id	sid	tid	token	lemma	pos
ejpam-6859	1	1	european	european	PROPN
ejpam-6859	1	2	journal	journal	PROPN
ejpam-6859	1	3	of	of	ADP
ejpam-6859	1	4	pure	pure	ADJ
ejpam-6859	1	5	and	and	CCONJ
ejpam-6859	1	6	applied	applied	ADJ
ejpam-6859	1	7	mathematics	mathematic	NOUN
ejpam-6859	1	8	2025	2025	NUM
ejpam-6859	1	9	,	,	PUNCT
ejpam-6859	1	10	vol	vol	NOUN
ejpam-6859	1	11	.	.	PROPN
ejpam-6859	1	12	18	18	NUM
ejpam-6859	1	13	,	,	PUNCT
ejpam-6859	1	14	issue	issue	NOUN
ejpam-6859	1	15	4	4	NUM
ejpam-6859	1	16	,	,	PUNCT
ejpam-6859	1	17	article	article	NOUN
ejpam-6859	1	18	number	number	NOUN
ejpam-6859	1	19	6859	6859	NUM
ejpam-6859	1	20	issn	issn	VERB
ejpam-6859	1	21	1307	1307	NUM
ejpam-6859	1	22	-	-	SYM
ejpam-6859	1	23	5543	5543	NUM
ejpam-6859	1	24	–	–	PUNCT
ejpam-6859	1	25	ejpam.com	ejpam.com	X
ejpam-6859	1	26	published	publish	VERB
ejpam-6859	1	27	by	by	ADP
ejpam-6859	1	28	new	new	PROPN
ejpam-6859	1	29	york	york	PROPN
ejpam-6859	1	30	business	business	PROPN
ejpam-6859	1	31	global	global	PROPN
ejpam-6859	1	32	on	on	ADP
ejpam-6859	1	33	finite	finite	ADJ
ejpam-6859	1	34	groups	group	NOUN
ejpam-6859	1	35	with	with	ADP
ejpam-6859	1	36	transfer	transfer	NOUN
ejpam-6859	1	37	maps	map	NOUN
ejpam-6859	1	38	and	and	CCONJ
ejpam-6859	1	39	weak	weak	ADJ
ejpam-6859	1	40	closure	closure	NOUN
ejpam-6859	1	41	abdulaziz	abdulaziz	PROPN
ejpam-6859	1	42	mutlaq	mutlaq	PROPN
ejpam-6859	1	43	alotaibi1	alotaibi1	PROPN
ejpam-6859	1	44	,	,	PUNCT
ejpam-6859	1	45	khalid	khalid	PROPN
ejpam-6859	1	46	al	al	PROPN
ejpam-6859	1	47	-	-	PUNCT
ejpam-6859	1	48	tahat2	tahat2	PROPN
ejpam-6859	1	49	,	,	PUNCT
ejpam-6859	1	50	khaled	khaled	PROPN
ejpam-6859	1	51	mustafa	mustafa	PROPN
ejpam-6859	1	52	al	al	PROPN
ejpam-6859	1	53	-	-	PUNCT
ejpam-6859	1	54	jamal2,∗	jamal2,∗	PROPN
ejpam-6859	1	55	1	1	NUM
ejpam-6859	1	56	department	department	NOUN
ejpam-6859	1	57	of	of	ADP
ejpam-6859	1	58	mathematics	mathematic	NOUN
ejpam-6859	1	59	,	,	PUNCT
ejpam-6859	1	60	college	college	NOUN
ejpam-6859	1	61	of	of	ADP
ejpam-6859	1	62	science	science	NOUN
ejpam-6859	1	63	and	and	CCONJ
ejpam-6859	1	64	humanities	humanity	NOUN
ejpam-6859	1	65	in	in	ADP
ejpam-6859	1	66	al	al	PROPN
ejpam-6859	1	67	-	-	PUNCT
ejpam-6859	1	68	kharj	kharj	PROPN
ejpam-6859	1	69	,	,	PUNCT
ejpam-6859	1	70	prince	prince	PROPN
ejpam-6859	1	71	sattam	sattam	PROPN
ejpam-6859	1	72	bin	bin	PROPN
ejpam-6859	1	73	abdulaziz	abdulaziz	PROPN
ejpam-6859	1	74	university	university	PROPN
ejpam-6859	1	75	,	,	PUNCT
ejpam-6859	1	76	al	al	PROPN
ejpam-6859	1	77	-	-	PUNCT
ejpam-6859	1	78	kharj	kharj	PROPN
ejpam-6859	1	79	11942	11942	NUM
ejpam-6859	1	80	,	,	PUNCT
ejpam-6859	1	81	saudi	saudi	PROPN
ejpam-6859	1	82	arabia	arabia	PROPN
ejpam-6859	1	83	2	2	NUM
ejpam-6859	1	84	faculty	faculty	NOUN
ejpam-6859	1	85	of	of	ADP
ejpam-6859	1	86	computer	computer	NOUN
ejpam-6859	1	87	studies	study	NOUN
ejpam-6859	1	88	,	,	PUNCT
ejpam-6859	1	89	arab	arab	ADJ
ejpam-6859	1	90	open	open	PROPN
ejpam-6859	1	91	university	university	PROPN
ejpam-6859	1	92	,	,	PUNCT
ejpam-6859	1	93	amman	amman	PROPN
ejpam-6859	1	94	,	,	PUNCT
ejpam-6859	1	95	jordan	jordan	PROPN
ejpam-6859	1	96	abstract	abstract	PROPN
ejpam-6859	1	97	.	.	PUNCT
ejpam-6859	2	1	let	let	VERB
ejpam-6859	2	2	g	g	PRON
ejpam-6859	2	3	be	be	AUX
ejpam-6859	2	4	a	a	DET
ejpam-6859	2	5	finite	finite	ADJ
ejpam-6859	2	6	group	group	NOUN
ejpam-6859	2	7	,	,	PUNCT
ejpam-6859	2	8	p	p	PROPN
ejpam-6859	2	9	∈	∈	PROPN
ejpam-6859	2	10	sylp(g	sylp(g	NOUN
ejpam-6859	2	11	)	)	PUNCT
ejpam-6859	2	12	and	and	CCONJ
ejpam-6859	2	13	w	w	ADP
ejpam-6859	2	14	⊆	⊆	NUM
ejpam-6859	2	15	p	p	NOUN
ejpam-6859	2	16	.	.	PUNCT
ejpam-6859	3	1	we	we	PRON
ejpam-6859	3	2	say	say	VERB
ejpam-6859	3	3	that	that	SCONJ
ejpam-6859	3	4	w	w	NOUN
ejpam-6859	3	5	is	be	AUX
ejpam-6859	3	6	weakly	weakly	ADV
ejpam-6859	3	7	closed	closed	ADJ
ejpam-6859	3	8	in	in	ADP
ejpam-6859	3	9	p	p	NOUN
ejpam-6859	3	10	with	with	ADP
ejpam-6859	3	11	respect	respect	NOUN
ejpam-6859	3	12	to	to	ADP
ejpam-6859	3	13	g	g	PROPN
ejpam-6859	3	14	if	if	SCONJ
ejpam-6859	3	15	w	w	PROPN
ejpam-6859	3	16	g	g	NOUN
ejpam-6859	3	17	⊆	⊆	NUM
ejpam-6859	3	18	p	p	NOUN
ejpam-6859	3	19	for	for	ADP
ejpam-6859	3	20	all	all	DET
ejpam-6859	3	21	g	g	PROPN
ejpam-6859	3	22	∈	∈	PROPN
ejpam-6859	3	23	g.	g.	NOUN
ejpam-6859	3	24	in	in	ADP
ejpam-6859	3	25	this	this	DET
ejpam-6859	3	26	paper	paper	NOUN
ejpam-6859	3	27	,	,	PUNCT
ejpam-6859	3	28	we	we	PRON
ejpam-6859	3	29	explore	explore	VERB
ejpam-6859	3	30	structural	structural	ADJ
ejpam-6859	3	31	properties	property	NOUN
ejpam-6859	3	32	of	of	ADP
ejpam-6859	3	33	finite	finite	ADJ
ejpam-6859	3	34	groups	group	NOUN
ejpam-6859	3	35	using	use	VERB
ejpam-6859	3	36	the	the	DET
ejpam-6859	3	37	transfer	transfer	NOUN
ejpam-6859	3	38	homomorphism	homomorphism	NOUN
ejpam-6859	3	39	and	and	CCONJ
ejpam-6859	3	40	the	the	DET
ejpam-6859	3	41	notion	notion	NOUN
ejpam-6859	3	42	of	of	ADP
ejpam-6859	3	43	weak	weak	ADJ
ejpam-6859	3	44	closure	closure	NOUN
ejpam-6859	3	45	in	in	ADP
ejpam-6859	3	46	sylow	sylow	NOUN
ejpam-6859	3	47	subgroups	subgroup	NOUN
ejpam-6859	3	48	.	.	PUNCT
ejpam-6859	4	1	we	we	PRON
ejpam-6859	4	2	establish	establish	VERB
ejpam-6859	4	3	that	that	SCONJ
ejpam-6859	4	4	if	if	SCONJ
ejpam-6859	4	5	a	a	DET
ejpam-6859	4	6	central	central	ADJ
ejpam-6859	4	7	subgroup	subgroup	NOUN
ejpam-6859	4	8	h	h	NOUN
ejpam-6859	4	9	≤	≤	NUM
ejpam-6859	4	10	z(g	z(g	NOUN
ejpam-6859	4	11	)	)	PUNCT
ejpam-6859	4	12	has	have	VERB
ejpam-6859	4	13	finite	finite	ADJ
ejpam-6859	4	14	index	index	NOUN
ejpam-6859	5	1	[	[	X
ejpam-6859	5	2	g	g	NOUN
ejpam-6859	5	3	:	:	PUNCT
ejpam-6859	5	4	h	h	X
ejpam-6859	5	5	]	]	X
ejpam-6859	5	6	coprime	coprime	NOUN
ejpam-6859	5	7	to	to	ADP
ejpam-6859	5	8	|h|	|h|	PROPN
ejpam-6859	5	9	,	,	PUNCT
ejpam-6859	5	10	then	then	ADV
ejpam-6859	5	11	g	g	PROPN
ejpam-6859	5	12	∼=	∼=	PROPN
ejpam-6859	5	13	h	h	NOUN
ejpam-6859	5	14	×	×	NOUN
ejpam-6859	5	15	ker(v	ker(v	PROPN
ejpam-6859	5	16	)	)	PUNCT
ejpam-6859	5	17	,	,	PUNCT
ejpam-6859	5	18	where	where	SCONJ
ejpam-6859	5	19	v	v	NOUN
ejpam-6859	5	20	:	:	PUNCT
ejpam-6859	5	21	g	g	NOUN
ejpam-6859	5	22	→	→	SYM
ejpam-6859	5	23	h	h	NOUN
ejpam-6859	5	24	is	be	AUX
ejpam-6859	5	25	the	the	DET
ejpam-6859	5	26	transfer	transfer	NOUN
ejpam-6859	5	27	.	.	PUNCT
ejpam-6859	6	1	furthermore	furthermore	ADV
ejpam-6859	6	2	,	,	PUNCT
ejpam-6859	6	3	we	we	PRON
ejpam-6859	6	4	characterize	characterize	VERB
ejpam-6859	6	5	weakly	weakly	ADJ
ejpam-6859	6	6	closed	closed	ADJ
ejpam-6859	6	7	subgroups	subgroup	NOUN
ejpam-6859	6	8	w	w	ADP
ejpam-6859	6	9	≤	≤	NOUN
ejpam-6859	6	10	p	p	NOUN
ejpam-6859	6	11	∈	∈	PROPN
ejpam-6859	6	12	sylp(g	sylp(g	PROPN
ejpam-6859	6	13	)	)	PUNCT
ejpam-6859	6	14	as	as	ADV
ejpam-6859	6	15	normal	normal	ADJ
ejpam-6859	6	16	in	in	ADP
ejpam-6859	6	17	both	both	PRON
ejpam-6859	6	18	ng(p	ng(p	NOUN
ejpam-6859	6	19	)	)	PUNCT
ejpam-6859	6	20	and	and	CCONJ
ejpam-6859	6	21	all	all	PRON
ejpam-6859	6	22	sylow	sylow	VERB
ejpam-6859	6	23	p	p	NOUN
ejpam-6859	6	24	-	-	PUNCT
ejpam-6859	6	25	subgroups	subgroup	NOUN
ejpam-6859	6	26	containing	contain	VERB
ejpam-6859	6	27	w	w	X
ejpam-6859	6	28	.	.	PUNCT
ejpam-6859	7	1	several	several	ADJ
ejpam-6859	7	2	consequences	consequence	NOUN
ejpam-6859	7	3	concerning	concern	VERB
ejpam-6859	7	4	conjugacy	conjugacy	NOUN
ejpam-6859	7	5	and	and	CCONJ
ejpam-6859	7	6	normality	normality	NOUN
ejpam-6859	7	7	are	be	AUX
ejpam-6859	7	8	discussed	discuss	VERB
ejpam-6859	7	9	.	.	PUNCT
ejpam-6859	8	1	2020	2020	NUM
ejpam-6859	8	2	mathematics	mathematic	NOUN
ejpam-6859	8	3	subject	subject	NOUN
ejpam-6859	8	4	classifications	classification	NOUN
ejpam-6859	8	5	:	:	PUNCT
ejpam-6859	8	6	20d10	20d10	NUM
ejpam-6859	8	7	,	,	PUNCT
ejpam-6859	8	8	20d15	20d15	NUM
ejpam-6859	8	9	,	,	PUNCT
ejpam-6859	8	10	20d20	20d20	NUM
ejpam-6859	8	11	key	key	ADJ
ejpam-6859	8	12	words	word	NOUN
ejpam-6859	8	13	and	and	CCONJ
ejpam-6859	8	14	phrases	phrase	NOUN
ejpam-6859	8	15	:	:	PUNCT
ejpam-6859	8	16	finite	finite	ADJ
ejpam-6859	8	17	groups	group	NOUN
ejpam-6859	8	18	,	,	PUNCT
ejpam-6859	8	19	weakly	weakly	ADV
ejpam-6859	8	20	closed	closed	ADJ
ejpam-6859	8	21	subgroup	subgroup	NOUN
ejpam-6859	8	22	,	,	PUNCT
ejpam-6859	8	23	sylow	sylow	VERB
ejpam-6859	8	24	p	p	PROPN
ejpam-6859	8	25	-	-	PUNCT
ejpam-6859	8	26	subgroup	subgroup	NOUN
ejpam-6859	8	27	1	1	NUM
ejpam-6859	8	28	.	.	PUNCT
ejpam-6859	9	1	introduction	introduction	NOUN
ejpam-6859	9	2	and	and	CCONJ
ejpam-6859	9	3	preliminaries	preliminary	NOUN
ejpam-6859	9	4	all	all	DET
ejpam-6859	9	5	groups	group	NOUN
ejpam-6859	9	6	are	be	AUX
ejpam-6859	9	7	assumed	assume	VERB
ejpam-6859	9	8	to	to	PART
ejpam-6859	9	9	be	be	AUX
ejpam-6859	9	10	finite	finite	VERB
ejpam-6859	9	11	.	.	PUNCT
ejpam-6859	10	1	the	the	DET
ejpam-6859	10	2	internal	internal	ADJ
ejpam-6859	10	3	structure	structure	NOUN
ejpam-6859	10	4	of	of	ADP
ejpam-6859	10	5	finite	finite	ADJ
ejpam-6859	10	6	groups	group	NOUN
ejpam-6859	10	7	has	have	AUX
ejpam-6859	10	8	long	long	ADV
ejpam-6859	10	9	been	be	AUX
ejpam-6859	10	10	investigated	investigate	VERB
ejpam-6859	10	11	through	through	ADP
ejpam-6859	10	12	the	the	DET
ejpam-6859	10	13	lens	lens	NOUN
ejpam-6859	10	14	of	of	ADP
ejpam-6859	10	15	transfer	transfer	NOUN
ejpam-6859	10	16	homomorphisms	homomorphism	NOUN
ejpam-6859	10	17	and	and	CCONJ
ejpam-6859	10	18	sylow	sylow	NOUN
ejpam-6859	10	19	theorem	theorem	VERB
ejpam-6859	10	20	[	[	X
ejpam-6859	10	21	1	1	NUM
ejpam-6859	10	22	]	]	PUNCT
ejpam-6859	10	23	,	,	PUNCT
ejpam-6859	10	24	tools	tool	NOUN
ejpam-6859	10	25	which	which	PRON
ejpam-6859	10	26	continue	continue	VERB
ejpam-6859	10	27	to	to	PART
ejpam-6859	10	28	provide	provide	VERB
ejpam-6859	10	29	profound	profound	ADJ
ejpam-6859	10	30	insights	insight	NOUN
ejpam-6859	10	31	into	into	ADP
ejpam-6859	10	32	group	group	NOUN
ejpam-6859	10	33	decompositions	decomposition	NOUN
ejpam-6859	10	34	and	and	CCONJ
ejpam-6859	10	35	subgroup	subgroup	NOUN
ejpam-6859	10	36	interactions	interaction	NOUN
ejpam-6859	10	37	[	[	X
ejpam-6859	10	38	2	2	NUM
ejpam-6859	10	39	]	]	PUNCT
ejpam-6859	10	40	.	.	PUNCT
ejpam-6859	11	1	the	the	DET
ejpam-6859	11	2	transfer	transfer	NOUN
ejpam-6859	11	3	map	map	NOUN
ejpam-6859	11	4	,	,	PUNCT
ejpam-6859	11	5	introduced	introduce	VERB
ejpam-6859	11	6	in	in	ADP
ejpam-6859	11	7	classical	classical	ADJ
ejpam-6859	11	8	group	group	NOUN
ejpam-6859	11	9	theory	theory	NOUN
ejpam-6859	11	10	,	,	PUNCT
ejpam-6859	11	11	remains	remain	VERB
ejpam-6859	11	12	a	a	DET
ejpam-6859	11	13	valuable	valuable	ADJ
ejpam-6859	11	14	technique	technique	NOUN
ejpam-6859	11	15	for	for	ADP
ejpam-6859	11	16	relating	relate	VERB
ejpam-6859	11	17	global	global	ADJ
ejpam-6859	11	18	properties	property	NOUN
ejpam-6859	11	19	of	of	ADP
ejpam-6859	11	20	a	a	DET
ejpam-6859	11	21	group	group	NOUN
ejpam-6859	11	22	to	to	ADP
ejpam-6859	11	23	its	its	PRON
ejpam-6859	11	24	substructures	substructure	NOUN
ejpam-6859	11	25	,	,	PUNCT
ejpam-6859	11	26	particularly	particularly	ADV
ejpam-6859	11	27	when	when	SCONJ
ejpam-6859	11	28	considering	consider	VERB
ejpam-6859	11	29	questions	question	NOUN
ejpam-6859	11	30	of	of	ADP
ejpam-6859	11	31	direct	direct	ADJ
ejpam-6859	11	32	product	product	NOUN
ejpam-6859	11	33	decompositions	decomposition	NOUN
ejpam-6859	11	34	and	and	CCONJ
ejpam-6859	11	35	coprime	coprime	NOUN
ejpam-6859	11	36	conditions	condition	NOUN
ejpam-6859	11	37	[	[	X
ejpam-6859	11	38	3	3	NUM
ejpam-6859	11	39	]	]	PUNCT
ejpam-6859	11	40	.	.	PUNCT
ejpam-6859	12	1	for	for	ADP
ejpam-6859	12	2	example	example	NOUN
ejpam-6859	12	3	,	,	PUNCT
ejpam-6859	12	4	if	if	SCONJ
ejpam-6859	12	5	h	h	NOUN
ejpam-6859	12	6	is	be	AUX
ejpam-6859	12	7	a	a	DET
ejpam-6859	12	8	finite	finite	ADJ
ejpam-6859	12	9	central	central	ADJ
ejpam-6859	12	10	subgroup	subgroup	NOUN
ejpam-6859	12	11	of	of	ADP
ejpam-6859	12	12	a	a	DET
ejpam-6859	12	13	group	group	NOUN
ejpam-6859	12	14	g	g	NOUN
ejpam-6859	12	15	,	,	PUNCT
ejpam-6859	12	16	and	and	CCONJ
ejpam-6859	12	17	the	the	DET
ejpam-6859	12	18	index	index	NOUN
ejpam-6859	13	1	[	[	X
ejpam-6859	13	2	g	g	NOUN
ejpam-6859	13	3	:	:	PUNCT
ejpam-6859	13	4	h	h	X
ejpam-6859	13	5	]	]	X
ejpam-6859	13	6	is	be	AUX
ejpam-6859	13	7	finite	finite	ADJ
ejpam-6859	13	8	and	and	CCONJ
ejpam-6859	13	9	relatively	relatively	ADV
ejpam-6859	13	10	prime	prime	ADJ
ejpam-6859	13	11	to	to	ADP
ejpam-6859	13	12	|	|	ADV
ejpam-6859	14	1	h	h	NOUN
ejpam-6859	15	1	|	|	ADV
ejpam-6859	15	2	,	,	PUNCT
ejpam-6859	15	3	then	then	ADV
ejpam-6859	15	4	the	the	DET
ejpam-6859	15	5	transfer	transfer	NOUN
ejpam-6859	15	6	homomorphism	homomorphism	NOUN
ejpam-6859	15	7	v	v	ADP
ejpam-6859	15	8	:	:	PUNCT
ejpam-6859	15	9	g	g	NOUN
ejpam-6859	15	10	→	→	SYM
ejpam-6859	15	11	h	h	NOUN
ejpam-6859	15	12	may	may	AUX
ejpam-6859	15	13	be	be	AUX
ejpam-6859	15	14	used	use	VERB
ejpam-6859	15	15	to	to	PART
ejpam-6859	15	16	show	show	VERB
ejpam-6859	15	17	that	that	SCONJ
ejpam-6859	15	18	g	g	PROPN
ejpam-6859	15	19	∼=	∼=	PROPN
ejpam-6859	15	20	h	h	NOUN
ejpam-6859	15	21	×	×	NOUN
ejpam-6859	15	22	ker(v	ker(v	PROPN
ejpam-6859	15	23	)	)	PUNCT
ejpam-6859	15	24	,	,	PUNCT
ejpam-6859	15	25	effectively	effectively	ADV
ejpam-6859	15	26	separating	separate	VERB
ejpam-6859	15	27	g	g	NOUN
ejpam-6859	15	28	into	into	ADP
ejpam-6859	15	29	two	two	NUM
ejpam-6859	15	30	commuting	commuting	NOUN
ejpam-6859	15	31	,	,	PUNCT
ejpam-6859	15	32	intersectingtrivially	intersectingtrivially	ADV
ejpam-6859	15	33	components	component	NOUN
ejpam-6859	16	1	[	[	X
ejpam-6859	16	2	4	4	NUM
ejpam-6859	16	3	]	]	PUNCT
ejpam-6859	16	4	.	.	PUNCT
ejpam-6859	17	1	this	this	DET
ejpam-6859	17	2	classical	classical	ADJ
ejpam-6859	17	3	result	result	NOUN
ejpam-6859	17	4	showcases	showcase	VERB
ejpam-6859	17	5	the	the	DET
ejpam-6859	17	6	interplay	interplay	NOUN
ejpam-6859	17	7	between	between	ADP
ejpam-6859	17	8	arithmetic	arithmetic	ADJ
ejpam-6859	17	9	conditions	condition	NOUN
ejpam-6859	17	10	and	and	CCONJ
ejpam-6859	17	11	the	the	DET
ejpam-6859	17	12	homomorphic	homomorphic	ADJ
ejpam-6859	17	13	structure	structure	NOUN
ejpam-6859	17	14	of	of	ADP
ejpam-6859	17	15	finite	finite	ADJ
ejpam-6859	17	16	groups	group	NOUN
ejpam-6859	17	17	[	[	X
ejpam-6859	17	18	5	5	NUM
ejpam-6859	17	19	]	]	PUNCT
ejpam-6859	17	20	and	and	CCONJ
ejpam-6859	17	21	[	[	X
ejpam-6859	17	22	6	6	NUM
ejpam-6859	17	23	]	]	PUNCT
ejpam-6859	17	24	.	.	PUNCT
ejpam-6859	18	1	beyond	beyond	ADP
ejpam-6859	18	2	this	this	PRON
ejpam-6859	18	3	,	,	PUNCT
ejpam-6859	18	4	the	the	DET
ejpam-6859	18	5	concept	concept	NOUN
ejpam-6859	18	6	of	of	ADP
ejpam-6859	18	7	weak	weak	ADJ
ejpam-6859	18	8	closure	closure	NOUN
ejpam-6859	18	9	has	have	AUX
ejpam-6859	18	10	emerged	emerge	VERB
ejpam-6859	18	11	as	as	ADP
ejpam-6859	18	12	a	a	DET
ejpam-6859	18	13	key	key	ADJ
ejpam-6859	18	14	feature	feature	NOUN
ejpam-6859	18	15	in	in	ADP
ejpam-6859	18	16	understanding	understanding	NOUN
ejpam-6859	18	17	conjugacy	conjugacy	ADJ
ejpam-6859	18	18	phenomena	phenomenon	NOUN
ejpam-6859	18	19	in	in	ADP
ejpam-6859	18	20	sylow	sylow	NOUN
ejpam-6859	18	21	subgroups	subgroup	NOUN
