id	sid	tid	token	lemma	pos
ejpam-3184	1	1	european	european	PROPN
ejpam-3184	1	2	journal	journal	PROPN
ejpam-3184	1	3	of	of	ADP
ejpam-3184	1	4	pure	pure	ADJ
ejpam-3184	1	5	and	and	CCONJ
ejpam-3184	1	6	applied	apply	VERB
ejpam-3184	1	7	mathematics	mathematic	NOUN
ejpam-3184	1	8	vol	vol	NOUN
ejpam-3184	1	9	.	.	PUNCT
ejpam-3184	2	1	11	11	NUM
ejpam-3184	2	2	,	,	PUNCT
ejpam-3184	2	3	no	no	INTJ
ejpam-3184	2	4	.	.	NOUN
ejpam-3184	2	5	1	1	NUM
ejpam-3184	2	6	,	,	PUNCT
ejpam-3184	2	7	2018	2018	NUM
ejpam-3184	2	8	,	,	PUNCT
ejpam-3184	2	9	160	160	NUM
ejpam-3184	2	10	-	-	SYM
ejpam-3184	2	11	168	168	NUM
ejpam-3184	2	12	issn	issn	PROPN
ejpam-3184	2	13	1307	1307	NUM
ejpam-3184	2	14	-	-	SYM
ejpam-3184	2	15	5543	5543	NUM
ejpam-3184	2	16	–	–	PUNCT
ejpam-3184	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3184	2	18	published	publish	VERB
ejpam-3184	2	19	by	by	ADP
ejpam-3184	2	20	new	new	PROPN
ejpam-3184	2	21	york	york	PROPN
ejpam-3184	2	22	business	business	PROPN
ejpam-3184	2	23	global	global	PROPN
ejpam-3184	2	24	the	the	DET
ejpam-3184	2	25	influence	influence	NOUN
ejpam-3184	2	26	of	of	ADP
ejpam-3184	2	27	cz	cz	NOUN
ejpam-3184	2	28	-	-	PUNCT
ejpam-3184	2	29	permutable	permutable	ADJ
ejpam-3184	2	30	subgroups	subgroup	NOUN
ejpam-3184	2	31	on	on	ADP
ejpam-3184	2	32	the	the	DET
ejpam-3184	2	33	structure	structure	NOUN
ejpam-3184	2	34	of	of	ADP
ejpam-3184	2	35	finite	finite	ADJ
ejpam-3184	2	36	groups	group	NOUN
ejpam-3184	2	37	m.	m.	PROPN
ejpam-3184	2	38	m.	m.	PROPN
ejpam-3184	2	39	al	al	PROPN
ejpam-3184	2	40	-	-	PROPN
ejpam-3184	2	41	shomrani1,∗	shomrani1,∗	PROPN
ejpam-3184	2	42	,	,	PUNCT
ejpam-3184	3	1	a.	a.	NOUN
ejpam-3184	3	2	a.	a.	PROPN
ejpam-3184	3	3	heliel2	heliel2	PROPN
ejpam-3184	4	1	1	1	NUM
ejpam-3184	5	1	department	department	NOUN
ejpam-3184	5	2	of	of	ADP
ejpam-3184	5	3	mathematics	mathematic	NOUN
ejpam-3184	5	4	,	,	PUNCT
ejpam-3184	5	5	faculty	faculty	NOUN
ejpam-3184	5	6	of	of	ADP
ejpam-3184	5	7	science	science	NOUN
ejpam-3184	5	8	,	,	PUNCT
ejpam-3184	5	9	northern	northern	ADJ
ejpam-3184	5	10	border	border	NOUN
ejpam-3184	5	11	university	university	PROPN
ejpam-3184	5	12	,	,	PUNCT
ejpam-3184	5	13	arar	arar	PROPN
ejpam-3184	5	14	,	,	PUNCT
ejpam-3184	5	15	saudi	saudi	PROPN
ejpam-3184	5	16	arabia	arabia	PROPN
ejpam-3184	5	17	2	2	NUM
ejpam-3184	5	18	department	department	NOUN
ejpam-3184	5	19	of	of	ADP
ejpam-3184	5	20	mathematics	mathematic	NOUN
ejpam-3184	5	21	,	,	PUNCT
ejpam-3184	5	22	faculty	faculty	NOUN
ejpam-3184	5	23	of	of	ADP
ejpam-3184	5	24	science	science	NOUN
ejpam-3184	5	25	62511	62511	NUM
ejpam-3184	5	26	,	,	PUNCT
ejpam-3184	5	27	beni	beni	ADJ
ejpam-3184	5	28	-	-	ADJ
ejpam-3184	5	29	suef	suef	ADJ
ejpam-3184	5	30	university	university	NOUN
ejpam-3184	5	31	,	,	PUNCT
ejpam-3184	5	32	beni	beni	NOUN
ejpam-3184	5	33	-	-	ADJ
ejpam-3184	5	34	suef	suef	NOUN
ejpam-3184	5	35	,	,	PUNCT
ejpam-3184	5	36	egypt	egypt	PROPN
ejpam-3184	5	37	abstract	abstract	PROPN
ejpam-3184	5	38	.	.	PUNCT
ejpam-3184	6	1	let	let	VERB
ejpam-3184	6	2	z	z	PRON
ejpam-3184	6	3	be	be	AUX
ejpam-3184	6	4	a	a	DET
ejpam-3184	6	5	complete	complete	ADJ
ejpam-3184	6	6	set	set	NOUN
ejpam-3184	6	7	of	of	ADP
ejpam-3184	6	8	sylow	sylow	NOUN
ejpam-3184	6	9	subgroups	subgroup	NOUN
ejpam-3184	6	10	of	of	ADP
ejpam-3184	6	11	a	a	DET
ejpam-3184	6	12	finite	finite	ADJ
ejpam-3184	6	13	group	group	NOUN
ejpam-3184	6	14	g	g	PROPN
ejpam-3184	6	15	,	,	PUNCT
ejpam-3184	6	16	that	that	ADV
ejpam-3184	6	17	is	is	ADV
ejpam-3184	6	18	,	,	PUNCT
ejpam-3184	6	19	for	for	ADP
ejpam-3184	6	20	each	each	DET
ejpam-3184	6	21	prime	prime	NOUN
ejpam-3184	6	22	p	p	NOUN
ejpam-3184	6	23	dividing	divide	VERB
ejpam-3184	6	24	the	the	DET
ejpam-3184	6	25	order	order	NOUN
ejpam-3184	6	26	of	of	ADP
ejpam-3184	6	27	g	g	NOUN
ejpam-3184	6	28	,	,	PUNCT
ejpam-3184	6	29	z	z	PROPN
ejpam-3184	6	30	contains	contain	VERB
ejpam-3184	6	31	exactly	exactly	ADV
ejpam-3184	6	32	one	one	NUM
ejpam-3184	6	33	and	and	CCONJ
ejpam-3184	6	34	only	only	ADV
ejpam-3184	6	35	one	one	NUM
ejpam-3184	6	36	sylow	sylow	NOUN
ejpam-3184	6	37	p	p	NOUN
ejpam-3184	6	38	-	-	PUNCT
ejpam-3184	6	39	subgroup	subgroup	NOUN
ejpam-3184	6	40	of	of	ADP
ejpam-3184	6	41	g	g	PROPN
ejpam-3184	6	42	,	,	PUNCT
ejpam-3184	6	43	say	say	VERB
ejpam-3184	6	44	gp	gp	NOUN
ejpam-3184	6	45	.	.	PUNCT
ejpam-3184	7	1	let	let	VERB
ejpam-3184	7	2	c	c	PRON
ejpam-3184	7	3	be	be	AUX
ejpam-3184	7	4	a	a	DET
ejpam-3184	7	5	nonempty	nonempty	ADJ
ejpam-3184	7	6	subset	subset	NOUN
ejpam-3184	7	7	of	of	ADP
ejpam-3184	7	8	g.	g.	PROPN
ejpam-3184	7	9	a	a	DET
ejpam-3184	7	10	subgroup	subgroup	NOUN
ejpam-3184	7	11	h	h	NOUN
ejpam-3184	7	12	of	of	ADP
ejpam-3184	7	13	g	g	PROPN
ejpam-3184	7	14	is	be	AUX
ejpam-3184	7	15	said	say	VERB
ejpam-3184	7	16	to	to	PART
ejpam-3184	7	17	be	be	AUX
ejpam-3184	7	18	c	c	NOUN
ejpam-3184	7	19	-	-	ADJ
ejpam-3184	7	20	z	z	NOUN
ejpam-3184	7	21	-	-	PUNCT
ejpam-3184	7	22	permutable	permutable	ADJ
ejpam-3184	7	23	(	(	PUNCT
ejpam-3184	7	24	conjugatez	conjugatez	NOUN
ejpam-3184	7	25	-	-	PUNCT
ejpam-3184	7	26	permutable	permutable	ADJ
ejpam-3184	7	27	)	)	PUNCT
ejpam-3184	7	28	subgroup	subgroup	NOUN
ejpam-3184	7	29	of	of	ADP
ejpam-3184	7	30	g	g	PROPN
ejpam-3184	7	31	if	if	SCONJ
ejpam-3184	7	32	there	there	PRON
ejpam-3184	7	33	exists	exist	VERB
ejpam-3184	7	34	some	some	DET
ejpam-3184	7	35	x	x	SYM
ejpam-3184	7	36	∈	∈	PROPN
ejpam-3184	7	37	c	c	NOUN
ejpam-3184	7	38	such	such	ADJ
ejpam-3184	7	39	that	that	DET
ejpam-3184	7	40	hxgp	hxgp	NOUN
ejpam-3184	7	41	=	=	SYM
ejpam-3184	7	42	gph	gph	PROPN
ejpam-3184	7	43	x	x	NOUN
ejpam-3184	7	44	,	,	PUNCT
ejpam-3184	7	45	for	for	ADP
ejpam-3184	7	46	all	all	DET
ejpam-3184	7	47	gp	gp	NOUN
ejpam-3184	7	48	∈	∈	PROPN
ejpam-3184	7	49	z.	z.	PROPN
ejpam-3184	7	50	we	we	PRON
ejpam-3184	7	51	investigate	investigate	VERB
ejpam-3184	7	52	the	the	DET
ejpam-3184	7	53	structure	structure	NOUN
ejpam-3184	7	54	of	of	ADP
ejpam-3184	7	55	the	the	DET
ejpam-3184	7	56	finite	finite	ADJ
ejpam-3184	7	57	group	group	NOUN
ejpam-3184	7	58	g	g	PROPN
ejpam-3184	7	59	under	under	ADP
ejpam-3184	7	60	the	the	DET
ejpam-3184	7	61	assumption	assumption	NOUN
ejpam-3184	7	62	that	that	SCONJ
ejpam-3184	7	63	certain	certain	ADJ
ejpam-3184	7	64	subgroups	subgroup	NOUN
ejpam-3184	7	65	of	of	ADP
ejpam-3184	7	66	prime	prime	ADJ
ejpam-3184	7	67	power	power	NOUN
ejpam-3184	7	68	orders	order	NOUN
ejpam-3184	7	69	of	of	ADP
ejpam-3184	7	70	g	g	NOUN
ejpam-3184	7	71	are	be	AUX
ejpam-3184	7	72	c	c	NOUN
ejpam-3184	7	73	-	-	PUNCT
ejpam-3184	7	74	z	z	ADJ
ejpam-3184	7	75	-	-	PUNCT
ejpam-3184	7	76	permutable	permutable	ADJ
ejpam-3184	7	77	subgroups	subgroup	NOUN
ejpam-3184	7	78	of	of	ADP
ejpam-3184	7	79	g.	g.	PROPN
ejpam-3184	7	80	2010	2010	NUM
ejpam-3184	7	81	mathematics	mathematic	NOUN
ejpam-3184	7	82	subject	subject	NOUN
ejpam-3184	7	83	classifications	classification	NOUN
ejpam-3184	7	84	:	:	PUNCT
ejpam-3184	7	85	20d10	20d10	NUM
ejpam-3184	7	86	,	,	PUNCT
ejpam-3184	7	87	20d15	20d15	NUM
ejpam-3184	7	88	,	,	PUNCT
ejpam-3184	7	89	20d20	20d20	NUM
ejpam-3184	7	90	,	,	PUNCT
ejpam-3184	7	91	20f16	20f16	NUM
ejpam-3184	7	92	.	.	PUNCT
ejpam-3184	8	1	key	key	ADJ
ejpam-3184	8	2	words	word	NOUN
ejpam-3184	8	3	and	and	CCONJ
ejpam-3184	8	4	phrases	phrase	NOUN
ejpam-3184	8	5	:	:	PUNCT
ejpam-3184	8	6	sylow	sylow	NOUN
ejpam-3184	8	7	subgroup	subgroup	NOUN
ejpam-3184	8	8	,	,	PUNCT
ejpam-3184	8	9	z	z	NOUN
ejpam-3184	8	10	-	-	PUNCT
ejpam-3184	8	11	permutable	permutable	ADJ
ejpam-3184	8	12	subgroup	subgroup	NOUN
ejpam-3184	8	13	,	,	PUNCT
ejpam-3184	8	14	c	c	PROPN
ejpam-3184	8	15	-	-	PUNCT
ejpam-3184	8	16	z	z	ADJ
ejpam-3184	8	17	-	-	PUNCT
ejpam-3184	8	18	permutable	permutable	ADJ
ejpam-3184	8	19	subgroup	subgroup	NOUN
ejpam-3184	8	20	,	,	PUNCT
ejpam-3184	8	21	p	p	NOUN
ejpam-3184	8	22	-	-	PUNCT
ejpam-3184	8	23	nilpotent	nilpotent	ADJ
ejpam-3184	8	24	group	group	NOUN
ejpam-3184	8	25	,	,	PUNCT
ejpam-3184	8	26	supersolvable	supersolvable	ADJ
ejpam-3184	8	27	group	group	NOUN
ejpam-3184	8	28	,	,	PUNCT
ejpam-3184	8	29	fitting	fitting	ADJ
ejpam-3184	8	30	subgroup	subgroup	NOUN
ejpam-3184	8	31	,	,	PUNCT
ejpam-3184	8	32	generalized	generalize	VERB
ejpam-3184	8	33	fitting	fitting	ADJ
ejpam-3184	8	34	subgroup	subgroup	NOUN
ejpam-3184	8	35	,	,	PUNCT
ejpam-3184	8	36	saturated	saturate	VERB
ejpam-3184	8	37	formation	formation	NOUN
ejpam-3184	8	38	.	.	PUNCT
ejpam-3184	9	1	1	1	X
ejpam-3184	9	2	.	.	X
ejpam-3184	9	3	introduction	introduction	NOUN
ejpam-3184	9	4	throughout	throughout	ADP
ejpam-3184	9	5	this	this	DET
ejpam-3184	9	6	article	article	NOUN
ejpam-3184	9	7	only	only	ADV
ejpam-3184	9	8	finite	finite	ADJ
ejpam-3184	9	9	groups	group	NOUN
ejpam-3184	9	10	are	be	AUX
ejpam-3184	9	11	considered	consider	VERB
ejpam-3184	9	12	.	.	PUNCT
ejpam-3184	10	1	we	we	PRON
ejpam-3184	10	2	use	use	VERB
ejpam-3184	10	3	conventional	conventional	ADJ
ejpam-3184	10	4	notions	notion	NOUN
ejpam-3184	10	5	and	and	CCONJ
ejpam-3184	10	6	notation	notation	NOUN
ejpam-3184	10	7	,	,	PUNCT
ejpam-3184	10	8	as	as	ADP
ejpam-3184	10	9	in	in	ADP
ejpam-3184	10	10	doerk	doerk	NOUN
ejpam-3184	10	11	and	and	CCONJ
ejpam-3184	10	12	hawkes	hawke	NOUN
ejpam-3184	10	13	[	[	X
ejpam-3184	10	14	2	2	NUM
ejpam-3184	10	15	]	]	PUNCT
ejpam-3184	10	16	.	.	PUNCT
ejpam-3184	11	1	in	in	ADP
ejpam-3184	11	2	addtion	addtion	NOUN
ejpam-3184	11	3	,	,	PUNCT
ejpam-3184	11	4	π(g	π(g	PROPN
ejpam-3184	11	5	)	)	PUNCT
ejpam-3184	11	6	denotes	denote	VERB
ejpam-3184	11	7	the	the	DET
ejpam-3184	11	8	set	set	NOUN
ejpam-3184	11	9	of	of	ADP
ejpam-3184	11	10	distinct	distinct	ADJ
ejpam-3184	11	11	primes	prime	NOUN
ejpam-3184	11	12	dividing	divide	VERB
ejpam-3184	11	13	|g|	|g|	PROPN
ejpam-3184	11	14	and	and	CCONJ
ejpam-3184	11	15	gp	gp	NOUN
ejpam-3184	11	16	is	be	AUX
ejpam-3184	11	17	a	a	DET
ejpam-3184	11	18	sylow	sylow	NOUN
ejpam-3184	11	19	p	p	NOUN
ejpam-3184	11	20	-	-	PUNCT
ejpam-3184	11	21	subgroup	subgroup	NOUN
ejpam-3184	11	22	of	of	ADP
ejpam-3184	11	23	the	the	DET
ejpam-3184	11	24	group	group	NOUN
ejpam-3184	11	25	g	g	NOUN
ejpam-3184	11	26	for	for	ADP
ejpam-3184	11	27	some	some	DET
ejpam-3184	11	28	prime	prime	ADJ
ejpam-3184	11	29	p	p	X
ejpam-3184	11	30	∈	∈	PROPN
ejpam-3184	11	31	π(g	π(g	PROPN
ejpam-3184	11	32	)	)	PUNCT
ejpam-3184	11	33	.	.	PUNCT
ejpam-3184	12	1	two	two	NUM
ejpam-3184	12	2	subgroups	subgroup	NOUN
ejpam-3184	12	3	h	h	NOUN
ejpam-3184	12	4	and	and	CCONJ
ejpam-3184	12	5	k	k	PROPN
ejpam-3184	12	6	of	of	ADP
ejpam-3184	12	7	a	a	DET
ejpam-3184	12	8	group	group	NOUN
ejpam-3184	12	9	g	g	NOUN
ejpam-3184	12	10	are	be	AUX
ejpam-3184	12	11	said	say	VERB
ejpam-3184	12	12	to	to	PART
ejpam-3184	12	13	be	be	AUX
ejpam-3184	12	14	permutable	permutable	ADJ
ejpam-3184	12	15	if	if	SCONJ
ejpam-3184	12	16	hk	hk	PROPN
ejpam-3184	12	17	=	=	SYM
ejpam-3184	12	18	kh	kh	PROPN
ejpam-3184	12	19	,	,	PUNCT
ejpam-3184	12	20	that	that	ADV
ejpam-3184	12	21	is	is	ADV
ejpam-3184	12	22	,	,	PUNCT
ejpam-3184	12	23	hk	hk	PROPN
ejpam-3184	12	24	is	be	AUX
ejpam-3184	12	25	a	a	DET
ejpam-3184	12	26	subgroup	subgroup	NOUN
ejpam-3184	12	27	of	of	ADP
ejpam-3184	12	28	g.	g.	PROPN
ejpam-3184	12	29	recall	recall	VERB
ejpam-3184	12	30	that	that	SCONJ
ejpam-3184	12	31	a	a	DET
ejpam-3184	12	32	subgroup	subgroup	NOUN
ejpam-3184	12	33	h	h	NOUN
ejpam-3184	12	34	of	of	ADP
ejpam-3184	12	35	a	a	DET
ejpam-3184	12	36	group	group	NOUN
ejpam-3184	12	37	g	g	PROPN
ejpam-3184	12	38	is	be	AUX
ejpam-3184	12	39	s	s	NOUN
ejpam-3184	12	40	-	-	ADJ
ejpam-3184	12	41	permutable	permutable	ADJ
ejpam-3184	12	42	(	(	PUNCT
ejpam-3184	12	43	or	or	CCONJ
ejpam-3184	12	44	s	s	NOUN
ejpam-3184	12	45	-	-	ADJ
ejpam-3184	12	46	quasinormal	quasinormal	ADJ
ejpam-3184	12	47	)	)	PUNCT
ejpam-3184	12	48	in	in	ADP
ejpam-3184	12	49	g	g	PROPN
ejpam-3184	12	50	if	if	SCONJ
ejpam-3184	12	51	h	h	NOUN
ejpam-3184	12	52	permutes	permute	VERB
ejpam-3184	12	53	with	with	ADP
ejpam-3184	12	54	every	every	DET
ejpam-3184	12	55	sylow	sylow	NOUN
ejpam-3184	12	56	subgroup	subgroup	NOUN
ejpam-3184	12	57	of	of	ADP
ejpam-3184	12	58	g.	g.	PROPN
ejpam-3184	12	59	this	this	DET
ejpam-3184	12	60	concept	concept	NOUN
ejpam-3184	12	61	was	be	AUX
ejpam-3184	12	62	introduced	introduce	VERB
ejpam-3184	12	63	by	by	ADP
ejpam-3184	12	64	kegel	kegel	PROPN
ejpam-3184	13	1	[	[	X
ejpam-3184	13	2	7	7	X
ejpam-3184	13	3	]	]	PUNCT
ejpam-3184	13	4	in	in	ADP
ejpam-3184	13	5	1962	1962	NUM
ejpam-3184	13	6	.	.	PUNCT
ejpam-3184	14	1	recently	recently	ADV
ejpam-3184	14	2	,	,	PUNCT
ejpam-3184	14	3	in	in	ADP
ejpam-3184	14	4	2003	2003	NUM
ejpam-3184	14	5	,	,	PUNCT
ejpam-3184	14	6	asaad	asaad	VERB
ejpam-3184	14	7	and	and	CCONJ
ejpam-3184	14	8	heliel	heliel	NOUN
ejpam-3184	15	1	[	[	X
ejpam-3184	15	2	1	1	X
ejpam-3184	15	3	]	]	PUNCT
ejpam-3184	15	4	introduced	introduce	VERB
ejpam-3184	15	5	the	the	DET
ejpam-3184	15	6	concept	concept	NOUN
ejpam-3184	15	7	of	of	ADP
ejpam-3184	15	8	z	z	NOUN
ejpam-3184	15	9	-	-	PUNCT
ejpam-3184	15	10	permutability	permutability	NOUN
ejpam-3184	15	11	which	which	PRON
ejpam-3184	15	12	generalizes	generalize	VERB
ejpam-3184	15	13	s	s	NOUN
ejpam-3184	15	14	-	-	NOUN
ejpam-3184	15	15	permutability	permutability	NOUN
ejpam-3184	15	16	as	as	SCONJ
ejpam-3184	15	17	follows	follow	VERB
ejpam-3184	15	18	:	:	PUNCT
ejpam-3184	15	19	let	let	VERB
ejpam-3184	15	20	z	z	PRON
ejpam-3184	15	21	be	be	AUX
ejpam-3184	15	22	a	a	DET
ejpam-3184	15	23	complete	complete	ADJ
ejpam-3184	15	24	set	set	NOUN
ejpam-3184	15	25	of	of	ADP
ejpam-3184	15	26	sylow	sylow	NOUN
ejpam-3184	15	27	subgroups	subgroup	NOUN
ejpam-3184	15	28	of	of	ADP
ejpam-3184	15	29	a	a	DET
ejpam-3184	15	30	group	group	NOUN
ejpam-3184	15	31	g.	g.	PROPN
ejpam-3184	15	32	a	a	DET
ejpam-3184	15	33	subgroup	subgroup	NOUN
ejpam-3184	15	34	h	h	NOUN
ejpam-3184	15	35	of	of	ADP
ejpam-3184	15	36	g	g	PROPN
ejpam-3184	15	37	is	be	AUX
ejpam-3184	15	38	said	say	VERB
ejpam-3184	15	39	to	to	PART
ejpam-3184	15	40	be	be	AUX
ejpam-3184	15	41	z	z	NOUN
ejpam-3184	15	42	-	-	NOUN
ejpam-3184	15	43	permutable	permutable	ADJ
ejpam-3184	15	44	in	in	ADP
ejpam-3184	15	45	g	g	PROPN
ejpam-3184	15	46	if	if	SCONJ
ejpam-3184	15	47	h	h	NOUN
ejpam-3184	15	48	permutes	permute	VERB
ejpam-3184	15	49	with	with	ADP
ejpam-3184	15	50	every	every	DET
ejpam-3184	15	51	∗corresponding	∗corresponde	VERB
ejpam-3184	15	52	author	author	NOUN
ejpam-3184	15	53	.	.	PUNCT
ejpam-3184	16	1	email	email	NOUN
ejpam-3184	16	2	addresses	address	NOUN
ejpam-3184	16	3	:	:	PUNCT
ejpam-3184	16	4	malshomrani@hotmail.com	malshomrani@hotmail.com	X
ejpam-3184	16	5	(	(	PUNCT
ejpam-3184	16	6	m.	m.	NOUN
ejpam-3184	16	7	m.	m.	PROPN
ejpam-3184	16	8	al	al	PROPN
ejpam-3184	16	9	-	-	PUNCT
ejpam-3184	16	10	shomrani	shomrani	PROPN
ejpam-3184	16	11	)	)	PUNCT
ejpam-3184	16	12	,	,	PUNCT
ejpam-3184	16	13	heliel9@yahoo.com	heliel9@yahoo.com	X
ejpam-3184	16	14	(	(	PUNCT
ejpam-3184	16	15	a.	a.	NOUN
ejpam-3184	16	16	a.	a.	NOUN
ejpam-3184	16	17	heliel	heliel	PROPN
ejpam-3184	16	18	)	)	PUNCT
ejpam-3184	16	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3184	17	1	160	160	NUM
ejpam-3184	17	2	c	c	NOUN
ejpam-3184	17	3	©	©	PROPN
ejpam-3184	17	4	2018	2018	NUM
ejpam-3184	17	5	ejpam	ejpam	VERB
ejpam-3184	17	6	all	all	DET
ejpam-3184	17	7	rights	right	NOUN
ejpam-3184	17	8	reserved	reserve	VERB
ejpam-3184	17	9	.	.	PUNCT
ejpam-3184	18	1	m.	m.	NOUN
ejpam-3184	18	2	m.	m.	PROPN
ejpam-3184	18	3	al	al	PROPN
ejpam-3184	18	4	-	-	PUNCT
ejpam-3184	18	5	shomrani	shomrani	PROPN
ejpam-3184	18	6	,	,	PUNCT
ejpam-3184	18	7	a.	a.	NOUN
ejpam-3184	18	8	a.	a.	NOUN
ejpam-3184	18	9	heliel	heliel	PROPN
ejpam-3184	18	10	/	/	SYM
ejpam-3184	18	11	eur	eur	PROPN
ejpam-3184	18	12	.	.	PUNCT
ejpam-3184	19	1	j.	j.	PROPN
ejpam-3184	19	2	pure	pure	PROPN
ejpam-3184	19	3	appl	appl	PROPN
ejpam-3184	19	4	.	.	PROPN
ejpam-3184	19	5	math	math	PROPN
ejpam-3184	19	6	,	,	PUNCT
ejpam-3184	19	7	11	11	NUM
ejpam-3184	19	8	(	(	PUNCT
ejpam-3184	19	9	1	1	NUM
ejpam-3184	19	10	)	)	PUNCT
ejpam-3184	19	11	(	(	PUNCT
ejpam-3184	19	12	2018	2018	NUM
ejpam-3184	19	13	)	)	PUNCT
ejpam-3184	19	14	,	,	PUNCT
ejpam-3184	19	15	160	160	NUM
ejpam-3184	19	16	-	-	SYM
ejpam-3184	19	17	168	168	NUM
ejpam-3184	19	18	161	161	NUM
ejpam-3184	19	19	member	member	NOUN
ejpam-3184	19	20	in	in	ADP
ejpam-3184	19	21	z.	z.	PROPN
ejpam-3184	19	22	more	more	ADV
ejpam-3184	19	23	recently	recently	ADV
ejpam-3184	19	24	,	,	PUNCT
ejpam-3184	19	25	in	in	ADP
ejpam-3184	19	26	2013	2013	NUM
ejpam-3184	19	27	,	,	PUNCT
ejpam-3184	19	28	heliel	heliel	NOUN
ejpam-3184	19	29	and	and	CCONJ
ejpam-3184	19	30	al	al	PROPN
ejpam-3184	19	31	-	-	PUNCT
ejpam-3184	19	32	gafri	gafri	PROPN
ejpam-3184	20	1	[	[	X
ejpam-3184	20	2	4	4	NUM
ejpam-3184	20	3	]	]	PUNCT
ejpam-3184	20	4	generalized	generalize	VERB
ejpam-3184	20	5	the	the	DET
ejpam-3184	20	6	concept	concept	NOUN
ejpam-3184	20	7	of	of	ADP
ejpam-3184	20	8	z	z	NOUN
ejpam-3184	20	9	-	-	NOUN
ejpam-3184	20	10	permutability	permutability	NOUN
ejpam-3184	20	11	by	by	ADP
ejpam-3184	20	12	introducing	introduce	VERB
ejpam-3184	20	13	a	a	DET
ejpam-3184	20	14	new	new	ADJ
ejpam-3184	20	15	subgroup	subgroup	NOUN
ejpam-3184	20	16	embedding	embed	VERB
ejpam-3184	20	17	property	property	NOUN
ejpam-3184	20	18	,	,	PUNCT
ejpam-3184	20	19	namely	namely	ADV
ejpam-3184	20	20	,	,	PUNCT
ejpam-3184	20	21	the	the	DET
ejpam-3184	20	22	conjugate	conjugate	ADJ
ejpam-3184	20	23	-	-	PUNCT
ejpam-3184	20	24	z	z	NOUN
ejpam-3184	20	25	-	-	NOUN
ejpam-3184	20	26	permutability	permutability	NOUN
ejpam-3184	20	27	.	.	PUNCT
ejpam-3184	21	1	let	let	VERB
ejpam-3184	21	2	c	c	PRON
ejpam-3184	21	3	be	be	AUX
ejpam-3184	21	4	a	a	DET
ejpam-3184	21	5	nonempty	nonempty	ADJ
ejpam-3184	21	6	subset	subset	NOUN
ejpam-3184	21	7	of	of	ADP
ejpam-3184	21	8	a	a	DET
ejpam-3184	21	9	group	group	NOUN
ejpam-3184	21	10	g	g	NOUN
ejpam-3184	21	11	and	and	CCONJ
ejpam-3184	21	12	z	z	NOUN
ejpam-3184	21	13	be	be	AUX
ejpam-3184	21	14	a	a	DET
ejpam-3184	21	15	complete	complete	ADJ
ejpam-3184	21	16	set	set	NOUN
ejpam-3184	21	17	of	of	ADP
ejpam-3184	21	18	sylow	sylow	NOUN
ejpam-3184	21	19	subgroups	subgroup	NOUN
ejpam-3184	21	20	of	of	ADP
ejpam-3184	21	21	g.	g.	PROPN
ejpam-3184	21	22	a	a	DET
ejpam-3184	21	23	subgroup	subgroup	NOUN
ejpam-3184	21	24	h	h	NOUN
ejpam-3184	21	25	of	of	ADP
ejpam-3184	21	26	g	g	PROPN
ejpam-3184	21	27	is	be	AUX
ejpam-3184	21	28	said	say	VERB
ejpam-3184	21	29	to	to	PART
ejpam-3184	21	30	be	be	AUX
ejpam-3184	21	31	c	c	NOUN
ejpam-3184	21	32	-	-	ADJ
ejpam-3184	21	33	z	z	ADJ
ejpam-3184	21	34	-	-	PUNCT
ejpam-3184	21	35	permutable	permutable	ADJ
ejpam-3184	21	36	subgroup	subgroup	NOUN
ejpam-3184	21	37	of	of	ADP
ejpam-3184	21	38	g	g	PROPN
ejpam-3184	21	39	if	if	SCONJ
ejpam-3184	21	40	there	there	PRON
ejpam-3184	21	41	exists	exist	VERB
ejpam-3184	21	42	some	some	DET
ejpam-3184	21	43	x	x	SYM
ejpam-3184	21	44	∈	∈	PROPN
ejpam-3184	21	45	c	c	NOUN
ejpam-3184	21	46	such	such	ADJ
ejpam-3184	21	47	that	that	DET
ejpam-3184	21	48	hxgp	hxgp	NOUN
ejpam-3184	21	49	=	=	SYM
ejpam-3184	21	50	gph	gph	PROPN
ejpam-3184	21	51	x	x	NOUN
ejpam-3184	21	52	,	,	PUNCT
ejpam-3184	21	53	for	for	ADP
ejpam-3184	21	54	all	all	DET
ejpam-3184	21	55	gp	gp	NOUN
ejpam-3184	21	56	∈	∈	PROPN
ejpam-3184	21	57	z.	z.	PROPN
ejpam-3184	21	58	remark	remark	VERB
ejpam-3184	21	59	1.2	1.2	NUM
ejpam-3184	21	60	and	and	CCONJ
ejpam-3184	21	61	examples	example	NOUN
ejpam-3184	21	62	1.3	1.3	NUM
ejpam-3184	21	63	and	and	CCONJ
ejpam-3184	21	64	1.4	1.4	NUM
ejpam-3184	21	65	in	in	ADP
ejpam-3184	21	66	[	[	X
ejpam-3184	21	67	4	4	NUM
ejpam-3184	21	68	]	]	PUNCT
ejpam-3184	21	69	show	show	VERB
ejpam-3184	21	70	that	that	SCONJ
ejpam-3184	21	71	c	c	X
ejpam-3184	21	72	-	-	PUNCT
ejpam-3184	21	73	z	z	NOUN
ejpam-3184	21	74	-	-	PUNCT
ejpam-3184	21	75	permutability	permutability	NOUN
ejpam-3184	21	76	is	be	AUX
ejpam-3184	21	77	a	a	DET
ejpam-3184	21	78	nontrivial	nontrivial	ADJ
ejpam-3184	21	79	generalization	generalization	NOUN
ejpam-3184	21	80	of	of	ADP
ejpam-3184	21	81	z	z	NOUN
ejpam-3184	21	82	-	-	NOUN
ejpam-3184	21	83	permutability	permutability	NOUN
ejpam-3184	21	84	.	.	PUNCT
ejpam-3184	22	1	this	this	DET
ejpam-3184	22	2	article	article	NOUN
ejpam-3184	22	3	may	may	AUX
ejpam-3184	22	4	be	be	AUX
ejpam-3184	22	5	viewed	view	VERB
ejpam-3184	22	6	as	as	ADP
ejpam-3184	22	7	a	a	DET
ejpam-3184	22	8	continuation	continuation	NOUN
ejpam-3184	22	9	of	of	ADP
ejpam-3184	22	10	heliel	heliel	PROPN
ejpam-3184	22	11	and	and	CCONJ
ejpam-3184	22	12	al	al	PROPN
ejpam-3184	22	13	-	-	PUNCT
ejpam-3184	22	14	gafri	gafri	PROPN
ejpam-3184	22	15	[	[	X
ejpam-3184	22	16	4	4	NUM
ejpam-3184	22	17	]	]	PUNCT
ejpam-3184	22	18	.	.	PUNCT
ejpam-3184	23	1	in	in	ADP
ejpam-3184	23	2	fact	fact	NOUN
ejpam-3184	23	3	,	,	PUNCT
ejpam-3184	23	4	we	we	PRON
ejpam-3184	23	5	extend	extend	VERB
ejpam-3184	23	6	and	and	CCONJ
ejpam-3184	23	7	improve	improve	VERB
ejpam-3184	23	8	the	the	DET
ejpam-3184	23	9	following	follow	VERB
ejpam-3184	23	10	theorem	theorem	NOUN
ejpam-3184	23	11	:	:	PUNCT
ejpam-3184	23	12	theorem	theorem	ADJ
ejpam-3184	23	13	1.1	1.1	NUM
ejpam-3184	23	14	.	.	PUNCT
ejpam-3184	24	1	[	[	X
ejpam-3184	24	2	[	[	X
ejpam-3184	24	3	4	4	NUM
ejpam-3184	24	4	]	]	PUNCT
ejpam-3184	24	5	,	,	PUNCT
ejpam-3184	24	6	theorem	theorem	VERB
ejpam-3184	24	7	3.11	3.11	NUM
ejpam-3184	24	8	]	]	PUNCT
ejpam-3184	24	9	let	let	VERB
ejpam-3184	24	10	f	f	PRON
ejpam-3184	24	11	be	be	AUX
ejpam-3184	24	12	a	a	DET
ejpam-3184	24	13	saturated	saturated	ADJ
ejpam-3184	24	14	formation	formation	NOUN
ejpam-3184	24	15	containing	contain	VERB
ejpam-3184	24	16	the	the	DET
ejpam-3184	24	17	class	class	NOUN
ejpam-3184	24	18	of	of	ADP
ejpam-3184	24	19	supersolvable	supersolvable	ADJ
ejpam-3184	24	20	groups	group	NOUN
ejpam-3184	24	21	u	u	NOUN
ejpam-3184	24	22	and	and	CCONJ
ejpam-3184	24	23	let	let	VERB
ejpam-3184	24	24	z	z	PRON
ejpam-3184	24	25	be	be	AUX
