id	sid	tid	token	lemma	pos
ejpam-6033	1	1	european	european	PROPN
ejpam-6033	1	2	journal	journal	PROPN
ejpam-6033	1	3	of	of	ADP
ejpam-6033	1	4	pure	pure	ADJ
ejpam-6033	1	5	and	and	CCONJ
ejpam-6033	1	6	applied	applied	ADJ
ejpam-6033	1	7	mathematics	mathematic	NOUN
ejpam-6033	1	8	2025	2025	NUM
ejpam-6033	1	9	,	,	PUNCT
ejpam-6033	1	10	vol	vol	NOUN
ejpam-6033	1	11	.	.	PROPN
ejpam-6033	1	12	18	18	NUM
ejpam-6033	1	13	,	,	PUNCT
ejpam-6033	1	14	issue	issue	NOUN
ejpam-6033	1	15	3	3	NUM
ejpam-6033	1	16	,	,	PUNCT
ejpam-6033	1	17	article	article	NOUN
ejpam-6033	1	18	number	number	NOUN
ejpam-6033	1	19	6033	6033	NUM
ejpam-6033	1	20	issn	issn	PROPN
ejpam-6033	1	21	1307	1307	NUM
ejpam-6033	1	22	-	-	SYM
ejpam-6033	1	23	5543	5543	NUM
ejpam-6033	1	24	–	–	PUNCT
ejpam-6033	1	25	ejpam.com	ejpam.com	X
ejpam-6033	1	26	published	publish	VERB
ejpam-6033	1	27	by	by	ADP
ejpam-6033	1	28	new	new	PROPN
ejpam-6033	1	29	york	york	PROPN
ejpam-6033	1	30	business	business	PROPN
ejpam-6033	1	31	global	global	ADJ
ejpam-6033	1	32	notes	note	NOUN
ejpam-6033	1	33	on	on	ADP
ejpam-6033	1	34	finite	finite	ADJ
ejpam-6033	1	35	groups	group	NOUN
ejpam-6033	1	36	with	with	ADP
ejpam-6033	1	37	nearly	nearly	ADV
ejpam-6033	1	38	sylow	sylow	NOUN
ejpam-6033	1	39	-	-	PUNCT
ejpam-6033	1	40	permutable	permutable	ADJ
ejpam-6033	1	41	and	and	CCONJ
ejpam-6033	1	42	nearly	nearly	ADV
ejpam-6033	1	43	sylow	sylow	NOUN
ejpam-6033	1	44	-	-	PUNCT
ejpam-6033	1	45	permutable	permutable	ADJ
ejpam-6033	1	46	-	-	PUNCT
ejpam-6033	1	47	transitive	transitive	NOUN
ejpam-6033	1	48	subgroups	subgroup	NOUN
ejpam-6033	1	49	abdulaziz	abdulaziz	PROPN
ejpam-6033	1	50	mutlaq	mutlaq	PROPN
ejpam-6033	1	51	alotaibi1	alotaibi1	PROPN
ejpam-6033	1	52	,	,	PUNCT
ejpam-6033	1	53	khalid	khalid	PROPN
ejpam-6033	1	54	al	al	PROPN
ejpam-6033	1	55	-	-	PUNCT
ejpam-6033	1	56	tahat2	tahat2	PROPN
ejpam-6033	1	57	,	,	PUNCT
ejpam-6033	1	58	khaled	khaled	PROPN
ejpam-6033	1	59	mustafa	mustafa	PROPN
ejpam-6033	1	60	al	al	PROPN
ejpam-6033	1	61	-	-	PUNCT
ejpam-6033	1	62	jamal2,∗	jamal2,∗	PROPN
ejpam-6033	1	63	1	1	NUM
ejpam-6033	1	64	department	department	NOUN
ejpam-6033	1	65	of	of	ADP
ejpam-6033	1	66	mathematics	mathematic	NOUN
ejpam-6033	1	67	,	,	PUNCT
ejpam-6033	1	68	college	college	NOUN
ejpam-6033	1	69	of	of	ADP
ejpam-6033	1	70	science	science	NOUN
ejpam-6033	1	71	and	and	CCONJ
ejpam-6033	1	72	humanities	humanity	NOUN
ejpam-6033	1	73	in	in	ADP
ejpam-6033	1	74	al	al	PROPN
ejpam-6033	1	75	-	-	PUNCT
ejpam-6033	1	76	kharj	kharj	PROPN
ejpam-6033	1	77	,	,	PUNCT
ejpam-6033	1	78	prince	prince	PROPN
ejpam-6033	1	79	sattam	sattam	PROPN
ejpam-6033	1	80	bin	bin	PROPN
ejpam-6033	1	81	abdulaziz	abdulaziz	PROPN
ejpam-6033	1	82	university	university	PROPN
ejpam-6033	1	83	,	,	PUNCT
ejpam-6033	1	84	saudi	saudi	PROPN
ejpam-6033	1	85	arabia	arabia	PROPN
ejpam-6033	1	86	2	2	NUM
ejpam-6033	1	87	faculty	faculty	NOUN
ejpam-6033	1	88	of	of	ADP
ejpam-6033	1	89	computer	computer	NOUN
ejpam-6033	1	90	studies	study	NOUN
ejpam-6033	1	91	,	,	PUNCT
ejpam-6033	1	92	arab	arab	ADJ
ejpam-6033	1	93	open	open	PROPN
ejpam-6033	1	94	university	university	PROPN
ejpam-6033	1	95	,	,	PUNCT
ejpam-6033	1	96	amman	amman	PROPN
ejpam-6033	1	97	,	,	PUNCT
ejpam-6033	1	98	jordan	jordan	PROPN
ejpam-6033	1	99	abstract	abstract	PROPN
ejpam-6033	1	100	.	.	PUNCT
ejpam-6033	2	1	let	let	VERB
ejpam-6033	2	2	g	g	PRON