ejpam-6859	18	22	.	.	PUNCT
ejpam-6859	19	1	given	give	VERB
ejpam-6859	19	2	a	a	DET
ejpam-6859	19	3	sylow	sylow	NOUN
ejpam-6859	19	4	p	p	NOUN
ejpam-6859	19	5	-	-	PUNCT
ejpam-6859	19	6	subgroup	subgroup	NOUN
ejpam-6859	19	7	p	p	NOUN
ejpam-6859	19	8	of	of	ADP
ejpam-6859	19	9	g	g	PROPN
ejpam-6859	19	10	,	,	PUNCT
ejpam-6859	19	11	a	a	DET
ejpam-6859	19	12	subgroup	subgroup	NOUN
ejpam-6859	19	13	∗corresponding	∗corresponde	VERB
ejpam-6859	19	14	author	author	NOUN
ejpam-6859	19	15	.	.	PUNCT
ejpam-6859	20	1	doi	doi	NOUN
ejpam-6859	20	2	:	:	PUNCT
ejpam-6859	20	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6859	https://doi.org/10.29020/nybg.ejpam.v18i4.6859	PROPN
ejpam-6859	20	4	email	email	NOUN
ejpam-6859	20	5	addresses	address	NOUN
ejpam-6859	20	6	:	:	PUNCT
ejpam-6859	20	7	am.alotaibi@psau.edu.sa	am.alotaibi@psau.edu.sa	PROPN
ejpam-6859	20	8	(	(	PUNCT
ejpam-6859	20	9	a.	a.	NOUN
ejpam-6859	20	10	m.	m.	NOUN
ejpam-6859	20	11	alotaibi	alotaibi	PROPN
ejpam-6859	20	12	)	)	PUNCT
ejpam-6859	20	13	,	,	PUNCT
ejpam-6859	20	14	k_tahat@aou.edu.jo	k_tahat@aou.edu.jo	PROPN
ejpam-6859	20	15	(	(	PUNCT
ejpam-6859	20	16	k.	k.	PROPN
ejpam-6859	20	17	al	al	PROPN
ejpam-6859	20	18	-	-	PROPN
ejpam-6859	20	19	tahat	tahat	PROPN
ejpam-6859	20	20	)	)	PUNCT
ejpam-6859	20	21	,	,	PUNCT
ejpam-6859	20	22	pt_aljammal@aou.edu.jo	pt_aljammal@aou.edu.jo	NOUN
ejpam-6859	20	23	(	(	PUNCT
ejpam-6859	20	24	k.	k.	PROPN
ejpam-6859	20	25	m.	m.	PROPN
ejpam-6859	20	26	al	al	PROPN
ejpam-6859	20	27	-	-	PUNCT
ejpam-6859	20	28	jamal	jamal	PROPN
ejpam-6859	20	29	)	)	PUNCT
ejpam-6859	20	30	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6859	21	1	1	1	NUM
ejpam-6859	21	2	copyright	copyright	NOUN
ejpam-6859	21	3	:	:	PUNCT
ejpam-6859	21	4	©	©	PROPN
ejpam-6859	21	5	2025	2025	NUM
ejpam-6859	21	6	the	the	DET
ejpam-6859	21	7	author(s	author(s	NOUN
ejpam-6859	21	8	)	)	PUNCT
ejpam-6859	21	9	.	.	PUNCT
ejpam-6859	22	1	(	(	PUNCT
ejpam-6859	22	2	cc	cc	NOUN
ejpam-6859	22	3	by	by	ADP
ejpam-6859	22	4	-	-	PUNCT
ejpam-6859	22	5	nc	nc	PROPN
ejpam-6859	22	6	4.0	4.0	NUM
ejpam-6859	22	7	)	)	PUNCT
ejpam-6859	22	8	a.	a.	NOUN
ejpam-6859	22	9	m.	m.	NOUN
ejpam-6859	22	10	alotaibi	alotaibi	PROPN
ejpam-6859	22	11	et	et	PROPN
ejpam-6859	22	12	al	al	PROPN
ejpam-6859	22	13	.	.	PUNCT
ejpam-6859	22	14	/	/	SYM
ejpam-6859	22	15	eur	eur	PROPN
ejpam-6859	22	16	.	.	PUNCT
ejpam-6859	23	1	j.	j.	PROPN
ejpam-6859	23	2	pure	pure	PROPN
ejpam-6859	23	3	appl	appl	PROPN
ejpam-6859	23	4	.	.	PROPN
ejpam-6859	23	5	math	math	PROPN
ejpam-6859	23	6	,	,	PUNCT
ejpam-6859	23	7	18	18	NUM
ejpam-6859	23	8	(	(	PUNCT
ejpam-6859	23	9	4	4	NUM
ejpam-6859	23	10	)	)	PUNCT
ejpam-6859	23	11	(	(	PUNCT
ejpam-6859	23	12	2025	2025	NUM
ejpam-6859	23	13	)	)	PUNCT
ejpam-6859	23	14	,	,	PUNCT
ejpam-6859	23	15	6859	6859	NUM
ejpam-6859	23	16	2	2	NUM
ejpam-6859	23	17	of	of	ADP
ejpam-6859	23	18	6	6	NUM
ejpam-6859	23	19	w	w	NOUN
ejpam-6859	23	20	⊆	⊆	NUM
ejpam-6859	23	21	p	p	NOUN
ejpam-6859	23	22	is	be	AUX
ejpam-6859	23	23	said	say	VERB
ejpam-6859	23	24	to	to	PART
ejpam-6859	23	25	be	be	AUX
ejpam-6859	23	26	weakly	weakly	ADV
ejpam-6859	23	27	closed	closed	ADJ
ejpam-6859	23	28	in	in	ADP
ejpam-6859	23	29	p	p	NOUN
ejpam-6859	23	30	with	with	ADP
ejpam-6859	23	31	respect	respect	NOUN
ejpam-6859	23	32	to	to	ADP
ejpam-6859	23	33	g	g	NOUN
ejpam-6859	23	34	if	if	SCONJ
ejpam-6859	23	35	no	no	DET
ejpam-6859	23	36	other	other	ADJ
ejpam-6859	23	37	g	g	NOUN
ejpam-6859	23	38	-	-	PUNCT
ejpam-6859	23	39	conjugate	conjugate	NOUN
ejpam-6859	23	40	of	of	ADP
ejpam-6859	23	41	w	w	NOUN
ejpam-6859	23	42	lies	lie	NOUN
ejpam-6859	23	43	within	within	ADP
ejpam-6859	23	44	p	p	PROPN
ejpam-6859	23	45	.	.	PUNCT
ejpam-6859	24	1	this	this	DET
ejpam-6859	24	2	property	property	NOUN
ejpam-6859	24	3	,	,	PUNCT
ejpam-6859	24	4	though	though	SCONJ
ejpam-6859	24	5	defined	define	VERB
ejpam-6859	24	6	in	in	ADP
ejpam-6859	24	7	terms	term	NOUN
ejpam-6859	24	8	of	of	ADP
ejpam-6859	24	9	conjugation	conjugation	NOUN
ejpam-6859	24	10	,	,	PUNCT
ejpam-6859	24	11	has	have	VERB
ejpam-6859	24	12	strong	strong	ADJ
ejpam-6859	24	13	implications	implication	NOUN
ejpam-6859	24	14	for	for	ADP
ejpam-6859	24	15	normality	normality	NOUN
ejpam-6859	24	16	:	:	PUNCT
ejpam-6859	24	17	w	w	NOUN
ejpam-6859	24	18	is	be	AUX
ejpam-6859	24	19	weakly	weakly	ADV
ejpam-6859	24	20	closed	closed	ADJ
ejpam-6859	24	21	if	if	SCONJ
ejpam-6859	24	22	and	and	CCONJ
ejpam-6859	24	23	only	only	ADV
ejpam-6859	24	24	if	if	SCONJ
ejpam-6859	24	25	it	it	PRON
ejpam-6859	24	26	is	be	AUX
ejpam-6859	24	27	normal	normal	ADJ
ejpam-6859	24	28	in	in	ADP
ejpam-6859	24	29	ng(p	ng(p	PUNCT
ejpam-6859	24	30	)	)	PUNCT
ejpam-6859	24	31	and	and	CCONJ
ejpam-6859	24	32	remains	remain	VERB
ejpam-6859	24	33	normal	normal	ADJ
ejpam-6859	24	34	in	in	ADP
ejpam-6859	24	35	every	every	DET
ejpam-6859	24	36	sylow	sylow	NOUN
ejpam-6859	24	37	p	p	NOUN
ejpam-6859	24	38	-	-	PUNCT
ejpam-6859	24	39	subgroup	subgroup	NOUN
ejpam-6859	24	40	of	of	ADP
ejpam-6859	24	41	g	g	PROPN
ejpam-6859	24	42	that	that	PRON
ejpam-6859	24	43	contains	contain	VERB
ejpam-6859	24	44	it	it	PRON
ejpam-6859	24	45	[	[	X
ejpam-6859	24	46	7	7	X
ejpam-6859	24	47	]	]	PUNCT
ejpam-6859	24	48	and	and	CCONJ
ejpam-6859	24	49	[	[	X
ejpam-6859	24	50	8	8	NUM
ejpam-6859	24	51	]	]	PUNCT
ejpam-6859	24	52	.	.	PUNCT
ejpam-6859	25	1	these	these	DET
ejpam-6859	25	2	conditions	condition	NOUN
ejpam-6859	25	3	align	align	VERB
ejpam-6859	25	4	well	well	ADV
ejpam-6859	25	5	with	with	ADP
ejpam-6859	25	6	results	result	NOUN
ejpam-6859	25	7	in	in	ADP
ejpam-6859	25	8	fusion	fusion	NOUN
ejpam-6859	25	9	theory	theory	NOUN
ejpam-6859	25	10	and	and	CCONJ
ejpam-6859	25	11	control	control	NOUN
ejpam-6859	25	12	of	of	ADP
ejpam-6859	25	13	transfer	transfer	NOUN
ejpam-6859	25	14	,	,	PUNCT
ejpam-6859	25	15	where	where	SCONJ
ejpam-6859	25	16	conjugacy	conjugacy	NOUN
ejpam-6859	25	17	within	within	ADP
ejpam-6859	25	18	sylow	sylow	NOUN
ejpam-6859	25	19	subgroups	subgroup	NOUN
ejpam-6859	25	20	plays	play	VERB
ejpam-6859	25	21	a	a	DET
ejpam-6859	25	22	critical	critical	ADJ
ejpam-6859	25	23	role	role	NOUN
ejpam-6859	25	24	in	in	ADP
ejpam-6859	25	25	understanding	understand	VERB
ejpam-6859	25	26	the	the	DET
ejpam-6859	25	27	larger	large	ADJ
ejpam-6859	25	28	ambient	ambient	ADJ
ejpam-6859	25	29	group	group	NOUN
ejpam-6859	25	30	[	[	X
ejpam-6859	25	31	9	9	NUM
ejpam-6859	25	32	]	]	PUNCT
ejpam-6859	25	33	.	.	PUNCT
ejpam-6859	26	1	this	this	DET
ejpam-6859	26	2	paper	paper	NOUN
ejpam-6859	26	3	develops	develop	VERB
ejpam-6859	26	4	the	the	DET
ejpam-6859	26	5	underlying	underlie	VERB
ejpam-6859	26	6	concepts	concept	NOUN
ejpam-6859	26	7	in	in	ADP
ejpam-6859	26	8	tandem	tandem	PROPN
ejpam-6859	26	9	,	,	PUNCT
ejpam-6859	26	10	beginning	begin	VERB
ejpam-6859	26	11	with	with	ADP
ejpam-6859	26	12	the	the	DET
ejpam-6859	26	13	identification	identification	NOUN
ejpam-6859	26	14	of	of	ADP
ejpam-6859	26	15	criteria	criterion	NOUN
ejpam-6859	26	16	that	that	PRON
ejpam-6859	26	17	allow	allow	VERB
ejpam-6859	26	18	a	a	DET
ejpam-6859	26	19	finite	finite	ADJ
ejpam-6859	26	20	group	group	NOUN
ejpam-6859	26	21	to	to	PART
ejpam-6859	26	22	be	be	AUX
ejpam-6859	26	23	analyzed	analyze	VERB
ejpam-6859	26	24	via	via	ADP
ejpam-6859	26	25	the	the	DET
ejpam-6859	26	26	transfer	transfer	NOUN
ejpam-6859	26	27	method	method	NOUN
ejpam-6859	26	28	,	,	PUNCT
ejpam-6859	26	29	and	and	CCONJ
ejpam-6859	26	30	proceeding	proceed	VERB
ejpam-6859	26	31	to	to	ADP
ejpam-6859	26	32	a	a	DET
ejpam-6859	26	33	detailed	detailed	ADJ
ejpam-6859	26	34	examination	examination	NOUN
ejpam-6859	26	35	of	of	ADP
ejpam-6859	26	36	the	the	DET
ejpam-6859	26	37	relationship	relationship	NOUN
ejpam-6859	26	38	between	between	ADP
ejpam-6859	26	39	weak	weak	ADJ
ejpam-6859	26	40	closure	closure	NOUN
ejpam-6859	26	41	and	and	CCONJ
ejpam-6859	26	42	normality	normality	NOUN
ejpam-6859	26	43	within	within	ADP
ejpam-6859	26	44	sylow	sylow	NOUN
ejpam-6859	26	45	subgroups	subgroup	NOUN
ejpam-6859	26	46	.	.	PUNCT
ejpam-6859	27	1	the	the	DET
ejpam-6859	27	2	central	central	ADJ
ejpam-6859	27	3	focus	focus	NOUN
ejpam-6859	27	4	is	be	AUX
ejpam-6859	27	5	on	on	ADP
ejpam-6859	27	6	how	how	SCONJ
ejpam-6859	27	7	the	the	DET
ejpam-6859	27	8	behavior	behavior	NOUN
ejpam-6859	27	9	of	of	ADP
ejpam-6859	27	10	local	local	ADJ
ejpam-6859	27	11	subgroups	subgroup	NOUN
ejpam-6859	27	12	both	both	DET
ejpam-6859	27	13	influences	influence	NOUN
ejpam-6859	27	14	and	and	CCONJ
ejpam-6859	27	15	reflects	reflect	VERB
ejpam-6859	27	16	the	the	DET
ejpam-6859	27	17	overall	overall	ADJ
ejpam-6859	27	18	structure	structure	NOUN
ejpam-6859	27	19	of	of	ADP
ejpam-6859	27	20	the	the	DET
ejpam-6859	27	21	group	group	NOUN
ejpam-6859	27	22	.	.	PUNCT
ejpam-6859	28	1	the	the	DET
ejpam-6859	28	2	following	follow	VERB
ejpam-6859	28	3	lemmas	lemma	NOUN
ejpam-6859	28	4	are	be	AUX
ejpam-6859	28	5	well	well	ADV
ejpam-6859	28	6	-	-	PUNCT
ejpam-6859	28	7	known	know	VERB
ejpam-6859	28	8	and	and	CCONJ
ejpam-6859	28	9	basic	basic	ADJ
ejpam-6859	28	10	concepts	concept	NOUN
ejpam-6859	28	11	:	:	PUNCT
ejpam-6859	28	12	lemma	lemma	PROPN
ejpam-6859	28	13	1	1	NUM
ejpam-6859	28	14	.	.	PUNCT
ejpam-6859	29	1	[	[	X
ejpam-6859	29	2	9]a	9]a	NUM
ejpam-6859	29	3	subgroup	subgroup	NOUN
ejpam-6859	29	4	h	h	NOUN
ejpam-6859	29	5	of	of	ADP
ejpam-6859	29	6	g	g	PROPN
ejpam-6859	29	7	having	have	VERB
ejpam-6859	29	8	order	order	NOUN
ejpam-6859	29	9	a	a	DET
ejpam-6859	29	10	power	power	NOUN
ejpam-6859	29	11	of	of	ADP
ejpam-6859	29	12	a	a	DET
ejpam-6859	29	13	prime	prime	NOUN
ejpam-6859	29	14	is	be	AUX
ejpam-6859	29	15	normal	normal	ADJ
ejpam-6859	29	16	if	if	SCONJ
ejpam-6859	29	17	and	and	CCONJ
ejpam-6859	29	18	only	only	ADV
ejpam-6859	29	19	if	if	SCONJ
ejpam-6859	29	20	it	it	PRON
ejpam-6859	29	21	is	be	AUX
ejpam-6859	29	22	subnormal	subnormal	ADJ
ejpam-6859	29	23	in	in	ADP
ejpam-6859	29	24	g	g	PROPN
ejpam-6859	29	25	and	and	CCONJ
ejpam-6859	29	26	weakly	weakly	ADV
ejpam-6859	29	27	closed	closed	ADJ
ejpam-6859	29	28	in	in	ADP
ejpam-6859	29	29	g.	g.	PROPN
ejpam-6859	29	30	lemma	lemma	PROPN
ejpam-6859	30	1	2	2	X
ejpam-6859	30	2	.	.	PUNCT
ejpam-6859	31	1	[	[	X
ejpam-6859	31	2	6	6	NUM
ejpam-6859	31	3	]	]	PUNCT
ejpam-6859	31	4	let	let	VERB
ejpam-6859	31	5	g	g	PRON
ejpam-6859	31	6	be	be	AUX
ejpam-6859	31	7	a	a	DET
ejpam-6859	31	8	group	group	NOUN
ejpam-6859	31	9	and	and	CCONJ
ejpam-6859	31	10	let	let	VERB
ejpam-6859	31	11	h	h	PRON
ejpam-6859	31	12	be	be	AUX
ejpam-6859	31	13	a	a	DET
ejpam-6859	31	14	weakly	weakly	ADJ
ejpam-6859	31	15	closed	closed	ADJ
ejpam-6859	31	16	subgroup	subgroup	NOUN
ejpam-6859	31	17	of	of	ADP
ejpam-6859	31	18	g	g	PROPN
ejpam-6859	31	19	of	of	ADP
ejpam-6859	31	20	prime	prime	ADJ
ejpam-6859	31	21	power	power	NOUN
ejpam-6859	31	22	order	order	NOUN
ejpam-6859	31	23	.	.	PUNCT
ejpam-6859	32	1	assume	assume	VERB
ejpam-6859	32	2	k	k	PROPN
ejpam-6859	32	3	≤	≤	ADJ
ejpam-6859	32	4	g	g	NOUN
ejpam-6859	32	5	and	and	CCONJ
ejpam-6859	32	6	n	n	PROPN
ejpam-6859	32	7	⊴	⊴	PROPN
ejpam-6859	32	8	g.	g.	PROPN
ejpam-6859	32	9	then	then	ADV
ejpam-6859	32	10	:	:	PUNCT
ejpam-6859	32	11	(	(	PUNCT
ejpam-6859	32	12	i	i	NOUN
ejpam-6859	32	13	)	)	PUNCT
ejpam-6859	32	14	if	if	SCONJ
ejpam-6859	32	15	h	h	PRON
ejpam-6859	33	1	≤	≤	X
ejpam-6859	34	1	k	k	NOUN
ejpam-6859	34	2	,	,	PUNCT
ejpam-6859	34	3	then	then	ADV
ejpam-6859	34	4	h	h	NOUN
ejpam-6859	34	5	is	be	AUX
ejpam-6859	34	6	weakly	weakly	ADV
ejpam-6859	34	7	closed	closed	ADJ
ejpam-6859	34	8	in	in	ADP
ejpam-6859	34	9	k.	k.	PROPN
ejpam-6859	34	10	(	(	PUNCT
ejpam-6859	34	11	ii	ii	PROPN
ejpam-6859	34	12	)	)	PUNCT
ejpam-6859	35	1	hn	hn	PROPN
ejpam-6859	35	2	/	/	SYM
ejpam-6859	35	3	n	n	PROPN
ejpam-6859	35	4	is	be	AUX
ejpam-6859	35	5	weakly	weakly	ADV
ejpam-6859	35	6	closed	closed	ADJ
ejpam-6859	35	7	in	in	ADP
ejpam-6859	35	8	g	g	PROPN
ejpam-6859	35	9	/	/	SYM
ejpam-6859	35	10	n	n	NOUN
ejpam-6859	35	11	and	and	CCONJ
ejpam-6859	35	12	hn	hn	PROPN
ejpam-6859	35	13	is	be	AUX
ejpam-6859	35	14	weakly	weakly	ADV
ejpam-6859	35	15	closed	closed	ADJ
ejpam-6859	35	16	in	in	ADP
ejpam-6859	36	1	g.	g.	PROPN
ejpam-6859	36	2	(	(	PUNCT
ejpam-6859	36	3	iii	iii	X
ejpam-6859	36	4	)	)	PUNCT
ejpam-6859	36	5	k	k	X
ejpam-6859	36	6	is	be	AUX
ejpam-6859	36	7	weakly	weakly	ADV
ejpam-6859	36	8	closed	closed	ADJ
ejpam-6859	36	9	in	in	ADP
ejpam-6859	36	10	g	g	PROPN
ejpam-6859	36	11	if	if	SCONJ
ejpam-6859	36	12	and	and	CCONJ
ejpam-6859	36	13	only	only	ADV
ejpam-6859	36	14	if	if	SCONJ
ejpam-6859	36	15	k	k	PROPN
ejpam-6859	36	16	/	/	SYM
ejpam-6859	36	17	n	n	PRON
ejpam-6859	36	18	is	be	AUX
ejpam-6859	36	19	weakly	weakly	ADV
ejpam-6859	36	20	closed	closed	ADJ
ejpam-6859	36	21	in	in	ADP
ejpam-6859	36	22	g.	g.	PROPN
ejpam-6859	36	23	lemma	lemma	PROPN
ejpam-6859	37	1	3	3	X
ejpam-6859	37	2	.	.	PUNCT
ejpam-6859	38	1	[	[	X
ejpam-6859	38	2	10	10	NUM
ejpam-6859	38	3	]	]	X
ejpam-6859	38	4	if	if	SCONJ
ejpam-6859	38	5	p	p	NOUN
ejpam-6859	38	6	is	be	AUX
ejpam-6859	38	7	a	a	DET
ejpam-6859	38	8	sylow	sylow	NOUN
ejpam-6859	38	9	p	p	NOUN
ejpam-6859	38	10	-	-	PUNCT
ejpam-6859	38	11	subgroup	subgroup	NOUN
ejpam-6859	38	12	of	of	ADP
ejpam-6859	38	13	a	a	DET
ejpam-6859	38	14	group	group	NOUN
ejpam-6859	38	15	g	g	NOUN
ejpam-6859	38	16	and	and	CCONJ
ejpam-6859	38	17	n	n	PROPN
ejpam-6859	38	18	⊴	⊴	ADP
ejpam-6859	38	19	g	g	ADP
ejpam-6859	38	20	such	such	ADJ
ejpam-6859	38	21	that	that	SCONJ
ejpam-6859	38	22	p	p	PROPN
ejpam-6859	38	23	∩n	∩n	NOUN
ejpam-6859	38	24	≤	≤	PUNCT
ejpam-6859	38	25	φ(p	φ(p	PROPN
ejpam-6859	38	26	)	)	PUNCT
ejpam-6859	38	27	,	,	PUNCT
ejpam-6859	38	28	then	then	ADV
ejpam-6859	38	29	n	n	X
ejpam-6859	38	30	is	be	AUX
ejpam-6859	38	31	p	p	NOUN
ejpam-6859	38	32	-	-	PUNCT
ejpam-6859	38	33	nilpotent	nilpotent	ADJ
ejpam-6859	38	34	.	.	PUNCT
ejpam-6859	39	1	definition	definition	NOUN
ejpam-6859	39	2	1	1	NUM
ejpam-6859	39	3	.	.	PUNCT
ejpam-6859	40	1	[	[	X
ejpam-6859	40	2	11	11	NUM
ejpam-6859	40	3	]	]	PUNCT
ejpam-6859	40	4	let	let	VERB
ejpam-6859	40	5	g	g	PRON
ejpam-6859	40	6	be	be	AUX
ejpam-6859	40	7	a	a	DET
ejpam-6859	40	8	finite	finite	ADJ
ejpam-6859	40	9	group	group	NOUN
ejpam-6859	40	10	,	,	PUNCT
ejpam-6859	40	11	p	p	PROPN
ejpam-6859	40	12	∈	∈	PROPN
ejpam-6859	40	13	sylp(g	sylp(g	PROPN
ejpam-6859	40	14	)	)	PUNCT
ejpam-6859	40	15	,	,	PUNCT
ejpam-6859	40	16	and	and	CCONJ
ejpam-6859	40	17	w	w	ADP
ejpam-6859	40	18	⊆	⊆	NUM
ejpam-6859	40	19	p	p	NOUN
ejpam-6859	40	20	.	.	PUNCT
ejpam-6859	41	1	we	we	PRON
ejpam-6859	41	2	say	say	VERB
ejpam-6859	41	3	that	that	SCONJ
ejpam-6859	41	4	w	w	NOUN
ejpam-6859	41	5	is	be	AUX
ejpam-6859	41	6	weakly	weakly	ADV
ejpam-6859	41	7	closed	closed	ADJ
ejpam-6859	41	8	in	in	ADP
ejpam-6859	41	9	p	p	NOUN
ejpam-6859	41	10	with	with	ADP
ejpam-6859	41	11	respect	respect	NOUN
ejpam-6859	41	12	to	to	ADP
ejpam-6859	41	13	g	g	NOUN
ejpam-6859	41	14	if	if	SCONJ
ejpam-6859	41	15	whenever	whenever	SCONJ
ejpam-6859	41	16	w	w	VERB
ejpam-6859	41	17	g	g	NOUN
ejpam-6859	41	18	⊆	⊆	NUM
ejpam-6859	41	19	p	p	NOUN
ejpam-6859	41	20	for	for	ADP