ejpam-3184	24	26	a	a	DET
ejpam-3184	24	27	complete	complete	ADJ
ejpam-3184	24	28	set	set	NOUN
ejpam-3184	24	29	of	of	ADP
ejpam-3184	24	30	sylow	sylow	NOUN
ejpam-3184	24	31	subgroups	subgroup	NOUN
ejpam-3184	24	32	of	of	ADP
ejpam-3184	24	33	a	a	DET
ejpam-3184	24	34	group	group	NOUN
ejpam-3184	24	35	g.	g.	NOUN
ejpam-3184	25	1	then	then	ADV
ejpam-3184	25	2	the	the	DET
ejpam-3184	25	3	following	follow	VERB
ejpam-3184	25	4	two	two	NUM
ejpam-3184	25	5	statements	statement	NOUN
ejpam-3184	25	6	are	be	AUX
ejpam-3184	25	7	equivalent	equivalent	ADJ
ejpam-3184	25	8	:	:	PUNCT
ejpam-3184	25	9	(	(	PUNCT
ejpam-3184	25	10	a	a	X
ejpam-3184	25	11	)	)	PUNCT
ejpam-3184	25	12	g	g	PROPN
ejpam-3184	25	13	∈	∈	PROPN
ejpam-3184	25	14	f.	f.	PROPN
ejpam-3184	25	15	(	(	PUNCT
ejpam-3184	25	16	b	b	X
ejpam-3184	25	17	)	)	PUNCT
ejpam-3184	25	18	there	there	PRON
ejpam-3184	25	19	is	be	VERB
ejpam-3184	25	20	a	a	DET
ejpam-3184	25	21	normal	normal	ADJ
ejpam-3184	25	22	subgroup	subgroup	NOUN
ejpam-3184	25	23	h	h	NOUN
ejpam-3184	25	24	in	in	ADP
ejpam-3184	25	25	g	g	PROPN
ejpam-3184	25	26	and	and	CCONJ
ejpam-3184	25	27	a	a	DET
ejpam-3184	25	28	solvable	solvable	ADJ
ejpam-3184	25	29	normal	normal	ADJ
ejpam-3184	25	30	subgroup	subgroup	NOUN
ejpam-3184	25	31	c	c	PROPN
ejpam-3184	25	32	of	of	ADP
ejpam-3184	25	33	f	f	PROPN
ejpam-3184	25	34	∗(h	∗(h	PROPN
ejpam-3184	25	35	)	)	PUNCT
ejpam-3184	26	1	such	such	ADJ
ejpam-3184	26	2	that	that	SCONJ
ejpam-3184	26	3	g	g	NOUN
ejpam-3184	26	4	/	/	SYM
ejpam-3184	26	5	h	h	NOUN
ejpam-3184	26	6	∈	∈	PROPN
ejpam-3184	26	7	f	f	X
ejpam-3184	26	8	,	,	PUNCT
ejpam-3184	26	9	and	and	CCONJ
ejpam-3184	26	10	the	the	DET
ejpam-3184	26	11	maximal	maximal	ADJ
ejpam-3184	26	12	subgroups	subgroup	NOUN
ejpam-3184	26	13	of	of	ADP
ejpam-3184	26	14	gp	gp	NOUN
ejpam-3184	26	15	∩f	∩f	PROPN
ejpam-3184	26	16	∗(h	∗(h	PROPN
ejpam-3184	26	17	)	)	PUNCT
ejpam-3184	26	18	are	be	AUX
ejpam-3184	26	19	c	c	NOUN
ejpam-3184	26	20	-	-	PUNCT
ejpam-3184	26	21	z	z	ADJ
ejpam-3184	26	22	-	-	PUNCT
ejpam-3184	26	23	permutable	permutable	ADJ
ejpam-3184	26	24	subgroups	subgroup	NOUN
ejpam-3184	26	25	of	of	ADP
ejpam-3184	26	26	g	g	NOUN
ejpam-3184	26	27	,	,	PUNCT
ejpam-3184	26	28	for	for	ADP
ejpam-3184	26	29	all	all	PRON
ejpam-3184	26	30	gp	gp	NOUN
ejpam-3184	26	31	∈	∈	PROPN
ejpam-3184	27	1	z	z	PROPN
ejpam-3184	27	2	,	,	PUNCT
ejpam-3184	27	3	where	where	SCONJ
ejpam-3184	27	4	f	f	PROPN
ejpam-3184	27	5	∗(h	∗(h	PROPN
ejpam-3184	27	6	)	)	PUNCT
ejpam-3184	27	7	is	be	AUX
ejpam-3184	27	8	the	the	DET
ejpam-3184	27	9	generalized	generalized	ADJ
ejpam-3184	27	10	fitting	fitting	ADJ
ejpam-3184	27	11	subgroup	subgroup	NOUN
ejpam-3184	27	12	of	of	ADP
ejpam-3184	27	13	h.	h.	PROPN
ejpam-3184	27	14	more	more	ADV
ejpam-3184	27	15	precisely	precisely	ADV
ejpam-3184	27	16	,	,	PUNCT
ejpam-3184	27	17	we	we	PRON
ejpam-3184	27	18	prove	prove	VERB
ejpam-3184	27	19	the	the	DET
ejpam-3184	27	20	following	follow	VERB
ejpam-3184	27	21	theorem	theorem	NOUN
ejpam-3184	27	22	:	:	PUNCT
ejpam-3184	27	23	theorem	theorem	NOUN
ejpam-3184	27	24	1.2	1.2	NUM
ejpam-3184	27	25	.	.	PUNCT
ejpam-3184	28	1	let	let	AUX
ejpam-3184	28	2	f	f	PRON
ejpam-3184	28	3	be	be	AUX
ejpam-3184	28	4	a	a	DET
ejpam-3184	28	5	saturated	saturated	ADJ
ejpam-3184	28	6	formation	formation	NOUN
ejpam-3184	28	7	containing	contain	VERB
ejpam-3184	28	8	the	the	DET
ejpam-3184	28	9	class	class	NOUN
ejpam-3184	28	10	of	of	ADP
ejpam-3184	28	11	supersolvable	supersolvable	ADJ
ejpam-3184	28	12	groups	group	NOUN
ejpam-3184	28	13	u.	u.	VERB
ejpam-3184	28	14	let	let	VERB
ejpam-3184	28	15	z	z	PRON
ejpam-3184	28	16	be	be	AUX
ejpam-3184	28	17	a	a	DET
ejpam-3184	28	18	complete	complete	ADJ
ejpam-3184	28	19	set	set	NOUN
ejpam-3184	28	20	of	of	ADP
ejpam-3184	28	21	sylow	sylow	NOUN
ejpam-3184	28	22	subgroups	subgroup	NOUN
ejpam-3184	28	23	of	of	ADP
ejpam-3184	28	24	a	a	DET
ejpam-3184	28	25	group	group	NOUN
ejpam-3184	28	26	g	g	NOUN
ejpam-3184	28	27	and	and	CCONJ
ejpam-3184	28	28	let	let	VERB
ejpam-3184	28	29	c	c	PRON
ejpam-3184	28	30	be	be	AUX
ejpam-3184	28	31	a	a	DET
ejpam-3184	28	32	solvable	solvable	ADJ
ejpam-3184	28	33	normal	normal	ADJ
ejpam-3184	28	34	subgroup	subgroup	NOUN
ejpam-3184	28	35	of	of	ADP
ejpam-3184	28	36	g.	g.	PROPN
ejpam-3184	28	37	then	then	ADV
ejpam-3184	28	38	the	the	DET
ejpam-3184	28	39	following	follow	VERB
ejpam-3184	28	40	two	two	NUM
ejpam-3184	28	41	statements	statement	NOUN
ejpam-3184	28	42	are	be	AUX
ejpam-3184	28	43	equivalent	equivalent	ADJ
ejpam-3184	28	44	:	:	PUNCT
ejpam-3184	28	45	(	(	PUNCT
ejpam-3184	28	46	a	a	X
ejpam-3184	28	47	)	)	PUNCT
ejpam-3184	28	48	g	g	PROPN
ejpam-3184	28	49	∈	∈	PROPN
ejpam-3184	28	50	f.	f.	PROPN
ejpam-3184	28	51	(	(	PUNCT
ejpam-3184	28	52	b	b	X
ejpam-3184	28	53	)	)	PUNCT
ejpam-3184	28	54	there	there	PRON
ejpam-3184	28	55	is	be	VERB
ejpam-3184	28	56	a	a	DET
ejpam-3184	28	57	normal	normal	ADJ
ejpam-3184	28	58	subgroup	subgroup	NOUN
ejpam-3184	28	59	h	h	NOUN
ejpam-3184	28	60	in	in	ADP
ejpam-3184	28	61	g	g	PROPN
ejpam-3184	28	62	such	such	ADJ
ejpam-3184	28	63	that	that	SCONJ
ejpam-3184	28	64	g	g	NOUN
ejpam-3184	28	65	/	/	SYM
ejpam-3184	28	66	h	h	NOUN
ejpam-3184	28	67	∈	∈	PROPN
ejpam-3184	28	68	f	f	PROPN
ejpam-3184	28	69	and	and	CCONJ
ejpam-3184	28	70	the	the	DET
ejpam-3184	28	71	maximal	maximal	ADJ
ejpam-3184	28	72	subgroups	subgroup	NOUN
ejpam-3184	28	73	of	of	ADP
ejpam-3184	28	74	gp	gp	NOUN
ejpam-3184	28	75	∩	∩	PROPN
ejpam-3184	28	76	f	f	PROPN
ejpam-3184	28	77	∗(h	∗(h	PROPN
ejpam-3184	28	78	)	)	PUNCT
ejpam-3184	28	79	are	be	AUX
ejpam-3184	28	80	c	c	NOUN
ejpam-3184	28	81	-	-	PUNCT
ejpam-3184	28	82	z	z	ADJ
ejpam-3184	28	83	-	-	PUNCT
ejpam-3184	28	84	permutable	permutable	ADJ
ejpam-3184	28	85	subgroups	subgroup	NOUN
ejpam-3184	28	86	of	of	ADP
ejpam-3184	28	87	g	g	NOUN
ejpam-3184	28	88	,	,	PUNCT
ejpam-3184	28	89	for	for	ADP
ejpam-3184	28	90	all	all	DET
ejpam-3184	28	91	gp	gp	NOUN
ejpam-3184	28	92	∈	∈	PROPN
ejpam-3184	28	93	z.	z.	PROPN
ejpam-3184	28	94	remark	remark	VERB
ejpam-3184	28	95	1.3	1.3	NUM
ejpam-3184	28	96	.	.	PUNCT
ejpam-3184	29	1	let	let	VERB
ejpam-3184	29	2	s(f	s(f	PROPN
ejpam-3184	29	3	∗(h	∗(h	PROPN
ejpam-3184	29	4	)	)	PUNCT
ejpam-3184	29	5	)	)	PUNCT
ejpam-3184	30	1	denotes	denote	VERB
ejpam-3184	30	2	the	the	DET
ejpam-3184	30	3	solvable	solvable	ADJ
ejpam-3184	30	4	radical	radical	NOUN
ejpam-3184	30	5	of	of	ADP
ejpam-3184	30	6	f	f	PROPN
ejpam-3184	30	7	∗(h	∗(h	PROPN
ejpam-3184	30	8	)	)	PUNCT
ejpam-3184	30	9	,	,	PUNCT
ejpam-3184	30	10	that	that	ADV
ejpam-3184	30	11	is	is	ADV
ejpam-3184	30	12	,	,	PUNCT
ejpam-3184	30	13	s(f	s(f	PROPN
ejpam-3184	30	14	∗(h	∗(h	PROPN
ejpam-3184	30	15	)	)	PUNCT
ejpam-3184	30	16	)	)	PUNCT
ejpam-3184	30	17	is	be	AUX
ejpam-3184	30	18	the	the	DET
ejpam-3184	30	19	unique	unique	ADJ
ejpam-3184	30	20	largest	large	ADJ
ejpam-3184	30	21	solvable	solvable	ADJ
ejpam-3184	30	22	normal	normal	ADJ
ejpam-3184	30	23	subgroup	subgroup	NOUN
ejpam-3184	30	24	of	of	ADP
ejpam-3184	30	25	f	f	PROPN
ejpam-3184	30	26	∗(h	∗(h	PROPN
ejpam-3184	30	27	)	)	PUNCT
ejpam-3184	30	28	.	.	PUNCT
ejpam-3184	31	1	in	in	ADP
ejpam-3184	31	2	theorem	theorem	NOUN
ejpam-3184	31	3	1.1	1.1	NUM
ejpam-3184	31	4	,	,	PUNCT
ejpam-3184	31	5	c	c	PROPN
ejpam-3184	31	6	is	be	AUX
ejpam-3184	31	7	a	a	DET
ejpam-3184	31	8	solvable	solvable	ADJ
ejpam-3184	31	9	normal	normal	ADJ
ejpam-3184	31	10	subgroup	subgroup	NOUN
ejpam-3184	31	11	of	of	ADP
ejpam-3184	31	12	f	f	PROPN
ejpam-3184	31	13	∗(h	∗(h	PROPN
ejpam-3184	31	14	)	)	PUNCT
ejpam-3184	31	15	.	.	PUNCT
ejpam-3184	32	1	therefore	therefore	ADV
ejpam-3184	32	2	,	,	PUNCT
ejpam-3184	32	3	c	c	PROPN
ejpam-3184	32	4	is	be	AUX
ejpam-3184	32	5	contained	contain	VERB
ejpam-3184	32	6	in	in	ADP
ejpam-3184	32	7	s(f	s(f	PROPN
ejpam-3184	32	8	∗(h	∗(h	PROPN
ejpam-3184	32	9	)	)	PUNCT
ejpam-3184	32	10	)	)	PUNCT
ejpam-3184	32	11	.	.	PUNCT
ejpam-3184	33	1	since	since	SCONJ
ejpam-3184	33	2	s(f	s(f	PROPN
ejpam-3184	33	3	∗(h	∗(h	PROPN
ejpam-3184	33	4	)	)	PUNCT
ejpam-3184	33	5	)	)	PUNCT
ejpam-3184	33	6	is	be	AUX
ejpam-3184	33	7	characteristic	characteristic	ADJ
ejpam-3184	33	8	in	in	ADP
ejpam-3184	33	9	f	f	PROPN
ejpam-3184	33	10	∗(h	∗(h	PROPN
ejpam-3184	33	11	)	)	PUNCT
ejpam-3184	33	12	and	and	CCONJ
ejpam-3184	33	13	f	f	PROPN
ejpam-3184	33	14	∗(h	∗(h	PROPN
ejpam-3184	33	15	)	)	PUNCT
ejpam-3184	33	16	is	be	AUX
ejpam-3184	33	17	normal	normal	ADJ
ejpam-3184	33	18	in	in	ADP
ejpam-3184	33	19	g	g	PROPN
ejpam-3184	33	20	,	,	PUNCT
ejpam-3184	33	21	we	we	PRON
ejpam-3184	33	22	have	have	VERB
ejpam-3184	33	23	that	that	DET
ejpam-3184	33	24	s(f	s(f	PROPN
ejpam-3184	33	25	∗(h	∗(h	PROPN
ejpam-3184	33	26	)	)	PUNCT
ejpam-3184	33	27	)	)	PUNCT
ejpam-3184	33	28	is	be	AUX
ejpam-3184	33	29	normal	normal	ADJ
ejpam-3184	33	30	in	in	ADP
ejpam-3184	33	31	g.	g.	PROPN
ejpam-3184	34	1	so	so	ADV
ejpam-3184	34	2	,	,	PUNCT
ejpam-3184	34	3	the	the	DET
ejpam-3184	34	4	maximal	maximal	ADJ
ejpam-3184	34	5	subgroups	subgroup	NOUN
ejpam-3184	34	6	of	of	ADP
ejpam-3184	34	7	gp	gp	NOUN
ejpam-3184	34	8	∩	∩	PROPN
ejpam-3184	34	9	f	f	PROPN
ejpam-3184	34	10	∗(h	∗(h	PROPN
ejpam-3184	34	11	)	)	PUNCT
ejpam-3184	34	12	are	be	AUX
ejpam-3184	34	13	s(f	s(f	PROPN
ejpam-3184	34	14	∗(h))-z	∗(h))-z	PROPN
ejpam-3184	34	15	-	-	PUNCT
ejpam-3184	34	16	permutable	permutable	ADJ
ejpam-3184	34	17	subgroups	subgroup	NOUN
ejpam-3184	34	18	of	of	ADP
ejpam-3184	34	19	g	g	NOUN
ejpam-3184	34	20	,	,	PUNCT
ejpam-3184	34	21	for	for	ADP
ejpam-3184	34	22	all	all	PRON
ejpam-3184	34	23	gp	gp	NOUN
ejpam-3184	34	24	∈	∈	PROPN
ejpam-3184	35	1	z	z	PROPN
ejpam-3184	35	2	,	,	PUNCT
ejpam-3184	35	3	where	where	SCONJ
ejpam-3184	35	4	s(f	s(f	PROPN
ejpam-3184	35	5	∗(h	∗(h	PROPN
ejpam-3184	35	6	)	)	PUNCT
ejpam-3184	35	7	)	)	PUNCT
ejpam-3184	35	8	is	be	AUX
ejpam-3184	35	9	a	a	DET
ejpam-3184	35	10	solvable	solvable	ADJ
ejpam-3184	35	11	normal	normal	ADJ
ejpam-3184	35	12	subgroup	subgroup	NOUN
ejpam-3184	35	13	of	of	ADP
ejpam-3184	35	14	g.	g.	PROPN
ejpam-3184	35	15	thus	thus	ADV
ejpam-3184	35	16	,	,	PUNCT
ejpam-3184	35	17	theorem	theorem	VERB
ejpam-3184	35	18	1.1	1.1	NUM
ejpam-3184	35	19	can	can	AUX
ejpam-3184	35	20	be	be	AUX
ejpam-3184	35	21	seen	see	VERB
ejpam-3184	35	22	as	as	ADP
ejpam-3184	35	23	an	an	DET
ejpam-3184	35	24	immediate	immediate	ADJ
ejpam-3184	35	25	consequence	consequence	NOUN
ejpam-3184	35	26	of	of	ADP
ejpam-3184	35	27	theorem	theorem	ADJ
ejpam-3184	35	28	1.2	1.2	NUM
ejpam-3184	35	29	.	.	NOUN
ejpam-3184	35	30	2	2	NUM
ejpam-3184	35	31	.	.	NOUN
ejpam-3184	35	32	basic	basic	ADJ
ejpam-3184	35	33	definitions	definition	NOUN
ejpam-3184	35	34	and	and	CCONJ
ejpam-3184	35	35	preliminaries	preliminary	NOUN
ejpam-3184	35	36	in	in	ADP
ejpam-3184	35	37	this	this	DET
ejpam-3184	35	38	section	section	NOUN
ejpam-3184	35	39	,	,	PUNCT
ejpam-3184	35	40	we	we	PRON
ejpam-3184	35	41	list	list	VERB
ejpam-3184	35	42	some	some	DET
ejpam-3184	35	43	definitions	definition	NOUN
ejpam-3184	35	44	and	and	CCONJ
ejpam-3184	35	45	known	know	VERB
ejpam-3184	35	46	results	result	NOUN
ejpam-3184	35	47	from	from	ADP
ejpam-3184	35	48	the	the	DET
ejpam-3184	35	49	literature	literature	NOUN
ejpam-3184	35	50	that	that	PRON
ejpam-3184	35	51	will	will	AUX
ejpam-3184	35	52	be	be	AUX
ejpam-3184	35	53	used	use	VERB
ejpam-3184	35	54	in	in	ADP
ejpam-3184	35	55	the	the	DET
ejpam-3184	35	56	sequel	sequel	NOUN
ejpam-3184	35	57	.	.	PUNCT
ejpam-3184	36	1	m.	m.	NOUN
ejpam-3184	36	2	m.	m.	PROPN
ejpam-3184	36	3	al	al	PROPN
ejpam-3184	36	4	-	-	PUNCT
ejpam-3184	36	5	shomrani	shomrani	PROPN
ejpam-3184	36	6	,	,	PUNCT
ejpam-3184	36	7	a.	a.	NOUN
ejpam-3184	36	8	a.	a.	NOUN
ejpam-3184	36	9	heliel	heliel	PROPN
ejpam-3184	36	10	/	/	SYM
ejpam-3184	36	11	eur	eur	PROPN
ejpam-3184	36	12	.	.	PUNCT
ejpam-3184	37	1	j.	j.	PROPN
ejpam-3184	37	2	pure	pure	PROPN
ejpam-3184	37	3	appl	appl	PROPN
ejpam-3184	37	4	.	.	PROPN
ejpam-3184	37	5	math	math	PROPN
ejpam-3184	37	6	,	,	PUNCT
ejpam-3184	37	7	11	11	NUM
ejpam-3184	37	8	(	(	PUNCT
ejpam-3184	37	9	1	1	NUM
ejpam-3184	37	10	)	)	PUNCT
ejpam-3184	37	11	(	(	PUNCT
ejpam-3184	37	12	2018	2018	NUM
ejpam-3184	37	13	)	)	PUNCT
ejpam-3184	37	14	,	,	PUNCT
ejpam-3184	37	15	160	160	NUM
ejpam-3184	37	16	-	-	SYM
ejpam-3184	37	17	168	168	NUM
ejpam-3184	37	18	162	162	NUM
ejpam-3184	37	19	let	let	VERB
ejpam-3184	37	20	f	f	PRON
ejpam-3184	37	21	be	be	AUX
ejpam-3184	37	22	a	a	DET
ejpam-3184	37	23	saturated	saturated	ADJ
ejpam-3184	37	24	formation	formation	NOUN
ejpam-3184	37	25	.	.	PUNCT
ejpam-3184	38	1	then	then	ADV
ejpam-3184	38	2	the	the	DET
ejpam-3184	38	3	f	f	NOUN
ejpam-3184	38	4	-	-	PUNCT
ejpam-3184	38	5	residual	residual	ADJ
ejpam-3184	38	6	,	,	PUNCT
ejpam-3184	38	7	denoted	denote	VERB
ejpam-3184	38	8	by	by	ADP
ejpam-3184	38	9	gf	gf	PROPN
ejpam-3184	38	10	,	,	PUNCT
ejpam-3184	38	11	is	be	AUX
ejpam-3184	38	12	the	the	DET
ejpam-3184	38	13	unique	unique	ADJ
ejpam-3184	38	14	smallest	small	ADJ
ejpam-3184	38	15	normal	normal	ADJ
ejpam-3184	38	16	subgroup	subgroup	NOUN
ejpam-3184	38	17	of	of	ADP
ejpam-3184	38	18	g	g	PROPN
ejpam-3184	38	19	such	such	ADJ
ejpam-3184	38	20	that	that	SCONJ
ejpam-3184	38	21	g	g	NOUN
ejpam-3184	38	22	/	/	SYM
ejpam-3184	38	23	gf	gf	PROPN
ejpam-3184	38	24	∈	∈	PROPN
ejpam-3184	38	25	f.	f.	PROPN
ejpam-3184	38	26	throughout	throughout	PROPN
ejpam-3184	38	27	,	,	PUNCT
ejpam-3184	38	28	u	u	NOUN
ejpam-3184	38	29	denotes	denote	VERB
ejpam-3184	38	30	the	the	DET
ejpam-3184	38	31	class	class	NOUN
ejpam-3184	38	32	of	of	ADP
ejpam-3184	38	33	supersolvable	supersolvable	ADJ
ejpam-3184	38	34	groups	group	NOUN
ejpam-3184	38	35	which	which	PRON
ejpam-3184	38	36	is	be	AUX
ejpam-3184	38	37	a	a	DET
ejpam-3184	38	38	saturated	saturate	VERB
ejpam-3184	38	39	formations	formation	NOUN
ejpam-3184	38	40	,	,	PUNCT
ejpam-3184	38	41	see	see	VERB
ejpam-3184	38	42	[	[	X
ejpam-3184	38	43	[	[	X
ejpam-3184	38	44	5	5	NUM
ejpam-3184	38	45	]	]	PUNCT
ejpam-3184	38	46	,	,	PUNCT
ejpam-3184	38	47	satz	satz	PROPN
ejpam-3184	38	48	8.6	8.6	NUM
ejpam-3184	38	49	,	,	PUNCT
ejpam-3184	38	50	p.	p.	NOUN
ejpam-3184	38	51	713	713	NUM
ejpam-3184	38	52	]	]	PUNCT
ejpam-3184	38	53	.	.	PUNCT
ejpam-3184	39	1	a	a	DET
ejpam-3184	39	2	normal	normal	ADJ
ejpam-3184	39	3	subgroup	subgroup	NOUN
ejpam-3184	39	4	n	n	PROPN
ejpam-3184	39	5	of	of	ADP
ejpam-3184	39	6	a	a	DET
ejpam-3184	39	7	group	group	NOUN
ejpam-3184	39	8	g	g	NOUN
ejpam-3184	39	9	is	be	AUX
ejpam-3184	39	10	an	an	DET
ejpam-3184	39	11	f	f	ADJ
ejpam-3184	39	12	-	-	PUNCT
ejpam-3184	39	13	hypercentral	hypercentral	ADJ
ejpam-3184	39	14	subgroup	subgroup	NOUN
ejpam-3184	39	15	of	of	ADP
ejpam-3184	39	16	g	g	PROPN
ejpam-3184	39	17	provided	provide	VERB
ejpam-3184	39	18	n	n	PROPN
ejpam-3184	39	19	possesses	possess	VERB
ejpam-3184	39	20	a	a	DET
ejpam-3184	39	21	chain	chain	NOUN
ejpam-3184	39	22	of	of	ADP
ejpam-3184	39	23	subgroups	subgroup	NOUN
ejpam-3184	39	24	1	1	NUM
ejpam-3184	39	25	=	=	SYM
ejpam-3184	39	26	n0	n0	X
ejpam-3184	39	27	e	e	X
ejpam-3184	39	28	n1	n1	PROPN
ejpam-3184	39	29	e	e	X
ejpam-3184	39	30	...	...	PUNCT
ejpam-3184	40	1	e	e	X
ejpam-3184	40	2	ns	ns	NUM
ejpam-3184	40	3	=	=	NOUN
ejpam-3184	40	4	n	n	PRON
ejpam-3184	40	5	such	such	ADJ
ejpam-3184	40	6	that	that	SCONJ
ejpam-3184	40	7	ni+1	ni+1	PROPN
ejpam-3184	40	8	/	/	SYM
ejpam-3184	40	9	ni	ni	PROPN
ejpam-3184	40	10	is	be	AUX
ejpam-3184	40	11	an	an	DET
ejpam-3184	40	12	f	f	ADJ
ejpam-3184	40	13	-	-	ADJ
ejpam-3184	40	14	central	central	ADJ
ejpam-3184	40	15	chief	chief	ADJ
ejpam-3184	40	16	factor	factor	NOUN
ejpam-3184	40	17	of	of	ADP
ejpam-3184	40	18	g	g	NOUN
ejpam-3184	40	19	,	,	PUNCT
ejpam-3184	40	20	see	see	VERB
ejpam-3184	40	21	[	[	X
ejpam-3184	40	22	[	[	X
ejpam-3184	40	23	2	2	NUM
ejpam-3184	40	24	]	]	PUNCT
ejpam-3184	40	25	,	,	PUNCT
ejpam-3184	40	26	p.	p.	NOUN
ejpam-3184	40	27	387	387	NUM
ejpam-3184	40	28	]	]	PUNCT
ejpam-3184	40	29	.	.	PUNCT
ejpam-3184	41	1	the	the	DET
ejpam-3184	41	2	product	product	NOUN
ejpam-3184	41	3	of	of	ADP
ejpam-3184	41	4	all	all	DET
ejpam-3184	41	5	f	f	ADJ
ejpam-3184	41	6	-	-	PUNCT
ejpam-3184	41	7	hypercentral	hypercentral	ADJ
ejpam-3184	41	8	subgroups	subgroup	NOUN
ejpam-3184	41	9	of	of	ADP
ejpam-3184	41	10	g	g	PROPN
ejpam-3184	41	11	is	be	AUX
ejpam-3184	41	12	again	again	ADV
ejpam-3184	41	13	an	an	DET
ejpam-3184	41	14	f	f	X
ejpam-3184	41	15	-	-	PUNCT
ejpam-3184	41	16	hypercentral	hypercentral	ADJ
ejpam-3184	41	17	subgroup	subgroup	NOUN
ejpam-3184	41	18	,	,	PUNCT
ejpam-3184	41	19	denoted	denote	VERB
ejpam-3184	41	20	by	by	ADP
ejpam-3184	41	21	zf(g	zf(g	NUM
ejpam-3184	41	22	)	)	PUNCT
ejpam-3184	41	23	,	,	PUNCT
ejpam-3184	41	24	and	and	CCONJ
ejpam-3184	41	25	called	call	VERB
ejpam-3184	41	26	the	the	DET
ejpam-3184	41	27	f	f	NOUN
ejpam-3184	41	28	-	-	PUNCT
ejpam-3184	41	29	hypercenter	hypercenter	NOUN
ejpam-3184	41	30	of	of	ADP
ejpam-3184	41	31	g	g	NOUN
ejpam-3184	41	32	,	,	PUNCT
ejpam-3184	41	33	see	see	VERB
ejpam-3184	41	34	[	[	X
ejpam-3184	41	35	[	[	X
ejpam-3184	41	36	2	2	NUM
ejpam-3184	41	37	]	]	PUNCT
ejpam-3184	41	38	,	,	PUNCT
ejpam-3184	41	39	iv	iv	X
ejpam-3184	41	40	,	,	PUNCT
ejpam-3184	41	41	6.8	6.8	NUM
ejpam-3184	41	42	]	]	PUNCT
ejpam-3184	41	43	.	.	PUNCT
ejpam-3184	42	1	for	for	ADP
ejpam-3184	42	2	the	the	DET
ejpam-3184	42	3	formation	formation	NOUN
ejpam-3184	42	4	u	u	NOUN
ejpam-3184	42	5	,	,	PUNCT
ejpam-3184	42	6	the	the	DET
ejpam-3184	42	7	u	u	NOUN
ejpam-3184	42	8	-	-	NOUN
ejpam-3184	42	9	hypercenter	hypercenter	NOUN
ejpam-3184	42	10	of	of	ADP
ejpam-3184	42	11	a	a	DET
ejpam-3184	42	12	group	group	NOUN
ejpam-3184	42	13	g	g	NOUN
ejpam-3184	42	14	,	,	PUNCT
ejpam-3184	42	15	denoted	denote	VERB
ejpam-3184	42	16	by	by	ADP
ejpam-3184	42	17	zu(g	zu(g	NOUN
ejpam-3184	42	18	)	)	PUNCT
ejpam-3184	42	19	,	,	PUNCT
ejpam-3184	42	20	is	be	AUX
ejpam-3184	42	21	the	the	DET
ejpam-3184	42	22	product	product	NOUN
ejpam-3184	42	23	of	of	ADP
ejpam-3184	42	24	all	all	DET
ejpam-3184	42	25	normal	normal	ADJ
ejpam-3184	42	26	subgroups	subgroup	NOUN
ejpam-3184	42	27	n	n	CCONJ
ejpam-3184	42	28	of	of	ADP
ejpam-3184	42	29	g	g	NOUN
ejpam-3184	42	30	such	such	ADJ
ejpam-3184	42	31	that	that	SCONJ
ejpam-3184	42	32	each	each	DET
ejpam-3184	42	33	chief	chief	ADJ
ejpam-3184	42	34	factor	factor	NOUN
ejpam-3184	42	35	of	of	ADP
ejpam-3184	42	36	g	g	NOUN
ejpam-3184	42	37	below	below	ADP
ejpam-3184	42	38	n	n	PRON
ejpam-3184	42	39	has	have	VERB
ejpam-3184	42	40	prime	prime	ADJ
ejpam-3184	42	41	order	order	NOUN
ejpam-3184	42	42	.	.	PUNCT
ejpam-3184	43	1	for	for	ADP
ejpam-3184	43	2	more	more	ADJ
ejpam-3184	43	3	details	detail	NOUN
ejpam-3184	43	4	about	about	ADP
ejpam-3184	43	5	saturated	saturate	VERB
ejpam-3184	43	6	formations	formation	NOUN
ejpam-3184	43	7	,	,	PUNCT
ejpam-3184	43	8	see	see	VERB
ejpam-3184	44	1	[	[	X
ejpam-3184	44	2	[	[	X
ejpam-3184	44	3	2	2	NUM
ejpam-3184	44	4	]	]	PUNCT
ejpam-3184	44	5	,	,	PUNCT
ejpam-3184	44	6	iv	iv	ADP
ejpam-3184	44	7	]	]	PUNCT
ejpam-3184	44	8	.	.	PUNCT
ejpam-3184	45	1	for	for	ADP
ejpam-3184	45	2	any	any	DET
ejpam-3184	45	3	groupg	groupg	NOUN
ejpam-3184	45	4	,	,	PUNCT
ejpam-3184	45	5	the	the	DET
ejpam-3184	45	6	generalized	generalized	ADJ
ejpam-3184	45	7	fitting	fitting	ADJ
ejpam-3184	45	8	subgroup	subgroup	NOUN
ejpam-3184	45	9	f	f	PROPN
ejpam-3184	45	10	∗(g	∗(g	PROPN
ejpam-3184	45	11	)	)	PUNCT
ejpam-3184	45	12	is	be	AUX
ejpam-3184	45	13	the	the	DET
ejpam-3184	45	14	unique	unique	ADJ
ejpam-3184	45	15	maximal	maximal	ADJ
ejpam-3184	45	16	normal	normal	ADJ
ejpam-3184	45	17	quasinilpotent	quasinilpotent	NOUN
ejpam-3184	45	18	subgroup	subgroup	NOUN
ejpam-3184	45	19	of	of	ADP
ejpam-3184	45	20	g.	g.	PROPN
ejpam-3184	45	21	in	in	ADP
ejpam-3184	45	22	fact	fact	NOUN
ejpam-3184	45	23	,	,	PUNCT
ejpam-3184	45	24	f	f	PROPN
ejpam-3184	45	25	∗(g	∗(g	PROPN
ejpam-3184	45	26	)	)	PUNCT
ejpam-3184	45	27	is	be	AUX
ejpam-3184	45	28	an	an	DET
ejpam-3184	45	29	important	important	ADJ
ejpam-3184	45	30	characteristic	characteristic	ADJ
ejpam-3184	45	31	subgroup	subgroup	NOUN
ejpam-3184	45	32	of	of	ADP
ejpam-3184	45	33	g	g	PROPN
ejpam-3184	46	1	and	and	CCONJ
ejpam-3184	46	2	it	it	PRON
ejpam-3184	46	3	is	be	AUX
ejpam-3184	46	4	a	a	DET
ejpam-3184	46	5	natural	natural	ADJ
ejpam-3184	46	6	generalization	generalization	NOUN
ejpam-3184	46	7	of	of	ADP
ejpam-3184	46	8	f	f	PROPN
ejpam-3184	46	9	(	(	PUNCT
ejpam-3184	46	10	g	g	NOUN
ejpam-3184	46	11	)	)	PUNCT
ejpam-3184	46	12	.	.	PUNCT
ejpam-3184	47	1	the	the	DET
ejpam-3184	47	2	basic	basic	ADJ
ejpam-3184	47	3	properties	property	NOUN
ejpam-3184	47	4	of	of	ADP
ejpam-3184	47	5	f	f	PROPN
ejpam-3184	47	6	∗(g	∗(g	PROPN
ejpam-3184	47	7	)	)	PUNCT
ejpam-3184	47	8	can	can	AUX
ejpam-3184	47	9	be	be	AUX
ejpam-3184	47	10	found	find	VERB
ejpam-3184	47	11	in	in	ADP
ejpam-3184	47	12	[	[	X
ejpam-3184	47	13	[	[	X
ejpam-3184	47	14	6	6	NUM
ejpam-3184	47	15	]	]	PUNCT
ejpam-3184	47	16	,	,	PUNCT
ejpam-3184	47	17	x	x	X
ejpam-3184	47	18	13	13	NUM
ejpam-3184	47	19	]	]	PUNCT
ejpam-3184	47	20	.	.	PUNCT
ejpam-3184	48	1	we	we	PRON
ejpam-3184	48	2	define	define	VERB
ejpam-3184	48	3	f	f	X
ejpam-3184	48	4	∗1	∗1	PROPN
ejpam-3184	48	5	(	(	PUNCT
ejpam-3184	48	6	g	g	NOUN
ejpam-3184	48	7	)	)	PUNCT
ejpam-3184	48	8	=	=	SYM
ejpam-3184	48	9	f	f	PROPN
ejpam-3184	48	10	∗(g	∗(g	PROPN
ejpam-3184	48	11	)	)	PUNCT
ejpam-3184	48	12	and	and	CCONJ
ejpam-3184	48	13	f	f	X
ejpam-3184	48	14	∗i	∗i	PROPN
ejpam-3184	48	15	(	(	PUNCT
ejpam-3184	48	16	g)/f	g)/f	PROPN
ejpam-3184	48	17	∗i−1(g	∗i−1(g	PROPN
ejpam-3184	48	18	)	)	PUNCT
ejpam-3184	48	19	=	=	SYM
ejpam-3184	49	1	f	f	X
ejpam-3184	49	2	∗(g	∗(g	PROPN
ejpam-3184	49	3	/	/	SYM
ejpam-3184	49	4	f	f	PROPN
ejpam-3184	49	5	∗i−1(g	∗i−1(g	PROPN
ejpam-3184	49	6	)	)	PUNCT
ejpam-3184	49	7	)	)	PUNCT
ejpam-3184	50	1	for	for	ADP
ejpam-3184	50	2	i	i	PRON
ejpam-3184	50	3	>	>	X
ejpam-3184	50	4	1	1	X
ejpam-3184	50	5	.	.	PUNCT
ejpam-3184	51	1	since	since	SCONJ
