam-5120	76	1	1	1	X
ejpam-5120	76	2	.	.	PUNCT
ejpam-5120	77	1	now	now	ADV
ejpam-5120	77	2	we	we	PRON
ejpam-5120	77	3	have	have	VERB
ejpam-5120	77	4	that	that	DET
ejpam-5120	77	5	k	k	PROPN
ejpam-5120	77	6	′	′	NUM
ejpam-5120	77	7	chark	chark	PROPN
ejpam-5120	77	8	◁g	◁g	PRON
ejpam-5120	77	9	which	which	PRON
ejpam-5120	77	10	implies	imply	VERB
ejpam-5120	77	11	that	that	SCONJ
ejpam-5120	77	12	k	k	PROPN
ejpam-5120	77	13	′	′	NUM
ejpam-5120	77	14	◁g	◁g	NOUN
ejpam-5120	78	1	and	and	CCONJ
ejpam-5120	78	2	moreover	moreover	ADV
ejpam-5120	78	3	k	k	PROPN
ejpam-5120	78	4	′	′	NOUN
ejpam-5120	78	5	is	be	AUX
ejpam-5120	78	6	p	p	NOUN
ejpam-5120	78	7	-	-	PUNCT
ejpam-5120	78	8	group	group	NOUN
ejpam-5120	78	9	as	as	ADP
ejpam-5120	78	10	op′	op′	X
ejpam-5120	78	11	(	(	PUNCT
ejpam-5120	78	12	g	g	NOUN
ejpam-5120	78	13	)	)	PUNCT
ejpam-5120	78	14	=	=	SYM
ejpam-5120	79	1	1	1	X
ejpam-5120	79	2	.	.	X
ejpam-5120	80	1	thenk	thenk	NOUN
ejpam-5120	80	2	has	have	VERB
ejpam-5120	80	3	a	a	DET
ejpam-5120	80	4	normal	normal	ADJ
ejpam-5120	80	5	sylow	sylow	NOUN
ejpam-5120	80	6	p	p	PROPN
ejpam-5120	80	7	-	-	PUNCT
ejpam-5120	80	8	subgroup	subgroup	NOUN
ejpam-5120	80	9	,	,	PUNCT
ejpam-5120	80	10	say	say	VERB
ejpam-5120	80	11	p1	p1	NOUN
ejpam-5120	80	12	,	,	PUNCT
ejpam-5120	80	13	and	and	CCONJ
ejpam-5120	80	14	so	so	ADV
ejpam-5120	80	15	p1◁g	p1◁g	PROPN
ejpam-5120	80	16	(	(	PUNCT
ejpam-5120	80	17	note	note	VERB
ejpam-5120	80	18	that	that	SCONJ
ejpam-5120	80	19	p1	p1	NOUN
ejpam-5120	80	20	is	be	AUX
ejpam-5120	80	21	characteritstic	characteritstic	ADJ
ejpam-5120	80	22	in	in	ADP
ejpam-5120	80	23	k	k	PROPN
ejpam-5120	80	24	and	and	CCONJ
ejpam-5120	80	25	k◁g	k◁g	PROPN
ejpam-5120	80	26	)	)	PUNCT
ejpam-5120	80	27	.	.	PUNCT
ejpam-5120	81	1	also	also	ADV
ejpam-5120	81	2	,	,	PUNCT
ejpam-5120	81	3	k	k	PROPN
ejpam-5120	81	4	possesses	possess	VERB
ejpam-5120	81	5	a	a	DET
ejpam-5120	81	6	p	p	NOUN
ejpam-5120	81	7	′	′	NUM
ejpam-5120	81	8	-hall	-hall	PROPN
ejpam-5120	81	9	subgroup	subgroup	NOUN
ejpam-5120	81	10	,	,	PUNCT
ejpam-5120	81	11	say	say	VERB
ejpam-5120	81	12	k1	k1	NOUN
ejpam-5120	81	13	.	.	PUNCT
ejpam-5120	82	1	the	the	DET
ejpam-5120	82	2	subgroup	subgroup	NOUN
ejpam-5120	82	3	k1	k1	PROPN
ejpam-5120	82	4	is	be	AUX
ejpam-5120	82	5	abelian	abelian	ADJ
ejpam-5120	82	6	since	since	SCONJ
ejpam-5120	82	7	k	k	PROPN
ejpam-5120	82	8	/	/	SYM
ejpam-5120	82	9	k	k	PROPN
ejpam-5120	82	10	′	′	NOUN
ejpam-5120	82	11	is	be	AUX
ejpam-5120	82	12	abelian	abelian	ADJ
ejpam-5120	82	13	with	with	ADP
ejpam-5120	82	14	k	k	PROPN
ejpam-5120	82	15	′	′	NOUN
ejpam-5120	82	16	=	=	SYM
ejpam-5120	82	17	p1	p1	PROPN
ejpam-5120	82	18	and	and	CCONJ
ejpam-5120	82	19	k	k	NOUN
ejpam-5120	82	20	/	/	SYM
ejpam-5120	82	21	p1	p1	NOUN
ejpam-5120	82	22	∼=	∼=	NOUN
ejpam-5120	82	23	k1	k1	NOUN
ejpam-5120	82	24	.	.	PUNCT
ejpam-5120	83	1	it	it	PRON
ejpam-5120	83	2	is	be	AUX
ejpam-5120	83	3	clear	clear	ADJ
ejpam-5120	83	4	that	that	SCONJ
ejpam-5120	83	5	g	g	PROPN
ejpam-5120	83	6	is	be	AUX
ejpam-5120	83	7	solvable	solvable	ADJ
ejpam-5120	83	8	.	.	PUNCT
ejpam-5120	84	1	if	if	SCONJ
ejpam-5120	84	2	p	p	PRON
ejpam-5120	84	3	◁	◁	PUNCT
ejpam-5120	84	4	g	g	NOUN
ejpam-5120	84	5	,	,	PUNCT
ejpam-5120	84	6	then	then	ADV
ejpam-5120	84	7	g	g	PROPN
ejpam-5120	84	8	/	/	SYM
ejpam-5120	84	9	p	p	NOUN
ejpam-5120	84	10	∼=	∼=	NOUN
ejpam-5120	84	11	k1	k1	NOUN
ejpam-5120	84	12	and	and	CCONJ
ejpam-5120	84	13	therefore	therefore	ADV
ejpam-5120	84	14	,	,	PUNCT
ejpam-5120	84	15	by	by	ADP
ejpam-5120	84	16	lemma	lemma	PROPN
ejpam-5120	84	17	2	2	NUM
ejpam-5120	84	18	,	,	PUNCT
ejpam-5120	84	19	(	(	PUNCT
ejpam-5120	84	20	taking	take	VERB
ejpam-5120	84	21	e	e	NOUN
ejpam-5120	84	22	=	=	SYM
ejpam-5120	84	23	p	p	PROPN
ejpam-5120	84	24	,	,	PUNCT
ejpam-5120	84	25	f	f	PROPN
ejpam-5120	84	26	∗(e	∗(e	PROPN
ejpam-5120	84	27	)	)	PUNCT
ejpam-5120	85	1	=	=	PUNCT
ejpam-5120	85	2	f	f	X
ejpam-5120	85	3	∗(p	∗(p	PROPN
ejpam-5120	85	4	)	)	PUNCT
ejpam-5120	86	1	=	=	SYM
ejpam-5120	86	2	f	f	X
ejpam-5120	86	3	(	(	PUNCT
ejpam-5120	86	4	p	p	NOUN
ejpam-5120	86	5	)	)	PUNCT
ejpam-5120	86	6	since	since	SCONJ
ejpam-5120	86	7	p	p	NOUN
ejpam-5120	86	8	is	be	AUX
ejpam-5120	86	9	solvable	solvable	ADJ
ejpam-5120	86	10	,	,	PUNCT
ejpam-5120	86	11	f	f	PROPN
ejpam-5120	86	12	(	(	PUNCT
ejpam-5120	86	13	p	p	NOUN
ejpam-5120	86	14	)	)	PUNCT
ejpam-5120	86	15	=	=	PUNCT
ejpam-5120	87	1	p	p	NOUN
ejpam-5120	87	2	from	from	ADP
ejpam-5120	87	3	the	the	DET
ejpam-5120	87	4	definition	definition	NOUN
ejpam-5120	87	5	,	,	PUNCT
ejpam-5120	87	6	d	d	NOUN
ejpam-5120	87	7	=	=	PUNCT
ejpam-5120	87	8	h	h	NOUN
ejpam-5120	87	9	with	with	ADP
ejpam-5120	87	10	order	order	NOUN
ejpam-5120	87	11	p	p	X
ejpam-5120	87	12	,	,	PUNCT
ejpam-5120	87	13	1	1	NUM
ejpam-5120	87	14	<	<	X
ejpam-5120	87	15	p	p	X
ejpam-5120	87	16	<	<	X
ejpam-5120	87	17	pn	pn	PROPN
ejpam-5120	87	18	,	,	PUNCT
ejpam-5120	87	19	and	and	CCONJ
ejpam-5120	87	20	all	all	DET
ejpam-5120	87	21	subgroups	subgroup	NOUN
ejpam-5120	87	22	h	h	NOUN
ejpam-5120	87	23	of	of	ADP
ejpam-5120	87	24	p	p	NOUN
ejpam-5120	87	25	are	be	AUX
ejpam-5120	87	26	weakly	weakly	ADJ
ejpam-5120	87	27	s	s	NOUN
ejpam-5120	87	28	-	-	ADJ
ejpam-5120	87	29	permutable	permutable	ADJ
ejpam-5120	87	30	)	)	PUNCT
ejpam-5120	87	31	g	g	NOUN
ejpam-5120	87	32	is	be	AUX
ejpam-5120	87	33	supersolvable	supersolvable	ADJ
ejpam-5120	87	34	,	,	PUNCT
ejpam-5120	87	35	in	in	ADP
ejpam-5120	87	36	particular	particular	ADJ
ejpam-5120	87	37	,	,	PUNCT
ejpam-5120	87	38	g	g	PROPN
ejpam-5120	87	39	′	′	NOUN
ejpam-5120	87	40	is	be	AUX
ejpam-5120	87	41	p	p	NOUN
ejpam-5120	87	42	-	-	PUNCT
ejpam-5120	87	43	nilpotent	nilpotent	ADJ
ejpam-5120	87	44	.	.	PUNCT
ejpam-5120	88	1	so	so	ADV
ejpam-5120	88	2	we	we	PRON
ejpam-5120	88	3	may	may	AUX
ejpam-5120	88	4	assume	assume	VERB
ejpam-5120	88	5	that	that	SCONJ
ejpam-5120	88	6	p	p	NOUN
ejpam-5120	88	7	is	be	AUX
ejpam-5120	88	8	not	not	PART
ejpam-5120	88	9	normal	normal	ADJ
ejpam-5120	88	10	in	in	ADP
ejpam-5120	88	11	g.	g.	PROPN
ejpam-5120	88	12	as	as	ADP
ejpam-5120	88	13	op′	op′	X
ejpam-5120	88	14	(	(	PUNCT
ejpam-5120	88	15	g	g	NOUN
ejpam-5120	88	16	)	)	PUNCT
ejpam-5120	88	17	=	=	SYM
ejpam-5120	88	18	1	1	X
ejpam-5120	88	19	,	,	PUNCT
ejpam-5120	88	20	p1	p1	NOUN
ejpam-5120	88	21	is	be	AUX
ejpam-5120	88	22	characteristic	characteristic	ADJ
ejpam-5120	88	23	in	in	ADP
ejpam-5120	88	24	g	g	PROPN
ejpam-5120	88	25	and	and	CCONJ
ejpam-5120	88	26	p	p	NOUN
ejpam-5120	88	27	⋪	⋪	PROPN
ejpam-5120	88	28	g	g	NOUN
ejpam-5120	88	29	,	,	PUNCT
ejpam-5120	88	30	we	we	PRON
ejpam-5120	88	31	have	have	VERB
ejpam-5120	88	32	f	f	PROPN
ejpam-5120	88	33	(	(	PUNCT
ejpam-5120	88	34	g	g	NOUN
ejpam-5120	88	35	)	)	PUNCT
ejpam-5120	88	36	=	=	SYM
ejpam-5120	88	37	p1	p1	NOUN
ejpam-5120	88	38	and	and	CCONJ
ejpam-5120	88	39	since	since	SCONJ
ejpam-5120	88	40	g	g	PROPN
ejpam-5120	88	41	is	be	AUX
ejpam-5120	88	42	solvable	solvable	ADJ
ejpam-5120	88	43	,	,	PUNCT
ejpam-5120	88	44	we	we	PRON
ejpam-5120	88	45	have	have	AUX
ejpam-5120	88	46	,	,	PUNCT
ejpam-5120	88	47	by	by	ADP
ejpam-5120	88	48	lemma	lemma	PROPN
ejpam-5120	88	49	3	3	NUM
ejpam-5120	88	50	(	(	PUNCT
ejpam-5120	88	51	1	1	NUM
ejpam-5120	88	52	)	)	PUNCT
ejpam-5120	88	53	,	,	PUNCT
ejpam-5120	89	1	that	that	SCONJ
ejpam-5120	89	2	cg(f	cg(f	PUNCT
ejpam-5120	89	3	(	(	PUNCT
ejpam-5120	89	4	g	g	NOUN
ejpam-5120	89	5	)	)	PUNCT
ejpam-5120	89	6	)	)	PUNCT
ejpam-5120	89	7	≤	≤	NUM
ejpam-5120	89	8	f	f	X
ejpam-5120	89	9	(	(	PUNCT
ejpam-5120	89	10	g	g	NOUN
ejpam-5120	89	11	)	)	PUNCT
ejpam-5120	89	12	=	=	SYM
ejpam-5120	89	13	p1	p1	PROPN
ejpam-5120	89	14	.	.	PUNCT
ejpam-5120	90	1	clearly	clearly	ADV
ejpam-5120	90	2	,	,	PUNCT
ejpam-5120	90	3	k1	k1	PROPN
ejpam-5120	90	4	is	be	AUX
ejpam-5120	90	5	a	a	DET
ejpam-5120	90	6	p	p	NOUN
ejpam-5120	90	7	′	′	NUM
ejpam-5120	90	8	-group	-group	NOUN
ejpam-5120	90	9	of	of	ADP
ejpam-5120	90	10	automorophisms	automorophism	NOUN
ejpam-5120	90	11	of	of	ADP
ejpam-5120	90	12	f	f	PROPN
ejpam-5120	90	13	(	(	PUNCT
ejpam-5120	90	14	g	g	NOUN
ejpam-5120	90	15	)	)	PUNCT
ejpam-5120	90	16	=	=	SYM
ejpam-5120	90	17	p1	p1	PROPN
ejpam-5120	90	18	.	.	PUNCT
ejpam-5120	91	1	hence	hence	ADV
ejpam-5120	91	2	,	,	PUNCT
ejpam-5120	91	3	if	if	SCONJ
ejpam-5120	91	4	each	each	DET
ejpam-5120	91	5	subgroup	subgroup	NOUN
ejpam-5120	91	6	of	of	ADP
ejpam-5120	91	7	p1	p1	PROPN
ejpam-5120	91	8	is	be	AUX
ejpam-5120	91	9	s	s	NOUN
ejpam-5120	91	10	-	-	NOUN
ejpam-5120	91	11	permutable	permutable	ADJ
ejpam-5120	91	12	in	in	ADP
ejpam-5120	91	13	k	k	NOUN
ejpam-5120	91	14	,	,	PUNCT
ejpam-5120	91	15	then	then	ADV
ejpam-5120	91	16	k1	k1	PROPN
ejpam-5120	91	17	is	be	AUX
ejpam-5120	91	18	cyclic	cyclic	ADJ
ejpam-5120	91	19	,	,	PUNCT
ejpam-5120	91	20	by	by	ADP
ejpam-5120	91	21	lemma	lemma	PROPN
ejpam-5120	91	22	6	6	NUM
ejpam-5120	91	23	,	,	PUNCT
ejpam-5120	91	24	and	and	CCONJ
ejpam-5120	91	25	so	so	ADV
ejpam-5120	91	26	p	p	PRON
ejpam-5120	91	27	is	be	AUX
ejpam-5120	91	28	the	the	DET
ejpam-5120	91	29	largest	large	ADJ
ejpam-5120	91	30	prime	prime	ADJ
ejpam-5120	91	31	dividing	divide	VERB
ejpam-5120	91	32	|g|	|g|	PROPN
ejpam-5120	91	33	(	(	PUNCT
ejpam-5120	91	34	otherwise	otherwise	ADV
ejpam-5120	91	35	we	we	PRON
ejpam-5120	91	36	have	have	AUX
ejpam-5120	91	37	a	a	DET
ejpam-5120	91	38	contradiction	contradiction	NOUN
ejpam-5120	91	39	)	)	PUNCT
ejpam-5120	91	40	.	.	PUNCT
ejpam-5120	92	1	this	this	PRON
ejpam-5120	92	2	means	mean	VERB
ejpam-5120	92	3	that	that	SCONJ
ejpam-5120	92	4	p	p	VERB
ejpam-5120	92	5	◁	◁	PUNCT
ejpam-5120	92	6	g	g	NOUN
ejpam-5120	92	7	,	,	PUNCT
ejpam-5120	92	8	a	a	DET
ejpam-5120	92	9	contradiction	contradiction	NOUN
ejpam-5120	92	10	.	.	PUNCT
ejpam-5120	93	1	thus	thus	ADV
ejpam-5120	93	2	p1	p1	NOUN
ejpam-5120	93	3	contains	contain	VERB
ejpam-5120	93	4	a	a	DET
ejpam-5120	93	5	subgroup	subgroup	NOUN
ejpam-5120	93	6	l	l	NOUN
ejpam-5120	93	7	of	of	ADP
ejpam-5120	93	8	order	order	NOUN
ejpam-5120	93	9	p	p	NOUN
ejpam-5120	93	10	such	such	ADJ
ejpam-5120	93	11	that	that	SCONJ
ejpam-5120	93	12	l	l	NOUN
ejpam-5120	93	13	is	be	AUX
ejpam-5120	93	14	not	not	PART
ejpam-5120	93	15	s	s	NOUN
ejpam-5120	93	16	-	-	NOUN
ejpam-5120	93	17	permutable	permutable	ADJ
ejpam-5120	93	18	in	in	ADP
ejpam-5120	93	19	k	k	PROPN
ejpam-5120	93	20	and	and	CCONJ
ejpam-5120	93	21	consequently	consequently	ADV
ejpam-5120	93	22	l	l	NOUN
ejpam-5120	93	23	is	be	AUX
ejpam-5120	93	24	not	not	PART
ejpam-5120	93	25	s	s	NOUN
ejpam-5120	93	26	-	-	NOUN
ejpam-5120	93	27	permutable	permutable	ADJ
ejpam-5120	93	28	in	in	ADP
ejpam-5120	93	29	g.	g.	PROPN
ejpam-5120	93	30	by	by	ADP
ejpam-5120	93	31	hypothesis	hypothesis	NOUN
ejpam-5120	93	32	,	,	PUNCT
ejpam-5120	93	33	l	l	PROPN
ejpam-5120	93	34	is	be	AUX
ejpam-5120	93	35	weakly	weakly	ADJ
ejpam-5120	93	36	s	s	NOUN
ejpam-5120	93	37	-	-	NOUN
ejpam-5120	93	38	permutable	permutable	ADJ
ejpam-5120	93	39	in	in	ADP
ejpam-5120	93	40	g.	g.	PROPN
ejpam-5120	93	41	hence	hence	ADV
ejpam-5120	93	42	,	,	PUNCT
ejpam-5120	93	43	there	there	PRON
ejpam-5120	93	44	exists	exist	VERB
ejpam-5120	93	45	a	a	DET
ejpam-5120	93	46	subgroup	subgroup	NOUN
ejpam-5120	93	47	k∗	k∗	NOUN
ejpam-5120	93	48	of	of	ADP
ejpam-5120	93	49	g	g	PROPN
ejpam-5120	94	1	such	such	ADJ
ejpam-5120	94	2	that	that	SCONJ
ejpam-5120	94	3	g	g	NOUN
ejpam-5120	94	4	=	=	PUNCT
ejpam-5120	94	5	lk∗	lk∗	NOUN
ejpam-5120	94	6	,	,	PUNCT
ejpam-5120	94	7	l	l	PROPN
ejpam-5120	94	8	∩	∩	ADJ
ejpam-5120	94	9	k∗	k∗	NOUN
ejpam-5120	94	10	=	=	SYM
ejpam-5120	94	11	1	1	NUM
ejpam-5120	94	12	and	and	CCONJ
ejpam-5120	94	13	k∗	k∗	VERB
ejpam-5120	95	1	◁	◁	X
ejpam-5120	95	2	g.	g.	NOUN
ejpam-5120	95	3	as	as	ADP
ejpam-5120	95	4	above	above	ADP
ejpam-5120	95	5	p2	p2	PROPN
ejpam-5120	95	6	◁	◁	X
ejpam-5120	95	7	g	g	NOUN
ejpam-5120	95	8	,	,	PUNCT
ejpam-5120	95	9	where	where	SCONJ
ejpam-5120	95	10	p2	p2	PROPN
ejpam-5120	95	11	is	be	AUX
ejpam-5120	95	12	a	a	DET
ejpam-5120	95	13	sylow	sylow	NOUN
ejpam-5120	95	14	p	p	NOUN
ejpam-5120	95	15	-	-	PUNCT
ejpam-5120	95	16	subgroup	subgroup	NOUN
ejpam-5120	95	17	of	of	ADP
ejpam-5120	95	18	k∗.	k∗.	PROPN
ejpam-5120	95	19	but	but	CCONJ
ejpam-5120	95	20	p1	p1	PROPN
ejpam-5120	95	21	̸=	̸=	PROPN
ejpam-5120	95	22	p2	p2	PROPN
ejpam-5120	95	23	because	because	SCONJ
ejpam-5120	95	24	l	l	NOUN
ejpam-5120	95	25	≤	≤	PROPN
ejpam-5120	95	26	p1	p1	NOUN
ejpam-5120	95	27	and	and	CCONJ
ejpam-5120	95	28	l	l	NOUN
ejpam-5120	95	29	≨	≨	PROPN
ejpam-5120	95	30	p1	p1	NOUN
ejpam-5120	95	31	,	,	PUNCT
ejpam-5120	95	32	then	then	ADV
ejpam-5120	95	33	p	p	NOUN
ejpam-5120	95	34	=	=	PUNCT
ejpam-5120	96	1	p1p2	p1p2	ADJ
ejpam-5120	96	2	◁	◁	PUNCT
ejpam-5120	96	3	g	g	NOUN
ejpam-5120	96	4	,	,	PUNCT
ejpam-5120	96	5	a	a	DET
ejpam-5120	96	6	contradiction	contradiction	NOUN
ejpam-5120	96	7	completing	complete	VERB
ejpam-5120	96	8	the	the	DET
ejpam-5120	96	9	proof	proof	NOUN
ejpam-5120	96	10	of	of	ADP
ejpam-5120	96	11	the	the	DET
ejpam-5120	96	12	theorem	theorem	NOUN
ejpam-5120	96	13	.	.	PROPN
ejpam-5120	97	1	as	as	ADP
ejpam-5120	97	2	a	a	DET
ejpam-5120	97	3	corollary	corollary	NOUN
ejpam-5120	97	4	of	of	ADP
ejpam-5120	97	5	theorem	theorem	ADJ
ejpam-5120	97	6	1	1	NUM
ejpam-5120	97	7	:	:	PUNCT
ejpam-5120	97	8	corollary	corollary	ADJ
ejpam-5120	97	9	1	1	NUM
ejpam-5120	97	10	.	.	PUNCT
ejpam-5120	98	1	if	if	SCONJ
ejpam-5120	98	2	each	each	DET
ejpam-5120	98	3	subgroup	subgroup	NOUN
ejpam-5120	98	4	of	of	ADP
ejpam-5120	98	5	prime	prime	ADJ
ejpam-5120	98	6	order	order	NOUN
ejpam-5120	98	7	of	of	ADP
ejpam-5120	98	8	g	g	PROPN
ejpam-5120	98	9	is	be	AUX
ejpam-5120	98	10	weakly	weakly	ADJ
ejpam-5120	98	11	s	s	NOUN
ejpam-5120	98	12	-	-	NOUN
ejpam-5120	98	13	permutable	permutable	ADJ
ejpam-5120	98	14	in	in	ADP
ejpam-5120	98	15	g	g	PROPN
ejpam-5120	98	16	,	,	PUNCT
ejpam-5120	98	17	then	then	ADV
ejpam-5120	98	18	g	g	PROPN
ejpam-5120	98	19	is	be	AUX
ejpam-5120	98	20	solvable	solvable	ADJ
ejpam-5120	98	21	,	,	PUNCT
ejpam-5120	98	22	l	l	NOUN
ejpam-5120	98	23	◁	◁	PUNCT
ejpam-5120	99	1	g	g	NOUN
ejpam-5120	99	2	′	′	NOUN
ejpam-5120	100	1	and	and	CCONJ
ejpam-5120	100	2	g	g	PROPN
ejpam-5120	100	3	′	′	NUM
ejpam-5120	100	4	/l	/l	PUNCT
ejpam-5120	100	5	is	be	AUX
ejpam-5120	100	6	nilpotent	nilpotent	ADJ
ejpam-5120	100	7	,	,	PUNCT
ejpam-5120	100	8	where	where	SCONJ
ejpam-5120	100	9	l	l	NOUN
ejpam-5120	100	10	is	be	AUX
ejpam-5120	100	11	a	a	DET
ejpam-5120	100	12	sylow	sylow	NOUN
ejpam-5120	100	13	2	2	NUM
ejpam-5120	100	14	-	-	PUNCT
ejpam-5120	100	15	subgroup	subgroup	NOUN
ejpam-5120	100	16	of	of	ADP
ejpam-5120	100	17	g	g	PROPN
ejpam-5120	100	18	′	′	NUM
ejpam-5120	100	19	.	.	PUNCT
ejpam-5120	101	1	proof	proof	NOUN
ejpam-5120	101	2	.	.	PUNCT
ejpam-5120	102	1	by	by	ADP
ejpam-5120	102	2	theorem	theorem	NOUN
ejpam-5120	102	3	1	1	NUM
ejpam-5120	102	4	,	,	PUNCT
ejpam-5120	102	5	g	g	NOUN
ejpam-5120	102	6	′	′	NUM
ejpam-5120	102	7	is	be	AUX
ejpam-5120	102	8	p	p	NOUN
ejpam-5120	102	9	-	-	PUNCT
ejpam-5120	102	10	nilpotent	nilpotent	ADJ
ejpam-5120	102	11	for	for	ADP
ejpam-5120	102	12	each	each	DET
ejpam-5120	102	13	odd	odd	ADJ
ejpam-5120	102	14	prime	prime	ADJ
ejpam-5120	102	15	p	p	NOUN
ejpam-5120	102	16	dividing	divide	VERB
ejpam-5120	102	17	|g|	|g|	ADJ
ejpam-5120	102	18	.	.	PUNCT
ejpam-5120	103	1	so	so	ADV
ejpam-5120	103	2	g	g	PROPN
ejpam-5120	103	3	′	′	NUM
ejpam-5120	103	4	/l	/l	PUNCT
ejpam-5120	104	1	is	be	AUX
ejpam-5120	104	2	nilpotent	nilpotent	ADJ
ejpam-5120	104	3	,	,	PUNCT
ejpam-5120	104	4	l	l	NOUN
ejpam-5120	104	5	is	be	AUX
ejpam-5120	104	6	a	a	DET
ejpam-5120	104	7	sylow	sylow	NOUN
ejpam-5120	104	8	2	2	NUM
ejpam-5120	104	9	-	-	PUNCT
ejpam-5120	104	10	subgroup	subgroup	NOUN
ejpam-5120	104	11	of	of	ADP
ejpam-5120	104	12	g	g	PROPN
ejpam-5120	104	13	′	′	NOUN
ejpam-5120	105	1	and	and	CCONJ
ejpam-5120	105	2	hence	hence	ADV
ejpam-5120	105	3	g	g	PROPN
ejpam-5120	105	4	is	be	AUX
ejpam-5120	105	5	solvable	solvable	ADJ
ejpam-5120	105	6	.	.	PUNCT
ejpam-5120	106	1	now	now	ADV
ejpam-5120	106	2	,	,	PUNCT
ejpam-5120	106	3	we	we	PRON
ejpam-5120	106	4	are	be	AUX
ejpam-5120	106	5	equipped	equip	VERB
ejpam-5120	106	6	to	to	PART
ejpam-5120	106	7	prove	prove	VERB
ejpam-5120	106	8	the	the	DET
ejpam-5120	106	9	main	main	ADJ
ejpam-5120	106	10	theorem	theorem	NOUN
ejpam-5120	106	11	:	:	PUNCT
ejpam-5120	106	12	proof	proof	NOUN
ejpam-5120	106	13	.	.	PUNCT
ejpam-5120	107	1	assume	assume	VERB
ejpam-5120	107	2	that	that	SCONJ
ejpam-5120	107	3	the	the	DET
ejpam-5120	107	4	result	result	NOUN
ejpam-5120	107	5	is	be	AUX
ejpam-5120	107	6	false	false	ADJ
ejpam-5120	107	7	and	and	CCONJ
ejpam-5120	107	8	let	let	VERB
ejpam-5120	107	9	g	g	PRON
ejpam-5120	107	10	be	be	AUX
ejpam-5120	107	11	a	a	DET
ejpam-5120	107	12	counterexample	counterexample	NOUN
ejpam-5120	107	13	of	of	ADP
ejpam-5120	107	14	minimal	minimal	ADJ
ejpam-5120	107	15	order	order	NOUN
ejpam-5120	107	16	.	.	PUNCT
ejpam-5120	108	1	then	then	ADV
ejpam-5120	108	2	:	:	PUNCT
ejpam-5120	108	3	(	(	PUNCT
ejpam-5120	108	4	1	1	X
ejpam-5120	108	5	)	)	PUNCT
ejpam-5120	108	6	op′	op′	NOUN
ejpam-5120	108	7	(	(	PUNCT
ejpam-5120	108	8	g	g	NOUN
ejpam-5120	108	9	)	)	PUNCT
ejpam-5120	108	10	=	=	SYM
ejpam-5120	109	1	1	1	X
ejpam-5120	109	2	.	.	X
ejpam-5120	109	3	assume	assume	VERB
ejpam-5120	109	4	that	that	SCONJ
ejpam-5120	109	5	op′	op′	PROPN