ejpam-6859	41	21	some	some	DET
ejpam-6859	41	22	g	g	PROPN
ejpam-6859	41	23	∈	∈	PROPN
ejpam-6859	41	24	g	g	NOUN
ejpam-6859	41	25	,	,	PUNCT
ejpam-6859	41	26	it	it	PRON
ejpam-6859	41	27	follows	follow	VERB
ejpam-6859	41	28	that	that	SCONJ
ejpam-6859	41	29	w	w	PROPN
ejpam-6859	41	30	g	g	PROPN
ejpam-6859	41	31	=	=	SYM
ejpam-6859	41	32	w.	w.	NOUN
ejpam-6859	41	33	definition	definition	NOUN
ejpam-6859	41	34	2	2	NUM
ejpam-6859	41	35	.	.	PUNCT
ejpam-6859	42	1	[	[	X
ejpam-6859	42	2	12	12	NUM
ejpam-6859	42	3	]	]	PUNCT
ejpam-6859	42	4	a	a	DET
ejpam-6859	42	5	subgroup	subgroup	NOUN
ejpam-6859	42	6	of	of	ADP
ejpam-6859	42	7	a	a	DET
ejpam-6859	42	8	group	group	NOUN
ejpam-6859	42	9	is	be	AUX
ejpam-6859	42	10	called	call	VERB
ejpam-6859	42	11	a	a	DET
ejpam-6859	42	12	characteristic	characteristic	ADJ
ejpam-6859	42	13	subgroup	subgroup	NOUN
ejpam-6859	42	14	if	if	SCONJ
ejpam-6859	42	15	,	,	PUNCT
ejpam-6859	42	16	for	for	ADP
ejpam-6859	42	17	every	every	DET
ejpam-6859	42	18	automorphism	automorphism	NOUN
ejpam-6859	42	19	of	of	ADP
ejpam-6859	42	20	g	g	NOUN
ejpam-6859	42	21	,	,	PUNCT
ejpam-6859	42	22	one	one	NUM
ejpam-6859	42	23	has	have	VERB
ejpam-6859	42	24	σ(h	σ(h	NOUN
ejpam-6859	42	25	)	)	PUNCT
ejpam-6859	43	1	=	=	SYM
ejpam-6859	43	2	h.	h.	PROPN
ejpam-6859	43	3	lemma	lemma	PROPN
ejpam-6859	43	4	4	4	X
ejpam-6859	43	5	.	.	PUNCT
ejpam-6859	44	1	let	let	VERB
ejpam-6859	44	2	g	g	NOUN
ejpam-6859	44	3	be	be	AUX
ejpam-6859	44	4	an	an	DET
ejpam-6859	44	5	abelian	abelian	ADJ
ejpam-6859	44	6	group	group	NOUN
ejpam-6859	44	7	and	and	CCONJ
ejpam-6859	44	8	h	h	NOUN
ejpam-6859	44	9	⊆	⊆	NUM
ejpam-6859	44	10	g	g	NOUN
ejpam-6859	44	11	has	have	AUX
ejpam-6859	44	12	index	index	NOUN
ejpam-6859	44	13	n.	n.	NOUN
ejpam-6859	44	14	the	the	DET
ejpam-6859	44	15	transfer	transfer	NOUN
ejpam-6859	44	16	homomorphism	homomorphism	NOUN
ejpam-6859	44	17	from	from	ADP
ejpam-6859	44	18	g	g	NOUN
ejpam-6859	44	19	to	to	ADP
ejpam-6859	44	20	h	h	NOUN
ejpam-6859	44	21	is	be	AUX
ejpam-6859	44	22	given	give	VERB
ejpam-6859	44	23	by	by	ADP
ejpam-6859	44	24	the	the	DET
ejpam-6859	44	25	map	map	NOUN
ejpam-6859	44	26	g	g	PROPN
ejpam-6859	44	27	→	→	SYM
ejpam-6859	44	28	gn	gn	PROPN
ejpam-6859	44	29	,	,	PUNCT
ejpam-6859	44	30	i.e.	i.e.	X
ejpam-6859	44	31	,	,	PUNCT
ejpam-6859	44	32	for	for	ADP
ejpam-6859	44	33	each	each	DET
ejpam-6859	44	34	g	g	PROPN
ejpam-6859	44	35	∈	∈	PROPN
ejpam-6859	44	36	g	g	NOUN
ejpam-6859	44	37	,	,	PUNCT
ejpam-6859	44	38	the	the	DET
ejpam-6859	44	39	transfer	transfer	NOUN
ejpam-6859	44	40	homomorphism	homomorphism	NOUN
ejpam-6859	44	41	maps	map	VERB
ejpam-6859	44	42	g	g	PROPN
ejpam-6859	44	43	to	to	ADP
ejpam-6859	44	44	gn	gn	PROPN
ejpam-6859	44	45	.	.	PUNCT
ejpam-6859	44	46	proof	proof	NOUN
ejpam-6859	44	47	.	.	PUNCT
ejpam-6859	45	1	we	we	PRON
ejpam-6859	45	2	need	need	VERB
ejpam-6859	45	3	to	to	PART
ejpam-6859	45	4	show	show	VERB
ejpam-6859	45	5	that	that	SCONJ
ejpam-6859	45	6	the	the	DET
ejpam-6859	45	7	transfer	transfer	NOUN
ejpam-6859	45	8	homomorphism	homomorphism	NOUN
ejpam-6859	45	9	τ	τ	X
ejpam-6859	45	10	:	:	PUNCT
ejpam-6859	45	11	g	g	PROPN
ejpam-6859	45	12	→	→	SYM
ejpam-6859	45	13	h	h	NOUN
ejpam-6859	45	14	is	be	AUX
ejpam-6859	45	15	the	the	DET
ejpam-6859	45	16	map	map	NOUN
ejpam-6859	45	17	g	g	PROPN
ejpam-6859	45	18	→	→	SYM
ejpam-6859	45	19	gn	gn	PROPN
ejpam-6859	45	20	.	.	PROPN
ejpam-6859	46	1	since	since	SCONJ
ejpam-6859	46	2	g	g	PROPN
ejpam-6859	46	3	is	be	AUX
ejpam-6859	46	4	abelian	abelian	ADJ
ejpam-6859	46	5	,	,	PUNCT
ejpam-6859	46	6	conjugation	conjugation	NOUN
ejpam-6859	46	7	by	by	ADP
ejpam-6859	46	8	any	any	DET
ejpam-6859	46	9	element	element	NOUN
ejpam-6859	46	10	of	of	ADP
ejpam-6859	46	11	g	g	PROPN
ejpam-6859	46	12	leaves	leave	VERB
ejpam-6859	46	13	elements	element	NOUN
ejpam-6859	46	14	of	of	ADP
ejpam-6859	46	15	h	h	NOUN
ejpam-6859	46	16	unchanged	unchanged	ADJ
ejpam-6859	46	17	.	.	PUNCT
ejpam-6859	47	1	thus	thus	ADV
ejpam-6859	47	2	,	,	PUNCT
ejpam-6859	47	3	for	for	ADP
ejpam-6859	47	4	all	all	DET
ejpam-6859	47	5	h	h	NOUN
ejpam-6859	47	6	∈	∈	PROPN
ejpam-6859	47	7	h	h	NOUN
ejpam-6859	47	8	,	,	PUNCT
ejpam-6859	47	9	we	we	PRON
ejpam-6859	47	10	have	have	VERB
ejpam-6859	47	11	:	:	PUNCT
ejpam-6859	48	1	ghg−1	ghg−1	PROPN
ejpam-6859	48	2	=	=	SYM
ejpam-6859	48	3	h.	h.	PROPN
ejpam-6859	48	4	now	now	ADV
ejpam-6859	48	5	g	g	PROPN
ejpam-6859	48	6	→	→	SYM
ejpam-6859	48	7	gn	gn	PROPN
ejpam-6859	48	8	.	.	PUNCT
ejpam-6859	49	1	the	the	DET
ejpam-6859	49	2	group	group	NOUN
ejpam-6859	49	3	g	g	PROPN
ejpam-6859	49	4	/	/	SYM
ejpam-6859	49	5	h	h	PROPN
ejpam-6859	49	6	has	have	VERB
ejpam-6859	49	7	index	index	NOUN
ejpam-6859	49	8	n	n	CCONJ
ejpam-6859	49	9	,	,	PUNCT
ejpam-6859	49	10	meaning	mean	VERB
ejpam-6859	49	11	there	there	PRON
ejpam-6859	49	12	are	be	VERB
ejpam-6859	49	13	n	n	DET
ejpam-6859	49	14	cosets	coset	NOUN
ejpam-6859	49	15	of	of	ADP
ejpam-6859	49	16	h	h	NOUN
ejpam-6859	49	17	in	in	ADP
ejpam-6859	49	18	g.	g.	PROPN
ejpam-6859	49	19	the	the	DET
ejpam-6859	49	20	g	g	PROPN
ejpam-6859	49	21	7→	7→	NUM
ejpam-6859	49	22	gn	gn	PROPN
ejpam-6859	49	23	in	in	ADP
ejpam-6859	49	24	the	the	DET
ejpam-6859	49	25	quotient	quotient	NOUN
ejpam-6859	49	26	group	group	NOUN
ejpam-6859	49	27	g	g	PROPN
ejpam-6859	49	28	/	/	SYM
ejpam-6859	49	29	h	h	NOUN
ejpam-6859	49	30	corresponds	correspond	VERB
ejpam-6859	49	31	to	to	ADP
ejpam-6859	49	32	raising	raise	VERB
ejpam-6859	49	33	each	each	DET
ejpam-6859	49	34	element	element	NOUN
ejpam-6859	49	35	to	to	ADP
ejpam-6859	49	36	the	the	DET
ejpam-6859	49	37	power	power	NOUN
ejpam-6859	49	38	of	of	ADP
ejpam-6859	49	39	n.	n.	NOUN
ejpam-6859	49	40	for	for	ADP
ejpam-6859	49	41	each	each	DET
ejpam-6859	49	42	g	g	PROPN
ejpam-6859	49	43	∈	∈	PROPN
ejpam-6859	49	44	g	g	NOUN
ejpam-6859	49	45	,	,	PUNCT
ejpam-6859	49	46	we	we	PRON
ejpam-6859	49	47	have	have	VERB
ejpam-6859	49	48	:	:	PUNCT
ejpam-6859	49	49	gn	gn	PROPN
ejpam-6859	49	50	∈	∈	PROPN
ejpam-6859	49	51	h.	h.	PROPN
ejpam-6859	50	1	thus	thus	ADV
ejpam-6859	50	2	,	,	PUNCT
ejpam-6859	50	3	the	the	DET
ejpam-6859	50	4	transfer	transfer	NOUN
ejpam-6859	50	5	homomorphism	homomorphism	NOUN
ejpam-6859	50	6	maps	map	VERB
ejpam-6859	50	7	each	each	DET
ejpam-6859	50	8	element	element	NOUN
ejpam-6859	50	9	g	g	PROPN
ejpam-6859	50	10	∈	∈	PROPN
ejpam-6859	50	11	g	g	PROPN
ejpam-6859	50	12	to	to	ADP
ejpam-6859	50	13	gn	gn	PROPN
ejpam-6859	50	14	in	in	ADP
ejpam-6859	50	15	h.	h.	PROPN
ejpam-6859	50	16	hence	hence	ADV
ejpam-6859	50	17	,	,	PUNCT
ejpam-6859	50	18	we	we	PRON
ejpam-6859	50	19	conclude	conclude	VERB
ejpam-6859	50	20	that	that	SCONJ
ejpam-6859	50	21	the	the	DET
ejpam-6859	50	22	transfer	transfer	NOUN
ejpam-6859	50	23	homomorphism	homomorphism	NOUN
ejpam-6859	50	24	from	from	ADP
ejpam-6859	50	25	g	g	NOUN
ejpam-6859	50	26	to	to	ADP
ejpam-6859	50	27	h	h	NOUN
ejpam-6859	50	28	is	be	AUX
ejpam-6859	50	29	the	the	DET
ejpam-6859	50	30	map	map	NOUN
ejpam-6859	50	31	g	g	PROPN
ejpam-6859	50	32	→	→	SYM
ejpam-6859	50	33	gn	gn	PROPN
ejpam-6859	50	34	,	,	PUNCT
ejpam-6859	50	35	as	as	SCONJ
ejpam-6859	50	36	required	require	VERB
ejpam-6859	50	37	.	.	PUNCT
ejpam-6859	51	1	lemma	lemma	PROPN
ejpam-6859	51	2	5	5	X
ejpam-6859	51	3	.	.	PUNCT
ejpam-6859	52	1	let	let	VERB
ejpam-6859	52	2	g	g	PRON
ejpam-6859	52	3	be	be	AUX
ejpam-6859	52	4	a	a	DET
ejpam-6859	52	5	group	group	NOUN
ejpam-6859	52	6	and	and	CCONJ
ejpam-6859	52	7	ǵ	ǵ	NOUN
ejpam-6859	52	8	 	 	SPACE
ejpam-6859	52	9	́is	́is	NOUN
ejpam-6859	52	10	commutator	commutator	NOUN
ejpam-6859	52	11	subgroup	subgroup	PROPN
ejpam-6859	52	12	.	.	PUNCT
ejpam-6859	53	1	the	the	DET
ejpam-6859	53	2	transfer	transfer	NOUN
ejpam-6859	53	3	homomorphism	homomorphism	NOUN
ejpam-6859	53	4	v	v	ADP
ejpam-6859	53	5	:	:	PUNCT
ejpam-6859	53	6	g	g	NOUN
ejpam-6859	53	7	→	→	SYM
ejpam-6859	53	8	g	g	NOUN
ejpam-6859	53	9	/	/	SYM
ejpam-6859	53	10	ǵ	ǵ	NOUN
ejpam-6859	53	11	is	be	AUX
ejpam-6859	53	12	the	the	DET
ejpam-6859	53	13	same	same	ADJ
ejpam-6859	53	14	as	as	ADP
ejpam-6859	53	15	the	the	DET
ejpam-6859	53	16	canonical	canonical	ADJ
ejpam-6859	53	17	homomorphism	homomorphism	NOUN
ejpam-6859	53	18	from	from	ADP
ejpam-6859	53	19	g	g	PRON
ejpam-6859	53	20	to	to	ADP
ejpam-6859	53	21	g	g	PROPN
ejpam-6859	53	22	/	/	SYM
ejpam-6859	53	23	ǵ.	ǵ.	NOUN
ejpam-6859	53	24	i.e.	i.e.	X
ejpam-6859	53	25	,	,	PUNCT
ejpam-6859	53	26	v(g	v(g	ADJ
ejpam-6859	53	27	)	)	PUNCT
ejpam-6859	53	28	=	=	SYM
ejpam-6859	53	29	gǵ	gǵ	NOUN
ejpam-6859	53	30	 	 	SPACE
ejpam-6859	53	31	́for	́for	ADP
ejpam-6859	53	32	all	all	DET
ejpam-6859	53	33	g	g	PROPN
ejpam-6859	53	34	∈	∈	PROPN
ejpam-6859	53	35	g.	g.	PROPN
ejpam-6859	53	36	a.	a.	PROPN
ejpam-6859	53	37	m.	m.	PROPN
ejpam-6859	53	38	alotaibi	alotaibi	PROPN
ejpam-6859	53	39	et	et	PROPN
ejpam-6859	53	40	al	al	PROPN
ejpam-6859	53	41	.	.	PUNCT
ejpam-6859	53	42	/	/	SYM
ejpam-6859	53	43	eur	eur	PROPN
ejpam-6859	53	44	.	.	PUNCT
ejpam-6859	54	1	j.	j.	PROPN
ejpam-6859	54	2	pure	pure	PROPN
ejpam-6859	54	3	appl	appl	PROPN
ejpam-6859	54	4	.	.	PROPN
ejpam-6859	54	5	math	math	PROPN
ejpam-6859	54	6	,	,	PUNCT
ejpam-6859	54	7	18	18	NUM
ejpam-6859	54	8	(	(	PUNCT
ejpam-6859	54	9	4	4	NUM
ejpam-6859	54	10	)	)	PUNCT
ejpam-6859	54	11	(	(	PUNCT
ejpam-6859	54	12	2025	2025	NUM
ejpam-6859	54	13	)	)	PUNCT
ejpam-6859	54	14	,	,	PUNCT
ejpam-6859	54	15	6859	6859	NUM
ejpam-6859	54	16	3	3	NUM
ejpam-6859	54	17	of	of	ADP
ejpam-6859	54	18	6	6	NUM
ejpam-6859	54	19	proof	proof	NOUN
ejpam-6859	54	20	.	.	PUNCT
ejpam-6859	55	1	the	the	DET
ejpam-6859	55	2	canonical	canonical	ADJ
ejpam-6859	55	3	homomorphism	homomorphism	NOUN
ejpam-6859	55	4	from	from	ADP
ejpam-6859	55	5	g	g	PRON
ejpam-6859	55	6	to	to	ADP
ejpam-6859	55	7	g	g	NOUN
ejpam-6859	55	8	/	/	SYM
ejpam-6859	55	9	ǵ	ǵ	NOUN
ejpam-6859	55	10	is	be	AUX
ejpam-6859	55	11	defined	define	VERB
ejpam-6859	55	12	by	by	ADP
ejpam-6859	55	13	π(g	π(g	PROPN
ejpam-6859	55	14	)	)	PUNCT
ejpam-6859	55	15	=	=	SYM
ejpam-6859	55	16	gǵ	gǵ	NOUN
ejpam-6859	55	17	for	for	ADP
ejpam-6859	55	18	each	each	DET
ejpam-6859	55	19	g	g	PROPN
ejpam-6859	55	20	∈	∈	PROPN
ejpam-6859	55	21	g.	g.	NOUN
ejpam-6859	56	1	this	this	PRON
ejpam-6859	56	2	is	be	AUX
ejpam-6859	56	3	the	the	DET
ejpam-6859	56	4	natural	natural	ADJ
ejpam-6859	56	5	projection	projection	NOUN
ejpam-6859	56	6	map	map	NOUN
ejpam-6859	56	7	that	that	PRON
ejpam-6859	56	8	sends	send	VERB
ejpam-6859	56	9	each	each	DET
ejpam-6859	56	10	element	element	NOUN
ejpam-6859	56	11	g	g	PROPN
ejpam-6859	56	12	∈	∈	PROPN
ejpam-6859	56	13	g	g	PROPN
ejpam-6859	56	14	to	to	ADP
ejpam-6859	56	15	its	its	PRON
ejpam-6859	56	16	coset	coset	NOUN
ejpam-6859	56	17	in	in	ADP
ejpam-6859	56	18	the	the	DET
ejpam-6859	56	19	quotient	quotient	NOUN
ejpam-6859	56	20	group	group	NOUN
ejpam-6859	56	21	g	g	PROPN
ejpam-6859	56	22	/	/	SYM
ejpam-6859	56	23	ǵ.	ǵ.	NOUN
ejpam-6859	57	1	the	the	DET
ejpam-6859	57	2	transfer	transfer	NOUN
ejpam-6859	57	3	homomorphism	homomorphism	NOUN
ejpam-6859	57	4	v	v	NOUN
ejpam-6859	57	5	from	from	ADP
ejpam-6859	57	6	g	g	PROPN
ejpam-6859	57	7	→	→	SYM
ejpam-6859	57	8	g	g	NOUN
ejpam-6859	57	9	/	/	SYM
ejpam-6859	57	10	ǵ	ǵ	NOUN
ejpam-6859	57	11	is	be	AUX
ejpam-6859	57	12	defined	define	VERB
ejpam-6859	57	13	as	as	ADP
ejpam-6859	57	14	:	:	PUNCT
ejpam-6859	57	15	v(g	v(g	ADJ
ejpam-6859	57	16	)	)	PUNCT
ejpam-6859	57	17	=	=	PUNCT
ejpam-6859	58	1	∑	∑	PUNCT
ejpam-6859	58	2	h∈ǵ	h∈ǵ	PROPN
ejpam-6859	58	3	ghg−1	ghg−1	PROPN
ejpam-6859	58	4	.	.	PUNCT
ejpam-6859	59	1	since	since	SCONJ
ejpam-6859	59	2	ǵ	ǵ	PROPN
ejpam-6859	59	3	is	be	AUX
ejpam-6859	59	4	the	the	DET
ejpam-6859	59	5	commutator	commutator	NOUN
ejpam-6859	59	6	subgroup	subgroup	NOUN
ejpam-6859	59	7	of	of	ADP
ejpam-6859	59	8	g	g	PROPN
ejpam-6859	59	9	,	,	PUNCT
ejpam-6859	59	10	and	and	CCONJ
ejpam-6859	59	11	g	g	NOUN
ejpam-6859	59	12	/	/	SYM
ejpam-6859	59	13	ǵ	ǵ	NOUN
ejpam-6859	59	14	is	be	AUX
ejpam-6859	59	15	abelian	abelian	NOUN
ejpam-6859	59	16	(	(	PUNCT
ejpam-6859	59	17	by	by	ADP
ejpam-6859	59	18	definition	definition	NOUN
ejpam-6859	59	19	of	of	ADP
ejpam-6859	59	20	the	the	DET
ejpam-6859	59	21	commutator	commutator	NOUN
ejpam-6859	59	22	subgroup	subgroup	PROPN
ejpam-6859	59	23	)	)	PUNCT
ejpam-6859	59	24	,	,	PUNCT
ejpam-6859	59	25	the	the	DET
ejpam-6859	59	26	conjugation	conjugation	NOUN
ejpam-6859	59	27	by	by	ADP
ejpam-6859	59	28	any	any	DET
ejpam-6859	59	29	element	element	NOUN
ejpam-6859	59	30	of	of	ADP
ejpam-6859	59	31	g	g	PROPN
ejpam-6859	59	32	leaves	leave	VERB
ejpam-6859	59	33	ǵ	ǵ	PROPN
ejpam-6859	59	34	invariant	invariant	ADJ
ejpam-6859	59	35	.	.	PUNCT
ejpam-6859	60	1	therefore	therefore	ADV
ejpam-6859	60	2	,	,	PUNCT
ejpam-6859	60	3	the	the	DET
ejpam-6859	60	4	action	action	NOUN
ejpam-6859	60	5	of	of	ADP
ejpam-6859	60	6	the	the	DET
ejpam-6859	60	7	transfer	transfer	NOUN
ejpam-6859	60	8	homomorphism	homomorphism	NOUN
ejpam-6859	60	9	v	v	NOUN
ejpam-6859	60	10	on	on	ADP
ejpam-6859	60	11	any	any	DET
ejpam-6859	60	12	g	g	PROPN
ejpam-6859	60	13	∈	∈	PROPN
ejpam-6859	60	14	g	g	NOUN
ejpam-6859	60	15	results	result	NOUN
ejpam-6859	60	16	in	in	ADP
ejpam-6859	60	17	the	the	DET
ejpam-6859	60	18	coset	coset	NOUN
ejpam-6859	60	19	gǵ	gǵ	NOUN
ejpam-6859	60	20	in	in	ADP
ejpam-6859	60	21	g	g	PROPN
ejpam-6859	60	22	/	/	SYM
ejpam-6859	60	23	ǵ.	ǵ.	NOUN
ejpam-6859	60	24	hence	hence	ADV
ejpam-6859	60	25	,	,	PUNCT
ejpam-6859	60	26	we	we	PRON
ejpam-6859	60	27	have	have	VERB
ejpam-6859	60	28	:	:	PUNCT
ejpam-6859	60	29	v(g	v(g	ADJ
ejpam-6859	60	30	)	)	PUNCT
ejpam-6859	60	31	=	=	VERB
ejpam-6859	60	32	gǵ	gǵ	NOUN
ejpam-6859	60	33	for	for	ADP
ejpam-6859	60	34	all	all	PRON
ejpam-6859	60	35	g	g	PROPN
ejpam-6859	60	36	∈	∈	PROPN
ejpam-6859	60	37	g.	g.	NOUN
ejpam-6859	60	38	example	example	NOUN
ejpam-6859	61	1	1	1	X
ejpam-6859	61	2	.	.	PUNCT
ejpam-6859	61	3	let	let	VERB
ejpam-6859	61	4	g	g	PROPN
ejpam-6859	61	5	=	=	PROPN
ejpam-6859	61	6	s3	s3	PROPN
ejpam-6859	61	7	,	,	PUNCT
ejpam-6859	61	8	the	the	DET
ejpam-6859	61	9	symmetric	symmetric	ADJ
ejpam-6859	61	10	group	group	NOUN
ejpam-6859	61	11	on	on	ADP
ejpam-6859	61	12	three	three	NUM
ejpam-6859	61	13	elements	element	NOUN
ejpam-6859	61	14	,	,	PUNCT
ejpam-6859	61	15	which	which	PRON
ejpam-6859	61	16	has	have	VERB
ejpam-6859	61	17	order	order	NOUN
ejpam-6859	61	18	6	6	NUM
ejpam-6859	61	19	.	.	PUNCT
ejpam-6859	62	1	the	the	DET
ejpam-6859	62	2	commutator	commutator	NOUN
ejpam-6859	62	3	subgroup	subgroup	PROPN
ejpam-6859	62	4	h	h	PROPN
ejpam-6859	62	5	of	of	ADP
ejpam-6859	62	6	s3	s3	PROPN
ejpam-6859	62	7	is	be	AUX
ejpam-6859	62	8	the	the	DET
ejpam-6859	62	9	alternating	alternate	VERB
ejpam-6859	62	10	group	group	NOUN
ejpam-6859	62	11	a3	a3	NOUN
ejpam-6859	62	12	,	,	PUNCT
ejpam-6859	62	13	consisting	consist	VERB
ejpam-6859	62	14	of	of	ADP
ejpam-6859	62	15	the	the	DET
ejpam-6859	62	16	even	even	ADJ
ejpam-6859	62	17	permutations	permutation	NOUN
ejpam-6859	62	18	.	.	PUNCT
ejpam-6859	63	1	this	this	DET
ejpam-6859	63	2	subgroup	subgroup	NOUN
ejpam-6859	63	3	has	have	VERB
ejpam-6859	63	4	order	order	NOUN
ejpam-6859	63	5	3	3	NUM
ejpam-6859	63	6	and	and	CCONJ