ejpam-3184	51	2	f	f	PROPN
ejpam-3184	51	3	∗(g	∗(g	PROPN
ejpam-3184	51	4	)	)	PUNCT
ejpam-3184	51	5	6=	6=	ADP
ejpam-3184	51	6	1	1	NUM
ejpam-3184	51	7	when	when	SCONJ
ejpam-3184	51	8	g	g	PROPN
ejpam-3184	51	9	6=	6=	PROPN
ejpam-3184	51	10	1	1	NUM
ejpam-3184	51	11	,	,	PUNCT
ejpam-3184	51	12	there	there	PRON
ejpam-3184	51	13	exists	exist	VERB
ejpam-3184	51	14	an	an	DET
ejpam-3184	51	15	integer	integer	NOUN
ejpam-3184	51	16	n	n	CCONJ
ejpam-3184	51	17	such	such	ADJ
ejpam-3184	51	18	that	that	SCONJ
ejpam-3184	51	19	f	f	PROPN
ejpam-3184	51	20	∗n(g	∗n(g	PROPN
ejpam-3184	51	21	)	)	PUNCT
ejpam-3184	51	22	=	=	SYM
ejpam-3184	51	23	g.	g.	NOUN
ejpam-3184	51	24	let	let	VERB
ejpam-3184	51	25	z	z	PRON
ejpam-3184	51	26	be	be	AUX
ejpam-3184	51	27	a	a	DET
ejpam-3184	51	28	complete	complete	ADJ
ejpam-3184	51	29	set	set	NOUN
ejpam-3184	51	30	of	of	ADP
ejpam-3184	51	31	sylow	sylow	NOUN
ejpam-3184	51	32	subgroups	subgroup	NOUN
ejpam-3184	51	33	of	of	ADP
ejpam-3184	51	34	a	a	DET
ejpam-3184	51	35	group	group	NOUN
ejpam-3184	51	36	g	g	NOUN
ejpam-3184	51	37	and	and	CCONJ
ejpam-3184	51	38	let	let	VERB
ejpam-3184	51	39	n	n	PRON
ejpam-3184	51	40	be	be	AUX
ejpam-3184	51	41	a	a	DET
ejpam-3184	51	42	normal	normal	ADJ
ejpam-3184	51	43	subgroup	subgroup	NOUN
ejpam-3184	51	44	of	of	ADP
ejpam-3184	51	45	g.	g.	PROPN
ejpam-3184	51	46	we	we	PRON
ejpam-3184	51	47	denote	denote	VERB
ejpam-3184	51	48	the	the	DET
ejpam-3184	51	49	following	follow	VERB
ejpam-3184	51	50	families	family	NOUN
ejpam-3184	51	51	of	of	ADP
ejpam-3184	51	52	subgroups	subgroup	NOUN
ejpam-3184	51	53	of	of	ADP
ejpam-3184	51	54	g	g	NOUN
ejpam-3184	51	55	,	,	PUNCT
ejpam-3184	51	56	g	g	NOUN
ejpam-3184	51	57	/	/	SYM
ejpam-3184	51	58	n	n	NOUN
ejpam-3184	51	59	and	and	CCONJ
ejpam-3184	51	60	n	n	CCONJ
ejpam-3184	51	61	,	,	PUNCT
ejpam-3184	51	62	respectively	respectively	ADV
ejpam-3184	51	63	:	:	PUNCT
ejpam-3184	51	64	zn	zn	PROPN
ejpam-3184	51	65	=	=	SYM
ejpam-3184	51	66	{	{	PUNCT
ejpam-3184	51	67	gpn	gpn	NOUN
ejpam-3184	51	68	:	:	PUNCT
ejpam-3184	51	69	gp	gp	NOUN
ejpam-3184	51	70	∈	∈	PROPN
ejpam-3184	52	1	z	z	X
ejpam-3184	52	2	}	}	PUNCT
ejpam-3184	52	3	,	,	PUNCT
ejpam-3184	52	4	zn	zn	PROPN
ejpam-3184	52	5	/	/	SYM
ejpam-3184	52	6	n	n	PROPN
ejpam-3184	52	7	=	=	PRON
ejpam-3184	52	8	{	{	PUNCT
ejpam-3184	52	9	gpn	gpn	PROPN
ejpam-3184	52	10	/	/	SYM
ejpam-3184	52	11	n	n	PROPN
ejpam-3184	52	12	:	:	PUNCT
ejpam-3184	52	13	gp	gp	NOUN
ejpam-3184	52	14	∈	∈	PROPN
ejpam-3184	53	1	z	z	X
ejpam-3184	53	2	}	}	PUNCT
ejpam-3184	53	3	,	,	PUNCT
ejpam-3184	53	4	z	z	NOUN
ejpam-3184	53	5	∩n	∩n	NOUN
ejpam-3184	53	6	=	=	PRON
ejpam-3184	53	7	{	{	PUNCT
ejpam-3184	53	8	gp	gp	NOUN
ejpam-3184	53	9	∩n	∩n	NOUN
ejpam-3184	53	10	:	:	PUNCT
ejpam-3184	53	11	gp	gp	PROPN
ejpam-3184	53	12	∈	∈	PROPN
ejpam-3184	54	1	z	z	X
ejpam-3184	54	2	}	}	PUNCT
ejpam-3184	54	3	.	.	PUNCT
ejpam-3184	55	1	the	the	DET
ejpam-3184	55	2	following	follow	VERB
ejpam-3184	55	3	lemmas	lemmas	PROPN
ejpam-3184	55	4	will	will	AUX
ejpam-3184	55	5	be	be	AUX
ejpam-3184	55	6	used	use	VERB
ejpam-3184	55	7	in	in	ADP
ejpam-3184	55	8	the	the	DET
ejpam-3184	55	9	sequel	sequel	NOUN
ejpam-3184	55	10	.	.	PUNCT
ejpam-3184	56	1	lemma	lemma	PROPN
ejpam-3184	56	2	2.1	2.1	NUM
ejpam-3184	56	3	.	.	PUNCT
ejpam-3184	57	1	let	let	VERB
ejpam-3184	57	2	z	z	PRON
ejpam-3184	57	3	be	be	AUX
ejpam-3184	57	4	a	a	DET
ejpam-3184	57	5	complete	complete	ADJ
ejpam-3184	57	6	set	set	NOUN
ejpam-3184	57	7	of	of	ADP
ejpam-3184	57	8	sylow	sylow	NOUN
ejpam-3184	57	9	subgroups	subgroup	NOUN
ejpam-3184	57	10	of	of	ADP
ejpam-3184	57	11	a	a	DET
ejpam-3184	57	12	group	group	NOUN
ejpam-3184	57	13	g	g	NOUN
ejpam-3184	57	14	,	,	PUNCT
ejpam-3184	57	15	c	c	AUX
ejpam-3184	57	16	be	be	AUX
ejpam-3184	57	17	a	a	DET
ejpam-3184	57	18	nonempty	nonempty	ADJ
ejpam-3184	57	19	subset	subset	NOUN
ejpam-3184	57	20	of	of	ADP
ejpam-3184	57	21	g	g	PROPN
ejpam-3184	57	22	and	and	CCONJ
ejpam-3184	57	23	n	n	CCONJ
ejpam-3184	57	24	be	be	VERB
ejpam-3184	57	25	a	a	DET
ejpam-3184	57	26	normal	normal	ADJ
ejpam-3184	57	27	subgroup	subgroup	NOUN
ejpam-3184	57	28	of	of	ADP
ejpam-3184	57	29	g.	g.	PROPN
ejpam-3184	57	30	then	then	ADV
ejpam-3184	57	31	:	:	PUNCT
ejpam-3184	57	32	(	(	PUNCT
ejpam-3184	57	33	a	a	X
ejpam-3184	57	34	)	)	PUNCT
ejpam-3184	57	35	z∩n	z∩n	PROPN
ejpam-3184	57	36	and	and	CCONJ
ejpam-3184	57	37	zn	zn	NUM
ejpam-3184	57	38	/	/	SYM
ejpam-3184	57	39	n	n	PROPN
ejpam-3184	57	40	are	be	AUX
ejpam-3184	57	41	complete	complete	ADJ
ejpam-3184	57	42	sets	set	NOUN
ejpam-3184	57	43	of	of	ADP
ejpam-3184	57	44	sylow	sylow	NOUN
ejpam-3184	57	45	subgroups	subgroup	NOUN
ejpam-3184	57	46	of	of	ADP
ejpam-3184	57	47	n	n	PROPN
ejpam-3184	57	48	and	and	CCONJ
ejpam-3184	57	49	g	g	NOUN
ejpam-3184	57	50	/	/	SYM
ejpam-3184	57	51	n	n	NOUN
ejpam-3184	57	52	,	,	PUNCT
ejpam-3184	57	53	respectively	respectively	ADV
ejpam-3184	57	54	.	.	PUNCT
ejpam-3184	58	1	(	(	PUNCT
ejpam-3184	58	2	b	b	X
ejpam-3184	58	3	)	)	PUNCT
ejpam-3184	58	4	if	if	SCONJ
ejpam-3184	58	5	u	u	NOUN
ejpam-3184	58	6	is	be	AUX
ejpam-3184	58	7	c	c	NOUN
ejpam-3184	58	8	-	-	ADJ
ejpam-3184	58	9	z	z	ADJ
ejpam-3184	58	10	-	-	PUNCT
ejpam-3184	58	11	permutable	permutable	ADJ
ejpam-3184	58	12	subgroup	subgroup	NOUN
ejpam-3184	58	13	of	of	ADP
ejpam-3184	58	14	g	g	PROPN
ejpam-3184	58	15	,	,	PUNCT
ejpam-3184	58	16	then	then	ADV
ejpam-3184	58	17	un	un	PROPN
ejpam-3184	58	18	/	/	SYM
ejpam-3184	58	19	n	n	PRON
ejpam-3184	58	20	is	be	AUX
ejpam-3184	58	21	cn	cn	PROPN
ejpam-3184	58	22	/	/	SYM
ejpam-3184	58	23	n	n	CCONJ
ejpam-3184	58	24	-zn	-zn	ADJ
ejpam-3184	58	25	/	/	SYM
ejpam-3184	58	26	n	n	CCONJ
ejpam-3184	58	27	-permutable	-permutable	ADJ
ejpam-3184	58	28	subgroup	subgroup	NOUN
ejpam-3184	58	29	of	of	ADP
ejpam-3184	58	30	g	g	PROPN
ejpam-3184	58	31	/	/	SYM
ejpam-3184	58	32	n	n	PROPN
ejpam-3184	58	33	.	.	PUNCT
ejpam-3184	59	1	(	(	PUNCT
ejpam-3184	59	2	c	c	X
ejpam-3184	59	3	)	)	PUNCT
ejpam-3184	59	4	if	if	SCONJ
ejpam-3184	59	5	u	u	NOUN
ejpam-3184	59	6	≤	≤	X
ejpam-3184	59	7	n	n	CCONJ
ejpam-3184	59	8	,	,	PUNCT
ejpam-3184	59	9	c	c	PROPN
ejpam-3184	59	10	⊆	⊆	NUM
ejpam-3184	59	11	n	n	NOUN
ejpam-3184	59	12	and	and	CCONJ
ejpam-3184	59	13	u	u	NOUN
ejpam-3184	59	14	is	be	AUX
ejpam-3184	59	15	c	c	NOUN
ejpam-3184	59	16	-	-	ADJ
ejpam-3184	59	17	z	z	ADJ
ejpam-3184	59	18	-	-	PUNCT
ejpam-3184	59	19	permutable	permutable	ADJ
ejpam-3184	59	20	subgroup	subgroup	NOUN
ejpam-3184	59	21	of	of	ADP
ejpam-3184	59	22	g	g	PROPN
ejpam-3184	59	23	,	,	PUNCT
ejpam-3184	59	24	then	then	ADV
ejpam-3184	59	25	u	u	NOUN
ejpam-3184	59	26	is	be	AUX
ejpam-3184	59	27	c	c	NOUN
ejpam-3184	59	28	-	-	PUNCT
ejpam-3184	59	29	z	z	NOUN
ejpam-3184	59	30	∩	∩	NOUN
ejpam-3184	59	31	n	n	CCONJ
ejpam-3184	59	32	permutable	permutable	ADJ
ejpam-3184	59	33	subgroup	subgroup	NOUN
ejpam-3184	59	34	of	of	ADP
ejpam-3184	59	35	n	n	PROPN
ejpam-3184	59	36	.	.	PUNCT
ejpam-3184	60	1	(	(	PUNCT
ejpam-3184	60	2	d	d	X
ejpam-3184	60	3	)	)	PUNCT
ejpam-3184	60	4	suppose	suppose	VERB
ejpam-3184	60	5	that	that	SCONJ
ejpam-3184	60	6	n	n	PROPN
ejpam-3184	60	7	≤	≤	X
ejpam-3184	60	8	u	u	NOUN
ejpam-3184	60	9	.	.	PUNCT
ejpam-3184	61	1	then	then	ADV
ejpam-3184	61	2	u	u	NOUN
ejpam-3184	61	3	is	be	AUX
ejpam-3184	61	4	c	c	NOUN
ejpam-3184	61	5	-	-	ADJ
ejpam-3184	61	6	z	z	ADJ
ejpam-3184	61	7	-	-	PUNCT
ejpam-3184	61	8	permutable	permutable	ADJ
ejpam-3184	61	9	subgroup	subgroup	NOUN
ejpam-3184	61	10	of	of	ADP
ejpam-3184	61	11	g	g	PROPN
ejpam-3184	61	12	if	if	SCONJ
ejpam-3184	62	1	and	and	CCONJ
ejpam-3184	62	2	only	only	ADV
ejpam-3184	62	3	if	if	SCONJ
ejpam-3184	62	4	u	u	NOUN
ejpam-3184	62	5	/	/	SYM
ejpam-3184	62	6	n	n	PRON
ejpam-3184	62	7	is	be	AUX
ejpam-3184	62	8	cn	cn	PROPN
ejpam-3184	62	9	/	/	SYM
ejpam-3184	62	10	n	n	CCONJ
ejpam-3184	62	11	-zn	-zn	ADJ
ejpam-3184	62	12	/	/	SYM
ejpam-3184	62	13	n	n	CCONJ
ejpam-3184	62	14	-permutable	-permutable	ADJ
ejpam-3184	62	15	subgroup	subgroup	NOUN
ejpam-3184	62	16	of	of	ADP
ejpam-3184	62	17	g	g	PROPN
ejpam-3184	62	18	/	/	SYM
ejpam-3184	62	19	n	n	PROPN
ejpam-3184	62	20	.	.	PUNCT
ejpam-3184	63	1	(	(	PUNCT
ejpam-3184	63	2	e	e	X
ejpam-3184	63	3	)	)	PUNCT
ejpam-3184	63	4	if	if	SCONJ
ejpam-3184	63	5	u	u	NOUN
ejpam-3184	63	6	is	be	AUX
ejpam-3184	63	7	c	c	NOUN
ejpam-3184	63	8	-	-	ADJ
ejpam-3184	63	9	z	z	ADJ
ejpam-3184	63	10	-	-	PUNCT
ejpam-3184	63	11	permutable	permutable	ADJ
ejpam-3184	63	12	subgroup	subgroup	NOUN
ejpam-3184	63	13	of	of	ADP
ejpam-3184	63	14	g	g	PROPN
ejpam-3184	63	15	,	,	PUNCT
ejpam-3184	63	16	then	then	ADV
ejpam-3184	63	17	u	u	PROPN
ejpam-3184	63	18	∩n	∩n	PROPN
ejpam-3184	63	19	is	be	AUX
ejpam-3184	63	20	c	c	NOUN
ejpam-3184	63	21	-	-	PUNCT
ejpam-3184	63	22	z	z	ADJ
ejpam-3184	63	23	-	-	PUNCT
ejpam-3184	63	24	permutable	permutable	ADJ
ejpam-3184	63	25	subgroup	subgroup	NOUN
ejpam-3184	63	26	of	of	ADP
ejpam-3184	63	27	g.	g.	PROPN
ejpam-3184	63	28	proof	proof	NOUN
ejpam-3184	63	29	.	.	PUNCT
ejpam-3184	64	1	for	for	ADP
ejpam-3184	64	2	(	(	PUNCT
ejpam-3184	64	3	a	a	X
ejpam-3184	64	4	)	)	PUNCT
ejpam-3184	64	5	,	,	PUNCT
ejpam-3184	64	6	see	see	VERB
ejpam-3184	64	7	[	[	X
ejpam-3184	64	8	[	[	X
ejpam-3184	64	9	1	1	NUM
ejpam-3184	64	10	]	]	PUNCT
ejpam-3184	64	11	,	,	PUNCT
ejpam-3184	64	12	lemma	lemma	PROPN
ejpam-3184	64	13	2.1(a	2.1(a	NUM
ejpam-3184	64	14	)	)	PUNCT
ejpam-3184	64	15	]	]	PUNCT
ejpam-3184	64	16	.	.	PUNCT
ejpam-3184	65	1	for	for	ADP
ejpam-3184	65	2	(	(	PUNCT
ejpam-3184	65	3	b	b	NOUN
ejpam-3184	65	4	)	)	PUNCT
ejpam-3184	65	5	,	,	PUNCT
ejpam-3184	65	6	(	(	PUNCT
ejpam-3184	65	7	c	c	X
ejpam-3184	65	8	)	)	PUNCT
ejpam-3184	65	9	and	and	CCONJ
ejpam-3184	65	10	(	(	PUNCT
ejpam-3184	65	11	d	d	NOUN
ejpam-3184	65	12	)	)	PUNCT
ejpam-3184	65	13	;	;	PUNCT
ejpam-3184	65	14	see	see	VERB
ejpam-3184	65	15	[	[	X
ejpam-3184	65	16	[	[	X
ejpam-3184	65	17	4	4	NUM
ejpam-3184	65	18	]	]	PUNCT
ejpam-3184	65	19	,	,	PUNCT
ejpam-3184	65	20	lemma	lemma	PROPN
ejpam-3184	65	21	2.1	2.1	NUM
ejpam-3184	65	22	]	]	PUNCT
ejpam-3184	65	23	.	.	PUNCT
ejpam-3184	66	1	(	(	PUNCT
ejpam-3184	66	2	e	e	X
ejpam-3184	66	3	)	)	PUNCT
ejpam-3184	66	4	let	let	VERB
ejpam-3184	66	5	gp	gp	NOUN
ejpam-3184	66	6	be	be	AUX
ejpam-3184	66	7	any	any	DET
ejpam-3184	66	8	member	member	NOUN
ejpam-3184	66	9	of	of	ADP
ejpam-3184	66	10	z.	z.	PROPN
ejpam-3184	66	11	by	by	ADP
ejpam-3184	66	12	hypothesis	hypothesis	NOUN
ejpam-3184	66	13	,	,	PUNCT
ejpam-3184	66	14	there	there	PRON
ejpam-3184	66	15	exists	exist	VERB
ejpam-3184	66	16	some	some	DET
ejpam-3184	66	17	x	x	SYM
ejpam-3184	66	18	∈	∈	PROPN
ejpam-3184	66	19	c	c	NOUN
ejpam-3184	66	20	such	such	ADJ
ejpam-3184	66	21	that	that	DET
ejpam-3184	66	22	uxgp	uxgp	NOUN
ejpam-3184	66	23	is	be	AUX
ejpam-3184	66	24	a	a	DET
ejpam-3184	66	25	subgroup	subgroup	NOUN
ejpam-3184	66	26	of	of	ADP
ejpam-3184	66	27	g	g	PROPN
ejpam-3184	66	28	,	,	PUNCT
ejpam-3184	66	29	that	that	ADV
ejpam-3184	66	30	is	is	ADV
ejpam-3184	66	31	,	,	PUNCT
ejpam-3184	66	32	uxgp	uxgp	VERB
ejpam-3184	66	33	=	=	SYM
ejpam-3184	67	1	gpu	gpu	PROPN
ejpam-3184	67	2	x.	x.	NOUN
ejpam-3184	67	3	let	let	VERB
ejpam-3184	67	4	k	k	PROPN
ejpam-3184	67	5	=	=	SYM
ejpam-3184	67	6	ux	ux	PROPN
ejpam-3184	67	7	.	.	PUNCT
ejpam-3184	68	1	it	it	PRON
ejpam-3184	68	2	is	be	AUX
ejpam-3184	68	3	clear	clear	ADJ
ejpam-3184	68	4	that	that	SCONJ
ejpam-3184	68	5	gpkn	gpkn	PROPN
ejpam-3184	68	6	is	be	AUX
ejpam-3184	68	7	a	a	DET
ejpam-3184	68	8	subgroup	subgroup	NOUN
ejpam-3184	68	9	of	of	ADP
ejpam-3184	68	10	g	g	PROPN
ejpam-3184	68	11	as	as	SCONJ
ejpam-3184	68	12	n	n	NUM
ejpam-3184	68	13	is	be	AUX
ejpam-3184	68	14	normal	normal	ADJ
ejpam-3184	68	15	in	in	ADP
ejpam-3184	68	16	g.	g.	PROPN
ejpam-3184	68	17	since	since	SCONJ
ejpam-3184	68	18	gp	gp	PROPN
ejpam-3184	68	19	∩	∩	NOUN
ejpam-3184	68	20	kn	kn	PROPN
ejpam-3184	68	21	is	be	AUX
ejpam-3184	68	22	a	a	DET
ejpam-3184	68	23	p	p	NOUN
ejpam-3184	68	24	-	-	PUNCT
ejpam-3184	68	25	subgroup	subgroup	NOUN
ejpam-3184	68	26	of	of	ADP
ejpam-3184	68	27	kn	kn	PROPN
ejpam-3184	68	28	and	and	CCONJ
ejpam-3184	68	29	m.	m.	PROPN
ejpam-3184	68	30	m.	m.	PROPN
ejpam-3184	69	1	al	al	PROPN
ejpam-3184	69	2	-	-	PUNCT
ejpam-3184	69	3	shomrani	shomrani	PROPN
ejpam-3184	69	4	,	,	PUNCT
ejpam-3184	69	5	a.	a.	NOUN
ejpam-3184	69	6	a.	a.	NOUN
ejpam-3184	69	7	heliel	heliel	PROPN
ejpam-3184	69	8	/	/	SYM
ejpam-3184	69	9	eur	eur	PROPN
ejpam-3184	69	10	.	.	PUNCT
ejpam-3184	70	1	j.	j.	PROPN
ejpam-3184	70	2	pure	pure	PROPN
ejpam-3184	70	3	appl	appl	PROPN
ejpam-3184	70	4	.	.	PROPN
ejpam-3184	70	5	math	math	PROPN
ejpam-3184	70	6	,	,	PUNCT
ejpam-3184	70	7	11	11	NUM
ejpam-3184	70	8	(	(	PUNCT
ejpam-3184	70	9	1	1	NUM
ejpam-3184	70	10	)	)	PUNCT
ejpam-3184	70	11	(	(	PUNCT
ejpam-3184	70	12	2018	2018	NUM
ejpam-3184	70	13	)	)	PUNCT
ejpam-3184	70	14	,	,	PUNCT
ejpam-3184	70	15	160	160	NUM
ejpam-3184	70	16	-	-	SYM
ejpam-3184	70	17	168	168	NUM
ejpam-3184	70	18	163	163	NUM
ejpam-3184	70	19	|kn	|kn	DET
ejpam-3184	70	20	:	:	PUNCT
ejpam-3184	70	21	gp	gp	NOUN
ejpam-3184	70	22	∩kn	∩kn	NOUN
ejpam-3184	71	1	|	|	ADV
ejpam-3184	71	2	=	=	SYM
ejpam-3184	71	3	|gpkn	|gpkn	NOUN
ejpam-3184	71	4	:	:	PUNCT
ejpam-3184	71	5	gp|	gp|	NOUN
ejpam-3184	71	6	is	be	AUX
ejpam-3184	71	7	a	a	DET
ejpam-3184	71	8	p′-number	p′-number	NUM
ejpam-3184	71	9	as	as	SCONJ
ejpam-3184	71	10	gp	gp	NOUN
ejpam-3184	71	11	is	be	AUX
ejpam-3184	71	12	a	a	DET
ejpam-3184	71	13	sylow	sylow	NOUN
ejpam-3184	71	14	p	p	NOUN
ejpam-3184	71	15	-	-	PUNCT
ejpam-3184	71	16	subgroup	subgroup	NOUN
ejpam-3184	71	17	of	of	ADP
ejpam-3184	71	18	gpkn	gpkn	PROPN
ejpam-3184	71	19	,	,	PUNCT
ejpam-3184	71	20	it	it	PRON
ejpam-3184	71	21	follows	follow	VERB
ejpam-3184	71	22	that	that	SCONJ
ejpam-3184	71	23	gp∩kn	gp∩kn	PROPN
ejpam-3184	71	24	is	be	AUX
ejpam-3184	71	25	a	a	DET
ejpam-3184	71	26	sylow	sylow	NOUN
ejpam-3184	71	27	p	p	NOUN
ejpam-3184	71	28	-	-	PUNCT
ejpam-3184	71	29	subgroup	subgroup	NOUN
ejpam-3184	71	30	of	of	ADP
ejpam-3184	71	31	kn	kn	PROPN
ejpam-3184	71	32	.	.	PUNCT
ejpam-3184	72	1	also	also	ADV
ejpam-3184	72	2	,	,	PUNCT
ejpam-3184	72	3	gp∩k	gp∩k	PROPN
ejpam-3184	72	4	is	be	AUX
ejpam-3184	72	5	a	a	DET
ejpam-3184	72	6	p	p	NOUN
ejpam-3184	72	7	-	-	PUNCT
ejpam-3184	72	8	subgroup	subgroup	NOUN
ejpam-3184	72	9	of	of	ADP
ejpam-3184	72	10	k	k	PROPN
ejpam-3184	72	11	and	and	CCONJ
ejpam-3184	72	12	|k	|k	NOUN
ejpam-3184	72	13	:	:	PUNCT
ejpam-3184	72	14	gp	gp	NOUN
ejpam-3184	72	15	∩k|	∩k|	NOUN
ejpam-3184	72	16	=	=	SYM
ejpam-3184	72	17	|kgp	|kgp	NOUN
ejpam-3184	72	18	:	:	PUNCT
ejpam-3184	72	19	gp|	gp|	NOUN
ejpam-3184	72	20	is	be	AUX
ejpam-3184	72	21	a	a	DET
ejpam-3184	72	22	p′-number	p′-number	NUM
ejpam-3184	72	23	.	.	PUNCT
ejpam-3184	73	1	consequently	consequently	ADV
ejpam-3184	73	2	,	,	PUNCT
ejpam-3184	73	3	gp∩k	gp∩k	PROPN
ejpam-3184	73	4	is	be	AUX
ejpam-3184	73	5	a	a	DET
ejpam-3184	73	6	sylow	sylow	NOUN
ejpam-3184	73	7	p	p	NOUN
ejpam-3184	73	8	-	-	PUNCT
ejpam-3184	73	9	subgroup	subgroup	NOUN
ejpam-3184	73	10	of	of	ADP
ejpam-3184	73	11	k.	k.	PROPN
ejpam-3184	73	12	therefore	therefore	ADV
ejpam-3184	73	13	,	,	PUNCT
ejpam-3184	73	14	gp∩k∩n	gp∩k∩n	PROPN
ejpam-3184	73	15	=	=	SYM
ejpam-3184	73	16	(	(	PUNCT
ejpam-3184	73	17	gp∩k)∩	gp∩k)∩	X
ejpam-3184	73	18	(	(	PUNCT
ejpam-3184	73	19	k∩n	k∩n	PROPN
ejpam-3184	73	20	)	)	PUNCT
ejpam-3184	73	21	is	be	AUX
ejpam-3184	73	22	a	a	DET
ejpam-3184	73	23	sylow	sylow	NOUN
ejpam-3184	73	24	p	p	NOUN
ejpam-3184	73	25	-	-	PUNCT
ejpam-3184	73	26	subgroup	subgroup	NOUN
ejpam-3184	73	27	of	of	ADP
ejpam-3184	73	28	k∩n	k∩n	PROPN
ejpam-3184	73	29	as	as	ADP
ejpam-3184	73	30	k∩n	k∩n	PROPN
ejpam-3184	73	31	is	be	AUX
ejpam-3184	73	32	a	a	DET
ejpam-3184	73	33	normal	normal	ADJ
ejpam-3184	73	34	subgroup	subgroup	NOUN
ejpam-3184	73	35	of	of	ADP
ejpam-3184	73	36	k.	k.	PROPN
ejpam-3184	73	37	if	if	SCONJ
ejpam-3184	73	38	m	m	PROPN
ejpam-3184	73	39	is	be	AUX
ejpam-3184	73	40	a	a	DET
ejpam-3184	73	41	subgroup	subgroup	NOUN
ejpam-3184	73	42	of	of	ADP
ejpam-3184	73	43	g	g	NOUN
ejpam-3184	73	44	,	,	PUNCT
ejpam-3184	73	45	let	let	VERB
ejpam-3184	73	46	|m	|m	DET
ejpam-3184	73	47	|p	|p	NOUN
ejpam-3184	73	48	denotes	denote	VERB
ejpam-3184	73	49	the	the	DET
ejpam-3184	73	50	largest	large	ADJ
ejpam-3184	73	51	power	power	NOUN
ejpam-3184	73	52	of	of	ADP
ejpam-3184	73	53	p	p	NOUN
ejpam-3184	73	54	dividing	divide	VERB
ejpam-3184	73	55	the	the	DET
ejpam-3184	73	56	order	order	NOUN
ejpam-3184	73	57	of	of	ADP
ejpam-3184	73	58	m	m	PROPN
ejpam-3184	73	59	.	.	PUNCT
ejpam-3184	74	1	as	as	ADP
ejpam-3184	74	2	|kn	|kn	NUM
ejpam-3184	74	3	|	|	NOUN
ejpam-3184	74	4	=	=	NOUN
ejpam-3184	74	5	|k||n	|k||n	NOUN
ejpam-3184	74	6	|	|	ADV
ejpam-3184	74	7	|k∩n	|k∩n	ADV
ejpam-3184	75	1	|	|	ADV
ejpam-3184	75	2	,	,	PUNCT
ejpam-3184	75	3	then	then	ADV
ejpam-3184	75	4	|kn	|kn	DET
ejpam-3184	75	5	|p	|p	NOUN
ejpam-3184	75	6	=	=	SYM
ejpam-3184	75	7	|k|p|n	|k|p|n	NOUN
ejpam-3184	75	8	|p	|p	PROPN
ejpam-3184	75	9	|k∩n	|k∩n	NOUN
ejpam-3184	75	10	|p	|p	PROPN
ejpam-3184	75	11	.	.	PUNCT
ejpam-3184	76	1	clearly	clearly	ADV
ejpam-3184	76	2	,	,	PUNCT
ejpam-3184	76	3	(	(	PUNCT
ejpam-3184	76	4	gp	gp	NOUN
ejpam-3184	76	5	∩k	∩k	NOUN
ejpam-3184	76	6	)	)	PUNCT
ejpam-3184	76	7	(	(	PUNCT
ejpam-3184	76	8	gp∩n	gp∩n	PROPN
ejpam-3184	76	9	)	)	PUNCT
ejpam-3184	76	10	≤	≤	NUM
ejpam-3184	76	11	gp	gp	NOUN
ejpam-3184	76	12	as	as	SCONJ
ejpam-3184	76	13	gp∩n	gp∩n	PROPN
ejpam-3184	76	14	is	be	AUX
ejpam-3184	76	15	a	a	DET
ejpam-3184	76	16	normal	normal	ADJ
ejpam-3184	76	17	subgroup	subgroup	NOUN
ejpam-3184	76	18	of	of	ADP
ejpam-3184	76	19	gp	gp	NOUN
ejpam-3184	76	20	and	and	CCONJ
ejpam-3184	76	21	so	so	ADV
ejpam-3184	76	22	(	(	PUNCT
ejpam-3184	76	23	gp∩k)(gp∩n	gp∩k)(gp∩n	NOUN
ejpam-3184	76	24	)	)	PUNCT
ejpam-3184	76	25	≤	≤	NOUN
ejpam-3184	76	26	gp∩kn	gp∩kn	PROPN
ejpam-3184	76	27	.	.	PUNCT
ejpam-3184	77	1	now	now	ADV
ejpam-3184	77	2	|(gp	|(gp	VERB
ejpam-3184	77	3	∩k)(gp	∩k)(gp	ADJ
ejpam-3184	77	4	∩n)|	∩n)|	PUNCT
ejpam-3184	77	5	=	=	PRON
ejpam-3184	77	6	|gp∩k||gp∩n	|gp∩k||gp∩n	VERB
ejpam-3184	77	7	|	|	ADV
ejpam-3184	77	8	|gp∩k∩n	|gp∩k∩n	PROPN
ejpam-3184	77	9	|	|	NOUN
ejpam-3184	77	10	=	=	SYM
ejpam-3184	77	11	|k|p|n	|k|p|n	NOUN
ejpam-3184	77	12	|p	|p	NOUN
ejpam-3184	77	13	|k∩n	|k∩n	NOUN
ejpam-3184	77	14	|p	|p	ADJ
ejpam-3184	77	15	=	=	SYM
ejpam-3184	77	16	|kn	|kn	X
ejpam-3184	77	17	|p	|p	X
ejpam-3184	77	18	=	=	SYM
ejpam-3184	77	19	|gp	|gp	NOUN
ejpam-3184	77	20	∩	∩	X
ejpam-3184	77	21	kn	kn	PROPN
ejpam-3184	77	22	|	|	ADV
ejpam-3184	77	23	and	and	CCONJ
ejpam-3184	77	24	hence	hence	ADV
ejpam-3184	77	25	(	(	PUNCT
ejpam-3184	77	26	gp	gp	X
ejpam-3184	77	27	∩	∩	PROPN
ejpam-3184	77	28	k)(gp	k)(gp	PROPN
ejpam-3184	77	29	∩	∩	PROPN
ejpam-3184	77	30	n	n	CCONJ
ejpam-3184	77	31	)	)	PUNCT
ejpam-3184	77	32	=	=	SYM
ejpam-3184	77	33	gp	gp	NOUN
ejpam-3184	77	34	∩	∩	X
ejpam-3184	77	35	kn	kn	PROPN
ejpam-3184	77	36	.	.	PUNCT
ejpam-3184	78	1	by	by	ADP
ejpam-3184	78	2	[	[	X
ejpam-3184	78	3	[	[	X
ejpam-3184	78	4	2	2	NUM
ejpam-3184	78	5	]	]	PUNCT
ejpam-3184	78	6	,	,	PUNCT
ejpam-3184	78	7	lemma	lemma	PROPN
ejpam-3184	78	8	1.2	1.2	NUM
ejpam-3184	78	9	,	,	PUNCT
ejpam-3184	78	10	p.	p.	NOUN
ejpam-3184	78	11	2	2	NUM
ejpam-3184	78	12	]	]	PUNCT
ejpam-3184	78	13	,	,	PUNCT
ejpam-3184	78	14	gp(k	gp(k	PUNCT
ejpam-3184	78	15	∩	∩	NOUN
ejpam-3184	78	16	n	n	CCONJ
ejpam-3184	78	17	)	)	PUNCT
ejpam-3184	78	18	=	=	SYM
ejpam-3184	78	19	gpk	gpk	PROPN
ejpam-3184	78	20	∩	∩	PROPN
ejpam-3184	78	21	gpn	gpn	X
ejpam-3184	78	22	which	which	PRON
ejpam-3184	78	23	is	be	AUX
ejpam-3184	78	24	a	a	DET
ejpam-3184	78	25	subgroup	subgroup	NOUN
ejpam-3184	78	26	of	of	ADP
ejpam-3184	78	27	g	g	PROPN
ejpam-3184	78	28	as	as	ADP
ejpam-3184	78	29	gpk	gpk	PROPN
ejpam-3184	78	30	and	and	CCONJ
ejpam-3184	78	31	gpn	gpn	PROPN
ejpam-3184	78	32	are	be	AUX
ejpam-3184	78	33	subgroups	subgroup	NOUN
ejpam-3184	78	34	of	of	ADP
ejpam-3184	78	35	g.	g.	PROPN
ejpam-3184	79	1	so	so	ADV
ejpam-3184	79	2	,	,	PUNCT
ejpam-3184	79	3	we	we	PRON
ejpam-3184	79	4	have	have	VERB
ejpam-3184	79	5	x	x	X
ejpam-3184	79	6	∈	∈	NOUN
ejpam-3184	79	7	c	c	NOUN
ejpam-3184	79	8	such	such	ADJ
ejpam-3184	79	9	that	that	DET
ejpam-3184	79	10	gp(u	gp(u	NOUN
ejpam-3184	79	11	∩n)x	∩n)x	NOUN
ejpam-3184	79	12	=	=	SYM
ejpam-3184	79	13	gp(u	gp(u	NOUN
ejpam-3184	79	14	x	x	SYM
ejpam-3184	79	15	∩n	∩n	NOUN
ejpam-3184	79	16	)	)	PUNCT
ejpam-3184	79	17	=	=	SYM
ejpam-3184	79	18	gp(k	gp(k	NOUN
ejpam-3184	79	19	∩n	∩n	NOUN
ejpam-3184	79	20	)	)	PUNCT
ejpam-3184	79	21	is	be	AUX
ejpam-3184	79	22	a	a	DET
ejpam-3184	79	23	subgroup	subgroup	NOUN
ejpam-3184	79	24	of	of	ADP
ejpam-3184	79	25	g	g	NOUN
ejpam-3184	79	26	,	,	PUNCT
ejpam-3184	79	27	for	for	ADP
ejpam-3184	79	28	all	all	DET
ejpam-3184	79	29	gp	gp	NOUN
ejpam-3184	79	30	∈	∈	PROPN
ejpam-3184	79	31	z.	z.	PROPN
ejpam-3184	79	32	thus	thus	ADV
ejpam-3184	79	33	,	,	PUNCT
ejpam-3184	79	34	u	u	PROPN
ejpam-3184	79	35	∩n	∩n	PROPN
ejpam-3184	79	36	is	be	AUX
ejpam-3184	79	37	c	c	NOUN
ejpam-3184	79	38	-	-	PUNCT
ejpam-3184	79	39	z	z	ADJ
ejpam-3184	79	40	-	-	PUNCT
ejpam-3184	79	41	permutable	permutable	ADJ
ejpam-3184	79	42	subgroup	subgroup	NOUN
ejpam-3184	79	43	of	of	ADP
ejpam-3184	79	44	g.	g.	PROPN
ejpam-3184	79	45	lemma	lemma	PROPN
ejpam-3184	79	46	2.2	2.2	NUM
ejpam-3184	79	47	.	.	PUNCT
ejpam-3184	80	1	let	let	VERB
ejpam-3184	80	2	z	z	PRON
ejpam-3184	80	3	be	be	AUX
ejpam-3184	80	4	a	a	DET
ejpam-3184	80	5	complete	complete	ADJ
ejpam-3184	80	6	set	set	NOUN
ejpam-3184	80	7	of	of	ADP
ejpam-3184	80	8	sylow	sylow	NOUN
ejpam-3184	80	9	subgroups	subgroup	NOUN
ejpam-3184	80	10	of	of	ADP
ejpam-3184	80	11	a	a	DET
ejpam-3184	80	12	group	group	NOUN
ejpam-3184	80	13	g	g	NOUN
ejpam-3184	80	14	and	and	CCONJ
ejpam-3184	80	15	c	c	PROPN
ejpam-3184	80	16	be	be	AUX
ejpam-3184	80	17	a	a	DET
ejpam-3184	80	18	nonempty	nonempty	ADJ
ejpam-3184	80	19	subset	subset	NOUN
ejpam-3184	80	20	of	of	ADP
ejpam-3184	80	21	g.	g.	PROPN
ejpam-3184	80	22	assume	assume	VERB