ejpam-5120	109	6	(	(	PUNCT
ejpam-5120	109	7	g	g	NOUN
ejpam-5120	109	8	)	)	PUNCT
ejpam-5120	109	9	̸=	̸=	PROPN
ejpam-5120	109	10	1	1	NUM
ejpam-5120	109	11	,	,	PUNCT
ejpam-5120	109	12	then	then	ADV
ejpam-5120	109	13	,	,	PUNCT
ejpam-5120	109	14	by	by	ADP
ejpam-5120	109	15	lemma	lemma	PROPN
ejpam-5120	109	16	5	5	NUM
ejpam-5120	109	17	(	(	PUNCT
ejpam-5120	109	18	4	4	NUM
ejpam-5120	109	19	)	)	PUNCT
ejpam-5120	109	20	,	,	PUNCT
ejpam-5120	109	21	g	g	NOUN
ejpam-5120	109	22	/	/	SYM
ejpam-5120	109	23	op′	op′	PROPN
ejpam-5120	109	24	(	(	PUNCT
ejpam-5120	109	25	g	g	NOUN
ejpam-5120	109	26	)	)	PUNCT
ejpam-5120	109	27	satisfies	satisfy	VERB
ejpam-5120	109	28	the	the	DET
ejpam-5120	109	29	hypothesis	hypothesis	NOUN
ejpam-5120	109	30	of	of	ADP
ejpam-5120	109	31	the	the	DET
ejpam-5120	109	32	theorem	theorem	NOUN
ejpam-5120	109	33	.	.	PUNCT
ejpam-5120	110	1	hence	hence	ADV
ejpam-5120	110	2	(	(	PUNCT
ejpam-5120	110	3	g	g	NOUN
ejpam-5120	110	4	/	/	SYM
ejpam-5120	110	5	op′	op′	PROPN
ejpam-5120	110	6	(	(	PUNCT
ejpam-5120	110	7	g	g	NOUN
ejpam-5120	110	8	)	)	PUNCT
ejpam-5120	110	9	)	)	PUNCT
ejpam-5120	111	1	′	′	NUM
ejpam-5120	112	1	=	=	PUNCT
ejpam-5120	112	2	g	g	PROPN
ejpam-5120	112	3	′	′	NUM
ejpam-5120	112	4	op′	op′	PROPN
ejpam-5120	112	5	(	(	PUNCT
ejpam-5120	112	6	g)/op′	g)/op′	PROPN
ejpam-5120	112	7	(	(	PUNCT
ejpam-5120	112	8	g	g	NOUN
ejpam-5120	112	9	)	)	PUNCT
ejpam-5120	112	10	∼=	∼=	NOUN
ejpam-5120	112	11	g	g	NOUN
ejpam-5120	112	12	′	′	NUM
ejpam-5120	112	13	/g	/g	PUNCT
ejpam-5120	113	1	′	′	NUM
ejpam-5120	113	2	∩	∩	ADJ
ejpam-5120	113	3	op′	op′	X
ejpam-5120	113	4	(	(	PUNCT
ejpam-5120	113	5	g	g	NOUN
ejpam-5120	113	6	)	)	PUNCT
ejpam-5120	113	7	is	be	AUX
ejpam-5120	113	8	p	p	NOUN
ejpam-5120	113	9	-	-	PUNCT
ejpam-5120	113	10	nilpotent	nilpotent	ADJ
ejpam-5120	113	11	by	by	ADP
ejpam-5120	113	12	the	the	DET
ejpam-5120	113	13	minimal	minimal	ADJ
ejpam-5120	113	14	choice	choice	NOUN
ejpam-5120	113	15	of	of	ADP
ejpam-5120	113	16	g	g	NOUN
ejpam-5120	113	17	and	and	CCONJ
ejpam-5120	113	18	so	so	ADV
ejpam-5120	113	19	g	g	NOUN
ejpam-5120	113	20	′	′	NUM
ejpam-5120	113	21	is	be	AUX
ejpam-5120	113	22	p	p	NOUN
ejpam-5120	113	23	-	-	PUNCT
ejpam-5120	113	24	nilpotent	nilpotent	ADJ
ejpam-5120	113	25	,	,	PUNCT
ejpam-5120	113	26	a	a	DET
ejpam-5120	113	27	contradiction	contradiction	NOUN
ejpam-5120	113	28	.	.	PUNCT
ejpam-5120	114	1	(	(	PUNCT
ejpam-5120	114	2	2	2	X
ejpam-5120	114	3	)	)	PUNCT
ejpam-5120	114	4	|d|	|d|	PROPN
ejpam-5120	114	5	>	>	PUNCT
ejpam-5120	115	1	p.	p.	PROPN
ejpam-5120	115	2	assume	assume	VERB
ejpam-5120	115	3	that	that	SCONJ
ejpam-5120	115	4	|d|	|d|	PROPN
ejpam-5120	115	5	=	=	PUNCT
ejpam-5120	116	1	p.	p.	NOUN
ejpam-5120	116	2	then	then	ADV
ejpam-5120	116	3	,	,	PUNCT
ejpam-5120	116	4	by	by	ADP
ejpam-5120	116	5	theorem	theorem	NOUN
ejpam-5120	116	6	1	1	NUM
ejpam-5120	116	7	,	,	PUNCT
ejpam-5120	116	8	g	g	NOUN
ejpam-5120	116	9	′	′	NUM
ejpam-5120	116	10	is	be	AUX
ejpam-5120	116	11	p	p	NOUN
ejpam-5120	116	12	-	-	PUNCT
ejpam-5120	116	13	nilpotent	nilpotent	ADJ
ejpam-5120	116	14	,	,	PUNCT
ejpam-5120	116	15	a	a	DET
ejpam-5120	116	16	contradiction	contradiction	NOUN
ejpam-5120	116	17	.	.	PUNCT
ejpam-5120	117	1	(	(	PUNCT
ejpam-5120	117	2	3	3	X
ejpam-5120	117	3	)	)	PUNCT
ejpam-5120	117	4	there	there	PRON
ejpam-5120	117	5	exists	exist	VERB
ejpam-5120	117	6	a	a	DET
ejpam-5120	117	7	subgroup	subgroup	NOUN
ejpam-5120	117	8	h	h	NOUN
ejpam-5120	117	9	of	of	ADP
ejpam-5120	117	10	p	p	NOUN
ejpam-5120	117	11	with	with	ADP
ejpam-5120	117	12	|h|	|h|	PROPN
ejpam-5120	117	13	=	=	PUNCT
ejpam-5120	117	14	|d|	|d|	PROPN
ejpam-5120	117	15	such	such	ADJ
ejpam-5120	117	16	that	that	SCONJ
ejpam-5120	117	17	h	h	NOUN
ejpam-5120	117	18	is	be	AUX
ejpam-5120	117	19	not	not	PART
ejpam-5120	117	20	s	s	NOUN
ejpam-5120	117	21	-	-	NOUN
ejpam-5120	117	22	permutable	permutable	ADJ
ejpam-5120	117	23	in	in	ADP
ejpam-5120	117	24	g.	g.	PROPN
ejpam-5120	117	25	assume	assume	VERB
ejpam-5120	117	26	that	that	SCONJ
ejpam-5120	117	27	all	all	DET
ejpam-5120	117	28	subgroups	subgroup	NOUN
ejpam-5120	117	29	h	h	VERB
ejpam-5120	117	30	of	of	ADP
ejpam-5120	117	31	p	p	NOUN
ejpam-5120	117	32	with	with	ADP
ejpam-5120	117	33	|h|	|h|	PROPN
ejpam-5120	117	34	=	=	SYM
ejpam-5120	117	35	|d|	|d|	PROPN
ejpam-5120	117	36	are	be	AUX
ejpam-5120	117	37	s	s	NOUN
ejpam-5120	117	38	-	-	NOUN
ejpam-5120	117	39	permutable	permutable	ADJ
ejpam-5120	117	40	in	in	ADP
ejpam-5120	117	41	g.	g.	PROPN
ejpam-5120	118	1	then	then	ADV
ejpam-5120	118	2	g	g	PROPN
ejpam-5120	118	3	′	′	NUM
ejpam-5120	118	4	is	be	AUX
ejpam-5120	118	5	p	p	NOUN
ejpam-5120	118	6	-	-	PUNCT
ejpam-5120	118	7	nilpotent	nilpotent	ADJ
ejpam-5120	118	8	,	,	PUNCT
ejpam-5120	118	9	by	by	ADP
ejpam-5120	118	10	lemma	lemma	PROPN
ejpam-5120	118	11	1	1	NUM
ejpam-5120	118	12	,	,	PUNCT
ejpam-5120	118	13	a	a	DET
ejpam-5120	118	14	contradiction	contradiction	NOUN
ejpam-5120	118	15	.	.	PUNCT
ejpam-5120	119	1	a.	a.	NOUN
ejpam-5120	119	2	a.	a.	PROPN
ejpam-5120	119	3	heliel	heliel	PROPN
ejpam-5120	119	4	et	et	PROPN
ejpam-5120	119	5	al	al	PROPN
ejpam-5120	119	6	.	.	PUNCT
ejpam-5120	119	7	/	/	SYM
ejpam-5120	119	8	eur	eur	PROPN
ejpam-5120	119	9	.	.	PUNCT
ejpam-5120	120	1	j.	j.	PROPN
ejpam-5120	120	2	pure	pure	PROPN
ejpam-5120	120	3	appl	appl	PROPN
ejpam-5120	120	4	.	.	PROPN
ejpam-5120	120	5	math	math	PROPN
ejpam-5120	120	6	,	,	PUNCT
ejpam-5120	120	7	17	17	NUM
ejpam-5120	120	8	(	(	PUNCT
ejpam-5120	120	9	2	2	NUM
ejpam-5120	120	10	)	)	PUNCT
ejpam-5120	120	11	(	(	PUNCT
ejpam-5120	120	12	2024	2024	NUM
ejpam-5120	120	13	)	)	PUNCT
ejpam-5120	120	14	,	,	PUNCT
ejpam-5120	120	15	810	810	NUM
ejpam-5120	120	16	-	-	SYM
ejpam-5120	120	17	818	818	NUM
ejpam-5120	120	18	814	814	NUM
ejpam-5120	120	19	now	now	ADV
ejpam-5120	120	20	,	,	PUNCT
ejpam-5120	120	21	we	we	PRON
ejpam-5120	120	22	distinguish	distinguish	VERB
ejpam-5120	120	23	two	two	NUM
ejpam-5120	120	24	cases	case	NOUN
ejpam-5120	120	25	:	:	PUNCT
ejpam-5120	120	26	case	case	NOUN
ejpam-5120	120	27	1	1	NUM
ejpam-5120	120	28	.	.	PUNCT
ejpam-5120	121	1	|p	|p	NOUN
ejpam-5120	121	2	:	:	PUNCT
ejpam-5120	121	3	d|	d|	PROPN
ejpam-5120	121	4	>	>	PUNCT
ejpam-5120	122	1	p.	p.	NOUN
ejpam-5120	122	2	then	then	ADV
ejpam-5120	122	3	,	,	PUNCT
ejpam-5120	122	4	(	(	PUNCT
ejpam-5120	122	5	4	4	X
ejpam-5120	122	6	)	)	PUNCT
ejpam-5120	122	7	g	g	NOUN
ejpam-5120	122	8	is	be	AUX
ejpam-5120	122	9	solvable	solvable	ADJ
ejpam-5120	122	10	and	and	CCONJ
ejpam-5120	122	11	f	f	PROPN
ejpam-5120	122	12	(	(	PUNCT
ejpam-5120	122	13	g	g	NOUN
ejpam-5120	122	14	)	)	PUNCT
ejpam-5120	122	15	is	be	AUX
ejpam-5120	122	16	a	a	DET
ejpam-5120	122	17	maximal	maximal	ADJ
ejpam-5120	122	18	subgroup	subgroup	NOUN
ejpam-5120	122	19	of	of	ADP
ejpam-5120	122	20	p	p	PROPN
ejpam-5120	122	21	.	.	PUNCT
ejpam-5120	123	1	by	by	ADP
ejpam-5120	123	2	(	(	PUNCT
ejpam-5120	123	3	3	3	NUM
ejpam-5120	123	4	)	)	PUNCT
ejpam-5120	123	5	,	,	PUNCT
ejpam-5120	123	6	there	there	PRON
ejpam-5120	123	7	exists	exist	VERB
ejpam-5120	123	8	a	a	DET
ejpam-5120	123	9	subgroup	subgroup	NOUN
ejpam-5120	123	10	h	h	NOUN
ejpam-5120	123	11	of	of	ADP
ejpam-5120	123	12	p	p	NOUN
ejpam-5120	123	13	with	with	ADP
ejpam-5120	123	14	|h|	|h|	PROPN
ejpam-5120	123	15	=	=	PUNCT
ejpam-5120	123	16	|d|	|d|	PROPN
ejpam-5120	123	17	such	such	ADJ
ejpam-5120	123	18	that	that	SCONJ
ejpam-5120	123	19	h	h	NOUN
ejpam-5120	123	20	is	be	AUX
ejpam-5120	123	21	not	not	PART
ejpam-5120	123	22	s	s	NOUN
ejpam-5120	123	23	-	-	NOUN
ejpam-5120	123	24	permutable	permutable	ADJ
ejpam-5120	123	25	in	in	ADP
ejpam-5120	123	26	g.	g.	PROPN
ejpam-5120	123	27	then	then	ADV
ejpam-5120	123	28	,	,	PUNCT
ejpam-5120	123	29	by	by	ADP
ejpam-5120	123	30	the	the	DET
ejpam-5120	123	31	hypothesis	hypothesis	NOUN
ejpam-5120	123	32	,	,	PUNCT
ejpam-5120	123	33	h	h	PROPN
ejpam-5120	123	34	is	be	AUX
ejpam-5120	123	35	weakly	weakly	ADJ
ejpam-5120	123	36	s	s	NOUN
ejpam-5120	123	37	-	-	NOUN
ejpam-5120	123	38	permutable	permutable	ADJ
ejpam-5120	123	39	in	in	ADP
ejpam-5120	123	40	g	g	PROPN
ejpam-5120	123	41	,	,	PUNCT
ejpam-5120	123	42	that	that	ADV
ejpam-5120	123	43	is	is	ADV
ejpam-5120	123	44	,	,	PUNCT
ejpam-5120	123	45	there	there	PRON
ejpam-5120	123	46	exists	exist	VERB
ejpam-5120	123	47	a	a	DET
ejpam-5120	123	48	subnormal	subnormal	ADJ
ejpam-5120	123	49	subgroup	subgroup	PROPN
ejpam-5120	123	50	t	t	PROPN
ejpam-5120	123	51	of	of	ADP
ejpam-5120	123	52	g	g	PROPN
ejpam-5120	123	53	such	such	ADJ
ejpam-5120	123	54	that	that	SCONJ
ejpam-5120	123	55	g	g	NOUN
ejpam-5120	123	56	=	=	PUNCT
ejpam-5120	123	57	ht	ht	PROPN
ejpam-5120	123	58	and	and	CCONJ
ejpam-5120	123	59	t	t	PROPN
ejpam-5120	123	60	∩h	∩h	PROPN
ejpam-5120	123	61	≤	≤	PROPN
ejpam-5120	123	62	hsg	hsg	PROPN
ejpam-5120	123	63	.	.	PUNCT
ejpam-5120	124	1	since	since	SCONJ
ejpam-5120	124	2	h	h	NOUN
ejpam-5120	124	3	is	be	AUX
ejpam-5120	124	4	not	not	PART
ejpam-5120	124	5	s	s	NOUN
ejpam-5120	124	6	-	-	NOUN
ejpam-5120	124	7	permutable	permutable	ADJ
ejpam-5120	124	8	in	in	ADP
ejpam-5120	124	9	g	g	PROPN
ejpam-5120	124	10	,	,	PUNCT
ejpam-5120	124	11	we	we	PRON
ejpam-5120	124	12	have	have	VERB
ejpam-5120	124	13	that	that	DET
ejpam-5120	124	14	hsg	hsg	VERB
ejpam-5120	124	15	̸=	̸=	PROPN
ejpam-5120	124	16	h	h	NOUN
ejpam-5120	125	1	and	and	CCONJ
ejpam-5120	125	2	so	so	ADV
ejpam-5120	125	3	t	t	PROPN
ejpam-5120	125	4	̸=	̸=	PROPN
ejpam-5120	125	5	g.	g.	PROPN
ejpam-5120	125	6	then	then	ADV
ejpam-5120	125	7	g	g	PROPN
ejpam-5120	125	8	has	have	VERB
ejpam-5120	125	9	a	a	DET
ejpam-5120	125	10	normal	normal	ADJ
ejpam-5120	125	11	subgroup	subgroup	NOUN
ejpam-5120	125	12	m	m	VERB
ejpam-5120	125	13	such	such	ADJ
ejpam-5120	125	14	that	that	SCONJ
ejpam-5120	125	15	t	t	PROPN
ejpam-5120	125	16	≤	≤	X
ejpam-5120	125	17	m	m	PROPN
ejpam-5120	125	18	and	and	CCONJ
ejpam-5120	125	19	|g	|g	NOUN
ejpam-5120	125	20	/	/	SYM
ejpam-5120	125	21	m	m	PROPN
ejpam-5120	125	22	|	|	NOUN
ejpam-5120	125	23	=	=	SYM
ejpam-5120	126	1	p.	p.	NOUN
ejpam-5120	126	2	let	let	VERB
ejpam-5120	126	3	a	a	PRON
ejpam-5120	126	4	be	be	AUX
ejpam-5120	126	5	a	a	DET
ejpam-5120	126	6	sylow	sylow	NOUN
ejpam-5120	126	7	p	p	NOUN
ejpam-5120	126	8	-	-	PUNCT
ejpam-5120	126	9	subgroup	subgroup	NOUN
ejpam-5120	126	10	of	of	ADP
ejpam-5120	126	11	m	m	PROPN
ejpam-5120	126	12	.	.	PUNCT
ejpam-5120	127	1	since	since	SCONJ
ejpam-5120	127	2	|p	|p	NOUN
ejpam-5120	127	3	:	:	PUNCT
ejpam-5120	127	4	d|	d|	X
ejpam-5120	127	5	>	>	X
ejpam-5120	128	1	p	p	X
ejpam-5120	128	2	,	,	PUNCT
ejpam-5120	128	3	we	we	PRON
ejpam-5120	128	4	have	have	VERB
ejpam-5120	128	5	that	that	SCONJ
ejpam-5120	128	6	a	a	PRON
ejpam-5120	128	7	has	have	VERB
ejpam-5120	128	8	a	a	DET
ejpam-5120	128	9	subgroup	subgroup	NOUN
ejpam-5120	128	10	d	d	NOUN
ejpam-5120	128	11	with	with	ADP
ejpam-5120	128	12	1	1	NUM
ejpam-5120	128	13	<	<	X
ejpam-5120	128	14	d	d	X
ejpam-5120	128	15	<	<	X
ejpam-5120	128	16	a.	a.	NOUN
ejpam-5120	128	17	then	then	ADV
ejpam-5120	128	18	,	,	PUNCT
ejpam-5120	128	19	by	by	ADP
ejpam-5120	128	20	the	the	DET
ejpam-5120	128	21	hypothesis	hypothesis	NOUN
ejpam-5120	128	22	,	,	PUNCT
ejpam-5120	128	23	all	all	DET
ejpam-5120	128	24	subgroups	subgroup	NOUN
ejpam-5120	128	25	l	l	NOUN
ejpam-5120	128	26	of	of	ADP
ejpam-5120	128	27	a	a	PRON
ejpam-5120	128	28	with	with	ADP
ejpam-5120	128	29	|l|	|l|	NOUN
ejpam-5120	128	30	=	=	SYM
ejpam-5120	128	31	|d|	|d|	PROPN
ejpam-5120	128	32	are	be	AUX
ejpam-5120	128	33	weakly	weakly	ADJ
ejpam-5120	128	34	s	s	NOUN
ejpam-5120	128	35	-	-	NOUN
ejpam-5120	128	36	permutable	permutable	ADJ
ejpam-5120	128	37	in	in	ADP
ejpam-5120	128	38	g	g	PROPN
ejpam-5120	128	39	and	and	CCONJ
ejpam-5120	128	40	so	so	ADV
ejpam-5120	128	41	all	all	DET
ejpam-5120	128	42	subgroups	subgroup	NOUN
ejpam-5120	128	43	l	l	ADV
ejpam-5120	128	44	of	of	ADP
ejpam-5120	128	45	a	a	PRON
ejpam-5120	128	46	with	with	ADP
ejpam-5120	128	47	|l|	|l|	NOUN
ejpam-5120	128	48	=	=	SYM
ejpam-5120	128	49	|d|	|d|	PROPN
ejpam-5120	128	50	are	be	AUX
ejpam-5120	128	51	weakly	weakly	ADJ
ejpam-5120	128	52	s	s	NOUN
ejpam-5120	128	53	-	-	NOUN
ejpam-5120	128	54	permutable	permutable	ADJ
ejpam-5120	128	55	in	in	ADP
ejpam-5120	128	56	m	m	PROPN
ejpam-5120	128	57	by	by	ADP
ejpam-5120	128	58	lemma	lemma	PROPN
ejpam-5120	128	59	5	5	NUM
ejpam-5120	128	60	(	(	PUNCT
ejpam-5120	128	61	iii	iii	NOUN
ejpam-5120	128	62	)	)	PUNCT
ejpam-5120	128	63	.	.	PUNCT
ejpam-5120	129	1	then	then	ADV
ejpam-5120	129	2	m	m	VERB
ejpam-5120	129	3	′	′	ADJ
ejpam-5120	129	4	is	be	AUX
ejpam-5120	129	5	p	p	NOUN
ejpam-5120	129	6	-	-	PUNCT
ejpam-5120	129	7	nilpotent	nilpotent	ADJ
ejpam-5120	129	8	by	by	ADP
ejpam-5120	129	9	choice	choice	NOUN
ejpam-5120	129	10	of	of	ADP
ejpam-5120	129	11	g.	g.	PROPN
ejpam-5120	129	12	hence	hence	ADV
ejpam-5120	129	13	,	,	PUNCT
ejpam-5120	129	14	m	m	VERB
ejpam-5120	129	15	′	′	ADJ
ejpam-5120	129	16	≤	≤	NUM
ejpam-5120	129	17	a	a	DET
ejpam-5120	129	18	as	as	ADV
ejpam-5120	129	19	op′	op′	X
ejpam-5120	129	20	(	(	PUNCT
ejpam-5120	129	21	g	g	NOUN
ejpam-5120	129	22	)	)	PUNCT
ejpam-5120	129	23	=	=	SYM
ejpam-5120	129	24	1	1	NUM
ejpam-5120	129	25	by	by	ADP
ejpam-5120	129	26	(	(	PUNCT
ejpam-5120	129	27	1	1	NUM
ejpam-5120	129	28	)	)	PUNCT
ejpam-5120	129	29	,	,	PUNCT
ejpam-5120	129	30	and	and	CCONJ
ejpam-5120	129	31	so	so	ADV
ejpam-5120	129	32	a	a	PRON
ejpam-5120	129	33	is	be	AUX
ejpam-5120	129	34	characteristic	characteristic	ADJ
ejpam-5120	129	35	in	in	ADP
ejpam-5120	129	36	m	m	PROPN
ejpam-5120	129	37	and	and	CCONJ
ejpam-5120	129	38	since	since	SCONJ
ejpam-5120	129	39	m	m	PROPN
ejpam-5120	129	40	is	be	AUX
ejpam-5120	129	41	normal	normal	ADJ
ejpam-5120	129	42	in	in	ADP
ejpam-5120	129	43	g	g	PROPN
ejpam-5120	129	44	,	,	PUNCT
ejpam-5120	129	45	we	we	PRON
ejpam-5120	129	46	have	have	VERB
ejpam-5120	129	47	a	a	DET
ejpam-5120	129	48	◁	◁	X
ejpam-5120	129	49	g.	g.	NOUN
ejpam-5120	129	50	since	since	SCONJ
ejpam-5120	129	51	m	m	PROPN
ejpam-5120	129	52	/	/	SYM
ejpam-5120	129	53	a	a	PRON
ejpam-5120	129	54	is	be	AUX
ejpam-5120	129	55	abelian	abelian	ADJ
ejpam-5120	129	56	and	and	CCONJ
ejpam-5120	129	57	|g	|g	NOUN
ejpam-5120	129	58	/	/	SYM
ejpam-5120	129	59	m	m	VERB
ejpam-5120	130	1	|	|	NOUN
ejpam-5120	130	2	=	=	SYM
ejpam-5120	130	3	p	p	NOUN
ejpam-5120	130	4	,	,	PUNCT
ejpam-5120	130	5	we	we	PRON
ejpam-5120	130	6	have	have	VERB
ejpam-5120	130	7	that	that	PRON
ejpam-5120	130	8	g	g	PROPN
ejpam-5120	130	9	is	be	AUX
ejpam-5120	130	10	solvable	solvable	ADJ
ejpam-5120	130	11	.	.	PUNCT
ejpam-5120	131	1	clearly	clearly	ADV
ejpam-5120	131	2	,	,	PUNCT
ejpam-5120	131	3	as	as	SCONJ
ejpam-5120	131	4	a	a	PRON
ejpam-5120	131	5	is	be	AUX
ejpam-5120	131	6	a	a	DET
ejpam-5120	131	7	normal	normal	ADJ
ejpam-5120	131	8	nilpotent	nilpotent	ADJ
ejpam-5120	131	9	subgroup	subgroup	NOUN
ejpam-5120	131	10	of	of	ADP
ejpam-5120	131	11	g	g	PROPN
ejpam-5120	131	12	,	,	PUNCT
ejpam-5120	131	13	a	a	DET
ejpam-5120	131	14	≤	≤	ADJ
ejpam-5120	131	15	f	f	X
ejpam-5120	131	16	(	(	PUNCT
ejpam-5120	131	17	g	g	NOUN
ejpam-5120	131	18	)	)	PUNCT
ejpam-5120	131	19	.	.	PUNCT
ejpam-5120	132	1	then	then	ADV
ejpam-5120	132	2	,	,	PUNCT
ejpam-5120	132	3	by	by	ADP
ejpam-5120	132	4	(	(	PUNCT
ejpam-5120	132	5	1	1	NUM
ejpam-5120	132	6	)	)	PUNCT
ejpam-5120	132	7	,	,	PUNCT
ejpam-5120	132	8	f	f	PROPN
ejpam-5120	132	9	(	(	PUNCT
ejpam-5120	132	10	g	g	NOUN
ejpam-5120	132	11	)	)	PUNCT
ejpam-5120	132	12	is	be	AUX
ejpam-5120	132	13	a	a	DET
ejpam-5120	132	14	p	p	NOUN
ejpam-5120	132	15	-	-	PUNCT
ejpam-5120	132	16	group	group	NOUN
ejpam-5120	132	17	.	.	PUNCT
ejpam-5120	133	1	since	since	SCONJ
ejpam-5120	133	2	g	g	PROPN
ejpam-5120	133	3	is	be	AUX
ejpam-5120	133	4	solvable	solvable	ADJ
ejpam-5120	133	5	,	,	PUNCT
ejpam-5120	133	6	we	we	PRON
ejpam-5120	133	7	have	have	VERB
ejpam-5120	133	8	that	that	PRON
ejpam-5120	133	9	g	g	PROPN
ejpam-5120	133	10	has	have	VERB
ejpam-5120	133	11	a	a	DET
ejpam-5120	133	12	p	p	NOUN
ejpam-5120	133	13	′	′	NUM
ejpam-5120	133	14	-hall	-hall	PROPN
ejpam-5120	133	15	subgroup	subgroup	PROPN
ejpam-5120	133	16	k	k	PROPN
ejpam-5120	134	1	and	and	CCONJ
ejpam-5120	134	2	so	so	ADV
ejpam-5120	134	3	k	k	PROPN
ejpam-5120	134	4	≤	≤	ADV
ejpam-5120	134	5	m	m	VERB
ejpam-5120	134	6	(	(	PUNCT
ejpam-5120	134	7	as	as	ADP
ejpam-5120	134	8	g	g	PROPN
ejpam-5120	134	9	=	=	SYM
ejpam-5120	134	10	ht	ht	PROPN
ejpam-5120	134	11	and	and	CCONJ
ejpam-5120	134	12	t	t	X
ejpam-5120	134	13	≤	≤	NUM
ejpam-5120	134	14	m	m	PROPN
ejpam-5120	134	15	)	)	PUNCT
ejpam-5120	134	16	.	.	PUNCT
ejpam-5120	135	1	then	then	ADV
ejpam-5120	135	2	k	k	PROPN
ejpam-5120	135	3	is	be	AUX
ejpam-5120	135	4	abelian	abelian	ADJ
ejpam-5120	135	5	.	.	PUNCT
ejpam-5120	136	1	hence	hence	ADV
ejpam-5120	136	2	if	if	SCONJ
ejpam-5120	136	3	p	p	PROPN
ejpam-5120	136	4	=	=	X
ejpam-5120	136	5	f	f	X
ejpam-5120	136	6	(	(	PUNCT
ejpam-5120	136	7	g	g	NOUN
ejpam-5120	136	8	)	)	PUNCT
ejpam-5120	136	9	,	,	PUNCT
ejpam-5120	136	10	g	g	NOUN
ejpam-5120	136	11	/	/	SYM
ejpam-5120	136	12	p	p	NOUN
ejpam-5120	136	13	∼=	∼=	PROPN
ejpam-5120	136	14	k	k	NOUN
ejpam-5120	137	1	and	and	CCONJ
ejpam-5120	137	2	so	so	ADV
ejpam-5120	137	3	p	p	PRON
ejpam-5120	137	4	≥	≥	NOUN
ejpam-5120	137	5	g	g	NOUN
ejpam-5120	137	6	′	′	NUM
ejpam-5120	137	7	,	,	PUNCT
ejpam-5120	137	8	that	that	ADV