ejpam-6859	63	7	is	be	AUX
ejpam-6859	63	8	generated	generate	VERB
ejpam-6859	63	9	by	by	ADP
ejpam-6859	63	10	the	the	DET
ejpam-6859	63	11	3	3	NUM
ejpam-6859	63	12	-	-	PUNCT
ejpam-6859	63	13	cycles	cycle	NOUN
ejpam-6859	63	14	(	(	PUNCT
ejpam-6859	63	15	123)(123)(123	123)(123)(123	NUM
ejpam-6859	63	16	)	)	PUNCT
ejpam-6859	63	17	and	and	CCONJ
ejpam-6859	63	18	(	(	PUNCT
ejpam-6859	63	19	132)(132)(132).the	132)(132)(132).the	DET
ejpam-6859	63	20	canonical	canonical	ADJ
ejpam-6859	63	21	homomorphism	homomorphism	NOUN
ejpam-6859	63	22	π	π	X
ejpam-6859	63	23	:	:	PUNCT
ejpam-6859	63	24	g	g	NOUN
ejpam-6859	63	25	→	→	SYM
ejpam-6859	63	26	g	g	NOUN
ejpam-6859	63	27	/	/	SYM
ejpam-6859	63	28	h	h	NOUN
ejpam-6859	63	29	is	be	AUX
ejpam-6859	63	30	defined	define	VERB
ejpam-6859	63	31	by	by	ADP
ejpam-6859	63	32	π(g	π(g	PROPN
ejpam-6859	63	33	)	)	PUNCT
ejpam-6859	63	34	=	=	SYM
ejpam-6859	63	35	gh	gh	PROPN
ejpam-6859	63	36	,	,	PUNCT
ejpam-6859	63	37	which	which	PRON
ejpam-6859	63	38	assigns	assign	VERB
ejpam-6859	63	39	to	to	ADP
ejpam-6859	63	40	each	each	DET
ejpam-6859	63	41	element	element	NOUN
ejpam-6859	63	42	g	g	ADP
ejpam-6859	63	43	the	the	DET
ejpam-6859	63	44	coset	coset	NOUN
ejpam-6859	63	45	of	of	ADP
ejpam-6859	63	46	g	g	NOUN
ejpam-6859	63	47	in	in	ADP
ejpam-6859	63	48	the	the	DET
ejpam-6859	63	49	quotient	quotient	NOUN
ejpam-6859	63	50	group	group	NOUN
ejpam-6859	63	51	g	g	PROPN
ejpam-6859	63	52	/	/	SYM
ejpam-6859	63	53	h.	h.	PROPN
ejpam-6859	63	54	in	in	ADP
ejpam-6859	63	55	this	this	DET
ejpam-6859	63	56	case	case	NOUN
ejpam-6859	63	57	,	,	PUNCT
ejpam-6859	63	58	we	we	PRON
ejpam-6859	63	59	have	have	VERB
ejpam-6859	63	60	g	g	NOUN
ejpam-6859	63	61	/	/	SYM
ejpam-6859	63	62	h	h	NOUN
ejpam-6859	63	63	=	=	SYM
ejpam-6859	63	64	s3	s3	PROPN
ejpam-6859	63	65	/	/	SYM
ejpam-6859	63	66	a3	a3	NOUN
ejpam-6859	63	67	,	,	PUNCT
ejpam-6859	63	68	which	which	PRON
ejpam-6859	63	69	is	be	AUX
ejpam-6859	63	70	isomorphic	isomorphic	ADJ
ejpam-6859	63	71	to	to	ADP
ejpam-6859	63	72	z/2z	z/2z	PROPN
ejpam-6859	63	73	since	since	SCONJ
ejpam-6859	63	74	there	there	PRON
ejpam-6859	63	75	are	be	VERB
ejpam-6859	63	76	exactly	exactly	ADV
ejpam-6859	63	77	two	two	NUM
ejpam-6859	63	78	cosets	coset	NOUN
ejpam-6859	63	79	corresponding	correspond	VERB
ejpam-6859	63	80	to	to	ADP
ejpam-6859	63	81	the	the	DET
ejpam-6859	63	82	parity	parity	NOUN
ejpam-6859	63	83	of	of	ADP
ejpam-6859	63	84	permutations	permutation	NOUN
ejpam-6859	63	85	(	(	PUNCT
ejpam-6859	63	86	even	even	ADV
ejpam-6859	63	87	or	or	CCONJ
ejpam-6859	63	88	odd	odd	ADJ
ejpam-6859	63	89	)	)	PUNCT
ejpam-6859	63	90	.	.	PUNCT
ejpam-6859	64	1	the	the	DET
ejpam-6859	64	2	transfer	transfer	NOUN
ejpam-6859	64	3	homomorphism	homomorphism	NOUN
ejpam-6859	64	4	v	v	ADP
ejpam-6859	64	5	:	:	PUNCT
ejpam-6859	64	6	g	g	NOUN
ejpam-6859	64	7	→	→	SYM
ejpam-6859	64	8	g	g	NOUN
ejpam-6859	64	9	/	/	SYM
ejpam-6859	64	10	h	h	NOUN
ejpam-6859	64	11	can	can	AUX
ejpam-6859	64	12	be	be	AUX
ejpam-6859	64	13	described	describe	VERB
ejpam-6859	64	14	intuitively	intuitively	ADV
ejpam-6859	64	15	as	as	ADP
ejpam-6859	64	16	measuring	measure	VERB
ejpam-6859	64	17	the	the	DET
ejpam-6859	64	18	effect	effect	NOUN
ejpam-6859	64	19	of	of	ADP
ejpam-6859	64	20	conjugation	conjugation	NOUN
ejpam-6859	64	21	on	on	ADP
ejpam-6859	64	22	h.	h.	PROPN
ejpam-6859	64	23	since	since	SCONJ
ejpam-6859	64	24	h	h	PROPN
ejpam-6859	64	25	=	=	NOUN
ejpam-6859	64	26	a3	a3	NOUN
ejpam-6859	64	27	is	be	AUX
ejpam-6859	64	28	a	a	DET
ejpam-6859	64	29	normal	normal	ADJ
ejpam-6859	64	30	subgroup	subgroup	NOUN
ejpam-6859	64	31	and	and	CCONJ
ejpam-6859	64	32	g	g	PROPN
ejpam-6859	64	33	/	/	SYM
ejpam-6859	64	34	h	h	NOUN
ejpam-6859	64	35	is	be	AUX
ejpam-6859	64	36	abelian	abelian	ADJ
ejpam-6859	64	37	,	,	PUNCT
ejpam-6859	64	38	conjugation	conjugation	NOUN
ejpam-6859	64	39	by	by	ADP
ejpam-6859	64	40	any	any	DET
ejpam-6859	64	41	element	element	NOUN
ejpam-6859	64	42	of	of	ADP
ejpam-6859	64	43	g	g	PROPN
ejpam-6859	64	44	leaves	leave	VERB
ejpam-6859	64	45	h	h	PROPN
ejpam-6859	64	46	invariant	invariant	ADJ
ejpam-6859	64	47	.	.	PUNCT
ejpam-6859	65	1	in	in	ADP
ejpam-6859	65	2	practice	practice	NOUN
ejpam-6859	65	3	,	,	PUNCT
ejpam-6859	65	4	for	for	ADP
ejpam-6859	65	5	any	any	DET
ejpam-6859	65	6	g	g	PROPN
ejpam-6859	65	7	∈	∈	PROPN
ejpam-6859	65	8	g	g	NOUN
ejpam-6859	65	9	,	,	PUNCT
ejpam-6859	65	10	the	the	DET
ejpam-6859	65	11	transfer	transfer	NOUN
ejpam-6859	65	12	homomorphism	homomorphism	NOUN
ejpam-6859	65	13	gives	give	VERB
ejpam-6859	65	14	the	the	DET
ejpam-6859	65	15	same	same	ADJ
ejpam-6859	65	16	result	result	NOUN
ejpam-6859	65	17	as	as	ADP
ejpam-6859	65	18	the	the	DET
ejpam-6859	65	19	canonical	canonical	ADJ
ejpam-6859	65	20	projection	projection	NOUN
ejpam-6859	65	21	.	.	PUNCT
ejpam-6859	66	1	now	now	ADV
ejpam-6859	66	2	,	,	PUNCT
ejpam-6859	66	3	if	if	SCONJ
ejpam-6859	66	4	g	g	PROPN
ejpam-6859	66	5	=	=	SYM
ejpam-6859	66	6	(	(	PUNCT
ejpam-6859	66	7	12	12	NUM
ejpam-6859	66	8	)	)	PUNCT
ejpam-6859	66	9	,	,	PUNCT
ejpam-6859	66	10	which	which	PRON
ejpam-6859	66	11	is	be	AUX
ejpam-6859	66	12	an	an	DET
ejpam-6859	66	13	odd	odd	ADJ
ejpam-6859	66	14	permutation	permutation	NOUN
ejpam-6859	66	15	,	,	PUNCT
ejpam-6859	66	16	the	the	DET
ejpam-6859	66	17	image	image	NOUN
ejpam-6859	66	18	under	under	ADP
ejpam-6859	66	19	the	the	DET
ejpam-6859	66	20	transfer	transfer	NOUN
ejpam-6859	66	21	homomorphism	homomorphism	NOUN
ejpam-6859	66	22	is	be	AUX
ejpam-6859	66	23	v((12	v((12	PROPN
ejpam-6859	66	24	)	)	PUNCT
ejpam-6859	66	25	)	)	PUNCT
ejpam-6859	67	1	=	=	PUNCT
ejpam-6859	67	2	(	(	PUNCT
ejpam-6859	67	3	12)h	12)h	NUM
ejpam-6859	67	4	,	,	PUNCT
ejpam-6859	67	5	the	the	DET
ejpam-6859	67	6	coset	coset	NOUN
ejpam-6859	67	7	corresponding	correspond	VERB
ejpam-6859	67	8	to	to	ADP
ejpam-6859	67	9	odd	odd	ADJ
ejpam-6859	67	10	permutations	permutation	NOUN
ejpam-6859	67	11	.	.	PUNCT
ejpam-6859	68	1	this	this	DET
ejpam-6859	68	2	exactly	exactly	ADV
ejpam-6859	68	3	matches	match	NOUN
ejpam-6859	68	4	π(12	π(12	NOUN
ejpam-6859	68	5	)	)	PUNCT
ejpam-6859	68	6	.	.	PUNCT
ejpam-6859	69	1	therefore	therefore	ADV
ejpam-6859	69	2	,	,	PUNCT
ejpam-6859	69	3	in	in	ADP
ejpam-6859	69	4	this	this	DET
ejpam-6859	69	5	example	example	NOUN
ejpam-6859	69	6	,	,	PUNCT
ejpam-6859	69	7	the	the	DET
ejpam-6859	69	8	transfer	transfer	NOUN
ejpam-6859	69	9	homomorphism	homomorphism	NOUN
ejpam-6859	69	10	v	v	ADP
ejpam-6859	69	11	coincides	coincide	NOUN
ejpam-6859	69	12	with	with	ADP
ejpam-6859	69	13	the	the	DET
ejpam-6859	69	14	canonical	canonical	ADJ
ejpam-6859	69	15	homomorphism	homomorphism	NOUN
ejpam-6859	69	16	π	π	X
ejpam-6859	69	17	.	.	PUNCT
ejpam-6859	70	1	both	both	CCONJ
ejpam-6859	70	2	the	the	DET
ejpam-6859	70	3	transfer	transfer	NOUN
ejpam-6859	70	4	homomorphism	homomorphism	NOUN
ejpam-6859	70	5	v	v	NOUN
ejpam-6859	70	6	and	and	CCONJ
ejpam-6859	70	7	the	the	DET
ejpam-6859	70	8	canonical	canonical	ADJ
ejpam-6859	70	9	homomorphism	homomorphism	NOUN
ejpam-6859	70	10	π	π	X
ejpam-6859	70	11	map	map	NOUN
ejpam-6859	70	12	(	(	PUNCT
ejpam-6859	70	13	12	12	NUM
ejpam-6859	70	14	)	)	PUNCT
ejpam-6859	70	15	to	to	ADP
ejpam-6859	70	16	the	the	DET
ejpam-6859	70	17	same	same	ADJ
ejpam-6859	70	18	coset	coset	NOUN
ejpam-6859	70	19	,	,	PUNCT
ejpam-6859	70	20	which	which	PRON
ejpam-6859	70	21	is	be	AUX
ejpam-6859	70	22	(	(	PUNCT
ejpam-6859	70	23	12)a3	12)a3	NUM
ejpam-6859	70	24	.	.	NOUN
ejpam-6859	70	25	2	2	NUM
ejpam-6859	70	26	.	.	X
ejpam-6859	70	27	main	main	ADJ
ejpam-6859	70	28	results	result	NOUN
ejpam-6859	70	29	in	in	ADP
ejpam-6859	70	30	this	this	DET
ejpam-6859	70	31	section	section	NOUN
ejpam-6859	71	1	,	,	PUNCT
ejpam-6859	71	2	we	we	PRON
ejpam-6859	71	3	present	present	VERB
ejpam-6859	71	4	the	the	DET
ejpam-6859	71	5	core	core	ADJ
ejpam-6859	71	6	theorems	theorem	NOUN
ejpam-6859	71	7	that	that	PRON
ejpam-6859	71	8	connect	connect	VERB
ejpam-6859	71	9	the	the	DET
ejpam-6859	71	10	transfer	transfer	NOUN
ejpam-6859	71	11	homomorphism	homomorphism	NOUN
ejpam-6859	71	12	and	and	CCONJ
ejpam-6859	71	13	the	the	DET
ejpam-6859	71	14	weak	weak	ADJ
ejpam-6859	71	15	closure	closure	NOUN
ejpam-6859	71	16	property	property	NOUN
ejpam-6859	71	17	within	within	ADP
ejpam-6859	71	18	sylow	sylow	NOUN
ejpam-6859	71	19	subgroups	subgroup	NOUN
ejpam-6859	71	20	.	.	PUNCT
ejpam-6859	72	1	these	these	DET
ejpam-6859	72	2	results	result	NOUN
ejpam-6859	72	3	provide	provide	VERB
ejpam-6859	72	4	explicit	explicit	ADJ
ejpam-6859	72	5	criteria	criterion	NOUN
ejpam-6859	72	6	for	for	ADP
ejpam-6859	72	7	identifying	identify	VERB
ejpam-6859	72	8	weakly	weakly	ADJ
ejpam-6859	72	9	closed	closed	ADJ
ejpam-6859	72	10	subgroups	subgroup	NOUN
ejpam-6859	72	11	and	and	CCONJ
ejpam-6859	72	12	reveal	reveal	VERB
ejpam-6859	72	13	their	their	PRON
ejpam-6859	72	14	structural	structural	ADJ
ejpam-6859	72	15	role	role	NOUN
ejpam-6859	72	16	in	in	ADP
ejpam-6859	72	17	finite	finite	PROPN
ejpam-6859	72	18	group	group	NOUN
ejpam-6859	72	19	theory	theory	NOUN
ejpam-6859	72	20	.	.	PUNCT
ejpam-6859	73	1	lemma	lemma	PROPN
ejpam-6859	73	2	6	6	NUM
ejpam-6859	73	3	.	.	PUNCT
ejpam-6859	74	1	let	let	VERB
ejpam-6859	74	2	g	g	PRON
ejpam-6859	74	3	be	be	AUX
ejpam-6859	74	4	a	a	DET
ejpam-6859	74	5	finite	finite	ADJ
ejpam-6859	74	6	group	group	NOUN
ejpam-6859	74	7	,	,	PUNCT
ejpam-6859	74	8	p	p	PROPN
ejpam-6859	74	9	∈	∈	PROPN
ejpam-6859	74	10	sylp(g	sylp(g	PROPN
ejpam-6859	74	11	)	)	PUNCT
ejpam-6859	74	12	,	,	PUNCT
ejpam-6859	74	13	p	p	NOUN
ejpam-6859	74	14	be	be	AUX
ejpam-6859	74	15	a	a	DET
ejpam-6859	74	16	sylow	sylow	NOUN
ejpam-6859	74	17	p	p	NOUN
ejpam-6859	74	18	-	-	PUNCT
ejpam-6859	74	19	subgroup	subgroup	NOUN
ejpam-6859	74	20	of	of	ADP
ejpam-6859	74	21	g	g	PROPN
ejpam-6859	74	22	,	,	PUNCT
ejpam-6859	74	23	and	and	CCONJ
ejpam-6859	74	24	suppose	suppose	VERB
ejpam-6859	74	25	g	g	PROPN
ejpam-6859	74	26	∈	∈	PROPN
ejpam-6859	74	27	g	g	PROPN
ejpam-6859	74	28	has	have	VERB
ejpam-6859	74	29	order	order	NOUN
ejpam-6859	74	30	p	p	X
ejpam-6859	74	31	,	,	PUNCT
ejpam-6859	74	32	g	g	PROPN
ejpam-6859	74	33	∈	∈	PROPN
ejpam-6859	74	34	ǵ(the	ǵ(the	PRON
ejpam-6859	74	35	commutator	commutator	NOUN
ejpam-6859	74	36	subgroup	subgroup	NOUN
ejpam-6859	74	37	of	of	ADP
ejpam-6859	74	38	g	g	PROPN
ejpam-6859	74	39	)	)	PUNCT
ejpam-6859	74	40	,	,	PUNCT
ejpam-6859	74	41	and	and	CCONJ
ejpam-6859	75	1	g	g	PROPN
ejpam-6859	75	2	/∈	/∈	PUNCT
ejpam-6859	76	1	ṕ	ṕ	NOUN
ejpam-6859	76	2	(	(	PUNCT
ejpam-6859	76	3	the	the	DET
ejpam-6859	76	4	commutator	commutator	NOUN
ejpam-6859	76	5	subgroup	subgroup	NOUN
ejpam-6859	76	6	of	of	ADP
ejpam-6859	76	7	p	p	PROPN
ejpam-6859	76	8	)	)	PUNCT
ejpam-6859	76	9	.	.	PUNCT
ejpam-6859	77	1	then	then	ADV
ejpam-6859	77	2	there	there	PRON
ejpam-6859	77	3	exists	exist	VERB
ejpam-6859	77	4	an	an	DET
ejpam-6859	77	5	element	element	NOUN
ejpam-6859	77	6	i	i	PRON
ejpam-6859	77	7	∈	∈	PROPN
ejpam-6859	77	8	g	g	NOUN
ejpam-6859	77	9	such	such	ADJ
ejpam-6859	77	10	that	that	SCONJ
ejpam-6859	77	11	i	i	PRON
ejpam-6859	77	12	∈	∈	PROPN
ejpam-6859	78	1	ṕand	ṕand	INTJ
ejpam-6859	79	1	i	i	PRON
ejpam-6859	79	2	/∈	/∈	PUNCT
ejpam-6859	80	1	p	p	X
ejpam-6859	80	2	.	.	PUNCT
ejpam-6859	81	1	proof	proof	NOUN
ejpam-6859	81	2	.	.	PUNCT
ejpam-6859	82	1	let	let	VERB
ejpam-6859	82	2	u	u	PRON
ejpam-6859	82	3	:	:	PUNCT
ejpam-6859	82	4	g	g	PROPN
ejpam-6859	82	5	→	→	SYM
ejpam-6859	82	6	p	p	X
ejpam-6859	82	7	/	/	SYM
ejpam-6859	82	8	ṕ	ṕ	NOUN
ejpam-6859	82	9	be	be	AUX
ejpam-6859	82	10	the	the	DET
ejpam-6859	82	11	transfer	transfer	NOUN
ejpam-6859	82	12	homomorphism	homomorphism	NOUN
ejpam-6859	82	13	from	from	ADP
ejpam-6859	82	14	g	g	PRON
ejpam-6859	82	15	to	to	ADP
ejpam-6859	82	16	p	p	X
ejpam-6859	82	17	/	/	SYM
ejpam-6859	82	18	ṕ	ṕ	NOUN
ejpam-6859	82	19	.	.	PUNCT
ejpam-6859	83	1	since	since	SCONJ
ejpam-6859	83	2	g	g	PROPN
ejpam-6859	83	3	∈	∈	PROPN
ejpam-6859	83	4	ǵ	ǵ	PROPN
ejpam-6859	83	5	and	and	CCONJ
ejpam-6859	83	6	g	g	NOUN
ejpam-6859	83	7	/∈	/∈	PUNCT
ejpam-6859	84	1	ṕ	ṕ	NOUN
ejpam-6859	84	2	it	it	PRON
ejpam-6859	84	3	follows	follow	VERB
ejpam-6859	84	4	that	that	SCONJ
ejpam-6859	84	5	g	g	PROPN
ejpam-6859	84	6	∈	∈	PROPN
ejpam-6859	84	7	ker(u	ker(u	PROPN
ejpam-6859	84	8	)	)	PUNCT
ejpam-6859	84	9	,	,	PUNCT
ejpam-6859	84	10	meaning	mean	VERB
ejpam-6859	84	11	u(g	u(g	PROPN
ejpam-6859	84	12	)	)	PUNCT
ejpam-6859	84	13	=	=	SYM
ejpam-6859	84	14	0	0	NUM
ejpam-6859	85	1	in	in	ADP
ejpam-6859	85	2	p	p	X
ejpam-6859	85	3	/	/	X
ejpam-6859	85	4	ṕ	ṕ	NOUN
ejpam-6859	85	5	.	.	PUNCT
ejpam-6859	86	1	by	by	ADP
ejpam-6859	86	2	the	the	DET
ejpam-6859	86	3	pretransfer	pretransfer	NOUN
ejpam-6859	86	4	map	map	NOUN
ejpam-6859	86	5	v	v	ADP
ejpam-6859	86	6	,	,	PUNCT
ejpam-6859	86	7	we	we	PRON
ejpam-6859	86	8	then	then	ADV
ejpam-6859	86	9	have	have	VERB
ejpam-6859	86	10	v	v	NOUN
ejpam-6859	86	11	(	(	PUNCT
ejpam-6859	86	12	g	g	NOUN
ejpam-6859	86	13	)	)	PUNCT
ejpam-6859	86	14	∈	∈	PROPN
ejpam-6859	86	15	ṕ	ṕ	NOUN
ejpam-6859	86	16	.	.	PUNCT
ejpam-6859	87	1	since	since	SCONJ
ejpam-6859	87	2	g	g	PROPN
ejpam-6859	87	3	/∈	/∈	PUNCT
ejpam-6859	88	1	ṕ	ṕ	NOUN
ejpam-6859	88	2	,	,	PUNCT
ejpam-6859	88	3	it	it	PRON
ejpam-6859	88	4	follows	follow	VERB
ejpam-6859	88	5	thatv	thatv	PROPN
ejpam-6859	88	6	(	(	PUNCT
ejpam-6859	88	7	g	g	NOUN
ejpam-6859	88	8	)	)	PUNCT
ejpam-6859	88	9	/∈	/∈	PUNCT
ejpam-6859	89	1	p	p	X
ejpam-6859	89	2	.	.	PUNCT
ejpam-6859	90	1	therefore	therefore	ADV
ejpam-6859	90	2	,	,	PUNCT
ejpam-6859	90	3	there	there	PRON
ejpam-6859	90	4	exists	exist	VERB
ejpam-6859	90	5	an	an	DET
ejpam-6859	90	6	element	element	NOUN
ejpam-6859	90	7	i	i	NOUN
ejpam-6859	90	8	=	=	SYM
ejpam-6859	90	9	v	v	ADJ
ejpam-6859	90	10	(	(	PUNCT
ejpam-6859	90	11	g	g	NOUN
ejpam-6859	90	12	)	)	PUNCT
ejpam-6859	90	13	∈	∈	PROPN
ejpam-6859	91	1	g	g	NOUN
ejpam-6859	91	2	such	such	ADJ
ejpam-6859	91	3	that	that	SCONJ
ejpam-6859	92	1	i	i	PRON
ejpam-6859	92	2	∈	∈	VERB
ejpam-6859	93	1	ṕ	ṕ	NOUN
ejpam-6859	94	1	but	but	CCONJ
ejpam-6859	94	2	i	i	PRON
ejpam-6859	94	3	/∈	/∈	VERB
ejpam-6859	95	1	p	p	X
ejpam-6859	95	2	,	,	PUNCT
ejpam-6859	95	3	completing	complete	VERB
ejpam-6859	95	4	the	the	DET
ejpam-6859	95	5	proof	proof	NOUN
ejpam-6859	95	6	.	.	PUNCT
ejpam-6859	96	1	a.	a.	PROPN
ejpam-6859	96	2	m.	m.	PROPN
ejpam-6859	96	3	alotaibi	alotaibi	PROPN
ejpam-6859	96	4	et	et	PROPN
ejpam-6859	96	5	al	al	PROPN
ejpam-6859	96	6	.	.	PUNCT
ejpam-6859	96	7	/	/	SYM
ejpam-6859	96	8	eur	eur	PROPN
ejpam-6859	96	9	.	.	PUNCT
ejpam-6859	97	1	j.	j.	PROPN
ejpam-6859	97	2	pure	pure	PROPN
ejpam-6859	97	3	appl	appl	PROPN
ejpam-6859	97	4	.	.	PROPN
ejpam-6859	97	5	math	math	PROPN
ejpam-6859	97	6	,	,	PUNCT
ejpam-6859	97	7	18	18	NUM
ejpam-6859	97	8	(	(	PUNCT
ejpam-6859	97	9	4	4	NUM
ejpam-6859	97	10	)	)	PUNCT
ejpam-6859	97	11	(	(	PUNCT
ejpam-6859	97	12	2025	2025	NUM
ejpam-6859	97	13	)	)	PUNCT
ejpam-6859	97	14	,	,	PUNCT
ejpam-6859	97	15	6859	6859	NUM
ejpam-6859	97	16	4	4	NUM
ejpam-6859	97	17	of	of	ADP
ejpam-6859	97	18	6	6	NUM
ejpam-6859	97	19	example	example	NOUN
ejpam-6859	97	20	2	2	NUM
ejpam-6859	97	21	.	.	X