ejpam-6033	2	3	be	be	AUX
ejpam-6033	2	4	a	a	DET
ejpam-6033	2	5	finite	finite	ADJ
ejpam-6033	2	6	group	group	NOUN
ejpam-6033	2	7	and	and	CCONJ
ejpam-6033	2	8	let	let	VERB
ejpam-6033	2	9	h	h	PRON
ejpam-6033	2	10	be	be	AUX
ejpam-6033	2	11	a	a	DET
ejpam-6033	2	12	subgroup	subgroup	NOUN
ejpam-6033	2	13	of	of	ADP
ejpam-6033	2	14	g.	g.	PROPN
ejpam-6033	2	15	we	we	PRON
ejpam-6033	2	16	called	call	VERB
ejpam-6033	2	17	h	h	NOUN
ejpam-6033	2	18	is	be	AUX
ejpam-6033	2	19	nearly	nearly	ADV
ejpam-6033	2	20	spermutable	spermutable	NOUN
ejpam-6033	2	21	in	in	ADP
ejpam-6033	2	22	g	g	PROPN
ejpam-6033	2	23	if	if	SCONJ
ejpam-6033	2	24	for	for	ADP
ejpam-6033	2	25	every	every	DET
ejpam-6033	2	26	prime	prime	NOUN
ejpam-6033	2	27	p	p	NOUN
ejpam-6033	2	28	such	such	ADJ
ejpam-6033	2	29	that	that	SCONJ
ejpam-6033	2	30	(	(	PUNCT
ejpam-6033	2	31	p	p	X
ejpam-6033	2	32	:	:	PUNCT
ejpam-6033	2	33	|h	|h	X
ejpam-6033	2	34	|=	|=	PUNCT
ejpam-6033	2	35	1	1	X
ejpam-6033	2	36	)	)	PUNCT
ejpam-6033	2	37	p	p	NOUN
ejpam-6033	2	38	-	-	PUNCT
ejpam-6033	2	39	subgroup	subgroup	NOUN
ejpam-6033	2	40	of	of	ADP
ejpam-6033	2	41	k.	k.	PROPN
ejpam-6033	2	42	we	we	PRON
ejpam-6033	2	43	shall	shall	AUX
ejpam-6033	2	44	denote	denote	VERB
ejpam-6033	2	45	this	this	PRON
ejpam-6033	2	46	by	by	ADP
ejpam-6033	2	47	(	(	PUNCT
ejpam-6033	2	48	h	h	NOUN
ejpam-6033	2	49	is	be	AUX
ejpam-6033	2	50	nsp	nsp	ADJ
ejpam-6033	2	51	in	in	ADP
ejpam-6033	2	52	g	g	NOUN
ejpam-6033	2	53	)	)	PUNCT
ejpam-6033	2	54	.	.	PUNCT
ejpam-6033	3	1	we	we	PRON
ejpam-6033	3	2	introduce	introduce	VERB
ejpam-6033	3	3	the	the	DET
ejpam-6033	3	4	class	class	NOUN
ejpam-6033	3	5	of	of	ADP
ejpam-6033	3	6	nearly	nearly	ADV
ejpam-6033	3	7	s	s	NOUN
ejpam-6033	3	8	-	-	ADJ
ejpam-6033	3	9	permutable	permutable	ADJ
ejpam-6033	3	10	transitive	transitive	ADJ
ejpam-6033	3	11	-groups	-group	NOUN
ejpam-6033	3	12	as	as	SCONJ
ejpam-6033	3	13	those	those	DET
ejpam-6033	3	14	groups	group	NOUN
ejpam-6033	3	15	in	in	ADP
ejpam-6033	3	16	which	which	PRON
ejpam-6033	3	17	nearly	nearly	ADV
ejpam-6033	3	18	s	s	VERB
ejpam-6033	3	19	-permutability	-permutability	NOUN
ejpam-6033	3	20	is	be	AUX
ejpam-6033	3	21	transitive	transitive	ADJ
ejpam-6033	3	22	among	among	ADP
ejpam-6033	3	23	subgroups	subgroup	NOUN
ejpam-6033	3	24	.	.	PUNCT
ejpam-6033	4	1	that	that	PRON
ejpam-6033	4	2	is	be	AUX
ejpam-6033	4	3	,	,	PUNCT
ejpam-6033	4	4	if	if	SCONJ
ejpam-6033	4	5	a	a	PRON
ejpam-6033	4	6	is	be	AUX
ejpam-6033	4	7	nsp	nsp	ADJ
ejpam-6033	4	8	in	in	ADP
ejpam-6033	4	9	b	b	NOUN
ejpam-6033	4	10	;	;	PUNCT
ejpam-6033	4	11	and	and	CCONJ
ejpam-6033	4	12	b	b	NOUN
ejpam-6033	4	13	is	be	AUX
ejpam-6033	4	14	nsp	nsp	ADJ
ejpam-6033	4	15	in	in	ADP
ejpam-6033	4	16	g	g	PROPN
ejpam-6033	4	17	,	,	PUNCT
ejpam-6033	4	18	then	then	ADV
ejpam-6033	4	19	a	a	PRON
ejpam-6033	4	20	is	be	AUX
ejpam-6033	4	21	nsp	nsp	ADJ
ejpam-6033	4	22	in	in	ADP
ejpam-6033	4	23	g	g	PROPN
ejpam-6033	4	24	:	:	PUNCT
ejpam-6033	4	25	in	in	ADP
ejpam-6033	4	26	this	this	DET
ejpam-6033	4	27	paper	paper	NOUN
ejpam-6033	4	28	we	we	PRON
ejpam-6033	4	29	study	study	VERB
ejpam-6033	4	30	some	some	PRON
ejpam-6033	4	31	characterize	characterize	VERB
ejpam-6033	4	32	finite	finite	ADJ
ejpam-6033	4	33	groups	group	NOUN
ejpam-6033	4	34	using	use	VERB
ejpam-6033	4	35	nsp	nsp	PROPN
ejpam-6033	4	36	and	and	CCONJ
ejpam-6033	4	37	nspt	nspt	PROPN
ejpam-6033	4	38	and	and	CCONJ