ejpam-3184	80	23	that	that	SCONJ
ejpam-3184	80	24	h	h	NOUN
ejpam-3184	80	25	is	be	AUX
ejpam-3184	80	26	a	a	DET
ejpam-3184	80	27	normal	normal	ADJ
ejpam-3184	80	28	subgroup	subgroup	NOUN
ejpam-3184	80	29	of	of	ADP
ejpam-3184	80	30	g	g	PROPN
ejpam-3184	80	31	such	such	ADJ
ejpam-3184	80	32	that	that	SCONJ
ejpam-3184	80	33	the	the	DET
ejpam-3184	80	34	maximal	maximal	ADJ
ejpam-3184	80	35	subgroups	subgroup	NOUN
ejpam-3184	80	36	of	of	ADP
ejpam-3184	80	37	z	z	PROPN
ejpam-3184	80	38	∩h	∩h	NOUN
ejpam-3184	80	39	are	be	AUX
ejpam-3184	80	40	c	c	NOUN
ejpam-3184	80	41	-	-	PUNCT
ejpam-3184	80	42	z	z	ADJ
ejpam-3184	80	43	-	-	PUNCT
ejpam-3184	80	44	permutable	permutable	ADJ
ejpam-3184	80	45	subgroups	subgroup	NOUN
ejpam-3184	80	46	of	of	ADP
ejpam-3184	80	47	g.	g.	PROPN
ejpam-3184	80	48	then	then	ADV
ejpam-3184	80	49	for	for	ADP
ejpam-3184	80	50	any	any	DET
ejpam-3184	80	51	nontrivial	nontrivial	ADJ
ejpam-3184	80	52	normal	normal	ADJ
ejpam-3184	80	53	subgroup	subgroup	NOUN
ejpam-3184	80	54	n	n	PROPN
ejpam-3184	80	55	of	of	ADP
ejpam-3184	80	56	g	g	PROPN
ejpam-3184	80	57	,	,	PUNCT
ejpam-3184	80	58	the	the	DET
ejpam-3184	80	59	maximal	maximal	ADJ
ejpam-3184	80	60	subgroups	subgroup	NOUN
ejpam-3184	80	61	of	of	ADP
ejpam-3184	80	62	(	(	PUNCT
ejpam-3184	80	63	zn	zn	NOUN
ejpam-3184	80	64	/	/	SYM
ejpam-3184	80	65	n	n	CCONJ
ejpam-3184	80	66	)	)	PUNCT
ejpam-3184	80	67	∩	∩	NOUN
ejpam-3184	80	68	(	(	PUNCT
ejpam-3184	80	69	hn	hn	PROPN
ejpam-3184	80	70	/	/	SYM
ejpam-3184	80	71	n	n	CCONJ
ejpam-3184	80	72	)	)	PUNCT
ejpam-3184	80	73	are	be	AUX
ejpam-3184	80	74	cn	cn	PROPN
ejpam-3184	80	75	/	/	SYM
ejpam-3184	80	76	n	n	CCONJ
ejpam-3184	80	77	-zn	-zn	ADJ
ejpam-3184	80	78	/	/	SYM
ejpam-3184	80	79	n	n	CCONJ
ejpam-3184	80	80	-permutable	-permutable	ADJ
ejpam-3184	80	81	subgroups	subgroup	NOUN
ejpam-3184	80	82	of	of	ADP
ejpam-3184	80	83	g	g	NOUN
ejpam-3184	80	84	/	/	SYM
ejpam-3184	80	85	n	n	NOUN
ejpam-3184	80	86	.	.	PUNCT
ejpam-3184	81	1	proof	proof	NOUN
ejpam-3184	81	2	.	.	PUNCT
ejpam-3184	82	1	see	see	VERB
ejpam-3184	83	1	[	[	X
ejpam-3184	83	2	[	[	X
ejpam-3184	83	3	4	4	NUM
ejpam-3184	83	4	]	]	PUNCT
ejpam-3184	83	5	,	,	PUNCT
ejpam-3184	83	6	lemma	lemma	PROPN
ejpam-3184	83	7	2.2	2.2	NUM
ejpam-3184	83	8	]	]	PUNCT
ejpam-3184	83	9	.	.	PUNCT
ejpam-3184	84	1	lemma	lemma	PROPN
ejpam-3184	84	2	2.3	2.3	NUM
ejpam-3184	84	3	.	.	PUNCT
ejpam-3184	85	1	let	let	VERB
ejpam-3184	85	2	g	g	PRON
ejpam-3184	85	3	be	be	AUX
ejpam-3184	85	4	a	a	DET
ejpam-3184	85	5	group	group	NOUN
ejpam-3184	85	6	.	.	PUNCT
ejpam-3184	86	1	then	then	ADV
ejpam-3184	86	2	:	:	PUNCT
ejpam-3184	86	3	(	(	PUNCT
ejpam-3184	86	4	a	a	X
ejpam-3184	86	5	)	)	PUNCT
ejpam-3184	86	6	f	f	NOUN
ejpam-3184	86	7	∗(g	∗(g	PROPN
ejpam-3184	86	8	)	)	PUNCT
ejpam-3184	87	1	=	=	SYM
ejpam-3184	87	2	f	f	PROPN
ejpam-3184	87	3	(	(	PUNCT
ejpam-3184	87	4	g)e(g	g)e(g	PROPN
ejpam-3184	87	5	)	)	PUNCT
ejpam-3184	87	6	and	and	CCONJ
ejpam-3184	88	1	[	[	X
ejpam-3184	88	2	f	f	X
ejpam-3184	88	3	(	(	PUNCT
ejpam-3184	88	4	g	g	NOUN
ejpam-3184	88	5	)	)	PUNCT
ejpam-3184	88	6	,	,	PUNCT
ejpam-3184	88	7	e(g	e(g	PROPN
ejpam-3184	88	8	)	)	PUNCT
ejpam-3184	88	9	]	]	PUNCT
ejpam-3184	89	1	=	=	PUNCT
ejpam-3184	89	2	1	1	NUM
ejpam-3184	89	3	,	,	PUNCT
ejpam-3184	89	4	where	where	SCONJ
ejpam-3184	89	5	e(g	e(g	NOUN
ejpam-3184	89	6	)	)	PUNCT
ejpam-3184	89	7	is	be	AUX
ejpam-3184	89	8	the	the	DET
ejpam-3184	89	9	layer	layer	NOUN
ejpam-3184	89	10	subgroup	subgroup	NOUN
ejpam-3184	89	11	of	of	ADP
ejpam-3184	89	12	g.	g.	PROPN
ejpam-3184	89	13	(	(	PUNCT
ejpam-3184	89	14	b	b	X
ejpam-3184	89	15	)	)	PUNCT
ejpam-3184	89	16	f	f	PROPN
ejpam-3184	89	17	∗(f	∗(f	PROPN
ejpam-3184	89	18	∗(g	∗(g	PROPN
ejpam-3184	89	19	)	)	PUNCT
ejpam-3184	89	20	)	)	PUNCT
ejpam-3184	90	1	=	=	PUNCT
ejpam-3184	90	2	f	f	X
ejpam-3184	90	3	∗(g	∗(g	PROPN
ejpam-3184	90	4	)	)	PUNCT
ejpam-3184	90	5	≥	≥	PROPN
ejpam-3184	90	6	f	f	X
ejpam-3184	90	7	(	(	PUNCT
ejpam-3184	90	8	g	g	NOUN
ejpam-3184	90	9	)	)	PUNCT
ejpam-3184	90	10	;	;	PUNCT
ejpam-3184	90	11	if	if	SCONJ
ejpam-3184	90	12	f	f	PROPN
ejpam-3184	90	13	∗(g	∗(g	PROPN
ejpam-3184	90	14	)	)	PUNCT
ejpam-3184	90	15	is	be	AUX
ejpam-3184	90	16	solvable	solvable	ADJ
ejpam-3184	90	17	,	,	PUNCT
ejpam-3184	90	18	then	then	ADV
ejpam-3184	90	19	f	f	PROPN
ejpam-3184	90	20	∗(g	∗(g	PROPN
ejpam-3184	90	21	)	)	PUNCT
ejpam-3184	91	1	=	=	SYM
ejpam-3184	91	2	f	f	X
ejpam-3184	91	3	(	(	PUNCT
ejpam-3184	91	4	g	g	NOUN
ejpam-3184	91	5	)	)	PUNCT
ejpam-3184	91	6	.	.	PUNCT
ejpam-3184	92	1	(	(	PUNCT
ejpam-3184	92	2	c	c	X
ejpam-3184	92	3	)	)	PUNCT
ejpam-3184	92	4	cg(f	cg(f	NOUN
ejpam-3184	92	5	∗(g	∗(g	PROPN
ejpam-3184	92	6	)	)	PUNCT
ejpam-3184	92	7	)	)	PUNCT
ejpam-3184	93	1	≤	≤	NUM
ejpam-3184	93	2	f	f	X
ejpam-3184	93	3	(	(	PUNCT
ejpam-3184	93	4	g	g	NOUN
ejpam-3184	93	5	)	)	PUNCT
ejpam-3184	93	6	.	.	PUNCT
ejpam-3184	94	1	(	(	PUNCT
ejpam-3184	94	2	d	d	X
ejpam-3184	94	3	)	)	PUNCT
ejpam-3184	94	4	suppose	suppose	VERB
ejpam-3184	94	5	that	that	SCONJ
ejpam-3184	94	6	n	n	PRON
ejpam-3184	94	7	is	be	AUX
ejpam-3184	94	8	a	a	DET
ejpam-3184	94	9	normal	normal	ADJ
ejpam-3184	94	10	subgroup	subgroup	NOUN
ejpam-3184	94	11	of	of	ADP
ejpam-3184	94	12	g	g	PROPN
ejpam-3184	94	13	contained	contain	VERB
ejpam-3184	94	14	in	in	ADP
ejpam-3184	94	15	φ(g	φ(g	PROPN
ejpam-3184	94	16	)	)	PUNCT
ejpam-3184	94	17	,	,	PUNCT
ejpam-3184	94	18	then	then	ADV
ejpam-3184	94	19	f	f	PROPN
ejpam-3184	94	20	∗(g	∗(g	PROPN
ejpam-3184	94	21	/	/	SYM
ejpam-3184	94	22	n	n	CCONJ
ejpam-3184	94	23	)	)	PUNCT
ejpam-3184	95	1	=	=	SYM
ejpam-3184	95	2	f	f	PROPN
ejpam-3184	95	3	∗(g)/n	∗(g)/n	NOUN
ejpam-3184	95	4	.	.	PUNCT
ejpam-3184	96	1	proof	proof	NOUN
ejpam-3184	96	2	.	.	PUNCT
ejpam-3184	97	1	(	(	PUNCT
ejpam-3184	97	2	a	a	X
ejpam-3184	97	3	)	)	PUNCT
ejpam-3184	97	4	,	,	PUNCT
ejpam-3184	97	5	(	(	PUNCT
ejpam-3184	97	6	b	b	X
ejpam-3184	97	7	)	)	PUNCT
ejpam-3184	97	8	and	and	CCONJ
ejpam-3184	97	9	(	(	PUNCT
ejpam-3184	97	10	c	c	X
ejpam-3184	97	11	)	)	PUNCT
ejpam-3184	97	12	can	can	AUX
ejpam-3184	97	13	be	be	AUX
ejpam-3184	97	14	found	find	VERB
ejpam-3184	97	15	in	in	ADP
ejpam-3184	97	16	[	[	X
ejpam-3184	97	17	[	[	X
ejpam-3184	97	18	6	6	NUM
ejpam-3184	97	19	]	]	PUNCT
ejpam-3184	97	20	,	,	PUNCT
ejpam-3184	97	21	x	x	X
ejpam-3184	97	22	13	13	NUM
ejpam-3184	97	23	]	]	PUNCT
ejpam-3184	97	24	.	.	PUNCT
ejpam-3184	98	1	for	for	ADP
ejpam-3184	98	2	(	(	PUNCT
ejpam-3184	98	3	d	d	NOUN
ejpam-3184	98	4	)	)	PUNCT
ejpam-3184	98	5	,	,	PUNCT
ejpam-3184	98	6	see	see	VERB
ejpam-3184	98	7	[	[	X
ejpam-3184	98	8	[	[	X
ejpam-3184	98	9	10	10	NUM
ejpam-3184	98	10	]	]	PUNCT
ejpam-3184	98	11	,	,	PUNCT
ejpam-3184	98	12	lemma	lemma	PROPN
ejpam-3184	98	13	2.3	2.3	NUM
ejpam-3184	98	14	(	(	PUNCT
ejpam-3184	98	15	8)	8)	NUM
ejpam-3184	98	16	]	]	PUNCT
ejpam-3184	98	17	.	.	PUNCT
ejpam-3184	99	1	lemma	lemma	PROPN
ejpam-3184	99	2	2.4	2.4	NUM
ejpam-3184	99	3	.	.	PUNCT
ejpam-3184	100	1	let	let	VERB
ejpam-3184	100	2	z	z	PRON
ejpam-3184	100	3	be	be	AUX
ejpam-3184	100	4	a	a	DET
ejpam-3184	100	5	complete	complete	ADJ
ejpam-3184	100	6	set	set	NOUN
ejpam-3184	100	7	of	of	ADP
ejpam-3184	100	8	sylow	sylow	NOUN
ejpam-3184	100	9	subgroups	subgroup	NOUN
ejpam-3184	100	10	of	of	ADP
ejpam-3184	100	11	a	a	DET
ejpam-3184	100	12	group	group	NOUN
ejpam-3184	100	13	g	g	NOUN
ejpam-3184	100	14	and	and	CCONJ
ejpam-3184	100	15	c	c	PROPN
ejpam-3184	100	16	be	be	AUX
ejpam-3184	100	17	a	a	DET
ejpam-3184	100	18	nonempty	nonempty	ADJ
ejpam-3184	100	19	subset	subset	NOUN
ejpam-3184	100	20	of	of	ADP
ejpam-3184	100	21	g.	g.	PROPN
ejpam-3184	100	22	suppose	suppose	VERB
ejpam-3184	100	23	that	that	SCONJ
ejpam-3184	100	24	p	p	PROPN
ejpam-3184	100	25	is	be	AUX
ejpam-3184	100	26	a	a	DET
ejpam-3184	100	27	normal	normal	ADJ
ejpam-3184	100	28	p	p	NOUN
ejpam-3184	100	29	-	-	PUNCT
ejpam-3184	100	30	subgroup	subgroup	NOUN
ejpam-3184	100	31	of	of	ADP
ejpam-3184	100	32	g	g	PROPN
ejpam-3184	100	33	,	,	PUNCT
ejpam-3184	100	34	where	where	SCONJ
ejpam-3184	100	35	p	p	NOUN
ejpam-3184	100	36	is	be	AUX
ejpam-3184	100	37	a	a	DET
ejpam-3184	100	38	prime	prime	NOUN
ejpam-3184	100	39	,	,	PUNCT
ejpam-3184	100	40	and	and	CCONJ
ejpam-3184	100	41	n	n	PRON
ejpam-3184	100	42	is	be	AUX
ejpam-3184	100	43	a	a	DET
ejpam-3184	100	44	minimal	minimal	ADJ
ejpam-3184	100	45	normal	normal	ADJ
ejpam-3184	100	46	subgroup	subgroup	NOUN
ejpam-3184	100	47	of	of	ADP
ejpam-3184	100	48	g	g	NOUN
ejpam-3184	100	49	with	with	ADP
ejpam-3184	100	50	n	n	DET
ejpam-3184	100	51	≤	≤	NOUN
ejpam-3184	100	52	p	p	NOUN
ejpam-3184	100	53	.	.	PUNCT
ejpam-3184	101	1	if	if	SCONJ
ejpam-3184	101	2	n	n	PRON
ejpam-3184	101	3	is	be	AUX
ejpam-3184	101	4	complemented	complement	VERB
ejpam-3184	101	5	in	in	ADP
ejpam-3184	101	6	p	p	NOUN
ejpam-3184	101	7	and	and	CCONJ
ejpam-3184	101	8	the	the	DET
ejpam-3184	101	9	maximal	maximal	ADJ
ejpam-3184	101	10	subgroups	subgroup	NOUN
ejpam-3184	101	11	of	of	ADP
ejpam-3184	101	12	p	p	NOUN
ejpam-3184	101	13	are	be	AUX
ejpam-3184	101	14	c	c	NOUN
ejpam-3184	101	15	-	-	PUNCT
ejpam-3184	101	16	z	z	ADJ
ejpam-3184	101	17	-	-	PUNCT
ejpam-3184	101	18	permutable	permutable	ADJ
ejpam-3184	101	19	subgroups	subgroup	NOUN
ejpam-3184	101	20	of	of	ADP
ejpam-3184	101	21	g	g	NOUN
ejpam-3184	101	22	,	,	PUNCT
ejpam-3184	101	23	then	then	ADV
ejpam-3184	101	24	the	the	DET
ejpam-3184	101	25	order	order	NOUN
ejpam-3184	101	26	of	of	ADP
ejpam-3184	101	27	n	n	PROPN
ejpam-3184	101	28	is	be	AUX
ejpam-3184	101	29	p.	p.	NOUN
ejpam-3184	101	30	proof	proof	NOUN
ejpam-3184	101	31	.	.	PUNCT
ejpam-3184	102	1	by	by	ADP
ejpam-3184	102	2	hypothesis	hypothesis	NOUN
ejpam-3184	102	3	,	,	PUNCT
ejpam-3184	102	4	there	there	PRON
ejpam-3184	102	5	exists	exist	VERB
ejpam-3184	102	6	a	a	DET
ejpam-3184	102	7	subgroup	subgroup	NOUN
ejpam-3184	102	8	h	h	NOUN
ejpam-3184	102	9	of	of	ADP
ejpam-3184	102	10	p	p	PRON
ejpam-3184	102	11	such	such	ADJ
ejpam-3184	102	12	that	that	SCONJ
ejpam-3184	102	13	p	p	PROPN
ejpam-3184	102	14	=	=	X
ejpam-3184	102	15	nh	nh	PROPN
ejpam-3184	102	16	and	and	CCONJ
ejpam-3184	102	17	n	n	PRON
ejpam-3184	102	18	∩h	∩h	NOUN
ejpam-3184	102	19	=	=	SYM
ejpam-3184	103	1	1	1	X
ejpam-3184	103	2	.	.	PUNCT
ejpam-3184	104	1	obviously	obviously	ADV
ejpam-3184	104	2	,	,	PUNCT
ejpam-3184	104	3	we	we	PRON
ejpam-3184	104	4	have	have	VERB
ejpam-3184	104	5	that	that	PRON
ejpam-3184	104	6	n	n	NOUN
ejpam-3184	104	7	≤	≤	NUM
ejpam-3184	104	8	gp	gp	NOUN
ejpam-3184	105	1	∈	∈	PROPN
ejpam-3184	105	2	z.	z.	PROPN
ejpam-3184	105	3	let	let	VERB
ejpam-3184	105	4	n	n	PRON
ejpam-3184	105	5	/	/	SYM
ejpam-3184	105	6	m	m	AUX
ejpam-3184	105	7	be	be	VERB
ejpam-3184	105	8	a	a	DET
ejpam-3184	105	9	chief	chief	ADJ
ejpam-3184	105	10	factor	factor	NOUN
ejpam-3184	105	11	of	of	ADP
ejpam-3184	105	12	gp	gp	NOUN
ejpam-3184	105	13	.	.	PUNCT
ejpam-3184	106	1	then	then	ADV
ejpam-3184	106	2	,	,	PUNCT
ejpam-3184	106	3	the	the	DET
ejpam-3184	106	4	order	order	NOUN
ejpam-3184	106	5	of	of	ADP
ejpam-3184	106	6	n	n	CCONJ
ejpam-3184	106	7	/	/	SYM
ejpam-3184	106	8	m	m	PROPN
ejpam-3184	106	9	is	be	AUX
ejpam-3184	106	10	p.	p.	NOUN
ejpam-3184	106	11	clearly	clearly	ADV
ejpam-3184	106	12	,	,	PUNCT
ejpam-3184	106	13	mh	mh	PROPN
ejpam-3184	106	14	is	be	AUX
ejpam-3184	106	15	a	a	DET
ejpam-3184	106	16	subgroup	subgroup	NOUN
ejpam-3184	106	17	of	of	ADP
ejpam-3184	106	18	p	p	NOUN
ejpam-3184	106	19	as	as	SCONJ
ejpam-3184	106	20	m	m	PROPN
ejpam-3184	106	21	is	be	AUX
ejpam-3184	106	22	normal	normal	ADJ
ejpam-3184	106	23	in	in	ADP
ejpam-3184	106	24	p	p	PROPN
ejpam-3184	106	25	.	.	PUNCT
ejpam-3184	107	1	since	since	SCONJ
ejpam-3184	107	2	m∩	m∩	PROPN
ejpam-3184	107	3	h	h	NOUN
ejpam-3184	107	4	=	=	NOUN
ejpam-3184	107	5	m	m	PROPN
ejpam-3184	107	6	∩	∩	NOUN
ejpam-3184	107	7	(	(	PUNCT
ejpam-3184	107	8	n	n	CCONJ
ejpam-3184	107	9	∩	∩	ADJ
ejpam-3184	107	10	h	h	NOUN
ejpam-3184	107	11	)	)	PUNCT
ejpam-3184	107	12	=	=	SYM
ejpam-3184	107	13	1	1	NUM
ejpam-3184	107	14	,	,	PUNCT
ejpam-3184	107	15	then	then	ADV
ejpam-3184	107	16	|p	|p	VERB
ejpam-3184	107	17	:	:	PUNCT
ejpam-3184	107	18	mh|	mh|	AUX
ejpam-3184	107	19	=	=	SYM
ejpam-3184	107	20	|nh	|nh	X
ejpam-3184	107	21	:	:	PUNCT
ejpam-3184	107	22	mh|	mh|	AUX
ejpam-3184	107	23	=	=	PUNCT
ejpam-3184	107	24	|n	|n	NOUN
ejpam-3184	107	25	:	:	PUNCT
ejpam-3184	107	26	m	m	VERB
ejpam-3184	107	27	|	|	NOUN
ejpam-3184	107	28	=	=	SYM
ejpam-3184	107	29	p	p	NOUN
ejpam-3184	107	30	and	and	CCONJ
ejpam-3184	107	31	hence	hence	ADV
ejpam-3184	107	32	mh	mh	PROPN
ejpam-3184	107	33	is	be	AUX
ejpam-3184	107	34	a	a	DET
ejpam-3184	107	35	maximal	maximal	ADJ
ejpam-3184	107	36	subgroup	subgroup	NOUN
ejpam-3184	107	37	of	of	ADP
ejpam-3184	107	38	p	p	PROPN
ejpam-3184	107	39	.	.	PUNCT
ejpam-3184	108	1	by	by	ADP
ejpam-3184	108	2	hypothesis	hypothesis	NOUN
ejpam-3184	108	3	,	,	PUNCT
ejpam-3184	108	4	mh	mh	PROPN
ejpam-3184	108	5	is	be	AUX
ejpam-3184	108	6	c	c	PROPN
ejpam-3184	108	7	-	-	ADJ
ejpam-3184	108	8	z	z	ADJ
ejpam-3184	108	9	-	-	PUNCT
ejpam-3184	108	10	permutable	permutable	ADJ
ejpam-3184	108	11	subgroup	subgroup	NOUN
ejpam-3184	108	12	of	of	ADP
ejpam-3184	108	13	g.	g.	PROPN
ejpam-3184	108	14	therefore	therefore	ADV
ejpam-3184	108	15	,	,	PUNCT
ejpam-3184	108	16	m	m	NOUN
ejpam-3184	108	17	=	=	ADJ
ejpam-3184	108	18	m(h	m(h	NOUN
ejpam-3184	108	19	∩	∩	NOUN
ejpam-3184	108	20	n	n	CCONJ
ejpam-3184	108	21	)	)	PUNCT
ejpam-3184	108	22	=	=	SYM
ejpam-3184	108	23	mh	mh	PROPN
ejpam-3184	108	24	∩	∩	NOUN
ejpam-3184	108	25	n	n	PART
ejpam-3184	108	26	is	be	AUX
ejpam-3184	108	27	c	c	NOUN
ejpam-3184	108	28	-	-	PUNCT
ejpam-3184	108	29	z	z	ADJ
ejpam-3184	108	30	-	-	PUNCT
ejpam-3184	108	31	permutable	permutable	ADJ
ejpam-3184	108	32	subgroup	subgroup	NOUN
ejpam-3184	108	33	of	of	ADP
ejpam-3184	108	34	g	g	PROPN
ejpam-3184	108	35	by	by	ADP
ejpam-3184	108	36	lemma	lemma	PROPN
ejpam-3184	108	37	m.	m.	PROPN
ejpam-3184	108	38	m.	m.	PROPN
ejpam-3184	109	1	al	al	PROPN
ejpam-3184	109	2	-	-	PUNCT
ejpam-3184	109	3	shomrani	shomrani	PROPN
ejpam-3184	109	4	,	,	PUNCT
ejpam-3184	109	5	a.	a.	NOUN
ejpam-3184	109	6	a.	a.	NOUN
ejpam-3184	109	7	heliel	heliel	PROPN
ejpam-3184	109	8	/	/	SYM
ejpam-3184	109	9	eur	eur	PROPN
ejpam-3184	109	10	.	.	PUNCT
ejpam-3184	110	1	j.	j.	PROPN
ejpam-3184	110	2	pure	pure	PROPN
ejpam-3184	110	3	appl	appl	PROPN
ejpam-3184	110	4	.	.	PROPN
ejpam-3184	110	5	math	math	PROPN
ejpam-3184	110	6	,	,	PUNCT
ejpam-3184	110	7	11	11	NUM
ejpam-3184	110	8	(	(	PUNCT
ejpam-3184	110	9	1	1	NUM
ejpam-3184	110	10	)	)	PUNCT
ejpam-3184	110	11	(	(	PUNCT
ejpam-3184	110	12	2018	2018	NUM
ejpam-3184	110	13	)	)	PUNCT
ejpam-3184	110	14	,	,	PUNCT
ejpam-3184	110	15	160	160	NUM
ejpam-3184	110	16	-	-	SYM
ejpam-3184	110	17	168	168	NUM
ejpam-3184	110	18	164	164	NUM
ejpam-3184	110	19	2.1(e	2.1(e	NUM
ejpam-3184	110	20	)	)	PUNCT
ejpam-3184	110	21	.	.	PUNCT
ejpam-3184	111	1	so	so	ADV
ejpam-3184	111	2	,	,	PUNCT
ejpam-3184	111	3	there	there	PRON
ejpam-3184	111	4	exists	exist	VERB
ejpam-3184	111	5	some	some	DET
ejpam-3184	111	6	x	x	SYM
ejpam-3184	111	7	∈	∈	PROPN
ejpam-3184	111	8	c	c	NOUN
ejpam-3184	111	9	such	such	ADJ
ejpam-3184	111	10	that	that	DET
ejpam-3184	111	11	mxgq	mxgq	NOUN
ejpam-3184	111	12	is	be	AUX
ejpam-3184	111	13	a	a	DET
ejpam-3184	111	14	subgroup	subgroup	NOUN
ejpam-3184	111	15	of	of	ADP
ejpam-3184	111	16	g	g	NOUN
ejpam-3184	111	17	,	,	PUNCT
ejpam-3184	111	18	for	for	ADP
ejpam-3184	111	19	all	all	DET
ejpam-3184	111	20	gq	gq	PROPN
ejpam-3184	111	21	∈	∈	PROPN
ejpam-3184	111	22	z.	z.	PROPN
ejpam-3184	112	1	this	this	PRON
ejpam-3184	112	2	implies	imply	VERB
ejpam-3184	112	3	that	that	SCONJ
ejpam-3184	112	4	mgx−1	mgx−1	PROPN
ejpam-3184	112	5	q	q	X
ejpam-3184	112	6	is	be	AUX
ejpam-3184	112	7	a	a	DET
ejpam-3184	112	8	subgroup	subgroup	NOUN
ejpam-3184	112	9	of	of	ADP
ejpam-3184	112	10	g	g	NOUN
ejpam-3184	112	11	,	,	PUNCT
ejpam-3184	112	12	for	for	SCONJ
ejpam-3184	112	13	all	all	DET
ejpam-3184	112	14	gq	gq	PROPN
ejpam-3184	112	15	∈	∈	PROPN
ejpam-3184	112	16	z.	z.	PROPN
ejpam-3184	112	17	assume	assume	VERB
ejpam-3184	112	18	that	that	SCONJ
ejpam-3184	112	19	q	q	PROPN
ejpam-3184	113	1	6=	6=	NUM
ejpam-3184	113	2	p.	p.	NOUN
ejpam-3184	113	3	since	since	SCONJ
ejpam-3184	113	4	m	m	PROPN
ejpam-3184	113	5	=	=	NOUN
ejpam-3184	113	6	m(n	m(n	PROPN
ejpam-3184	113	7	∩	∩	ADJ
ejpam-3184	113	8	gx−1	gx−1	NOUN
ejpam-3184	113	9	q	q	NOUN
ejpam-3184	113	10	)	)	PUNCT
ejpam-3184	113	11	=	=	SYM
ejpam-3184	114	1	n	n	NUM
ejpam-3184	114	2	∩mgx−1	∩mgx−1	NOUN
ejpam-3184	114	3	q	q	X
ejpam-3184	114	4	and	and	CCONJ
ejpam-3184	114	5	n	n	PROPN
ejpam-3184	114	6	∩mgx−1	∩mgx−1	NOUN
ejpam-3184	114	7	q	q	X
ejpam-3184	114	8	is	be	AUX
ejpam-3184	114	9	normal	normal	ADJ
ejpam-3184	114	10	in	in	ADP
ejpam-3184	114	11	mgx−1	mgx−1	PROPN
ejpam-3184	114	12	q	q	PROPN
ejpam-3184	114	13	,	,	PUNCT
ejpam-3184	114	14	it	it	PRON
ejpam-3184	114	15	follows	follow	VERB
ejpam-3184	114	16	that	that	SCONJ
ejpam-3184	114	17	gx−1	gx−1	PROPN
ejpam-3184	114	18	q	q	NOUN
ejpam-3184	114	19	≤	≤	NUM
ejpam-3184	114	20	ng(m	ng(m	NUM
ejpam-3184	114	21	)	)	PUNCT
ejpam-3184	114	22	.	.	PUNCT
ejpam-3184	115	1	if	if	SCONJ
ejpam-3184	115	2	q	q	PRON
ejpam-3184	115	3	=	=	SYM
ejpam-3184	115	4	p	p	X
ejpam-3184	115	5	,	,	PUNCT
ejpam-3184	115	6	then	then	ADV
ejpam-3184	115	7	m	m	VERB
ejpam-3184	115	8	is	be	AUX
ejpam-3184	115	9	normal	normal	ADJ
ejpam-3184	115	10	in	in	ADP
ejpam-3184	115	11	gp	gp	NOUN
ejpam-3184	115	12	and	and	CCONJ
ejpam-3184	115	13	so	so	ADV
ejpam-3184	115	14	gp	gp	NOUN
ejpam-3184	115	15	≤	≤	NUM
ejpam-3184	115	16	ng(m	ng(m	NUM
ejpam-3184	115	17	)	)	PUNCT
ejpam-3184	115	18	.	.	PUNCT
ejpam-3184	116	1	therefore	therefore	ADV
ejpam-3184	116	2	,	,	PUNCT
ejpam-3184	116	3	ng(m	ng(m	NUM
ejpam-3184	116	4	)	)	PUNCT
ejpam-3184	116	5	=	=	SYM
ejpam-3184	116	6	g	g	NOUN
ejpam-3184	116	7	and	and	CCONJ
ejpam-3184	116	8	hence	hence	ADV
ejpam-3184	116	9	m	m	VERB
ejpam-3184	116	10	is	be	AUX
ejpam-3184	116	11	normal	normal	ADJ
ejpam-3184	116	12	in	in	ADP
ejpam-3184	116	13	g.	g.	PROPN
ejpam-3184	116	14	but	but	CCONJ
ejpam-3184	116	15	n	n	PRON
ejpam-3184	116	16	is	be	AUX
ejpam-3184	116	17	a	a	DET
ejpam-3184	116	18	minimal	minimal	ADJ
ejpam-3184	116	19	normal	normal	ADJ
ejpam-3184	116	20	subgroup	subgroup	NOUN
ejpam-3184	116	21	of	of	ADP
ejpam-3184	116	22	g	g	PROPN
ejpam-3184	116	23	and	and	CCONJ
ejpam-3184	116	24	m	m	PROPN
ejpam-3184	116	25	is	be	AUX
ejpam-3184	116	26	a	a	DET
ejpam-3184	116	27	maximal	maximal	ADJ
ejpam-3184	116	28	subgroup	subgroup	NOUN
ejpam-3184	116	29	of	of	ADP
ejpam-3184	116	30	n	n	PROPN
ejpam-3184	116	31	,	,	PUNCT
ejpam-3184	116	32	thus	thus	ADV
ejpam-3184	116	33	m	m	VERB
ejpam-3184	116	34	=	=	SYM
ejpam-3184	116	35	1	1	NUM
ejpam-3184	116	36	and	and	CCONJ
ejpam-3184	116	37	the	the	DET
ejpam-3184	116	38	order	order	NOUN
ejpam-3184	116	39	of	of	ADP
ejpam-3184	116	40	n	n	PROPN
ejpam-3184	116	41	is	be	AUX
ejpam-3184	116	42	p.	p.	PROPN
ejpam-3184	116	43	lemma	lemma	PROPN
ejpam-3184	116	44	2.5	2.5	NUM
ejpam-3184	116	45	.	.	PUNCT
ejpam-3184	117	1	let	let	VERB
ejpam-3184	117	2	g	g	PRON
ejpam-3184	117	3	be	be	AUX
ejpam-3184	117	4	a	a	DET
ejpam-3184	117	5	group	group	NOUN
ejpam-3184	117	6	.	.	PUNCT
ejpam-3184	118	1	then	then	ADV
ejpam-3184	118	2	:	:	PUNCT
ejpam-3184	118	3	(	(	PUNCT
ejpam-3184	118	4	a	a	X
ejpam-3184	118	5	)	)	PUNCT
ejpam-3184	118	6	e(g	e(g	PROPN
ejpam-3184	118	7	)	)	PUNCT
ejpam-3184	118	8	,	,	PUNCT
ejpam-3184	118	9	the	the	DET
ejpam-3184	118	10	layer	layer	NOUN
ejpam-3184	118	11	subgroup	subgroup	NOUN
ejpam-3184	118	12	of	of	ADP
ejpam-3184	118	13	g	g	PROPN
ejpam-3184	118	14	,	,	PUNCT
ejpam-3184	118	15	is	be	AUX
ejpam-3184	118	16	a	a	DET
ejpam-3184	118	17	perfect	perfect	ADJ
ejpam-3184	118	18	quasinilpotent	quasinilpotent	NOUN
ejpam-3184	118	19	characteristic	characteristic	ADJ
ejpam-3184	118	20	subgroup	subgroup	NOUN
ejpam-3184	118	21	of	of	ADP
ejpam-3184	118	22	g.	g.	PROPN
ejpam-3184	118	23	(	(	PUNCT
ejpam-3184	118	24	b	b	X
ejpam-3184	118	25	)	)	PUNCT
ejpam-3184	118	26	if	if	SCONJ
ejpam-3184	118	27	m	m	NOUN
ejpam-3184	118	28	is	be	AUX
ejpam-3184	118	29	a	a	DET
ejpam-3184	118	30	perfect	perfect	ADJ
ejpam-3184	118	31	quasinilpotent	quasinilpotent	NOUN
ejpam-3184	118	32	subnormal	subnormal	ADJ
ejpam-3184	118	33	subgroup	subgroup	NOUN
ejpam-3184	118	34	of	of	ADP
ejpam-3184	118	35	g	g	PROPN
ejpam-3184	118	36	,	,	PUNCT
ejpam-3184	118	37	then	then	ADV
ejpam-3184	118	38	m	m	VERB
ejpam-3184	118	39	≤	≤	PROPN
ejpam-3184	118	40	e(g	e(g	PROPN
ejpam-3184	118	41	)	)	PUNCT
ejpam-3184	118	42	.	.	PUNCT
ejpam-3184	119	1	(	(	PUNCT
ejpam-3184	119	2	c	c	X
ejpam-3184	119	3	)	)	PUNCT
ejpam-3184	119	4	if	if	SCONJ
ejpam-3184	119	5	m	m	NOUN
ejpam-3184	119	6	is	be	AUX
ejpam-3184	119	7	a	a	DET
ejpam-3184	119	8	solvable	solvable	ADJ
ejpam-3184	119	9	subgroup	subgroup	NOUN
ejpam-3184	119	10	of	of	ADP
ejpam-3184	119	11	g	g	PROPN
ejpam-3184	119	12	and	and	CCONJ
ejpam-3184	119	13	e(g	e(g	PROPN
ejpam-3184	119	14	)	)	PUNCT
ejpam-3184	119	15	≤	≤	NOUN
ejpam-3184	119	16	ng(m	ng(m	NUM
ejpam-3184	119	17	)	)	PUNCT
ejpam-3184	119	18	,	,	PUNCT
ejpam-3184	119	19	then	then	ADV
ejpam-3184	119	20	[	[	X
ejpam-3184	119	21	e(g),m	e(g),m	X
ejpam-3184	119	22	]	]	X
ejpam-3184	119	23	=	=	SYM
ejpam-3184	119	24	1	1	X
ejpam-3184	119	25	.	.	PUNCT
ejpam-3184	119	26	proof	proof	NOUN
ejpam-3184	119	27	.	.	PUNCT
ejpam-3184	120	1	for	for	ADP
ejpam-3184	120	2	(	(	PUNCT
ejpam-3184	120	3	a	a	X
ejpam-3184	120	4	)	)	PUNCT
ejpam-3184	120	5	,	,	PUNCT
ejpam-3184	120	6	see	see	VERB
ejpam-3184	120	7	[	[	X
ejpam-3184	120	8	[	[	X
ejpam-3184	120	9	6	6	NUM
ejpam-3184	120	10	]	]	PUNCT
ejpam-3184	120	11	,	,	PUNCT
ejpam-3184	120	12	definition	definition	NOUN
ejpam-3184	120	13	13.14	13.14	NUM
ejpam-3184	120	14	,	,	PUNCT
ejpam-3184	120	15	p.	p.	NOUN
ejpam-3184	120	16	128	128	NUM
ejpam-3184	120	17	]	]	PUNCT
ejpam-3184	120	18	.	.	PUNCT
ejpam-3184	121	1	for	for	ADP