ejpam-6859	97	22	consider	consider	VERB
ejpam-6859	97	23	the	the	DET
ejpam-6859	97	24	symmetric	symmetric	ADJ
ejpam-6859	97	25	group	group	PROPN
ejpam-6859	97	26	s5	s5	PROPN
ejpam-6859	97	27	,	,	PUNCT
ejpam-6859	97	28	the	the	DET
ejpam-6859	97	29	group	group	NOUN
ejpam-6859	97	30	of	of	ADP
ejpam-6859	97	31	all	all	DET
ejpam-6859	97	32	permutations	permutation	NOUN
ejpam-6859	97	33	on	on	ADP
ejpam-6859	97	34	5	5	NUM
ejpam-6859	97	35	elements	element	NOUN
ejpam-6859	97	36	.	.	PUNCT
ejpam-6859	98	1	let	let	VERB
ejpam-6859	98	2	p	p	NOUN
ejpam-6859	98	3	=	=	NOUN
ejpam-6859	98	4	2	2	NUM
ejpam-6859	98	5	,	,	PUNCT
ejpam-6859	98	6	so	so	SCONJ
ejpam-6859	98	7	we	we	PRON
ejpam-6859	98	8	are	be	AUX
ejpam-6859	98	9	interested	interested	ADJ
ejpam-6859	98	10	in	in	ADP
ejpam-6859	98	11	sylow	sylow	NOUN
ejpam-6859	98	12	2	2	NUM
ejpam-6859	98	13	-	-	PUNCT
ejpam-6859	98	14	subgroups	subgroup	NOUN
ejpam-6859	98	15	of	of	ADP
ejpam-6859	98	16	s5	s5	PROPN
ejpam-6859	98	17	.	.	PUNCT
ejpam-6859	99	1	the	the	DET
ejpam-6859	99	2	order	order	NOUN
ejpam-6859	99	3	of	of	ADP
ejpam-6859	99	4	a	a	DET
ejpam-6859	99	5	sylow	sylow	NOUN
ejpam-6859	99	6	2	2	NUM
ejpam-6859	99	7	-	-	PUNCT
ejpam-6859	99	8	subgroup	subgroup	NOUN
ejpam-6859	99	9	of	of	ADP
ejpam-6859	99	10	s5	s5	PROPN
ejpam-6859	99	11	is	be	AUX
ejpam-6859	99	12	the	the	DET
ejpam-6859	99	13	highest	high	ADJ
ejpam-6859	99	14	power	power	NOUN
ejpam-6859	99	15	of	of	ADP
ejpam-6859	99	16	2	2	NUM
ejpam-6859	99	17	dividing	divide	VERB
ejpam-6859	99	18	120	120	NUM
ejpam-6859	99	19	,	,	PUNCT
ejpam-6859	99	20	which	which	PRON
ejpam-6859	99	21	is	be	AUX
ejpam-6859	99	22	8	8	NUM
ejpam-6859	99	23	.	.	PUNCT
ejpam-6859	100	1	hence	hence	ADV
ejpam-6859	100	2	,	,	PUNCT
ejpam-6859	100	3	the	the	DET
ejpam-6859	100	4	sylow	sylow	NOUN
ejpam-6859	100	5	2	2	NUM
ejpam-6859	100	6	-	-	PUNCT
ejpam-6859	100	7	subgroups	subgroup	NOUN
ejpam-6859	100	8	of	of	ADP
ejpam-6859	100	9	s5	s5	PROPN
ejpam-6859	100	10	have	have	VERB
ejpam-6859	100	11	order	order	NOUN
ejpam-6859	100	12	8	8	NUM
ejpam-6859	100	13	.	.	PUNCT
ejpam-6859	101	1	the	the	DET
ejpam-6859	101	2	commutator	commutator	NOUN
ejpam-6859	101	3	subgroup	subgroup	PROPN
ejpam-6859	101	4	ǵ	ǵ	PROPN
ejpam-6859	101	5	of	of	ADP
ejpam-6859	101	6	s5	s5	PROPN
ejpam-6859	101	7	is	be	AUX
ejpam-6859	101	8	the	the	DET
ejpam-6859	101	9	alternating	alternate	VERB
ejpam-6859	101	10	group	group	NOUN
ejpam-6859	101	11	a5	a5	PROPN
ejpam-6859	101	12	,	,	PUNCT
ejpam-6859	101	13	consisting	consist	VERB
ejpam-6859	101	14	of	of	ADP
ejpam-6859	101	15	all	all	DET
ejpam-6859	101	16	even	even	ADV
ejpam-6859	101	17	permutations	permutation	NOUN
ejpam-6859	101	18	.	.	PUNCT
ejpam-6859	102	1	the	the	DET
ejpam-6859	102	2	order	order	NOUN
ejpam-6859	102	3	of	of	ADP
ejpam-6859	102	4	a5	a5	PROPN
ejpam-6859	102	5	is	be	AUX
ejpam-6859	102	6	60	60	NUM
ejpam-6859	102	7	.	.	PUNCT
ejpam-6859	103	1	consider	consider	VERB
ejpam-6859	103	2	the	the	DET
ejpam-6859	103	3	permutation	permutation	NOUN
ejpam-6859	103	4	g	g	NOUN
ejpam-6859	103	5	=	=	SYM
ejpam-6859	103	6	(	(	PUNCT
ejpam-6859	103	7	12)(34	12)(34	NUM
ejpam-6859	103	8	)	)	PUNCT
ejpam-6859	103	9	,	,	PUNCT
ejpam-6859	103	10	which	which	PRON
ejpam-6859	103	11	swaps	swap	VERB
ejpam-6859	103	12	elements	element	NOUN
ejpam-6859	103	13	1	1	NUM
ejpam-6859	103	14	with	with	ADP
ejpam-6859	103	15	2	2	NUM
ejpam-6859	103	16	and	and	CCONJ
ejpam-6859	103	17	3	3	NUM
ejpam-6859	103	18	with	with	ADP
ejpam-6859	103	19	4	4	NUM
ejpam-6859	103	20	.	.	PUNCT
ejpam-6859	104	1	this	this	DET
ejpam-6859	104	2	permutation	permutation	NOUN
ejpam-6859	104	3	has	have	VERB
ejpam-6859	104	4	order	order	NOUN
ejpam-6859	104	5	2	2	NUM
ejpam-6859	104	6	,	,	PUNCT
ejpam-6859	104	7	and	and	CCONJ
ejpam-6859	104	8	since	since	SCONJ
ejpam-6859	104	9	it	it	PRON
ejpam-6859	104	10	is	be	AUX
ejpam-6859	104	11	an	an	DET
ejpam-6859	104	12	even	even	ADJ
ejpam-6859	104	13	permutation	permutation	NOUN
ejpam-6859	104	14	,	,	PUNCT
ejpam-6859	104	15	we	we	PRON
ejpam-6859	104	16	know	know	VERB
ejpam-6859	104	17	g	g	PROPN
ejpam-6859	104	18	∈	∈	PROPN
ejpam-6859	104	19	a5	a5	PROPN
ejpam-6859	104	20	=	=	PUNCT
ejpam-6859	104	21	ǵ.	ǵ.	NOUN
ejpam-6859	104	22	suppose	suppose	VERB
ejpam-6859	104	23	we	we	PRON
ejpam-6859	104	24	consider	consider	VERB
ejpam-6859	104	25	the	the	DET
ejpam-6859	104	26	sylow	sylow	NOUN
ejpam-6859	104	27	2	2	NUM
ejpam-6859	104	28	-	-	PUNCT
ejpam-6859	104	29	subgroup	subgroup	NOUN
ejpam-6859	104	30	p	p	NOUN
ejpam-6859	104	31	=	=	PUNCT
ejpam-6859	104	32	〈	〈	PROPN
ejpam-6859	104	33	(	(	PUNCT
ejpam-6859	104	34	12)(34	12)(34	NUM
ejpam-6859	104	35	)	)	PUNCT
ejpam-6859	104	36	,	,	PUNCT
ejpam-6859	104	37	(	(	PUNCT
ejpam-6859	104	38	13)(24	13)(24	NUM
ejpam-6859	104	39	)	)	PUNCT
ejpam-6859	104	40	,	,	PUNCT
ejpam-6859	104	41	(	(	PUNCT
ejpam-6859	104	42	14)(23	14)(23	NOUN
ejpam-6859	104	43	)	)	PUNCT
ejpam-6859	104	44	〉	〉	PROPN
ejpam-6859	104	45	,	,	PUNCT
ejpam-6859	104	46	a	a	DET
ejpam-6859	104	47	group	group	NOUN
ejpam-6859	104	48	of	of	ADP
ejpam-6859	104	49	order	order	NOUN
ejpam-6859	104	50	8	8	NUM
ejpam-6859	104	51	.	.	PUNCT
ejpam-6859	105	1	the	the	DET
ejpam-6859	105	2	commutator	commutator	NOUN
ejpam-6859	105	3	subgroup	subgroup	NOUN
ejpam-6859	105	4	of	of	ADP
ejpam-6859	105	5	p	p	PROPN
ejpam-6859	105	6	,	,	PUNCT
ejpam-6859	105	7	denoted	denote	VERB
ejpam-6859	105	8	ṕ	ṕ	NOUN
ejpam-6859	105	9	,	,	PUNCT
ejpam-6859	105	10	consists	consist	VERB
ejpam-6859	105	11	of	of	ADP
ejpam-6859	105	12	the	the	DET
ejpam-6859	105	13	commutators	commutator	NOUN
ejpam-6859	105	14	of	of	ADP
ejpam-6859	105	15	elements	element	NOUN
ejpam-6859	105	16	of	of	ADP
ejpam-6859	105	17	p	p	PROPN
ejpam-6859	105	18	.	.	PUNCT
ejpam-6859	106	1	however	however	ADV
ejpam-6859	106	2	,	,	PUNCT
ejpam-6859	106	3	g	g	PROPN
ejpam-6859	106	4	=	=	SYM
ejpam-6859	106	5	(	(	PUNCT
ejpam-6859	106	6	12)(34	12)(34	NUM
ejpam-6859	106	7	)	)	PUNCT
ejpam-6859	106	8	is	be	AUX
ejpam-6859	106	9	not	not	PART
ejpam-6859	106	10	in	in	ADP
ejpam-6859	106	11	ṕ	ṕ	NOUN
ejpam-6859	106	12	,	,	PUNCT
ejpam-6859	106	13	because	because	SCONJ
ejpam-6859	106	14	it	it	PRON
ejpam-6859	106	15	can	can	AUX
ejpam-6859	106	16	not	not	PART
ejpam-6859	106	17	be	be	AUX
ejpam-6859	106	18	written	write	VERB
ejpam-6859	106	19	as	as	ADP
ejpam-6859	106	20	a	a	DET
ejpam-6859	106	21	commutator	commutator	NOUN
ejpam-6859	106	22	of	of	ADP
ejpam-6859	106	23	elements	element	NOUN
ejpam-6859	106	24	of	of	ADP
ejpam-6859	106	25	p	p	NOUN
ejpam-6859	106	26	due	due	ADP
ejpam-6859	106	27	to	to	ADP
ejpam-6859	106	28	the	the	DET
ejpam-6859	106	29	structure	structure	NOUN
ejpam-6859	106	30	of	of	ADP
ejpam-6859	106	31	p	p	PROPN
ejpam-6859	106	32	.	.	PUNCT
ejpam-6859	107	1	according	accord	VERB
ejpam-6859	107	2	lemma	lemma	PROPN
ejpam-6859	107	3	6	6	NUM
ejpam-6859	107	4	,	,	PUNCT
ejpam-6859	107	5	there	there	PRON
ejpam-6859	107	6	must	must	AUX
ejpam-6859	107	7	exist	exist	VERB
ejpam-6859	107	8	an	an	DET
ejpam-6859	107	9	element	element	NOUN
ejpam-6859	107	10	i	i	PRON
ejpam-6859	107	11	∈	∈	PROPN
ejpam-6859	107	12	gi	gi	VERB
ejpam-6859	108	1	such	such	ADJ
ejpam-6859	108	2	that	that	SCONJ
ejpam-6859	108	3	i	i	PRON
ejpam-6859	108	4	∈	∈	PROPN
ejpam-6859	108	5	ṕ	ṕ	VERB
ejpam-6859	108	6	i	i	PRON
ejpam-6859	108	7	in	in	ADP
ejpam-6859	108	8	ṕ	ṕ	PROPN
ejpam-6859	109	1	i	i	NOUN
ejpam-6859	109	2	∈	∈	PROPN
ejpam-6859	110	1	ṕ	ṕ	NOUN
ejpam-6859	111	1	but	but	CCONJ
ejpam-6859	111	2	i	i	PRON
ejpam-6859	111	3	/∈	/∈	PUNCT
ejpam-6859	112	1	pi	pi	PROPN
ejpam-6859	112	2	notin	notin	PROPN
ejpam-6859	112	3	pi	pi	PROPN
ejpam-6859	112	4	/∈	/∈	PUNCT
ejpam-6859	113	1	p	p	X
ejpam-6859	113	2	.	.	PUNCT
ejpam-6859	114	1	in	in	ADP
ejpam-6859	114	2	this	this	DET
ejpam-6859	114	3	case	case	NOUN
ejpam-6859	114	4	,	,	PUNCT
ejpam-6859	114	5	the	the	DET
ejpam-6859	114	6	element	element	NOUN
ejpam-6859	114	7	i	i	PRON
ejpam-6859	114	8	that	that	PRON
ejpam-6859	114	9	satisfies	satisfy	VERB
ejpam-6859	114	10	this	this	PRON
ejpam-6859	114	11	is	be	AUX
ejpam-6859	114	12	i	i	PRON
ejpam-6859	114	13	=	=	PUNCT
ejpam-6859	114	14	(	(	PUNCT
ejpam-6859	114	15	12)(34	12)(34	NUM
ejpam-6859	114	16	)	)	PUNCT
ejpam-6859	114	17	,	,	PUNCT
ejpam-6859	114	18	which	which	PRON
ejpam-6859	114	19	lies	lie	VERB
ejpam-6859	114	20	in	in	ADP
ejpam-6859	114	21	ǵ	ǵ	PROPN
ejpam-6859	114	22	=	=	PUNCT
ejpam-6859	114	23	a5	a5	PROPN
ejpam-6859	114	24	but	but	CCONJ
ejpam-6859	114	25	not	not	PART
ejpam-6859	114	26	in	in	ADP
ejpam-6859	114	27	p	p	NOUN
ejpam-6859	114	28	,	,	PUNCT
ejpam-6859	114	29	and	and	CCONJ
ejpam-6859	115	1	i	i	PRON
ejpam-6859	115	2	∈	∈	PROPN
ejpam-6859	115	3	ṕ	ṕ	VERB
ejpam-6859	115	4	i	i	PRON
ejpam-6859	115	5	,	,	PUNCT
ejpam-6859	115	6	since	since	SCONJ
ejpam-6859	115	7	g	g	PROPN
ejpam-6859	115	8	∈	∈	PROPN
ejpam-6859	115	9	ǵ.	ǵ.	NOUN
ejpam-6859	115	10	proposition	proposition	NOUN
ejpam-6859	115	11	1	1	X
ejpam-6859	115	12	.	.	PUNCT
ejpam-6859	116	1	let	let	VERB
ejpam-6859	116	2	g	g	PRON
ejpam-6859	116	3	be	be	AUX
ejpam-6859	116	4	a	a	DET
ejpam-6859	116	5	group	group	NOUN
ejpam-6859	116	6	,	,	PUNCT
ejpam-6859	116	7	and	and	CCONJ
ejpam-6859	116	8	let	let	VERB
ejpam-6859	116	9	ǵdenote	ǵdenote	VERB
ejpam-6859	116	10	its	its	PRON
ejpam-6859	116	11	commutator	commutator	NOUN
ejpam-6859	116	12	subgroup	subgroup	NOUN
ejpam-6859	116	13	.	.	PUNCT
ejpam-6859	117	1	the	the	DET
ejpam-6859	117	2	transfer	transfer	NOUN
ejpam-6859	117	3	homomorphism	homomorphism	NOUN
ejpam-6859	117	4	v	v	ADP
ejpam-6859	117	5	:	:	PUNCT
ejpam-6859	117	6	g	g	NOUN
ejpam-6859	117	7	→	→	SYM
ejpam-6859	117	8	g	g	NOUN
ejpam-6859	117	9	/	/	SYM
ejpam-6859	117	10	g′is	g′is	NOUN
ejpam-6859	117	11	identical	identical	ADJ
ejpam-6859	117	12	to	to	ADP
ejpam-6859	117	13	the	the	DET
ejpam-6859	117	14	canonical	canonical	ADJ
ejpam-6859	117	15	homomorphism	homomorphism	NOUN
ejpam-6859	117	16	from	from	ADP
ejpam-6859	117	17	g	g	PROPN
ejpam-6859	117	18	→	→	SYM
ejpam-6859	117	19	g	g	NOUN
ejpam-6859	117	20	/	/	SYM
ejpam-6859	117	21	ǵthat	ǵthat	PRON
ejpam-6859	117	22	is	be	AUX
ejpam-6859	117	23	,	,	PUNCT
ejpam-6859	117	24	for	for	ADP
ejpam-6859	117	25	all	all	PRON
ejpam-6859	117	26	g	g	PROPN
ejpam-6859	117	27	∈	∈	PROPN
ejpam-6859	117	28	g	g	NOUN
ejpam-6859	117	29	,	,	PUNCT
ejpam-6859	117	30	we	we	PRON
ejpam-6859	117	31	have	have	AUX
ejpam-6859	117	32	:	:	PUNCT
ejpam-6859	117	33	v(g	v(g	ADJ
ejpam-6859	117	34	)	)	PUNCT
ejpam-6859	117	35	=	=	SYM
ejpam-6859	117	36	gǵ	gǵ	NOUN
ejpam-6859	117	37	where	where	SCONJ
ejpam-6859	117	38	v(g	v(g	VERB
ejpam-6859	117	39	)	)	PUNCT
ejpam-6859	117	40	is	be	AUX
ejpam-6859	117	41	the	the	DET
ejpam-6859	117	42	transfer	transfer	NOUN
ejpam-6859	117	43	homomorphism	homomorphism	NOUN
ejpam-6859	117	44	and	and	CCONJ
ejpam-6859	117	45	gǵ	gǵ	NOUN
ejpam-6859	117	46	is	be	AUX
ejpam-6859	117	47	the	the	DET
ejpam-6859	117	48	coset	coset	NOUN
ejpam-6859	117	49	of	of	ADP
ejpam-6859	117	50	g	g	NOUN
ejpam-6859	117	51	in	in	ADP
ejpam-6859	117	52	the	the	DET
ejpam-6859	117	53	quotient	quotient	NOUN
ejpam-6859	117	54	group	group	NOUN
ejpam-6859	117	55	g	g	PROPN
ejpam-6859	117	56	/	/	SYM
ejpam-6859	117	57	ǵ.	ǵ.	NOUN
ejpam-6859	118	1	proof	proof	NOUN
ejpam-6859	119	1	.	.	PUNCT
ejpam-6859	120	1	the	the	DET
ejpam-6859	120	2	canonical	canonical	ADJ
ejpam-6859	120	3	homomorphism	homomorphism	NOUN
ejpam-6859	120	4	from	from	ADP
ejpam-6859	120	5	g	g	PROPN
ejpam-6859	120	6	→	→	SYM
ejpam-6859	120	7	g	g	NOUN
ejpam-6859	120	8	/	/	SYM
ejpam-6859	120	9	ǵ	ǵ	NOUN
ejpam-6859	120	10	is	be	AUX
ejpam-6859	120	11	defined	define	VERB
ejpam-6859	120	12	by	by	ADP
ejpam-6859	120	13	π(g	π(g	PROPN
ejpam-6859	120	14	)	)	PUNCT
ejpam-6859	120	15	=	=	SYM
ejpam-6859	120	16	gǵ	gǵ	NOUN
ejpam-6859	120	17	for	for	ADP
ejpam-6859	120	18	each	each	DET
ejpam-6859	120	19	g	g	PROPN
ejpam-6859	120	20	∈	∈	PROPN
ejpam-6859	120	21	g	g	NOUN
ejpam-6859	120	22	,	,	PUNCT
ejpam-6859	120	23	which	which	PRON
ejpam-6859	120	24	is	be	AUX
ejpam-6859	120	25	the	the	DET
ejpam-6859	120	26	natural	natural	ADJ
ejpam-6859	120	27	projection	projection	NOUN
ejpam-6859	120	28	map	map	NOUN
ejpam-6859	120	29	sending	send	VERB
ejpam-6859	120	30	g	g	NOUN
ejpam-6859	120	31	to	to	ADP
ejpam-6859	120	32	its	its	PRON
ejpam-6859	120	33	coset	coset	NOUN
ejpam-6859	120	34	in	in	ADP
ejpam-6859	120	35	the	the	DET
ejpam-6859	120	36	quotient	quotient	NOUN
ejpam-6859	120	37	group	group	NOUN
ejpam-6859	121	1	g	g	PROPN
ejpam-6859	121	2	/	/	SYM
ejpam-6859	121	3	ǵ.	ǵ.	NOUN
ejpam-6859	122	1	the	the	DET
ejpam-6859	122	2	transfer	transfer	NOUN
ejpam-6859	122	3	homomorphism	homomorphism	NOUN
ejpam-6859	122	4	v	v	NOUN
ejpam-6859	122	5	is	be	AUX
ejpam-6859	122	6	defined	define	VERB
ejpam-6859	122	7	as	as	ADP
ejpam-6859	122	8	:	:	PUNCT
ejpam-6859	122	9	v(g	v(g	NUM
ejpam-6859	122	10	)	)	PUNCT
ejpam-6859	122	11	=	=	SYM
ejpam-6859	122	12	σh∈ǵghg	σh∈ǵghg	PROPN
ejpam-6859	122	13	−1	−1	NOUN
ejpam-6859	122	14	.	.	PUNCT
ejpam-6859	123	1	since	since	SCONJ
ejpam-6859	123	2	ǵ	ǵ	PROPN
ejpam-6859	123	3	is	be	AUX
ejpam-6859	123	4	the	the	DET
ejpam-6859	123	5	commutator	commutator	NOUN
ejpam-6859	123	6	subgroup	subgroup	NOUN
ejpam-6859	123	7	of	of	ADP
ejpam-6859	123	8	g	g	PROPN
ejpam-6859	123	9	,	,	PUNCT
ejpam-6859	123	10	and	and	CCONJ
ejpam-6859	123	11	g	g	NOUN
ejpam-6859	123	12	/	/	SYM
ejpam-6859	123	13	ǵ	ǵ	NOUN
ejpam-6859	123	14	is	be	AUX
ejpam-6859	123	15	abelian	abelian	ADJ
ejpam-6859	123	16	,	,	PUNCT
ejpam-6859	123	17	the	the	DET
ejpam-6859	123	18	conjugation	conjugation	NOUN
ejpam-6859	123	19	by	by	ADP
ejpam-6859	123	20	any	any	DET
ejpam-6859	123	21	element	element	NOUN
ejpam-6859	123	22	of	of	ADP
ejpam-6859	123	23	g	g	PROPN
ejpam-6859	123	24	leaves	leave	VERB
ejpam-6859	123	25	ǵ	ǵ	PROPN
ejpam-6859	123	26	invariant	invariant	ADJ
ejpam-6859	123	27	.	.	PUNCT
ejpam-6859	124	1	therefore	therefore	ADV
ejpam-6859	124	2	,	,	PUNCT
ejpam-6859	124	3	the	the	DET
ejpam-6859	124	4	action	action	NOUN
ejpam-6859	124	5	of	of	ADP
ejpam-6859	124	6	the	the	DET
ejpam-6859	124	7	transfer	transfer	NOUN
ejpam-6859	124	8	homomorphism	homomorphism	NOUN
ejpam-6859	124	9	v	v	NOUN
ejpam-6859	124	10	on	on	ADP
ejpam-6859	124	11	any	any	DET
ejpam-6859	124	12	g	g	PROPN
ejpam-6859	124	13	∈	∈	PROPN
ejpam-6859	124	14	g	g	NOUN
ejpam-6859	124	15	results	result	NOUN
ejpam-6859	124	16	in	in	ADP
ejpam-6859	124	17	the	the	DET
ejpam-6859	124	18	coset	coset	NOUN
ejpam-6859	124	19	gǵ	gǵ	NOUN
ejpam-6859	124	20	in	in	ADP
ejpam-6859	124	21	g	g	PROPN
ejpam-6859	124	22	/	/	SYM
ejpam-6859	124	23	ǵ.	ǵ.	NOUN
ejpam-6859	124	24	hence	hence	ADV
ejpam-6859	124	25	,	,	PUNCT
ejpam-6859	124	26	v(g	v(g	ADJ
ejpam-6859	124	27	)	)	PUNCT
ejpam-6859	124	28	=	=	VERB
ejpam-6859	124	29	gǵ	gǵ	NOUN
ejpam-6859	124	30	for	for	ADP
ejpam-6859	124	31	all	all	PRON
ejpam-6859	124	32	g	g	PROPN
ejpam-6859	124	33	∈	∈	PROPN
ejpam-6859	124	34	g	g	NOUN
ejpam-6859	124	35	,	,	PUNCT
ejpam-6859	124	36	establishing	establish	VERB
ejpam-6859	124	37	that	that	SCONJ
ejpam-6859	124	38	the	the	DET
ejpam-6859	124	39	transfer	transfer	NOUN