ejpam-5120	137	9	is	is	ADV
ejpam-5120	137	10	,	,	PUNCT
ejpam-5120	137	11	g	g	PROPN
ejpam-5120	137	12	′	′	NUM
ejpam-5120	137	13	is	be	AUX
ejpam-5120	137	14	p	p	NOUN
ejpam-5120	137	15	-	-	PUNCT
ejpam-5120	137	16	nilpotent	nilpotent	ADJ
ejpam-5120	137	17	,	,	PUNCT
ejpam-5120	137	18	contradiction	contradiction	NOUN
ejpam-5120	137	19	.	.	PUNCT
ejpam-5120	138	1	then	then	ADV
ejpam-5120	138	2	a	a	PRON
ejpam-5120	138	3	=	=	SYM
ejpam-5120	138	4	f	f	X
ejpam-5120	138	5	(	(	PUNCT
ejpam-5120	138	6	g	g	NOUN
ejpam-5120	138	7	)	)	PUNCT
ejpam-5120	138	8	.	.	PUNCT
ejpam-5120	139	1	(	(	PUNCT
ejpam-5120	139	2	5	5	X
ejpam-5120	139	3	)	)	PUNCT
ejpam-5120	139	4	φ(g	φ(g	ADJ
ejpam-5120	139	5	)	)	PUNCT
ejpam-5120	139	6	̸=	̸=	PROPN
ejpam-5120	139	7	1	1	NUM
ejpam-5120	139	8	.	.	PUNCT
ejpam-5120	139	9	assume	assume	VERB
ejpam-5120	139	10	that	that	SCONJ
ejpam-5120	139	11	φ(g	φ(g	NOUN
ejpam-5120	139	12	)	)	PUNCT
ejpam-5120	139	13	=	=	SYM
ejpam-5120	140	1	1	1	X
ejpam-5120	140	2	.	.	PUNCT
ejpam-5120	140	3	since	since	SCONJ
ejpam-5120	140	4	g	g	PROPN
ejpam-5120	140	5	is	be	AUX
ejpam-5120	140	6	solvable	solvable	ADJ
ejpam-5120	140	7	,	,	PUNCT
ejpam-5120	140	8	from	from	ADP
ejpam-5120	140	9	(	(	PUNCT
ejpam-5120	140	10	4	4	NUM
ejpam-5120	140	11	)	)	PUNCT
ejpam-5120	140	12	,	,	PUNCT
ejpam-5120	140	13	it	it	PRON
ejpam-5120	140	14	follows	follow	VERB
ejpam-5120	140	15	,	,	PUNCT
ejpam-5120	140	16	by	by	ADP
ejpam-5120	140	17	lemma	lemma	PROPN
ejpam-5120	140	18	6	6	NUM
ejpam-5120	140	19	,	,	PUNCT
ejpam-5120	140	20	that	that	PRON
ejpam-5120	140	21	a	a	DET
ejpam-5120	140	22	=	=	SYM
ejpam-5120	140	23	f	f	X
ejpam-5120	140	24	(	(	PUNCT
ejpam-5120	140	25	g	g	NOUN
ejpam-5120	140	26	)	)	PUNCT
ejpam-5120	140	27	is	be	AUX
ejpam-5120	140	28	a	a	DET
ejpam-5120	140	29	direct	direct	ADJ
ejpam-5120	140	30	product	product	NOUN
ejpam-5120	140	31	of	of	ADP
ejpam-5120	140	32	abelian	abelian	PROPN
ejpam-5120	140	33	minimal	minimal	ADJ
ejpam-5120	140	34	normal	normal	ADJ
ejpam-5120	140	35	subgroups	subgroup	NOUN
ejpam-5120	140	36	of	of	ADP
ejpam-5120	140	37	g.	g.	PROPN
ejpam-5120	140	38	but	but	CCONJ
ejpam-5120	140	39	a	a	DET
ejpam-5120	140	40	=	=	X
ejpam-5120	140	41	f	f	X
ejpam-5120	140	42	(	(	PUNCT
ejpam-5120	140	43	g	g	NOUN
ejpam-5120	140	44	)	)	PUNCT
ejpam-5120	140	45	has	have	VERB
ejpam-5120	140	46	a	a	DET
ejpam-5120	140	47	maximal	maximal	ADJ
ejpam-5120	140	48	subgroup	subgroup	NOUN
ejpam-5120	140	49	b	b	PROPN
ejpam-5120	140	50	such	such	DET
ejpam-5120	140	51	that	that	DET
ejpam-5120	140	52	b	b	NOUN
ejpam-5120	140	53	is	be	AUX
ejpam-5120	140	54	normal	normal	ADJ
ejpam-5120	140	55	in	in	ADP
ejpam-5120	140	56	g.	g.	PROPN
ejpam-5120	140	57	then	then	ADV
ejpam-5120	140	58	,	,	PUNCT
ejpam-5120	140	59	by	by	ADP
ejpam-5120	140	60	[	[	X
ejpam-5120	140	61	3	3	NUM
ejpam-5120	140	62	,	,	PUNCT
ejpam-5120	140	63	a.	a.	NOUN
ejpam-5120	140	64	(	(	PUNCT
ejpam-5120	140	65	913	913	NUM
ejpam-5120	140	66	)	)	PUNCT
ejpam-5120	140	67	,	,	PUNCT
ejpam-5120	140	68	p.	p.	NOUN
ejpam-5120	140	69	33	33	NUM
ejpam-5120	140	70	]	]	PUNCT
ejpam-5120	140	71	,	,	PUNCT
ejpam-5120	140	72	for	for	ADP
ejpam-5120	140	73	some	some	DET
ejpam-5120	140	74	minimal	minimal	ADJ
ejpam-5120	140	75	normal	normal	ADJ
ejpam-5120	140	76	subgroup	subgroup	NOUN
ejpam-5120	140	77	l	l	NOUN
ejpam-5120	140	78	of	of	ADP
ejpam-5120	140	79	g	g	PROPN
ejpam-5120	140	80	contained	contain	VERB
ejpam-5120	140	81	in	in	ADP
ejpam-5120	140	82	a	a	DET
ejpam-5120	140	83	=	=	SYM
ejpam-5120	140	84	f	f	X
ejpam-5120	140	85	(	(	PUNCT
ejpam-5120	140	86	g	g	NOUN
ejpam-5120	140	87	)	)	PUNCT
ejpam-5120	140	88	,	,	PUNCT
ejpam-5120	140	89	we	we	PRON
ejpam-5120	140	90	have	have	VERB
ejpam-5120	140	91	|l|	|l|	NOUN
ejpam-5120	140	92	=	=	SYM
ejpam-5120	141	1	p.	p.	NOUN
ejpam-5120	141	2	then	then	ADV
ejpam-5120	141	3	g	g	NOUN
ejpam-5120	141	4	/	/	SYM
ejpam-5120	141	5	cg(l	cg(l	NOUN
ejpam-5120	141	6	)	)	PUNCT
ejpam-5120	141	7	is	be	AUX
ejpam-5120	141	8	abelian	abelian	ADJ
ejpam-5120	141	9	and	and	CCONJ
ejpam-5120	141	10	g	g	NOUN
ejpam-5120	141	11	′	′	ADJ
ejpam-5120	141	12	≤	≤	NUM
ejpam-5120	141	13	cg(l	cg(l	NOUN
ejpam-5120	141	14	)	)	PUNCT
ejpam-5120	141	15	.	.	PUNCT
ejpam-5120	142	1	since	since	SCONJ
ejpam-5120	142	2	|d|	|d|	PROPN
ejpam-5120	142	3	>	>	X
ejpam-5120	142	4	p	p	X
ejpam-5120	142	5	from	from	ADP
ejpam-5120	142	6	(	(	PUNCT
ejpam-5120	142	7	2	2	NUM
ejpam-5120	142	8	)	)	PUNCT
ejpam-5120	142	9	,	,	PUNCT
ejpam-5120	142	10	then	then	ADV
ejpam-5120	142	11	g	g	PROPN
ejpam-5120	142	12	/	/	SYM
ejpam-5120	142	13	l	l	NOUN
ejpam-5120	142	14	satifies	satifie	NOUN
ejpam-5120	142	15	the	the	DET
ejpam-5120	142	16	hypothesis	hypothesis	NOUN
ejpam-5120	142	17	of	of	ADP
ejpam-5120	142	18	the	the	DET
ejpam-5120	142	19	lemma	lemma	PROPN
ejpam-5120	142	20	5	5	NUM
ejpam-5120	142	21	,	,	PUNCT
ejpam-5120	142	22	and	and	CCONJ
ejpam-5120	142	23	so	so	ADV
ejpam-5120	142	24	(	(	PUNCT
ejpam-5120	142	25	g	g	NOUN
ejpam-5120	142	26	/	/	SYM
ejpam-5120	142	27	l	l	NOUN
ejpam-5120	142	28	)	)	PUNCT
ejpam-5120	142	29	′	′	VERB
ejpam-5120	143	1	∼=	∼=	ADV
ejpam-5120	143	2	g	g	NOUN
ejpam-5120	143	3	′	′	NUM
ejpam-5120	143	4	/(g	/(g	PUNCT
ejpam-5120	144	1	′	′	NUM
ejpam-5120	144	2	∩	∩	X
ejpam-5120	144	3	l	l	NOUN
ejpam-5120	144	4	)	)	PUNCT
ejpam-5120	144	5	is	be	AUX
ejpam-5120	144	6	p	p	NOUN
ejpam-5120	144	7	-	-	PUNCT
ejpam-5120	144	8	nilpotent	nilpotent	ADJ
ejpam-5120	144	9	by	by	ADP
ejpam-5120	144	10	the	the	DET
ejpam-5120	144	11	choice	choice	NOUN
ejpam-5120	144	12	of	of	ADP
ejpam-5120	144	13	g	g	NOUN
ejpam-5120	144	14	and	and	CCONJ
ejpam-5120	144	15	since	since	SCONJ
ejpam-5120	144	16	g	g	NOUN
ejpam-5120	144	17	′	′	ADJ
ejpam-5120	144	18	≤	≤	NUM
ejpam-5120	144	19	cg(l	cg(l	NOUN
ejpam-5120	144	20	)	)	PUNCT
ejpam-5120	144	21	,	,	PUNCT
ejpam-5120	144	22	we	we	PRON
ejpam-5120	144	23	have	have	VERB
ejpam-5120	144	24	that	that	PRON
ejpam-5120	144	25	g	g	PROPN
ejpam-5120	144	26	′	′	NUM
ejpam-5120	144	27	is	be	AUX
ejpam-5120	144	28	p	p	NOUN
ejpam-5120	144	29	-	-	PUNCT
ejpam-5120	144	30	nilpotent	nilpotent	ADJ
ejpam-5120	144	31	,	,	PUNCT
ejpam-5120	144	32	contradiction	contradiction	NOUN
ejpam-5120	144	33	.	.	PUNCT
ejpam-5120	145	1	(	(	PUNCT
ejpam-5120	145	2	6	6	X
ejpam-5120	145	3	)	)	PUNCT
ejpam-5120	145	4	|φ(g)|	|φ(g)|	NOUN
ejpam-5120	145	5	≥	≥	NUM
ejpam-5120	145	6	|d|	|d|	PROPN
ejpam-5120	145	7	.	.	PUNCT
ejpam-5120	146	1	assume	assume	VERB
ejpam-5120	146	2	that	that	SCONJ
ejpam-5120	146	3	|φ(g)|	|φ(g)|	ADP
ejpam-5120	146	4	<	<	X
ejpam-5120	146	5	|d|	|d|	NOUN
ejpam-5120	146	6	.	.	PUNCT
ejpam-5120	147	1	by	by	ADP
ejpam-5120	147	2	(	(	PUNCT
ejpam-5120	147	3	4	4	NUM
ejpam-5120	147	4	)	)	PUNCT
ejpam-5120	147	5	,	,	PUNCT
ejpam-5120	147	6	φ(g	φ(g	PROPN
ejpam-5120	147	7	)	)	PUNCT
ejpam-5120	147	8	<	<	X
ejpam-5120	147	9	f	f	X
ejpam-5120	147	10	(	(	PUNCT
ejpam-5120	147	11	g	g	NOUN
ejpam-5120	147	12	)	)	PUNCT
ejpam-5120	147	13	=	=	PUNCT
ejpam-5120	147	14	a	a	DET
ejpam-5120	147	15	<	<	X
ejpam-5120	147	16	p	p	X
ejpam-5120	147	17	.	.	PUNCT
ejpam-5120	148	1	then	then	ADV
ejpam-5120	148	2	g	g	PROPN
ejpam-5120	148	3	/	/	SYM
ejpam-5120	148	4	φ(g	φ(g	PROPN
ejpam-5120	148	5	)	)	PUNCT
ejpam-5120	148	6	satifies	satifie	NOUN
ejpam-5120	148	7	the	the	DET
ejpam-5120	148	8	hypothesis	hypothesis	NOUN
ejpam-5120	148	9	of	of	ADP
ejpam-5120	148	10	the	the	DET
ejpam-5120	148	11	lemma	lemma	PROPN
ejpam-5120	148	12	5	5	NUM
ejpam-5120	148	13	,	,	PUNCT
ejpam-5120	148	14	so	so	CCONJ
ejpam-5120	148	15	(	(	PUNCT
ejpam-5120	148	16	g	g	NOUN
ejpam-5120	148	17	/	/	SYM
ejpam-5120	148	18	φ(g	φ(g	PROPN
ejpam-5120	148	19	)	)	PUNCT
ejpam-5120	148	20	)	)	PUNCT
ejpam-5120	149	1	′	′	NUM
ejpam-5120	150	1	=	=	PUNCT
ejpam-5120	150	2	g	g	NOUN
ejpam-5120	150	3	′	′	NUM
ejpam-5120	150	4	φ(g)/φ(g	φ(g)/φ(g	NOUN
ejpam-5120	150	5	)	)	PUNCT
ejpam-5120	150	6	∼=	∼=	NOUN
ejpam-5120	150	7	g	g	NOUN
ejpam-5120	150	8	′	′	NUM
ejpam-5120	150	9	/(g	/(g	PUNCT
ejpam-5120	151	1	′	′	NUM
ejpam-5120	151	2	∩φ(g	∩φ(g	NOUN
ejpam-5120	151	3	)	)	PUNCT
ejpam-5120	151	4	)	)	PUNCT
ejpam-5120	151	5	is	be	AUX
ejpam-5120	151	6	p	p	NOUN
ejpam-5120	151	7	-	-	PUNCT
ejpam-5120	151	8	nilpotent	nilpotent	ADJ
ejpam-5120	151	9	by	by	ADP
ejpam-5120	151	10	the	the	DET
ejpam-5120	151	11	choice	choice	NOUN
ejpam-5120	151	12	of	of	ADP
ejpam-5120	151	13	g	g	NOUN
ejpam-5120	151	14	and	and	CCONJ
ejpam-5120	151	15	it	it	PRON
ejpam-5120	151	16	follows	follow	VERB
ejpam-5120	151	17	easily	easily	ADV
ejpam-5120	151	18	that	that	SCONJ
ejpam-5120	151	19	g	g	PROPN
ejpam-5120	151	20	′	′	NUM
ejpam-5120	151	21	is	be	AUX
ejpam-5120	151	22	p	p	NOUN
ejpam-5120	151	23	-	-	PUNCT
ejpam-5120	151	24	nilpotent	nilpotent	ADJ
ejpam-5120	151	25	,	,	PUNCT
ejpam-5120	151	26	contradiction	contradiction	NOUN
ejpam-5120	151	27	.	.	PUNCT
ejpam-5120	152	1	(	(	PUNCT
ejpam-5120	152	2	7	7	X
ejpam-5120	152	3	)	)	PUNCT
ejpam-5120	152	4	let	let	VERB
ejpam-5120	152	5	l	l	NOUN
ejpam-5120	152	6	be	be	AUX
ejpam-5120	152	7	a	a	DET
ejpam-5120	152	8	minimal	minimal	ADJ
ejpam-5120	152	9	normal	normal	ADJ
ejpam-5120	152	10	subgroup	subgroup	NOUN
ejpam-5120	152	11	of	of	ADP
ejpam-5120	152	12	g	g	PROPN
ejpam-5120	152	13	such	such	ADJ
ejpam-5120	152	14	that	that	SCONJ
ejpam-5120	152	15	l	l	NOUN
ejpam-5120	152	16	≤	≤	X
ejpam-5120	152	17	φ(g	φ(g	NOUN
ejpam-5120	152	18	)	)	PUNCT
ejpam-5120	152	19	.	.	PUNCT
ejpam-5120	153	1	then	then	ADV
ejpam-5120	153	2	|l|	|l|	VERB
ejpam-5120	153	3	≤	≤	ADJ
ejpam-5120	153	4	|d|	|d|	PROPN
ejpam-5120	153	5	.	.	PUNCT
ejpam-5120	154	1	assume	assume	VERB
ejpam-5120	154	2	that	that	SCONJ
ejpam-5120	154	3	|l|	|l|	VERB
ejpam-5120	154	4	>	>	X
ejpam-5120	154	5	|d|	|d|	PROPN
ejpam-5120	154	6	.	.	PUNCT
ejpam-5120	155	1	then	then	ADV
ejpam-5120	155	2	every	every	DET
ejpam-5120	155	3	subgroup	subgroup	NOUN
ejpam-5120	155	4	of	of	ADP
ejpam-5120	155	5	l	l	NOUN
ejpam-5120	155	6	with	with	ADP
ejpam-5120	155	7	order	order	NOUN
ejpam-5120	155	8	equals	equal	VERB
ejpam-5120	155	9	to	to	ADP
ejpam-5120	155	10	|d|	|d|	PROPN
ejpam-5120	155	11	is	be	AUX
ejpam-5120	155	12	weakly	weakly	ADJ
ejpam-5120	155	13	s	s	NOUN
ejpam-5120	155	14	-	-	NOUN
ejpam-5120	155	15	permutable	permutable	ADJ
ejpam-5120	155	16	in	in	ADP
ejpam-5120	155	17	g	g	PROPN
ejpam-5120	155	18	and	and	CCONJ
ejpam-5120	155	19	so	so	ADV
ejpam-5120	155	20	,	,	PUNCT
ejpam-5120	155	21	by	by	ADP
ejpam-5120	155	22	lemma	lemma	PROPN
ejpam-5120	155	23	7	7	NUM
ejpam-5120	155	24	,	,	PUNCT
ejpam-5120	155	25	some	some	DET
ejpam-5120	155	26	maximal	maximal	ADJ
ejpam-5120	155	27	subgroup	subgroup	NOUN
ejpam-5120	155	28	of	of	ADP
ejpam-5120	155	29	l	l	NOUN
ejpam-5120	155	30	is	be	AUX
ejpam-5120	155	31	normal	normal	ADJ
ejpam-5120	155	32	in	in	ADP
ejpam-5120	155	33	g.	g.	PROPN
ejpam-5120	155	34	then	then	ADV
ejpam-5120	155	35	|l|	|l|	VERB
ejpam-5120	156	1	=	=	PUNCT
ejpam-5120	156	2	p	p	X
ejpam-5120	156	3	>	>	X
ejpam-5120	156	4	|d|	|d|	PROPN
ejpam-5120	156	5	which	which	PRON
ejpam-5120	156	6	contradicts	contradict	VERB
ejpam-5120	156	7	(	(	PUNCT
ejpam-5120	156	8	2	2	NUM
ejpam-5120	156	9	)	)	PUNCT
ejpam-5120	156	10	.	.	PUNCT
ejpam-5120	157	1	thus	thus	ADV
ejpam-5120	157	2	|l|	|l|	VERB
ejpam-5120	157	3	≤	≤	NUM
ejpam-5120	157	4	|d|	|d|	PROPN
ejpam-5120	157	5	.	.	PUNCT
ejpam-5120	158	1	(	(	PUNCT
ejpam-5120	158	2	8)	8)	NUM
ejpam-5120	158	3	there	there	ADV
ejpam-5120	158	4	exists	exist	VERB
ejpam-5120	158	5	a	a	DET
ejpam-5120	158	6	subgroup	subgroup	NOUN
ejpam-5120	158	7	l1	l1	PROPN
ejpam-5120	158	8	of	of	ADP
ejpam-5120	158	9	a	a	DET
ejpam-5120	158	10	=	=	SYM
ejpam-5120	158	11	f	f	X
ejpam-5120	158	12	(	(	PUNCT
ejpam-5120	158	13	g	g	NOUN
ejpam-5120	158	14	)	)	PUNCT
ejpam-5120	158	15	with	with	ADP
ejpam-5120	158	16	|l1|	|l1|	NOUN
ejpam-5120	158	17	=	=	SYM
ejpam-5120	158	18	|d|	|d|	PROPN
ejpam-5120	158	19	such	such	ADJ
ejpam-5120	158	20	that	that	PRON
ejpam-5120	158	21	is	be	AUX
ejpam-5120	158	22	not	not	PART
ejpam-5120	158	23	spermutable	spermutable	NOUN
ejpam-5120	158	24	.	.	PUNCT
ejpam-5120	159	1	assume	assume	VERB
ejpam-5120	159	2	that	that	SCONJ
ejpam-5120	159	3	all	all	DET
ejpam-5120	159	4	subgroups	subgroup	NOUN
ejpam-5120	159	5	of	of	ADP
ejpam-5120	159	6	l1	l1	PROPN
ejpam-5120	159	7	of	of	ADP
ejpam-5120	159	8	a	a	PRON
ejpam-5120	159	9	with	with	ADP
ejpam-5120	159	10	|l1|	|l1|	NOUN
ejpam-5120	159	11	=	=	SYM
ejpam-5120	159	12	|d|	|d|	PROPN
ejpam-5120	159	13	are	be	AUX
ejpam-5120	159	14	s	s	NOUN
ejpam-5120	159	15	-	-	NOUN
ejpam-5120	159	16	permutable	permutable	ADJ
ejpam-5120	159	17	.	.	PUNCT
ejpam-5120	160	1	by	by	ADP
ejpam-5120	160	2	(	(	PUNCT
ejpam-5120	160	3	5	5	NUM
ejpam-5120	160	4	)	)	PUNCT
ejpam-5120	160	5	,	,	PUNCT
ejpam-5120	160	6	φ(g	φ(g	PROPN
ejpam-5120	160	7	)	)	PUNCT
ejpam-5120	160	8	̸=	̸=	PROPN
ejpam-5120	160	9	1	1	NUM
ejpam-5120	160	10	and	and	CCONJ
ejpam-5120	160	11	so	so	ADV
ejpam-5120	160	12	φ(g	φ(g	PROPN
ejpam-5120	160	13	)	)	PUNCT
ejpam-5120	160	14	contains	contain	VERB
ejpam-5120	160	15	a	a	DET
ejpam-5120	160	16	minimal	minimal	ADJ
ejpam-5120	160	17	normal	normal	ADJ
ejpam-5120	160	18	subgroup	subgroup	NOUN
ejpam-5120	160	19	l	l	NOUN
ejpam-5120	160	20	such	such	ADJ
ejpam-5120	160	21	that	that	PRON
ejpam-5120	160	22	|l|	|l|	NOUN
ejpam-5120	160	23	≤	≤	PUNCT
ejpam-5120	160	24	|d|	|d|	PROPN
ejpam-5120	160	25	by	by	ADP
ejpam-5120	160	26	(	(	PUNCT
ejpam-5120	160	27	7	7	NUM
ejpam-5120	160	28	)	)	PUNCT
ejpam-5120	160	29	.	.	PUNCT
ejpam-5120	161	1	consider	consider	VERB
ejpam-5120	161	2	a.	a.	NOUN
ejpam-5120	161	3	a.	a.	PROPN
ejpam-5120	161	4	heliel	heliel	PROPN
ejpam-5120	161	5	et	et	PROPN
ejpam-5120	161	6	al	al	PROPN
ejpam-5120	161	7	.	.	PUNCT
ejpam-5120	161	8	/	/	SYM
ejpam-5120	161	9	eur	eur	PROPN
ejpam-5120	161	10	.	.	PUNCT
ejpam-5120	162	1	j.	j.	PROPN
ejpam-5120	162	2	pure	pure	PROPN
ejpam-5120	162	3	appl	appl	PROPN
ejpam-5120	162	4	.	.	PROPN
ejpam-5120	162	5	math	math	PROPN
ejpam-5120	162	6	,	,	PUNCT
ejpam-5120	162	7	17	17	NUM
ejpam-5120	162	8	(	(	PUNCT
ejpam-5120	162	9	2	2	NUM
ejpam-5120	162	10	)	)	PUNCT
ejpam-5120	162	11	(	(	PUNCT
ejpam-5120	162	12	2024	2024	NUM
ejpam-5120	162	13	)	)	PUNCT
ejpam-5120	162	14	,	,	PUNCT
ejpam-5120	162	15	810	810	NUM
ejpam-5120	162	16	-	-	SYM
ejpam-5120	162	17	818	818	NUM
ejpam-5120	162	18	815	815	NUM
ejpam-5120	162	19	the	the	DET
ejpam-5120	162	20	factor	factor	NOUN
ejpam-5120	162	21	group	group	NOUN
ejpam-5120	162	22	g	g	PROPN
ejpam-5120	162	23	/	/	SYM
ejpam-5120	162	24	l.	l.	PROPN
ejpam-5120	162	25	if	if	SCONJ
ejpam-5120	162	26	|l|	|l|	NOUN
ejpam-5120	162	27	=	=	SYM
ejpam-5120	162	28	|d|	|d|	PROPN
ejpam-5120	162	29	,	,	PUNCT
ejpam-5120	162	30	then	then	ADV
ejpam-5120	162	31	every	every	DET
ejpam-5120	162	32	subgroup	subgroup	NOUN
ejpam-5120	162	33	of	of	ADP
ejpam-5120	162	34	a	a	DET
ejpam-5120	162	35	/	/	SYM
ejpam-5120	162	36	l	l	NOUN
ejpam-5120	162	37	of	of	ADP
ejpam-5120	162	38	order	order	NOUN
ejpam-5120	162	39	p	p	NOUN
ejpam-5120	162	40	is	be	AUX
ejpam-5120	162	41	s	s	NOUN
ejpam-5120	162	42	-	-	NOUN
ejpam-5120	162	43	permutable	permutable	ADJ
ejpam-5120	162	44	in	in	ADP
ejpam-5120	162	45	g	g	PROPN
ejpam-5120	162	46	/	/	SYM
ejpam-5120	162	47	l.	l.	NOUN
ejpam-5120	162	48	since	since	SCONJ
ejpam-5120	162	49	l	l	NOUN
ejpam-5120	162	50	≤	≤	X
ejpam-5120	162	51	φ(g	φ(g	NOUN
ejpam-5120	162	52	)	)	PUNCT
ejpam-5120	162	53	,	,	PUNCT
ejpam-5120	162	54	we	we	PRON
ejpam-5120	162	55	have	have	VERB
ejpam-5120	162	56	that	that	DET
ejpam-5120	162	57	f	f	PROPN
ejpam-5120	162	58	(	(	PUNCT
ejpam-5120	162	59	g	g	PROPN
ejpam-5120	162	60	/	/	SYM
ejpam-5120	162	61	l	l	NOUN
ejpam-5120	162	62	)	)	PUNCT
ejpam-5120	163	1	=	=	SYM
ejpam-5120	163	2	f	f	X
ejpam-5120	163	3	(	(	PUNCT
ejpam-5120	163	4	g)/l	g)/l	PROPN
ejpam-5120	163	5	=	=	PROPN
ejpam-5120	163	6	a	a	X
ejpam-5120	163	7	/	/	SYM
ejpam-5120	163	8	l.	l.	NOUN
ejpam-5120	163	9	since	since	SCONJ
ejpam-5120	163	10	g	g	PROPN
ejpam-5120	163	11	is	be	AUX
ejpam-5120	163	12	solvable	solvable	ADJ
ejpam-5120	163	13	by	by	ADP
ejpam-5120	163	14	(	(	PUNCT
ejpam-5120	163	15	4	4	NUM
ejpam-5120	163	16	)	)	PUNCT
ejpam-5120	163	17	,	,	PUNCT
ejpam-5120	163	18	we	we	PRON
ejpam-5120	163	19	have	have	VERB
ejpam-5120	163	20	that	that	DET
ejpam-5120	163	21	c(g	c(g	PROPN
ejpam-5120	163	22	/	/	SYM
ejpam-5120	163	23	φ(g))(f	φ(g))(f	PROPN
ejpam-5120	163	24	(	(	PUNCT
ejpam-5120	163	25	g	g	NOUN
ejpam-5120	163	26	/	/	SYM
ejpam-5120	163	27	l	l	NOUN
ejpam-5120	163	28	)	)	PUNCT
ejpam-5120	163	29	)	)	PUNCT
ejpam-5120	164	1	=	=	PUNCT
ejpam-5120	164	2	c(g	c(g	PROPN
ejpam-5120	164	3	/	/	SYM
ejpam-5120	164	4	φ(g))(f	φ(g))(f	PROPN
ejpam-5120	164	5	(	(	PUNCT
ejpam-5120	164	6	g)/l	g)/l	PROPN
ejpam-5120	164	7	)	)	PUNCT
ejpam-5120	164	8	≤	≤	NUM
ejpam-5120	165	1	f	f	X
ejpam-5120	165	2	(	(	PUNCT
ejpam-5120	165	3	g	g	NOUN
ejpam-5120	165	4	/	/	SYM
ejpam-5120	165	5	l	l	NOUN
ejpam-5120	165	6	)	)	PUNCT
ejpam-5120	166	1	=	=	SYM
ejpam-5120	166	2	f	f	X
ejpam-5120	166	3	(	(	PUNCT
ejpam-5120	166	4	g)/l	g)/l	PROPN
ejpam-5120	166	5	=	=	PROPN
ejpam-5120	166	6	a	a	X
ejpam-5120	166	7	/	/	SYM
ejpam-5120	166	8	l.	l.	NOUN
ejpam-5120	166	9	then	then	ADV
ejpam-5120	166	10	k̄	k̄	PROPN
ejpam-5120	166	11	=	=	PUNCT
ejpam-5120	166	12	kl	kl	X
ejpam-5120	166	13	/	/	SYM
ejpam-5120	166	14	l	l	NOUN