ejpam-6033	4	39	we	we	PRON
ejpam-6033	4	40	compare	compare	VERB
ejpam-6033	4	41	some	some	DET
ejpam-6033	4	42	subgroups	subgroup	NOUN
ejpam-6033	4	43	with	with	ADP
ejpam-6033	4	44	groups	group	NOUN
ejpam-6033	4	45	under	under	ADP
ejpam-6033	4	46	study	study	NOUN
ejpam-6033	4	47	,	,	PUNCT
ejpam-6033	4	48	supported	support	VERB
ejpam-6033	4	49	by	by	ADP
ejpam-6033	4	50	theorems	theorem	NOUN
ejpam-6033	4	51	and	and	CCONJ
ejpam-6033	4	52	examples	example	NOUN
ejpam-6033	4	53	.	.	PUNCT
ejpam-6033	5	1	2020	2020	NUM
ejpam-6033	5	2	mathematics	mathematic	NOUN
ejpam-6033	5	3	subject	subject	NOUN
ejpam-6033	5	4	classifications	classification	NOUN
ejpam-6033	5	5	:	:	PUNCT
ejpam-6033	5	6	20d10	20d10	NUM
ejpam-6033	5	7	,	,	PUNCT
ejpam-6033	5	8	20d20	20d20	NUM
ejpam-6033	5	9	,	,	PUNCT
ejpam-6033	5	10	20d35	20d35	NUM
ejpam-6033	5	11	key	key	ADJ
ejpam-6033	5	12	words	word	NOUN
ejpam-6033	5	13	and	and	CCONJ
ejpam-6033	5	14	phrases	phrase	NOUN
ejpam-6033	5	15	:	:	PUNCT
ejpam-6033	5	16	s	s	X
ejpam-6033	5	17	-	-	PUNCT
ejpam-6033	5	18	permutable	permutable	ADJ
ejpam-6033	5	19	subgroup	subgroup	NOUN
ejpam-6033	5	20	,	,	PUNCT
ejpam-6033	5	21	sylow	sylow	PROPN
ejpam-6033	5	22	subgroup	subgroup	PROPN
ejpam-6033	5	23	,	,	PUNCT
ejpam-6033	5	24	permutable	permutable	ADJ
ejpam-6033	5	25	subgroup	subgroup	NOUN
ejpam-6033	5	26	,	,	PUNCT
ejpam-6033	5	27	nearly	nearly	ADV
ejpam-6033	5	28	s	s	NOUN
ejpam-6033	5	29	-	-	ADJ
ejpam-6033	5	30	permutable	permutable	ADJ
ejpam-6033	5	31	subgroup	subgroup	NOUN
ejpam-6033	5	32	,	,	PUNCT
ejpam-6033	5	33	nearly	nearly	ADV
ejpam-6033	5	34	s	s	NOUN
ejpam-6033	5	35	-	-	PUNCT
ejpam-6033	5	36	permutable	permutable	ADJ
ejpam-6033	5	37	1	1	NUM
ejpam-6033	5	38	.	.	PUNCT
ejpam-6033	6	1	introduction	introduction	NOUN
ejpam-6033	6	2	in	in	ADP
ejpam-6033	6	3	this	this	DET
ejpam-6033	6	4	paper	paper	NOUN
ejpam-6033	7	1	,	,	PUNCT
ejpam-6033	7	2	all	all	DET
ejpam-6033	7	3	groups	group	NOUN
ejpam-6033	7	4	under	under	ADP
ejpam-6033	7	5	discussion	discussion	NOUN
ejpam-6033	7	6	are	be	AUX
ejpam-6033	7	7	finite	finite	ADJ
ejpam-6033	7	8	.	.	PUNCT
ejpam-6033	8	1	a	a	DET
ejpam-6033	8	2	subgroup	subgroup	NOUN
ejpam-6033	8	3	h	h	NOUN
ejpam-6033	8	4	of	of	ADP
ejpam-6033	8	5	a	a	DET
ejpam-6033	8	6	group	group	NOUN
ejpam-6033	8	7	g	g	NOUN
ejpam-6033	8	8	is	be	AUX
ejpam-6033	8	9	said	say	VERB
ejpam-6033	8	10	to	to	PART
ejpam-6033	8	11	commute	commute	VERB
ejpam-6033	8	12	with	with	ADP
ejpam-6033	8	13	another	another	DET
ejpam-6033	8	14	subgroup	subgroup	NOUN
ejpam-6033	8	15	k	k	PROPN
ejpam-6033	8	16	if	if	SCONJ
ejpam-6033	8	17	the	the	DET
ejpam-6033	8	18	product	product	NOUN
ejpam-6033	8	19	hk	hk	PROPN
ejpam-6033	8	20	is	be	AUX
ejpam-6033	8	21	also	also	ADV
ejpam-6033	8	22	a	a	DET
ejpam-6033	8	23	subgroup	subgroup	NOUN
ejpam-6033	8	24	of	of	ADP
ejpam-6033	8	25	g.	g.	PROPN
ejpam-6033	8	26	if	if	SCONJ
ejpam-6033	8	27	h	h	NOUN
ejpam-6033	8	28	commutes	commute	VERB
ejpam-6033	8	29	with	with	ADP
ejpam-6033	8	30	every	every	DET
ejpam-6033	8	31	subgroup	subgroup	NOUN
ejpam-6033	8	32	(	(	PUNCT
ejpam-6033	8	33	or	or	CCONJ
ejpam-6033	8	34	every	every	DET
ejpam-6033	8	35	sylow	sylow	NOUN
ejpam-6033	8	36	subgroup	subgroup	NOUN
ejpam-6033	8	37	)	)	PUNCT
ejpam-6033	8	38	of	of	ADP
ejpam-6033	8	39	g	g	PROPN
ejpam-6033	8	40	,	,	PUNCT
ejpam-6033	8	41	it	it	PRON
ejpam-6033	8	42	is	be	AUX