ejpam-6859	124	40	homomorphism	homomorphism	NOUN
ejpam-6859	124	41	is	be	AUX
ejpam-6859	124	42	the	the	DET
ejpam-6859	124	43	same	same	ADJ
ejpam-6859	124	44	as	as	ADP
ejpam-6859	124	45	the	the	DET
ejpam-6859	124	46	canonical	canonical	ADJ
ejpam-6859	124	47	homomorphism	homomorphism	NOUN
ejpam-6859	124	48	.	.	PUNCT
ejpam-6859	125	1	theorem	theorem	NOUN
ejpam-6859	125	2	1	1	NUM
ejpam-6859	125	3	.	.	PUNCT
ejpam-6859	126	1	let	let	VERB
ejpam-6859	126	2	g	g	PRON
ejpam-6859	126	3	be	be	AUX
ejpam-6859	126	4	a	a	DET
ejpam-6859	126	5	simple	simple	ADJ
ejpam-6859	126	6	group	group	NOUN
ejpam-6859	126	7	,	,	PUNCT
ejpam-6859	126	8	and	and	CCONJ
ejpam-6859	126	9	let	let	VERB
ejpam-6859	126	10	p	p	PRON
ejpam-6859	126	11	be	be	AUX
ejpam-6859	126	12	an	an	DET
ejpam-6859	126	13	abelian	abelian	ADJ
ejpam-6859	126	14	sylow	sylow	NOUN
ejpam-6859	126	15	2	2	NUM
ejpam-6859	126	16	-	-	PUNCT
ejpam-6859	126	17	subgroup	subgroup	NOUN
ejpam-6859	126	18	of	of	ADP
ejpam-6859	126	19	g	g	NOUN
ejpam-6859	126	20	of	of	ADP
ejpam-6859	126	21	order	order	NOUN
ejpam-6859	126	22	25	25	NUM
ejpam-6859	126	23	.	.	PUNCT
ejpam-6859	127	1	then	then	ADV
ejpam-6859	127	2	p	p	PROPN
ejpam-6859	127	3	is	be	AUX
ejpam-6859	127	4	elementary	elementary	ADJ
ejpam-6859	127	5	abelian	abelian	NOUN
ejpam-6859	127	6	.	.	PUNCT
ejpam-6859	128	1	proof	proof	NOUN
ejpam-6859	128	2	.	.	PUNCT
ejpam-6859	129	1	now	now	ADV
ejpam-6859	129	2	,	,	PUNCT
ejpam-6859	129	3	p	p	NOUN
ejpam-6859	129	4	is	be	AUX
ejpam-6859	129	5	abelian	abelian	ADJ
ejpam-6859	129	6	and	and	CCONJ
ejpam-6859	129	7	of	of	ADP
ejpam-6859	129	8	order	order	NOUN
ejpam-6859	129	9	25	25	NUM
ejpam-6859	129	10	,	,	PUNCT
ejpam-6859	129	11	it	it	PRON
ejpam-6859	129	12	must	must	AUX
ejpam-6859	129	13	be	be	AUX
ejpam-6859	129	14	isomorphic	isomorphic	ADJ
ejpam-6859	129	15	to	to	ADP
ejpam-6859	129	16	either	either	CCONJ
ejpam-6859	129	17	z/25z	z/25z	PROPN
ejpam-6859	129	18	or	or	CCONJ
ejpam-6859	129	19	z/5z	z/5z	NUM
ejpam-6859	129	20	×	×	NOUN
ejpam-6859	129	21	z/5z	z/5z	NUM
ejpam-6859	129	22	however	however	ADV
ejpam-6859	129	23	,	,	PUNCT
ejpam-6859	129	24	g	g	PROPN
ejpam-6859	129	25	is	be	AUX
ejpam-6859	129	26	simple	simple	ADJ
ejpam-6859	129	27	,	,	PUNCT
ejpam-6859	129	28	and	and	CCONJ
ejpam-6859	129	29	if	if	SCONJ
ejpam-6859	129	30	p	p	DET
ejpam-6859	129	31	∼=	∼=	PROPN
ejpam-6859	129	32	z/25z	z/25z	NOUN
ejpam-6859	129	33	,	,	PUNCT
ejpam-6859	129	34	then	then	ADV
ejpam-6859	129	35	the	the	DET
ejpam-6859	129	36	cyclic	cyclic	ADJ
ejpam-6859	129	37	group	group	NOUN
ejpam-6859	129	38	generated	generate	VERB
ejpam-6859	129	39	by	by	ADP
ejpam-6859	129	40	an	an	DET
ejpam-6859	129	41	element	element	NOUN
ejpam-6859	129	42	of	of	ADP
ejpam-6859	129	43	order	order	NOUN
ejpam-6859	129	44	25	25	NUM
ejpam-6859	129	45	would	would	AUX
ejpam-6859	129	46	be	be	AUX
ejpam-6859	129	47	a	a	DET
ejpam-6859	129	48	nontrivial	nontrivial	ADJ
ejpam-6859	129	49	normal	normal	ADJ
ejpam-6859	129	50	subgroup	subgroup	NOUN
ejpam-6859	129	51	of	of	ADP
ejpam-6859	129	52	g	g	PROPN
ejpam-6859	129	53	,	,	PUNCT
ejpam-6859	129	54	contradicting	contradict	VERB
ejpam-6859	129	55	the	the	DET
ejpam-6859	129	56	simplicity	simplicity	NOUN
ejpam-6859	129	57	of	of	ADP
ejpam-6859	129	58	g.	g.	PROPN
ejpam-6859	129	59	therefore	therefore	ADV
ejpam-6859	129	60	,	,	PUNCT
ejpam-6859	129	61	p	p	PROPN
ejpam-6859	129	62	must	must	AUX
ejpam-6859	129	63	be	be	AUX
ejpam-6859	129	64	isomorphic	isomorphic	ADJ
ejpam-6859	129	65	to	to	ADP
ejpam-6859	129	66	z/5z	z/5z	NUM
ejpam-6859	129	67	×	×	NOUN
ejpam-6859	129	68	z/5z	z/5z	NUM
ejpam-6859	129	69	.	.	PUNCT
ejpam-6859	130	1	the	the	DET
ejpam-6859	130	2	group	group	NOUN
ejpam-6859	130	3	z/5z	z/5z	PROPN
ejpam-6859	130	4	×	×	NOUN
ejpam-6859	130	5	z/5z	z/5z	NUM
ejpam-6859	130	6	is	be	AUX
ejpam-6859	130	7	elementary	elementary	ADJ
ejpam-6859	130	8	abelian	abelian	NOUN
ejpam-6859	130	9	because	because	SCONJ
ejpam-6859	130	10	it	it	PRON
ejpam-6859	130	11	can	can	AUX
ejpam-6859	130	12	be	be	AUX
ejpam-6859	130	13	viewed	view	VERB
ejpam-6859	130	14	as	as	ADP
ejpam-6859	130	15	a	a	DET
ejpam-6859	130	16	2dimensional	2dimensional	NUM
ejpam-6859	130	17	vector	vector	NOUN
ejpam-6859	130	18	space	space	NOUN
ejpam-6859	130	19	over	over	ADP
ejpam-6859	130	20	z/2z	z/2z	PROPN
ejpam-6859	130	21	,	,	PUNCT
ejpam-6859	130	22	where	where	SCONJ
ejpam-6859	130	23	every	every	DET
ejpam-6859	130	24	non	non	ADJ
ejpam-6859	130	25	-	-	ADJ
ejpam-6859	130	26	identity	identity	ADJ
ejpam-6859	130	27	element	element	NOUN
ejpam-6859	130	28	has	have	VERB
ejpam-6859	130	29	order	order	NOUN
ejpam-6859	130	30	2	2	NUM
ejpam-6859	130	31	.	.	PUNCT
ejpam-6859	131	1	hence	hence	ADV
ejpam-6859	131	2	,	,	PUNCT
ejpam-6859	131	3	p	p	PROPN
ejpam-6859	131	4	is	be	AUX
ejpam-6859	131	5	elementary	elementary	ADJ
ejpam-6859	131	6	abelian	abelian	NOUN
ejpam-6859	131	7	.	.	PUNCT
ejpam-6859	132	1	thus	thus	ADV
ejpam-6859	132	2	,	,	PUNCT
ejpam-6859	132	3	p	p	PROPN
ejpam-6859	132	4	is	be	AUX
ejpam-6859	132	5	elementary	elementary	ADJ
ejpam-6859	132	6	abelian	abelian	NOUN
ejpam-6859	132	7	.	.	PUNCT
ejpam-6859	133	1	theorem	theorem	NOUN
ejpam-6859	133	2	2	2	NUM
ejpam-6859	133	3	.	.	PUNCT
ejpam-6859	134	1	let	let	VERB
ejpam-6859	134	2	p	p	PROPN
ejpam-6859	134	3	∈	∈	PROPN
ejpam-6859	134	4	sylp(g	sylp(g	PROPN
ejpam-6859	134	5	)	)	PUNCT
ejpam-6859	134	6	,	,	PUNCT
ejpam-6859	134	7	and	and	CCONJ
ejpam-6859	134	8	suppose	suppose	VERB
ejpam-6859	134	9	h	h	NOUN
ejpam-6859	134	10	and	and	CCONJ
ejpam-6859	134	11	k	k	PROPN
ejpam-6859	134	12	are	be	AUX
ejpam-6859	134	13	normal	normal	ADJ
ejpam-6859	134	14	subgroups	subgroup	NOUN
ejpam-6859	134	15	of	of	ADP
ejpam-6859	134	16	p	p	NOUN
ejpam-6859	134	17	that	that	PRON
ejpam-6859	134	18	are	be	AUX
ejpam-6859	134	19	conjugate	conjugate	ADJ
ejpam-6859	134	20	in	in	ADP
ejpam-6859	134	21	g.	g.	PROPN
ejpam-6859	134	22	then	then	ADV
ejpam-6859	134	23	,	,	PUNCT
ejpam-6859	134	24	h	h	NOUN
ejpam-6859	134	25	and	and	CCONJ
ejpam-6859	134	26	k	k	PROPN
ejpam-6859	134	27	are	be	AUX
ejpam-6859	134	28	conjugate	conjugate	ADJ
ejpam-6859	134	29	in	in	ADP
ejpam-6859	134	30	the	the	DET
ejpam-6859	134	31	normalizer	normalizer	PROPN
ejpam-6859	134	32	ng(p	ng(p	NOUN
ejpam-6859	134	33	)	)	PUNCT
ejpam-6859	134	34	of	of	ADP
ejpam-6859	134	35	p	p	NOUN
ejpam-6859	134	36	.	.	PUNCT
ejpam-6859	135	1	if	if	SCONJ
ejpam-6859	135	2	h	h	NOUN
ejpam-6859	135	3	is	be	AUX
ejpam-6859	135	4	characteristic	characteristic	ADJ
ejpam-6859	135	5	in	in	ADP
ejpam-6859	135	6	p	p	PROPN
ejpam-6859	135	7	,	,	PUNCT
ejpam-6859	135	8	then	then	ADV
ejpam-6859	135	9	h	h	PROPN
ejpam-6859	135	10	=	=	PROPN
ejpam-6859	135	11	k.	k.	PROPN
ejpam-6859	135	12	a.	a.	PROPN
ejpam-6859	135	13	m.	m.	PROPN
ejpam-6859	135	14	alotaibi	alotaibi	PROPN
ejpam-6859	135	15	et	et	PROPN
ejpam-6859	135	16	al	al	PROPN
ejpam-6859	135	17	.	.	PUNCT
ejpam-6859	135	18	/	/	SYM
ejpam-6859	135	19	eur	eur	PROPN
ejpam-6859	135	20	.	.	PUNCT
ejpam-6859	136	1	j.	j.	PROPN
ejpam-6859	136	2	pure	pure	PROPN
ejpam-6859	136	3	appl	appl	PROPN
ejpam-6859	136	4	.	.	PROPN
ejpam-6859	136	5	math	math	PROPN
ejpam-6859	136	6	,	,	PUNCT
ejpam-6859	136	7	18	18	NUM
ejpam-6859	136	8	(	(	PUNCT
ejpam-6859	136	9	4	4	NUM
ejpam-6859	136	10	)	)	PUNCT
ejpam-6859	136	11	(	(	PUNCT
ejpam-6859	136	12	2025	2025	NUM
ejpam-6859	136	13	)	)	PUNCT
ejpam-6859	136	14	,	,	PUNCT
ejpam-6859	136	15	6859	6859	NUM
ejpam-6859	136	16	5	5	NUM
ejpam-6859	136	17	of	of	ADP
ejpam-6859	136	18	6	6	NUM
ejpam-6859	136	19	proof	proof	NOUN
ejpam-6859	136	20	.	.	PUNCT
ejpam-6859	137	1	let	let	VERB
ejpam-6859	137	2	h	h	NOUN
ejpam-6859	137	3	and	and	CCONJ
ejpam-6859	137	4	k	k	PROPN
ejpam-6859	137	5	be	be	AUX
ejpam-6859	137	6	conjugate	conjugate	ADJ
ejpam-6859	137	7	in	in	ADP
ejpam-6859	137	8	g	g	NOUN
ejpam-6859	137	9	,	,	PUNCT
ejpam-6859	137	10	meaning	mean	VERB
ejpam-6859	137	11	there	there	PRON
ejpam-6859	137	12	exists	exist	VERB
ejpam-6859	137	13	g	g	PROPN
ejpam-6859	137	14	∈	∈	PROPN
ejpam-6859	137	15	g	g	PROPN
ejpam-6859	137	16	such	such	ADJ
ejpam-6859	138	1	that	that	SCONJ
ejpam-6859	138	2	k	k	PROPN
ejpam-6859	138	3	=	=	PUNCT
ejpam-6859	138	4	ghg−1	ghg−1	PROPN
ejpam-6859	138	5	.	.	PUNCT
ejpam-6859	139	1	since	since	SCONJ
ejpam-6859	139	2	both	both	DET
ejpam-6859	139	3	h	h	NOUN
ejpam-6859	139	4	and	and	CCONJ
ejpam-6859	139	5	k	k	PROPN
ejpam-6859	139	6	are	be	AUX
ejpam-6859	139	7	normal	normal	ADJ
ejpam-6859	139	8	subgroups	subgroup	NOUN
ejpam-6859	139	9	of	of	ADP
ejpam-6859	139	10	p	p	NOUN
ejpam-6859	139	11	,	,	PUNCT
ejpam-6859	139	12	we	we	PRON
ejpam-6859	139	13	have	have	VERB
ejpam-6859	139	14	h	h	NOUN
ejpam-6859	139	15	⊴	⊴	ADP
ejpam-6859	139	16	p	p	PROPN
ejpam-6859	139	17	and	and	CCONJ
ejpam-6859	139	18	k	k	PROPN
ejpam-6859	139	19	⊴	⊴	ADP
ejpam-6859	139	20	p	p	X
ejpam-6859	139	21	,	,	PUNCT
ejpam-6859	139	22	so	so	CCONJ
ejpam-6859	139	23	for	for	ADP
ejpam-6859	139	24	every	every	DET
ejpam-6859	139	25	p	p	NOUN
ejpam-6859	139	26	∈	∈	PROPN
ejpam-6859	139	27	p	p	NOUN
ejpam-6859	139	28	,	,	PUNCT
ejpam-6859	139	29	we	we	PRON
ejpam-6859	139	30	have	have	VERB
ejpam-6859	139	31	php−1	php−1	NOUN
ejpam-6859	139	32	=	=	NOUN
ejpam-6859	139	33	h	h	NOUN
ejpam-6859	139	34	and	and	CCONJ
ejpam-6859	139	35	pkp−1	pkp−1	PROPN
ejpam-6859	139	36	=	=	PROPN
ejpam-6859	139	37	k.	k.	PROPN
ejpam-6859	139	38	to	to	PART
ejpam-6859	139	39	show	show	VERB
ejpam-6859	139	40	that	that	SCONJ
ejpam-6859	139	41	h	h	NOUN
ejpam-6859	139	42	and	and	CCONJ
ejpam-6859	139	43	k	k	PROPN
ejpam-6859	139	44	are	be	AUX
ejpam-6859	139	45	conjugate	conjugate	ADJ
ejpam-6859	139	46	in	in	ADP
ejpam-6859	139	47	ng(p	ng(p	NOUN
ejpam-6859	139	48	)	)	PUNCT
ejpam-6859	139	49	,	,	PUNCT
ejpam-6859	139	50	note	note	VERB
ejpam-6859	139	51	that	that	SCONJ
ejpam-6859	139	52	k	k	PROPN
ejpam-6859	139	53	=	=	PUNCT
ejpam-6859	139	54	ghg−1	ghg−1	PROPN
ejpam-6859	139	55	.	.	PUNCT
ejpam-6859	139	56	to	to	PART
ejpam-6859	139	57	ensure	ensure	VERB
ejpam-6859	139	58	k	k	PROPN
ejpam-6859	139	59	is	be	AUX
ejpam-6859	139	60	conjugate	conjugate	ADJ
ejpam-6859	139	61	in	in	ADP
ejpam-6859	139	62	ng(p	ng(p	NOUN
ejpam-6859	139	63	)	)	PUNCT
ejpam-6859	139	64	,	,	PUNCT
ejpam-6859	139	65	we	we	PRON
ejpam-6859	139	66	require	require	VERB
ejpam-6859	139	67	that	that	SCONJ
ejpam-6859	139	68	g	g	PROPN
ejpam-6859	139	69	∈	∈	PROPN
ejpam-6859	139	70	ng(p	ng(p	PUNCT
ejpam-6859	139	71	)	)	PUNCT
ejpam-6859	139	72	,	,	PUNCT
ejpam-6859	139	73	and	and	CCONJ
ejpam-6859	139	74	since	since	SCONJ
ejpam-6859	139	75	h	h	NOUN
ejpam-6859	139	76	and	and	CCONJ
ejpam-6859	139	77	k	k	PROPN
ejpam-6859	139	78	lie	lie	VERB
ejpam-6859	139	79	within	within	ADP
ejpam-6859	139	80	p	p	NOUN
ejpam-6859	139	81	,	,	PUNCT
ejpam-6859	139	82	g	g	PROPN
ejpam-6859	139	83	must	must	AUX
ejpam-6859	139	84	normalize	normalize	VERB
ejpam-6859	139	85	p	p	X
ejpam-6859	139	86	.	.	PUNCT
ejpam-6859	140	1	therefore	therefore	ADV
ejpam-6859	140	2	,	,	PUNCT
ejpam-6859	140	3	g	g	PROPN
ejpam-6859	140	4	∈	∈	PROPN
ejpam-6859	140	5	ng(p	ng(p	NOUN
ejpam-6859	140	6	)	)	PUNCT
ejpam-6859	140	7	,	,	PUNCT
ejpam-6859	140	8	and	and	CCONJ
ejpam-6859	140	9	thus	thus	ADV
ejpam-6859	140	10	h	h	NOUN
ejpam-6859	140	11	and	and	CCONJ
ejpam-6859	140	12	k	k	PROPN
ejpam-6859	140	13	are	be	AUX
ejpam-6859	140	14	conjugate	conjugate	ADJ
ejpam-6859	140	15	in	in	ADP
ejpam-6859	140	16	ng(p	ng(p	PUNCT
ejpam-6859	140	17	)	)	PUNCT
ejpam-6859	140	18	.	.	PUNCT
ejpam-6859	141	1	next	next	ADV
ejpam-6859	141	2	,	,	PUNCT
ejpam-6859	141	3	suppose	suppose	VERB
ejpam-6859	141	4	h	h	NOUN
ejpam-6859	141	5	is	be	AUX
ejpam-6859	141	6	characteristic	characteristic	ADJ
ejpam-6859	141	7	in	in	ADP
ejpam-6859	141	8	p	p	PROPN
ejpam-6859	141	9	.	.	PUNCT
ejpam-6859	142	1	by	by	ADP
ejpam-6859	142	2	definition	definition	NOUN
ejpam-6859	142	3	2	2	NUM
ejpam-6859	142	4	,	,	PUNCT
ejpam-6859	142	5	since	since	SCONJ
ejpam-6859	142	6	h	h	NOUN
ejpam-6859	142	7	andk	andk	NOUN
ejpam-6859	142	8	are	be	AUX
ejpam-6859	142	9	conjugate	conjugate	ADJ
ejpam-6859	142	10	inng(p	inng(p	ADV
ejpam-6859	142	11	)	)	PUNCT
ejpam-6859	142	12	,	,	PUNCT
ejpam-6859	142	13	there	there	PRON
ejpam-6859	142	14	exists	exist	VERB
ejpam-6859	142	15	some	some	DET
ejpam-6859	142	16	n	n	PRON
ejpam-6859	142	17	∈	∈	PROPN
ejpam-6859	142	18	ng(p	ng(p	NOUN
ejpam-6859	142	19	)	)	PUNCT
ejpam-6859	142	20	such	such	ADJ
ejpam-6859	142	21	that	that	SCONJ
ejpam-6859	142	22	k	k	PROPN
ejpam-6859	142	23	=	=	SYM
ejpam-6859	142	24	nhn−1	nhn−1	PROPN
ejpam-6859	142	25	.	.	PUNCT
ejpam-6859	143	1	however	however	ADV
ejpam-6859	143	2	,	,	PUNCT
ejpam-6859	143	3	since	since	SCONJ
ejpam-6859	143	4	h	h	NOUN
ejpam-6859	143	5	is	be	AUX
ejpam-6859	143	6	characteristic	characteristic	ADJ
ejpam-6859	143	7	in	in	ADP
ejpam-6859	143	8	p	p	PROPN
ejpam-6859	143	9	,	,	PUNCT
ejpam-6859	143	10	k	k	PROPN
ejpam-6859	143	11	must	must	AUX
ejpam-6859	143	12	be	be	AUX
ejpam-6859	143	13	identical	identical	ADJ
ejpam-6859	143	14	to	to	ADP
ejpam-6859	143	15	h.	h.	PROPN
ejpam-6859	143	16	theorem	theorem	PROPN
ejpam-6859	143	17	3	3	X
ejpam-6859	143	18	.	.	PUNCT
ejpam-6859	144	1	let	let	VERB
ejpam-6859	144	2	g	g	PRON
ejpam-6859	144	3	be	be	AUX
ejpam-6859	144	4	a	a	DET
ejpam-6859	144	5	finite	finite	ADJ
ejpam-6859	144	6	group	group	NOUN
ejpam-6859	144	7	,	,	PUNCT
ejpam-6859	144	8	and	and	CCONJ
ejpam-6859	144	9	suppose	suppose	VERB
ejpam-6859	144	10	that	that	SCONJ
ejpam-6859	144	11	w	w	ADP
ejpam-6859	144	12	⊆	⊆	NUM
ejpam-6859	144	13	p	p	ADP
ejpam-6859	144	14	⊆	⊆	NUM
ejpam-6859	144	15	g	g	NOUN
ejpam-6859	144	16	,	,	PUNCT
ejpam-6859	144	17	where	where	SCONJ
ejpam-6859	144	18	p	p	PROPN
ejpam-6859	144	19	∈	∈	PROPN
ejpam-6859	144	20	sylp(g).we	sylp(g).we	NOUN
ejpam-6859	144	21	say	say	VERB
ejpam-6859	144	22	that	that	SCONJ
ejpam-6859	144	23	w	w	NOUN
ejpam-6859	144	24	is	be	AUX
ejpam-6859	144	25	weakly	weakly	ADV
ejpam-6859	144	26	closed	closed	ADJ
ejpam-6859	144	27	in	in	ADP
ejpam-6859	144	28	p	p	NOUN
ejpam-6859	144	29	with	with	ADP
ejpam-6859	144	30	respect	respect	NOUN
ejpam-6859	144	31	to	to	ADP
ejpam-6859	144	32	g	g	PRON
ejpam-6859	144	33	if	if	SCONJ
ejpam-6859	144	34	for	for	ADP
ejpam-6859	144	35	every	every	DET
ejpam-6859	144	36	g	g	PROPN
ejpam-6859	144	37	∈	∈	PROPN
ejpam-6859	144	38	ggw	ggw	NOUN
ejpam-6859	144	39	g	g	PROPN
ejpam-6859	144	40	⊆	⊆	NUM
ejpam-6859	144	41	p	p	X
ejpam-6859	144	42	=	=	NOUN
ejpam-6859	144	43	⇒w	⇒w	NOUN
ejpam-6859	144	44	g	g	PROPN
ejpam-6859	144	45	=	=	SYM
ejpam-6859	144	46	w	w	PROPN
ejpam-6859	144	47	.	.	PUNCT
ejpam-6859	145	1	then	then	ADV
ejpam-6859	145	2	w	w	NOUN
ejpam-6859	145	3	is	be	AUX
ejpam-6859	145	4	weakly	weakly	ADV
ejpam-6859	145	5	closed	closed	ADJ
ejpam-6859	145	6	in	in	ADP
ejpam-6859	145	7	p	p	NOUN
ejpam-6859	145	8	with	with	ADP
ejpam-6859	145	9	respect	respect	NOUN
ejpam-6859	145	10	to	to	ADP
ejpam-6859	145	11	g	g	PRON
ejpam-6859	145	12	if	if	SCONJ
ejpam-6859	146	1	and	and	CCONJ
ejpam-6859	146	2	only	only	ADV
ejpam-6859	146	3	if	if	SCONJ
ejpam-6859	146	4	w	w	NOUN
ejpam-6859	146	5	⊴	⊴	NOUN
ejpam-6859	146	6	ng(p	ng(p	NUM