ejpam-5120	166	15	∼=	∼=	PROPN
ejpam-5120	166	16	k	k	NOUN
ejpam-5120	166	17	is	be	AUX
ejpam-5120	166	18	a	a	DET
ejpam-5120	166	19	p	p	NOUN
ejpam-5120	166	20	′	′	NUM
ejpam-5120	166	21	-group	-group	NOUN
ejpam-5120	166	22	of	of	ADP
ejpam-5120	166	23	automorphisms	automorphism	NOUN
ejpam-5120	166	24	of	of	ADP
ejpam-5120	166	25	a	a	DET
ejpam-5120	166	26	/	/	SYM
ejpam-5120	166	27	l	l	NOUN
ejpam-5120	166	28	and	and	CCONJ
ejpam-5120	166	29	every	every	DET
ejpam-5120	166	30	subgroup	subgroup	NOUN
ejpam-5120	166	31	of	of	ADP
ejpam-5120	166	32	a	a	DET
ejpam-5120	166	33	/	/	SYM
ejpam-5120	166	34	l	l	NOUN
ejpam-5120	166	35	of	of	ADP
ejpam-5120	166	36	prime	prime	ADJ
ejpam-5120	166	37	order	order	NOUN
ejpam-5120	166	38	is	be	AUX
ejpam-5120	166	39	k̄	k̄	ADV
ejpam-5120	166	40	invariant	invariant	ADJ
ejpam-5120	166	41	.	.	PUNCT
ejpam-5120	167	1	then	then	ADV
ejpam-5120	167	2	k̄	k̄	VERB
ejpam-5120	167	3	∼=	∼=	PROPN
ejpam-5120	167	4	k	k	NOUN
ejpam-5120	167	5	is	be	AUX
ejpam-5120	167	6	cyclic	cyclic	ADJ
ejpam-5120	167	7	by	by	ADP
ejpam-5120	167	8	lemma	lemma	PROPN
ejpam-5120	167	9	6	6	NUM
ejpam-5120	167	10	.	.	PUNCT
ejpam-5120	168	1	also	also	ADV
ejpam-5120	168	2	,	,	PUNCT
ejpam-5120	168	3	as	as	SCONJ
ejpam-5120	168	4	g	g	PROPN
ejpam-5120	168	5	is	be	AUX
ejpam-5120	168	6	solvable	solvable	ADJ
ejpam-5120	168	7	,	,	PUNCT
ejpam-5120	168	8	g	g	PROPN
ejpam-5120	168	9	contains	contain	VERB
ejpam-5120	168	10	a	a	DET
ejpam-5120	168	11	hall	hall	PROPN
ejpam-5120	168	12	subgroup	subgroup	PROPN
ejpam-5120	168	13	pq	pq	PROPN
ejpam-5120	168	14	,	,	PUNCT
ejpam-5120	168	15	where	where	SCONJ
ejpam-5120	168	16	q	q	NOUN
ejpam-5120	168	17	is	be	AUX
ejpam-5120	168	18	a	a	DET
ejpam-5120	168	19	sylow	sylow	NOUN
ejpam-5120	168	20	q	q	NOUN
ejpam-5120	168	21	-	-	NOUN
ejpam-5120	168	22	subgroup	subgroup	NOUN
ejpam-5120	168	23	of	of	ADP
ejpam-5120	168	24	g	g	PROPN
ejpam-5120	168	25	and	and	CCONJ
ejpam-5120	168	26	q	q	PROPN
ejpam-5120	168	27	̸=	̸=	PROPN
ejpam-5120	168	28	p.	p.	NOUN
ejpam-5120	168	29	hence	hence	ADV
ejpam-5120	168	30	,	,	PUNCT
ejpam-5120	168	31	if	if	SCONJ
ejpam-5120	168	32	p	p	PRON
ejpam-5120	168	33	<	<	X
ejpam-5120	168	34	q	q	X
ejpam-5120	168	35	,	,	PUNCT
ejpam-5120	168	36	pq	pq	PROPN
ejpam-5120	168	37	is	be	AUX
ejpam-5120	168	38	p	p	NOUN
ejpam-5120	168	39	-	-	PUNCT
ejpam-5120	168	40	nilpotent	nilpotent	ADJ
ejpam-5120	168	41	and	and	CCONJ
ejpam-5120	168	42	so	so	ADV
ejpam-5120	168	43	q	q	ADJ
ejpam-5120	168	44	≤	≤	NUM
ejpam-5120	168	45	cg(a	cg(a	X
ejpam-5120	168	46	)	)	PUNCT
ejpam-5120	169	1	=	=	SYM
ejpam-5120	169	2	cg(f	cg(f	X
ejpam-5120	169	3	(	(	PUNCT
ejpam-5120	169	4	g	g	NOUN
ejpam-5120	169	5	)	)	PUNCT
ejpam-5120	169	6	)	)	PUNCT
ejpam-5120	170	1	≤	≤	NUM
ejpam-5120	170	2	f	f	X
ejpam-5120	170	3	(	(	PUNCT
ejpam-5120	170	4	g	g	NOUN
ejpam-5120	170	5	)	)	PUNCT
ejpam-5120	170	6	=	=	SYM
ejpam-5120	171	1	a	a	NOUN
ejpam-5120	171	2	,	,	PUNCT
ejpam-5120	171	3	a	a	DET
ejpam-5120	171	4	contradiction	contradiction	NOUN
ejpam-5120	171	5	.	.	PUNCT
ejpam-5120	172	1	thus	thus	ADV
ejpam-5120	172	2	p	p	X
ejpam-5120	172	3	is	be	AUX
ejpam-5120	172	4	the	the	DET
ejpam-5120	172	5	largest	large	ADJ
ejpam-5120	172	6	prime	prime	ADJ
ejpam-5120	172	7	dividing	dividing	NOUN
ejpam-5120	172	8	|g|	|g|	PROPN
ejpam-5120	172	9	.	.	PUNCT
ejpam-5120	173	1	since	since	SCONJ
ejpam-5120	173	2	k	k	PROPN
ejpam-5120	173	3	is	be	AUX
ejpam-5120	173	4	cyclic	cyclic	ADJ
ejpam-5120	173	5	,	,	PUNCT
ejpam-5120	173	6	we	we	PRON
ejpam-5120	173	7	have	have	VERB
ejpam-5120	173	8	by	by	ADP
ejpam-5120	173	9	burnside	burnside	NOUN
ejpam-5120	173	10	’s	’s	PART
ejpam-5120	173	11	theorem	theorem	NOUN
ejpam-5120	173	12	[	[	X
ejpam-5120	173	13	5	5	NUM
ejpam-5120	173	14	,	,	PUNCT
ejpam-5120	173	15	satz	satz	X
ejpam-5120	173	16	2.8	2.8	NUM
ejpam-5120	173	17	,	,	PUNCT
ejpam-5120	173	18	p.	p.	NOUN
ejpam-5120	173	19	420	420	NUM
ejpam-5120	173	20	]	]	PUNCT
ejpam-5120	173	21	,	,	PUNCT
ejpam-5120	173	22	that	that	SCONJ
ejpam-5120	173	23	p	p	NOUN
ejpam-5120	173	24	is	be	AUX
ejpam-5120	173	25	normal	normal	ADJ
ejpam-5120	173	26	in	in	ADP
ejpam-5120	173	27	g	g	PROPN
ejpam-5120	173	28	,	,	PUNCT
ejpam-5120	173	29	a	a	DET
ejpam-5120	173	30	contradiction	contradiction	NOUN
ejpam-5120	173	31	.	.	PUNCT
ejpam-5120	174	1	thus	thus	ADV
ejpam-5120	174	2	that	that	PRON
ejpam-5120	174	3	assume	assume	VERB
ejpam-5120	174	4	|l|	|l|	VERB
ejpam-5120	174	5	<	<	X
ejpam-5120	174	6	|d|	|d|	PROPN
ejpam-5120	174	7	.	.	PUNCT
ejpam-5120	175	1	it	it	PRON
ejpam-5120	175	2	is	be	AUX
ejpam-5120	175	3	easy	easy	ADJ
ejpam-5120	175	4	to	to	PART
ejpam-5120	175	5	see	see	VERB
ejpam-5120	175	6	that	that	SCONJ
ejpam-5120	175	7	g	g	PROPN
ejpam-5120	175	8	/	/	SYM
ejpam-5120	175	9	l	l	NOUN
ejpam-5120	175	10	satisfies	satisfie	NOUN
ejpam-5120	175	11	the	the	DET
ejpam-5120	175	12	hypothesis	hypothesis	NOUN
ejpam-5120	175	13	of	of	ADP
ejpam-5120	175	14	the	the	DET
ejpam-5120	175	15	theorem	theorem	NOUN
ejpam-5120	175	16	and	and	CCONJ
ejpam-5120	175	17	so	so	ADV
ejpam-5120	175	18	(	(	PUNCT
ejpam-5120	175	19	g	g	NOUN
ejpam-5120	175	20	/	/	SYM
ejpam-5120	175	21	l	l	NOUN
ejpam-5120	175	22	)	)	PUNCT
ejpam-5120	175	23	′	′	VERB
ejpam-5120	176	1	∼=	∼=	ADV
ejpam-5120	176	2	g	g	NOUN
ejpam-5120	176	3	′	′	NUM
ejpam-5120	176	4	/g	/g	PUNCT
ejpam-5120	177	1	′	′	NUM
ejpam-5120	177	2	∩	∩	NOUN
ejpam-5120	177	3	l	l	NOUN
ejpam-5120	177	4	is	be	AUX
ejpam-5120	177	5	p	p	NOUN
ejpam-5120	177	6	-	-	PUNCT
ejpam-5120	177	7	nilpotent	nilpotent	ADJ
ejpam-5120	177	8	by	by	ADP
ejpam-5120	177	9	the	the	DET
ejpam-5120	177	10	choice	choice	NOUN
ejpam-5120	177	11	of	of	ADP
ejpam-5120	177	12	g	g	PROPN
ejpam-5120	177	13	and	and	CCONJ
ejpam-5120	177	14	,	,	PUNCT
ejpam-5120	177	15	since	since	SCONJ
ejpam-5120	177	16	g	g	NOUN
ejpam-5120	177	17	′	′	NUM
ejpam-5120	177	18	∩	∩	NOUN
ejpam-5120	177	19	l	l	NOUN
ejpam-5120	177	20	≤	≤	X
ejpam-5120	177	21	φ(g	φ(g	NOUN
ejpam-5120	177	22	)	)	PUNCT
ejpam-5120	177	23	,	,	PUNCT
ejpam-5120	177	24	we	we	PRON
ejpam-5120	177	25	have	have	VERB
ejpam-5120	177	26	that	that	PRON
ejpam-5120	177	27	g	g	PROPN
ejpam-5120	177	28	′	′	NUM
ejpam-5120	177	29	is	be	AUX
ejpam-5120	177	30	p	p	NOUN
ejpam-5120	177	31	-	-	PUNCT
ejpam-5120	177	32	nilpotent	nilpotent	ADJ
ejpam-5120	177	33	,	,	PUNCT
ejpam-5120	177	34	a	a	DET
ejpam-5120	177	35	contradiction	contradiction	NOUN
ejpam-5120	177	36	.	.	PUNCT
ejpam-5120	178	1	(	(	PUNCT
ejpam-5120	178	2	9	9	X
ejpam-5120	178	3	)	)	PUNCT
ejpam-5120	178	4	finishing	finish	VERB
ejpam-5120	178	5	the	the	DET
ejpam-5120	178	6	proof	proof	NOUN
ejpam-5120	178	7	of	of	ADP
ejpam-5120	178	8	case	case	NOUN
ejpam-5120	178	9	1	1	NUM
ejpam-5120	178	10	.	.	PUNCT
ejpam-5120	179	1	by	by	ADP
ejpam-5120	179	2	(	(	PUNCT
ejpam-5120	179	3	8)	8)	NUM
ejpam-5120	179	4	,	,	PUNCT
ejpam-5120	179	5	there	there	PRON
ejpam-5120	179	6	exists	exist	VERB
ejpam-5120	179	7	a	a	DET
ejpam-5120	179	8	subgroup	subgroup	NOUN
ejpam-5120	179	9	l1	l1	PROPN
ejpam-5120	179	10	of	of	ADP
ejpam-5120	179	11	a	a	DET
ejpam-5120	179	12	=	=	SYM
ejpam-5120	179	13	f	f	X
ejpam-5120	179	14	(	(	PUNCT
ejpam-5120	179	15	g	g	NOUN
ejpam-5120	179	16	)	)	PUNCT
ejpam-5120	179	17	with	with	ADP
ejpam-5120	179	18	|l1|	|l1|	NOUN
ejpam-5120	179	19	=	=	SYM
ejpam-5120	179	20	|d|	|d|	PROPN
ejpam-5120	179	21	such	such	ADJ
ejpam-5120	179	22	that	that	PRON
ejpam-5120	179	23	is	be	AUX
ejpam-5120	179	24	not	not	PART
ejpam-5120	179	25	spermutable	spermutable	NOUN
ejpam-5120	179	26	.	.	PUNCT
ejpam-5120	180	1	by	by	ADP
ejpam-5120	180	2	the	the	DET
ejpam-5120	180	3	hypothesis	hypothesis	NOUN
ejpam-5120	180	4	,	,	PUNCT
ejpam-5120	180	5	l1	l1	PROPN
ejpam-5120	180	6	is	be	AUX
ejpam-5120	180	7	weakly	weakly	ADJ
ejpam-5120	180	8	s	s	NOUN
ejpam-5120	180	9	-	-	NOUN
ejpam-5120	180	10	permutable	permutable	ADJ
ejpam-5120	180	11	in	in	ADP
ejpam-5120	180	12	g.	g.	PROPN
ejpam-5120	180	13	then	then	ADV
ejpam-5120	180	14	there	there	PRON
ejpam-5120	180	15	exists	exist	VERB
ejpam-5120	180	16	a	a	DET
ejpam-5120	180	17	subnormal	subnormal	ADJ
ejpam-5120	180	18	subgroup	subgroup	NOUN
ejpam-5120	180	19	t1	t1	NOUN
ejpam-5120	180	20	of	of	ADP
ejpam-5120	180	21	g	g	NOUN
ejpam-5120	181	1	such	such	ADJ
ejpam-5120	181	2	that	that	SCONJ
ejpam-5120	181	3	g	g	PROPN
ejpam-5120	181	4	=	=	PUNCT
ejpam-5120	181	5	l1t1	l1t1	PROPN
ejpam-5120	181	6	and	and	CCONJ
ejpam-5120	181	7	t1	t1	VERB
ejpam-5120	181	8	∩l1	∩l1	NUM
ejpam-5120	181	9	≤	≤	NUM
ejpam-5120	181	10	(	(	PUNCT
ejpam-5120	181	11	l1)sg	l1)sg	ADJ
ejpam-5120	181	12	̸=	̸=	PROPN
ejpam-5120	181	13	l1	l1	PROPN
ejpam-5120	181	14	and	and	CCONJ
ejpam-5120	181	15	so	so	ADV
ejpam-5120	181	16	t1	t1	PROPN
ejpam-5120	181	17	̸=	̸=	PROPN
ejpam-5120	181	18	g.	g.	PROPN
ejpam-5120	181	19	hence	hence	ADV
ejpam-5120	181	20	,	,	PUNCT
ejpam-5120	181	21	there	there	PRON
ejpam-5120	181	22	exists	exist	VERB
ejpam-5120	181	23	normal	normal	ADJ
ejpam-5120	181	24	subgroup	subgroup	NOUN
ejpam-5120	181	25	m1	m1	PROPN
ejpam-5120	181	26	of	of	ADP
ejpam-5120	181	27	g	g	PROPN
ejpam-5120	181	28	such	such	ADJ
ejpam-5120	181	29	that	that	SCONJ
ejpam-5120	181	30	t1	t1	PROPN
ejpam-5120	181	31	≤	≤	ADJ
ejpam-5120	181	32	m1	m1	PROPN
ejpam-5120	181	33	and	and	CCONJ
ejpam-5120	181	34	|g	|g	NOUN
ejpam-5120	181	35	/	/	SYM
ejpam-5120	181	36	m1|	m1|	PROPN
ejpam-5120	181	37	=	=	SYM
ejpam-5120	181	38	p.	p.	NOUN
ejpam-5120	181	39	by	by	ADP
ejpam-5120	181	40	lemma	lemma	PROPN
ejpam-5120	181	41	5	5	NUM
ejpam-5120	181	42	,	,	PUNCT
ejpam-5120	181	43	all	all	DET
ejpam-5120	181	44	subgroups	subgroup	NOUN
ejpam-5120	181	45	l2	l2	VERB
ejpam-5120	181	46	of	of	ADP
ejpam-5120	181	47	p2	p2	NOUN
ejpam-5120	181	48	,	,	PUNCT
ejpam-5120	181	49	where	where	SCONJ
ejpam-5120	181	50	p2	p2	PROPN
ejpam-5120	181	51	is	be	AUX
ejpam-5120	181	52	a	a	DET
ejpam-5120	181	53	sylow	sylow	NOUN
ejpam-5120	181	54	p	p	NOUN
ejpam-5120	181	55	-	-	PUNCT
ejpam-5120	181	56	subgroup	subgroup	NOUN
ejpam-5120	181	57	of	of	ADP
ejpam-5120	181	58	m1	m1	PROPN
ejpam-5120	181	59	with	with	ADP
ejpam-5120	181	60	|l2|	|l2|	NOUN
ejpam-5120	181	61	=	=	SYM
ejpam-5120	181	62	|d|	|d|	PROPN
ejpam-5120	181	63	are	be	AUX
ejpam-5120	181	64	weakly	weakly	ADJ
ejpam-5120	181	65	s	s	NOUN
ejpam-5120	181	66	-	-	NOUN
ejpam-5120	181	67	permutable	permutable	ADJ
ejpam-5120	181	68	in	in	ADP
ejpam-5120	181	69	m1	m1	PROPN
ejpam-5120	181	70	.	.	PUNCT
ejpam-5120	182	1	then	then	ADV
ejpam-5120	182	2	m	m	VERB
ejpam-5120	182	3	′	′	NUM
ejpam-5120	182	4	1	1	NUM
ejpam-5120	182	5	is	be	AUX
ejpam-5120	182	6	p	p	NOUN
ejpam-5120	182	7	-	-	PUNCT
ejpam-5120	182	8	nilpotent	nilpotent	ADJ
ejpam-5120	182	9	by	by	ADP
ejpam-5120	182	10	the	the	DET
ejpam-5120	182	11	choice	choice	NOUN
ejpam-5120	182	12	of	of	ADP
ejpam-5120	182	13	g.	g.	PROPN
ejpam-5120	182	14	as	as	ADP
ejpam-5120	182	15	op′	op′	PROPN
ejpam-5120	182	16	=	=	NOUN
ejpam-5120	182	17	1	1	NUM
ejpam-5120	182	18	from	from	ADP
ejpam-5120	182	19	(	(	PUNCT
ejpam-5120	182	20	1	1	NUM
ejpam-5120	182	21	)	)	PUNCT
ejpam-5120	182	22	,	,	PUNCT
ejpam-5120	182	23	we	we	PRON
ejpam-5120	182	24	have	have	VERB
ejpam-5120	182	25	m	m	VERB
ejpam-5120	182	26	′	′	NUM
ejpam-5120	182	27	1	1	NUM
ejpam-5120	182	28	≤	≤	NUM
ejpam-5120	182	29	p2	p2	NOUN
ejpam-5120	182	30	.	.	PUNCT
ejpam-5120	183	1	then	then	ADV
ejpam-5120	183	2	p2	p2	PROPN
ejpam-5120	183	3	is	be	AUX
ejpam-5120	183	4	characteristic	characteristic	ADJ
ejpam-5120	183	5	in	in	ADP
ejpam-5120	183	6	m1	m1	PROPN
ejpam-5120	183	7	,	,	PUNCT
ejpam-5120	183	8	and	and	CCONJ
ejpam-5120	183	9	since	since	SCONJ
ejpam-5120	183	10	m1	m1	PROPN
ejpam-5120	183	11	⊴	⊴	ADP
ejpam-5120	183	12	g	g	PROPN
ejpam-5120	183	13	,	,	PUNCT
ejpam-5120	183	14	it	it	PRON
ejpam-5120	183	15	follows	follow	VERB
ejpam-5120	183	16	that	that	SCONJ
ejpam-5120	183	17	p2	p2	PROPN
ejpam-5120	183	18	⊴	⊴	ADP
ejpam-5120	183	19	g.	g.	PROPN
ejpam-5120	183	20	since	since	SCONJ
ejpam-5120	183	21	g	g	PROPN
ejpam-5120	183	22	=	=	SYM
ejpam-5120	183	23	l1t1	l1t1	PROPN
ejpam-5120	183	24	=	=	SYM
ejpam-5120	183	25	l1m1	l1m1	PROPN
ejpam-5120	183	26	,	,	PUNCT
ejpam-5120	183	27	p2	p2	PROPN
ejpam-5120	183	28	⊴	⊴	ADP
ejpam-5120	183	29	g	g	PROPN
ejpam-5120	183	30	,	,	PUNCT
ejpam-5120	183	31	and	and	CCONJ
ejpam-5120	183	32	l1	l1	PROPN
ejpam-5120	184	1	⊴	⊴	PROPN
ejpam-5120	184	2	a	a	DET
ejpam-5120	184	3	⊴	⊴	NUM
ejpam-5120	184	4	m	m	NOUN
ejpam-5120	184	5	⊴	⊴	ADP
ejpam-5120	184	6	g	g	NOUN
ejpam-5120	184	7	,	,	PUNCT
ejpam-5120	184	8	we	we	PRON
ejpam-5120	184	9	have	have	VERB
ejpam-5120	184	10	that	that	DET
ejpam-5120	184	11	p	p	NOUN
ejpam-5120	185	1	=	=	X
ejpam-5120	185	2	l1p2	l1p2	AUX
ejpam-5120	185	3	is	be	AUX
ejpam-5120	185	4	a	a	DET
ejpam-5120	185	5	subnormal	subnormal	PROPN
ejpam-5120	185	6	hall	hall	PROPN
ejpam-5120	185	7	subgroup	subgroup	NOUN
ejpam-5120	185	8	of	of	ADP
ejpam-5120	185	9	g	g	PROPN
ejpam-5120	186	1	and	and	CCONJ
ejpam-5120	186	2	so	so	ADV
ejpam-5120	186	3	p	p	NOUN
ejpam-5120	186	4	⊴	⊴	ADP
ejpam-5120	186	5	g	g	PROPN
ejpam-5120	186	6	,	,	PUNCT
ejpam-5120	186	7	a	a	DET
ejpam-5120	186	8	contradiction	contradiction	NOUN
ejpam-5120	186	9	.	.	PUNCT
ejpam-5120	187	1	case	case	NOUN
ejpam-5120	187	2	2	2	NUM
ejpam-5120	187	3	.	.	PUNCT
ejpam-5120	187	4	|p	|p	NOUN
ejpam-5120	187	5	:	:	PUNCT
ejpam-5120	187	6	d|	d|	PROPN
ejpam-5120	187	7	=	=	PUNCT
ejpam-5120	188	1	p.	p.	NOUN
ejpam-5120	188	2	then	then	ADV
ejpam-5120	188	3	,	,	PUNCT
ejpam-5120	188	4	(	(	PUNCT
ejpam-5120	188	5	10	10	NUM
ejpam-5120	188	6	)	)	PUNCT
ejpam-5120	188	7	there	there	PRON
ejpam-5120	188	8	exists	exist	VERB
ejpam-5120	188	9	a	a	DET
ejpam-5120	188	10	maximal	maximal	ADJ
ejpam-5120	188	11	subgroup	subgroup	NOUN
ejpam-5120	188	12	l	l	NOUN
ejpam-5120	188	13	of	of	ADP
ejpam-5120	188	14	p	p	NOUN
ejpam-5120	188	15	with	with	ADP
ejpam-5120	188	16	|l|	|l|	NOUN
ejpam-5120	188	17	=	=	SYM
ejpam-5120	188	18	|d|	|d|	PROPN
ejpam-5120	188	19	such	such	ADJ
ejpam-5120	188	20	that	that	SCONJ
ejpam-5120	188	21	l	l	NOUN
ejpam-5120	188	22	is	be	AUX
ejpam-5120	188	23	not	not	PART
ejpam-5120	188	24	spermutable	spermutable	NOUN
ejpam-5120	188	25	in	in	ADP
ejpam-5120	188	26	g.	g.	PROPN
ejpam-5120	188	27	assume	assume	VERB
ejpam-5120	188	28	that	that	SCONJ
ejpam-5120	188	29	all	all	DET
ejpam-5120	188	30	maximal	maximal	ADJ
ejpam-5120	188	31	subgroups	subgroup	NOUN
ejpam-5120	188	32	l	l	NOUN
ejpam-5120	188	33	of	of	ADP
ejpam-5120	188	34	p	p	NOUN
ejpam-5120	188	35	with	with	ADP
ejpam-5120	188	36	|l|	|l|	NOUN
ejpam-5120	188	37	=	=	SYM
ejpam-5120	188	38	|d|	|d|	PROPN
ejpam-5120	188	39	are	be	AUX
ejpam-5120	188	40	s	s	NOUN
ejpam-5120	188	41	-	-	NOUN
ejpam-5120	188	42	permutable	permutable	ADJ
ejpam-5120	188	43	in	in	ADP
ejpam-5120	188	44	g.	g.	PROPN
ejpam-5120	188	45	then	then	ADV
ejpam-5120	188	46	by	by	ADP
ejpam-5120	188	47	lemma	lemma	PROPN
ejpam-5120	188	48	1	1	NUM
ejpam-5120	188	49	,	,	PUNCT
ejpam-5120	188	50	g	g	NOUN
ejpam-5120	188	51	′	′	NUM
ejpam-5120	188	52	is	be	AUX
ejpam-5120	188	53	p	p	NOUN
ejpam-5120	188	54	-	-	PUNCT
ejpam-5120	188	55	nilpotent	nilpotent	ADJ
ejpam-5120	188	56	,	,	PUNCT
ejpam-5120	188	57	a	a	DET
ejpam-5120	188	58	contradiction	contradiction	NOUN
ejpam-5120	188	59	.	.	PUNCT
ejpam-5120	189	1	(	(	PUNCT
ejpam-5120	189	2	11	11	NUM
ejpam-5120	189	3	)	)	PUNCT
ejpam-5120	189	4	there	there	PRON
ejpam-5120	189	5	exists	exist	VERB
ejpam-5120	189	6	a	a	DET
ejpam-5120	189	7	proper	proper	ADJ
ejpam-5120	189	8	normal	normal	ADJ
ejpam-5120	189	9	subgroup	subgroup	NOUN
ejpam-5120	189	10	m	m	NOUN
ejpam-5120	189	11	of	of	ADP
ejpam-5120	189	12	g	g	PROPN
ejpam-5120	189	13	such	such	ADJ
ejpam-5120	189	14	that	that	SCONJ
ejpam-5120	189	15	|g	|g	PROPN
ejpam-5120	189	16	/	/	SYM
ejpam-5120	189	17	m	m	VERB
ejpam-5120	189	18	|	|	NOUN
ejpam-5120	189	19	=	=	SYM
ejpam-5120	189	20	p	p	NOUN
ejpam-5120	189	21	,	,	PUNCT
ejpam-5120	189	22	g	g	PROPN
ejpam-5120	189	23	=	=	VERB
ejpam-5120	189	24	lt	lt	PRON
ejpam-5120	189	25	,	,	PUNCT
ejpam-5120	189	26	l	l	X
ejpam-5120	189	27	∩	∩	X
ejpam-5120	189	28	t	t	NOUN
ejpam-5120	189	29	=	=	SYM
ejpam-5120	189	30	(	(	PUNCT
ejpam-5120	189	31	l)sg	l)sg	PROPN
ejpam-5120	189	32	,	,	PUNCT
ejpam-5120	189	33	where	where	SCONJ
ejpam-5120	189	34	t	t	PROPN
ejpam-5120	189	35	is	be	AUX
ejpam-5120	189	36	a	a	DET
ejpam-5120	189	37	subnormal	subnormal	ADJ
ejpam-5120	189	38	subgroup	subgroup	NOUN
ejpam-5120	189	39	of	of	ADP
ejpam-5120	189	40	g	g	PROPN
ejpam-5120	189	41	and	and	CCONJ
ejpam-5120	189	42	t	t	PROPN
ejpam-5120	189	43	≤	≤	NUM
ejpam-5120	189	44	m	m	VERB
ejpam-5120	189	45	<	<	X
ejpam-5120	189	46	g.	g.	X
ejpam-5120	189	47	by	by	ADP
ejpam-5120	189	48	(	(	PUNCT
ejpam-5120	189	49	10	10	NUM
ejpam-5120	189	50	)	)	PUNCT
ejpam-5120	189	51	,	,	PUNCT
ejpam-5120	189	52	l	l	NOUN
ejpam-5120	189	53	is	be	AUX
ejpam-5120	189	54	not	not	PART
ejpam-5120	189	55	s	s	NOUN
ejpam-5120	189	56	-	-	NOUN
ejpam-5120	189	57	permutable	permutable	ADJ
ejpam-5120	189	58	in	in	ADP
ejpam-5120	189	59	g.	g.	PROPN
ejpam-5120	189	60	then	then	ADV
ejpam-5120	189	61	by	by	ADP
ejpam-5120	189	62	the	the	DET
ejpam-5120	189	63	hypothesis	hypothesis	NOUN
ejpam-5120	189	64	,	,	PUNCT
ejpam-5120	189	65	l	l	NOUN
ejpam-5120	189	66	is	be	AUX
ejpam-5120	189	67	weakly	weakly	ADJ
ejpam-5120	189	68	s	s	NOUN