ejpam-6033	8	43	called	call	VERB
ejpam-6033	8	44	a	a	DET
ejpam-6033	8	45	permutable	permutable	ADJ
ejpam-6033	8	46	(	(	PUNCT
ejpam-6033	8	47	or	or	CCONJ
ejpam-6033	8	48	s	s	NOUN
ejpam-6033	8	49	-	-	PUNCT
ejpam-6033	8	50	permutable	permutable	ADJ
ejpam-6033	8	51	)	)	PUNCT
ejpam-6033	8	52	subgroup	subgroup	NOUN
ejpam-6033	9	1	[	[	X
ejpam-6033	9	2	1	1	NUM
ejpam-6033	9	3	]	]	PUNCT
ejpam-6033	9	4	.	.	PUNCT
ejpam-6033	10	1	a	a	DET
ejpam-6033	10	2	well	well	ADV
ejpam-6033	10	3	-	-	PUNCT
ejpam-6033	10	4	known	know	VERB
ejpam-6033	10	5	fact	fact	NOUN
ejpam-6033	10	6	in	in	ADP
ejpam-6033	10	7	group	group	NOUN
ejpam-6033	10	8	theory	theory	NOUN
ejpam-6033	10	9	is	be	AUX
ejpam-6033	10	10	that	that	SCONJ
ejpam-6033	10	11	normal	normal	ADJ
ejpam-6033	10	12	p	p	ADJ
ejpam-6033	10	13	-	-	PUNCT
ejpam-6033	10	14	sylow	sylow	NOUN
ejpam-6033	10	15	subgroups	subgroup	NOUN
ejpam-6033	10	16	imply	imply	VERB
ejpam-6033	10	17	nilpotency	nilpotency	NOUN
ejpam-6033	10	18	,	,	PUNCT
ejpam-6033	10	19	as	as	SCONJ
ejpam-6033	10	20	normality	normality	NOUN
ejpam-6033	10	21	plays	play	VERB
ejpam-6033	10	22	a	a	DET
ejpam-6033	10	23	central	central	ADJ
ejpam-6033	10	24	role	role	NOUN
ejpam-6033	10	25	in	in	ADP
ejpam-6033	10	26	subgroup	subgroup	NOUN
ejpam-6033	10	27	structure	structure	NOUN
ejpam-6033	10	28	.	.	PUNCT
ejpam-6033	11	1	one	one	NUM
ejpam-6033	11	2	fundamental	fundamental	ADJ
ejpam-6033	11	3	property	property	NOUN
ejpam-6033	11	4	of	of	ADP
ejpam-6033	11	5	normal	normal	ADJ
ejpam-6033	11	6	subgroups	subgroup	NOUN
ejpam-6033	11	7	is	be	AUX
ejpam-6033	11	8	that	that	SCONJ
ejpam-6033	11	9	if	if	SCONJ
ejpam-6033	11	10	n	n	PRON
ejpam-6033	11	11	is	be	AUX
ejpam-6033	11	12	a	a	DET
ejpam-6033	11	13	normal	normal	ADJ
ejpam-6033	11	14	subgroup	subgroup	NOUN
ejpam-6033	11	15	of	of	ADP
ejpam-6033	11	16	g	g	PROPN
ejpam-6033	11	17	and	and	CCONJ
ejpam-6033	11	18	h	h	NOUN
ejpam-6033	11	19	is	be	AUX
ejpam-6033	11	20	any	any	DET
ejpam-6033	11	21	subgroup	subgroup	NOUN
ejpam-6033	11	22	of	of	ADP
ejpam-6033	11	23	g	g	PROPN
ejpam-6033	11	24	,	,	PUNCT
ejpam-6033	11	25	then	then	ADV
ejpam-6033	11	26	nh	nh	PROPN
ejpam-6033	12	1	=	=	SYM
ejpam-6033	12	2	hn	hn	PROPN
ejpam-6033	12	3	.	.	PUNCT
ejpam-6033	13	1	however	however	ADV
ejpam-6033	13	2	,	,	PUNCT
ejpam-6033	13	3	it	it	PRON
ejpam-6033	13	4	has	have	AUX
ejpam-6033	13	5	been	be	AUX
ejpam-6033	13	6	observed	observe	VERB
ejpam-6033	13	7	that	that	SCONJ
ejpam-6033	13	8	some	some	DET
ejpam-6033	13	9	subgroups	subgroup	NOUN
ejpam-6033	13	10	,	,	PUNCT
ejpam-6033	13	11	although	although	SCONJ
ejpam-6033	13	12	not	not	PART
ejpam-6033	13	13	normal	normal	ADJ
ejpam-6033	13	14	,	,	PUNCT
ejpam-6033	13	15	still	still	ADV
ejpam-6033	13	16	commute	commute	VERB
ejpam-6033	13	17	with	with	ADP
ejpam-6033	13	18	every	every	DET
ejpam-6033	13	19	subgroup	subgroup	NOUN
ejpam-6033	13	20	in	in	ADP
ejpam-6033	13	21	the	the	DET
ejpam-6033	13	22	group	group	NOUN
ejpam-6033	13	23	[	[	X
ejpam-6033	13	24	2	2	NUM
ejpam-6033	13	25	]	]	PUNCT
ejpam-6033	13	26	.	.	PUNCT
ejpam-6033	14	1	according	accord	VERB
ejpam-6033	14	2	to	to	ADP
ejpam-6033	14	3	[	[	X
ejpam-6033	14	4	1	1	NUM
ejpam-6033	14	5	]	]	PUNCT
ejpam-6033	14	6	,	,	PUNCT
ejpam-6033	14	7	an	an	DET
ejpam-6033	14	8	s	s	NOUN
ejpam-6033	14	9	-	-	PUNCT
ejpam-6033	14	10	permutable	permutable	ADJ
ejpam-6033	14	11	subgroup	subgroup	NOUN
ejpam-6033	14	12	of	of	ADP