ejpam-3184	121	2	(	(	PUNCT
ejpam-3184	121	3	b	b	NOUN
ejpam-3184	121	4	)	)	PUNCT
ejpam-3184	121	5	and	and	CCONJ
ejpam-3184	121	6	(	(	PUNCT
ejpam-3184	121	7	c	c	NOUN
ejpam-3184	121	8	)	)	PUNCT
ejpam-3184	121	9	,	,	PUNCT
ejpam-3184	121	10	see	see	VERB
ejpam-3184	121	11	[	[	X
ejpam-3184	121	12	[	[	X
ejpam-3184	121	13	6	6	NUM
ejpam-3184	121	14	]	]	PUNCT
ejpam-3184	121	15	,	,	PUNCT
ejpam-3184	121	16	theorem	theorem	VERB
ejpam-3184	121	17	13.15(a	13.15(a	NUM
ejpam-3184	121	18	)	)	PUNCT
ejpam-3184	121	19	,	,	PUNCT
ejpam-3184	121	20	p.	p.	NOUN
ejpam-3184	121	21	128	128	NUM
ejpam-3184	121	22	and	and	CCONJ
ejpam-3184	121	23	lemma	lemma	PROPN
ejpam-3184	121	24	13.16(b	13.16(b	NUM
ejpam-3184	121	25	)	)	PUNCT
ejpam-3184	121	26	,	,	PUNCT
ejpam-3184	122	1	p.	p.	NOUN
ejpam-3184	122	2	128–129	128–129	NUM
ejpam-3184	122	3	]	]	X
ejpam-3184	122	4	,	,	PUNCT
ejpam-3184	122	5	respectively	respectively	ADV
ejpam-3184	122	6	.	.	PUNCT
ejpam-3184	123	1	lemma	lemma	PROPN
ejpam-3184	123	2	2.6	2.6	NUM
ejpam-3184	123	3	.	.	PUNCT
ejpam-3184	124	1	let	let	VERB
ejpam-3184	124	2	z	z	PRON
ejpam-3184	124	3	be	be	AUX
ejpam-3184	124	4	a	a	DET
ejpam-3184	124	5	complete	complete	ADJ
ejpam-3184	124	6	set	set	NOUN
ejpam-3184	124	7	of	of	ADP
ejpam-3184	124	8	sylow	sylow	NOUN
ejpam-3184	124	9	subgroups	subgroup	NOUN
ejpam-3184	124	10	of	of	ADP
ejpam-3184	124	11	a	a	DET
ejpam-3184	124	12	group	group	NOUN
ejpam-3184	124	13	g	g	NOUN
ejpam-3184	124	14	and	and	CCONJ
ejpam-3184	124	15	c	c	PROPN
ejpam-3184	124	16	be	be	AUX
ejpam-3184	124	17	a	a	DET
ejpam-3184	124	18	solvable	solvable	ADJ
ejpam-3184	124	19	normal	normal	ADJ
ejpam-3184	124	20	subgroup	subgroup	NOUN
ejpam-3184	124	21	of	of	ADP
ejpam-3184	124	22	g.	g.	PROPN
ejpam-3184	124	23	if	if	SCONJ
ejpam-3184	124	24	p	p	NOUN
ejpam-3184	124	25	is	be	AUX
ejpam-3184	124	26	the	the	DET
ejpam-3184	124	27	smallest	small	ADJ
ejpam-3184	124	28	prime	prime	NOUN
ejpam-3184	124	29	dividing	divide	VERB
ejpam-3184	124	30	the	the	DET
ejpam-3184	124	31	order	order	NOUN
ejpam-3184	124	32	of	of	ADP
ejpam-3184	124	33	g	g	PROPN
ejpam-3184	124	34	and	and	CCONJ
ejpam-3184	124	35	the	the	DET
ejpam-3184	124	36	maximal	maximal	ADJ
ejpam-3184	124	37	subgroups	subgroup	NOUN
ejpam-3184	124	38	of	of	ADP
ejpam-3184	124	39	gp	gp	NOUN
ejpam-3184	124	40	∈	∈	PROPN
ejpam-3184	124	41	z	z	NOUN
ejpam-3184	124	42	are	be	AUX
ejpam-3184	124	43	c	c	NOUN
ejpam-3184	124	44	-	-	PUNCT
ejpam-3184	124	45	z	z	ADJ
ejpam-3184	124	46	-	-	PUNCT
ejpam-3184	124	47	permutable	permutable	ADJ
ejpam-3184	124	48	subgroups	subgroup	NOUN
ejpam-3184	124	49	of	of	ADP
ejpam-3184	124	50	g	g	NOUN
ejpam-3184	124	51	,	,	PUNCT
ejpam-3184	124	52	then	then	ADV
ejpam-3184	124	53	g	g	PROPN
ejpam-3184	124	54	is	be	AUX
ejpam-3184	124	55	p	p	NOUN
ejpam-3184	124	56	-	-	PUNCT
ejpam-3184	124	57	nilpotent	nilpotent	ADJ
ejpam-3184	124	58	.	.	PUNCT
ejpam-3184	125	1	proof	proof	NOUN
ejpam-3184	125	2	.	.	PUNCT
ejpam-3184	126	1	see	see	VERB
ejpam-3184	127	1	[	[	X
ejpam-3184	127	2	[	[	X
ejpam-3184	127	3	4	4	NUM
ejpam-3184	127	4	]	]	PUNCT
ejpam-3184	127	5	,	,	PUNCT
ejpam-3184	127	6	theorem	theorem	VERB
ejpam-3184	127	7	3.1	3.1	NUM
ejpam-3184	127	8	]	]	PUNCT
ejpam-3184	127	9	.	.	PUNCT
ejpam-3184	128	1	lemma	lemma	PROPN
ejpam-3184	128	2	2.7	2.7	NUM
ejpam-3184	128	3	.	.	PUNCT
ejpam-3184	129	1	let	let	VERB
ejpam-3184	129	2	f	f	PRON
ejpam-3184	129	3	be	be	AUX
ejpam-3184	129	4	a	a	DET
ejpam-3184	129	5	saturated	saturated	ADJ
ejpam-3184	129	6	formation	formation	NOUN
ejpam-3184	129	7	containing	contain	VERB
ejpam-3184	129	8	the	the	DET
ejpam-3184	129	9	class	class	NOUN
ejpam-3184	129	10	of	of	ADP
ejpam-3184	129	11	supersolvable	supersolvable	ADJ
ejpam-3184	129	12	groups	group	NOUN
ejpam-3184	129	13	u	u	NOUN
ejpam-3184	129	14	,	,	PUNCT
ejpam-3184	129	15	z	z	PROPN
ejpam-3184	129	16	be	be	AUX
ejpam-3184	129	17	a	a	DET
ejpam-3184	129	18	complete	complete	ADJ
ejpam-3184	129	19	set	set	NOUN
ejpam-3184	129	20	of	of	ADP
ejpam-3184	129	21	sylow	sylow	NOUN
ejpam-3184	129	22	subgroups	subgroup	NOUN
ejpam-3184	129	23	of	of	ADP
ejpam-3184	129	24	a	a	DET
ejpam-3184	129	25	group	group	NOUN
ejpam-3184	129	26	g	g	NOUN
ejpam-3184	129	27	and	and	CCONJ
ejpam-3184	129	28	c	c	PROPN
ejpam-3184	129	29	be	be	AUX
ejpam-3184	129	30	a	a	DET
ejpam-3184	129	31	solvable	solvable	ADJ
ejpam-3184	129	32	normal	normal	ADJ
ejpam-3184	129	33	subgroup	subgroup	NOUN
ejpam-3184	129	34	of	of	ADP
ejpam-3184	129	35	g.	g.	PROPN
ejpam-3184	130	1	then	then	ADV
ejpam-3184	130	2	the	the	DET
ejpam-3184	130	3	following	follow	VERB
ejpam-3184	130	4	two	two	NUM
ejpam-3184	130	5	statements	statement	NOUN
ejpam-3184	130	6	are	be	AUX
ejpam-3184	130	7	equivalent	equivalent	ADJ
ejpam-3184	130	8	:	:	PUNCT
ejpam-3184	130	9	(	(	PUNCT
ejpam-3184	130	10	a	a	X
ejpam-3184	130	11	)	)	PUNCT
ejpam-3184	130	12	g	g	PROPN
ejpam-3184	130	13	∈	∈	PROPN
ejpam-3184	130	14	f.	f.	PROPN
ejpam-3184	130	15	(	(	PUNCT
ejpam-3184	130	16	b	b	X
ejpam-3184	130	17	)	)	PUNCT
ejpam-3184	130	18	there	there	PRON
ejpam-3184	130	19	is	be	VERB
ejpam-3184	130	20	a	a	DET
ejpam-3184	130	21	normal	normal	ADJ
ejpam-3184	130	22	subgroup	subgroup	NOUN
ejpam-3184	130	23	h	h	NOUN
ejpam-3184	130	24	in	in	ADP
ejpam-3184	130	25	g	g	PROPN
ejpam-3184	130	26	such	such	ADJ
ejpam-3184	130	27	that	that	SCONJ
ejpam-3184	130	28	g	g	NOUN
ejpam-3184	130	29	/	/	SYM
ejpam-3184	130	30	h	h	NOUN
ejpam-3184	130	31	∈	∈	PROPN
ejpam-3184	130	32	f	f	PROPN
ejpam-3184	130	33	and	and	CCONJ
ejpam-3184	130	34	the	the	DET
ejpam-3184	130	35	maximal	maximal	ADJ
ejpam-3184	130	36	subgroups	subgroup	NOUN
ejpam-3184	130	37	of	of	ADP
ejpam-3184	130	38	gp	gp	NOUN
ejpam-3184	130	39	∩h	∩h	NOUN
ejpam-3184	130	40	are	be	AUX
ejpam-3184	130	41	c	c	NOUN
ejpam-3184	130	42	-	-	PUNCT
ejpam-3184	130	43	z	z	ADJ
ejpam-3184	130	44	-	-	PUNCT
ejpam-3184	130	45	permutable	permutable	ADJ
ejpam-3184	130	46	subgroups	subgroup	NOUN
ejpam-3184	130	47	of	of	ADP
ejpam-3184	130	48	g	g	NOUN
ejpam-3184	130	49	,	,	PUNCT
ejpam-3184	130	50	for	for	ADP
ejpam-3184	130	51	all	all	DET
ejpam-3184	130	52	gp	gp	NOUN
ejpam-3184	130	53	∈	∈	PROPN
ejpam-3184	130	54	z.	z.	NOUN
ejpam-3184	130	55	proof	proof	NOUN
ejpam-3184	130	56	.	.	PUNCT
ejpam-3184	131	1	see	see	VERB
ejpam-3184	132	1	[	[	X
ejpam-3184	132	2	[	[	X
ejpam-3184	132	3	4	4	NUM
ejpam-3184	132	4	]	]	PUNCT
ejpam-3184	132	5	,	,	PUNCT
ejpam-3184	132	6	theorem	theorem	VERB
ejpam-3184	132	7	3.2	3.2	NUM
ejpam-3184	132	8	]	]	PUNCT
ejpam-3184	132	9	.	.	PUNCT
ejpam-3184	133	1	lemma	lemma	PROPN
ejpam-3184	133	2	2.8	2.8	NUM
ejpam-3184	133	3	.	.	PUNCT
ejpam-3184	133	4	suppose	suppose	VERB
ejpam-3184	133	5	that	that	SCONJ
ejpam-3184	133	6	g	g	PROPN
ejpam-3184	133	7	is	be	AUX
ejpam-3184	133	8	a	a	DET
ejpam-3184	133	9	finite	finite	ADJ
ejpam-3184	133	10	non	non	ADJ
ejpam-3184	133	11	-	-	ADJ
ejpam-3184	133	12	abelian	abelian	ADJ
ejpam-3184	133	13	simple	simple	ADJ
ejpam-3184	133	14	group	group	NOUN
ejpam-3184	133	15	.	.	PUNCT
ejpam-3184	134	1	then	then	ADV
ejpam-3184	134	2	there	there	PRON
ejpam-3184	134	3	exists	exist	VERB
ejpam-3184	134	4	an	an	DET
ejpam-3184	134	5	odd	odd	ADJ
ejpam-3184	134	6	prime	prime	ADJ
ejpam-3184	134	7	r	r	NOUN
ejpam-3184	134	8	∈	∈	PROPN
ejpam-3184	134	9	π	π	X
ejpam-3184	134	10	(	(	PUNCT
ejpam-3184	134	11	g	g	NOUN
ejpam-3184	134	12	)	)	PUNCT
ejpam-3184	134	13	such	such	ADJ
ejpam-3184	134	14	that	that	SCONJ
ejpam-3184	134	15	g	g	PROPN
ejpam-3184	134	16	has	have	VERB
ejpam-3184	134	17	no	no	DET
ejpam-3184	134	18	hall	hall	NOUN
ejpam-3184	134	19	{	{	PUNCT
ejpam-3184	134	20	2	2	NUM
ejpam-3184	134	21	,	,	PUNCT
ejpam-3184	134	22	r}-subgroup	r}-subgroup	NOUN
ejpam-3184	134	23	.	.	PUNCT
ejpam-3184	135	1	proof	proof	NOUN
ejpam-3184	135	2	.	.	PUNCT
ejpam-3184	136	1	see	see	VERB
ejpam-3184	137	1	[	[	X
ejpam-3184	137	2	[	[	X
ejpam-3184	137	3	8	8	NUM
ejpam-3184	137	4	]	]	PUNCT
ejpam-3184	137	5	,	,	PUNCT
ejpam-3184	137	6	lemma	lemma	PROPN
ejpam-3184	137	7	2.6	2.6	NUM
ejpam-3184	137	8	]	]	PUNCT
ejpam-3184	137	9	.	.	PUNCT
ejpam-3184	138	1	m.	m.	NOUN
ejpam-3184	138	2	m.	m.	PROPN
ejpam-3184	138	3	al	al	PROPN
ejpam-3184	138	4	-	-	PUNCT
ejpam-3184	138	5	shomrani	shomrani	PROPN
ejpam-3184	138	6	,	,	PUNCT
ejpam-3184	138	7	a.	a.	NOUN
ejpam-3184	138	8	a.	a.	NOUN
ejpam-3184	138	9	heliel	heliel	PROPN
ejpam-3184	138	10	/	/	SYM
ejpam-3184	138	11	eur	eur	PROPN
ejpam-3184	138	12	.	.	PUNCT
ejpam-3184	139	1	j.	j.	PROPN
ejpam-3184	139	2	pure	pure	PROPN
ejpam-3184	139	3	appl	appl	PROPN
ejpam-3184	139	4	.	.	PROPN
ejpam-3184	139	5	math	math	PROPN
ejpam-3184	139	6	,	,	PUNCT
ejpam-3184	139	7	11	11	NUM
ejpam-3184	139	8	(	(	PUNCT
ejpam-3184	139	9	1	1	NUM
ejpam-3184	139	10	)	)	PUNCT
ejpam-3184	139	11	(	(	PUNCT
ejpam-3184	139	12	2018	2018	NUM
ejpam-3184	139	13	)	)	PUNCT
ejpam-3184	139	14	,	,	PUNCT
ejpam-3184	139	15	160	160	NUM
ejpam-3184	139	16	-	-	SYM
ejpam-3184	139	17	168	168	NUM
ejpam-3184	139	18	165	165	NUM
ejpam-3184	139	19	3	3	NUM
ejpam-3184	139	20	.	.	PUNCT
ejpam-3184	139	21	results	result	NOUN
ejpam-3184	139	22	first	first	ADV
ejpam-3184	139	23	,	,	PUNCT
ejpam-3184	139	24	we	we	PRON
ejpam-3184	139	25	prove	prove	VERB
ejpam-3184	139	26	the	the	DET
ejpam-3184	139	27	following	follow	VERB
ejpam-3184	139	28	lemma	lemma	PROPN
ejpam-3184	139	29	:	:	PUNCT
ejpam-3184	139	30	lemma	lemma	PROPN
ejpam-3184	139	31	3.1	3.1	NUM
ejpam-3184	139	32	.	.	PUNCT
ejpam-3184	140	1	let	let	VERB
ejpam-3184	140	2	z	z	PRON
ejpam-3184	140	3	be	be	AUX
ejpam-3184	140	4	a	a	DET
ejpam-3184	140	5	complete	complete	ADJ
ejpam-3184	140	6	set	set	NOUN
ejpam-3184	140	7	of	of	ADP
ejpam-3184	140	8	sylow	sylow	NOUN
ejpam-3184	140	9	subgroups	subgroup	NOUN
ejpam-3184	140	10	of	of	ADP
ejpam-3184	140	11	a	a	DET
ejpam-3184	140	12	group	group	NOUN
ejpam-3184	140	13	g	g	NOUN
ejpam-3184	140	14	and	and	CCONJ
ejpam-3184	140	15	c	c	PROPN
ejpam-3184	140	16	be	be	AUX
ejpam-3184	140	17	a	a	DET
ejpam-3184	140	18	nonempty	nonempty	ADJ
ejpam-3184	140	19	subset	subset	NOUN
ejpam-3184	140	20	of	of	ADP
ejpam-3184	140	21	g.	g.	PROPN
ejpam-3184	140	22	suppose	suppose	VERB
ejpam-3184	140	23	that	that	SCONJ
ejpam-3184	140	24	p	p	PROPN
ejpam-3184	140	25	is	be	AUX
ejpam-3184	140	26	a	a	DET
ejpam-3184	140	27	normal	normal	ADJ
ejpam-3184	140	28	p	p	NOUN
ejpam-3184	140	29	-	-	PUNCT
ejpam-3184	140	30	subgroup	subgroup	NOUN
ejpam-3184	140	31	of	of	ADP
ejpam-3184	140	32	g.	g.	PROPN
ejpam-3184	140	33	if	if	SCONJ
ejpam-3184	140	34	the	the	DET
ejpam-3184	140	35	maximal	maximal	ADJ
ejpam-3184	140	36	subgroups	subgroup	NOUN
ejpam-3184	140	37	of	of	ADP
ejpam-3184	140	38	p	p	NOUN
ejpam-3184	140	39	are	be	AUX
ejpam-3184	140	40	c	c	NOUN
ejpam-3184	140	41	-	-	PUNCT
ejpam-3184	140	42	z	z	ADJ
ejpam-3184	140	43	-	-	PUNCT
ejpam-3184	140	44	permutable	permutable	ADJ
ejpam-3184	140	45	subgroups	subgroup	NOUN
ejpam-3184	140	46	of	of	ADP
ejpam-3184	140	47	g	g	NOUN
ejpam-3184	140	48	,	,	PUNCT
ejpam-3184	140	49	then	then	ADV
ejpam-3184	140	50	p	p	X
ejpam-3184	140	51	≤	≤	NOUN
ejpam-3184	140	52	zu(g	zu(g	NUM
ejpam-3184	140	53	)	)	PUNCT
ejpam-3184	140	54	.	.	PUNCT
ejpam-3184	141	1	proof	proof	NOUN
ejpam-3184	141	2	.	.	PUNCT
ejpam-3184	142	1	assume	assume	VERB
ejpam-3184	142	2	that	that	SCONJ
ejpam-3184	142	3	the	the	DET
ejpam-3184	142	4	result	result	NOUN
ejpam-3184	142	5	is	be	AUX
ejpam-3184	142	6	false	false	ADJ
ejpam-3184	142	7	and	and	CCONJ
ejpam-3184	142	8	let	let	VERB
ejpam-3184	142	9	g	g	PRON
ejpam-3184	142	10	be	be	AUX
ejpam-3184	142	11	a	a	DET
ejpam-3184	142	12	counterexample	counterexample	NOUN
ejpam-3184	142	13	of	of	ADP
ejpam-3184	142	14	minimal	minimal	ADJ
ejpam-3184	142	15	order	order	NOUN
ejpam-3184	142	16	.	.	PUNCT
ejpam-3184	143	1	if	if	SCONJ
ejpam-3184	143	2	φ(p	φ(p	PROPN
ejpam-3184	143	3	)	)	PUNCT
ejpam-3184	144	1	6=	6=	ADP
ejpam-3184	144	2	1	1	NUM
ejpam-3184	144	3	,	,	PUNCT
ejpam-3184	144	4	then	then	ADV
ejpam-3184	144	5	the	the	DET
ejpam-3184	144	6	maximal	maximal	ADJ
ejpam-3184	144	7	subgroups	subgroup	NOUN
ejpam-3184	144	8	of	of	ADP
ejpam-3184	144	9	p	p	X
ejpam-3184	144	10	/	/	SYM
ejpam-3184	144	11	φ(p	φ(p	PROPN
ejpam-3184	144	12	)	)	PUNCT
ejpam-3184	144	13	are	be	AUX
ejpam-3184	144	14	cφ(p	cφ(p	PUNCT
ejpam-3184	144	15	)	)	PUNCT
ejpam-3184	145	1	/φ(p	/φ(p	PUNCT
ejpam-3184	145	2	)	)	PUNCT
ejpam-3184	146	1	-zφ(p	-zφ(p	X
ejpam-3184	146	2	)	)	PUNCT
ejpam-3184	146	3	/φ(p	/φ(p	X
ejpam-3184	146	4	)	)	PUNCT
ejpam-3184	147	1	permutable	permutable	ADJ
ejpam-3184	147	2	subgroups	subgroup	NOUN
ejpam-3184	147	3	of	of	ADP
ejpam-3184	147	4	g	g	NOUN
ejpam-3184	147	5	/	/	SYM
ejpam-3184	147	6	φ(p	φ(p	PROPN
ejpam-3184	147	7	)	)	PUNCT
ejpam-3184	147	8	by	by	ADP
ejpam-3184	147	9	lemma	lemma	PROPN
ejpam-3184	147	10	2.1(d	2.1(d	NUM
ejpam-3184	147	11	)	)	PUNCT
ejpam-3184	147	12	.	.	PUNCT
ejpam-3184	148	1	then	then	ADV
ejpam-3184	148	2	,	,	PUNCT
ejpam-3184	148	3	by	by	ADP
ejpam-3184	148	4	the	the	DET
ejpam-3184	148	5	minimal	minimal	ADJ
ejpam-3184	148	6	choice	choice	NOUN
ejpam-3184	148	7	of	of	ADP
ejpam-3184	148	8	g	g	NOUN
ejpam-3184	148	9	,	,	PUNCT
ejpam-3184	148	10	p	p	X
ejpam-3184	148	11	/	/	SYM
ejpam-3184	148	12	φ(p	φ(p	PROPN
ejpam-3184	148	13	)	)	PUNCT
ejpam-3184	149	1	≤	≤	NOUN
ejpam-3184	149	2	zu(g	zu(g	PROPN
ejpam-3184	149	3	/	/	SYM
ejpam-3184	149	4	φ(p	φ(p	PROPN
ejpam-3184	149	5	)	)	PUNCT
ejpam-3184	149	6	)	)	PUNCT
ejpam-3184	149	7	.	.	PUNCT
ejpam-3184	150	1	hence	hence	ADV
ejpam-3184	150	2	,	,	PUNCT
ejpam-3184	150	3	by	by	ADP
ejpam-3184	150	4	[	[	X
ejpam-3184	150	5	[	[	X
ejpam-3184	150	6	11	11	NUM
ejpam-3184	150	7	]	]	PUNCT
ejpam-3184	150	8	,	,	PUNCT
ejpam-3184	150	9	theorem	theorem	VERB
ejpam-3184	150	10	7.19	7.19	NUM
ejpam-3184	150	11	,	,	PUNCT
ejpam-3184	150	12	p.	p.	NOUN
ejpam-3184	150	13	39	39	NUM
ejpam-3184	150	14	]	]	PUNCT
ejpam-3184	150	15	,	,	PUNCT
ejpam-3184	150	16	p	p	PROPN
ejpam-3184	150	17	≤	≤	NOUN
ejpam-3184	150	18	zu(g	zu(g	NUM
ejpam-3184	150	19	)	)	PUNCT
ejpam-3184	150	20	,	,	PUNCT
ejpam-3184	150	21	a	a	DET
ejpam-3184	150	22	contradiction	contradiction	NOUN
ejpam-3184	150	23	.	.	PUNCT
ejpam-3184	151	1	thus	thus	ADV
ejpam-3184	151	2	,	,	PUNCT
ejpam-3184	151	3	we	we	PRON
ejpam-3184	151	4	may	may	AUX
ejpam-3184	151	5	assume	assume	VERB
ejpam-3184	151	6	that	that	SCONJ
ejpam-3184	151	7	,	,	PUNCT
ejpam-3184	151	8	φ(p	φ(p	PROPN
ejpam-3184	151	9	)	)	PUNCT
ejpam-3184	152	1	=	=	PUNCT
ejpam-3184	152	2	1	1	NUM
ejpam-3184	153	1	and	and	CCONJ
ejpam-3184	153	2	so	so	ADV
ejpam-3184	153	3	p	p	PRON
ejpam-3184	153	4	is	be	AUX
ejpam-3184	153	5	elementary	elementary	ADJ
ejpam-3184	153	6	abelian	abelian	NOUN
ejpam-3184	153	7	p	p	PROPN
ejpam-3184	153	8	-	-	PUNCT
ejpam-3184	153	9	group	group	NOUN
ejpam-3184	153	10	.	.	PUNCT
ejpam-3184	154	1	let	let	VERB
ejpam-3184	154	2	n	n	PRON
ejpam-3184	154	3	be	be	AUX
ejpam-3184	154	4	a	a	DET
ejpam-3184	154	5	minimal	minimal	ADJ
ejpam-3184	154	6	normal	normal	ADJ
ejpam-3184	154	7	subgroup	subgroup	NOUN
ejpam-3184	154	8	of	of	ADP
ejpam-3184	154	9	g	g	PROPN
ejpam-3184	154	10	contained	contain	VERB
ejpam-3184	154	11	in	in	ADP
ejpam-3184	154	12	p	p	PROPN
ejpam-3184	154	13	.	.	PUNCT
ejpam-3184	155	1	since	since	SCONJ
ejpam-3184	155	2	n	n	ADV
ejpam-3184	155	3	∩φ(p	∩φ(p	ADJ
ejpam-3184	155	4	)	)	PUNCT
ejpam-3184	155	5	=	=	SYM
ejpam-3184	155	6	1	1	NUM
ejpam-3184	155	7	as	as	ADP
ejpam-3184	155	8	φ(p	φ(p	PROPN
ejpam-3184	155	9	)	)	PUNCT
ejpam-3184	155	10	=	=	PUNCT
ejpam-3184	155	11	1	1	X
ejpam-3184	155	12	,	,	PUNCT
ejpam-3184	155	13	it	it	PRON
ejpam-3184	155	14	follows	follow	VERB
ejpam-3184	155	15	,	,	PUNCT
ejpam-3184	155	16	by	by	ADP
ejpam-3184	155	17	[	[	X
ejpam-3184	155	18	[	[	X
ejpam-3184	155	19	2	2	NUM
ejpam-3184	155	20	]	]	PUNCT
ejpam-3184	155	21	,	,	PUNCT
ejpam-3184	155	22	theorem	theorem	VERB
ejpam-3184	155	23	9.2(f	9.2(f	NUM
ejpam-3184	155	24	)	)	PUNCT
ejpam-3184	155	25	,	,	PUNCT
ejpam-3184	155	26	p.	p.	NOUN
ejpam-3184	155	27	30	30	NUM
ejpam-3184	155	28	]	]	PUNCT
ejpam-3184	155	29	,	,	PUNCT
ejpam-3184	155	30	that	that	PRON
ejpam-3184	155	31	n	n	PRON
ejpam-3184	155	32	is	be	AUX
ejpam-3184	155	33	complemented	complement	VERB
ejpam-3184	155	34	in	in	ADP
ejpam-3184	155	35	p	p	PROPN
ejpam-3184	155	36	.	.	PUNCT
ejpam-3184	156	1	the	the	DET
ejpam-3184	156	2	hypothesis	hypothesis	NOUN
ejpam-3184	156	3	and	and	CCONJ
ejpam-3184	156	4	lemma	lemma	PROPN
ejpam-3184	156	5	2.4	2.4	NUM
ejpam-3184	156	6	imply	imply	NOUN
ejpam-3184	156	7	that	that	SCONJ
ejpam-3184	156	8	the	the	DET
ejpam-3184	156	9	order	order	NOUN
ejpam-3184	156	10	of	of	ADP
ejpam-3184	156	11	n	n	NOUN
ejpam-3184	156	12	is	be	AUX
ejpam-3184	156	13	p.	p.	NOUN
ejpam-3184	156	14	if	if	SCONJ
ejpam-3184	156	15	n	n	PROPN
ejpam-3184	156	16	=	=	SYM
ejpam-3184	156	17	p	p	X
ejpam-3184	156	18	,	,	PUNCT
ejpam-3184	156	19	then	then	ADV
ejpam-3184	156	20	p	p	X
ejpam-3184	156	21	≤	≤	NOUN
ejpam-3184	156	22	zu(g	zu(g	NUM
ejpam-3184	156	23	)	)	PUNCT
ejpam-3184	156	24	by	by	ADP
ejpam-3184	156	25	the	the	DET
ejpam-3184	156	26	definition	definition	NOUN
ejpam-3184	156	27	of	of	ADP
ejpam-3184	156	28	zu(g	zu(g	NOUN
ejpam-3184	156	29	)	)	PUNCT
ejpam-3184	156	30	,	,	PUNCT
ejpam-3184	156	31	a	a	DET
ejpam-3184	156	32	contradiction	contradiction	NOUN
ejpam-3184	156	33	.	.	PUNCT
ejpam-3184	157	1	so	so	ADV
ejpam-3184	157	2	,	,	PUNCT
ejpam-3184	157	3	we	we	PRON
ejpam-3184	157	4	may	may	AUX
ejpam-3184	157	5	assume	assume	VERB
ejpam-3184	157	6	that	that	SCONJ
ejpam-3184	157	7	n	n	PROPN
ejpam-3184	157	8	6=	6=	X
ejpam-3184	157	9	p	p	X
ejpam-3184	157	10	.	.	PUNCT
ejpam-3184	158	1	it	it	PRON
ejpam-3184	158	2	is	be	AUX
ejpam-3184	158	3	easy	easy	ADJ
ejpam-3184	158	4	to	to	PART
ejpam-3184	158	5	see	see	VERB
ejpam-3184	158	6	that	that	SCONJ
ejpam-3184	158	7	φ(p	φ(p	PROPN
ejpam-3184	158	8	/	/	SYM
ejpam-3184	158	9	n	n	CCONJ
ejpam-3184	158	10	)	)	PUNCT
ejpam-3184	158	11	=	=	SYM
ejpam-3184	159	1	1	1	X
ejpam-3184	159	2	.	.	X
ejpam-3184	159	3	let	let	AUX
ejpam-3184	159	4	m	m	PRON
ejpam-3184	159	5	/	/	SYM
ejpam-3184	159	6	n	n	PRON
ejpam-3184	159	7	be	be	AUX
ejpam-3184	159	8	a	a	DET
ejpam-3184	159	9	maximal	maximal	ADJ
ejpam-3184	159	10	subgroup	subgroup	NOUN
ejpam-3184	159	11	of	of	ADP
ejpam-3184	159	12	p	p	PROPN
ejpam-3184	159	13	/	/	SYM
ejpam-3184	159	14	n	n	PROPN
ejpam-3184	159	15	.	.	PUNCT
ejpam-3184	160	1	then	then	ADV
ejpam-3184	160	2	m	m	VERB
ejpam-3184	160	3	is	be	AUX
ejpam-3184	160	4	a	a	DET
ejpam-3184	160	5	maximal	maximal	ADJ
ejpam-3184	160	6	subgroup	subgroup	NOUN
ejpam-3184	160	7	of	of	ADP
ejpam-3184	160	8	p	p	NOUN
ejpam-3184	160	9	as	as	ADP
ejpam-3184	160	10	|p	|p	NOUN
ejpam-3184	160	11	:	:	PUNCT
ejpam-3184	160	12	m	m	VERB
ejpam-3184	160	13	|	|	NOUN
ejpam-3184	160	14	=	=	PUNCT
ejpam-3184	160	15	|p	|p	X
ejpam-3184	160	16	/	/	SYM
ejpam-3184	160	17	n	n	NUM
ejpam-3184	160	18	:	:	PUNCT
ejpam-3184	160	19	m	m	X
ejpam-3184	160	20	/	/	SYM
ejpam-3184	160	21	n	n	PROPN
ejpam-3184	160	22	|	|	ADV
ejpam-3184	160	23	=	=	SYM
ejpam-3184	161	1	p.	p.	NOUN
ejpam-3184	161	2	by	by	ADP
ejpam-3184	161	3	hypothesis	hypothesis	NOUN
ejpam-3184	161	4	and	and	CCONJ
ejpam-3184	161	5	lemma	lemma	PROPN
ejpam-3184	161	6	2.1(b	2.1(b	NUM
ejpam-3184	161	7	)	)	PUNCT
ejpam-3184	161	8	,	,	PUNCT
ejpam-3184	161	9	m	m	PROPN
ejpam-3184	161	10	/	/	SYM
ejpam-3184	161	11	n	n	PROPN
ejpam-3184	161	12	is	be	AUX
ejpam-3184	161	13	cn	cn	PROPN
ejpam-3184	161	14	/	/	SYM
ejpam-3184	161	15	n	n	CCONJ
ejpam-3184	161	16	-zn	-zn	ADJ
ejpam-3184	161	17	/	/	SYM
ejpam-3184	161	18	n	n	CCONJ
ejpam-3184	161	19	-permutable	-permutable	ADJ
ejpam-3184	161	20	subgroup	subgroup	NOUN
ejpam-3184	161	21	of	of	ADP
ejpam-3184	161	22	g	g	PROPN
ejpam-3184	161	23	/	/	SYM
ejpam-3184	161	24	n	n	PROPN
ejpam-3184	161	25	.	.	PUNCT
ejpam-3184	162	1	so	so	ADV
ejpam-3184	162	2	,	,	PUNCT
ejpam-3184	162	3	the	the	DET
ejpam-3184	162	4	maximal	maximal	ADJ
ejpam-3184	162	5	subgroups	subgroup	NOUN
ejpam-3184	162	6	of	of	ADP
ejpam-3184	162	7	p	p	X
ejpam-3184	162	8	/	/	SYM
ejpam-3184	162	9	n	n	NOUN
ejpam-3184	162	10	are	be	AUX
ejpam-3184	162	11	cn	cn	PROPN
ejpam-3184	162	12	/	/	SYM
ejpam-3184	162	13	n	n	CCONJ
ejpam-3184	162	14	-zn	-zn	ADJ
ejpam-3184	162	15	/	/	SYM
ejpam-3184	162	16	n	n	CCONJ
ejpam-3184	162	17	-permutable	-permutable	ADJ
ejpam-3184	162	18	subgroups	subgroup	NOUN
ejpam-3184	162	19	of	of	ADP
ejpam-3184	162	20	g	g	NOUN
ejpam-3184	162	21	/	/	SYM
ejpam-3184	162	22	n	n	PROPN
ejpam-3184	162	23	.	.	PUNCT
ejpam-3184	163	1	therefore	therefore	ADV
ejpam-3184	163	2	,	,	PUNCT
ejpam-3184	163	3	p	p	X
ejpam-3184	163	4	/	/	SYM
ejpam-3184	163	5	n	n	CCONJ
ejpam-3184	163	6	≤	≤	NOUN
ejpam-3184	163	7	zu(g	zu(g	NOUN
ejpam-3184	163	8	/	/	SYM
ejpam-3184	163	9	n	n	CCONJ
ejpam-3184	163	10	)	)	PUNCT
ejpam-3184	163	11	by	by	ADP
ejpam-3184	163	12	the	the	DET
ejpam-3184	163	13	minimal	minimal	ADJ
ejpam-3184	163	14	choice	choice	NOUN
ejpam-3184	163	15	of	of	ADP
ejpam-3184	163	16	g.	g.	PROPN
ejpam-3184	163	17	but	but	CCONJ
ejpam-3184	163	18	zu(g	zu(g	NOUN
ejpam-3184	163	19	/	/	SYM
ejpam-3184	163	20	n	n	CCONJ
ejpam-3184	163	21	)	)	PUNCT
ejpam-3184	163	22	=	=	PUNCT
ejpam-3184	164	1	zu(g)/n	zu(g)/n	NUM
ejpam-3184	164	2	by	by	ADP
ejpam-3184	164	3	[	[	X
ejpam-3184	164	4	[	[	X
ejpam-3184	164	5	11	11	NUM
ejpam-3184	164	6	]	]	PUNCT
ejpam-3184	164	7	,	,	PUNCT
ejpam-3184	164	8	lemma	lemma	PROPN
ejpam-3184	164	9	7.1(ii	7.1(ii	NUM
ejpam-3184	164	10	)	)	PUNCT
ejpam-3184	164	11	,	,	PUNCT
ejpam-3184	164	12	p.	p.	NOUN
ejpam-3184	164	13	30	30	NUM
ejpam-3184	164	14	]	]	PUNCT
ejpam-3184	164	15	,	,	PUNCT
ejpam-3184	164	16	then	then	ADV
ejpam-3184	164	17	p	p	X
ejpam-3184	164	18	≤	≤	NOUN
ejpam-3184	164	19	zu(g	zu(g	NUM
ejpam-3184	164	20	)	)	PUNCT
ejpam-3184	164	21	,	,	PUNCT
ejpam-3184	164	22	a	a	DET
ejpam-3184	164	23	contradiction	contradiction	NOUN
ejpam-3184	164	24	completing	complete	VERB
ejpam-3184	164	25	the	the	DET
ejpam-3184	164	26	proof	proof	NOUN