ejpam-5120	189	69	-	-	NOUN
ejpam-5120	189	70	permutable	permutable	ADJ
ejpam-5120	189	71	in	in	ADP
ejpam-5120	189	72	g.	g.	PROPN
ejpam-5120	189	73	hence	hence	ADV
ejpam-5120	189	74	there	there	PRON
ejpam-5120	189	75	exists	exist	VERB
ejpam-5120	189	76	a	a	DET
ejpam-5120	189	77	subnormal	subnormal	ADJ
ejpam-5120	189	78	subgroup	subgroup	PROPN
ejpam-5120	189	79	t	t	PROPN
ejpam-5120	189	80	in	in	ADP
ejpam-5120	189	81	g	g	PROPN
ejpam-5120	189	82	such	such	ADJ
ejpam-5120	189	83	that	that	DET
ejpam-5120	189	84	g	g	NOUN
ejpam-5120	189	85	=	=	PUNCT
ejpam-5120	189	86	lt	lt	PROPN
ejpam-5120	189	87	and	and	CCONJ
ejpam-5120	189	88	t	t	PROPN
ejpam-5120	189	89	∩	∩	ADJ
ejpam-5120	189	90	l	l	NOUN
ejpam-5120	189	91	≤	≤	NUM
ejpam-5120	189	92	(	(	PUNCT
ejpam-5120	189	93	l)sg	l)sg	PROPN
ejpam-5120	189	94	̸=	̸=	PROPN
ejpam-5120	189	95	l	l	NOUN
ejpam-5120	189	96	,	,	PUNCT
ejpam-5120	189	97	since	since	SCONJ
ejpam-5120	189	98	l	l	NOUN
ejpam-5120	189	99	is	be	AUX
ejpam-5120	189	100	not	not	PART
ejpam-5120	189	101	weakly	weakly	ADJ
ejpam-5120	189	102	s	s	NOUN
ejpam-5120	189	103	-	-	NOUN
ejpam-5120	189	104	permutable	permutable	ADJ
ejpam-5120	189	105	in	in	ADP
ejpam-5120	189	106	g.	g.	PROPN
ejpam-5120	190	1	so	so	SCONJ
ejpam-5120	190	2	t	t	PROPN
ejpam-5120	190	3	̸=	̸=	PROPN
ejpam-5120	190	4	g	g	PROPN
ejpam-5120	191	1	and	and	CCONJ
ejpam-5120	191	2	there	there	PRON
ejpam-5120	191	3	exists	exist	VERB
ejpam-5120	191	4	a	a	DET
ejpam-5120	191	5	normal	normal	ADJ
ejpam-5120	191	6	subgroup	subgroup	NOUN
ejpam-5120	191	7	m	m	NOUN
ejpam-5120	191	8	of	of	ADP
ejpam-5120	191	9	g	g	PROPN
ejpam-5120	191	10	such	such	ADJ
ejpam-5120	191	11	that	that	SCONJ
ejpam-5120	191	12	|g	|g	PROPN
ejpam-5120	191	13	/	/	SYM
ejpam-5120	191	14	m	m	VERB
ejpam-5120	191	15	|	|	NOUN
ejpam-5120	191	16	=	=	SYM
ejpam-5120	191	17	p	p	PROPN
ejpam-5120	191	18	and	and	CCONJ
ejpam-5120	191	19	t	t	PROPN
ejpam-5120	191	20	≤	≤	NUM
ejpam-5120	191	21	m	m	VERB
ejpam-5120	191	22	<	<	X
ejpam-5120	191	23	g.	g.	PROPN
ejpam-5120	191	24	(	(	PUNCT
ejpam-5120	191	25	12	12	NUM
ejpam-5120	191	26	)	)	PUNCT
ejpam-5120	191	27	(	(	PUNCT
ejpam-5120	191	28	l)sg	l)sg	PROPN
ejpam-5120	191	29	̸=	̸=	PROPN
ejpam-5120	191	30	1	1	NUM
ejpam-5120	191	31	.	.	PUNCT
ejpam-5120	192	1	assume	assume	VERB
ejpam-5120	192	2	that	that	SCONJ
ejpam-5120	192	3	(	(	PUNCT
ejpam-5120	192	4	l)sg	l)sg	NOUN
ejpam-5120	192	5	=	=	SYM
ejpam-5120	192	6	1	1	NUM
ejpam-5120	192	7	.	.	PUNCT
ejpam-5120	193	1	then	then	ADV
ejpam-5120	193	2	,	,	PUNCT
ejpam-5120	193	3	by	by	ADP
ejpam-5120	193	4	(	(	PUNCT
ejpam-5120	193	5	11	11	NUM
ejpam-5120	193	6	)	)	PUNCT
ejpam-5120	193	7	,	,	PUNCT
ejpam-5120	193	8	g	g	NOUN
ejpam-5120	193	9	=	=	SYM
ejpam-5120	193	10	lt	lt	PROPN
ejpam-5120	193	11	and	and	CCONJ
ejpam-5120	193	12	t	t	PROPN
ejpam-5120	193	13	∩	∩	ADJ
ejpam-5120	193	14	l	l	NOUN
ejpam-5120	193	15	=	=	SYM
ejpam-5120	193	16	1	1	NUM
ejpam-5120	193	17	,	,	PUNCT
ejpam-5120	193	18	where	where	SCONJ
ejpam-5120	193	19	t	t	PROPN
ejpam-5120	193	20	is	be	AUX
ejpam-5120	193	21	a	a	DET
ejpam-5120	193	22	subnormal	subnormal	ADJ
ejpam-5120	193	23	subgroup	subgroup	NOUN
ejpam-5120	193	24	of	of	ADP
ejpam-5120	193	25	g	g	PROPN
ejpam-5120	193	26	and	and	CCONJ
ejpam-5120	193	27	there	there	PRON
ejpam-5120	193	28	exists	exist	VERB
ejpam-5120	193	29	a	a	DET
ejpam-5120	193	30	normal	normal	ADJ
ejpam-5120	193	31	subgroup	subgroup	NOUN
ejpam-5120	193	32	m	m	NOUN
ejpam-5120	193	33	of	of	ADP
ejpam-5120	193	34	g	g	PROPN
ejpam-5120	193	35	such	such	ADJ
ejpam-5120	193	36	that	that	SCONJ
ejpam-5120	193	37	|g	|g	PROPN
ejpam-5120	193	38	/	/	SYM
ejpam-5120	193	39	m	m	VERB
ejpam-5120	193	40	|	|	NOUN
ejpam-5120	193	41	=	=	SYM
ejpam-5120	193	42	p	p	PROPN
ejpam-5120	193	43	and	and	CCONJ
ejpam-5120	193	44	t	t	PROPN
ejpam-5120	193	45	≤	≤	NUM
ejpam-5120	193	46	m	m	VERB
ejpam-5120	193	47	<	<	X
ejpam-5120	193	48	g.	g.	PROPN
ejpam-5120	193	49	let	let	VERB
ejpam-5120	193	50	p1	p1	PROPN
ejpam-5120	193	51	be	be	AUX
ejpam-5120	193	52	a	a	DET
ejpam-5120	193	53	sylow	sylow	NOUN
ejpam-5120	193	54	p	p	NOUN
ejpam-5120	193	55	-	-	PUNCT
ejpam-5120	193	56	subgroup	subgroup	NOUN
ejpam-5120	193	57	of	of	ADP
ejpam-5120	193	58	m	m	PROPN
ejpam-5120	193	59	.	.	PUNCT
ejpam-5120	194	1	if	if	SCONJ
ejpam-5120	194	2	p1	p1	PROPN
ejpam-5120	194	3	is	be	AUX
ejpam-5120	194	4	s	s	NOUN
ejpam-5120	194	5	-	-	NOUN
ejpam-5120	194	6	permutable	permutable	ADJ
ejpam-5120	194	7	in	in	ADP
ejpam-5120	194	8	a.	a.	NOUN
ejpam-5120	194	9	a.	a.	NOUN
ejpam-5120	194	10	heliel	heliel	PROPN
ejpam-5120	194	11	et	et	PROPN
ejpam-5120	194	12	al	al	PROPN
ejpam-5120	194	13	.	.	PUNCT
ejpam-5120	194	14	/	/	SYM
ejpam-5120	194	15	eur	eur	PROPN
ejpam-5120	194	16	.	.	PUNCT
ejpam-5120	195	1	j.	j.	PROPN
ejpam-5120	195	2	pure	pure	PROPN
ejpam-5120	195	3	appl	appl	PROPN
ejpam-5120	195	4	.	.	PROPN
ejpam-5120	195	5	math	math	PROPN
ejpam-5120	195	6	,	,	PUNCT
ejpam-5120	195	7	17	17	NUM
ejpam-5120	195	8	(	(	PUNCT
ejpam-5120	195	9	2	2	NUM
ejpam-5120	195	10	)	)	PUNCT
ejpam-5120	195	11	(	(	PUNCT
ejpam-5120	195	12	2024	2024	NUM
ejpam-5120	195	13	)	)	PUNCT
ejpam-5120	195	14	,	,	PUNCT
ejpam-5120	195	15	810	810	NUM
ejpam-5120	195	16	-	-	SYM
ejpam-5120	195	17	818	818	NUM
ejpam-5120	195	18	816	816	NUM
ejpam-5120	195	19	g	g	NOUN
ejpam-5120	195	20	,	,	PUNCT
ejpam-5120	195	21	then	then	ADV
ejpam-5120	195	22	p1	p1	PROPN
ejpam-5120	195	23	⊴	⊴	ADP
ejpam-5120	195	24	g.	g.	PROPN
ejpam-5120	195	25	if	if	SCONJ
ejpam-5120	195	26	φ(p1	φ(p1	NOUN
ejpam-5120	195	27	)	)	PUNCT
ejpam-5120	195	28	̸=	̸=	PROPN
ejpam-5120	195	29	1	1	NUM
ejpam-5120	195	30	,	,	PUNCT
ejpam-5120	195	31	then	then	ADV
ejpam-5120	195	32	g	g	PROPN
ejpam-5120	195	33	/	/	SYM
ejpam-5120	195	34	φ(p1	φ(p1	NOUN
ejpam-5120	195	35	)	)	PUNCT
ejpam-5120	195	36	satisfies	satisfy	VERB
ejpam-5120	195	37	the	the	DET
ejpam-5120	195	38	hypothesis	hypothesis	NOUN
ejpam-5120	195	39	of	of	ADP
ejpam-5120	195	40	the	the	DET
ejpam-5120	195	41	theorem	theorem	NOUN
ejpam-5120	195	42	and	and	CCONJ
ejpam-5120	195	43	hence	hence	ADV
ejpam-5120	195	44	(	(	PUNCT
ejpam-5120	195	45	g	g	NOUN
ejpam-5120	195	46	/	/	SYM
ejpam-5120	195	47	φ(p1	φ(p1	NOUN
ejpam-5120	195	48	)	)	PUNCT
ejpam-5120	195	49	)	)	PUNCT
ejpam-5120	196	1	′	′	VERB
ejpam-5120	197	1	∼=	∼=	ADV
ejpam-5120	197	2	g	g	NOUN
ejpam-5120	197	3	′	′	NUM
ejpam-5120	197	4	/g	/g	PUNCT
ejpam-5120	198	1	′	′	NUM
ejpam-5120	198	2	∩	∩	ADJ
ejpam-5120	198	3	φ(p1	φ(p1	NOUN
ejpam-5120	198	4	)	)	PUNCT
ejpam-5120	198	5	is	be	AUX
ejpam-5120	198	6	p	p	NOUN
ejpam-5120	198	7	-	-	PUNCT
ejpam-5120	198	8	nilpotent	nilpotent	ADJ
ejpam-5120	198	9	by	by	ADP
ejpam-5120	198	10	the	the	DET
ejpam-5120	198	11	choice	choice	NOUN
ejpam-5120	198	12	of	of	ADP
ejpam-5120	198	13	g	g	NOUN
ejpam-5120	198	14	,	,	PUNCT
ejpam-5120	198	15	and	and	CCONJ
ejpam-5120	198	16	since	since	SCONJ
ejpam-5120	198	17	g	g	NOUN
ejpam-5120	198	18	′	′	NUM
ejpam-5120	198	19	∩	∩	ADJ
ejpam-5120	198	20	φ(p1	φ(p1	NOUN
ejpam-5120	198	21	)	)	PUNCT
ejpam-5120	198	22	≤	≤	NOUN
ejpam-5120	198	23	φ(g	φ(g	PROPN
ejpam-5120	198	24	)	)	PUNCT
ejpam-5120	198	25	,	,	PUNCT
ejpam-5120	198	26	we	we	PRON
ejpam-5120	198	27	have	have	VERB
ejpam-5120	198	28	that	that	PRON
ejpam-5120	198	29	g	g	PROPN
ejpam-5120	198	30	′	′	NUM
ejpam-5120	198	31	is	be	AUX
ejpam-5120	198	32	p	p	NOUN
ejpam-5120	198	33	-	-	PUNCT
ejpam-5120	198	34	nilpotent	nilpotent	ADJ
ejpam-5120	198	35	,	,	PUNCT
ejpam-5120	198	36	a	a	DET
ejpam-5120	198	37	contradiction	contradiction	NOUN
ejpam-5120	198	38	.	.	PUNCT
ejpam-5120	199	1	thus	thus	ADV
ejpam-5120	199	2	φ(p1	φ(p1	NOUN
ejpam-5120	199	3	)	)	PUNCT
ejpam-5120	199	4	=	=	SYM
ejpam-5120	200	1	1	1	X
ejpam-5120	200	2	.	.	PUNCT
ejpam-5120	201	1	now	now	ADV
ejpam-5120	201	2	it	it	PRON
ejpam-5120	201	3	is	be	AUX
ejpam-5120	201	4	clear	clear	ADJ
ejpam-5120	201	5	that	that	SCONJ
ejpam-5120	201	6	p1	p1	PROPN
ejpam-5120	201	7	∩	∩	NOUN
ejpam-5120	201	8	t	t	PROPN
ejpam-5120	201	9	is	be	AUX
ejpam-5120	201	10	a	a	DET
ejpam-5120	201	11	normal	normal	ADJ
ejpam-5120	201	12	sylow	sylow	NOUN
ejpam-5120	201	13	p	p	PROPN
ejpam-5120	201	14	-	-	PUNCT
ejpam-5120	201	15	subgroup	subgroup	NOUN
ejpam-5120	201	16	of	of	ADP
ejpam-5120	201	17	t	t	PROPN
ejpam-5120	201	18	of	of	ADP
ejpam-5120	201	19	order	order	NOUN
ejpam-5120	202	1	p.	p.	NOUN
ejpam-5120	202	2	then	then	ADV
ejpam-5120	202	3	t	t	PROPN
ejpam-5120	202	4	/	/	SYM
ejpam-5120	202	5	ct	ct	PROPN
ejpam-5120	202	6	(	(	PUNCT
ejpam-5120	202	7	p1	p1	PROPN
ejpam-5120	202	8	∩	∩	ADJ
ejpam-5120	202	9	t	t	PROPN
ejpam-5120	202	10	)	)	PUNCT
ejpam-5120	202	11	is	be	AUX
ejpam-5120	202	12	abelian	abelian	ADJ
ejpam-5120	202	13	and	and	CCONJ
ejpam-5120	202	14	t	t	NOUN
ejpam-5120	202	15	′	′	NUM
ejpam-5120	202	16	≤	≤	NUM
ejpam-5120	203	1	ct	ct	PROPN
ejpam-5120	203	2	(	(	PUNCT
ejpam-5120	203	3	p1	p1	PROPN
ejpam-5120	203	4	∩	∩	PROPN
ejpam-5120	203	5	t	t	PROPN
ejpam-5120	203	6	)	)	PUNCT
ejpam-5120	203	7	which	which	PRON
ejpam-5120	203	8	implies	imply	VERB
ejpam-5120	203	9	that	that	SCONJ
ejpam-5120	203	10	t	t	NOUN
ejpam-5120	203	11	′	′	NOUN
ejpam-5120	203	12	=	=	SYM
ejpam-5120	203	13	p1	p1	PROPN
ejpam-5120	203	14	∩	∩	PROPN
ejpam-5120	203	15	t	t	PROPN
ejpam-5120	203	16	.	.	PUNCT
ejpam-5120	204	1	by	by	ADP
ejpam-5120	204	2	shur	shur	NOUN
ejpam-5120	204	3	-	-	PUNCT
ejpam-5120	204	4	zassenhaus	zassenhaus	NOUN
ejpam-5120	204	5	theorem	theorem	NOUN
ejpam-5120	204	6	,	,	PUNCT
ejpam-5120	204	7	t	t	NOUN
ejpam-5120	204	8	=	=	SYM
ejpam-5120	204	9	(	(	PUNCT
ejpam-5120	204	10	p1	p1	PROPN
ejpam-5120	204	11	∩	∩	NOUN
ejpam-5120	204	12	t	t	PROPN
ejpam-5120	204	13	)	)	PUNCT
ejpam-5120	204	14	k	k	NOUN
ejpam-5120	204	15	,	,	PUNCT
ejpam-5120	204	16	where	where	SCONJ
ejpam-5120	204	17	k	k	PROPN
ejpam-5120	204	18	is	be	AUX
ejpam-5120	204	19	an	an	DET
ejpam-5120	204	20	abelian	abelian	ADJ
ejpam-5120	204	21	p	p	NOUN
ejpam-5120	204	22	′	′	NUM
ejpam-5120	204	23	-hall	-hall	PROPN
ejpam-5120	204	24	subgroup	subgroup	NOUN
ejpam-5120	204	25	of	of	ADP
ejpam-5120	204	26	t	t	PROPN
ejpam-5120	204	27	.	.	PUNCT
ejpam-5120	205	1	since	since	SCONJ
ejpam-5120	205	2	g	g	NOUN
ejpam-5120	205	3	=	=	NOUN
ejpam-5120	205	4	l(p1	l(p1	NOUN
ejpam-5120	205	5	∩	∩	NOUN
ejpam-5120	205	6	t	t	NOUN
ejpam-5120	205	7	)	)	PUNCT
ejpam-5120	205	8	k	k	PROPN
ejpam-5120	205	9	=	=	SYM
ejpam-5120	205	10	pk	pk	PROPN
ejpam-5120	205	11	,	,	PUNCT
ejpam-5120	205	12	that	that	ADV
ejpam-5120	205	13	is	is	ADV
ejpam-5120	205	14	,	,	PUNCT
ejpam-5120	205	15	g	g	PROPN
ejpam-5120	205	16	is	be	AUX
ejpam-5120	205	17	product	product	NOUN
ejpam-5120	205	18	of	of	ADP
ejpam-5120	205	19	two	two	NUM
ejpam-5120	205	20	nilpotent	nilpotent	ADJ
ejpam-5120	205	21	groups	group	NOUN
ejpam-5120	205	22	,	,	PUNCT
ejpam-5120	205	23	then	then	ADV
ejpam-5120	205	24	g	g	PROPN
ejpam-5120	205	25	is	be	AUX
ejpam-5120	205	26	solvable	solvable	ADJ
ejpam-5120	205	27	by	by	ADP
ejpam-5120	205	28	kegel	kegel	NOUN
ejpam-5120	205	29	-	-	PUNCT
ejpam-5120	205	30	wielandt	wielandt	NOUN
ejpam-5120	205	31	theorem	theorem	VERB
ejpam-5120	205	32	.	.	PUNCT
ejpam-5120	206	1	thus	thus	ADV
ejpam-5120	206	2	p1	p1	PROPN
ejpam-5120	206	3	=	=	SYM
ejpam-5120	206	4	op(g	op(g	X
ejpam-5120	206	5	)	)	PUNCT
ejpam-5120	207	1	=	=	SYM
ejpam-5120	207	2	f	f	X
ejpam-5120	207	3	(	(	PUNCT
ejpam-5120	207	4	g	g	NOUN
ejpam-5120	207	5	)	)	PUNCT
ejpam-5120	207	6	.	.	PUNCT
ejpam-5120	208	1	we	we	PRON
ejpam-5120	208	2	can	can	AUX
ejpam-5120	208	3	assume	assume	VERB
ejpam-5120	208	4	that	that	SCONJ
ejpam-5120	208	5	p	p	PROPN
ejpam-5120	208	6	⋬	⋬	X
ejpam-5120	208	7	g	g	NOUN
ejpam-5120	208	8	(	(	PUNCT
ejpam-5120	208	9	otherwise	otherwise	ADV
ejpam-5120	208	10	,	,	PUNCT
ejpam-5120	208	11	g	g	NOUN
ejpam-5120	208	12	′	′	NOUN
ejpam-5120	208	13	≤	≤	PROPN
ejpam-5120	209	1	p	p	NOUN
ejpam-5120	209	2	,	,	PUNCT
ejpam-5120	209	3	a	a	DET
ejpam-5120	209	4	contradiction	contradiction	NOUN
ejpam-5120	209	5	)	)	PUNCT
ejpam-5120	209	6	.	.	PUNCT
ejpam-5120	210	1	if	if	SCONJ
ejpam-5120	210	2	φ(g	φ(g	NOUN
ejpam-5120	210	3	)	)	PUNCT
ejpam-5120	210	4	̸=	̸=	PROPN
ejpam-5120	210	5	1	1	NUM
ejpam-5120	210	6	,	,	PUNCT
ejpam-5120	210	7	then	then	ADV
ejpam-5120	210	8	φ(g	φ(g	PROPN
ejpam-5120	210	9	)	)	PUNCT
ejpam-5120	210	10	<	<	X
ejpam-5120	210	11	p1	p1	PROPN
ejpam-5120	210	12	=	=	SYM
ejpam-5120	210	13	f	f	PROPN
ejpam-5120	210	14	(	(	PUNCT
ejpam-5120	210	15	g	g	NOUN
ejpam-5120	210	16	)	)	PUNCT
ejpam-5120	210	17	.	.	PUNCT
ejpam-5120	211	1	by	by	ADP
ejpam-5120	211	2	choice	choice	NOUN
ejpam-5120	211	3	of	of	ADP
ejpam-5120	211	4	g	g	NOUN
ejpam-5120	211	5	,	,	PUNCT
ejpam-5120	211	6	(	(	PUNCT
ejpam-5120	211	7	g	g	NOUN
ejpam-5120	211	8	/	/	SYM
ejpam-5120	211	9	φ(g	φ(g	PROPN
ejpam-5120	211	10	)	)	PUNCT
ejpam-5120	211	11	)	)	PUNCT
ejpam-5120	211	12	′	′	NUM
ejpam-5120	212	1	=	=	PUNCT
ejpam-5120	212	2	g	g	NOUN
ejpam-5120	212	3	′	′	NUM
ejpam-5120	212	4	/g	/g	PUNCT
ejpam-5120	213	1	′	′	NUM
ejpam-5120	213	2	∩	∩	NOUN
ejpam-5120	213	3	φ(g	φ(g	NOUN
ejpam-5120	213	4	)	)	PUNCT
ejpam-5120	213	5	is	be	AUX
ejpam-5120	213	6	p	p	NOUN
ejpam-5120	213	7	-	-	PUNCT
ejpam-5120	213	8	nilpotent	nilpotent	ADJ
ejpam-5120	213	9	and	and	CCONJ
ejpam-5120	213	10	so	so	ADV
ejpam-5120	213	11	g	g	NOUN
ejpam-5120	213	12	′	′	NUM
ejpam-5120	213	13	is	be	AUX
ejpam-5120	213	14	p	p	NOUN
ejpam-5120	213	15	-	-	PUNCT
ejpam-5120	213	16	nilpotent	nilpotent	ADJ
ejpam-5120	213	17	,	,	PUNCT
ejpam-5120	213	18	a	a	DET
ejpam-5120	213	19	contradiction	contradiction	NOUN
ejpam-5120	213	20	.	.	PUNCT
ejpam-5120	214	1	thus	thus	ADV
ejpam-5120	214	2	φ(g	φ(g	NOUN
ejpam-5120	214	3	)	)	PUNCT
ejpam-5120	214	4	=	=	SYM
ejpam-5120	215	1	1	1	X
ejpam-5120	215	2	.	.	PUNCT
ejpam-5120	215	3	then	then	ADV
ejpam-5120	215	4	p1	p1	PROPN
ejpam-5120	215	5	=	=	SYM
ejpam-5120	215	6	f	f	PROPN
ejpam-5120	215	7	(	(	PUNCT
ejpam-5120	215	8	g	g	NOUN
ejpam-5120	215	9	)	)	PUNCT
ejpam-5120	215	10	a	a	DET
ejpam-5120	215	11	direct	direct	ADJ
ejpam-5120	215	12	product	product	NOUN
ejpam-5120	215	13	of	of	ADP
ejpam-5120	215	14	minimal	minimal	ADJ
ejpam-5120	215	15	normal	normal	ADJ
ejpam-5120	215	16	subgroups	subgroup	NOUN
ejpam-5120	215	17	of	of	ADP
ejpam-5120	215	18	g.	g.	PROPN
ejpam-5120	215	19	hence	hence	ADV
ejpam-5120	215	20	,	,	PUNCT
ejpam-5120	215	21	if	if	SCONJ
ejpam-5120	215	22	l1	l1	PROPN
ejpam-5120	215	23	and	and	CCONJ
ejpam-5120	215	24	l2	l2	NOUN
ejpam-5120	215	25	are	be	AUX
ejpam-5120	215	26	two	two	NUM
ejpam-5120	215	27	distinct	distinct	ADJ
ejpam-5120	215	28	minimal	minimal	ADJ
ejpam-5120	215	29	normal	normal	ADJ
ejpam-5120	215	30	subgroups	subgroup	NOUN
ejpam-5120	215	31	of	of	ADP
ejpam-5120	215	32	g	g	NOUN
ejpam-5120	215	33	,	,	PUNCT
ejpam-5120	215	34	then	then	ADV
ejpam-5120	215	35	(	(	PUNCT
ejpam-5120	215	36	g	g	NOUN
ejpam-5120	215	37	/	/	SYM
ejpam-5120	215	38	l1	l1	PROPN
ejpam-5120	215	39	)	)	PUNCT
ejpam-5120	215	40	′	′	PUNCT
ejpam-5120	216	1	and	and	CCONJ
ejpam-5120	216	2	(	(	PUNCT
ejpam-5120	216	3	g	g	NOUN
ejpam-5120	216	4	/	/	SYM
ejpam-5120	216	5	l2	l2	NOUN
ejpam-5120	216	6	)	)	PUNCT
ejpam-5120	216	7	′	′	NUM
ejpam-5120	216	8	are	be	AUX
ejpam-5120	216	9	p	p	NOUN
ejpam-5120	216	10	-	-	PUNCT
ejpam-5120	216	11	nilpotent	nilpotent	ADJ
ejpam-5120	216	12	by	by	ADP
ejpam-5120	216	13	choice	choice	NOUN
ejpam-5120	216	14	of	of	ADP
ejpam-5120	216	15	g	g	NOUN
ejpam-5120	216	16	and	and	CCONJ
ejpam-5120	216	17	so	so	ADV
ejpam-5120	216	18	g	g	NOUN
ejpam-5120	216	19	′	′	NUM
ejpam-5120	216	20	is	be	AUX
ejpam-5120	216	21	p	p	NOUN
ejpam-5120	216	22	-	-	PUNCT
ejpam-5120	216	23	nilpotent	nilpotent	ADJ
ejpam-5120	216	24	,	,	PUNCT
ejpam-5120	216	25	a	a	DET
ejpam-5120	216	26	contradiction	contradiction	NOUN
ejpam-5120	216	27	.	.	PUNCT
ejpam-5120	217	1	thus	thus	ADV
ejpam-5120	217	2	p1	p1	PROPN
ejpam-5120	217	3	=	=	SYM
ejpam-5120	217	4	op(g	op(g	X
ejpam-5120	217	5	)	)	PUNCT
ejpam-5120	217	6	=	=	SYM
ejpam-5120	218	1	f	f	X
ejpam-5120	218	2	(	(	PUNCT
ejpam-5120	218	3	g	g	NOUN
ejpam-5120	218	4	)	)	PUNCT
ejpam-5120	218	5	is	be	AUX
ejpam-5120	218	6	the	the	DET
ejpam-5120	218	7	unique	unique	ADJ
ejpam-5120	218	8	minimal	minimal	ADJ
ejpam-5120	218	9	normal	normal	ADJ
ejpam-5120	218	10	subgroups	subgroup	NOUN
ejpam-5120	218	11	of	of	ADP
ejpam-5120	218	12	g	g	NOUN
ejpam-5120	218	13	by	by	ADP
ejpam-5120	218	14	[	[	X
ejpam-5120	218	15	2	2	NUM
ejpam-5120	218	16	,	,	PUNCT
ejpam-5120	218	17	a	a	DET
ejpam-5120	218	18	,	,	PUNCT
ejpam-5120	218	19	14.3	14.3	NUM
ejpam-5120	218	20	]	]	PUNCT
ejpam-5120	218	21	,	,	PUNCT
ejpam-5120	218	22	p1	p1	PROPN
ejpam-5120	218	23	≤	≤	NOUN
ejpam-5120	218	24	ng(t	ng(t	PUNCT
ejpam-5120	218	25	)	)	PUNCT
ejpam-5120	218	26	which	which	PRON
ejpam-5120	218	27	implies	imply	VERB
ejpam-5120	218	28	that	that	SCONJ
ejpam-5120	218	29	t	t	PROPN
ejpam-5120	218	30	⊴	⊴	ADP
ejpam-5120	218	31	m	m	PROPN
ejpam-5120	218	32	.	.	PUNCT
ejpam-5120	219	1	now	now	ADV
ejpam-5120	219	2	as	as	SCONJ
ejpam-5120	219	3	g	g	PROPN
ejpam-5120	219	4	is	be	AUX
ejpam-5120	219	5	solvable	solvable	ADJ
ejpam-5120	219	6	,	,	PUNCT
ejpam-5120	219	7	g	g	PROPN
ejpam-5120	219	8	contains	contain	VERB
ejpam-5120	219	9	a	a	DET
ejpam-5120	219	10	hall	hall	PROPN
ejpam-5120	219	11	subgroup	subgroup	PROPN
ejpam-5120	219	12	pq	pq	PROPN
ejpam-5120	219	13	,	,	PUNCT
ejpam-5120	219	14	where	where	SCONJ