ejpam-6859	146	7	)	)	PUNCT
ejpam-6859	146	8	and	and	CCONJ
ejpam-6859	146	9	w	w	ADP
ejpam-6859	146	10	⊴	⊴	ADP
ejpam-6859	146	11	q	q	NOUN
ejpam-6859	146	12	for	for	ADP
ejpam-6859	146	13	every	every	DET
ejpam-6859	146	14	q	q	PROPN
ejpam-6859	146	15	∈	∈	PROPN
ejpam-6859	146	16	sylp(g	sylp(g	NOUN
ejpam-6859	146	17	)	)	PUNCT
ejpam-6859	147	1	such	such	ADJ
ejpam-6859	147	2	that	that	SCONJ
ejpam-6859	147	3	w	w	ADP
ejpam-6859	147	4	⊆	⊆	NUM
ejpam-6859	147	5	q.	q.	NOUN
ejpam-6859	147	6	proof	proof	NOUN
ejpam-6859	147	7	.	.	PUNCT
ejpam-6859	148	1	⇒	⇒	NOUN
ejpam-6859	148	2	)	)	PUNCT
ejpam-6859	148	3	assume	assume	VERB
ejpam-6859	148	4	w	w	NOUN
ejpam-6859	148	5	is	be	AUX
ejpam-6859	148	6	weakly	weakly	ADV
ejpam-6859	148	7	closed	closed	ADJ
ejpam-6859	148	8	in	in	ADP
ejpam-6859	148	9	p	p	NOUN
ejpam-6859	148	10	with	with	ADP
ejpam-6859	148	11	respect	respect	NOUN
ejpam-6859	148	12	to	to	ADP
ejpam-6859	148	13	g.	g.	NOUN
ejpam-6859	148	14	since	since	SCONJ
ejpam-6859	148	15	ng(p	ng(p	NOUN
ejpam-6859	148	16	)	)	PUNCT
ejpam-6859	149	1	≤	≤	NOUN
ejpam-6859	149	2	g	g	NOUN
ejpam-6859	149	3	,	,	PUNCT
ejpam-6859	149	4	then	then	ADV
ejpam-6859	149	5	for	for	ADP
ejpam-6859	149	6	all	all	DET
ejpam-6859	149	7	n	n	PRON
ejpam-6859	149	8	∈	∈	NOUN
ejpam-6859	149	9	ng(p	ng(p	NOUN
ejpam-6859	149	10	)	)	PUNCT
ejpam-6859	149	11	,	,	PUNCT
ejpam-6859	149	12	we	we	PRON
ejpam-6859	149	13	have	have	VERB
ejpam-6859	149	14	wn	wn	PROPN
ejpam-6859	149	15	≤	≤	PROPN
ejpam-6859	149	16	p	p	NOUN
ejpam-6859	149	17	.	.	PUNCT
ejpam-6859	150	1	by	by	ADP
ejpam-6859	150	2	weak	weak	ADJ
ejpam-6859	150	3	closure	closure	NOUN
ejpam-6859	150	4	,	,	PUNCT
ejpam-6859	150	5	wn	wn	PROPN
ejpam-6859	150	6	=	=	PROPN
ejpam-6859	150	7	w	w	PROPN
ejpam-6859	150	8	.	.	PUNCT
ejpam-6859	151	1	hence	hence	ADV
ejpam-6859	151	2	,	,	PUNCT
ejpam-6859	151	3	w	w	PROPN
ejpam-6859	151	4	is	be	AUX
ejpam-6859	151	5	invariant	invariant	ADJ
ejpam-6859	151	6	under	under	ADP
ejpam-6859	151	7	conjugation	conjugation	NOUN
ejpam-6859	151	8	by	by	ADP
ejpam-6859	151	9	all	all	DET
ejpam-6859	151	10	elements	element	NOUN
ejpam-6859	151	11	of	of	ADP
ejpam-6859	151	12	ng(p	ng(p	NOUN
ejpam-6859	151	13	)	)	PUNCT
ejpam-6859	151	14	,	,	PUNCT
ejpam-6859	151	15	i.e.	i.e.	X
ejpam-6859	151	16	,	,	PUNCT
ejpam-6859	151	17	w	w	NOUN
ejpam-6859	151	18	⊴	⊴	NUM
ejpam-6859	151	19	ng(p	ng(p	NUM
ejpam-6859	151	20	)	)	PUNCT
ejpam-6859	151	21	.	.	PUNCT
ejpam-6859	152	1	let	let	VERB
ejpam-6859	152	2	q	q	PROPN
ejpam-6859	152	3	∈	∈	PROPN
ejpam-6859	152	4	sylp(g	sylp(g	PROPN
ejpam-6859	152	5	)	)	PUNCT
ejpam-6859	152	6	with	with	ADP
ejpam-6859	152	7	w	w	NOUN
ejpam-6859	152	8	≤	≤	NUM
ejpam-6859	152	9	q.	q.	NOUN
ejpam-6859	152	10	by	by	ADP
ejpam-6859	152	11	sylow	sylow	PROPN
ejpam-6859	152	12	’s	’s	PART
ejpam-6859	152	13	theorem	theorem	PROPN
ejpam-6859	152	14	,	,	PUNCT
ejpam-6859	152	15	q	q	X
ejpam-6859	153	1	=	=	PUNCT
ejpam-6859	153	2	p	p	X
ejpam-6859	153	3	g	g	NOUN
ejpam-6859	153	4	for	for	ADP
ejpam-6859	153	5	some	some	DET
ejpam-6859	153	6	g	g	NOUN
ejpam-6859	153	7	∈	∈	PROPN
ejpam-6859	153	8	g	g	NOUN
ejpam-6859	153	9	,	,	PUNCT
ejpam-6859	153	10	so	so	SCONJ
ejpam-6859	153	11	w	w	PROPN
ejpam-6859	153	12	≤	≤	PROPN
ejpam-6859	153	13	pg	pg	AUX
ejpam-6859	153	14	⇒	⇒	NOUN
ejpam-6859	153	15	wg−1	wg−1	PROPN
ejpam-6859	153	16	≤	≤	PROPN
ejpam-6859	153	17	p	p	X
ejpam-6859	153	18	.	.	PUNCT
ejpam-6859	154	1	by	by	ADP
ejpam-6859	154	2	weak	weak	ADJ
ejpam-6859	154	3	closure	closure	NOUN
ejpam-6859	154	4	,	,	PUNCT
ejpam-6859	154	5	wg−1	wg−1	PROPN
ejpam-6859	154	6	=	=	PUNCT
ejpam-6859	154	7	w	w	PROPN
ejpam-6859	154	8	⇒	⇒	PROPN
ejpam-6859	154	9	w	w	ADP
ejpam-6859	154	10	g	g	PROPN
ejpam-6859	154	11	=	=	PROPN
ejpam-6859	154	12	w	w	PROPN
ejpam-6859	154	13	⊆	⊆	NUM
ejpam-6859	154	14	p	p	NOUN
ejpam-6859	154	15	g	g	NOUN
ejpam-6859	154	16	=	=	SYM
ejpam-6859	154	17	q.for	q.for	ADP
ejpam-6859	154	18	any	any	DET
ejpam-6859	154	19	x	x	SYM
ejpam-6859	154	20	∈	∈	PROPN
ejpam-6859	154	21	qx	qx	PROPN
ejpam-6859	154	22	,	,	PUNCT
ejpam-6859	154	23	write	write	VERB
ejpam-6859	154	24	x	x	PUNCT
ejpam-6859	154	25	=	=	PUNCT
ejpam-6859	154	26	gpg−1	gpg−1	PROPN
ejpam-6859	154	27	for	for	ADP
ejpam-6859	154	28	some	some	DET
ejpam-6859	154	29	p	p	NOUN
ejpam-6859	154	30	∈	∈	PROPN
ejpam-6859	154	31	p	p	NOUN
ejpam-6859	154	32	.	.	PUNCT
ejpam-6859	155	1	then	then	ADV
ejpam-6859	155	2	w	w	ADP
ejpam-6859	155	3	x	x	SYM
ejpam-6859	155	4	=	=	PUNCT
ejpam-6859	155	5	w	w	PUNCT
ejpam-6859	155	6	gpg−1	gpg−1	NOUN
ejpam-6859	155	7	=	=	SYM
ejpam-6859	155	8	(	(	PUNCT
ejpam-6859	155	9	w	w	PROPN
ejpam-6859	155	10	g)pg	g)pg	PROPN
ejpam-6859	155	11	−1	−1	NOUN
ejpam-6859	155	12	=	=	SYM
ejpam-6859	155	13	w	w	PROPN
ejpam-6859	155	14	pg−1	pg−1	PROPN
ejpam-6859	155	15	.	.	PUNCT
ejpam-6859	156	1	since	since	SCONJ
ejpam-6859	156	2	w	w	PROPN
ejpam-6859	156	3	g	g	PROPN
ejpam-6859	156	4	≤	≤	NUM
ejpam-6859	156	5	q	q	NOUN
ejpam-6859	156	6	,	,	PUNCT
ejpam-6859	156	7	and	and	CCONJ
ejpam-6859	156	8	p	p	NOUN
ejpam-6859	156	9	∈	∈	PROPN
ejpam-6859	156	10	p	p	NOUN
ejpam-6859	156	11	,	,	PUNCT
ejpam-6859	156	12	w	w	PROPN
ejpam-6859	156	13	pg−1	pg−1	PROPN
ejpam-6859	156	14	≤	≤	NUM
ejpam-6859	156	15	q.	q.	NOUN
ejpam-6859	157	1	but	but	CCONJ
ejpam-6859	157	2	this	this	PRON
ejpam-6859	157	3	is	be	AUX
ejpam-6859	157	4	again	again	ADV
ejpam-6859	157	5	a	a	DET
ejpam-6859	157	6	g	g	NOUN
ejpam-6859	157	7	-	-	PUNCT
ejpam-6859	157	8	conjugate	conjugate	NOUN
ejpam-6859	157	9	of	of	ADP
ejpam-6859	157	10	w	w	NOUN
ejpam-6859	157	11	lying	lie	VERB
ejpam-6859	157	12	in	in	ADP
ejpam-6859	157	13	p	p	NOUN
ejpam-6859	157	14	,	,	PUNCT
ejpam-6859	157	15	so	so	ADV
ejpam-6859	157	16	again	again	ADV
ejpam-6859	157	17	by	by	ADP
ejpam-6859	157	18	weak	weak	ADJ
ejpam-6859	157	19	closure	closure	NOUN
ejpam-6859	157	20	,	,	PUNCT
ejpam-6859	157	21	w	w	PROPN
ejpam-6859	157	22	pg−1	pg−1	NOUN
ejpam-6859	157	23	=	=	PUNCT
ejpam-6859	157	24	w	w	ADJ
ejpam-6859	157	25	⇒	⇒	NOUN
ejpam-6859	157	26	w	w	NOUN
ejpam-6859	157	27	x	x	SYM
ejpam-6859	157	28	=	=	PUNCT
ejpam-6859	157	29	w	w	PROPN
ejpam-6859	157	30	.	.	PUNCT
ejpam-6859	158	1	thus	thus	ADV
ejpam-6859	158	2	,	,	PUNCT
ejpam-6859	158	3	w	w	PROPN
ejpam-6859	158	4	⊴	⊴	PROPN
ejpam-6859	158	5	q.	q.	NOUN
ejpam-6859	158	6	⇐	⇐	PROPN
ejpam-6859	158	7	=)	=)	PROPN
ejpam-6859	158	8	now	now	ADV
ejpam-6859	158	9	assume	assume	VERB
ejpam-6859	158	10	:	:	PUNCT
ejpam-6859	158	11	w	w	X
ejpam-6859	158	12	⊴	⊴	ADP
ejpam-6859	158	13	ng(p	ng(p	NUM
ejpam-6859	158	14	)	)	PUNCT
ejpam-6859	158	15	,	,	PUNCT
ejpam-6859	158	16	for	for	ADP
ejpam-6859	158	17	every	every	DET
ejpam-6859	158	18	q	q	PROPN
ejpam-6859	158	19	∈	∈	PROPN
ejpam-6859	158	20	sylp(g	sylp(g	NOUN
ejpam-6859	158	21	)	)	PUNCT
ejpam-6859	158	22	with	with	ADP
ejpam-6859	158	23	w	w	NOUN
ejpam-6859	158	24	≤	≤	PROPN
ejpam-6859	158	25	qw	qw	NOUN
ejpam-6859	158	26	,	,	PUNCT
ejpam-6859	158	27	we	we	PRON
ejpam-6859	158	28	have	have	VERB
ejpam-6859	158	29	w	w	NOUN
ejpam-6859	158	30	⊴	⊴	ADP
ejpam-6859	158	31	qw	qw	X
ejpam-6859	158	32	.	.	PUNCT
ejpam-6859	159	1	let	let	VERB
ejpam-6859	159	2	g	g	PROPN
ejpam-6859	159	3	∈	∈	PROPN
ejpam-6859	159	4	g	g	ADP
ejpam-6859	159	5	such	such	DET
ejpam-6859	159	6	that	that	PRON
ejpam-6859	159	7	w	w	PROPN
ejpam-6859	159	8	g	g	NOUN
ejpam-6859	159	9	≤	≤	NUM
ejpam-6859	159	10	p	p	NOUN
ejpam-6859	159	11	.	.	PUNCT
ejpam-6859	160	1	then	then	ADV
ejpam-6859	160	2	p	p	PROPN
ejpam-6859	160	3	g	g	PROPN
ejpam-6859	160	4	is	be	AUX
ejpam-6859	160	5	another	another	DET
ejpam-6859	160	6	sylow	sylow	NOUN
ejpam-6859	160	7	p	p	NOUN
ejpam-6859	160	8	-	-	PUNCT
ejpam-6859	160	9	subgroup	subgroup	NOUN
ejpam-6859	160	10	of	of	ADP
ejpam-6859	160	11	g	g	PROPN
ejpam-6859	160	12	,	,	PUNCT
ejpam-6859	160	13	so	so	SCONJ
ejpam-6859	160	14	there	there	PRON
ejpam-6859	160	15	exists	exist	VERB
ejpam-6859	160	16	x	x	X
ejpam-6859	160	17	∈	∈	PROPN
ejpam-6859	160	18	g	g	NOUN
ejpam-6859	160	19	such	such	ADJ
ejpam-6859	160	20	that	that	SCONJ
ejpam-6859	160	21	p	p	NOUN
ejpam-6859	160	22	g	g	NOUN
ejpam-6859	160	23	=	=	SYM
ejpam-6859	160	24	p	p	X
ejpam-6859	160	25	x	x	NOUN
ejpam-6859	160	26	,	,	PUNCT
ejpam-6859	160	27	or	or	CCONJ
ejpam-6859	160	28	equivalently	equivalently	ADV
ejpam-6859	160	29	gx−1	gx−1	PROPN
ejpam-6859	160	30	∈	∈	PROPN
ejpam-6859	160	31	ng(p	ng(p	PUNCT
ejpam-6859	160	32	)	)	PUNCT
ejpam-6859	160	33	.	.	PUNCT
ejpam-6859	161	1	define	define	VERB
ejpam-6859	161	2	h	h	NOUN
ejpam-6859	161	3	=	=	PUNCT
ejpam-6859	161	4	gx−1	gx−1	NOUN
ejpam-6859	161	5	∈	∈	PROPN
ejpam-6859	161	6	ng(p	ng(p	PUNCT
ejpam-6859	161	7	)	)	PUNCT
ejpam-6859	162	1	=	=	SYM
ejpam-6859	162	2	⇒	⇒	VERB
ejpam-6859	162	3	g	g	PROPN
ejpam-6859	162	4	=	=	SYM
ejpam-6859	162	5	hxh	hxh	PROPN
ejpam-6859	162	6	.	.	PUNCT
ejpam-6859	163	1	then	then	ADV
ejpam-6859	163	2	:	:	PUNCT
ejpam-6859	163	3	w	w	PROPN
ejpam-6859	163	4	g	g	PROPN
ejpam-6859	163	5	=	=	SYM
ejpam-6859	163	6	whx	whx	NOUN
ejpam-6859	163	7	=	=	SYM
ejpam-6859	163	8	(	(	PUNCT
ejpam-6859	163	9	w	w	NOUN
ejpam-6859	163	10	x)h	x)h	PROPN
ejpam-6859	163	11	.	.	PUNCT
ejpam-6859	164	1	since	since	SCONJ
ejpam-6859	164	2	w	w	PROPN
ejpam-6859	164	3	x	x	SYM
ejpam-6859	164	4	≤	≤	NUM
ejpam-6859	164	5	p	p	NOUN
ejpam-6859	165	1	x	x	X
ejpam-6859	165	2	=	=	PUNCT
ejpam-6859	165	3	p	p	NOUN
ejpam-6859	165	4	g	g	NOUN
ejpam-6859	165	5	=	=	SYM
ejpam-6859	165	6	p	p	NOUN
ejpam-6859	165	7	,	,	PUNCT
ejpam-6859	165	8	and	and	CCONJ
ejpam-6859	165	9	w	w	NOUN
ejpam-6859	165	10	⊴	⊴	ADJ
ejpam-6859	165	11	ng(p	ng(p	NUM
ejpam-6859	165	12	)	)	PUNCT
ejpam-6859	166	1	=	=	NOUN
ejpam-6859	166	2	⇒	⇒	NOUN
ejpam-6859	166	3	(	(	PUNCT
ejpam-6859	166	4	w	w	NOUN
ejpam-6859	166	5	x)h	x)h	PROPN
ejpam-6859	167	1	=	=	PUNCT
ejpam-6859	167	2	w	w	PROPN
ejpam-6859	167	3	x.	x.	NOUN
ejpam-6859	168	1	so	so	ADV
ejpam-6859	168	2	w	w	PROPN
ejpam-6859	168	3	g	g	PROPN
ejpam-6859	168	4	=	=	SYM
ejpam-6859	168	5	w	w	PROPN
ejpam-6859	168	6	x	x	NOUN
ejpam-6859	168	7	,	,	PUNCT
ejpam-6859	168	8	but	but	CCONJ
ejpam-6859	168	9	w	w	NOUN
ejpam-6859	168	10	x	x	PROPN
ejpam-6859	168	11	⊆	⊆	NUM
ejpam-6859	168	12	p	p	NOUN
ejpam-6859	168	13	,	,	PUNCT
ejpam-6859	168	14	so	so	CCONJ
ejpam-6859	168	15	it	it	PRON
ejpam-6859	168	16	is	be	AUX
ejpam-6859	168	17	a	a	DET
ejpam-6859	168	18	g	g	NOUN
ejpam-6859	168	19	-	-	PUNCT
ejpam-6859	168	20	conjugate	conjugate	NOUN
ejpam-6859	168	21	of	of	ADP
ejpam-6859	168	22	w	w	NOUN
ejpam-6859	168	23	lying	lie	VERB
ejpam-6859	168	24	in	in	ADP
ejpam-6859	168	25	p	p	PROPN
ejpam-6859	168	26	.	.	PUNCT
ejpam-6859	169	1	now	now	ADV
ejpam-6859	169	2	,	,	PUNCT
ejpam-6859	169	3	since	since	SCONJ
ejpam-6859	169	4	w	w	PROPN
ejpam-6859	169	5	⊴	⊴	ADP
ejpam-6859	169	6	q	q	NOUN
ejpam-6859	169	7	for	for	ADP
ejpam-6859	169	8	any	any	DET
ejpam-6859	169	9	sylowp	sylowp	NOUN
ejpam-6859	169	10	-	-	PUNCT
ejpam-6859	169	11	subgroup	subgroup	NOUN
ejpam-6859	169	12	q	q	NOUN
ejpam-6859	169	13	containing	contain	VERB
ejpam-6859	169	14	it	it	PRON
ejpam-6859	169	15	,	,	PUNCT
ejpam-6859	169	16	and	and	CCONJ
ejpam-6859	169	17	w	w	NOUN
ejpam-6859	169	18	x	x	PROPN
ejpam-6859	169	19	⊆	⊆	NUM
ejpam-6859	169	20	p	p	NOUN
ejpam-6859	169	21	,	,	PUNCT
ejpam-6859	169	22	and	and	CCONJ
ejpam-6859	169	23	w	w	ADP
ejpam-6859	169	24	x	x	X
ejpam-6859	169	25	⊴	⊴	PROPN
ejpam-6859	169	26	p	p	NOUN
ejpam-6859	169	27	,	,	PUNCT
ejpam-6859	169	28	it	it	PRON
ejpam-6859	169	29	must	must	AUX
ejpam-6859	169	30	be	be	AUX
ejpam-6859	169	31	that	that	PRON
ejpam-6859	169	32	w	w	NOUN
ejpam-6859	169	33	x	x	SYM
ejpam-6859	169	34	=	=	SYM
ejpam-6859	169	35	w	w	PROPN
ejpam-6859	169	36	.	.	PUNCT
ejpam-6859	170	1	hence	hence	ADV
ejpam-6859	170	2	w	w	PROPN
ejpam-6859	170	3	g	g	PROPN
ejpam-6859	170	4	=	=	SYM
ejpam-6859	170	5	w	w	PROPN
ejpam-6859	170	6	,	,	PUNCT
ejpam-6859	170	7	so	so	ADV
ejpam-6859	170	8	w	w	NOUN
ejpam-6859	170	9	is	be	AUX
ejpam-6859	170	10	weakly	weakly	ADV
ejpam-6859	170	11	closed	closed	ADJ
ejpam-6859	170	12	in	in	ADP
ejpam-6859	170	13	p	p	NOUN
ejpam-6859	170	14	with	with	ADP
ejpam-6859	170	15	respect	respect	NOUN
ejpam-6859	170	16	to	to	ADP
ejpam-6859	170	17	g.	g.	PROPN
ejpam-6859	170	18	corollary	corollary	NOUN
ejpam-6859	170	19	1	1	PROPN
ejpam-6859	170	20	.	.	PUNCT
ejpam-6859	171	1	let	let	VERB
ejpam-6859	171	2	g	g	PRON
ejpam-6859	171	3	be	be	AUX
ejpam-6859	171	4	a	a	DET
ejpam-6859	171	5	finite	finite	ADJ
ejpam-6859	171	6	group	group	NOUN
ejpam-6859	171	7	and	and	CCONJ
ejpam-6859	171	8	p	p	NOUN
ejpam-6859	171	9	be	be	AUX
ejpam-6859	171	10	a	a	DET
ejpam-6859	171	11	prime	prime	NOUN
ejpam-6859	171	12	,	,	PUNCT
ejpam-6859	171	13	and	and	CCONJ
ejpam-6859	171	14	let	let	VERB
ejpam-6859	171	15	p	p	PRON
ejpam-6859	171	16	∈	∈	PROPN
ejpam-6859	171	17	sylp	sylp	NOUN
ejpam-6859	171	18	(	(	PUNCT
ejpam-6859	171	19	g).suppose	g).suppose	PROPN
ejpam-6859	171	20	w	w	NOUN
ejpam-6859	171	21	≤	≤	NUM
ejpam-6859	171	22	p	p	NOUN
ejpam-6859	171	23	is	be	AUX
ejpam-6859	171	24	weakly	weakly	ADV
ejpam-6859	171	25	closed	closed	ADJ
ejpam-6859	171	26	in	in	ADP
ejpam-6859	171	27	p	p	NOUN
ejpam-6859	171	28	with	with	ADP
ejpam-6859	171	29	respect	respect	NOUN
ejpam-6859	171	30	to	to	ADP
ejpam-6859	171	31	g	g	PROPN
ejpam-6859	171	32	,	,	PUNCT
ejpam-6859	171	33	i.e	i.e	PROPN
ejpam-6859	171	34	..	..	PUNCT
ejpam-6859	171	35	∀g	∀g	NOUN
ejpam-6859	171	36	∈	∈	PROPN
ejpam-6859	171	37	g	g	NOUN
ejpam-6859	171	38	:	:	PUNCT
ejpam-6859	171	39	w	w	PROPN
ejpam-6859	171	40	g	g	NOUN
ejpam-6859	171	41	≤	≤	NUM
ejpam-6859	171	42	p	p	NOUN
ejpam-6859	171	43	=	=	NOUN
ejpam-6859	171	44	⇒	⇒	NOUN
ejpam-6859	171	45	w	w	NOUN
ejpam-6859	171	46	g	g	PROPN
ejpam-6859	171	47	=	=	PROPN
ejpam-6859	171	48	w	w	NOUN
ejpam-6859	171	49	.then	.then	VERB
ejpam-6859	171	50	every	every	DET
ejpam-6859	171	51	g	g	NOUN
ejpam-6859	171	52	-	-	PUNCT
ejpam-6859	171	53	conjugate	conjugate	NOUN
ejpam-6859	171	54	of	of	ADP
ejpam-6859	171	55	w	w	NOUN
ejpam-6859	171	56	that	that	PRON
ejpam-6859	171	57	is	be	AUX
ejpam-6859	171	58	contained	contain	VERB
ejpam-6859	171	59	in	in	ADP
ejpam-6859	171	60	p	p	NOUN
ejpam-6859	171	61	is	be	AUX
ejpam-6859	171	62	(	(	PUNCT
ejpam-6859	171	63	trivially	trivially	ADV
ejpam-6859	171	64	)	)	PUNCT
ejpam-6859	171	65	p	p	NOUN
ejpam-6859	171	66	-conjugate	-conjugate	NOUN
ejpam-6859	171	67	to	to	ADP
ejpam-6859	171	68	w	w	PROPN
ejpam-6859	171	69	.	.	PUNCT
ejpam-6859	172	1	3	3	X
ejpam-6859	172	2	.	.	X
ejpam-6859	172	3	conclusion	conclusion	NOUN
ejpam-6859	172	4	this	this	DET
ejpam-6859	172	5	study	study	NOUN
ejpam-6859	172	6	investigated	investigate	VERB
ejpam-6859	172	7	the	the	DET
ejpam-6859	172	8	internal	internal	ADJ
ejpam-6859	172	9	structure	structure	NOUN
ejpam-6859	172	10	of	of	ADP
ejpam-6859	172	11	finite	finite	ADJ
ejpam-6859	172	12	groups	group	NOUN
ejpam-6859	172	13	via	via	ADP
ejpam-6859	172	14	the	the	DET
ejpam-6859	172	15	transfer	transfer	NOUN
ejpam-6859	172	16	homomorphism	homomorphism	NOUN
ejpam-6859	172	17	v	v	ADP
ejpam-6859	172	18	:	:	PUNCT
ejpam-6859	172	19	g	g	NOUN
ejpam-6859	172	20	→	→	SYM
ejpam-6859	172	21	h	h	NOUN
ejpam-6859	172	22	and	and	CCONJ
ejpam-6859	172	23	the	the	DET