ejpam-3184	164	27	of	of	ADP
ejpam-3184	164	28	the	the	DET
ejpam-3184	164	29	lemma	lemma	PROPN
ejpam-3184	164	30	.	.	PUNCT
ejpam-3184	165	1	now	now	ADV
ejpam-3184	165	2	we	we	PRON
ejpam-3184	165	3	can	can	AUX
ejpam-3184	165	4	prove	prove	VERB
ejpam-3184	165	5	:	:	PUNCT
ejpam-3184	165	6	theorem	theorem	NOUN
ejpam-3184	165	7	3.2	3.2	NUM
ejpam-3184	165	8	.	.	PUNCT
ejpam-3184	166	1	let	let	VERB
ejpam-3184	166	2	f	f	PRON
ejpam-3184	166	3	be	be	AUX
ejpam-3184	166	4	a	a	DET
ejpam-3184	166	5	saturated	saturated	ADJ
ejpam-3184	166	6	formation	formation	NOUN
ejpam-3184	166	7	containing	contain	VERB
ejpam-3184	166	8	the	the	DET
ejpam-3184	166	9	class	class	NOUN
ejpam-3184	166	10	of	of	ADP
ejpam-3184	166	11	supersolvable	supersolvable	ADJ
ejpam-3184	166	12	groups	group	NOUN
ejpam-3184	166	13	u	u	NOUN
ejpam-3184	166	14	,	,	PUNCT
ejpam-3184	166	15	z	z	PROPN
ejpam-3184	166	16	be	be	AUX
ejpam-3184	166	17	a	a	DET
ejpam-3184	166	18	complete	complete	ADJ
ejpam-3184	166	19	set	set	NOUN
ejpam-3184	166	20	of	of	ADP
ejpam-3184	166	21	sylow	sylow	NOUN
ejpam-3184	166	22	subgroups	subgroup	NOUN
ejpam-3184	166	23	of	of	ADP
ejpam-3184	166	24	a	a	DET
ejpam-3184	166	25	group	group	NOUN
ejpam-3184	166	26	g	g	NOUN
ejpam-3184	166	27	and	and	CCONJ
ejpam-3184	166	28	c	c	PROPN
ejpam-3184	166	29	be	be	AUX
ejpam-3184	166	30	a	a	DET
ejpam-3184	166	31	solvable	solvable	ADJ
ejpam-3184	166	32	normal	normal	ADJ
ejpam-3184	166	33	subgroup	subgroup	NOUN
ejpam-3184	166	34	of	of	ADP
ejpam-3184	166	35	g.	g.	PROPN
ejpam-3184	167	1	then	then	ADV
ejpam-3184	167	2	the	the	DET
ejpam-3184	167	3	following	follow	VERB
ejpam-3184	167	4	two	two	NUM
ejpam-3184	167	5	statements	statement	NOUN
ejpam-3184	167	6	are	be	AUX
ejpam-3184	167	7	equivalent	equivalent	ADJ
ejpam-3184	167	8	:	:	PUNCT
ejpam-3184	167	9	(	(	PUNCT
ejpam-3184	167	10	a	a	X
ejpam-3184	167	11	)	)	PUNCT
ejpam-3184	167	12	g	g	PROPN
ejpam-3184	167	13	∈	∈	PROPN
ejpam-3184	167	14	f.	f.	PROPN
ejpam-3184	167	15	(	(	PUNCT
ejpam-3184	167	16	b	b	X
ejpam-3184	167	17	)	)	PUNCT
ejpam-3184	167	18	there	there	PRON
ejpam-3184	167	19	is	be	VERB
ejpam-3184	167	20	a	a	DET
ejpam-3184	167	21	normal	normal	ADJ
ejpam-3184	167	22	subgroup	subgroup	NOUN
ejpam-3184	167	23	h	h	NOUN
ejpam-3184	167	24	in	in	ADP
ejpam-3184	167	25	g	g	PROPN
ejpam-3184	168	1	such	such	ADJ
ejpam-3184	168	2	that	that	SCONJ
ejpam-3184	168	3	g	g	NOUN
ejpam-3184	168	4	/	/	SYM
ejpam-3184	168	5	h	h	NOUN
ejpam-3184	168	6	∈	∈	PROPN
ejpam-3184	169	1	f	f	PROPN
ejpam-3184	169	2	,	,	PUNCT
ejpam-3184	169	3	f	f	PROPN
ejpam-3184	169	4	∗(h	∗(h	PROPN
ejpam-3184	169	5	)	)	PUNCT
ejpam-3184	170	1	=	=	SYM
ejpam-3184	170	2	f	f	PROPN
ejpam-3184	170	3	(	(	PUNCT
ejpam-3184	170	4	h	h	NOUN
ejpam-3184	170	5	)	)	PUNCT
ejpam-3184	170	6	and	and	CCONJ
ejpam-3184	170	7	the	the	DET
ejpam-3184	170	8	maximal	maximal	ADJ
ejpam-3184	170	9	subgroups	subgroup	NOUN
ejpam-3184	170	10	of	of	ADP
ejpam-3184	170	11	the	the	DET
ejpam-3184	170	12	sylow	sylow	NOUN
ejpam-3184	170	13	subgroups	subgroup	NOUN
ejpam-3184	170	14	of	of	ADP
ejpam-3184	170	15	f	f	PROPN
ejpam-3184	170	16	(	(	PUNCT
ejpam-3184	170	17	h	h	NOUN
ejpam-3184	170	18	)	)	PUNCT
ejpam-3184	170	19	are	be	AUX
ejpam-3184	170	20	c	c	NOUN
ejpam-3184	170	21	-	-	PUNCT
ejpam-3184	170	22	z	z	ADJ
ejpam-3184	170	23	-	-	PUNCT
ejpam-3184	170	24	permutable	permutable	ADJ
ejpam-3184	170	25	subgroups	subgroup	NOUN
ejpam-3184	170	26	of	of	ADP
ejpam-3184	170	27	g	g	NOUN
ejpam-3184	170	28	,	,	PUNCT
ejpam-3184	170	29	for	for	ADP
ejpam-3184	170	30	all	all	DET
ejpam-3184	170	31	gp	gp	NOUN
ejpam-3184	170	32	∈	∈	PROPN
ejpam-3184	170	33	z.	z.	NOUN
ejpam-3184	170	34	proof	proof	NOUN
ejpam-3184	170	35	.	.	PUNCT
ejpam-3184	171	1	we	we	PRON
ejpam-3184	171	2	need	need	VERB
ejpam-3184	171	3	only	only	ADV
ejpam-3184	171	4	to	to	PART
ejpam-3184	171	5	prove	prove	VERB
ejpam-3184	171	6	(	(	PUNCT
ejpam-3184	171	7	b)⇒	b)⇒	PROPN
ejpam-3184	171	8	(	(	PUNCT
ejpam-3184	171	9	a	a	NOUN
ejpam-3184	171	10	)	)	PUNCT
ejpam-3184	171	11	.	.	PUNCT
ejpam-3184	172	1	let	let	VERB
ejpam-3184	172	2	p	p	PRON
ejpam-3184	172	3	be	be	AUX
ejpam-3184	172	4	any	any	DET
ejpam-3184	172	5	sylow	sylow	NOUN
ejpam-3184	172	6	p	p	NOUN
ejpam-3184	172	7	-	-	PUNCT
ejpam-3184	172	8	subgroup	subgroup	NOUN
ejpam-3184	172	9	of	of	ADP
ejpam-3184	172	10	f	f	PROPN
ejpam-3184	172	11	(	(	PUNCT
ejpam-3184	172	12	h	h	NOUN
ejpam-3184	172	13	)	)	PUNCT
ejpam-3184	172	14	.	.	PUNCT
ejpam-3184	173	1	clearly	clearly	ADV
ejpam-3184	173	2	,	,	PUNCT
ejpam-3184	173	3	p	p	NOUN
ejpam-3184	173	4	is	be	AUX
ejpam-3184	173	5	normal	normal	ADJ
ejpam-3184	173	6	in	in	ADP
ejpam-3184	173	7	g.	g.	PROPN
ejpam-3184	173	8	the	the	DET
ejpam-3184	173	9	hypothesis	hypothesis	NOUN
ejpam-3184	173	10	and	and	CCONJ
ejpam-3184	173	11	lemma	lemma	PROPN
ejpam-3184	173	12	3.1	3.1	NUM
ejpam-3184	173	13	imply	imply	NOUN
ejpam-3184	173	14	that	that	SCONJ
ejpam-3184	173	15	p	p	X
ejpam-3184	173	16	≤	≤	NOUN
ejpam-3184	173	17	zu(g	zu(g	NUM
ejpam-3184	173	18	)	)	PUNCT
ejpam-3184	173	19	.	.	PUNCT
ejpam-3184	174	1	since	since	SCONJ
ejpam-3184	174	2	this	this	PRON
ejpam-3184	174	3	is	be	AUX
ejpam-3184	174	4	true	true	ADJ
ejpam-3184	174	5	for	for	ADP
ejpam-3184	174	6	any	any	DET
ejpam-3184	174	7	sylow	sylow	NOUN
ejpam-3184	174	8	p	p	NOUN
ejpam-3184	174	9	-	-	PUNCT
ejpam-3184	174	10	subgroup	subgroup	NOUN
ejpam-3184	174	11	of	of	ADP
ejpam-3184	174	12	f	f	PROPN
ejpam-3184	174	13	(	(	PUNCT
ejpam-3184	174	14	g	g	PROPN
ejpam-3184	174	15	)	)	PUNCT
ejpam-3184	174	16	,	,	PUNCT
ejpam-3184	174	17	we	we	PRON
ejpam-3184	174	18	have	have	VERB
ejpam-3184	174	19	that	that	PRON
ejpam-3184	174	20	f	f	PROPN
ejpam-3184	174	21	(	(	PUNCT
ejpam-3184	174	22	h	h	NOUN
ejpam-3184	174	23	)	)	PUNCT
ejpam-3184	174	24	≤	≤	NOUN
ejpam-3184	174	25	zu(g	zu(g	NUM
ejpam-3184	174	26	)	)	PUNCT
ejpam-3184	174	27	.	.	PUNCT
ejpam-3184	175	1	note	note	VERB
ejpam-3184	175	2	that	that	SCONJ
ejpam-3184	175	3	[	[	X
ejpam-3184	175	4	gu	gu	X
ejpam-3184	175	5	,	,	PUNCT
ejpam-3184	175	6	f	f	PROPN
ejpam-3184	175	7	(	(	PUNCT
ejpam-3184	175	8	h	h	NOUN
ejpam-3184	175	9	)	)	PUNCT
ejpam-3184	175	10	]	]	PUNCT
ejpam-3184	175	11	≤	≤	NOUN
ejpam-3184	176	1	[	[	X
ejpam-3184	176	2	gu	gu	NOUN
ejpam-3184	176	3	,	,	PUNCT
ejpam-3184	176	4	zu(g	zu(g	NUM
ejpam-3184	176	5	)	)	PUNCT
ejpam-3184	176	6	]	]	PUNCT
ejpam-3184	177	1	=	=	PUNCT
ejpam-3184	177	2	1	1	NUM
ejpam-3184	177	3	by	by	ADP
ejpam-3184	177	4	[	[	X
ejpam-3184	177	5	[	[	X
ejpam-3184	177	6	2	2	NUM
ejpam-3184	177	7	]	]	PUNCT
ejpam-3184	177	8	,	,	PUNCT
ejpam-3184	177	9	theorem	theorem	VERB
ejpam-3184	177	10	6.10	6.10	NUM
ejpam-3184	177	11	,	,	PUNCT
ejpam-3184	177	12	p.	p.	NOUN
ejpam-3184	177	13	390	390	NUM
ejpam-3184	177	14	]	]	PUNCT
ejpam-3184	177	15	and	and	CCONJ
ejpam-3184	177	16	hence	hence	ADV
ejpam-3184	177	17	gu	gu	VERB
ejpam-3184	177	18	≤	≤	NOUN
ejpam-3184	177	19	cg(f	cg(f	PUNCT
ejpam-3184	177	20	(	(	PUNCT
ejpam-3184	177	21	h	h	NOUN
ejpam-3184	177	22	)	)	PUNCT
ejpam-3184	177	23	)	)	PUNCT
ejpam-3184	177	24	.	.	PUNCT
ejpam-3184	178	1	therefore	therefore	ADV
ejpam-3184	178	2	,	,	PUNCT
ejpam-3184	178	3	g	g	NOUN
ejpam-3184	178	4	/	/	SYM
ejpam-3184	178	5	cg(f	cg(f	NUM
ejpam-3184	178	6	(	(	PUNCT
ejpam-3184	178	7	h	h	NOUN
ejpam-3184	178	8	)	)	PUNCT
ejpam-3184	178	9	)	)	PUNCT
ejpam-3184	178	10	is	be	AUX
ejpam-3184	178	11	an	an	DET
ejpam-3184	178	12	epimorphic	epimorphic	ADJ
ejpam-3184	178	13	image	image	NOUN
ejpam-3184	178	14	of	of	ADP
ejpam-3184	178	15	g	g	PROPN
ejpam-3184	178	16	/	/	SYM
ejpam-3184	178	17	gu	gu	NOUN
ejpam-3184	178	18	∈	∈	PROPN
ejpam-3184	178	19	u	u	NOUN
ejpam-3184	178	20	⊆	⊆	NUM
ejpam-3184	178	21	f	f	PROPN
ejpam-3184	178	22	and	and	CCONJ
ejpam-3184	178	23	so	so	ADV
ejpam-3184	178	24	g	g	PROPN
ejpam-3184	178	25	/	/	SYM
ejpam-3184	178	26	cg(f	cg(f	NOUN
ejpam-3184	178	27	(	(	PUNCT
ejpam-3184	178	28	h	h	NOUN
ejpam-3184	178	29	)	)	PUNCT
ejpam-3184	178	30	)	)	PUNCT
ejpam-3184	179	1	∈	∈	PROPN
ejpam-3184	179	2	u	u	NOUN
ejpam-3184	179	3	⊆	⊆	NUM
ejpam-3184	179	4	f.	f.	PROPN
ejpam-3184	179	5	consequently	consequently	ADV
ejpam-3184	179	6	,	,	PUNCT
ejpam-3184	179	7	g	g	PROPN
ejpam-3184	179	8	/	/	SYM
ejpam-3184	179	9	ch(f	ch(f	NUM
ejpam-3184	179	10	(	(	PUNCT
ejpam-3184	179	11	h	h	NOUN
ejpam-3184	179	12	)	)	PUNCT
ejpam-3184	179	13	)	)	PUNCT
ejpam-3184	180	1	=	=	SYM
ejpam-3184	180	2	g/	g/	NOUN
ejpam-3184	180	3	(	(	PUNCT
ejpam-3184	180	4	cg(f	cg(f	X
ejpam-3184	180	5	(	(	PUNCT
ejpam-3184	180	6	h	h	NOUN
ejpam-3184	180	7	)	)	PUNCT
ejpam-3184	180	8	)	)	PUNCT
ejpam-3184	181	1	∩h	∩h	NOUN
ejpam-3184	181	2	)	)	PUNCT
ejpam-3184	182	1	∈	∈	PROPN
ejpam-3184	182	2	f	f	PROPN
ejpam-3184	182	3	as	as	ADP
ejpam-3184	182	4	g	g	PROPN
ejpam-3184	182	5	/	/	SYM
ejpam-3184	182	6	cg(f	cg(f	NUM
ejpam-3184	182	7	(	(	PUNCT
ejpam-3184	182	8	h	h	NOUN
ejpam-3184	182	9	)	)	PUNCT
ejpam-3184	182	10	)	)	PUNCT
ejpam-3184	183	1	∈	∈	PROPN
ejpam-3184	183	2	f	f	PROPN
ejpam-3184	183	3	and	and	CCONJ
ejpam-3184	183	4	g	g	PROPN
ejpam-3184	183	5	/	/	SYM
ejpam-3184	183	6	h	h	NOUN
ejpam-3184	183	7	∈	∈	PROPN
ejpam-3184	183	8	f.	f.	PROPN
ejpam-3184	183	9	but	but	CCONJ
ejpam-3184	183	10	ch(f	ch(f	NUM
ejpam-3184	183	11	(	(	PUNCT
ejpam-3184	183	12	h	h	NOUN
ejpam-3184	183	13	)	)	PUNCT
ejpam-3184	183	14	)	)	PUNCT
ejpam-3184	183	15	≤	≤	NUM
ejpam-3184	184	1	f	f	X
ejpam-3184	184	2	(	(	PUNCT
ejpam-3184	184	3	h	h	NOUN
ejpam-3184	184	4	)	)	PUNCT
ejpam-3184	184	5	holds	hold	VERB
ejpam-3184	184	6	by	by	ADP
ejpam-3184	184	7	lemma	lemma	PROPN
ejpam-3184	184	8	2.3(c	2.3(c	NUM
ejpam-3184	184	9	)	)	PUNCT
ejpam-3184	184	10	and	and	CCONJ
ejpam-3184	184	11	the	the	DET
ejpam-3184	184	12	fact	fact	NOUN
ejpam-3184	184	13	that	that	SCONJ
ejpam-3184	184	14	f	f	PROPN
ejpam-3184	184	15	∗(h	∗(h	PROPN
ejpam-3184	184	16	)	)	PUNCT
ejpam-3184	185	1	=	=	SYM
ejpam-3184	185	2	f	f	PROPN
ejpam-3184	185	3	(	(	PUNCT
ejpam-3184	185	4	h	h	NOUN
ejpam-3184	185	5	)	)	PUNCT
ejpam-3184	185	6	,	,	PUNCT
ejpam-3184	185	7	then	then	ADV
ejpam-3184	185	8	m.	m.	PROPN
ejpam-3184	185	9	m.	m.	PROPN
ejpam-3184	185	10	al	al	PROPN
ejpam-3184	185	11	-	-	PUNCT
ejpam-3184	185	12	shomrani	shomrani	PROPN
ejpam-3184	185	13	,	,	PUNCT
ejpam-3184	185	14	a.	a.	NOUN
ejpam-3184	185	15	a.	a.	NOUN
ejpam-3184	185	16	heliel	heliel	PROPN
ejpam-3184	185	17	/	/	SYM
ejpam-3184	185	18	eur	eur	PROPN
ejpam-3184	185	19	.	.	PUNCT
ejpam-3184	186	1	j.	j.	PROPN
ejpam-3184	186	2	pure	pure	PROPN
ejpam-3184	186	3	appl	appl	PROPN
ejpam-3184	186	4	.	.	PROPN
ejpam-3184	186	5	math	math	PROPN
ejpam-3184	186	6	,	,	PUNCT
ejpam-3184	186	7	11	11	NUM
ejpam-3184	186	8	(	(	PUNCT
ejpam-3184	186	9	1	1	NUM
ejpam-3184	186	10	)	)	PUNCT
ejpam-3184	186	11	(	(	PUNCT
ejpam-3184	186	12	2018	2018	NUM
ejpam-3184	186	13	)	)	PUNCT
ejpam-3184	186	14	,	,	PUNCT
ejpam-3184	186	15	160	160	NUM
ejpam-3184	186	16	-	-	SYM
ejpam-3184	186	17	168	168	NUM
ejpam-3184	186	18	166	166	NUM
ejpam-3184	186	19	g	g	NOUN
ejpam-3184	186	20	/	/	SYM
ejpam-3184	186	21	f	f	PROPN
ejpam-3184	186	22	(	(	PUNCT
ejpam-3184	186	23	h	h	NOUN
ejpam-3184	186	24	)	)	PUNCT
ejpam-3184	186	25	is	be	AUX
ejpam-3184	186	26	an	an	DET
ejpam-3184	186	27	epimorphic	epimorphic	ADJ
ejpam-3184	186	28	image	image	NOUN
ejpam-3184	186	29	of	of	ADP
ejpam-3184	186	30	g	g	NOUN
ejpam-3184	186	31	/	/	SYM
ejpam-3184	186	32	ch(f	ch(f	NUM
ejpam-3184	186	33	(	(	PUNCT
ejpam-3184	186	34	h	h	NOUN
ejpam-3184	186	35	)	)	PUNCT
ejpam-3184	186	36	)	)	PUNCT
ejpam-3184	186	37	,	,	PUNCT
ejpam-3184	187	1	thus	thus	ADV
ejpam-3184	187	2	g	g	PROPN
ejpam-3184	187	3	/	/	SYM
ejpam-3184	187	4	f	f	PROPN
ejpam-3184	187	5	(	(	PUNCT
ejpam-3184	187	6	h	h	NOUN
ejpam-3184	187	7	)	)	PUNCT
ejpam-3184	187	8	∈	∈	PROPN
ejpam-3184	187	9	f.	f.	NOUN
ejpam-3184	187	10	applying	apply	VERB
ejpam-3184	187	11	lemma	lemma	PROPN
ejpam-3184	187	12	2.7	2.7	NUM
ejpam-3184	187	13	yields	yield	NOUN
ejpam-3184	187	14	g	g	PROPN
ejpam-3184	187	15	∈	∈	PROPN
ejpam-3184	187	16	f.	f.	NOUN
ejpam-3184	187	17	this	this	PRON
ejpam-3184	187	18	comletes	comlete	VERB
ejpam-3184	187	19	the	the	DET
ejpam-3184	187	20	proof	proof	NOUN
ejpam-3184	187	21	of	of	ADP
ejpam-3184	187	22	the	the	DET
ejpam-3184	187	23	theorem	theorem	NOUN
ejpam-3184	187	24	.	.	PUNCT
ejpam-3184	188	1	the	the	DET
ejpam-3184	188	2	following	follow	VERB
ejpam-3184	188	3	lemma	lemma	PROPN
ejpam-3184	188	4	is	be	AUX
ejpam-3184	188	5	a	a	DET
ejpam-3184	188	6	criterion	criterion	NOUN
ejpam-3184	188	7	for	for	ADP
ejpam-3184	188	8	the	the	DET
ejpam-3184	188	9	solvability	solvability	NOUN
ejpam-3184	188	10	of	of	ADP
ejpam-3184	188	11	finite	finite	ADJ
ejpam-3184	188	12	groups	group	NOUN
ejpam-3184	188	13	:	:	PUNCT
ejpam-3184	188	14	lemma	lemma	PROPN
ejpam-3184	188	15	3.3	3.3	NUM
ejpam-3184	188	16	.	.	PUNCT
ejpam-3184	189	1	let	let	VERB
ejpam-3184	189	2	g	g	PRON
ejpam-3184	189	3	be	be	AUX
ejpam-3184	189	4	a	a	DET
ejpam-3184	189	5	group	group	NOUN
ejpam-3184	189	6	.	.	PUNCT
ejpam-3184	190	1	then	then	ADV
ejpam-3184	190	2	the	the	DET
ejpam-3184	190	3	following	follow	VERB
ejpam-3184	190	4	two	two	NUM
ejpam-3184	190	5	statements	statement	NOUN
ejpam-3184	190	6	are	be	AUX
ejpam-3184	190	7	equivalent	equivalent	ADJ
ejpam-3184	190	8	:	:	PUNCT
ejpam-3184	190	9	(	(	PUNCT
ejpam-3184	190	10	a	a	X
ejpam-3184	190	11	)	)	PUNCT
ejpam-3184	190	12	g	g	NOUN
ejpam-3184	190	13	is	be	AUX
ejpam-3184	190	14	solvable	solvable	ADJ
ejpam-3184	190	15	.	.	PUNCT
ejpam-3184	191	1	(	(	PUNCT
ejpam-3184	191	2	b	b	X
ejpam-3184	191	3	)	)	PUNCT
ejpam-3184	191	4	g	g	NOUN
ejpam-3184	191	5	has	have	VERB
ejpam-3184	191	6	a	a	DET
ejpam-3184	191	7	complete	complete	ADJ
ejpam-3184	191	8	set	set	NOUN
ejpam-3184	191	9	z	z	NOUN
ejpam-3184	191	10	of	of	ADP
ejpam-3184	191	11	sylow	sylow	NOUN
ejpam-3184	191	12	subgroups	subgroup	NOUN
ejpam-3184	191	13	such	such	ADJ
ejpam-3184	191	14	that	that	PRON
ejpam-3184	191	15	gp	gp	NOUN
ejpam-3184	191	16	∈	∈	PROPN
ejpam-3184	191	17	z	z	PROPN
ejpam-3184	191	18	is	be	AUX
ejpam-3184	191	19	z	z	NOUN
ejpam-3184	191	20	-	-	ADJ
ejpam-3184	191	21	permutable	permutable	ADJ
ejpam-3184	191	22	subgroup	subgroup	NOUN
ejpam-3184	191	23	of	of	ADP
ejpam-3184	191	24	g	g	PROPN
ejpam-3184	191	25	,	,	PUNCT
ejpam-3184	191	26	where	where	SCONJ
ejpam-3184	191	27	p	p	NOUN
ejpam-3184	191	28	is	be	AUX
ejpam-3184	191	29	the	the	DET
ejpam-3184	191	30	smallest	small	ADJ
ejpam-3184	191	31	prime	prime	NOUN
ejpam-3184	191	32	dividing	divide	VERB
ejpam-3184	191	33	the	the	DET
ejpam-3184	191	34	order	order	NOUN
ejpam-3184	191	35	of	of	ADP
ejpam-3184	191	36	g.	g.	PROPN
ejpam-3184	191	37	proof	proof	NOUN
ejpam-3184	191	38	.	.	PUNCT
ejpam-3184	192	1	(	(	PUNCT
ejpam-3184	192	2	a)⇒	a)⇒	PROPN
ejpam-3184	192	3	(	(	PUNCT
ejpam-3184	192	4	b	b	NOUN
ejpam-3184	192	5	)	)	PUNCT
ejpam-3184	192	6	.	.	PUNCT
ejpam-3184	193	1	since	since	SCONJ
ejpam-3184	193	2	g	g	PROPN
ejpam-3184	193	3	is	be	AUX
ejpam-3184	193	4	solvable	solvable	ADJ
ejpam-3184	193	5	,	,	PUNCT
ejpam-3184	193	6	then	then	ADV
ejpam-3184	193	7	g	g	PROPN
ejpam-3184	193	8	has	have	VERB
ejpam-3184	193	9	a	a	DET
ejpam-3184	193	10	sylow	sylow	NOUN
ejpam-3184	193	11	basis	basis	NOUN
ejpam-3184	193	12	s	s	VERB
ejpam-3184	193	13	by	by	ADP
ejpam-3184	193	14	[	[	X
ejpam-3184	193	15	9	9	NUM
ejpam-3184	193	16	,	,	PUNCT
ejpam-3184	193	17	theorem	theorem	ADJ
ejpam-3184	193	18	9.3.11	9.3.11	NOUN
ejpam-3184	193	19	,	,	PUNCT
ejpam-3184	193	20	p.	p.	NOUN
ejpam-3184	193	21	229	229	NUM
ejpam-3184	193	22	]	]	PUNCT
ejpam-3184	193	23	.	.	PUNCT
ejpam-3184	194	1	let	let	VERB
ejpam-3184	194	2	p	p	PRON
ejpam-3184	194	3	be	be	AUX
ejpam-3184	194	4	the	the	DET
ejpam-3184	194	5	smallest	small	ADJ
ejpam-3184	194	6	prime	prime	NOUN
ejpam-3184	194	7	dividing	divide	VERB
ejpam-3184	194	8	the	the	DET
ejpam-3184	194	9	order	order	NOUN
ejpam-3184	194	10	of	of	ADP
ejpam-3184	194	11	g	g	NOUN
ejpam-3184	194	12	and	and	CCONJ
ejpam-3184	194	13	let	let	VERB
ejpam-3184	194	14	gp	gp	NOUN
ejpam-3184	194	15	be	be	AUX
ejpam-3184	194	16	the	the	DET
ejpam-3184	194	17	sylow	sylow	NOUN
ejpam-3184	194	18	p	p	NOUN
ejpam-3184	194	19	-	-	PUNCT
ejpam-3184	194	20	subgroup	subgroup	NOUN
ejpam-3184	194	21	of	of	ADP
ejpam-3184	194	22	g	g	PROPN
ejpam-3184	194	23	in	in	ADP
ejpam-3184	194	24	s.	s.	PROPN
ejpam-3184	194	25	by	by	ADP
ejpam-3184	194	26	the	the	DET
ejpam-3184	194	27	definition	definition	NOUN
ejpam-3184	194	28	of	of	ADP
ejpam-3184	194	29	the	the	DET
ejpam-3184	194	30	sylow	sylow	NOUN
ejpam-3184	194	31	basis	basis	NOUN
ejpam-3184	194	32	s	s	X
ejpam-3184	194	33	,	,	PUNCT
ejpam-3184	194	34	we	we	PRON
ejpam-3184	194	35	have	have	VERB
ejpam-3184	194	36	that	that	DET
ejpam-3184	194	37	gpgq	gpgq	PROPN
ejpam-3184	194	38	is	be	AUX
ejpam-3184	194	39	a	a	DET
ejpam-3184	194	40	subgroup	subgroup	NOUN
ejpam-3184	194	41	of	of	ADP
ejpam-3184	194	42	g	g	NOUN
ejpam-3184	194	43	,	,	PUNCT
ejpam-3184	194	44	for	for	ADP
ejpam-3184	194	45	all	all	DET
ejpam-3184	194	46	gq	gq	PROPN
ejpam-3184	194	47	∈	∈	PROPN
ejpam-3184	194	48	s	s	NOUN
ejpam-3184	194	49	,	,	PUNCT
ejpam-3184	194	50	where	where	SCONJ
ejpam-3184	194	51	q	q	NOUN
ejpam-3184	194	52	is	be	AUX
ejpam-3184	194	53	a	a	DET
ejpam-3184	194	54	prime	prime	NOUN
ejpam-3184	194	55	.	.	PUNCT
ejpam-3184	195	1	thus	thus	ADV
ejpam-3184	195	2	we	we	PRON
ejpam-3184	195	3	can	can	AUX
ejpam-3184	195	4	take	take	VERB
ejpam-3184	195	5	z	z	NOUN
ejpam-3184	195	6	=	=	SYM
ejpam-3184	195	7	s	s	NOUN
ejpam-3184	195	8	and	and	CCONJ
ejpam-3184	195	9	we	we	PRON
ejpam-3184	195	10	have	have	AUX
ejpam-3184	195	11	gp	gp	NOUN
ejpam-3184	195	12	is	be	AUX
ejpam-3184	195	13	z	z	NOUN
ejpam-3184	195	14	-	-	ADJ
ejpam-3184	195	15	permutable	permutable	ADJ
ejpam-3184	195	16	subgroup	subgroup	NOUN
ejpam-3184	195	17	of	of	ADP
ejpam-3184	195	18	g.	g.	PROPN
ejpam-3184	195	19	(	(	PUNCT
ejpam-3184	195	20	b)⇒	b)⇒	PROPN
ejpam-3184	195	21	(	(	PUNCT
ejpam-3184	195	22	a	a	NOUN
ejpam-3184	195	23	)	)	PUNCT
ejpam-3184	195	24	.	.	PUNCT
ejpam-3184	196	1	assume	assume	VERB
ejpam-3184	196	2	that	that	SCONJ
ejpam-3184	196	3	the	the	DET
ejpam-3184	196	4	result	result	NOUN
ejpam-3184	196	5	is	be	AUX
ejpam-3184	196	6	false	false	ADJ
ejpam-3184	196	7	and	and	CCONJ
ejpam-3184	196	8	let	let	VERB
ejpam-3184	196	9	g	g	PRON
ejpam-3184	196	10	be	be	AUX
ejpam-3184	196	11	a	a	DET
ejpam-3184	196	12	counterexample	counterexample	NOUN
ejpam-3184	196	13	of	of	ADP
ejpam-3184	196	14	minimal	minimal	ADJ
ejpam-3184	196	15	order	order	NOUN
ejpam-3184	196	16	.	.	PUNCT
ejpam-3184	197	1	by	by	ADP
ejpam-3184	197	2	feit	feit	PROPN
ejpam-3184	197	3	-	-	PUNCT
ejpam-3184	197	4	thompson	thompson	NOUN
ejpam-3184	197	5	theorem	theorem	NOUN
ejpam-3184	197	6	[	[	X
ejpam-3184	197	7	3	3	NUM
ejpam-3184	197	8	]	]	PUNCT
ejpam-3184	197	9	,	,	PUNCT
ejpam-3184	197	10	we	we	PRON
ejpam-3184	197	11	may	may	AUX
ejpam-3184	197	12	assume	assume	VERB
ejpam-3184	197	13	that	that	SCONJ
ejpam-3184	197	14	p	p	X
ejpam-3184	197	15	=	=	NOUN
ejpam-3184	197	16	2	2	X
ejpam-3184	197	17	.	.	PUNCT
ejpam-3184	197	18	since	since	SCONJ
ejpam-3184	197	19	g2	g2	PROPN
ejpam-3184	197	20	∈	∈	PROPN
ejpam-3184	197	21	z	z	PROPN
ejpam-3184	197	22	is	be	AUX
ejpam-3184	197	23	z	z	NOUN
ejpam-3184	197	24	-	-	ADJ
ejpam-3184	197	25	permutable	permutable	ADJ
ejpam-3184	197	26	subgroup	subgroup	NOUN
ejpam-3184	197	27	of	of	ADP
ejpam-3184	197	28	g	g	PROPN
ejpam-3184	197	29	,	,	PUNCT
ejpam-3184	197	30	it	it	PRON
ejpam-3184	197	31	follows	follow	VERB
ejpam-3184	197	32	that	that	SCONJ
ejpam-3184	197	33	g2gq	g2gq	PRON
ejpam-3184	197	34	is	be	AUX
ejpam-3184	197	35	a	a	DET
ejpam-3184	197	36	subgroup	subgroup	NOUN
ejpam-3184	197	37	of	of	ADP
ejpam-3184	197	38	g	g	NOUN
ejpam-3184	197	39	,	,	PUNCT
ejpam-3184	197	40	for	for	ADP
ejpam-3184	197	41	every	every	DET
ejpam-3184	197	42	odd	odd	ADJ
ejpam-3184	197	43	prime	prime	NOUN
ejpam-3184	197	44	q	q	NOUN
ejpam-3184	197	45	dividing	divide	VERB
ejpam-3184	197	46	the	the	DET
ejpam-3184	197	47	order	order	NOUN
ejpam-3184	197	48	of	of	ADP
ejpam-3184	197	49	g	g	NOUN
ejpam-3184	197	50	,	,	PUNCT
ejpam-3184	197	51	where	where	SCONJ
ejpam-3184	197	52	gq	gq	PROPN
ejpam-3184	197	53	∈	∈	PROPN
ejpam-3184	197	54	z.	z.	PROPN
ejpam-3184	197	55	therefore	therefore	ADV
ejpam-3184	197	56	,	,	PUNCT
ejpam-3184	197	57	g	g	PROPN
ejpam-3184	197	58	is	be	AUX
ejpam-3184	197	59	not	not	PART
ejpam-3184	197	60	simple	simple	ADJ
ejpam-3184	197	61	by	by	ADP
ejpam-3184	197	62	lemma	lemma	PROPN
ejpam-3184	197	63	2.8	2.8	NUM
ejpam-3184	197	64	.	.	PUNCT
ejpam-3184	198	1	let	let	VERB
ejpam-3184	198	2	n	n	PRON
ejpam-3184	198	3	be	be	AUX
ejpam-3184	198	4	a	a	DET
ejpam-3184	198	5	nontrivial	nontrivial	ADJ
ejpam-3184	198	6	proper	proper	ADJ
ejpam-3184	198	7	normal	normal	ADJ
ejpam-3184	198	8	subgroup	subgroup	NOUN
ejpam-3184	198	9	of	of	ADP
ejpam-3184	198	10	g.	g.	PROPN
ejpam-3184	198	11	clearly	clearly	ADV
ejpam-3184	198	12	,	,	PUNCT
ejpam-3184	198	13	g2	g2	PROPN
ejpam-3184	198	14	∩n	∩n	PROPN
ejpam-3184	198	15	and	and	CCONJ
ejpam-3184	198	16	g2n	g2n	PROPN
ejpam-3184	198	17	/	/	SYM
ejpam-3184	198	18	n	n	NOUN
ejpam-3184	198	19	are	be	AUX
ejpam-3184	198	20	sylow	sylow	NOUN
ejpam-3184	198	21	2	2	NUM
ejpam-3184	198	22	-	-	PUNCT
ejpam-3184	198	23	subgroups	subgroup	NOUN
ejpam-3184	198	24	of	of	ADP
ejpam-3184	198	25	n	n	PRON
ejpam-3184	198	26	and	and	CCONJ
ejpam-3184	198	27	g	g	NOUN
ejpam-3184	198	28	/	/	SYM
ejpam-3184	198	29	n	n	NOUN
ejpam-3184	198	30	,	,	PUNCT
ejpam-3184	198	31	respectively	respectively	ADV
ejpam-3184	198	32	.	.	PUNCT
ejpam-3184	199	1	by	by	ADP
ejpam-3184	199	2	lemma	lemma	PROPN
ejpam-3184	199	3	2.1(e	2.1(e	NUM
ejpam-3184	199	4	)	)	PUNCT
ejpam-3184	199	5	,	,	PUNCT
ejpam-3184	199	6	g2	g2	PROPN
ejpam-3184	199	7	∩	∩	NOUN
ejpam-3184	199	8	n	n	PRON
ejpam-3184	199	9	is	be	AUX
ejpam-3184	199	10	z	z	ADJ
ejpam-3184	199	11	-	-	ADJ
ejpam-3184	199	12	permutable	permutable	ADJ
ejpam-3184	199	13	subgroup	subgroup	NOUN