ejpam-6033	14	13	a	a	DET
ejpam-6033	14	14	group	group	NOUN
ejpam-6033	14	15	is	be	AUX
ejpam-6033	14	16	subnormal	subnormal	ADJ
ejpam-6033	14	17	.	.	PUNCT
ejpam-6033	15	1	in	in	ADP
ejpam-6033	15	2	contrast	contrast	NOUN
ejpam-6033	15	3	,	,	PUNCT
ejpam-6033	15	4	nearly	nearly	ADV
ejpam-6033	15	5	s	s	NOUN
ejpam-6033	15	6	-	-	PUNCT
ejpam-6033	15	7	permutability	permutability	NOUN
ejpam-6033	15	8	does	do	AUX
ejpam-6033	15	9	not	not	PART
ejpam-6033	15	10	necessarily	necessarily	ADV
ejpam-6033	15	11	imply	imply	VERB
ejpam-6033	15	12	subnormality	subnormality	NOUN
ejpam-6033	15	13	[	[	X
ejpam-6033	15	14	3	3	NUM
ejpam-6033	15	15	]	]	PUNCT
ejpam-6033	15	16	.	.	PUNCT
ejpam-6033	16	1	a	a	DET
ejpam-6033	16	2	notable	notable	ADJ
ejpam-6033	16	3	example	example	NOUN
ejpam-6033	16	4	is	be	AUX
ejpam-6033	16	5	the	the	DET
ejpam-6033	16	6	dihedral	dihedral	ADJ
ejpam-6033	16	7	group	group	NOUN
ejpam-6033	16	8	d18	d18	NOUN
ejpam-6033	16	9	=	=	SYM
ejpam-6033	16	10	⟨r	⟨r	PROPN
ejpam-6033	16	11	,	,	PUNCT
ejpam-6033	16	12	s	s	PART
ejpam-6033	16	13	:	:	PUNCT
ejpam-6033	16	14	r9	r9	PROPN
ejpam-6033	16	15	=	=	SYM
ejpam-6033	16	16	s2	s2	PROPN
ejpam-6033	16	17	=	=	SYM
ejpam-6033	16	18	e	e	NOUN
ejpam-6033	16	19	,	,	PUNCT
ejpam-6033	16	20	rs	rs	PROPN
ejpam-6033	16	21	=	=	SYM
ejpam-6033	16	22	sr8	sr8	PROPN
ejpam-6033	16	23	⟩	⟩	PROPN
ejpam-6033	16	24	,	,	PUNCT
ejpam-6033	16	25	which	which	PRON
ejpam-6033	16	26	contains	contain	VERB
ejpam-6033	16	27	nearly	nearly	ADV
ejpam-6033	16	28	s	s	NOUN
ejpam-6033	16	29	-	-	ADJ
ejpam-6033	16	30	permutable	permutable	ADJ
ejpam-6033	16	31	subgroups	subgroup	NOUN
ejpam-6033	16	32	that	that	PRON
ejpam-6033	16	33	are	be	AUX
ejpam-6033	16	34	not	not	PART
ejpam-6033	16	35	subnormal	subnormal	ADJ
ejpam-6033	16	36	[	[	X
ejpam-6033	16	37	4	4	NUM
ejpam-6033	16	38	,	,	PUNCT
ejpam-6033	16	39	5	5	NUM
ejpam-6033	16	40	]	]	PUNCT
ejpam-6033	16	41	.	.	PUNCT
ejpam-6033	17	1	this	this	DET
ejpam-6033	17	2	∗corresponding	∗corresponde	VERB
ejpam-6033	17	3	author	author	NOUN
ejpam-6033	17	4	.	.	PUNCT
ejpam-6033	18	1	doi	doi	NOUN
ejpam-6033	18	2	:	:	PUNCT
ejpam-6033	18	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6033	https://doi.org/10.29020/nybg.ejpam.v18i3.6033	ADJ
ejpam-6033	18	4	email	email	NOUN
ejpam-6033	18	5	addresses	address	VERB
ejpam-6033	18	6	:	:	PUNCT
ejpam-6033	18	7	am.alotaibi@psau.edu.sa	am.alotaibi@psau.edu.sa	PROPN
ejpam-6033	18	8	(	(	PUNCT
ejpam-6033	18	9	a.	a.	NOUN
ejpam-6033	18	10	m.	m.	NOUN
ejpam-6033	18	11	alotaibi	alotaibi	PROPN
ejpam-6033	18	12	)	)	PUNCT
ejpam-6033	18	13	,	,	PUNCT
ejpam-6033	19	1	ktahat@aou.edu.jo	ktahat@aou.edu.jo	NOUN
ejpam-6033	19	2	(	(	PUNCT
ejpam-6033	19	3	k.al	k.al	PROPN
ejpam-6033	19	4	−	−	PROPN
ejpam-6033	19	5	tahat	tahat	PROPN
ejpam-6033	19	6	)	)	PUNCT
ejpam-6033	19	7	,	,	PUNCT
ejpam-6033	19	8	pt	pt	NOUN
ejpam-6033	19	9	aljammal@aou.edu.jo	aljammal@aou.edu.jo	NOUN
ejpam-6033	19	10	(	(	PUNCT
ejpam-6033	19	11	k.m.al	k.m.al	PROPN
ejpam-6033	19	12	−	−	PROPN
ejpam-6033	19	13	jamal	jamal	PROPN
ejpam-6033	19	14	)	)	PUNCT
ejpam-6033	19	15	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6033	19	16	1	1	NUM
ejpam-6033	19	17	copyright	copyright	NOUN
ejpam-6033	19	18	:	:	PUNCT
ejpam-6033	20	1	©	©	PROPN
ejpam-6033	20	2	2025	2025	NUM
ejpam-6033	20	3	the	the	DET
ejpam-6033	20	4	author(s	author(s	NOUN
ejpam-6033	20	5	)	)	PUNCT