ejpam-5120	219	15	q	q	NOUN
ejpam-5120	219	16	is	be	AUX
ejpam-5120	219	17	a	a	DET
ejpam-5120	219	18	sylow	sylow	NOUN
ejpam-5120	219	19	q	q	NOUN
ejpam-5120	219	20	-	-	NOUN
ejpam-5120	219	21	subgroup	subgroup	NOUN
ejpam-5120	219	22	of	of	ADP
ejpam-5120	219	23	g	g	PROPN
ejpam-5120	219	24	and	and	CCONJ
ejpam-5120	219	25	p	p	PROPN
ejpam-5120	219	26	̸=	̸=	PROPN
ejpam-5120	219	27	q.	q.	NOUN
ejpam-5120	219	28	hence	hence	ADV
ejpam-5120	219	29	,	,	PUNCT
ejpam-5120	219	30	if	if	SCONJ
ejpam-5120	219	31	p	p	PRON
ejpam-5120	219	32	<	<	X
ejpam-5120	219	33	q	q	X
ejpam-5120	219	34	,	,	PUNCT
ejpam-5120	219	35	pq	pq	PROPN
ejpam-5120	219	36	is	be	AUX
ejpam-5120	219	37	p	p	NOUN
ejpam-5120	219	38	-	-	PUNCT
ejpam-5120	219	39	nilpotent	nilpotent	ADJ
ejpam-5120	219	40	and	and	CCONJ
ejpam-5120	219	41	so	so	ADV
ejpam-5120	219	42	q	q	ADJ
ejpam-5120	219	43	≤	≤	NUM
ejpam-5120	219	44	cg(f	cg(f	PUNCT
ejpam-5120	219	45	(	(	PUNCT
ejpam-5120	219	46	g	g	NOUN
ejpam-5120	219	47	)	)	PUNCT
ejpam-5120	219	48	)	)	PUNCT
ejpam-5120	220	1	≤	≤	NUM
ejpam-5120	220	2	f	f	X
ejpam-5120	220	3	(	(	PUNCT
ejpam-5120	220	4	g	g	NOUN
ejpam-5120	220	5	)	)	PUNCT
ejpam-5120	220	6	,	,	PUNCT
ejpam-5120	220	7	a	a	DET
ejpam-5120	220	8	contradiction	contradiction	NOUN
ejpam-5120	220	9	.	.	PUNCT
ejpam-5120	221	1	thus	thus	ADV
ejpam-5120	221	2	p	p	X
ejpam-5120	221	3	is	be	AUX
ejpam-5120	221	4	the	the	DET
ejpam-5120	221	5	largest	large	ADJ
ejpam-5120	221	6	prime	prime	ADJ
ejpam-5120	221	7	dividing	dividing	NOUN
ejpam-5120	221	8	|g|	|g|	PROPN
ejpam-5120	221	9	.	.	PUNCT
ejpam-5120	222	1	now	now	ADV
ejpam-5120	222	2	t	t	PROPN
ejpam-5120	222	3	=	=	SYM
ejpam-5120	222	4	(	(	PUNCT
ejpam-5120	222	5	p1	p1	PROPN
ejpam-5120	222	6	∩	∩	NOUN
ejpam-5120	222	7	t	t	PROPN
ejpam-5120	222	8	)	)	PUNCT
ejpam-5120	223	1	k	k	PROPN
ejpam-5120	223	2	and	and	CCONJ
ejpam-5120	223	3	k	k	PROPN
ejpam-5120	223	4	is	be	AUX
ejpam-5120	223	5	not	not	PART
ejpam-5120	223	6	normal	normal	ADJ
ejpam-5120	223	7	in	in	ADP
ejpam-5120	223	8	t	t	PROPN
ejpam-5120	223	9	=	=	SYM
ejpam-5120	223	10	(	(	PUNCT
ejpam-5120	223	11	p1	p1	PROPN
ejpam-5120	223	12	∩	∩	NOUN
ejpam-5120	223	13	t	t	PROPN
ejpam-5120	223	14	)	)	PUNCT
ejpam-5120	224	1	k	k	NOUN
ejpam-5120	224	2	,	,	PUNCT
ejpam-5120	224	3	otherwise	otherwise	ADV
ejpam-5120	224	4	k	k	PROPN
ejpam-5120	224	5	⊴	⊴	PROPN
ejpam-5120	224	6	t	t	PROPN
ejpam-5120	224	7	⊴	⊴	ADP
ejpam-5120	224	8	m	m	PROPN
ejpam-5120	224	9	,	,	PUNCT
ejpam-5120	224	10	that	that	ADV
ejpam-5120	224	11	is	is	ADV
ejpam-5120	224	12	,	,	PUNCT
ejpam-5120	224	13	k	k	PROPN
ejpam-5120	224	14	≤	≤	NUM
ejpam-5120	224	15	op′	op′	X
ejpam-5120	224	16	(	(	PUNCT
ejpam-5120	224	17	g	g	NOUN
ejpam-5120	224	18	)	)	PUNCT
ejpam-5120	224	19	=	=	SYM
ejpam-5120	224	20	1	1	NUM
ejpam-5120	224	21	,	,	PUNCT
ejpam-5120	224	22	a	a	DET
ejpam-5120	224	23	contradiction	contradiction	NOUN
ejpam-5120	224	24	.	.	PUNCT
ejpam-5120	225	1	hence	hence	ADV
ejpam-5120	225	2	t	t	PROPN
ejpam-5120	225	3	is	be	AUX
ejpam-5120	225	4	a	a	DET
ejpam-5120	225	5	frobenius	frobenius	ADJ
ejpam-5120	225	6	group	group	NOUN
ejpam-5120	225	7	and	and	CCONJ
ejpam-5120	225	8	so	so	ADV
ejpam-5120	225	9	k	k	PROPN
ejpam-5120	225	10	is	be	AUX
ejpam-5120	225	11	cyclic	cyclic	ADJ
ejpam-5120	225	12	which	which	PRON
ejpam-5120	225	13	implies	imply	VERB
ejpam-5120	225	14	that	that	SCONJ
ejpam-5120	225	15	p	p	NOUN
ejpam-5120	225	16	⊴	⊴	ADP
ejpam-5120	225	17	g	g	PROPN
ejpam-5120	225	18	,	,	PUNCT
ejpam-5120	225	19	a	a	DET
ejpam-5120	225	20	contradiction	contradiction	NOUN
ejpam-5120	225	21	.	.	PUNCT
ejpam-5120	226	1	thus	thus	ADV
ejpam-5120	226	2	p1	p1	NOUN
ejpam-5120	226	3	is	be	AUX
ejpam-5120	226	4	not	not	PART
ejpam-5120	226	5	s	s	NOUN
ejpam-5120	226	6	-	-	NOUN
ejpam-5120	226	7	permutable	permutable	ADJ
ejpam-5120	226	8	in	in	ADP
ejpam-5120	226	9	g.	g.	NOUN
ejpam-5120	226	10	by	by	ADP
ejpam-5120	226	11	the	the	DET
ejpam-5120	226	12	hypothesis	hypothesis	NOUN
ejpam-5120	226	13	,	,	PUNCT
ejpam-5120	226	14	p1	p1	PROPN
ejpam-5120	226	15	is	be	AUX
ejpam-5120	226	16	weakly	weakly	ADJ
ejpam-5120	226	17	s	s	NOUN
ejpam-5120	226	18	-	-	NOUN
ejpam-5120	226	19	permutable	permutable	ADJ
ejpam-5120	226	20	in	in	ADP
ejpam-5120	226	21	g.	g.	PROPN
ejpam-5120	226	22	then	then	ADV
ejpam-5120	226	23	there	there	PRON
ejpam-5120	226	24	exists	exist	VERB
ejpam-5120	226	25	a	a	DET
ejpam-5120	226	26	subnormal	subnormal	ADJ
ejpam-5120	226	27	subgroup	subgroup	NOUN
ejpam-5120	226	28	k1	k1	PROPN
ejpam-5120	226	29	of	of	ADP
ejpam-5120	226	30	g	g	PROPN
ejpam-5120	226	31	such	such	ADJ
ejpam-5120	226	32	that	that	SCONJ
ejpam-5120	226	33	g	g	NOUN
ejpam-5120	226	34	=	=	SYM
ejpam-5120	226	35	p1k1	p1k1	NOUN
ejpam-5120	226	36	and	and	CCONJ
ejpam-5120	226	37	p1	p1	PROPN
ejpam-5120	226	38	∩	∩	NOUN
ejpam-5120	226	39	k1	k1	NOUN
ejpam-5120	226	40	≤	≤	NUM
ejpam-5120	226	41	(	(	PUNCT
ejpam-5120	226	42	p1)sg	p1)sg	NOUN
ejpam-5120	226	43	<	<	X
ejpam-5120	226	44	p1	p1	PROPN
ejpam-5120	226	45	.	.	PUNCT
ejpam-5120	227	1	hence	hence	ADV
ejpam-5120	227	2	,	,	PUNCT
ejpam-5120	227	3	if	if	SCONJ
ejpam-5120	227	4	(	(	PUNCT
ejpam-5120	227	5	p1)sg	p1)sg	NOUN
ejpam-5120	227	6	=	=	SYM
ejpam-5120	227	7	1	1	NUM
ejpam-5120	227	8	,	,	PUNCT
ejpam-5120	227	9	then	then	ADV
ejpam-5120	227	10	g	g	PROPN
ejpam-5120	227	11	=	=	PUNCT
ejpam-5120	227	12	p1k1	p1k1	PROPN
ejpam-5120	227	13	and	and	CCONJ
ejpam-5120	227	14	p1	p1	PROPN
ejpam-5120	227	15	∩k1	∩k1	PART
ejpam-5120	228	1	=	=	SYM
ejpam-5120	228	2	1	1	X
ejpam-5120	228	3	.	.	PUNCT
ejpam-5120	229	1	clearly	clearly	ADV
ejpam-5120	229	2	,	,	PUNCT
ejpam-5120	229	3	m	m	VERB
ejpam-5120	229	4	=	=	X
ejpam-5120	229	5	p1(m	p1(m	PROPN
ejpam-5120	229	6	∩k1	∩k1	PRON
ejpam-5120	229	7	)	)	PUNCT
ejpam-5120	229	8	and	and	CCONJ
ejpam-5120	229	9	m	m	PROPN
ejpam-5120	229	10	∩k1	∩k1	VERB
ejpam-5120	229	11	is	be	AUX
ejpam-5120	229	12	subnormal	subnormal	ADJ
ejpam-5120	229	13	in	in	ADP
ejpam-5120	229	14	g.	g.	PROPN
ejpam-5120	229	15	since	since	SCONJ
ejpam-5120	229	16	m	m	PROPN
ejpam-5120	229	17	∩k1	∩k1	VERB
ejpam-5120	229	18	is	be	AUX
ejpam-5120	229	19	a	a	DET
ejpam-5120	229	20	p	p	NOUN
ejpam-5120	229	21	′	′	NUM
ejpam-5120	229	22	-group	-group	NOUN
ejpam-5120	229	23	,	,	PUNCT
ejpam-5120	229	24	we	we	PRON
ejpam-5120	229	25	have	have	VERB
ejpam-5120	229	26	m	m	PROPN
ejpam-5120	229	27	∩k1	∩k1	VERB
ejpam-5120	229	28	≤	≤	NUM
ejpam-5120	229	29	op′	op′	X
ejpam-5120	230	1	(	(	PUNCT
ejpam-5120	230	2	g	g	NOUN
ejpam-5120	230	3	)	)	PUNCT
ejpam-5120	230	4	=	=	SYM
ejpam-5120	230	5	1	1	NUM
ejpam-5120	230	6	by	by	ADP
ejpam-5120	230	7	(	(	PUNCT
ejpam-5120	230	8	1	1	NUM
ejpam-5120	230	9	)	)	PUNCT
ejpam-5120	230	10	,	,	PUNCT
ejpam-5120	230	11	that	that	ADV
ejpam-5120	230	12	is	is	ADV
ejpam-5120	230	13	,	,	PUNCT
ejpam-5120	230	14	m	m	VERB
ejpam-5120	230	15	∩k1	∩k1	NOUN
ejpam-5120	230	16	=	=	SYM
ejpam-5120	230	17	1	1	NUM
ejpam-5120	230	18	which	which	PRON
ejpam-5120	230	19	means	mean	VERB
ejpam-5120	230	20	that	that	SCONJ
ejpam-5120	230	21	p1	p1	NOUN
ejpam-5120	230	22	⊴	⊴	ADP
ejpam-5120	230	23	g	g	PROPN
ejpam-5120	230	24	,	,	PUNCT
ejpam-5120	230	25	a	a	DET
ejpam-5120	230	26	contradiction	contradiction	NOUN
ejpam-5120	230	27	.	.	PUNCT
ejpam-5120	231	1	thus	thus	ADV
ejpam-5120	231	2	we	we	PRON
ejpam-5120	231	3	may	may	AUX
ejpam-5120	231	4	assume	assume	VERB
ejpam-5120	231	5	that	that	SCONJ
ejpam-5120	231	6	(	(	PUNCT
ejpam-5120	231	7	p1)sg	p1)sg	NOUN
ejpam-5120	231	8	̸=	̸=	PROPN
ejpam-5120	231	9	1	1	NUM
ejpam-5120	231	10	.	.	PUNCT
ejpam-5120	232	1	then	then	ADV
ejpam-5120	232	2	(	(	PUNCT
ejpam-5120	232	3	p1)sg	p1)sg	NOUN
ejpam-5120	232	4	≤	≤	NOUN
ejpam-5120	232	5	op(g	op(g	PUNCT
ejpam-5120	232	6	)	)	PUNCT
ejpam-5120	232	7	̸=	̸=	PROPN
ejpam-5120	232	8	1	1	NUM
ejpam-5120	232	9	.	.	PUNCT
ejpam-5120	232	10	assume	assume	VERB
ejpam-5120	232	11	that	that	SCONJ
ejpam-5120	232	12	φ(op(g	φ(op(g	ADP
ejpam-5120	232	13	)	)	PUNCT
ejpam-5120	232	14	)	)	PUNCT
ejpam-5120	233	1	̸=	̸=	PROPN
ejpam-5120	233	2	1	1	NUM
ejpam-5120	233	3	.	.	PUNCT
ejpam-5120	234	1	then	then	ADV
ejpam-5120	234	2	g	g	PROPN
ejpam-5120	234	3	′	′	NUM
ejpam-5120	234	4	/g	/g	PUNCT
ejpam-5120	235	1	′	′	NUM
ejpam-5120	235	2	∩	∩	NOUN
ejpam-5120	235	3	φ(op(g	φ(op(g	ADP
ejpam-5120	235	4	)	)	PUNCT
ejpam-5120	235	5	)	)	PUNCT
ejpam-5120	235	6	is	be	AUX
ejpam-5120	235	7	p	p	NOUN
ejpam-5120	235	8	-	-	PUNCT
ejpam-5120	235	9	nilpotent	nilpotent	ADJ
ejpam-5120	235	10	by	by	ADP
ejpam-5120	235	11	the	the	DET
ejpam-5120	235	12	choice	choice	NOUN
ejpam-5120	235	13	of	of	ADP
ejpam-5120	235	14	g	g	NOUN
ejpam-5120	236	1	and	and	CCONJ
ejpam-5120	236	2	so	so	ADV
ejpam-5120	236	3	g	g	NOUN
ejpam-5120	236	4	′	′	NUM
ejpam-5120	236	5	is	be	AUX
ejpam-5120	236	6	p	p	NOUN
ejpam-5120	236	7	-	-	PUNCT
ejpam-5120	236	8	nilpotent	nilpotent	ADJ
ejpam-5120	236	9	,	,	PUNCT
ejpam-5120	236	10	a	a	DET
ejpam-5120	236	11	contradiction	contradiction	NOUN
ejpam-5120	236	12	.	.	PUNCT
ejpam-5120	237	1	thus	thus	ADV
ejpam-5120	237	2	φ(op(g	φ(op(g	ADP
ejpam-5120	237	3	)	)	PUNCT
ejpam-5120	237	4	)	)	PUNCT
ejpam-5120	238	1	=	=	SYM
ejpam-5120	238	2	1	1	NUM
ejpam-5120	238	3	and	and	CCONJ
ejpam-5120	238	4	so	so	ADV
ejpam-5120	238	5	op(g	op(g	PUNCT
ejpam-5120	238	6	)	)	PUNCT
ejpam-5120	239	1	=	=	SYM
ejpam-5120	239	2	f	f	X
ejpam-5120	239	3	(	(	PUNCT
ejpam-5120	239	4	g	g	NOUN
ejpam-5120	239	5	)	)	PUNCT
ejpam-5120	239	6	is	be	AUX
ejpam-5120	239	7	elementary	elementary	ADJ
ejpam-5120	239	8	abelian	abelian	PROPN
ejpam-5120	239	9	.	.	PUNCT
ejpam-5120	240	1	assume	assume	VERB
ejpam-5120	240	2	that	that	SCONJ
ejpam-5120	240	3	φ(op(g	φ(op(g	ADP
ejpam-5120	240	4	)	)	PUNCT
ejpam-5120	240	5	)	)	PUNCT
ejpam-5120	240	6	≰	≰	PROPN
ejpam-5120	240	7	m	m	PRON
ejpam-5120	240	8	.	.	PUNCT
ejpam-5120	241	1	if	if	SCONJ
ejpam-5120	241	2	op(g	op(g	NUM
ejpam-5120	241	3	)	)	PUNCT
ejpam-5120	241	4	<	<	X
ejpam-5120	241	5	|d|	|d|	PROPN
ejpam-5120	241	6	,	,	PUNCT
ejpam-5120	241	7	then	then	ADV
ejpam-5120	241	8	g	g	PROPN
ejpam-5120	241	9	′	′	NUM
ejpam-5120	241	10	/g	/g	PUNCT
ejpam-5120	241	11	′	′	NUM
ejpam-5120	241	12	∩	∩	NOUN
ejpam-5120	241	13	φ(op(g	φ(op(g	ADP
ejpam-5120	241	14	)	)	PUNCT
ejpam-5120	241	15	)	)	PUNCT
ejpam-5120	242	1	=	=	PUNCT
ejpam-5120	243	1	g	g	NOUN
ejpam-5120	243	2	′	′	NOUN
ejpam-5120	243	3	is	be	AUX
ejpam-5120	243	4	p	p	NOUN
ejpam-5120	243	5	-	-	PUNCT
ejpam-5120	243	6	nilpotent	nilpotent	ADJ
ejpam-5120	243	7	by	by	ADP
ejpam-5120	243	8	the	the	DET
ejpam-5120	243	9	choice	choice	NOUN
ejpam-5120	243	10	of	of	ADP
ejpam-5120	243	11	g	g	NOUN
ejpam-5120	243	12	,	,	PUNCT
ejpam-5120	243	13	a	a	DET
ejpam-5120	243	14	contradiction	contradiction	NOUN
ejpam-5120	243	15	.	.	PUNCT
ejpam-5120	244	1	thus	thus	ADV
ejpam-5120	244	2	op(g	op(g	PUNCT
ejpam-5120	244	3	)	)	PUNCT
ejpam-5120	244	4	=	=	SYM
ejpam-5120	244	5	|d|	|d|	PROPN
ejpam-5120	244	6	.	.	PUNCT
ejpam-5120	245	1	so	so	ADV
ejpam-5120	245	2	op(g	op(g	PUNCT
ejpam-5120	245	3	)	)	PUNCT
ejpam-5120	246	1	∩m	∩m	PUNCT
ejpam-5120	247	1	=	=	PUNCT
ejpam-5120	247	2	1	1	NUM
ejpam-5120	247	3	which	which	PRON
ejpam-5120	247	4	means	mean	VERB
ejpam-5120	247	5	that	that	SCONJ
ejpam-5120	247	6	|p	|p	PROPN
ejpam-5120	247	7	|	|	NOUN
ejpam-5120	247	8	=	=	SYM
ejpam-5120	247	9	p2	p2	PROPN
ejpam-5120	247	10	and	and	CCONJ
ejpam-5120	247	11	op(g	op(g	NUM
ejpam-5120	247	12	)	)	PUNCT
ejpam-5120	248	1	=	=	SYM
ejpam-5120	248	2	|d|	|d|	PROPN
ejpam-5120	248	3	=	=	SYM
ejpam-5120	248	4	p	p	PROPN
ejpam-5120	248	5	and	and	CCONJ
ejpam-5120	248	6	this	this	DET
ejpam-5120	248	7	contradiction	contradiction	NOUN
ejpam-5120	248	8	(	(	PUNCT
ejpam-5120	248	9	2	2	NUM
ejpam-5120	248	10	)	)	PUNCT
ejpam-5120	248	11	.	.	PUNCT
ejpam-5120	249	1	thus	thus	ADV
ejpam-5120	249	2	op(g	op(g	X
ejpam-5120	249	3	)	)	PUNCT
ejpam-5120	249	4	≤	≤	NUM
ejpam-5120	249	5	m	m	PROPN
ejpam-5120	249	6	and	and	CCONJ
ejpam-5120	249	7	op(g	op(g	NUM
ejpam-5120	249	8	)	)	PUNCT
ejpam-5120	249	9	is	be	AUX
ejpam-5120	249	10	a	a	DET
ejpam-5120	249	11	sylow	sylow	NOUN
ejpam-5120	249	12	p	p	NOUN
ejpam-5120	249	13	-	-	PUNCT
ejpam-5120	249	14	subgroup	subgroup	NOUN
ejpam-5120	249	15	of	of	ADP
ejpam-5120	249	16	m	m	PROPN
ejpam-5120	249	17	and	and	CCONJ
ejpam-5120	249	18	op(g	op(g	NUM
ejpam-5120	249	19	)	)	PUNCT
ejpam-5120	249	20	=	=	SYM
ejpam-5120	249	21	p1	p1	PROPN
ejpam-5120	249	22	,	,	PUNCT
ejpam-5120	249	23	a	a	DET
ejpam-5120	249	24	contradiction	contradiction	NOUN
ejpam-5120	249	25	as	as	ADP
ejpam-5120	249	26	p1	p1	NOUN
ejpam-5120	249	27	is	be	AUX
ejpam-5120	249	28	not	not	PART
ejpam-5120	249	29	s	s	NOUN
ejpam-5120	249	30	-	-	NOUN
ejpam-5120	249	31	permutable	permutable	ADJ
ejpam-5120	249	32	in	in	ADP
ejpam-5120	249	33	g.	g.	PROPN
ejpam-5120	249	34	thus	thus	ADV
ejpam-5120	249	35	(	(	PUNCT
ejpam-5120	249	36	l)sg	l)sg	PROPN
ejpam-5120	249	37	̸=	̸=	PROPN
ejpam-5120	249	38	1	1	NUM
ejpam-5120	249	39	.	.	PUNCT
ejpam-5120	250	1	(	(	PUNCT
ejpam-5120	250	2	13	13	NUM
ejpam-5120	250	3	)	)	PUNCT
ejpam-5120	250	4	finishing	finish	VERB
ejpam-5120	250	5	the	the	DET
ejpam-5120	250	6	proof	proof	NOUN
ejpam-5120	250	7	of	of	ADP
ejpam-5120	250	8	case	case	NOUN
ejpam-5120	250	9	2	2	NUM
ejpam-5120	250	10	.	.	PUNCT
ejpam-5120	251	1	by	by	ADP
ejpam-5120	251	2	(	(	PUNCT
ejpam-5120	251	3	12	12	NUM
ejpam-5120	251	4	)	)	PUNCT
ejpam-5120	251	5	,	,	PUNCT
ejpam-5120	251	6	(	(	PUNCT
ejpam-5120	251	7	l)sg	l)sg	PROPN
ejpam-5120	251	8	̸=	̸=	PROPN
ejpam-5120	251	9	1	1	NUM
ejpam-5120	251	10	.	.	PUNCT
ejpam-5120	252	1	then	then	ADV
ejpam-5120	252	2	(	(	PUNCT
ejpam-5120	252	3	l)sg	l)sg	PROPN
ejpam-5120	252	4	≤	≤	PROPN
ejpam-5120	252	5	op(g	op(g	PUNCT
ejpam-5120	252	6	)	)	PUNCT
ejpam-5120	252	7	̸=	̸=	PROPN
ejpam-5120	252	8	1	1	NUM
ejpam-5120	252	9	.	.	PUNCT
ejpam-5120	252	10	assume	assume	VERB
ejpam-5120	252	11	that	that	SCONJ
ejpam-5120	252	12	φ(op(g	φ(op(g	ADP
ejpam-5120	252	13	)	)	PUNCT
ejpam-5120	252	14	)	)	PUNCT
ejpam-5120	253	1	̸=	̸=	PROPN
ejpam-5120	253	2	1	1	NUM
ejpam-5120	253	3	.	.	PUNCT
ejpam-5120	254	1	then	then	ADV
ejpam-5120	254	2	g	g	PROPN
ejpam-5120	254	3	′	′	NUM
ejpam-5120	254	4	/g	/g	PUNCT
ejpam-5120	254	5	′∩	′∩	PROPN
ejpam-5120	254	6	φ(op(g	φ(op(g	PROPN
ejpam-5120	254	7	)	)	PUNCT
ejpam-5120	254	8	)	)	PUNCT
ejpam-5120	254	9	is	be	AUX
ejpam-5120	254	10	p	p	NOUN
ejpam-5120	254	11	-	-	PUNCT
ejpam-5120	254	12	nilpotent	nilpotent	ADJ
ejpam-5120	254	13	by	by	ADP
ejpam-5120	254	14	the	the	DET
ejpam-5120	254	15	choice	choice	NOUN
ejpam-5120	254	16	of	of	ADP
ejpam-5120	254	17	g	g	NOUN
ejpam-5120	254	18	,	,	PUNCT
ejpam-5120	254	19	and	and	CCONJ
ejpam-5120	254	20	so	so	ADV
ejpam-5120	254	21	g	g	NOUN
ejpam-5120	254	22	′	′	NUM
ejpam-5120	254	23	is	be	AUX
ejpam-5120	254	24	p	p	NOUN
ejpam-5120	254	25	-	-	PUNCT
ejpam-5120	254	26	nilpotent	nilpotent	ADJ
ejpam-5120	254	27	,	,	PUNCT
ejpam-5120	254	28	a	a	DET
ejpam-5120	254	29	contradiction	contradiction	NOUN
ejpam-5120	254	30	.	.	PUNCT
ejpam-5120	255	1	thus	thus	ADV
ejpam-5120	255	2	φ(op(g	φ(op(g	ADP
ejpam-5120	255	3	)	)	PUNCT
ejpam-5120	255	4	)	)	PUNCT
ejpam-5120	256	1	=	=	SYM
ejpam-5120	256	2	1	1	NUM
ejpam-5120	256	3	,	,	PUNCT
ejpam-5120	256	4	and	and	CCONJ
ejpam-5120	256	5	so	so	ADV
ejpam-5120	256	6	op(g	op(g	PUNCT
ejpam-5120	256	7	)	)	PUNCT
ejpam-5120	256	8	is	be	AUX
ejpam-5120	256	9	elementary	elementary	ADJ
ejpam-5120	256	10	abelian	abelian	NOUN
ejpam-5120	256	11	.	.	PUNCT
ejpam-5120	257	1	if	if	SCONJ
ejpam-5120	257	2	op(g	op(g	NUM
ejpam-5120	257	3	)	)	PUNCT
ejpam-5120	257	4	<	<	X
ejpam-5120	257	5	|d|	|d|	PROPN
ejpam-5120	257	6	,	,	PUNCT
ejpam-5120	257	7	then	then	ADV
ejpam-5120	257	8	g	g	PROPN
ejpam-5120	257	9	′	′	NUM
ejpam-5120	257	10	/g	/g	PUNCT
ejpam-5120	258	1	′	′	NUM
ejpam-5120	258	2	∩op(g	∩op(g	NOUN
ejpam-5120	258	3	)	)	PUNCT
ejpam-5120	258	4	is	be	AUX
ejpam-5120	258	5	p	p	NOUN
ejpam-5120	258	6	-	-	PUNCT
ejpam-5120	258	7	nilpotent	nilpotent	ADJ
ejpam-5120	258	8	by	by	ADP
ejpam-5120	258	9	the	the	DET
ejpam-5120	258	10	choice	choice	NOUN
ejpam-5120	258	11	of	of	ADP
ejpam-5120	258	12	g	g	PROPN
ejpam-5120	258	13	and	and	CCONJ
ejpam-5120	258	14	so	so	ADV
ejpam-5120	258	15	g	g	PROPN
ejpam-5120	258	16	is	be	AUX
ejpam-5120	258	17	p	p	NOUN
ejpam-5120	258	18	-	-	PUNCT
ejpam-5120	258	19	solvable	solvable	ADJ
ejpam-5120	258	20	.	.	PUNCT
ejpam-5120	259	1	since	since	SCONJ
ejpam-5120	259	2	op′	op′	PROPN
ejpam-5120	259	3	(	(	PUNCT
ejpam-5120	259	4	g	g	NOUN
ejpam-5120	259	5	)	)	PUNCT
ejpam-5120	259	6	=	=	SYM
ejpam-5120	259	7	1	1	NUM
ejpam-5120	259	8	by	by	ADP
ejpam-5120	259	9	(	(	PUNCT
ejpam-5120	259	10	1	1	NUM
ejpam-5120	259	11	)	)	PUNCT
ejpam-5120	259	12	,	,	PUNCT
ejpam-5120	259	13	we	we	PRON
ejpam-5120	259	14	have	have	VERB
ejpam-5120	259	15	,	,	PUNCT
ejpam-5120	259	16	by	by	ADP
ejpam-5120	259	17	lemma	lemma	PROPN
ejpam-5120	259	18	8	8	NUM
ejpam-5120	259	19	,	,	PUNCT
ejpam-5120	259	20	that	that	DET
ejpam-5120	259	21	cg(op(g	cg(op(g	NOUN
ejpam-5120	259	22	)	)	PUNCT
ejpam-5120	259	23	)	)	PUNCT
ejpam-5120	260	1	=	=	SYM
ejpam-5120	260	2	op(g	op(g	NUM
ejpam-5120	260	3	)	)	PUNCT
ejpam-5120	260	4	.	.	PUNCT
ejpam-5120	261	1	if	if	SCONJ
ejpam-5120	261	2	op(g	op(g	NUM
ejpam-5120	261	3	)	)	PUNCT
ejpam-5120	261	4	∩	∩	NOUN
ejpam-5120	261	5	φ(g	φ(g	ADJ
ejpam-5120	261	6	)	)	PUNCT
ejpam-5120	261	7	̸=	̸=	PROPN