ejpam-3184	199	14	of	of	ADP
ejpam-3184	199	15	g.	g.	PROPN
ejpam-3184	199	16	therefore	therefore	ADV
ejpam-3184	199	17	,	,	PUNCT
ejpam-3184	199	18	g2	g2	PROPN
ejpam-3184	199	19	∩n	∩n	PROPN
ejpam-3184	199	20	is	be	AUX
ejpam-3184	199	21	z	z	NOUN
ejpam-3184	199	22	∩n	∩n	PROPN
ejpam-3184	199	23	-permutable	-permutable	ADJ
ejpam-3184	199	24	subgroup	subgroup	NOUN
ejpam-3184	199	25	of	of	ADP
ejpam-3184	199	26	n	n	NUM
ejpam-3184	199	27	by	by	ADP
ejpam-3184	199	28	lemma	lemma	PROPN
ejpam-3184	199	29	2.1(c	2.1(c	NUM
ejpam-3184	199	30	)	)	PUNCT
ejpam-3184	199	31	.	.	PUNCT
ejpam-3184	200	1	also	also	ADV
ejpam-3184	200	2	,	,	PUNCT
ejpam-3184	200	3	g2n	g2n	PROPN
ejpam-3184	200	4	/	/	SYM
ejpam-3184	200	5	n	n	PROPN
ejpam-3184	200	6	is	be	AUX
ejpam-3184	200	7	zn	zn	PROPN
ejpam-3184	200	8	/	/	SYM
ejpam-3184	200	9	n	n	CCONJ
ejpam-3184	200	10	-permutable	-permutable	ADJ
ejpam-3184	200	11	subgroup	subgroup	NOUN
ejpam-3184	200	12	of	of	ADP
ejpam-3184	200	13	g	g	PROPN
ejpam-3184	200	14	/	/	SYM
ejpam-3184	200	15	n	n	NOUN
ejpam-3184	200	16	by	by	ADP
ejpam-3184	200	17	lemma	lemma	PROPN
ejpam-3184	200	18	2.1(b	2.1(b	NUM
ejpam-3184	200	19	)	)	PUNCT
ejpam-3184	200	20	.	.	PUNCT
ejpam-3184	201	1	if	if	SCONJ
ejpam-3184	201	2	2	2	NUM
ejpam-3184	201	3	divides	divide	VERB
ejpam-3184	201	4	the	the	DET
ejpam-3184	201	5	order	order	NOUN
ejpam-3184	201	6	of	of	ADP
ejpam-3184	201	7	n	n	PROPN
ejpam-3184	201	8	,	,	PUNCT
ejpam-3184	201	9	then	then	ADV
ejpam-3184	201	10	n	n	PRON
ejpam-3184	201	11	is	be	AUX
ejpam-3184	201	12	solvable	solvable	ADJ
ejpam-3184	201	13	by	by	ADP
ejpam-3184	201	14	the	the	DET
ejpam-3184	201	15	minimal	minimal	ADJ
ejpam-3184	201	16	choice	choice	NOUN
ejpam-3184	201	17	of	of	ADP
ejpam-3184	201	18	g	g	NOUN
ejpam-3184	201	19	and	and	CCONJ
ejpam-3184	201	20	if	if	SCONJ
ejpam-3184	201	21	2	2	NUM
ejpam-3184	201	22	does	do	AUX
ejpam-3184	201	23	not	not	PART
ejpam-3184	201	24	divide	divide	VERB
ejpam-3184	201	25	the	the	DET
ejpam-3184	201	26	order	order	NOUN
ejpam-3184	201	27	of	of	ADP
ejpam-3184	201	28	n	n	PROPN
ejpam-3184	201	29	,	,	PUNCT
ejpam-3184	201	30	then	then	ADV
ejpam-3184	201	31	n	n	PRON
ejpam-3184	201	32	is	be	AUX
ejpam-3184	201	33	solvable	solvable	ADJ
ejpam-3184	201	34	by	by	ADP
ejpam-3184	201	35	feit	feit	PROPN
ejpam-3184	201	36	-	-	PUNCT
ejpam-3184	201	37	thompson	thompson	NOUN
ejpam-3184	201	38	theorem	theorem	NOUN
ejpam-3184	201	39	[	[	X
ejpam-3184	201	40	3	3	NUM
ejpam-3184	201	41	]	]	PUNCT
ejpam-3184	201	42	.	.	PUNCT
ejpam-3184	202	1	the	the	DET
ejpam-3184	202	2	same	same	ADJ
ejpam-3184	202	3	argument	argument	NOUN
ejpam-3184	202	4	holds	hold	VERB
ejpam-3184	202	5	for	for	ADP
ejpam-3184	202	6	g	g	NOUN
ejpam-3184	202	7	/	/	SYM
ejpam-3184	202	8	n	n	NOUN
ejpam-3184	202	9	,	,	PUNCT
ejpam-3184	202	10	thus	thus	ADV
ejpam-3184	202	11	g	g	PROPN
ejpam-3184	202	12	/	/	SYM
ejpam-3184	202	13	n	n	PRON
ejpam-3184	202	14	is	be	AUX
ejpam-3184	202	15	solvable	solvable	ADJ
ejpam-3184	202	16	.	.	PUNCT
ejpam-3184	203	1	since	since	SCONJ
ejpam-3184	203	2	n	n	PROPN
ejpam-3184	203	3	and	and	CCONJ
ejpam-3184	203	4	g	g	PROPN
ejpam-3184	203	5	/	/	SYM
ejpam-3184	203	6	n	n	X
ejpam-3184	203	7	are	be	AUX
ejpam-3184	203	8	solvable	solvable	ADJ
ejpam-3184	203	9	,	,	PUNCT
ejpam-3184	203	10	we	we	PRON
ejpam-3184	203	11	have	have	VERB
ejpam-3184	203	12	that	that	PRON
ejpam-3184	203	13	g	g	PROPN
ejpam-3184	203	14	is	be	AUX
ejpam-3184	203	15	solvable	solvable	ADJ
ejpam-3184	203	16	,	,	PUNCT
ejpam-3184	203	17	a	a	DET
ejpam-3184	203	18	contradiction	contradiction	NOUN
ejpam-3184	203	19	completing	complete	VERB
ejpam-3184	203	20	the	the	DET
ejpam-3184	203	21	proof	proof	NOUN
ejpam-3184	203	22	of	of	ADP
ejpam-3184	203	23	the	the	DET
ejpam-3184	203	24	lemma	lemma	PROPN
ejpam-3184	203	25	.	.	PUNCT
ejpam-3184	204	1	proof	proof	NOUN
ejpam-3184	204	2	of	of	ADP
ejpam-3184	204	3	theorem	theorem	ADJ
ejpam-3184	204	4	1.2	1.2	NUM
ejpam-3184	204	5	.	.	PUNCT
ejpam-3184	205	1	we	we	PRON
ejpam-3184	205	2	need	need	VERB
ejpam-3184	205	3	only	only	ADV
ejpam-3184	205	4	to	to	PART
ejpam-3184	205	5	prove	prove	VERB
ejpam-3184	205	6	(	(	PUNCT
ejpam-3184	205	7	b)⇒	b)⇒	PROPN
ejpam-3184	205	8	(	(	PUNCT
ejpam-3184	205	9	a	a	NOUN
ejpam-3184	205	10	)	)	PUNCT
ejpam-3184	205	11	as	as	ADP
ejpam-3184	205	12	(	(	PUNCT
ejpam-3184	205	13	a)⇒	a)⇒	PROPN
ejpam-3184	205	14	(	(	PUNCT
ejpam-3184	205	15	b	b	NOUN
ejpam-3184	205	16	)	)	PUNCT
ejpam-3184	205	17	is	be	AUX
ejpam-3184	205	18	true	true	ADJ
ejpam-3184	205	19	withh	withh	NOUN
ejpam-3184	205	20	=	=	SYM
ejpam-3184	205	21	1	1	X
ejpam-3184	205	22	.	.	PUNCT
ejpam-3184	206	1	let	let	AUX
ejpam-3184	206	2	e(g	e(g	PROPN
ejpam-3184	206	3	)	)	PUNCT
ejpam-3184	206	4	be	be	AUX
ejpam-3184	206	5	the	the	DET
ejpam-3184	206	6	layer	layer	NOUN
ejpam-3184	206	7	subgroup	subgroup	NOUN
ejpam-3184	206	8	of	of	ADP
ejpam-3184	206	9	g.	g.	PROPN
ejpam-3184	206	10	since	since	SCONJ
ejpam-3184	206	11	c	c	PROPN
ejpam-3184	206	12	is	be	AUX
ejpam-3184	206	13	a	a	DET
ejpam-3184	206	14	solvable	solvable	ADJ
ejpam-3184	206	15	normal	normal	ADJ
ejpam-3184	206	16	subgroup	subgroup	NOUN
ejpam-3184	206	17	of	of	ADP
ejpam-3184	206	18	g	g	PROPN
ejpam-3184	206	19	,	,	PUNCT
ejpam-3184	206	20	it	it	PRON
ejpam-3184	206	21	follows	follow	VERB
ejpam-3184	206	22	,	,	PUNCT
ejpam-3184	206	23	by	by	ADP
ejpam-3184	206	24	lemma	lemma	PROPN
ejpam-3184	206	25	2.5(c	2.5(c	NUM
ejpam-3184	206	26	)	)	PUNCT
ejpam-3184	206	27	,	,	PUNCT
ejpam-3184	207	1	that	that	SCONJ
ejpam-3184	207	2	[	[	X
ejpam-3184	207	3	e(g	e(g	NOUN
ejpam-3184	207	4	)	)	PUNCT
ejpam-3184	207	5	,	,	PUNCT
ejpam-3184	207	6	c	c	X
ejpam-3184	207	7	]	]	X
ejpam-3184	207	8	=	=	SYM
ejpam-3184	207	9	1	1	NUM
ejpam-3184	207	10	and	and	CCONJ
ejpam-3184	207	11	so	so	ADV
ejpam-3184	207	12	c	c	PROPN
ejpam-3184	207	13	≤	≤	NOUN
ejpam-3184	207	14	cg(e(g	cg(e(g	NOUN
ejpam-3184	207	15	)	)	PUNCT
ejpam-3184	207	16	)	)	PUNCT
ejpam-3184	207	17	.	.	PUNCT
ejpam-3184	208	1	by	by	ADP
ejpam-3184	208	2	lemma	lemma	PROPN
ejpam-3184	208	3	2.3(a	2.3(a	NUM
ejpam-3184	208	4	)	)	PUNCT
ejpam-3184	208	5	,	,	PUNCT
ejpam-3184	208	6	we	we	PRON
ejpam-3184	208	7	have	have	VERB
ejpam-3184	208	8	that	that	DET
ejpam-3184	208	9	f	f	PROPN
ejpam-3184	208	10	∗(h	∗(h	PROPN
ejpam-3184	208	11	)	)	PUNCT
ejpam-3184	208	12	=	=	SYM
ejpam-3184	208	13	f	f	PROPN
ejpam-3184	208	14	(	(	PUNCT
ejpam-3184	208	15	h)e(h	h)e(h	NOUN
ejpam-3184	208	16	)	)	PUNCT
ejpam-3184	208	17	.	.	PUNCT
ejpam-3184	209	1	moreover	moreover	ADV
ejpam-3184	209	2	,	,	PUNCT
ejpam-3184	209	3	e(h	e(h	PROPN
ejpam-3184	209	4	)	)	PUNCT
ejpam-3184	209	5	is	be	AUX
ejpam-3184	209	6	a	a	DET
ejpam-3184	209	7	perfect	perfect	ADJ
ejpam-3184	209	8	quasinilpotent	quasinilpotent	NOUN
ejpam-3184	209	9	characteristic	characteristic	ADJ
ejpam-3184	209	10	subgroup	subgroup	NOUN
ejpam-3184	209	11	of	of	ADP
ejpam-3184	209	12	h	h	PROPN
ejpam-3184	209	13	by	by	ADP
ejpam-3184	209	14	lemma	lemma	PROPN
ejpam-3184	209	15	2.5(a	2.5(a	NUM
ejpam-3184	209	16	)	)	PUNCT
ejpam-3184	209	17	.	.	PUNCT
ejpam-3184	210	1	now	now	ADV
ejpam-3184	210	2	e(h	e(h	PROPN
ejpam-3184	210	3	)	)	PUNCT
ejpam-3184	210	4	char	char	NOUN
ejpam-3184	210	5	h	h	NOUN
ejpam-3184	210	6	and	and	CCONJ
ejpam-3184	210	7	h	h	NOUN
ejpam-3184	210	8	is	be	AUX
ejpam-3184	210	9	normal	normal	ADJ
ejpam-3184	210	10	in	in	ADP
ejpam-3184	210	11	g	g	PROPN
ejpam-3184	210	12	,	,	PUNCT
ejpam-3184	210	13	then	then	ADV
ejpam-3184	210	14	e(h	e(h	PROPN
ejpam-3184	210	15	)	)	PUNCT
ejpam-3184	210	16	is	be	AUX
ejpam-3184	210	17	normal	normal	ADJ
ejpam-3184	210	18	in	in	ADP
ejpam-3184	210	19	g.	g.	PROPN
ejpam-3184	210	20	note	note	VERB
ejpam-3184	210	21	that	that	SCONJ
ejpam-3184	210	22	e(h	e(h	PROPN
ejpam-3184	210	23	)	)	PUNCT
ejpam-3184	210	24	≤	≤	PROPN
ejpam-3184	210	25	e(g	e(g	PROPN
ejpam-3184	210	26	)	)	PUNCT
ejpam-3184	210	27	by	by	ADP
ejpam-3184	210	28	lemma	lemma	PROPN
ejpam-3184	210	29	2.5(b	2.5(b	NUM
ejpam-3184	210	30	)	)	PUNCT
ejpam-3184	210	31	,	,	PUNCT
ejpam-3184	210	32	and	and	CCONJ
ejpam-3184	210	33	hence	hence	ADV
ejpam-3184	210	34	c	c	X
ejpam-3184	210	35	≤	≤	NUM
ejpam-3184	210	36	cg(e(h	cg(e(h	NOUN
ejpam-3184	210	37	)	)	PUNCT
ejpam-3184	210	38	)	)	PUNCT
ejpam-3184	210	39	.	.	PUNCT
ejpam-3184	211	1	now	now	ADV
ejpam-3184	211	2	we	we	PRON
ejpam-3184	211	3	will	will	AUX
ejpam-3184	211	4	show	show	VERB
ejpam-3184	211	5	that	that	SCONJ
ejpam-3184	211	6	e(h	e(h	PROPN
ejpam-3184	211	7	)	)	PUNCT
ejpam-3184	211	8	is	be	AUX
ejpam-3184	211	9	solvable	solvable	ADJ
ejpam-3184	211	10	.	.	PUNCT
ejpam-3184	212	1	by	by	ADP
ejpam-3184	212	2	feit	feit	PROPN
ejpam-3184	212	3	-	-	PUNCT
ejpam-3184	212	4	thompson	thompson	NOUN
ejpam-3184	212	5	theorem	theorem	NOUN
ejpam-3184	212	6	[	[	X
ejpam-3184	212	7	3	3	NUM
ejpam-3184	212	8	]	]	PUNCT
ejpam-3184	212	9	,	,	PUNCT
ejpam-3184	212	10	we	we	PRON
ejpam-3184	212	11	may	may	AUX
ejpam-3184	212	12	assume	assume	VERB
ejpam-3184	212	13	that	that	SCONJ
ejpam-3184	212	14	2	2	NUM
ejpam-3184	212	15	divides	divide	VERB
ejpam-3184	212	16	the	the	DET
ejpam-3184	212	17	order	order	NOUN
ejpam-3184	212	18	of	of	ADP
ejpam-3184	212	19	e(h	e(h	PROPN
ejpam-3184	212	20	)	)	PUNCT
ejpam-3184	212	21	.	.	PUNCT
ejpam-3184	213	1	clearly	clearly	ADV
ejpam-3184	213	2	,	,	PUNCT
ejpam-3184	213	3	z	z	NOUN
ejpam-3184	213	4	∩	∩	X
ejpam-3184	213	5	e(h	e(h	X
ejpam-3184	213	6	)	)	PUNCT
ejpam-3184	213	7	is	be	AUX
ejpam-3184	213	8	a	a	DET
ejpam-3184	213	9	complete	complete	ADJ
ejpam-3184	213	10	set	set	NOUN
ejpam-3184	213	11	of	of	ADP
ejpam-3184	213	12	sylow	sylow	NOUN
ejpam-3184	213	13	subgroups	subgroup	NOUN
ejpam-3184	213	14	of	of	ADP
ejpam-3184	213	15	e(h	e(h	PROPN
ejpam-3184	213	16	)	)	PUNCT
ejpam-3184	213	17	by	by	ADP
ejpam-3184	213	18	lemma	lemma	PROPN
ejpam-3184	213	19	2.1(a	2.1(a	NUM
ejpam-3184	213	20	)	)	PUNCT
ejpam-3184	213	21	.	.	PUNCT
ejpam-3184	214	1	let	let	VERB
ejpam-3184	214	2	u	u	PRON
ejpam-3184	214	3	be	be	AUX
ejpam-3184	214	4	a	a	DET
ejpam-3184	214	5	maximal	maximal	ADJ
ejpam-3184	214	6	subgroup	subgroup	NOUN
ejpam-3184	214	7	of	of	ADP
ejpam-3184	214	8	g2∩f	g2∩f	PROPN
ejpam-3184	214	9	∗(h	∗(h	PROPN
ejpam-3184	214	10	)	)	PUNCT
ejpam-3184	214	11	,	,	PUNCT
ejpam-3184	214	12	where	where	SCONJ
ejpam-3184	214	13	g2	g2	PROPN
ejpam-3184	214	14	∈	∈	PROPN
ejpam-3184	214	15	z.	z.	PROPN
ejpam-3184	214	16	the	the	DET
ejpam-3184	214	17	hypothesis	hypothesis	NOUN
ejpam-3184	214	18	and	and	CCONJ
ejpam-3184	214	19	lemma	lemma	PROPN
ejpam-3184	214	20	2.1(e	2.1(e	NUM
ejpam-3184	214	21	)	)	PUNCT
ejpam-3184	214	22	imply	imply	VERB
ejpam-3184	214	23	that	that	SCONJ
ejpam-3184	214	24	u	u	PROPN
ejpam-3184	214	25	∩e(h	∩e(h	PROPN
ejpam-3184	214	26	)	)	PUNCT
ejpam-3184	214	27	is	be	AUX
ejpam-3184	214	28	c	c	NOUN
ejpam-3184	214	29	-	-	PUNCT
ejpam-3184	214	30	z	z	ADJ
ejpam-3184	214	31	-	-	PUNCT
ejpam-3184	214	32	permutable	permutable	ADJ
ejpam-3184	214	33	subgroup	subgroup	NOUN
ejpam-3184	214	34	of	of	ADP
ejpam-3184	214	35	g.	g.	PROPN
ejpam-3184	215	1	so	so	ADV
ejpam-3184	215	2	,	,	PUNCT
ejpam-3184	215	3	there	there	PRON
ejpam-3184	215	4	exists	exist	VERB
ejpam-3184	215	5	some	some	DET
ejpam-3184	215	6	x	x	SYM
ejpam-3184	215	7	∈	∈	PROPN
ejpam-3184	215	8	c	c	NOUN
ejpam-3184	215	9	such	such	ADJ
ejpam-3184	215	10	that	that	PRON
ejpam-3184	215	11	(	(	PUNCT
ejpam-3184	215	12	u	u	NOUN
ejpam-3184	215	13	∩e(h))xgq	∩e(h))xgq	PROPN
ejpam-3184	215	14	is	be	AUX
ejpam-3184	215	15	a	a	DET
ejpam-3184	215	16	subgroup	subgroup	NOUN
ejpam-3184	215	17	of	of	ADP
ejpam-3184	215	18	g	g	NOUN
ejpam-3184	215	19	,	,	PUNCT
ejpam-3184	215	20	for	for	ADP
ejpam-3184	215	21	all	all	DET
ejpam-3184	215	22	gq	gq	PROPN
ejpam-3184	215	23	∈	∈	PROPN
ejpam-3184	215	24	z.	z.	PROPN
ejpam-3184	215	25	but	but	CCONJ
ejpam-3184	215	26	(	(	PUNCT
ejpam-3184	215	27	u	u	NOUN
ejpam-3184	215	28	∩	∩	NOUN
ejpam-3184	215	29	e(h))x	e(h))x	PROPN
ejpam-3184	215	30	=	=	SYM
ejpam-3184	215	31	u	u	NOUN
ejpam-3184	215	32	∩	∩	NOUN
ejpam-3184	215	33	e(h	e(h	PROPN
ejpam-3184	215	34	)	)	PUNCT
ejpam-3184	215	35	as	as	ADP
ejpam-3184	215	36	x	x	X
ejpam-3184	215	37	∈	∈	PROPN
ejpam-3184	215	38	c	c	NOUN
ejpam-3184	215	39	≤	≤	NUM
ejpam-3184	215	40	cg(e(h	cg(e(h	NOUN
ejpam-3184	215	41	)	)	PUNCT
ejpam-3184	215	42	)	)	PUNCT
ejpam-3184	215	43	≤	≤	NOUN
ejpam-3184	215	44	cg(u	cg(u	ADJ
ejpam-3184	215	45	∩	∩	NOUN
ejpam-3184	215	46	e(h	e(h	PROPN
ejpam-3184	215	47	)	)	PUNCT
ejpam-3184	215	48	)	)	PUNCT
ejpam-3184	215	49	,	,	PUNCT
ejpam-3184	215	50	then	then	ADV
ejpam-3184	215	51	(	(	PUNCT
ejpam-3184	215	52	u	u	NOUN
ejpam-3184	215	53	∩	∩	X
ejpam-3184	215	54	e(h))gq	e(h))gq	PRON
ejpam-3184	215	55	m.	m.	NOUN
ejpam-3184	215	56	m.	m.	PROPN
ejpam-3184	215	57	al	al	PROPN
ejpam-3184	215	58	-	-	PUNCT
ejpam-3184	215	59	shomrani	shomrani	PROPN
ejpam-3184	215	60	,	,	PUNCT
ejpam-3184	215	61	a.	a.	NOUN
ejpam-3184	215	62	a.	a.	NOUN
ejpam-3184	215	63	heliel	heliel	PROPN
ejpam-3184	215	64	/	/	SYM
ejpam-3184	215	65	eur	eur	PROPN
ejpam-3184	215	66	.	.	PUNCT
ejpam-3184	216	1	j.	j.	PROPN
ejpam-3184	216	2	pure	pure	PROPN
ejpam-3184	216	3	appl	appl	PROPN
ejpam-3184	216	4	.	.	PROPN
ejpam-3184	216	5	math	math	PROPN
ejpam-3184	216	6	,	,	PUNCT
ejpam-3184	216	7	11	11	NUM
ejpam-3184	216	8	(	(	PUNCT
ejpam-3184	216	9	1	1	NUM
ejpam-3184	216	10	)	)	PUNCT
ejpam-3184	216	11	(	(	PUNCT
ejpam-3184	216	12	2018	2018	NUM
ejpam-3184	216	13	)	)	PUNCT
ejpam-3184	216	14	,	,	PUNCT
ejpam-3184	216	15	160	160	NUM
ejpam-3184	216	16	-	-	SYM
ejpam-3184	216	17	168	168	NUM
ejpam-3184	216	18	167	167	NUM
ejpam-3184	216	19	is	be	AUX
ejpam-3184	216	20	a	a	DET
ejpam-3184	216	21	subgroup	subgroup	NOUN
ejpam-3184	216	22	of	of	ADP
ejpam-3184	216	23	g	g	NOUN
ejpam-3184	216	24	,	,	PUNCT
ejpam-3184	216	25	for	for	ADP
ejpam-3184	216	26	all	all	DET
ejpam-3184	216	27	gq	gq	PROPN
ejpam-3184	216	28	∈	∈	PROPN
ejpam-3184	216	29	z.	z.	PROPN
ejpam-3184	216	30	therefore	therefore	ADV
ejpam-3184	216	31	,	,	PUNCT
ejpam-3184	216	32	u	u	NOUN
ejpam-3184	216	33	∩	∩	NOUN
ejpam-3184	216	34	e(h	e(h	X
ejpam-3184	216	35	)	)	PUNCT
ejpam-3184	216	36	is	be	AUX
ejpam-3184	216	37	z	z	NOUN
ejpam-3184	216	38	-	-	ADJ
ejpam-3184	216	39	permutable	permutable	ADJ
ejpam-3184	216	40	subgroup	subgroup	NOUN
ejpam-3184	216	41	of	of	ADP
ejpam-3184	216	42	g.	g.	PROPN
ejpam-3184	216	43	by	by	ADP
ejpam-3184	216	44	lemma	lemma	PROPN
ejpam-3184	216	45	2.1(c	2.1(c	NUM
ejpam-3184	216	46	)	)	PUNCT
ejpam-3184	216	47	,	,	PUNCT
ejpam-3184	216	48	u	u	NOUN
ejpam-3184	216	49	∩	∩	X
ejpam-3184	216	50	e(h	e(h	X
ejpam-3184	216	51	)	)	PUNCT
ejpam-3184	216	52	is	be	AUX
ejpam-3184	216	53	z	z	NOUN
ejpam-3184	216	54	∩	∩	ADJ
ejpam-3184	216	55	e(h)-permutable	e(h)-permutable	ADJ
ejpam-3184	216	56	subgroup	subgroup	NOUN
ejpam-3184	216	57	of	of	ADP
ejpam-3184	216	58	e(h	e(h	PROPN
ejpam-3184	216	59	)	)	PUNCT
ejpam-3184	216	60	.	.	PUNCT
ejpam-3184	217	1	suppose	suppose	VERB
ejpam-3184	217	2	that	that	SCONJ
ejpam-3184	217	3	g2	g2	PROPN
ejpam-3184	217	4	∩	∩	ADJ
ejpam-3184	217	5	e(h	e(h	X
ejpam-3184	217	6	)	)	PUNCT
ejpam-3184	217	7	=	=	SYM
ejpam-3184	217	8	g2	g2	PROPN
ejpam-3184	217	9	∩	∩	PROPN
ejpam-3184	217	10	f	f	PROPN
ejpam-3184	217	11	∗(h	∗(h	PROPN
ejpam-3184	217	12	)	)	PUNCT
ejpam-3184	217	13	.	.	PUNCT
ejpam-3184	218	1	by	by	ADP
ejpam-3184	218	2	the	the	DET
ejpam-3184	218	3	hypothesis	hypothesis	NOUN
ejpam-3184	218	4	and	and	CCONJ
ejpam-3184	218	5	the	the	DET
ejpam-3184	218	6	previous	previous	ADJ
ejpam-3184	218	7	arguments	argument	NOUN
ejpam-3184	218	8	,	,	PUNCT
ejpam-3184	218	9	the	the	DET
ejpam-3184	218	10	maximal	maximal	ADJ
ejpam-3184	218	11	subgroups	subgroup	NOUN
ejpam-3184	218	12	of	of	ADP
ejpam-3184	218	13	g2	g2	PROPN
ejpam-3184	218	14	∩	∩	ADJ
ejpam-3184	218	15	e(h	e(h	X
ejpam-3184	218	16	)	)	PUNCT
ejpam-3184	218	17	are	be	AUX
ejpam-3184	218	18	z	z	NOUN
ejpam-3184	218	19	∩	∩	ADJ
ejpam-3184	218	20	e(h)-permutable	e(h)-permutable	ADJ
ejpam-3184	218	21	subgroups	subgroup	NOUN
ejpam-3184	218	22	of	of	ADP
ejpam-3184	218	23	e(h	e(h	PROPN
ejpam-3184	218	24	)	)	PUNCT
ejpam-3184	218	25	.	.	PUNCT
ejpam-3184	219	1	consequently	consequently	ADV
ejpam-3184	219	2	,	,	PUNCT
ejpam-3184	219	3	e(h	e(h	PROPN
ejpam-3184	219	4	)	)	PUNCT
ejpam-3184	219	5	is	be	AUX
ejpam-3184	219	6	2	2	NUM
ejpam-3184	219	7	-	-	PUNCT
ejpam-3184	219	8	nilpotent	nilpotent	NOUN
ejpam-3184	219	9	by	by	ADP
ejpam-3184	219	10	lemma	lemma	PROPN
ejpam-3184	219	11	2.6	2.6	NUM
ejpam-3184	219	12	,	,	PUNCT
ejpam-3184	219	13	where	where	SCONJ
ejpam-3184	219	14	c	c	NOUN
ejpam-3184	219	15	=	=	NOUN
ejpam-3184	219	16	1	1	NUM
ejpam-3184	219	17	in	in	ADP
ejpam-3184	219	18	this	this	DET
ejpam-3184	219	19	case	case	NOUN
ejpam-3184	219	20	.	.	PUNCT
ejpam-3184	220	1	so	so	ADV
ejpam-3184	220	2	,	,	PUNCT
ejpam-3184	220	3	e(h	e(h	PROPN
ejpam-3184	220	4	)	)	PUNCT
ejpam-3184	220	5	=	=	PUNCT
ejpam-3184	220	6	(	(	PUNCT
ejpam-3184	220	7	g2∩e(h))k	g2∩e(h))k	PROPN
ejpam-3184	220	8	,	,	PUNCT
ejpam-3184	220	9	where	where	SCONJ
ejpam-3184	220	10	k	k	PROPN
ejpam-3184	220	11	is	be	AUX
ejpam-3184	220	12	a	a	DET
ejpam-3184	220	13	normal	normal	ADJ
ejpam-3184	220	14	hall	hall	NOUN
ejpam-3184	220	15	2′-subgroup	2′-subgroup	NUM
ejpam-3184	220	16	of	of	ADP
ejpam-3184	220	17	e(h	e(h	PROPN
ejpam-3184	220	18	)	)	PUNCT
ejpam-3184	220	19	.	.	PUNCT
ejpam-3184	221	1	because	because	SCONJ
ejpam-3184	221	2	k	k	PROPN
ejpam-3184	221	3	is	be	AUX
ejpam-3184	221	4	solvable	solvable	ADJ
ejpam-3184	221	5	by	by	ADP
ejpam-3184	221	6	feit	feit	PROPN
ejpam-3184	221	7	-	-	PUNCT
ejpam-3184	221	8	thompson	thompson	NOUN
ejpam-3184	221	9	theorem	theorem	NOUN
ejpam-3184	221	10	[	[	X
ejpam-3184	221	11	3	3	NUM
ejpam-3184	221	12	]	]	PUNCT
ejpam-3184	221	13	and	and	CCONJ
ejpam-3184	221	14	g	g	NOUN
ejpam-3184	221	15	/	/	SYM
ejpam-3184	221	16	k	k	PROPN
ejpam-3184	221	17	∼=	∼=	PROPN
ejpam-3184	221	18	g2	g2	PROPN
ejpam-3184	221	19	∩	∩	NOUN
ejpam-3184	221	20	e(h	e(h	X
ejpam-3184	221	21	)	)	PUNCT
ejpam-3184	221	22	is	be	AUX
ejpam-3184	221	23	solvable	solvable	ADJ
ejpam-3184	221	24	,	,	PUNCT
ejpam-3184	221	25	it	it	PRON
ejpam-3184	221	26	follows	follow	VERB
ejpam-3184	221	27	that	that	SCONJ
ejpam-3184	221	28	e(h	e(h	PROPN
ejpam-3184	221	29	)	)	PUNCT
ejpam-3184	221	30	is	be	AUX
ejpam-3184	221	31	solvable	solvable	ADJ
ejpam-3184	221	32	.	.	PUNCT
ejpam-3184	222	1	thus	thus	ADV
ejpam-3184	222	2	,	,	PUNCT
ejpam-3184	222	3	we	we	PRON
ejpam-3184	222	4	may	may	AUX
ejpam-3184	222	5	assume	assume	VERB
ejpam-3184	222	6	that	that	SCONJ
ejpam-3184	222	7	g2	g2	PROPN
ejpam-3184	222	8	∩	∩	ADJ
ejpam-3184	222	9	e(h	e(h	X
ejpam-3184	222	10	)	)	PUNCT
ejpam-3184	222	11	is	be	AUX
ejpam-3184	222	12	a	a	DET
ejpam-3184	222	13	proper	proper	ADJ
ejpam-3184	222	14	subgroup	subgroup	NOUN
ejpam-3184	222	15	of	of	ADP
ejpam-3184	222	16	g2	g2	PROPN
ejpam-3184	222	17	∩	∩	PROPN
ejpam-3184	222	18	f	f	PROPN
ejpam-3184	222	19	∗(h	∗(h	PROPN
ejpam-3184	222	20	)	)	PUNCT
ejpam-3184	222	21	.	.	PUNCT
ejpam-3184	223	1	then	then	ADV
ejpam-3184	223	2	we	we	PRON
ejpam-3184	223	3	can	can	AUX
ejpam-3184	223	4	choose	choose	VERB
ejpam-3184	223	5	u	u	NOUN
ejpam-3184	223	6	to	to	PART
ejpam-3184	223	7	be	be	AUX
ejpam-3184	223	8	a	a	DET
ejpam-3184	223	9	maximal	maximal	ADJ
ejpam-3184	223	10	subgroup	subgroup	NOUN
ejpam-3184	223	11	of	of	ADP
ejpam-3184	223	12	g2	g2	PROPN
ejpam-3184	223	13	∩f	∩f	PROPN
ejpam-3184	223	14	∗(h	∗(h	PROPN
ejpam-3184	223	15	)	)	PUNCT
ejpam-3184	223	16	such	such	ADJ
ejpam-3184	223	17	that	that	SCONJ
ejpam-3184	223	18	g2	g2	PROPN
ejpam-3184	223	19	∩e(h	∩e(h	PROPN
ejpam-3184	223	20	)	)	PUNCT
ejpam-3184	223	21	≤	≤	NOUN
ejpam-3184	223	22	u	u	NOUN
ejpam-3184	223	23	.	.	PUNCT
ejpam-3184	224	1	therefore	therefore	ADV
ejpam-3184	224	2	,	,	PUNCT
ejpam-3184	224	3	g2	g2	PROPN
ejpam-3184	224	4	∩e(h	∩e(h	PROPN
ejpam-3184	224	5	)	)	PUNCT
ejpam-3184	224	6	=	=	SYM
ejpam-3184	224	7	u	u	NOUN
ejpam-3184	224	8	∩e(h	∩e(h	PROPN
ejpam-3184	224	9	)	)	PUNCT
ejpam-3184	224	10	as	as	ADP
ejpam-3184	224	11	g2	g2	PROPN
ejpam-3184	224	12	∩e(h	∩e(h	PROPN
ejpam-3184	224	13	)	)	PUNCT
ejpam-3184	224	14	is	be	AUX
ejpam-3184	224	15	a	a	DET
ejpam-3184	224	16	sylow	sylow	NOUN
ejpam-3184	224	17	2	2	NUM
ejpam-3184	224	18	-	-	PUNCT
ejpam-3184	224	19	subgroup	subgroup	NOUN
ejpam-3184	224	20	of	of	ADP
ejpam-3184	224	21	e(h	e(h	PROPN
ejpam-3184	224	22	)	)	PUNCT
ejpam-3184	224	23	.	.	PUNCT
ejpam-3184	225	1	now	now	ADV
ejpam-3184	225	2	we	we	PRON
ejpam-3184	225	3	have	have	VERB
ejpam-3184	225	4	that	that	PRON
ejpam-3184	225	5	g2∩e(h	g2∩e(h	VERB
ejpam-3184	225	6	)	)	PUNCT
ejpam-3184	225	7	=	=	SYM
ejpam-3184	225	8	u	u	NOUN
ejpam-3184	225	9	∩e(h	∩e(h	PROPN
ejpam-3184	225	10	)	)	PUNCT
ejpam-3184	225	11	,	,	PUNCT
ejpam-3184	225	12	as	as	SCONJ
ejpam-3184	225	13	we	we	PRON
ejpam-3184	225	14	proved	prove	VERB
ejpam-3184	225	15	in	in	ADP
ejpam-3184	225	16	the	the	DET
ejpam-3184	225	17	beginning	beginning	NOUN
ejpam-3184	225	18	,	,	PUNCT
ejpam-3184	225	19	is	be	AUX
ejpam-3184	225	20	z∩e(h)-permutable	z∩e(h)-permutable	ADJ
ejpam-3184	225	21	subgroup	subgroup	NOUN
ejpam-3184	225	22	of	of	ADP
ejpam-3184	225	23	e(h	e(h	PROPN
ejpam-3184	225	24	)	)	PUNCT
ejpam-3184	225	25	.	.	PUNCT
ejpam-3184	226	1	this	this	PRON
ejpam-3184	226	2	implies	imply	VERB
ejpam-3184	226	3	that	that	SCONJ
ejpam-3184	226	4	e(h	e(h	PROPN
ejpam-3184	226	5	)	)	PUNCT
ejpam-3184	226	6	is	be	AUX
ejpam-3184	226	7	solvable	solvable	ADJ
ejpam-3184	226	8	by	by	ADP
ejpam-3184	226	9	lemma	lemma	PROPN
ejpam-3184	226	10	3.3	3.3	NUM
ejpam-3184	226	11	.	.	PUNCT
ejpam-3184	227	1	so	so	ADV
ejpam-3184	227	2	,	,	PUNCT
ejpam-3184	227	3	in	in	ADP
ejpam-3184	227	4	either	either	DET
ejpam-3184	227	5	case	case	NOUN
ejpam-3184	227	6	,	,	PUNCT
ejpam-3184	227	7	e(h	e(h	PROPN
ejpam-3184	227	8	)	)	PUNCT
ejpam-3184	227	9	is	be	AUX
ejpam-3184	227	10	solvable	solvable	ADJ
ejpam-3184	227	11	.	.	PUNCT
ejpam-3184	228	1	but	but	CCONJ