ejpam-6033	20	6	.	.	PUNCT
ejpam-6033	21	1	(	(	PUNCT
ejpam-6033	21	2	cc	cc	NOUN
ejpam-6033	21	3	by	by	ADP
ejpam-6033	21	4	-	-	PUNCT
ejpam-6033	21	5	nc	nc	PROPN
ejpam-6033	21	6	4.0	4.0	NUM
ejpam-6033	21	7	)	)	PUNCT
ejpam-6033	21	8	a.	a.	NOUN
ejpam-6033	21	9	m.	m.	NOUN
ejpam-6033	21	10	alotaibiang	alotaibiang	PROPN
ejpam-6033	21	11	,	,	PUNCT
ejpam-6033	21	12	k.	k.	PROPN
ejpam-6033	21	13	al	al	PROPN
ejpam-6033	21	14	-	-	PROPN
ejpam-6033	21	15	tahat	tahat	PROPN
ejpam-6033	21	16	,	,	PUNCT
ejpam-6033	21	17	k.	k.	PROPN
ejpam-6033	21	18	m.	m.	PROPN
ejpam-6033	21	19	al	al	PROPN
ejpam-6033	21	20	-	-	PROPN
ejpam-6033	21	21	jamal	jamal	PROPN
ejpam-6033	21	22	/	/	SYM
ejpam-6033	21	23	eur	eur	PROPN
ejpam-6033	21	24	.	.	PUNCT
ejpam-6033	22	1	j.	j.	PROPN
ejpam-6033	22	2	pure	pure	PROPN
ejpam-6033	22	3	appl	appl	PROPN
ejpam-6033	22	4	.	.	PROPN
ejpam-6033	22	5	math	math	PROPN
ejpam-6033	22	6	,	,	PUNCT
ejpam-6033	22	7	18	18	NUM
ejpam-6033	22	8	(	(	PUNCT
ejpam-6033	22	9	3	3	NUM
ejpam-6033	22	10	)	)	PUNCT
ejpam-6033	22	11	(	(	PUNCT
ejpam-6033	22	12	2025	2025	NUM
ejpam-6033	22	13	)	)	PUNCT
ejpam-6033	22	14	,	,	PUNCT
ejpam-6033	22	15	6033	6033	NUM
ejpam-6033	22	16	2	2	NUM
ejpam-6033	22	17	of	of	ADP
ejpam-6033	22	18	8	8	NUM
ejpam-6033	22	19	highlights	highlight	NOUN
ejpam-6033	22	20	the	the	DET
ejpam-6033	22	21	significance	significance	NOUN
ejpam-6033	22	22	of	of	ADP
ejpam-6033	22	23	studying	study	VERB
ejpam-6033	22	24	the	the	DET
ejpam-6033	22	25	structural	structural	ADJ
ejpam-6033	22	26	differences	difference	NOUN
ejpam-6033	22	27	between	between	ADP
ejpam-6033	22	28	these	these	DET
ejpam-6033	22	29	subgroup	subgroup	NOUN
ejpam-6033	22	30	properties	property	NOUN
ejpam-6033	22	31	.	.	PUNCT
ejpam-6033	23	1	motivated	motivate	VERB
ejpam-6033	23	2	by	by	ADP
ejpam-6033	23	3	this	this	PRON
ejpam-6033	23	4	,	,	PUNCT
ejpam-6033	23	5	our	our	PRON
ejpam-6033	23	6	research	research	NOUN
ejpam-6033	23	7	focuses	focus	VERB
ejpam-6033	23	8	on	on	ADP
ejpam-6033	23	9	nearly	nearly	ADV
ejpam-6033	23	10	s	s	NOUN
ejpam-6033	23	11	-	-	ADJ
ejpam-6033	23	12	permutable	permutable	ADJ
ejpam-6033	23	13	subgroups	subgroup	NOUN
ejpam-6033	23	14	and	and	CCONJ
ejpam-6033	23	15	introduces	introduce	VERB
ejpam-6033	23	16	a	a	DET
ejpam-6033	23	17	new	new	ADJ
ejpam-6033	23	18	class	class	NOUN
ejpam-6033	23	19	of	of	ADP
ejpam-6033	23	20	groups	group	NOUN
ejpam-6033	23	21	called	call	VERB
ejpam-6033	23	22	nspt	nspt	PROPN
ejpam-6033	23	23	-groups	-group	NOUN
ejpam-6033	23	24	,	,	PUNCT
ejpam-6033	23	25	in	in	ADP
ejpam-6033	23	26	which	which	PRON
ejpam-6033	23	27	the	the	DET
ejpam-6033	23	28	property	property	NOUN
ejpam-6033	23	29	of	of	ADP
ejpam-6033	23	30	nearly	nearly	ADV
ejpam-6033	23	31	s	s	NOUN
ejpam-6033	23	32	-	-	NOUN
ejpam-6033	23	33	permutability	permutability	NOUN
ejpam-6033	23	34	is	be	AUX
ejpam-6033	23	35	transitive	transitive	ADJ
ejpam-6033	23	36	among	among	ADP
ejpam-6033	23	37	subgroups	subgroup	NOUN
ejpam-6033	23	38	.	.	PUNCT
ejpam-6033	24	1	that	that	PRON
ejpam-6033	24	2	is	be	AUX
ejpam-6033	24	3	,	,	PUNCT
ejpam-6033	24	4	if	if	SCONJ
ejpam-6033	24	5	a	a	PRON
ejpam-6033	24	6	is	be	AUX
ejpam-6033	24	7	nearly	nearly	ADV
ejpam-6033	24	8	s	s	NOUN
ejpam-6033	24	9	-	-	NOUN
ejpam-6033	24	10	permutable	permutable	ADJ
ejpam-6033	24	11	in	in	ADP
ejpam-6033	24	12	b	b	NOUN
ejpam-6033	24	13	,	,	PUNCT