ejpam-6859	172	24	weakclosure	weakclosure	ADJ
ejpam-6859	172	25	property	property	NOUN
ejpam-6859	172	26	in	in	ADP
ejpam-6859	172	27	a	a	DET
ejpam-6859	172	28	sylow	sylow	NOUN
ejpam-6859	172	29	subgroup	subgroup	NOUN
ejpam-6859	172	30	p	p	PROPN
ejpam-6859	172	31	∈	∈	PROPN
ejpam-6859	172	32	sylp(g	sylp(g	PROPN
ejpam-6859	172	33	)	)	PUNCT
ejpam-6859	172	34	,	,	PUNCT
ejpam-6859	172	35	characterized	characterize	VERB
ejpam-6859	172	36	by	by	ADP
ejpam-6859	172	37	the	the	DET
ejpam-6859	172	38	conditions	condition	NOUN
ejpam-6859	172	39	w	w	ADP
ejpam-6859	172	40	⊴	⊴	PROPN
ejpam-6859	172	41	ng	ng	PROPN
ejpam-6859	172	42	(	(	PUNCT
ejpam-6859	172	43	p	p	NOUN
ejpam-6859	172	44	)	)	PUNCT
ejpam-6859	172	45	and	and	CCONJ
ejpam-6859	172	46	w	w	ADP
ejpam-6859	172	47	⊴	⊴	ADP
ejpam-6859	172	48	q	q	NOUN
ejpam-6859	172	49	for	for	ADP
ejpam-6859	172	50	every	every	DET
ejpam-6859	172	51	q	q	PROPN
ejpam-6859	172	52	∈	∈	PROPN
ejpam-6859	172	53	sylp(g	sylp(g	NOUN
ejpam-6859	172	54	)	)	PUNCT
ejpam-6859	172	55	with	with	ADP
ejpam-6859	172	56	a.	a.	NOUN
ejpam-6859	172	57	m.	m.	PROPN
ejpam-6859	172	58	alotaibi	alotaibi	PROPN
ejpam-6859	172	59	et	et	PROPN
ejpam-6859	172	60	al	al	PROPN
ejpam-6859	172	61	.	.	PUNCT
ejpam-6859	172	62	/	/	SYM
ejpam-6859	172	63	eur	eur	PROPN
ejpam-6859	172	64	.	.	PUNCT
ejpam-6859	173	1	j.	j.	PROPN
ejpam-6859	173	2	pure	pure	PROPN
ejpam-6859	173	3	appl	appl	PROPN
ejpam-6859	173	4	.	.	PROPN
ejpam-6859	173	5	math	math	PROPN
ejpam-6859	173	6	,	,	PUNCT
ejpam-6859	173	7	18	18	NUM
ejpam-6859	173	8	(	(	PUNCT
ejpam-6859	173	9	4	4	NUM
ejpam-6859	173	10	)	)	PUNCT
ejpam-6859	173	11	(	(	PUNCT
ejpam-6859	173	12	2025	2025	NUM
ejpam-6859	173	13	)	)	PUNCT
ejpam-6859	173	14	,	,	PUNCT
ejpam-6859	173	15	6859	6859	NUM
ejpam-6859	173	16	6	6	NUM
ejpam-6859	173	17	of	of	ADP
ejpam-6859	173	18	6	6	NUM
ejpam-6859	173	19	w	w	PROPN
ejpam-6859	173	20	≤	≤	PUNCT
ejpam-6859	173	21	q.	q.	NOUN
ejpam-6859	173	22	the	the	DET
ejpam-6859	173	23	results	result	NOUN
ejpam-6859	173	24	unify	unify	VERB
ejpam-6859	173	25	classical	classical	ADJ
ejpam-6859	173	26	subgroup	subgroup	NOUN
ejpam-6859	173	27	properties	property	NOUN
ejpam-6859	173	28	with	with	ADP
ejpam-6859	173	29	modern	modern	ADJ
ejpam-6859	173	30	insights	insight	NOUN
ejpam-6859	173	31	into	into	ADP
ejpam-6859	173	32	conjugacy	conjugacy	ADJ
ejpam-6859	173	33	control	control	NOUN
ejpam-6859	173	34	and	and	CCONJ
ejpam-6859	173	35	normality	normality	NOUN
ejpam-6859	173	36	within	within	ADP
ejpam-6859	173	37	p	p	ADJ
ejpam-6859	173	38	-	-	PUNCT
ejpam-6859	173	39	local	local	ADJ
ejpam-6859	173	40	settings	setting	NOUN
ejpam-6859	173	41	.	.	PUNCT
ejpam-6859	174	1	future	future	ADJ
ejpam-6859	174	2	work	work	NOUN
ejpam-6859	174	3	could	could	AUX
ejpam-6859	174	4	explore	explore	VERB
ejpam-6859	174	5	generalizing	generalize	VERB
ejpam-6859	174	6	these	these	DET
ejpam-6859	174	7	characterizations	characterization	NOUN
ejpam-6859	174	8	to	to	ADP
ejpam-6859	174	9	other	other	ADJ
ejpam-6859	174	10	subgroup	subgroup	NOUN
ejpam-6859	174	11	invariance	invariance	NOUN
ejpam-6859	174	12	concepts	concept	NOUN
ejpam-6859	174	13	in	in	ADP
ejpam-6859	174	14	algebra	algebra	NOUN
ejpam-6859	174	15	,	,	PUNCT
ejpam-6859	174	16	aiming	aim	VERB
ejpam-6859	174	17	to	to	PART
ejpam-6859	174	18	identify	identify	VERB
ejpam-6859	174	19	broader	broad	ADJ
ejpam-6859	174	20	structural	structural	ADJ
ejpam-6859	174	21	patterns	pattern	NOUN
ejpam-6859	174	22	in	in	ADP
ejpam-6859	174	23	finite	finite	PROPN
ejpam-6859	174	24	group	group	NOUN
ejpam-6859	174	25	theory	theory	NOUN
ejpam-6859	174	26	.	.	PUNCT
ejpam-6859	175	1	acknowledgements	acknowledgement	NOUN
ejpam-6859	175	2	this	this	DET
ejpam-6859	175	3	study	study	NOUN
ejpam-6859	175	4	is	be	AUX
ejpam-6859	175	5	supported	support	VERB
ejpam-6859	175	6	via	via	ADP
ejpam-6859	175	7	funding	funding	NOUN
ejpam-6859	175	8	from	from	ADP
ejpam-6859	175	9	prince	prince	PROPN
ejpam-6859	175	10	sattam	sattam	PROPN
ejpam-6859	175	11	bin	bin	PROPN
ejpam-6859	175	12	abdulaziz	abdulaziz	PROPN
ejpam-6859	175	13	university	university	PROPN
ejpam-6859	175	14	project	project	NOUN
ejpam-6859	175	15	number	number	NOUN
ejpam-6859	175	16	(	(	PUNCT
ejpam-6859	175	17	psau/2025	psau/2025	NOUN
ejpam-6859	175	18	/	/	SYM
ejpam-6859	175	19	r/1446	r/1446	PROPN
ejpam-6859	175	20	)	)	PUNCT
ejpam-6859	175	21	.	.	PUNCT
ejpam-6859	176	1	references	reference	NOUN
ejpam-6859	176	2	[	[	X
ejpam-6859	176	3	1	1	NUM
ejpam-6859	176	4	]	]	PUNCT
ejpam-6859	176	5	k.	k.	PROPN
ejpam-6859	176	6	m.	m.	PROPN
ejpam-6859	176	7	aljamal	aljamal	PROPN
ejpam-6859	176	8	,	,	PUNCT
ejpam-6859	176	9	a.	a.	NOUN
ejpam-6859	176	10	t.	t.	PROPN
ejpam-6859	176	11	ab	ab	PROPN
ejpam-6859	176	12	ghani	ghani	PROPN
ejpam-6859	176	13	,	,	PUNCT
ejpam-6859	176	14	and	and	CCONJ
ejpam-6859	176	15	r.	r.	PROPN
ejpam-6859	176	16	m.	m.	PROPN
ejpam-6859	176	17	saleh	saleh	PROPN
ejpam-6859	176	18	.	.	PUNCT
ejpam-6859	177	1	on	on	ADP
ejpam-6859	177	2	preimages	preimage	NOUN
ejpam-6859	177	3	of	of	ADP
ejpam-6859	177	4	technology	technology	NOUN
ejpam-6859	177	5	.	.	PUNCT
ejpam-6859	178	1	in	in	ADP
ejpam-6859	178	2	proceedings	proceeding	NOUN
ejpam-6859	178	3	of	of	ADP
ejpam-6859	178	4	the	the	DET
ejpam-6859	178	5	international	international	ADJ
ejpam-6859	178	6	conference	conference	NOUN
ejpam-6859	178	7	on	on	ADP
ejpam-6859	178	8	information	information	NOUN
ejpam-6859	178	9	technology	technology	NOUN
ejpam-6859	178	10	(	(	PUNCT
ejpam-6859	178	11	icit	icit	PROPN
ejpam-6859	178	12	)	)	PUNCT
ejpam-6859	178	13	,	,	PUNCT
ejpam-6859	178	14	pages	page	VERB
ejpam-6859	178	15	340–343	340–343	NUM
ejpam-6859	178	16	.	.	PUNCT
ejpam-6859	179	1	ieee	ieee	PROPN
ejpam-6859	179	2	,	,	PUNCT
ejpam-6859	179	3	2021	2021	NUM
ejpam-6859	179	4	.	.	PUNCT
ejpam-6859	180	1	[	[	X
ejpam-6859	180	2	2	2	NUM
ejpam-6859	180	3	]	]	PUNCT
ejpam-6859	180	4	a.	a.	NOUN
ejpam-6859	180	5	m.	m.	NOUN
ejpam-6859	180	6	alotaibi	alotaibi	PROPN
ejpam-6859	180	7	and	and	CCONJ
ejpam-6859	180	8	k.	k.	PROPN
ejpam-6859	180	9	m.	m.	PROPN
ejpam-6859	180	10	aljamal	aljamal	PROPN
ejpam-6859	180	11	.	.	PUNCT
ejpam-6859	181	1	exploring	explore	VERB
ejpam-6859	181	2	the	the	DET
ejpam-6859	181	3	associated	associated	ADJ
ejpam-6859	181	4	groups	group	NOUN
ejpam-6859	181	5	of	of	ADP
ejpam-6859	181	6	quasi	quasi	ADJ
ejpam-6859	181	7	-	-	ADJ
ejpam-6859	181	8	free	free	ADJ
ejpam-6859	181	9	groups	group	NOUN
ejpam-6859	181	10	.	.	PUNCT
ejpam-6859	182	1	european	european	ADJ
ejpam-6859	182	2	journal	journal	PROPN
ejpam-6859	182	3	of	of	ADP
ejpam-6859	182	4	pure	pure	ADJ
ejpam-6859	182	5	and	and	CCONJ
ejpam-6859	182	6	applied	applied	ADJ
ejpam-6859	182	7	mathematics	mathematic	NOUN
ejpam-6859	182	8	,	,	PUNCT
ejpam-6859	182	9	17(3):2329–2335	17(3):2329–2335	NUM
ejpam-6859	182	10	,	,	PUNCT
ejpam-6859	182	11	2024	2024	NUM
ejpam-6859	182	12	.	.	PUNCT
ejpam-6859	183	1	[	[	X
ejpam-6859	183	2	3	3	NUM
ejpam-6859	183	3	]	]	PUNCT
ejpam-6859	183	4	a.	a.	NOUN
ejpam-6859	183	5	alotaibi	alotaibi	NOUN
ejpam-6859	183	6	.	.	PUNCT
ejpam-6859	184	1	sign	sign	NOUN
ejpam-6859	184	2	-	-	PUNCT
ejpam-6859	184	3	symmetry	symmetry	NOUN
ejpam-6859	184	4	and	and	CCONJ
ejpam-6859	184	5	frustration	frustration	NOUN
ejpam-6859	184	6	index	index	NOUN
ejpam-6859	184	7	in	in	ADP
ejpam-6859	184	8	signed	sign	VERB
ejpam-6859	184	9	graphs	graph	NOUN
ejpam-6859	184	10	.	.	PUNCT
ejpam-6859	185	1	master	master	NOUN
ejpam-6859	185	2	’s	’s	PART
ejpam-6859	185	3	thesis	thesis	NOUN
ejpam-6859	185	4	,	,	PUNCT
ejpam-6859	185	5	mississippi	mississippi	PROPN
ejpam-6859	185	6	state	state	PROPN
ejpam-6859	185	7	university	university	PROPN
ejpam-6859	185	8	,	,	PUNCT
ejpam-6859	185	9	2023	2023	NUM
ejpam-6859	185	10	.	.	PUNCT
ejpam-6859	186	1	[	[	X
ejpam-6859	186	2	4	4	NUM
ejpam-6859	186	3	]	]	PUNCT
ejpam-6859	186	4	a.	a.	NOUN
ejpam-6859	186	5	m.	m.	NOUN
ejpam-6859	186	6	alotaibi	alotaibi	PROPN
ejpam-6859	186	7	,	,	PUNCT
ejpam-6859	186	8	k.	k.	PROPN
ejpam-6859	186	9	al	al	PROPN
ejpam-6859	186	10	-	-	PROPN
ejpam-6859	186	11	tahat	tahat	PROPN
ejpam-6859	186	12	,	,	PUNCT
ejpam-6859	186	13	and	and	CCONJ
ejpam-6859	186	14	k.	k.	PROPN
ejpam-6859	186	15	m.	m.	PROPN
ejpam-6859	186	16	aljamal	aljamal	PROPN
ejpam-6859	186	17	.	.	PUNCT
ejpam-6859	187	1	notes	note	NOUN
ejpam-6859	187	2	on	on	ADP
ejpam-6859	187	3	finite	finite	ADJ
ejpam-6859	187	4	groups	group	NOUN
ejpam-6859	187	5	with	with	ADP
ejpam-6859	187	6	nearly	nearly	ADV
ejpam-6859	187	7	spermutable	spermutable	NOUN
ejpam-6859	187	8	and	and	CCONJ
ejpam-6859	187	9	nearly	nearly	ADV
ejpam-6859	187	10	s	s	NOUN
ejpam-6859	187	11	-	-	PUNCT
ejpam-6859	187	12	permutable	permutable	ADJ
ejpam-6859	187	13	-	-	PUNCT
ejpam-6859	187	14	transitive	transitive	ADJ
ejpam-6859	187	15	subgroups	subgroup	NOUN
ejpam-6859	187	16	.	.	PUNCT
ejpam-6859	188	1	european	european	ADJ
ejpam-6859	188	2	journal	journal	PROPN
ejpam-6859	188	3	of	of	ADP
ejpam-6859	188	4	pure	pure	ADJ
ejpam-6859	188	5	and	and	CCONJ
ejpam-6859	188	6	applied	applied	ADJ
ejpam-6859	188	7	mathematics	mathematic	NOUN
ejpam-6859	188	8	,	,	PUNCT
ejpam-6859	188	9	18(3):6033–6033	18(3):6033–6033	NUM
ejpam-6859	188	10	,	,	PUNCT
ejpam-6859	188	11	2025	2025	NUM
ejpam-6859	188	12	.	.	PUNCT
ejpam-6859	189	1	[	[	X
ejpam-6859	189	2	5	5	X
ejpam-6859	189	3	]	]	PUNCT
ejpam-6859	189	4	w.	w.	PROPN
ejpam-6859	189	5	burnside	burnside	PROPN
ejpam-6859	189	6	.	.	PUNCT
ejpam-6859	190	1	theory	theory	NOUN
ejpam-6859	190	2	of	of	ADP
ejpam-6859	190	3	groups	group	NOUN
ejpam-6859	190	4	of	of	ADP
ejpam-6859	190	5	finite	finite	ADJ
ejpam-6859	190	6	order	order	NOUN
ejpam-6859	190	7	.	.	PUNCT
ejpam-6859	191	1	cambridge	cambridge	PROPN
ejpam-6859	191	2	university	university	PROPN
ejpam-6859	191	3	press	press	NOUN
ejpam-6859	191	4	,	,	PUNCT
ejpam-6859	191	5	2	2	NUM
ejpam-6859	191	6	edition	edition	NOUN
ejpam-6859	191	7	,	,	PUNCT
ejpam-6859	191	8	1911	1911	NUM
ejpam-6859	191	9	.	.	PUNCT
ejpam-6859	192	1	[	[	X
ejpam-6859	192	2	6	6	NUM
ejpam-6859	192	3	]	]	PUNCT
ejpam-6859	192	4	i.	i.	PROPN
ejpam-6859	192	5	m.	m.	PROPN
ejpam-6859	192	6	isaacs	isaacs	PROPN
ejpam-6859	192	7	.	.	PUNCT
ejpam-6859	193	1	finite	finite	PROPN
ejpam-6859	193	2	group	group	PROPN
ejpam-6859	193	3	theory	theory	NOUN
ejpam-6859	193	4	,	,	PUNCT
ejpam-6859	193	5	volume	volume	NOUN
ejpam-6859	193	6	92	92	NUM
ejpam-6859	193	7	of	of	ADP
ejpam-6859	193	8	graduate	graduate	NOUN
ejpam-6859	193	9	studies	study	NOUN
ejpam-6859	193	10	in	in	ADP
ejpam-6859	193	11	mathematics	mathematic	NOUN
ejpam-6859	193	12	.	.	PUNCT
ejpam-6859	194	1	american	american	PROPN
ejpam-6859	194	2	mathematical	mathematical	PROPN
ejpam-6859	194	3	society	society	NOUN
ejpam-6859	194	4	,	,	PUNCT
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ejpam-6859	194	6	.	.	PUNCT
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ejpam-6859	195	2	7	7	X
ejpam-6859	195	3	]	]	X
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ejpam-6859	195	5	gorenstein	gorenstein	PROPN
ejpam-6859	195	6	.	.	PUNCT
ejpam-6859	196	1	finite	finite	PROPN
ejpam-6859	196	2	groups	group	NOUN
ejpam-6859	196	3	.	.	PUNCT
ejpam-6859	197	1	harper	harper	NOUN
ejpam-6859	197	2	&	&	CCONJ
ejpam-6859	197	3	row	row	PROPN
ejpam-6859	197	4	,	,	PUNCT
ejpam-6859	197	5	1968	1968	NUM
ejpam-6859	197	6	.	.	PUNCT
ejpam-6859	198	1	[	[	X
ejpam-6859	198	2	8	8	X
ejpam-6859	198	3	]	]	X
ejpam-6859	198	4	j.	j.	PROPN
ejpam-6859	198	5	l.	l.	PROPN
ejpam-6859	198	6	alperin	alperin	PROPN
ejpam-6859	198	7	.	.	PUNCT
ejpam-6859	199	1	local	local	ADJ
ejpam-6859	199	2	representation	representation	NOUN
ejpam-6859	199	3	theory	theory	NOUN
ejpam-6859	199	4	.	.	PUNCT
ejpam-6859	200	1	cambridge	cambridge	PROPN
ejpam-6859	200	2	university	university	PROPN
ejpam-6859	200	3	press	press	NOUN
ejpam-6859	200	4	,	,	PUNCT
ejpam-6859	200	5	1986	1986	NUM
ejpam-6859	200	6	.	.	PUNCT
ejpam-6859	201	1	[	[	X
ejpam-6859	201	2	9	9	NUM
ejpam-6859	201	3	]	]	PUNCT
ejpam-6859	201	4	m.	m.	NOUN
ejpam-6859	201	5	aschbacher	aschbacher	PROPN
ejpam-6859	201	6	,	,	PUNCT
ejpam-6859	201	7	r.	r.	PROPN
ejpam-6859	201	8	kessar	kessar	PROPN
ejpam-6859	201	9	,	,	PUNCT
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ejpam-6859	201	11	b.	b.	PROPN
ejpam-6859	201	12	oliver	oliver	PROPN
ejpam-6859	201	13	.	.	PUNCT
ejpam-6859	201	14	fusion	fusion	NOUN
ejpam-6859	201	15	systems	system	NOUN
ejpam-6859	201	16	in	in	ADP
ejpam-6859	201	17	algebra	algebra	NOUN
ejpam-6859	201	18	and	and	CCONJ
ejpam-6859	201	19	topology	topology	NOUN
ejpam-6859	201	20	.	.	PUNCT
ejpam-6859	202	1	cambridge	cambridge	PROPN
ejpam-6859	202	2	university	university	PROPN
ejpam-6859	202	3	press	press	PROPN
ejpam-6859	202	4	,	,	PUNCT
ejpam-6859	202	5	new	new	PROPN
ejpam-6859	202	6	york	york	PROPN
ejpam-6859	202	7	,	,	PUNCT
ejpam-6859	202	8	ny	ny	PROPN
ejpam-6859	202	9	,	,	PUNCT
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ejpam-6859	202	11	.	.	PUNCT
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ejpam-6859	203	5	tate	tate	PROPN
ejpam-6859	203	6	.	.	PUNCT
ejpam-6859	204	1	nilpotent	nilpotent	PROPN
ejpam-6859	204	2	quotient	quotient	NOUN
ejpam-6859	204	3	groups	group	NOUN
ejpam-6859	204	4	.	.	PUNCT
ejpam-6859	205	1	topology	topology	NOUN
ejpam-6859	205	2	,	,	PUNCT
ejpam-6859	205	3	3:109–111	3:109–111	PROPN
ejpam-6859	205	4	,	,	PUNCT
ejpam-6859	205	5	1964	1964	NUM
ejpam-6859	205	6	.	.	PUNCT
ejpam-6859	206	1	[	[	X
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ejpam-6859	206	6	.	.	PUNCT
ejpam-6859	207	1	frobenius	frobenius	PROPN
ejpam-6859	207	2	categories	category	NOUN
ejpam-6859	207	3	versus	versus	ADP
ejpam-6859	207	4	fusion	fusion	NOUN
ejpam-6859	207	5	systems	system	NOUN
ejpam-6859	207	6	.	.	PUNCT
ejpam-6859	208	1	groups	group	NOUN
ejpam-6859	208	2	,	,	PUNCT
ejpam-6859	208	3	geometry	geometry	NOUN
ejpam-6859	208	4	,	,	PUNCT
ejpam-6859	208	5	and	and	CCONJ
ejpam-6859	208	6	dynamics	dynamic	NOUN
ejpam-6859	208	7	,	,	PUNCT
ejpam-6859	208	8	3(1):59–120	3(1):59–120	NUM
ejpam-6859	208	9	,	,	PUNCT
ejpam-6859	208	10	2009	2009	NUM
ejpam-6859	208	11	.	.	PUNCT
ejpam-6859	209	1	[	[	X
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ejpam-6859	209	3	]	]	X
ejpam-6859	209	4	d.	d.	PROPN
ejpam-6859	209	5	s.	s.	PROPN
ejpam-6859	209	6	dummit	dummit	PROPN
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ejpam-6859	209	8	r.	r.	PROPN
ejpam-6859	209	9	m.	m.	PROPN
ejpam-6859	209	10	foote	foote	PROPN
ejpam-6859	209	11	.	.	PUNCT
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ejpam-6859	210	2	algebra	algebra	PROPN
ejpam-6859	210	3	.	.	PUNCT
ejpam-6859	211	1	john	john	PROPN
ejpam-6859	211	2	wiley	wiley	PROPN
ejpam-6859	211	3	&	&	CCONJ
ejpam-6859	211	4	sons	sons	PROPN
ejpam-6859	211	5	,	,	PUNCT
ejpam-6859	211	6	hoboken	hoboken	PROPN
ejpam-6859	211	7	,	,	PUNCT
ejpam-6859	211	8	nj	nj	PROPN
ejpam-6859	211	9	,	,	PUNCT
ejpam-6859	211	10	3	3	NUM
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ejpam-6859	211	12	,	,	PUNCT
ejpam-6859	211	13	2004	2004	NUM
ejpam-6859	211	14	.	.	PUNCT