ejpam-3184	228	2	e(h	e(h	PROPN
ejpam-3184	228	3	)	)	PUNCT
ejpam-3184	228	4	is	be	AUX
ejpam-3184	228	5	perfect	perfect	ADJ
ejpam-3184	228	6	,	,	PUNCT
ejpam-3184	228	7	then	then	ADV
ejpam-3184	228	8	e(h	e(h	PROPN
ejpam-3184	228	9	)	)	PUNCT
ejpam-3184	228	10	=	=	SYM
ejpam-3184	229	1	1	1	NUM
ejpam-3184	229	2	and	and	CCONJ
ejpam-3184	229	3	therefore	therefore	ADV
ejpam-3184	229	4	f	f	PROPN
ejpam-3184	229	5	∗(h	∗(h	PROPN
ejpam-3184	229	6	)	)	PUNCT
ejpam-3184	230	1	=	=	SYM
ejpam-3184	230	2	f	f	PROPN
ejpam-3184	230	3	(	(	PUNCT
ejpam-3184	230	4	h	h	NOUN
ejpam-3184	230	5	)	)	PUNCT
ejpam-3184	230	6	.	.	PUNCT
ejpam-3184	231	1	applying	apply	VERB
ejpam-3184	231	2	theorem	theorem	ADJ
ejpam-3184	231	3	3.2	3.2	NUM
ejpam-3184	231	4	yields	yield	NOUN
ejpam-3184	231	5	g	g	PROPN
ejpam-3184	231	6	∈	∈	PROPN
ejpam-3184	231	7	f.	f.	PROPN
ejpam-3184	231	8	this	this	PRON
ejpam-3184	231	9	completes	complete	VERB
ejpam-3184	231	10	the	the	DET
ejpam-3184	231	11	proof	proof	NOUN
ejpam-3184	231	12	of	of	ADP
ejpam-3184	231	13	the	the	DET
ejpam-3184	231	14	theorem	theorem	NOUN
ejpam-3184	231	15	.	.	PUNCT
ejpam-3184	232	1	the	the	DET
ejpam-3184	232	2	next	next	ADJ
ejpam-3184	232	3	theorem	theorem	NOUN
ejpam-3184	232	4	is	be	AUX
ejpam-3184	232	5	an	an	DET
ejpam-3184	232	6	improvement	improvement	NOUN
ejpam-3184	232	7	of	of	ADP
ejpam-3184	232	8	theorem	theorem	NOUN
ejpam-3184	232	9	3.12	3.12	NUM
ejpam-3184	232	10	in	in	ADP
ejpam-3184	232	11	[	[	X
ejpam-3184	232	12	4	4	NUM
ejpam-3184	232	13	]	]	PUNCT
ejpam-3184	232	14	:	:	PUNCT
ejpam-3184	232	15	theorem	theorem	NOUN
ejpam-3184	232	16	3.4	3.4	NUM
ejpam-3184	232	17	.	.	PUNCT
ejpam-3184	233	1	let	let	VERB
ejpam-3184	233	2	f	f	PRON
ejpam-3184	233	3	be	be	AUX
ejpam-3184	233	4	a	a	DET
ejpam-3184	233	5	saturated	saturated	ADJ
ejpam-3184	233	6	formation	formation	NOUN
ejpam-3184	233	7	containing	contain	VERB
ejpam-3184	233	8	the	the	DET
ejpam-3184	233	9	class	class	NOUN
ejpam-3184	233	10	of	of	ADP
ejpam-3184	233	11	supersolvable	supersolvable	ADJ
ejpam-3184	233	12	groups	group	NOUN
ejpam-3184	233	13	u	u	NOUN
ejpam-3184	233	14	,	,	PUNCT
ejpam-3184	233	15	z	z	PROPN
ejpam-3184	233	16	be	be	AUX
ejpam-3184	233	17	a	a	DET
ejpam-3184	233	18	complete	complete	ADJ
ejpam-3184	233	19	set	set	NOUN
ejpam-3184	233	20	of	of	ADP
ejpam-3184	233	21	sylow	sylow	NOUN
ejpam-3184	233	22	subgroups	subgroup	NOUN
ejpam-3184	233	23	of	of	ADP
ejpam-3184	233	24	a	a	DET
ejpam-3184	233	25	group	group	NOUN
ejpam-3184	233	26	g	g	NOUN
ejpam-3184	233	27	and	and	CCONJ
ejpam-3184	233	28	c	c	PROPN
ejpam-3184	233	29	be	be	AUX
ejpam-3184	233	30	a	a	DET
ejpam-3184	233	31	solvable	solvable	ADJ
ejpam-3184	233	32	normal	normal	ADJ
ejpam-3184	233	33	subgroup	subgroup	NOUN
ejpam-3184	233	34	of	of	ADP
ejpam-3184	233	35	g.	g.	PROPN
ejpam-3184	234	1	then	then	ADV
ejpam-3184	234	2	the	the	DET
ejpam-3184	234	3	following	follow	VERB
ejpam-3184	234	4	two	two	NUM
ejpam-3184	234	5	statements	statement	NOUN
ejpam-3184	234	6	are	be	AUX
ejpam-3184	234	7	equivalent	equivalent	ADJ
ejpam-3184	234	8	:	:	PUNCT
ejpam-3184	234	9	(	(	PUNCT
ejpam-3184	234	10	a	a	X
ejpam-3184	234	11	)	)	PUNCT
ejpam-3184	234	12	g	g	PROPN
ejpam-3184	234	13	∈	∈	PROPN
ejpam-3184	234	14	f.	f.	PROPN
ejpam-3184	234	15	(	(	PUNCT
ejpam-3184	234	16	b	b	X
ejpam-3184	234	17	)	)	PUNCT
ejpam-3184	234	18	there	there	PRON
ejpam-3184	234	19	is	be	VERB
ejpam-3184	234	20	a	a	DET
ejpam-3184	234	21	normal	normal	ADJ
ejpam-3184	234	22	subgroup	subgroup	NOUN
ejpam-3184	234	23	h	h	NOUN
ejpam-3184	234	24	in	in	ADP
ejpam-3184	234	25	g	g	PROPN
ejpam-3184	234	26	such	such	ADJ
ejpam-3184	234	27	that	that	SCONJ
ejpam-3184	234	28	g	g	NOUN
ejpam-3184	234	29	/	/	SYM
ejpam-3184	234	30	h	h	NOUN
ejpam-3184	234	31	∈	∈	PROPN
ejpam-3184	234	32	f	f	PROPN
ejpam-3184	234	33	and	and	CCONJ
ejpam-3184	234	34	the	the	DET
ejpam-3184	234	35	maximal	maximal	ADJ
ejpam-3184	234	36	subgroups	subgroup	NOUN
ejpam-3184	234	37	of	of	ADP
ejpam-3184	234	38	gp∩f	gp∩f	PROPN
ejpam-3184	234	39	∗n(h	∗n(h	PROPN
ejpam-3184	234	40	)	)	PUNCT
ejpam-3184	234	41	are	be	AUX
ejpam-3184	234	42	c	c	NOUN
ejpam-3184	234	43	-	-	PUNCT
ejpam-3184	234	44	z	z	ADJ
ejpam-3184	234	45	-	-	PUNCT
ejpam-3184	234	46	permutable	permutable	ADJ
ejpam-3184	234	47	subgroups	subgroup	NOUN
ejpam-3184	234	48	of	of	ADP
ejpam-3184	234	49	g	g	NOUN
ejpam-3184	234	50	,	,	PUNCT
ejpam-3184	234	51	for	for	ADP
ejpam-3184	234	52	all	all	DET
ejpam-3184	234	53	gp	gp	NOUN
ejpam-3184	234	54	∈	∈	PROPN
ejpam-3184	234	55	z	z	PROPN
ejpam-3184	234	56	,	,	PUNCT
ejpam-3184	234	57	for	for	ADP
ejpam-3184	234	58	some	some	DET
ejpam-3184	234	59	positive	positive	ADJ
ejpam-3184	234	60	integer	integer	NOUN
ejpam-3184	234	61	n.	n.	NOUN
ejpam-3184	234	62	proof	proof	NOUN
ejpam-3184	234	63	.	.	PUNCT
ejpam-3184	235	1	we	we	PRON
ejpam-3184	235	2	need	need	VERB
ejpam-3184	235	3	only	only	ADV
ejpam-3184	235	4	to	to	PART
ejpam-3184	235	5	prove	prove	VERB
ejpam-3184	235	6	(	(	PUNCT
ejpam-3184	235	7	b)⇒	b)⇒	PROPN
ejpam-3184	235	8	(	(	PUNCT
ejpam-3184	235	9	a	a	NOUN
ejpam-3184	235	10	)	)	PUNCT
ejpam-3184	235	11	as	as	ADP
ejpam-3184	235	12	(	(	PUNCT
ejpam-3184	235	13	a)⇒	a)⇒	PROPN
ejpam-3184	235	14	(	(	PUNCT
ejpam-3184	235	15	b	b	NOUN
ejpam-3184	235	16	)	)	PUNCT
ejpam-3184	235	17	is	be	AUX
ejpam-3184	235	18	true	true	ADJ
ejpam-3184	235	19	with	with	ADP
ejpam-3184	235	20	h	h	NOUN
ejpam-3184	235	21	=	=	NOUN
ejpam-3184	235	22	1	1	X
ejpam-3184	235	23	.	.	PUNCT
ejpam-3184	236	1	if	if	SCONJ
ejpam-3184	236	2	n	n	NOUN
ejpam-3184	236	3	=	=	SYM
ejpam-3184	236	4	1	1	NUM
ejpam-3184	236	5	,	,	PUNCT
ejpam-3184	236	6	then	then	ADV
ejpam-3184	236	7	g	g	PROPN
ejpam-3184	236	8	∈	∈	PROPN
ejpam-3184	236	9	f	f	X
ejpam-3184	236	10	by	by	ADP
ejpam-3184	236	11	theorem	theorem	NOUN
ejpam-3184	236	12	1.2	1.2	NUM
ejpam-3184	236	13	.	.	PUNCT
ejpam-3184	237	1	so	so	ADV
ejpam-3184	237	2	,	,	PUNCT
ejpam-3184	237	3	we	we	PRON
ejpam-3184	237	4	may	may	AUX
ejpam-3184	237	5	assume	assume	VERB
ejpam-3184	237	6	that	that	SCONJ
ejpam-3184	237	7	n	n	PROPN
ejpam-3184	237	8	>	>	X
ejpam-3184	237	9	1	1	X
ejpam-3184	237	10	.	.	PUNCT
ejpam-3184	238	1	let	let	VERB
ejpam-3184	238	2	k	k	PROPN
ejpam-3184	238	3	=	=	PUNCT
ejpam-3184	238	4	f	f	PROPN
ejpam-3184	238	5	∗n−1(h	∗n−1(h	PROPN
ejpam-3184	238	6	)	)	PUNCT
ejpam-3184	238	7	.	.	PUNCT
ejpam-3184	239	1	it	it	PRON
ejpam-3184	239	2	is	be	AUX
ejpam-3184	239	3	clear	clear	ADJ
ejpam-3184	239	4	that	that	SCONJ
ejpam-3184	239	5	(	(	PUNCT
ejpam-3184	239	6	g	g	NOUN
ejpam-3184	239	7	/	/	SYM
ejpam-3184	239	8	k)/(h	k)/(h	PROPN
ejpam-3184	239	9	/	/	SYM
ejpam-3184	239	10	k	k	NOUN
ejpam-3184	239	11	)	)	PUNCT
ejpam-3184	239	12	∼=	∼=	ADP
ejpam-3184	239	13	g	g	NOUN
ejpam-3184	239	14	/	/	SYM
ejpam-3184	239	15	h	h	NOUN
ejpam-3184	239	16	∈	∈	PROPN
ejpam-3184	239	17	f.	f.	PROPN
ejpam-3184	239	18	by	by	ADP
ejpam-3184	239	19	lemma	lemma	PROPN
ejpam-3184	239	20	2.2	2.2	NUM
ejpam-3184	239	21	,	,	PUNCT
ejpam-3184	239	22	the	the	DET
ejpam-3184	239	23	maximal	maximal	ADJ
ejpam-3184	239	24	subgroups	subgroup	NOUN
ejpam-3184	239	25	of	of	ADP
ejpam-3184	239	26	(	(	PUNCT
ejpam-3184	239	27	zk	zk	PROPN
ejpam-3184	239	28	/	/	SYM
ejpam-3184	239	29	k	k	NOUN
ejpam-3184	239	30	)	)	PUNCT
ejpam-3184	239	31	∩	∩	NOUN
ejpam-3184	239	32	(	(	PUNCT
ejpam-3184	239	33	f	f	PROPN
ejpam-3184	239	34	∗n(h)/k	∗n(h)/k	PROPN
ejpam-3184	239	35	)	)	PUNCT
ejpam-3184	239	36	=	=	PUNCT
ejpam-3184	239	37	(	(	PUNCT
ejpam-3184	239	38	zk	zk	PROPN
ejpam-3184	239	39	/	/	SYM
ejpam-3184	239	40	k	k	NOUN
ejpam-3184	239	41	)	)	PUNCT
ejpam-3184	239	42	∩	∩	PROPN
ejpam-3184	239	43	f	f	PROPN
ejpam-3184	239	44	∗(h	∗(h	PROPN
ejpam-3184	239	45	/	/	SYM
ejpam-3184	239	46	k	k	NOUN
ejpam-3184	239	47	)	)	PUNCT
ejpam-3184	239	48	are	be	AUX
ejpam-3184	240	1	ck	ck	PROPN
ejpam-3184	240	2	/	/	SYM
ejpam-3184	240	3	k	k	ADJ
ejpam-3184	240	4	-	-	PUNCT
ejpam-3184	240	5	zk	zk	ADJ
ejpam-3184	240	6	/	/	SYM
ejpam-3184	240	7	kpermutable	kpermutable	ADJ
ejpam-3184	240	8	subgroups	subgroup	NOUN
ejpam-3184	240	9	of	of	ADP
ejpam-3184	240	10	g	g	PROPN
ejpam-3184	240	11	/	/	SYM
ejpam-3184	240	12	k.	k.	PROPN
ejpam-3184	240	13	hence	hence	ADV
ejpam-3184	240	14	,	,	PUNCT
ejpam-3184	240	15	g	g	PROPN
ejpam-3184	240	16	/	/	SYM
ejpam-3184	240	17	k	k	PROPN
ejpam-3184	240	18	∈	∈	PROPN
ejpam-3184	240	19	f	f	X
ejpam-3184	240	20	by	by	ADP
ejpam-3184	240	21	theorem	theorem	NOUN
ejpam-3184	240	22	1.2	1.2	NUM
ejpam-3184	240	23	.	.	PUNCT
ejpam-3184	241	1	thus	thus	ADV
ejpam-3184	241	2	g	g	PROPN
ejpam-3184	241	3	/	/	SYM
ejpam-3184	241	4	f	f	PROPN
ejpam-3184	241	5	∗n(h	∗n(h	PROPN
ejpam-3184	241	6	)	)	PUNCT
ejpam-3184	241	7	∼=	∼=	PROPN
ejpam-3184	241	8	(	(	PUNCT
ejpam-3184	241	9	g	g	PROPN
ejpam-3184	241	10	/	/	SYM
ejpam-3184	241	11	k)/(f	k)/(f	PROPN
ejpam-3184	241	12	∗n(h)/k	∗n(h)/k	PROPN
ejpam-3184	241	13	)	)	PUNCT
ejpam-3184	241	14	∈	∈	PROPN
ejpam-3184	241	15	f	f	PROPN
ejpam-3184	241	16	and	and	CCONJ
ejpam-3184	241	17	the	the	DET
ejpam-3184	241	18	maximal	maximal	ADJ
ejpam-3184	241	19	subgroups	subgroup	NOUN
ejpam-3184	241	20	of	of	ADP
ejpam-3184	241	21	gp	gp	NOUN
ejpam-3184	241	22	∩	∩	X
ejpam-3184	241	23	f	f	PROPN
ejpam-3184	241	24	∗n(h	∗n(h	PROPN
ejpam-3184	241	25	)	)	PUNCT
ejpam-3184	241	26	are	be	AUX
ejpam-3184	241	27	c	c	NOUN
ejpam-3184	241	28	-	-	PUNCT
ejpam-3184	241	29	z	z	ADJ
ejpam-3184	241	30	-	-	PUNCT
ejpam-3184	241	31	permutable	permutable	ADJ
ejpam-3184	241	32	subgroups	subgroup	NOUN
ejpam-3184	241	33	of	of	ADP
ejpam-3184	241	34	g	g	NOUN
ejpam-3184	241	35	,	,	PUNCT
ejpam-3184	241	36	for	for	ADP
ejpam-3184	241	37	all	all	DET
ejpam-3184	241	38	gp	gp	NOUN
ejpam-3184	241	39	∈	∈	PROPN
ejpam-3184	241	40	z.	z.	PROPN
ejpam-3184	241	41	applying	apply	VERB
ejpam-3184	241	42	lemma	lemma	PROPN
ejpam-3184	241	43	2.7	2.7	NUM
ejpam-3184	241	44	yields	yield	NOUN
ejpam-3184	241	45	g	g	PROPN
ejpam-3184	241	46	∈	∈	PROPN
ejpam-3184	241	47	f.	f.	PROPN
ejpam-3184	241	48	this	this	PRON
ejpam-3184	241	49	completes	complete	VERB
ejpam-3184	241	50	the	the	DET
ejpam-3184	241	51	proof	proof	NOUN
ejpam-3184	241	52	of	of	ADP
ejpam-3184	241	53	the	the	DET
ejpam-3184	241	54	theorem	theorem	NOUN
ejpam-3184	241	55	.	.	PUNCT
ejpam-3184	242	1	acknowledgements	acknowledgement	NOUN
ejpam-3184	242	2	this	this	DET
ejpam-3184	242	3	paper	paper	NOUN
ejpam-3184	242	4	was	be	AUX
ejpam-3184	242	5	financially	financially	ADV
ejpam-3184	242	6	supported	support	VERB
ejpam-3184	242	7	by	by	ADP
ejpam-3184	242	8	the	the	DET
ejpam-3184	242	9	deanship	deanship	NOUN
ejpam-3184	242	10	of	of	ADP
ejpam-3184	242	11	scientific	scientific	ADJ
ejpam-3184	242	12	research	research	NOUN
ejpam-3184	242	13	,	,	PUNCT
ejpam-3184	242	14	northern	northern	ADJ
ejpam-3184	242	15	border	border	NOUN
ejpam-3184	242	16	university	university	NOUN
ejpam-3184	242	17	,	,	PUNCT
ejpam-3184	242	18	under	under	ADP
ejpam-3184	242	19	the	the	DET
ejpam-3184	242	20	project	project	NOUN
ejpam-3184	243	1	no	no	NOUN
ejpam-3184	243	2	.	.	NOUN
ejpam-3184	243	3	434	434	NUM
ejpam-3184	243	4	-	-	SYM
ejpam-3184	243	5	071	071	NUM
ejpam-3184	243	6	.	.	PUNCT
ejpam-3184	244	1	the	the	DET
ejpam-3184	244	2	authors	author	NOUN
ejpam-3184	244	3	would	would	AUX
ejpam-3184	244	4	like	like	VERB
ejpam-3184	244	5	to	to	PART
ejpam-3184	244	6	thank	thank	VERB
ejpam-3184	244	7	the	the	DET
ejpam-3184	244	8	deanship	deanship	NOUN
ejpam-3184	244	9	of	of	ADP
ejpam-3184	244	10	scientific	scientific	ADJ
ejpam-3184	244	11	research	research	NOUN
ejpam-3184	244	12	for	for	ADP
ejpam-3184	244	13	their	their	PRON
ejpam-3184	244	14	financial	financial	ADJ
ejpam-3184	244	15	support	support	NOUN
ejpam-3184	244	16	.	.	PUNCT
ejpam-3184	245	1	the	the	DET
ejpam-3184	245	2	authors	author	NOUN
ejpam-3184	245	3	also	also	ADV
ejpam-3184	245	4	thank	thank	VERB
ejpam-3184	245	5	prof	prof	PROPN
ejpam-3184	245	6	.	.	PUNCT
ejpam-3184	246	1	m.	m.	PROPN
ejpam-3184	246	2	asaad	asaad	VERB
ejpam-3184	246	3	for	for	ADP
ejpam-3184	246	4	his	his	PRON
ejpam-3184	246	5	helpful	helpful	ADJ
ejpam-3184	246	6	comments	comment	NOUN
ejpam-3184	246	7	.	.	PUNCT
ejpam-3184	247	1	references	reference	NOUN
ejpam-3184	247	2	168	168	NUM
ejpam-3184	247	3	references	reference	NOUN
ejpam-3184	247	4	[	[	X
ejpam-3184	247	5	1	1	NUM
ejpam-3184	247	6	]	]	PUNCT
ejpam-3184	247	7	m.	m.	NOUN
ejpam-3184	247	8	asaad	asaad	NOUN
ejpam-3184	247	9	and	and	CCONJ
ejpam-3184	247	10	a.	a.	NOUN
ejpam-3184	247	11	a.	a.	NOUN
ejpam-3184	247	12	heliel	heliel	PROPN
ejpam-3184	247	13	.	.	PUNCT
ejpam-3184	248	1	on	on	ADP
ejpam-3184	248	2	permutable	permutable	ADJ
ejpam-3184	248	3	subgroups	subgroup	NOUN
ejpam-3184	248	4	of	of	ADP
ejpam-3184	248	5	finite	finite	ADJ
ejpam-3184	248	6	groups	group	NOUN
ejpam-3184	248	7	,	,	PUNCT
ejpam-3184	248	8	arch	arch	NOUN
ejpam-3184	248	9	.	.	PUNCT
ejpam-3184	249	1	math	math	NOUN
ejpam-3184	249	2	.	.	PUNCT
ejpam-3184	250	1	(	(	PUNCT
ejpam-3184	250	2	basel	basel	PROPN
ejpam-3184	250	3	)	)	PUNCT
ejpam-3184	250	4	,	,	PUNCT
ejpam-3184	250	5	80	80	NUM
ejpam-3184	250	6	(	(	PUNCT
ejpam-3184	250	7	2003	2003	NUM
ejpam-3184	250	8	)	)	PUNCT
ejpam-3184	250	9	,	,	PUNCT
ejpam-3184	250	10	113–118	113–118	NUM
ejpam-3184	250	11	.	.	PUNCT
ejpam-3184	251	1	[	[	X
ejpam-3184	251	2	2	2	NUM
ejpam-3184	251	3	]	]	PUNCT
ejpam-3184	251	4	k.	k.	NOUN
ejpam-3184	251	5	doerk	doerk	PROPN
ejpam-3184	251	6	and	and	CCONJ
ejpam-3184	251	7	t.	t.	PROPN
ejpam-3184	251	8	hawkes	hawkes	PROPN
ejpam-3184	251	9	.	.	PUNCT
ejpam-3184	252	1	finite	finite	VERB
ejpam-3184	252	2	soluble	soluble	ADJ
ejpam-3184	252	3	groups	group	NOUN
ejpam-3184	252	4	,	,	PUNCT
ejpam-3184	252	5	walter	walter	PROPN
ejpam-3184	252	6	de	de	PROPN
ejpam-3184	252	7	gruyter	gruyter	PROPN
ejpam-3184	252	8	,	,	PUNCT
ejpam-3184	252	9	berlin	berlin	PROPN
ejpam-3184	252	10	,	,	PUNCT
ejpam-3184	252	11	new	new	PROPN
ejpam-3184	252	12	york	york	PROPN
ejpam-3184	252	13	,	,	PUNCT
ejpam-3184	252	14	1992	1992	NUM
ejpam-3184	252	15	.	.	PUNCT
ejpam-3184	253	1	[	[	X
ejpam-3184	253	2	3	3	X
ejpam-3184	253	3	]	]	X
ejpam-3184	253	4	w.	w.	PROPN
ejpam-3184	253	5	feit	feit	PROPN
ejpam-3184	253	6	and	and	CCONJ
ejpam-3184	253	7	j.	j.	PROPN
ejpam-3184	253	8	g.	g.	PROPN
ejpam-3184	253	9	thompson	thompson	PROPN
ejpam-3184	253	10	.	.	PUNCT
ejpam-3184	254	1	solvability	solvability	NOUN
ejpam-3184	254	2	of	of	ADP
ejpam-3184	254	3	groups	group	NOUN
ejpam-3184	254	4	of	of	ADP
ejpam-3184	254	5	odd	odd	ADJ
ejpam-3184	254	6	order	order	NOUN
ejpam-3184	254	7	,	,	PUNCT
ejpam-3184	254	8	pacific	pacific	PROPN
ejpam-3184	254	9	j.	j.	PROPN
ejpam-3184	254	10	math	math	PROPN
ejpam-3184	254	11	.	.	PUNCT
ejpam-3184	255	1	,	,	PUNCT
ejpam-3184	255	2	13	13	NUM
ejpam-3184	255	3	(	(	PUNCT
ejpam-3184	255	4	1963	1963	NUM
ejpam-3184	255	5	)	)	PUNCT
ejpam-3184	255	6	,	,	PUNCT
ejpam-3184	255	7	775–1029	775–1029	NUM
ejpam-3184	255	8	.	.	PUNCT
ejpam-3184	256	1	[	[	X
ejpam-3184	256	2	4	4	NUM
ejpam-3184	256	3	]	]	PUNCT
ejpam-3184	256	4	a.	a.	NOUN
ejpam-3184	256	5	a.	a.	NOUN
ejpam-3184	256	6	heliel	heliel	PROPN
ejpam-3184	256	7	and	and	CCONJ
ejpam-3184	256	8	t.	t.	PROPN
ejpam-3184	256	9	m.	m.	PROPN
ejpam-3184	256	10	al	al	PROPN
ejpam-3184	256	11	-	-	PUNCT
ejpam-3184	256	12	gafri	gafri	PROPN
ejpam-3184	256	13	.	.	PUNCT
ejpam-3184	257	1	on	on	ADP
ejpam-3184	257	2	conjugate	conjugate	ADJ
ejpam-3184	257	3	-	-	PUNCT
ejpam-3184	257	4	z	z	NOUN
ejpam-3184	257	5	-	-	PUNCT
ejpam-3184	257	6	permutable	permutable	ADJ
ejpam-3184	257	7	subgroups	subgroup	NOUN
ejpam-3184	257	8	of	of	ADP
ejpam-3184	257	9	finite	finite	ADJ
ejpam-3184	257	10	groups	group	NOUN
ejpam-3184	257	11	,	,	PUNCT
ejpam-3184	257	12	j.	j.	PROPN
ejpam-3184	257	13	algebra	algebra	PROPN
ejpam-3184	257	14	appl	appl	PROPN
ejpam-3184	257	15	.	.	PROPN
ejpam-3184	258	1	,	,	PUNCT
ejpam-3184	258	2	12	12	NUM
ejpam-3184	258	3	(	(	PUNCT
ejpam-3184	258	4	9	9	NUM
ejpam-3184	258	5	)	)	PUNCT
ejpam-3184	258	6	(	(	PUNCT
ejpam-3184	258	7	2013	2013	NUM
ejpam-3184	258	8	)	)	PUNCT
ejpam-3184	258	9	,	,	PUNCT
ejpam-3184	258	10	[	[	X
ejpam-3184	258	11	5	5	X
ejpam-3184	258	12	]	]	PUNCT
ejpam-3184	258	13	b.	b.	PROPN
ejpam-3184	258	14	huppert	huppert	PROPN
ejpam-3184	258	15	.	.	PUNCT
ejpam-3184	259	1	endliche	endliche	PROPN
ejpam-3184	259	2	gruppen	gruppen	VERB
ejpam-3184	259	3	i	i	PROPN
ejpam-3184	259	4	,	,	PUNCT
ejpam-3184	259	5	springer	springer	NOUN
ejpam-3184	259	6	-	-	PUNCT
ejpam-3184	259	7	verlag	verlag	PROPN
ejpam-3184	259	8	,	,	PUNCT
ejpam-3184	259	9	berlin	berlin	PROPN
ejpam-3184	259	10	,	,	PUNCT
ejpam-3184	259	11	1979	1979	NUM
ejpam-3184	259	12	.	.	PUNCT
ejpam-3184	260	1	[	[	X
ejpam-3184	260	2	6	6	NUM
ejpam-3184	260	3	]	]	PUNCT
ejpam-3184	260	4	b.	b.	PROPN
ejpam-3184	260	5	huppert	huppert	PROPN
ejpam-3184	260	6	and	and	CCONJ
ejpam-3184	260	7	n.	n.	PROPN
ejpam-3184	260	8	blackburn	blackburn	PROPN
ejpam-3184	260	9	.	.	PUNCT
ejpam-3184	261	1	finite	finite	PROPN
ejpam-3184	261	2	groups	groups	PROPN
ejpam-3184	261	3	iii	iii	PROPN
ejpam-3184	261	4	,	,	PUNCT
ejpam-3184	261	5	berlin	berlin	PROPN
ejpam-3184	261	6	,	,	PUNCT
ejpam-3184	261	7	heidelberg	heidelberg	PROPN
ejpam-3184	261	8	,	,	PUNCT
ejpam-3184	261	9	new	new	PROPN
ejpam-3184	261	10	york	york	PROPN
ejpam-3184	261	11	,	,	PUNCT
ejpam-3184	261	12	1982	1982	NUM
ejpam-3184	261	13	.	.	PUNCT
ejpam-3184	262	1	[	[	X
ejpam-3184	262	2	7	7	X
ejpam-3184	262	3	]	]	X
ejpam-3184	262	4	o.	o.	PROPN
ejpam-3184	262	5	h.	h.	PROPN
ejpam-3184	262	6	kegel	kegel	PROPN
ejpam-3184	262	7	.	.	PUNCT
ejpam-3184	263	1	sylow	sylow	NOUN
ejpam-3184	263	2	-	-	PUNCT
ejpam-3184	263	3	gruppen	gruppen	NOUN
ejpam-3184	263	4	und	und	NOUN
ejpam-3184	263	5	subnormalteiler	subnormalteiler	NOUN
ejpam-3184	263	6	endlicher	endlicher	PROPN
ejpam-3184	263	7	gruppen	gruppen	PROPN
ejpam-3184	263	8	,	,	PUNCT
ejpam-3184	263	9	math	math	NOUN
ejpam-3184	263	10	.	.	PUNCT
ejpam-3184	264	1	z.	z.	PROPN
ejpam-3184	264	2	,	,	PUNCT
ejpam-3184	264	3	78	78	NUM
ejpam-3184	264	4	(	(	PUNCT
ejpam-3184	264	5	1962	1962	NUM
ejpam-3184	264	6	)	)	PUNCT
ejpam-3184	264	7	,	,	PUNCT
ejpam-3184	264	8	205–221	205–221	NUM
ejpam-3184	264	9	.	.	PUNCT
ejpam-3184	265	1	[	[	X
ejpam-3184	265	2	8	8	NUM
ejpam-3184	265	3	]	]	X
ejpam-3184	265	4	y.	y.	PROPN
ejpam-3184	265	5	li	li	PROPN
ejpam-3184	265	6	and	and	CCONJ
ejpam-3184	265	7	x.	x.	PROPN
ejpam-3184	265	8	li	li	PROPN
ejpam-3184	265	9	.	.	PROPN
ejpam-3184	266	1	z	z	ADJ
ejpam-3184	266	2	-	-	PUNCT
ejpam-3184	266	3	permutable	permutable	ADJ
ejpam-3184	266	4	subgroups	subgroup	NOUN
ejpam-3184	266	5	and	and	CCONJ
ejpam-3184	266	6	p	p	NOUN
ejpam-3184	266	7	-	-	PUNCT
ejpam-3184	266	8	nilpotency	nilpotency	NOUN
ejpam-3184	266	9	of	of	ADP
ejpam-3184	266	10	finite	finite	ADJ
ejpam-3184	266	11	groups	group	NOUN
ejpam-3184	266	12	,	,	PUNCT
ejpam-3184	266	13	j.	j.	PROPN
ejpam-3184	266	14	pure	pure	PROPN
ejpam-3184	266	15	appl	appl	PROPN
ejpam-3184	266	16	.	.	PUNCT
ejpam-3184	267	1	algebra	algebra	NOUN
ejpam-3184	267	2	,	,	PUNCT
ejpam-3184	267	3	202	202	NUM
ejpam-3184	267	4	(	(	PUNCT
ejpam-3184	267	5	2005	2005	NUM
ejpam-3184	267	6	)	)	PUNCT
ejpam-3184	267	7	,	,	PUNCT
ejpam-3184	267	8	72–81	72–81	NUM
ejpam-3184	267	9	.	.	PUNCT
ejpam-3184	268	1	[	[	X
ejpam-3184	268	2	9	9	NUM
ejpam-3184	268	3	]	]	PUNCT
ejpam-3184	268	4	w.	w.	PROPN
ejpam-3184	268	5	r.	r.	PROPN
ejpam-3184	268	6	scott	scott	PROPN
ejpam-3184	268	7	.	.	PUNCT
ejpam-3184	269	1	group	group	PROPN
ejpam-3184	269	2	theory	theory	NOUN
ejpam-3184	269	3	,	,	PUNCT
ejpam-3184	269	4	prentice	prentice	NOUN
ejpam-3184	269	5	-	-	PUNCT
ejpam-3184	269	6	hall	hall	NOUN
ejpam-3184	269	7	,	,	PUNCT
ejpam-3184	269	8	englewood	englewood	PROPN
ejpam-3184	269	9	cliffs	cliffs	PROPN
ejpam-3184	269	10	,	,	PUNCT
ejpam-3184	269	11	new	new	PROPN
ejpam-3184	269	12	jersey	jersey	PROPN
ejpam-3184	269	13	,	,	PUNCT
ejpam-3184	269	14	1964	1964	NUM
ejpam-3184	269	15	.	.	PUNCT
ejpam-3184	270	1	[	[	X
ejpam-3184	270	2	10	10	NUM
ejpam-3184	270	3	]	]	X
ejpam-3184	270	4	h.	h.	PROPN
ejpam-3184	270	5	wei	wei	PROPN
ejpam-3184	270	6	,	,	PUNCT
ejpam-3184	270	7	y.	y.	PROPN
ejpam-3184	270	8	wang	wang	PROPN
ejpam-3184	270	9	and	and	CCONJ
ejpam-3184	270	10	y.	y.	PROPN
ejpam-3184	270	11	li	li	PROPN
ejpam-3184	270	12	.	.	PUNCT
ejpam-3184	271	1	on	on	ADP
ejpam-3184	271	2	c	c	NOUN
ejpam-3184	271	3	-	-	ADJ
ejpam-3184	271	4	normal	normal	ADJ
ejpam-3184	271	5	maximal	maximal	ADJ
ejpam-3184	271	6	and	and	CCONJ
ejpam-3184	271	7	minimal	minimal	ADJ
ejpam-3184	271	8	subgroups	subgroup	NOUN
ejpam-3184	271	9	of	of	ADP
ejpam-3184	271	10	sylow	sylow	NOUN
ejpam-3184	271	11	subgroups	subgroup	NOUN
ejpam-3184	271	12	of	of	ADP
ejpam-3184	271	13	finite	finite	PROPN
ejpam-3184	271	14	groups	groups	PROPN
ejpam-3184	271	15	ii	ii	PROPN
ejpam-3184	271	16	,	,	PUNCT
ejpam-3184	271	17	comm	comm	NOUN
ejpam-3184	271	18	.	.	PUNCT
ejpam-3184	272	1	algebra	algebra	PROPN
ejpam-3184	272	2	,	,	PUNCT
ejpam-3184	272	3	31(10	31(10	NUM
ejpam-3184	272	4	)	)	PUNCT
ejpam-3184	272	5	(	(	PUNCT
ejpam-3184	272	6	2003	2003	NUM
ejpam-3184	272	7	)	)	PUNCT
ejpam-3184	272	8	,	,	PUNCT
ejpam-3184	272	9	4807–4816	4807–4816	NUM
ejpam-3184	272	10	.	.	PUNCT
ejpam-3184	273	1	[	[	X
ejpam-3184	273	2	11	11	NUM
ejpam-3184	273	3	]	]	PUNCT
ejpam-3184	273	4	m.	m.	NOUN
ejpam-3184	273	5	weinstein	weinstein	PROPN
ejpam-3184	273	6	(	(	PUNCT
ejpam-3184	273	7	editor	editor	NOUN
ejpam-3184	273	8	)	)	PUNCT
ejpam-3184	273	9	,	,	PUNCT
ejpam-3184	273	10	between	between	ADP
ejpam-3184	273	11	nilpotent	nilpotent	NOUN
ejpam-3184	273	12	and	and	CCONJ
ejpam-3184	273	13	solvable	solvable	ADJ
ejpam-3184	273	14	,	,	PUNCT
ejpam-3184	273	15	passaic	passaic	PROPN
ejpam-3184	273	16	:	:	PUNCT
ejpam-3184	273	17	polygonal	polygonal	ADJ
ejpam-3184	273	18	publishing	publishing	NOUN
ejpam-3184	273	19	house	house	NOUN
ejpam-3184	273	20	,	,	PUNCT
ejpam-3184	273	21	1982	1982	NUM
ejpam-3184	273	22	.	.	PUNCT