ejpam-6033	24	14	and	and	CCONJ
ejpam-6033	24	15	b	b	NOUN
ejpam-6033	24	16	is	be	AUX
ejpam-6033	24	17	nearly	nearly	ADV
ejpam-6033	24	18	s	s	NOUN
ejpam-6033	24	19	-	-	NOUN
ejpam-6033	24	20	permutable	permutable	ADJ
ejpam-6033	24	21	in	in	ADP
ejpam-6033	24	22	g	g	PROPN
ejpam-6033	24	23	,	,	PUNCT
ejpam-6033	24	24	then	then	ADV
ejpam-6033	24	25	a	a	PRON
ejpam-6033	24	26	is	be	AUX
ejpam-6033	24	27	nearly	nearly	ADV
ejpam-6033	24	28	s	s	NOUN
ejpam-6033	24	29	-	-	NOUN
ejpam-6033	24	30	permutable	permutable	ADJ
ejpam-6033	24	31	in	in	ADP
ejpam-6033	24	32	g	g	PROPN
ejpam-6033	24	33	[	[	X
ejpam-6033	24	34	6	6	NUM
ejpam-6033	24	35	]	]	PUNCT
ejpam-6033	24	36	.	.	PUNCT
ejpam-6033	25	1	several	several	ADJ
ejpam-6033	25	2	generalizations	generalization	NOUN
ejpam-6033	25	3	of	of	ADP
ejpam-6033	25	4	normality	normality	NOUN
ejpam-6033	25	5	and	and	CCONJ
ejpam-6033	25	6	subnormality	subnormality	NOUN
ejpam-6033	25	7	have	have	AUX
ejpam-6033	25	8	been	be	AUX
ejpam-6033	25	9	investigated	investigate	VERB
ejpam-6033	25	10	in	in	ADP
ejpam-6033	25	11	the	the	DET
ejpam-6033	25	12	literature	literature	NOUN
ejpam-6033	25	13	,	,	PUNCT
ejpam-6033	25	14	including	include	VERB
ejpam-6033	25	15	c	c	NOUN
ejpam-6033	25	16	-	-	PUNCT
ejpam-6033	25	17	normality	normality	NOUN
ejpam-6033	25	18	and	and	CCONJ
ejpam-6033	25	19	s	s	NOUN
ejpam-6033	25	20	-	-	NOUN
ejpam-6033	25	21	permutability	permutability	NOUN
ejpam-6033	25	22	.	.	PUNCT
ejpam-6033	26	1	for	for	ADP
ejpam-6033	26	2	example	example	NOUN
ejpam-6033	26	3	,	,	PUNCT
ejpam-6033	26	4	soluble	soluble	ADJ
ejpam-6033	26	5	t	t	PROPN
ejpam-6033	26	6	-groups	-group	NOUN
ejpam-6033	26	7	(	(	PUNCT
ejpam-6033	26	8	where	where	SCONJ
ejpam-6033	26	9	every	every	DET
ejpam-6033	26	10	subnormal	subnormal	ADJ
ejpam-6033	26	11	subgroup	subgroup	NOUN
ejpam-6033	26	12	is	be	AUX
ejpam-6033	26	13	normal	normal	ADJ
ejpam-6033	26	14	)	)	PUNCT
ejpam-6033	26	15	were	be	AUX
ejpam-6033	26	16	studied	study	VERB
ejpam-6033	26	17	in	in	ADP
ejpam-6033	26	18	[	[	X
ejpam-6033	26	19	7	7	NUM
ejpam-6033	26	20	]	]	PUNCT
ejpam-6033	26	21	,	,	PUNCT
ejpam-6033	26	22	and	and	CCONJ
ejpam-6033	26	23	similar	similar	ADJ
ejpam-6033	26	24	results	result	NOUN
ejpam-6033	26	25	for	for	ADP
ejpam-6033	26	26	spermutability	spermutability	NOUN
ejpam-6033	26	27	were	be	AUX
ejpam-6033	26	28	developed	develop	VERB
ejpam-6033	26	29	in	in	ADP
ejpam-6033	26	30	[	[	X
ejpam-6033	26	31	8	8	NUM
ejpam-6033	26	32	,	,	PUNCT
ejpam-6033	26	33	9	9	NUM
ejpam-6033	26	34	]	]	PUNCT
ejpam-6033	26	35	.	.	PUNCT
ejpam-6033	27	1	analogous	analogous	ADJ
ejpam-6033	27	2	results	result	NOUN
ejpam-6033	27	3	for	for	ADP
ejpam-6033	27	4	nearly	nearly	ADV
ejpam-6033	27	5	s	s	NOUN
ejpam-6033	27	6	-	-	NOUN
ejpam-6033	27	7	permutability	permutability	NOUN
ejpam-6033	27	8	were	be	AUX
ejpam-6033	27	9	given	give	VERB
ejpam-6033	27	10	in	in	ADP
ejpam-6033	27	11	[	[	X
ejpam-6033	27	12	10	10	NUM
ejpam-6033	27	13	]	]	PUNCT
ejpam-6033	27	14	,	,	PUNCT
ejpam-6033	27	15	where	where	SCONJ
ejpam-6033	27	16	the	the	DET
ejpam-6033	27	17	structure	structure	NOUN
ejpam-6033	27	18	of	of	ADP
ejpam-6033	27	19	soluble	soluble	ADJ
ejpam-6033	27	20	groups	group	NOUN
ejpam-6033	27	21	with	with	ADP
ejpam-6033	27	22	nearly	nearly	ADV
ejpam-6033	27	23	s	s	NOUN
ejpam-6033	27	24	-	-	ADJ
ejpam-6033	27	25	permutable	permutable	ADJ
ejpam-6033	27	26	subnormal	subnormal	ADJ