ejpam-5120	261	8	1	1	NUM
ejpam-5120	261	9	,	,	PUNCT
ejpam-5120	261	10	then	then	ADV
ejpam-5120	261	11	g	g	PROPN
ejpam-5120	261	12	′	′	NUM
ejpam-5120	261	13	is	be	AUX
ejpam-5120	261	14	p	p	NOUN
ejpam-5120	261	15	-	-	PUNCT
ejpam-5120	261	16	nilpotent	nilpotent	ADJ
ejpam-5120	261	17	,	,	PUNCT
ejpam-5120	261	18	a	a	DET
ejpam-5120	261	19	contradiction	contradiction	NOUN
ejpam-5120	261	20	.	.	PUNCT
ejpam-5120	262	1	thus	thus	ADV
ejpam-5120	262	2	op(g	op(g	PUNCT
ejpam-5120	262	3	)	)	PUNCT
ejpam-5120	262	4	is	be	AUX
ejpam-5120	262	5	the	the	DET
ejpam-5120	262	6	unique	unique	ADJ
ejpam-5120	262	7	minimal	minimal	ADJ
ejpam-5120	262	8	normal	normal	ADJ
ejpam-5120	262	9	subgroups	subgroup	NOUN
ejpam-5120	262	10	of	of	ADP
ejpam-5120	262	11	g.	g.	PROPN
ejpam-5120	262	12	since	since	SCONJ
ejpam-5120	262	13	m	m	PROPN
ejpam-5120	262	14	⊴	⊴	ADP
ejpam-5120	262	15	g	g	PROPN
ejpam-5120	262	16	,	,	PUNCT
ejpam-5120	262	17	we	we	PRON
ejpam-5120	262	18	have	have	VERB
ejpam-5120	262	19	op(g	op(g	NOUN
ejpam-5120	262	20	)	)	PUNCT
ejpam-5120	262	21	∩	∩	NOUN
ejpam-5120	262	22	m	m	NOUN
ejpam-5120	262	23	=	=	SYM
ejpam-5120	262	24	1	1	NUM
ejpam-5120	262	25	or	or	CCONJ
ejpam-5120	262	26	op(g	op(g	NUM
ejpam-5120	262	27	)	)	PUNCT
ejpam-5120	262	28	≤	≤	NUM
ejpam-5120	262	29	m	m	NOUN
ejpam-5120	262	30	.	.	PUNCT
ejpam-5120	263	1	if	if	SCONJ
ejpam-5120	263	2	op(g	op(g	NUM
ejpam-5120	263	3	)	)	PUNCT
ejpam-5120	263	4	∩	∩	NOUN
ejpam-5120	263	5	m	m	NOUN
ejpam-5120	263	6	=	=	SYM
ejpam-5120	263	7	1	1	NUM
ejpam-5120	263	8	,	,	PUNCT
ejpam-5120	263	9	then	then	ADV
ejpam-5120	263	10	g	g	PROPN
ejpam-5120	263	11	′	′	NUM
ejpam-5120	263	12	is	be	AUX
ejpam-5120	263	13	p	p	NOUN
ejpam-5120	263	14	-	-	PUNCT
ejpam-5120	263	15	nilpotent	nilpotent	ADJ
ejpam-5120	263	16	,	,	PUNCT
ejpam-5120	263	17	a	a	DET
ejpam-5120	263	18	contradiction	contradiction	NOUN
ejpam-5120	263	19	.	.	PUNCT
ejpam-5120	264	1	assume	assume	VERB
ejpam-5120	264	2	that	that	SCONJ
ejpam-5120	264	3	op(g	op(g	X
ejpam-5120	264	4	)	)	PUNCT
ejpam-5120	264	5	≤	≤	NUM
ejpam-5120	264	6	m	m	NOUN
ejpam-5120	264	7	and	and	CCONJ
ejpam-5120	264	8	let	let	VERB
ejpam-5120	264	9	p1	p1	PROPN
ejpam-5120	264	10	be	be	AUX
ejpam-5120	264	11	a	a	DET
ejpam-5120	264	12	sylow	sylow	NOUN
ejpam-5120	264	13	p	p	NOUN
ejpam-5120	264	14	-	-	PUNCT
ejpam-5120	264	15	subgroup	subgroup	NOUN
ejpam-5120	264	16	of	of	ADP
ejpam-5120	264	17	m	m	PROPN
ejpam-5120	264	18	.	.	PUNCT
ejpam-5120	265	1	by	by	ADP
ejpam-5120	265	2	hypothesis	hypothesis	NOUN
ejpam-5120	265	3	,	,	PUNCT
ejpam-5120	265	4	p1	p1	PROPN
ejpam-5120	265	5	is	be	AUX
ejpam-5120	265	6	weakly	weakly	ADJ
ejpam-5120	265	7	s	s	NOUN
ejpam-5120	265	8	-	-	NOUN
ejpam-5120	265	9	permutable	permutable	ADJ
ejpam-5120	265	10	in	in	ADP
ejpam-5120	265	11	g.	g.	PROPN
ejpam-5120	265	12	then	then	ADV
ejpam-5120	265	13	there	there	PRON
ejpam-5120	265	14	exists	exist	VERB
ejpam-5120	265	15	a	a	DET
ejpam-5120	265	16	subnormal	subnormal	ADJ
ejpam-5120	265	17	subgroup	subgroup	PROPN
ejpam-5120	265	18	k1	k1	PROPN
ejpam-5120	265	19	references	reference	NOUN
ejpam-5120	265	20	817	817	NUM
ejpam-5120	265	21	of	of	ADP
ejpam-5120	265	22	g	g	PRON
ejpam-5120	265	23	such	such	ADJ
ejpam-5120	265	24	that	that	SCONJ
ejpam-5120	265	25	g	g	NOUN
ejpam-5120	265	26	=	=	SYM
ejpam-5120	265	27	p1k1	p1k1	NOUN
ejpam-5120	265	28	and	and	CCONJ
ejpam-5120	265	29	p1	p1	PROPN
ejpam-5120	265	30	∩	∩	NOUN
ejpam-5120	265	31	k1	k1	NOUN
ejpam-5120	265	32	≤	≤	NUM
ejpam-5120	265	33	(	(	PUNCT
ejpam-5120	265	34	p1)sg	p1)sg	NOUN
ejpam-5120	265	35	≤	≤	PROPN
ejpam-5120	265	36	p1	p1	NOUN
ejpam-5120	265	37	.	.	PUNCT
ejpam-5120	266	1	if	if	SCONJ
ejpam-5120	266	2	(	(	PUNCT
ejpam-5120	266	3	p1)sg	p1)sg	NOUN
ejpam-5120	266	4	=	=	SYM
ejpam-5120	266	5	p1	p1	PROPN
ejpam-5120	266	6	,	,	PUNCT
ejpam-5120	266	7	then	then	ADV
ejpam-5120	266	8	p	p	NOUN
ejpam-5120	266	9	⊴	⊴	ADP
ejpam-5120	266	10	g	g	PROPN
ejpam-5120	266	11	and	and	CCONJ
ejpam-5120	266	12	this	this	PRON
ejpam-5120	266	13	means	mean	VERB
ejpam-5120	266	14	that	that	SCONJ
ejpam-5120	266	15	op(g	op(g	PUNCT
ejpam-5120	266	16	)	)	PUNCT
ejpam-5120	266	17	=	=	SYM
ejpam-5120	266	18	p1	p1	PROPN
ejpam-5120	266	19	,	,	PUNCT
ejpam-5120	266	20	a	a	DET
ejpam-5120	266	21	contradiction	contradiction	NOUN
ejpam-5120	266	22	.	.	PUNCT
ejpam-5120	267	1	thus	thus	ADV
ejpam-5120	267	2	(	(	PUNCT
ejpam-5120	267	3	p1)sg	p1)sg	NOUN
ejpam-5120	267	4	<	<	X
ejpam-5120	267	5	p1	p1	PROPN
ejpam-5120	267	6	.	.	PUNCT
ejpam-5120	268	1	if	if	SCONJ
ejpam-5120	268	2	(	(	PUNCT
ejpam-5120	268	3	p1)sg	p1)sg	NOUN
ejpam-5120	268	4	=	=	SYM
ejpam-5120	268	5	1	1	NUM
ejpam-5120	268	6	,	,	PUNCT
ejpam-5120	268	7	then	then	ADV
ejpam-5120	268	8	p1	p1	NOUN
ejpam-5120	268	9	∩k1	∩k1	X
ejpam-5120	269	1	=	=	SYM
ejpam-5120	269	2	1	1	NUM
ejpam-5120	269	3	which	which	PRON
ejpam-5120	269	4	implies	imply	VERB
ejpam-5120	269	5	that	that	PRON
ejpam-5120	269	6	op(g	op(g	PUNCT
ejpam-5120	269	7	)	)	PUNCT
ejpam-5120	270	1	∩k1	∩k1	PUNCT
ejpam-5120	271	1	=	=	SYM
ejpam-5120	271	2	1	1	NUM
ejpam-5120	271	3	and	and	CCONJ
ejpam-5120	271	4	so	so	ADV
ejpam-5120	271	5	op(g)k1	op(g)k1	PROPN
ejpam-5120	272	1	=	=	SYM
ejpam-5120	272	2	op(g)×k1	op(g)×k1	NOUN
ejpam-5120	272	3	,	,	PUNCT
ejpam-5120	272	4	a	a	DET
ejpam-5120	272	5	contradiction	contradiction	NOUN
ejpam-5120	272	6	.	.	PUNCT
ejpam-5120	273	1	thus	thus	ADV
ejpam-5120	273	2	we	we	PRON
ejpam-5120	273	3	may	may	AUX
ejpam-5120	273	4	assume	assume	VERB
ejpam-5120	273	5	that	that	SCONJ
ejpam-5120	273	6	(	(	PUNCT
ejpam-5120	273	7	p1)sg	p1)sg	NOUN
ejpam-5120	273	8	̸=	̸=	PROPN
ejpam-5120	273	9	1	1	NUM
ejpam-5120	273	10	.	.	PUNCT
ejpam-5120	274	1	then	then	ADV
ejpam-5120	274	2	(	(	PUNCT
ejpam-5120	274	3	p1)sg	p1)sg	NOUN
ejpam-5120	274	4	≤	≤	PROPN
ejpam-5120	274	5	op(g	op(g	NUM
ejpam-5120	274	6	)	)	PUNCT
ejpam-5120	274	7	.	.	PUNCT
ejpam-5120	275	1	we	we	PRON
ejpam-5120	275	2	agrue	agrue	VERB
ejpam-5120	275	3	that	that	SCONJ
ejpam-5120	275	4	φ(g	φ(g	NOUN
ejpam-5120	275	5	)	)	PUNCT
ejpam-5120	275	6	=	=	SYM
ejpam-5120	276	1	1	1	X
ejpam-5120	276	2	.	.	X
ejpam-5120	277	1	if	if	SCONJ
ejpam-5120	277	2	not	not	PART
ejpam-5120	277	3	,	,	PUNCT
ejpam-5120	277	4	op(g	op(g	NOUN
ejpam-5120	277	5	)	)	PUNCT
ejpam-5120	278	1	≤	≤	NUM
ejpam-5120	278	2	φ(g	φ(g	PROPN
ejpam-5120	278	3	)	)	PUNCT
ejpam-5120	278	4	which	which	PRON
ejpam-5120	278	5	means	mean	VERB
ejpam-5120	278	6	that	that	SCONJ
ejpam-5120	279	1	g	g	PROPN
ejpam-5120	279	2	′	′	NUM
ejpam-5120	279	3	/g	/g	PUNCT
ejpam-5120	280	1	′	′	NUM
ejpam-5120	280	2	∩	∩	NOUN
ejpam-5120	280	3	φ(g	φ(g	NOUN
ejpam-5120	280	4	)	)	PUNCT
ejpam-5120	280	5	is	be	AUX
ejpam-5120	280	6	p	p	NOUN
ejpam-5120	280	7	-	-	PUNCT
ejpam-5120	280	8	nilpotent	nilpotent	ADJ
ejpam-5120	280	9	and	and	CCONJ
ejpam-5120	280	10	so	so	ADV
ejpam-5120	280	11	g	g	NOUN
ejpam-5120	280	12	′	′	NUM
ejpam-5120	280	13	is	be	AUX
ejpam-5120	280	14	p	p	NOUN
ejpam-5120	280	15	-	-	PUNCT
ejpam-5120	280	16	nilpotent	nilpotent	ADJ
ejpam-5120	280	17	,	,	PUNCT
ejpam-5120	280	18	a	a	DET
ejpam-5120	280	19	contradiction	contradiction	NOUN
ejpam-5120	280	20	.	.	PUNCT
ejpam-5120	281	1	thus	thus	ADV
ejpam-5120	281	2	φ(g	φ(g	NOUN
ejpam-5120	281	3	)	)	PUNCT
ejpam-5120	281	4	=	=	SYM
ejpam-5120	282	1	1	1	X
ejpam-5120	282	2	.	.	PUNCT
ejpam-5120	282	3	then	then	ADV
ejpam-5120	282	4	there	there	PRON
ejpam-5120	282	5	exists	exist	VERB
ejpam-5120	282	6	a	a	DET
ejpam-5120	282	7	maximal	maximal	ADJ
ejpam-5120	282	8	subgroup	subgroup	NOUN
ejpam-5120	282	9	s	s	PROPN
ejpam-5120	282	10	of	of	ADP
ejpam-5120	282	11	g	g	NOUN
ejpam-5120	283	1	such	such	ADJ
ejpam-5120	283	2	that	that	SCONJ
ejpam-5120	283	3	g	g	PROPN
ejpam-5120	283	4	=	=	SYM
ejpam-5120	283	5	op(g)s	op(g)s	PROPN
ejpam-5120	283	6	,	,	PUNCT
ejpam-5120	283	7	op(g	op(g	NUM
ejpam-5120	283	8	)	)	PUNCT
ejpam-5120	283	9	∩	∩	NOUN
ejpam-5120	283	10	s	s	PART
ejpam-5120	283	11	=	=	SYM
ejpam-5120	283	12	1	1	X
ejpam-5120	283	13	.	.	PUNCT
ejpam-5120	284	1	we	we	PRON
ejpam-5120	284	2	agrue	agrue	VERB
ejpam-5120	284	3	that	that	PRON
ejpam-5120	284	4	op(g	op(g	PUNCT
ejpam-5120	284	5	)	)	PUNCT
ejpam-5120	284	6	≰	≰	PROPN
ejpam-5120	284	7	k1	k1	NOUN
ejpam-5120	284	8	.	.	PUNCT
ejpam-5120	285	1	if	if	SCONJ
ejpam-5120	285	2	not	not	PART
ejpam-5120	285	3	,	,	PUNCT
ejpam-5120	285	4	op(g	op(g	NOUN
ejpam-5120	285	5	)	)	PUNCT
ejpam-5120	286	1	≤	≤	NUM
ejpam-5120	286	2	k1	k1	NOUN
ejpam-5120	286	3	.	.	PUNCT
ejpam-5120	287	1	then	then	ADV
ejpam-5120	287	2	there	there	PRON
ejpam-5120	287	3	exists	exist	VERB
ejpam-5120	287	4	a	a	DET
ejpam-5120	287	5	maximal	maximal	ADJ
ejpam-5120	287	6	subgroup	subgroup	NOUN
ejpam-5120	287	7	v	v	NOUN
ejpam-5120	287	8	of	of	ADP
ejpam-5120	287	9	p	p	PRON
ejpam-5120	287	10	such	such	ADJ
ejpam-5120	287	11	that	that	PRON
ejpam-5120	287	12	op(g	op(g	NUM
ejpam-5120	287	13	)	)	PUNCT
ejpam-5120	287	14	≰	≰	PROPN
ejpam-5120	287	15	v	v	NOUN
ejpam-5120	287	16	(	(	PUNCT
ejpam-5120	287	17	because	because	SCONJ
ejpam-5120	287	18	if	if	SCONJ
ejpam-5120	287	19	every	every	DET
ejpam-5120	287	20	a	a	DET
ejpam-5120	287	21	maximal	maximal	ADJ
ejpam-5120	287	22	subgroup	subgroup	NOUN
ejpam-5120	287	23	v	v	NOUN
ejpam-5120	287	24	of	of	ADP
ejpam-5120	287	25	p	p	NOUN
ejpam-5120	287	26	containing	contain	VERB
ejpam-5120	287	27	op(g	op(g	PUNCT
ejpam-5120	287	28	)	)	PUNCT
ejpam-5120	287	29	,	,	PUNCT
ejpam-5120	287	30	then	then	ADV
ejpam-5120	287	31	op(g	op(g	PUNCT
ejpam-5120	287	32	)	)	PUNCT
ejpam-5120	287	33	≤	≤	NUM
ejpam-5120	287	34	φ(p	φ(p	PROPN
ejpam-5120	287	35	)	)	PUNCT
ejpam-5120	288	1	and	and	CCONJ
ejpam-5120	288	2	so	so	ADV
ejpam-5120	288	3	p	p	NOUN
ejpam-5120	288	4	=	=	NOUN
ejpam-5120	288	5	op(g)(p	op(g)(p	NOUN
ejpam-5120	288	6	∩	∩	NOUN
ejpam-5120	288	7	s	s	PART
ejpam-5120	288	8	)	)	PUNCT
ejpam-5120	288	9	=	=	SYM
ejpam-5120	288	10	φ(p	φ(p	PROPN
ejpam-5120	288	11	)	)	PUNCT
ejpam-5120	289	1	(	(	PUNCT
ejpam-5120	289	2	p	p	NOUN
ejpam-5120	289	3	∩	∩	X
ejpam-5120	289	4	s	s	PART
ejpam-5120	289	5	)	)	PUNCT
ejpam-5120	289	6	=	=	SYM
ejpam-5120	289	7	φ(p	φ(p	PROPN
ejpam-5120	289	8	)	)	PUNCT
ejpam-5120	289	9	and	and	CCONJ
ejpam-5120	289	10	this	this	PRON
ejpam-5120	289	11	is	be	AUX
ejpam-5120	289	12	impossible	impossible	ADJ
ejpam-5120	289	13	)	)	PUNCT
ejpam-5120	289	14	.	.	PUNCT
ejpam-5120	290	1	this	this	DET
ejpam-5120	290	2	v	v	NOUN
ejpam-5120	290	3	is	be	AUX
ejpam-5120	290	4	not	not	PART
ejpam-5120	290	5	s	s	NOUN
ejpam-5120	290	6	-	-	NOUN
ejpam-5120	290	7	permutable	permutable	ADJ
ejpam-5120	290	8	in	in	ADP
ejpam-5120	290	9	g	g	PROPN
ejpam-5120	290	10	and	and	CCONJ
ejpam-5120	290	11	so	so	ADV
ejpam-5120	290	12	v	v	NOUN
ejpam-5120	290	13	is	be	AUX
ejpam-5120	290	14	weakly	weakly	ADJ
ejpam-5120	290	15	s	s	NOUN
ejpam-5120	290	16	-	-	NOUN
ejpam-5120	290	17	permutable	permutable	ADJ
ejpam-5120	290	18	in	in	ADP
ejpam-5120	290	19	g.	g.	PROPN
ejpam-5120	290	20	then	then	ADV
ejpam-5120	290	21	there	there	PRON
ejpam-5120	290	22	exists	exist	VERB
ejpam-5120	290	23	a	a	DET
ejpam-5120	290	24	subnormal	subnormal	ADJ
ejpam-5120	290	25	subgroup	subgroup	PROPN
ejpam-5120	290	26	t	t	PROPN
ejpam-5120	290	27	of	of	ADP
ejpam-5120	290	28	g	g	PROPN
ejpam-5120	290	29	such	such	ADJ
ejpam-5120	290	30	that	that	SCONJ
ejpam-5120	290	31	g	g	PROPN
ejpam-5120	290	32	=	=	SYM
ejpam-5120	290	33	v	v	ADP
ejpam-5120	290	34	t	t	NOUN
ejpam-5120	290	35	and	and	CCONJ
ejpam-5120	290	36	v	v	ADP
ejpam-5120	290	37	∩	∩	NOUN
ejpam-5120	290	38	t	t	NOUN
ejpam-5120	290	39	≤	≤	NUM
ejpam-5120	290	40	(	(	PUNCT
ejpam-5120	290	41	v	v	NOUN
ejpam-5120	290	42	)	)	PUNCT
ejpam-5120	290	43	sg	sg	PROPN
ejpam-5120	290	44	.	.	PUNCT
ejpam-5120	291	1	then	then	ADV
ejpam-5120	291	2	(	(	PUNCT
ejpam-5120	291	3	v	v	NOUN
ejpam-5120	291	4	)	)	PUNCT
ejpam-5120	291	5	sg	sg	ADP
ejpam-5120	291	6	≤	≤	NUM
ejpam-5120	291	7	op(g	op(g	PUNCT
ejpam-5120	291	8	)	)	PUNCT
ejpam-5120	291	9	and	and	CCONJ
ejpam-5120	291	10	this	this	PRON
ejpam-5120	291	11	implies	imply	VERB
ejpam-5120	291	12	that	that	SCONJ
ejpam-5120	291	13	v	v	NUM
ejpam-5120	291	14	∩	∩	NOUN
ejpam-5120	291	15	t	t	NOUN
ejpam-5120	291	16	≤	≤	NOUN
ejpam-5120	291	17	v	v	ADP
ejpam-5120	291	18	∩	∩	NOUN
ejpam-5120	291	19	op(g	op(g	NUM
ejpam-5120	291	20	)	)	PUNCT
ejpam-5120	291	21	≤	≤	NOUN
ejpam-5120	291	22	v	v	ADP
ejpam-5120	291	23	∩	∩	ADJ
ejpam-5120	291	24	t	t	NOUN
ejpam-5120	291	25	.	.	PUNCT
ejpam-5120	292	1	thus	thus	ADV
ejpam-5120	292	2	v	v	ADP
ejpam-5120	292	3	∩	∩	NOUN
ejpam-5120	292	4	op(g	op(g	NUM
ejpam-5120	292	5	)	)	PUNCT
ejpam-5120	292	6	=	=	SYM
ejpam-5120	292	7	v	v	NUM
ejpam-5120	292	8	∩	∩	PROPN
ejpam-5120	292	9	t	t	NOUN
ejpam-5120	292	10	and	and	CCONJ
ejpam-5120	292	11	v	v	ADP
ejpam-5120	292	12	∩	∩	NOUN
ejpam-5120	292	13	t	t	NOUN
ejpam-5120	292	14	≤	≤	NUM
ejpam-5120	292	15	(	(	PUNCT
ejpam-5120	292	16	v	v	NOUN
ejpam-5120	292	17	)	)	PUNCT
ejpam-5120	292	18	sg	sg	ADP
ejpam-5120	292	19	≤	≤	NUM
ejpam-5120	292	20	v	v	ADP
ejpam-5120	292	21	∩op(g	∩op(g	NOUN
ejpam-5120	292	22	)	)	PUNCT
ejpam-5120	292	23	.	.	PUNCT
ejpam-5120	293	1	now	now	ADV
ejpam-5120	293	2	v	v	ADP
ejpam-5120	293	3	∩op(g	∩op(g	NOUN
ejpam-5120	293	4	)	)	PUNCT
ejpam-5120	293	5	=	=	PUNCT
ejpam-5120	293	6	(	(	PUNCT
ejpam-5120	293	7	v	v	NOUN
ejpam-5120	293	8	)	)	PUNCT
ejpam-5120	293	9	sg	sg	PROPN
ejpam-5120	293	10	is	be	AUX
ejpam-5120	293	11	normal	normal	ADJ
ejpam-5120	293	12	in	in	ADP
ejpam-5120	293	13	p	p	PROPN
ejpam-5120	293	14	and	and	CCONJ
ejpam-5120	293	15	(	(	PUNCT
ejpam-5120	293	16	v	v	NOUN
ejpam-5120	293	17	)	)	PUNCT
ejpam-5120	293	18	sg	sg	PROPN
ejpam-5120	293	19	is	be	AUX
ejpam-5120	293	20	s	s	NOUN
ejpam-5120	293	21	-	-	NOUN
ejpam-5120	293	22	permutable	permutable	ADJ
ejpam-5120	293	23	in	in	ADP
ejpam-5120	293	24	g	g	PROPN
ejpam-5120	293	25	implies	imply	VERB
ejpam-5120	293	26	that	that	SCONJ
ejpam-5120	293	27	(	(	PUNCT
ejpam-5120	293	28	v	v	NOUN
ejpam-5120	293	29	)	)	PUNCT
ejpam-5120	293	30	sg	sg	PROPN
ejpam-5120	293	31	⊴	⊴	PROPN
ejpam-5120	293	32	g.	g.	PROPN
ejpam-5120	293	33	hence	hence	ADV
ejpam-5120	293	34	v	v	ADP
ejpam-5120	293	35	∩	∩	NOUN
ejpam-5120	293	36	t	t	NOUN
ejpam-5120	293	37	=	=	SYM
ejpam-5120	293	38	(	(	PUNCT
ejpam-5120	293	39	v	v	NOUN
ejpam-5120	293	40	)	)	PUNCT
ejpam-5120	293	41	sg	sg	ADP
ejpam-5120	293	42	≤	≤	NUM
ejpam-5120	293	43	op(g	op(g	NUM
ejpam-5120	293	44	)	)	PUNCT
ejpam-5120	293	45	≤	≤	NOUN
ejpam-5120	293	46	v	v	NOUN
ejpam-5120	293	47	,	,	PUNCT
ejpam-5120	293	48	a	a	DET
ejpam-5120	293	49	contradiction	contradiction	NOUN
ejpam-5120	293	50	(	(	PUNCT
ejpam-5120	293	51	note	note	VERB
ejpam-5120	293	52	that	that	SCONJ
ejpam-5120	293	53	(	(	PUNCT
ejpam-5120	293	54	v	v	NOUN
ejpam-5120	293	55	)	)	PUNCT
ejpam-5120	293	56	sg	sg	ADP
ejpam-5120	293	57	̸=	̸=	PROPN
ejpam-5120	293	58	1	1	NUM
ejpam-5120	293	59	because	because	SCONJ
ejpam-5120	293	60	if	if	SCONJ
ejpam-5120	293	61	(	(	PUNCT
ejpam-5120	293	62	v	v	NOUN
ejpam-5120	293	63	)	)	PUNCT
ejpam-5120	293	64	sg	sg	NOUN
ejpam-5120	293	65	=	=	SYM
ejpam-5120	293	66	1	1	NUM
ejpam-5120	293	67	,	,	PUNCT
ejpam-5120	293	68	then	then	ADV
ejpam-5120	293	69	op(g	op(g	PUNCT
ejpam-5120	293	70	)	)	PUNCT
ejpam-5120	293	71	=	=	SYM
ejpam-5120	294	1	p	p	NOUN
ejpam-5120	294	2	and	and	CCONJ
ejpam-5120	294	3	g	g	NOUN
ejpam-5120	294	4	/	/	SYM
ejpam-5120	294	5	cg(op(g	cg(op(g	NOUN
ejpam-5120	294	6	)	)	PUNCT
ejpam-5120	294	7	)	)	PUNCT
ejpam-5120	294	8	is	be	AUX
ejpam-5120	294	9	abelian	abelian	ADJ
ejpam-5120	294	10	which	which	PRON
ejpam-5120	294	11	means	mean	VERB
ejpam-5120	294	12	g	g	NOUN
ejpam-5120	294	13	′	′	NOUN
ejpam-5120	294	14	≤	≤	NUM
ejpam-5120	294	15	cg(op(g	cg(op(g	NOUN
ejpam-5120	294	16	)	)	PUNCT
ejpam-5120	294	17	)	)	PUNCT
ejpam-5120	295	1	and	and	CCONJ
ejpam-5120	295	2	since	since	SCONJ
ejpam-5120	295	3	g	g	PROPN
ejpam-5120	295	4	′	′	NUM
ejpam-5120	295	5	/g	/g	PUNCT
ejpam-5120	295	6	′	′	NUM
ejpam-5120	295	7	∩	∩	NOUN
ejpam-5120	295	8	op(g	op(g	NUM
ejpam-5120	295	9	)	)	PUNCT
ejpam-5120	295	10	is	be	AUX
ejpam-5120	295	11	p	p	NOUN
ejpam-5120	295	12	-	-	PUNCT
ejpam-5120	295	13	nilpotent	nilpotent	ADJ
ejpam-5120	295	14	,	,	PUNCT
ejpam-5120	295	15	it	it	PRON
ejpam-5120	295	16	follows	follow	VERB
ejpam-5120	295	17	that	that	SCONJ
ejpam-5120	295	18	g	g	PROPN
ejpam-5120	295	19	′	′	NUM
ejpam-5120	295	20	is	be	AUX
ejpam-5120	295	21	p	p	NOUN
ejpam-5120	295	22	-	-	PUNCT
ejpam-5120	295	23	nilpotent	nilpotent	ADJ
ejpam-5120	295	24	,	,	PUNCT
ejpam-5120	295	25	a	a	DET
ejpam-5120	295	26	contradiction	contradiction	NOUN
ejpam-5120	295	27	)	)	PUNCT
ejpam-5120	295	28	.	.	PUNCT
ejpam-5120	296	1	thus	thus	ADV
ejpam-5120	296	2	op(g	op(g	X
ejpam-5120	296	3	)	)	PUNCT
ejpam-5120	296	4	≰	≰	PROPN
ejpam-5120	296	5	k1	k1	NOUN
ejpam-5120	296	6	and	and	CCONJ
ejpam-5120	296	7	g/(k1)g	g/(k1)g	NOUN
ejpam-5120	296	8	is	be	AUX
ejpam-5120	296	9	a	a	DET
ejpam-5120	296	10	p	p	NOUN
ejpam-5120	296	11	-	-	PUNCT
ejpam-5120	296	12	group	group	NOUN
ejpam-5120	296	13	and	and	CCONJ
ejpam-5120	296	14	since	since	SCONJ
ejpam-5120	296	15	g	g	PROPN
ejpam-5120	296	16	′	′	NUM
ejpam-5120	296	17	/g	/g	PUNCT
ejpam-5120	297	1	′	′	NUM
ejpam-5120	297	2	∩	∩	NOUN
ejpam-5120	297	3	op(g	op(g	NUM
ejpam-5120	297	4	)	)	PUNCT
ejpam-5120	297	5	is	be	AUX
ejpam-5120	297	6	p	p	NOUN
ejpam-5120	297	7	-	-	PUNCT
ejpam-5120	297	8	nilpotent	nilpotent	ADJ
ejpam-5120	297	9	,	,	PUNCT
ejpam-5120	297	10	a	a	DET
ejpam-5120	297	11	contradiction	contradiction	NOUN
ejpam-5120	297	12	.	.	PUNCT
ejpam-5120	298	1	now	now	ADV
ejpam-5120	298	2	we	we	PRON
ejpam-5120	298	3	can	can	AUX
ejpam-5120	298	4	assume	assume	VERB
ejpam-5120	298	5	that	that	SCONJ
ejpam-5120	298	6	|op(g)|	|op(g)|	NOUN
ejpam-5120	298	7	=	=	PROPN
ejpam-5120	298	8	|d|	|d|	PROPN
ejpam-5120	298	9	.	.	PUNCT
ejpam-5120	299	1	then	then	ADV
ejpam-5120	299	2	op(g	op(g	PUNCT
ejpam-5120	299	3	)	)	PUNCT
ejpam-5120	299	4	is	be	AUX
ejpam-5120	299	5	a	a	DET
ejpam-5120	299	6	maximal	maximal	ADJ
ejpam-5120	299	7	in	in	ADP
ejpam-5120	299	8	p	p	PROPN
ejpam-5120	299	9	.	.	PUNCT
ejpam-5120	300	1	also	also	ADV
ejpam-5120	300	2	op(g	op(g	PUNCT
ejpam-5120	300	3	)	)	PUNCT
ejpam-5120	300	4	is	be	AUX
ejpam-5120	300	5	elementary	elementary	ADJ
ejpam-5120	300	6	abelian	abelian	NOUN
ejpam-5120	300	7	and	and	CCONJ
ejpam-5120	300	8	op(g	op(g	NUM
ejpam-5120	300	9	)	)	PUNCT
ejpam-5120	300	10	≰	≰	PROPN
ejpam-5120	300	11	m	m	VERB
ejpam-5120	300	12	because	because	SCONJ
ejpam-5120	300	13	p1	p1	PROPN
ejpam-5120	300	14	∈	∈	PROPN
ejpam-5120	300	15	sylp(m	sylp(m	NOUN
ejpam-5120	300	16	)	)	PUNCT
ejpam-5120	300	17	is	be	AUX
ejpam-5120	300	18	not	not	PART
ejpam-5120	300	19	s	s	NOUN
ejpam-5120	300	20	-	-	NOUN
ejpam-5120	300	21	permutable	permutable	ADJ
ejpam-5120	300	22	in	in	ADP
ejpam-5120	300	23	g.	g.	PROPN
ejpam-5120	300	24	because	because	SCONJ
ejpam-5120	300	25	φ(g	φ(g	PROPN
ejpam-5120	300	26	)	)	PUNCT
ejpam-5120	300	27	is	be	AUX
ejpam-5120	300	28	a	a	DET
ejpam-5120	300	29	p	p	NOUN
ejpam-5120	300	30	-	-	PUNCT
ejpam-5120	300	31	group	group	NOUN
ejpam-5120	300	32	and	and	CCONJ
ejpam-5120	300	33	op(g	op(g	NUM
ejpam-5120	300	34	)	)	PUNCT
ejpam-5120	300	35	≰	≰	PROPN
ejpam-5120	300	36	m	m	VERB
ejpam-5120	300	37	,	,	PUNCT
ejpam-5120	300	38	we	we	PRON
ejpam-5120	300	39	have	have	AUX
ejpam-5120	300	40	φ(g	φ(g	NOUN
ejpam-5120	300	41	)	)	PUNCT
ejpam-5120	300	42	<	<	X
ejpam-5120	300	43	op(g	op(g	NUM
ejpam-5120	300	44	)	)	PUNCT
ejpam-5120	300	45	and	and	CCONJ
ejpam-5120	300	46	φ(g	φ(g	PROPN
ejpam-5120	300	47	)	)	PUNCT
ejpam-5120	300	48	=	=	SYM
ejpam-5120	300	49	1	1	NUM
ejpam-5120	300	50	,	,	PUNCT
ejpam-5120	300	51	that	that	ADV
ejpam-5120	300	52	is	is	ADV
ejpam-5120	300	53	,	,	PUNCT
ejpam-5120	300	54	op(g	op(g	PUNCT
ejpam-5120	300	55	)	)	PUNCT
ejpam-5120	301	1	is	be	AUX
ejpam-5120	301	2	the	the	DET
ejpam-5120	301	3	unique	unique	ADJ
ejpam-5120	301	4	minimal	minimal	ADJ
ejpam-5120	301	5	normal	normal	ADJ
ejpam-5120	301	6	subgroups	subgroup	NOUN
ejpam-5120	301	7	of	of	ADP
ejpam-5120	301	8	g.	g.	PROPN
ejpam-5120	301	9	hence	hence	ADV
ejpam-5120	301	10	op(g	op(g	PUNCT
ejpam-5120	301	11	)	)	PUNCT
ejpam-5120	302	1	∩m	∩m	PROPN
ejpam-5120	302	2	=	=	PUNCT
ejpam-5120	302	3	1	1	NUM
ejpam-5120	302	4	and	and	CCONJ
ejpam-5120	302	5	|op(g)|	|op(g)|	NOUN
ejpam-5120	303	1	=	=	SYM
ejpam-5120	303	2	|d|	|d|	PROPN
ejpam-5120	303	3	=	=	SYM
ejpam-5120	304	1	p	p	PROPN
ejpam-5120	304	2	,	,	PUNCT
ejpam-5120	304	3	a	a	DET
ejpam-5120	304	4	contradiction	contradiction	NOUN
ejpam-5120	304	5	with	with	ADP
ejpam-5120	304	6	(	(	PUNCT
ejpam-5120	304	7	2	2	NUM
ejpam-5120	304	8	)	)	PUNCT
ejpam-5120	304	9	.	.	PUNCT
ejpam-5120	305	1	as	as	ADP
ejpam-5120	305	2	immediate	immediate	ADJ
ejpam-5120	305	3	consequences	consequence	NOUN
ejpam-5120	305	4	of	of	ADP
ejpam-5120	305	5	the	the	DET
ejpam-5120	305	6	main	main	ADJ
ejpam-5120	305	7	theorem	theorem	NOUN
ejpam-5120	305	8	we	we	PRON
ejpam-5120	305	9	have	have	VERB
ejpam-5120	305	10	:	:	PUNCT
ejpam-5120	305	11	corollary	corollary	ADJ
ejpam-5120	305	12	2	2	NUM
ejpam-5120	305	13	.	.	PUNCT
ejpam-5120	306	1	(	(	PUNCT
ejpam-5120	306	2	[	[	X
ejpam-5120	306	3	5	5	NUM
ejpam-5120	306	4	]	]	PUNCT
ejpam-5120	306	5	,	,	PUNCT
ejpam-5120	306	6	theorem	theorem	ADJ
ejpam-5120	306	7	d	d	NOUN
ejpam-5120	306	8	)	)	PUNCT
ejpam-5120	306	9	suppose	suppose	VERB
ejpam-5120	306	10	that	that	SCONJ
ejpam-5120	306	11	each	each	DET
ejpam-5120	306	12	sylow	sylow	NOUN
ejpam-5120	306	13	subgroup	subgroup	NOUN
ejpam-5120	306	14	p	p	PROPN
ejpam-5120	306	15	of	of	ADP
ejpam-5120	306	16	g	g	PROPN
ejpam-5120	306	17	has	have	VERB
ejpam-5120	306	18	a	a	DET
ejpam-5120	306	19	subgroup	subgroup	NOUN
ejpam-5120	306	20	d	d	NOUN
ejpam-5120	306	21	such	such	ADJ
ejpam-5120	306	22	that	that	SCONJ
ejpam-5120	306	23	1	1	NUM
ejpam-5120	306	24	<	<	X
ejpam-5120	306	25	|d|	|d|	PROPN
ejpam-5120	306	26	<	<	X
ejpam-5120	306	27	|p	|p	PROPN
ejpam-5120	307	1	|	|	ADV
ejpam-5120	307	2	and	and	CCONJ
ejpam-5120	307	3	all	all	DET
ejpam-5120	307	4	subgroups	subgroup	NOUN
ejpam-5120	307	5	h	h	VERB
ejpam-5120	307	6	of	of	ADP
ejpam-5120	307	7	p	p	NOUN
ejpam-5120	307	8	with	with	ADP
ejpam-5120	307	9	|h|	|h|	PROPN
ejpam-5120	307	10	=	=	SYM
ejpam-5120	307	11	|d|	|d|	PROPN
ejpam-5120	307	12	are	be	AUX
ejpam-5120	307	13	c	c	NOUN
ejpam-5120	307	14	-normal	-normal	ADJ
ejpam-5120	307	15	in	in	ADP
ejpam-5120	307	16	g.	g.	PROPN
ejpam-5120	307	17	then	then	ADV
ejpam-5120	307	18	g	g	PROPN
ejpam-5120	307	19	is	be	AUX
ejpam-5120	307	20	solvable	solvable	ADJ
ejpam-5120	307	21	.	.	PUNCT
ejpam-5120	308	1	corollary	corollary	ADJ
ejpam-5120	308	2	3	3	NUM
ejpam-5120	308	3	.	.	PUNCT
ejpam-5120	309	1	(	(	PUNCT
ejpam-5120	309	2	[	[	X
ejpam-5120	309	3	6	6	NUM
ejpam-5120	309	4	]	]	PUNCT
ejpam-5120	309	5	,	,	PUNCT
ejpam-5120	309	6	corollary	corollary	ADJ
ejpam-5120	309	7	1	1	NUM
ejpam-5120	309	8	)	)	PUNCT
ejpam-5120	309	9	let	let	VERB
ejpam-5120	309	10	p	p	PRON
ejpam-5120	309	11	be	be	AUX
ejpam-5120	309	12	a	a	DET
ejpam-5120	309	13	sylow	sylow	NOUN
ejpam-5120	309	14	p	p	NOUN
ejpam-5120	309	15	-	-	PUNCT
ejpam-5120	309	16	subgroup	subgroup	NOUN
ejpam-5120	309	17	of	of	ADP
ejpam-5120	309	18	g	g	PROPN
ejpam-5120	309	19	(	(	PUNCT
ejpam-5120	309	20	p	p	X
ejpam-5120	309	21	>	>	X
ejpam-5120	309	22	2	2	NUM
ejpam-5120	309	23	)	)	PUNCT
ejpam-5120	309	24	.	.	PUNCT
ejpam-5120	310	1	suppose	suppose	VERB
ejpam-5120	310	2	that	that	SCONJ
ejpam-5120	310	3	p	p	PROPN
ejpam-5120	310	4	has	have	VERB
ejpam-5120	310	5	a	a	DET
ejpam-5120	310	6	subgroup	subgroup	NOUN
ejpam-5120	310	7	d	d	NOUN
ejpam-5120	310	8	such	such	ADJ
ejpam-5120	310	9	that	that	SCONJ
ejpam-5120	310	10	1	1	NUM
ejpam-5120	310	11	<	<	X
ejpam-5120	310	12	|d|	|d|	PROPN
ejpam-5120	310	13	<	<	X
ejpam-5120	310	14	|p	|p	PROPN
ejpam-5120	311	1	|	|	ADV
ejpam-5120	311	2	and	and	CCONJ
ejpam-5120	311	3	all	all	DET
ejpam-5120	311	4	subgroups	subgroup	NOUN
ejpam-5120	311	5	h	h	VERB
ejpam-5120	311	6	of	of	ADP
ejpam-5120	311	7	p	p	NOUN
ejpam-5120	311	8	with	with	ADP
ejpam-5120	311	9	|h|	|h|	PROPN
ejpam-5120	311	10	=	=	SYM
ejpam-5120	311	11	|d|	|d|	PROPN
ejpam-5120	311	12	are	be	AUX
ejpam-5120	311	13	permutable	permutable	ADJ
ejpam-5120	311	14	in	in	ADP
ejpam-5120	311	15	g.	g.	PROPN
ejpam-5120	311	16	then	then	ADV
ejpam-5120	311	17	g	g	PROPN
ejpam-5120	311	18	′	′	NUM
ejpam-5120	311	19	is	be	AUX
ejpam-5120	311	20	p	p	NOUN
ejpam-5120	311	21	-	-	PUNCT
ejpam-5120	311	22	nilpotent	nilpotent	ADJ
ejpam-5120	311	23	.	.	PUNCT
ejpam-5120	312	1	acknowledgements	acknowledgement	NOUN
ejpam-5120	312	2	the	the	DET
ejpam-5120	312	3	authors	author	NOUN
ejpam-5120	312	4	extend	extend	VERB
ejpam-5120	312	5	their	their	PRON
ejpam-5120	312	6	appreciation	appreciation	NOUN
ejpam-5120	312	7	to	to	ADP
ejpam-5120	312	8	the	the	DET
ejpam-5120	312	9	deanship	deanship	NOUN
ejpam-5120	312	10	of	of	ADP
ejpam-5120	312	11	scientific	scientific	ADJ
ejpam-5120	312	12	research	research	NOUN
ejpam-5120	312	13	(	(	PUNCT
ejpam-5120	312	14	dsr	dsr	NOUN
ejpam-5120	312	15	)	)	PUNCT
ejpam-5120	312	16	at	at	ADP
ejpam-5120	312	17	northern	northern	ADJ
ejpam-5120	312	18	border	border	NOUN
ejpam-5120	312	19	university	university	PROPN
ejpam-5120	312	20	,	,	PUNCT
ejpam-5120	312	21	arar	arar	PROPN
ejpam-5120	312	22	,	,	PUNCT
ejpam-5120	312	23	ksa	ksa	PROPN
ejpam-5120	312	24	for	for	ADP
ejpam-5120	312	25	funding	fund	VERB
ejpam-5120	312	26	this	this	DET
ejpam-5120	312	27	research	research	NOUN
ejpam-5120	312	28	work	work	NOUN
ejpam-5120	312	29	”	"	PUNCT
ejpam-5120	312	30	through	through	ADP
ejpam-5120	312	31	the	the	DET
ejpam-5120	312	32	project	project	NOUN
ejpam-5120	312	33	number	number	NOUN
ejpam-5120	312	34	”	"	PUNCT
ejpam-5120	312	35	nbu	nbu	PROPN
ejpam-5120	312	36	-	-	PUNCT
ejpam-5120	312	37	ffr-2024	ffr-2024	NOUN
ejpam-5120	312	38	-	-	PUNCT
ejpam-5120	312	39	2089	2089	NUM
ejpam-5120	312	40	-	-	SYM
ejpam-5120	312	41	01	01	NUM
ejpam-5120	312	42	.	.	PUNCT
ejpam-5120	313	1	also	also	ADV
ejpam-5120	313	2	,	,	PUNCT
ejpam-5120	313	3	the	the	DET
ejpam-5120	313	4	authors	author	NOUN
ejpam-5120	313	5	thank	thank	VERB
ejpam-5120	313	6	the	the	DET
ejpam-5120	313	7	reviewers	reviewer	NOUN
ejpam-5120	313	8	for	for	ADP
ejpam-5120	313	9	their	their	PRON
ejpam-5120	313	10	helpful	helpful	ADJ
ejpam-5120	313	11	suggestions	suggestion	NOUN
ejpam-5120	313	12	and	and	CCONJ
ejpam-5120	313	13	comments	comment	NOUN
ejpam-5120	313	14	.	.	PUNCT
ejpam-5120	314	1	references	reference	NOUN
ejpam-5120	314	2	[	[	X
ejpam-5120	314	3	1	1	NUM
ejpam-5120	314	4	]	]	PUNCT
ejpam-5120	314	5	a.	a.	NOUN
ejpam-5120	314	6	ballester	ballester	NOUN
ejpam-5120	314	7	-	-	PUNCT
ejpam-5120	314	8	bolinches	bolinches	PROPN
ejpam-5120	314	9	,	,	PUNCT
ejpam-5120	314	10	y.	y.	PROPN
ejpam-5120	314	11	wang	wang	PROPN
ejpam-5120	314	12	,	,	PUNCT
ejpam-5120	314	13	and	and	CCONJ
ejpam-5120	314	14	x.	x.	NOUN
ejpam-5120	314	15	guo	guo	PROPN
ejpam-5120	314	16	.	.	PUNCT
ejpam-5120	315	1	c	c	X
ejpam-5120	315	2	-	-	PUNCT
ejpam-5120	315	3	supplemented	supplement	VERB
ejpam-5120	315	4	subgroups	subgroup	NOUN
ejpam-5120	315	5	of	of	ADP
ejpam-5120	315	6	finite	finite	ADJ
ejpam-5120	315	7	groups	group	NOUN
ejpam-5120	315	8	.	.	PUNCT
ejpam-5120	316	1	glasgow	glasgow	PROPN
ejpam-5120	316	2	math	math	PROPN
ejpam-5120	316	3	.	.	PUNCT
ejpam-5120	317	1	j.	j.	PROPN
ejpam-5120	317	2	,	,	PUNCT
ejpam-5120	317	3	42:383–389	42:383–389	PROPN
ejpam-5120	317	4	,	,	PUNCT
ejpam-5120	317	5	2000	2000	NUM
ejpam-5120	317	6	.	.	PUNCT
ejpam-5120	318	1	references	reference	NOUN
ejpam-5120	318	2	818	818	NUM
ejpam-5120	318	3	[	[	X
ejpam-5120	318	4	2	2	NUM
ejpam-5120	318	5	]	]	PUNCT
ejpam-5120	318	6	k.	k.	NOUN
ejpam-5120	318	7	doerk	doerk	PROPN
ejpam-5120	318	8	and	and	CCONJ
ejpam-5120	318	9	t.	t.	PROPN
ejpam-5120	318	10	hawkes	hawkes	PROPN
ejpam-5120	318	11	.	.	PUNCT
ejpam-5120	319	1	finite	finite	VERB
ejpam-5120	319	2	soluble	soluble	ADJ
ejpam-5120	319	3	groups	group	NOUN
ejpam-5120	319	4	.	.	PUNCT
ejpam-5120	320	1	walter	walter	PROPN
ejpam-5120	320	2	de	de	PROPN
ejpam-5120	320	3	gruyter	gruyter	PROPN
ejpam-5120	320	4	,	,	PUNCT
ejpam-5120	320	5	1992	1992	NUM
ejpam-5120	320	6	.	.	PUNCT
ejpam-5120	321	1	[	[	X
ejpam-5120	321	2	3	3	X
ejpam-5120	321	3	]	]	X
ejpam-5120	321	4	d.	d.	PROPN
ejpam-5120	321	5	gorenstein	gorenstein	PROPN
ejpam-5120	321	6	.	.	PUNCT
ejpam-5120	322	1	finite	finite	PROPN
ejpam-5120	322	2	groups	group	NOUN
ejpam-5120	322	3	.	.	PUNCT
ejpam-5120	323	1	ams	ams	PROPN
ejpam-5120	323	2	chelsea	chelsea	PROPN
ejpam-5120	323	3	publishing	publishing	PROPN
ejpam-5120	323	4	,	,	PUNCT
ejpam-5120	323	5	1980	1980	NUM
ejpam-5120	323	6	.	.	PUNCT
ejpam-5120	324	1	[	[	X
ejpam-5120	324	2	4	4	NUM
ejpam-5120	324	3	]	]	PUNCT
ejpam-5120	324	4	a.	a.	NOUN
ejpam-5120	324	5	a.	a.	NOUN
ejpam-5120	324	6	heliel	heliel	PROPN
ejpam-5120	324	7	.	.	PUNCT
ejpam-5120	325	1	a	a	DET
ejpam-5120	325	2	note	note	NOUN
ejpam-5120	325	3	on	on	ADP
ejpam-5120	325	4	c	c	NOUN
ejpam-5120	325	5	-	-	PUNCT
ejpam-5120	325	6	supplemented	supplement	VERB
ejpam-5120	325	7	subgroups	subgroup	NOUN
ejpam-5120	325	8	of	of	ADP
ejpam-5120	325	9	finite	finite	ADJ
ejpam-5120	325	10	groups	group	NOUN
ejpam-5120	325	11	.	.	PUNCT
ejpam-5120	326	1	comm	comm	NOUN
ejpam-5120	326	2	.	.	PUNCT
ejpam-5120	327	1	algebra	algebra	PROPN
ejpam-5120	327	2	,	,	PUNCT
ejpam-5120	327	3	42:1650–1656	42:1650–1656	PROPN
ejpam-5120	327	4	,	,	PUNCT
ejpam-5120	327	5	2014	2014	NUM
ejpam-5120	327	6	.	.	PUNCT
ejpam-5120	328	1	[	[	X
ejpam-5120	328	2	5	5	X
ejpam-5120	328	3	]	]	PUNCT
ejpam-5120	328	4	r.	r.	PROPN
ejpam-5120	328	5	a.	a.	PROPN
ejpam-5120	328	6	hijazi	hijazi	PROPN
ejpam-5120	328	7	.	.	PUNCT
ejpam-5120	329	1	a	a	DET
ejpam-5120	329	2	note	note	NOUN
ejpam-5120	329	3	on	on	ADP
ejpam-5120	329	4	solvability	solvability	NOUN
ejpam-5120	329	5	of	of	ADP
ejpam-5120	329	6	finite	finite	ADJ
ejpam-5120	329	7	groups	group	NOUN
ejpam-5120	329	8	.	.	PUNCT
ejpam-5120	330	1	journal	journal	NOUN
ejpam-5120	330	2	of	of	ADP
ejpam-5120	330	3	advances	advance	NOUN
ejpam-5120	330	4	in	in	ADP
ejpam-5120	330	5	mathematics	mathematic	NOUN
ejpam-5120	330	6	,	,	PUNCT
ejpam-5120	330	7	10	10	NUM
ejpam-5120	330	8	,	,	PUNCT
ejpam-5120	330	9	2015	2015	NUM
ejpam-5120	330	10	.	.	PUNCT
ejpam-5120	331	1	[	[	X
ejpam-5120	331	2	6	6	NUM
ejpam-5120	331	3	]	]	PUNCT
ejpam-5120	331	4	r.	r.	PROPN
ejpam-5120	331	5	a.	a.	PROPN
ejpam-5120	331	6	hijazi	hijazi	PROPN
ejpam-5120	331	7	and	and	CCONJ
ejpam-5120	331	8	f.	f.	PROPN
ejpam-5120	331	9	m.	m.	PROPN
ejpam-5120	331	10	charaf	charaf	PROPN
ejpam-5120	331	11	.	.	PUNCT
ejpam-5120	332	1	finite	finite	ADJ
ejpam-5120	332	2	groups	group	NOUN
ejpam-5120	332	3	with	with	ADP
ejpam-5120	332	4	certain	certain	ADJ
ejpam-5120	332	5	permutability	permutability	NOUN
ejpam-5120	332	6	criteria	criterion	NOUN
ejpam-5120	332	7	.	.	PUNCT
ejpam-5120	333	1	ejpam	ejpam	NOUN
ejpam-5120	333	2	,	,	PUNCT
ejpam-5120	333	3	12:571–576	12:571–576	NUM
ejpam-5120	333	4	,	,	PUNCT
ejpam-5120	333	5	2019	2019	NUM
ejpam-5120	333	6	.	.	PUNCT
ejpam-5120	334	1	[	[	X
ejpam-5120	334	2	7	7	X
ejpam-5120	334	3	]	]	X
ejpam-5120	334	4	b.	b.	PROPN
ejpam-5120	334	5	huppert	huppert	PROPN
ejpam-5120	334	6	.	.	PUNCT
ejpam-5120	335	1	endliche	endliche	PROPN
ejpam-5120	335	2	gruppen	gruppen	PROPN
ejpam-5120	335	3	i.	i.	PROPN
ejpam-5120	335	4	springer	springer	PROPN
ejpam-5120	335	5	,	,	PUNCT
ejpam-5120	335	6	berlin	berlin	PROPN
ejpam-5120	335	7	-	-	PUNCT
ejpam-5120	335	8	new	new	PROPN
ejpam-5120	335	9	york	york	PROPN
ejpam-5120	335	10	,	,	PUNCT
ejpam-5120	335	11	1979	1979	NUM
ejpam-5120	335	12	.	.	PUNCT
ejpam-5120	336	1	[	[	X
ejpam-5120	336	2	8	8	NUM
ejpam-5120	336	3	]	]	X
ejpam-5120	336	4	o.	o.	PROPN
ejpam-5120	336	5	h.	h.	PROPN
ejpam-5120	336	6	kegel	kegel	PROPN
ejpam-5120	336	7	.	.	PUNCT
ejpam-5120	337	1	sylow	sylow	NOUN
ejpam-5120	337	2	-	-	PUNCT
ejpam-5120	337	3	gruppen	gruppen	NOUN
ejpam-5120	337	4	und	und	NOUN
ejpam-5120	337	5	subnormalteiler	subnormalteiler	NOUN
ejpam-5120	337	6	endlicher	endlicher	PROPN
ejpam-5120	337	7	gruppen	gruppen	PROPN
ejpam-5120	337	8	.	.	PUNCT
ejpam-5120	338	1	math	math	NOUN
ejpam-5120	338	2	.	.	PUNCT
ejpam-5120	339	1	z.	z.	PROPN
ejpam-5120	339	2	,	,	PUNCT
ejpam-5120	339	3	78:205	78:205	NUM
ejpam-5120	339	4	–	–	PUNCT
ejpam-5120	339	5	221	221	NUM
ejpam-5120	339	6	,	,	PUNCT
ejpam-5120	339	7	1962	1962	NUM
ejpam-5120	339	8	.	.	PUNCT
ejpam-5120	340	1	[	[	X
ejpam-5120	340	2	9	9	NUM
ejpam-5120	340	3	]	]	PUNCT
ejpam-5120	340	4	a.	a.	NOUN
ejpam-5120	340	5	n.	n.	PROPN
ejpam-5120	340	6	skiba	skiba	PROPN
ejpam-5120	340	7	.	.	PUNCT
ejpam-5120	341	1	on	on	ADP
ejpam-5120	341	2	weakly	weakly	ADJ
ejpam-5120	341	3	s	s	NOUN
ejpam-5120	341	4	-	-	ADJ
ejpam-5120	341	5	permutable	permutable	ADJ
ejpam-5120	341	6	subgroups	subgroup	NOUN
ejpam-5120	341	7	of	of	ADP
ejpam-5120	341	8	finite	finite	ADJ
ejpam-5120	341	9	groups	group	NOUN
ejpam-5120	341	10	.	.	PUNCT
ejpam-5120	342	1	j.	j.	PROPN
ejpam-5120	342	2	algebra	algebra	PROPN
ejpam-5120	342	3	,	,	PUNCT
ejpam-5120	342	4	315:192	315:192	PROPN
ejpam-5120	342	5	–	–	PUNCT
ejpam-5120	342	6	209	209	NUM
ejpam-5120	342	7	,	,	PUNCT
ejpam-5120	342	8	2007	2007	NUM
ejpam-5120	342	9	.	.	PUNCT
ejpam-5120	343	1	[	[	X
ejpam-5120	343	2	10	10	NUM
ejpam-5120	343	3	]	]	X
ejpam-5120	343	4	y.	y.	PROPN
ejpam-5120	343	5	wang	wang	PROPN
ejpam-5120	343	6	.	.	PUNCT
ejpam-5120	344	1	c	c	X
ejpam-5120	344	2	-	-	PUNCT
ejpam-5120	344	3	normality	normality	NOUN
ejpam-5120	344	4	of	of	ADP
ejpam-5120	344	5	groups	group	NOUN
ejpam-5120	344	6	and	and	CCONJ
ejpam-5120	344	7	its	its	PRON
ejpam-5120	344	8	properties	property	NOUN
ejpam-5120	344	9	.	.	PUNCT
ejpam-5120	345	1	j.	j.	PROPN
ejpam-5120	345	2	algebra	algebra	PROPN
ejpam-5120	345	3	,	,	PUNCT
ejpam-5120	345	4	180:954–965	180:954–965	NUM
ejpam-5120	345	5	,	,	PUNCT
ejpam-5120	345	6	1996	1996	NUM
ejpam-5120	345	7	.	.	PUNCT
ejpam-5120	346	1	[	[	X
ejpam-5120	346	2	11	11	NUM
ejpam-5120	346	3	]	]	PUNCT
ejpam-5120	346	4	m.	m.	NOUN
ejpam-5120	346	5	weinstein	weinstein	PROPN
ejpam-5120	346	6	.	.	PUNCT
ejpam-5120	347	1	between	between	ADP
ejpam-5120	347	2	nilpotent	nilpotent	NOUN
ejpam-5120	347	3	and	and	CCONJ
ejpam-5120	347	4	solvable	solvable	ADJ
ejpam-5120	347	5	.	.	PUNCT
ejpam-5120	348	1	polygonal	polygonal	ADJ
ejpam-5120	348	2	publishing	publishing	PROPN
ejpam-5120	348	3	house	house	PROPN
ejpam-5120	348	4	,	,	PUNCT
ejpam-5120	348	5	passaic	passaic	PROPN
ejpam-5120	348	6	,	,	PUNCT
ejpam-5120	348	7	nj	nj	PROPN
ejpam-5120	348	8	,	,	PUNCT
ejpam-5120	348	9	1982	1982	NUM
ejpam-5120	348	10	.	.	PUNCT