ejpam-6033	27	27	subgroups	subgroup	NOUN
ejpam-6033	27	28	was	be	AUX
ejpam-6033	27	29	described	describe	VERB
ejpam-6033	27	30	.	.	PUNCT
ejpam-6033	28	1	2	2	X
ejpam-6033	28	2	.	.	X
ejpam-6033	28	3	preliminaries	preliminary	NOUN
ejpam-6033	28	4	this	this	DET
ejpam-6033	28	5	section	section	NOUN
ejpam-6033	28	6	will	will	AUX
ejpam-6033	28	7	introduce	introduce	VERB
ejpam-6033	28	8	fundamental	fundamental	ADJ
ejpam-6033	28	9	theories	theory	NOUN
ejpam-6033	28	10	and	and	CCONJ
ejpam-6033	28	11	concepts	concept	NOUN
ejpam-6033	28	12	related	relate	VERB
ejpam-6033	28	13	to	to	ADP
ejpam-6033	28	14	groups	group	NOUN
ejpam-6033	28	15	and	and	CCONJ
ejpam-6033	28	16	subgroups	subgroup	NOUN
ejpam-6033	28	17	,	,	PUNCT
ejpam-6033	28	18	which	which	PRON
ejpam-6033	28	19	serve	serve	VERB
ejpam-6033	28	20	as	as	ADP
ejpam-6033	28	21	the	the	DET
ejpam-6033	28	22	foundation	foundation	NOUN
ejpam-6033	28	23	for	for	ADP
ejpam-6033	28	24	abstract	abstract	ADJ
ejpam-6033	28	25	algebra	algebra	NOUN
ejpam-6033	28	26	and	and	CCONJ
ejpam-6033	28	27	will	will	AUX
ejpam-6033	28	28	be	be	AUX
ejpam-6033	28	29	applied	apply	VERB
ejpam-6033	28	30	later	later	ADV
ejpam-6033	28	31	.	.	PUNCT
ejpam-6033	29	1	definition	definition	NOUN
ejpam-6033	29	2	1	1	NUM
ejpam-6033	29	3	.	.	PUNCT
ejpam-6033	30	1	[	[	X
ejpam-6033	30	2	10	10	NUM
ejpam-6033	30	3	]	]	X
ejpam-6033	30	4	a	a	DET
ejpam-6033	30	5	subgroup	subgroup	NOUN
ejpam-6033	30	6	h	h	NOUN
ejpam-6033	30	7	of	of	ADP
ejpam-6033	30	8	g	g	PROPN
ejpam-6033	30	9	is	be	AUX
ejpam-6033	30	10	termed	term	VERB
ejpam-6033	30	11	nearly	nearly	ADV
ejpam-6033	30	12	s	s	NOUN
ejpam-6033	30	13	-	-	NOUN
ejpam-6033	30	14	permutable	permutable	ADJ
ejpam-6033	30	15	in	in	ADP
ejpam-6033	30	16	g	g	PROPN
ejpam-6033	30	17	if	if	SCONJ
ejpam-6033	30	18	,	,	PUNCT
ejpam-6033	30	19	for	for	ADP
ejpam-6033	30	20	every	every	DET
ejpam-6033	30	21	prime	prime	NOUN
ejpam-6033	30	22	p	p	NOUN
ejpam-6033	30	23	that	that	PRON
ejpam-6033	30	24	does	do	AUX
ejpam-6033	30	25	not	not	PART
ejpam-6033	30	26	divide	divide	VERB
ejpam-6033	30	27	the	the	DET
ejpam-6033	30	28	order	order	NOUN
ejpam-6033	30	29	of	of	ADP
ejpam-6033	30	30	h	h	NOUN
ejpam-6033	30	31	,	,	PUNCT
ejpam-6033	30	32	and	and	CCONJ
ejpam-6033	30	33	for	for	ADP
ejpam-6033	30	34	every	every	DET
ejpam-6033	30	35	subgroup	subgroup	NOUN
ejpam-6033	30	36	k	k	PROPN
ejpam-6033	30	37	of	of	ADP
ejpam-6033	30	38	g	g	PROPN
ejpam-6033	30	39	containing	contain	VERB
ejpam-6033	30	40	h	h	NOUN
ejpam-6033	30	41	,	,	PUNCT
ejpam-6033	30	42	the	the	DET
ejpam-6033	30	43	normalizer	normalizer	PROPN
ejpam-6033	30	44	nk(h)includes	nk(h)include	VERB
ejpam-6033	30	45	at	at	ADV
ejpam-6033	30	46	least	least	ADV
ejpam-6033	30	47	one	one	NUM
ejpam-6033	30	48	sylow	sylow	NOUN
ejpam-6033	30	49	p	p	NOUN
ejpam-6033	30	50	-	-	PUNCT
ejpam-6033	30	51	subgroup	subgroup	NOUN
ejpam-6033	30	52	of	of	ADP
ejpam-6033	30	53	k.	k.	PROPN
ejpam-6033	30	54	we	we	PRON
ejpam-6033	30	55	use	use	VERB
ejpam-6033	30	56	the	the	DET
ejpam-6033	30	57	notation	notation	NOUN
ejpam-6033	30	58	h	h	NOUN
ejpam-6033	30	59	nspg	nspg	ADJ
ejpam-6033	30	60	to	to	PART
ejpam-6033	30	61	signify	signify	VERB
ejpam-6033	30	62	that	that	SCONJ
ejpam-6033	30	63	h	h	NOUN
ejpam-6033	30	64	is	be	AUX
ejpam-6033	30	65	nearly	nearly	ADV
ejpam-6033	30	66	s	s	NOUN
ejpam-6033	30	67	-	-	NOUN
ejpam-6033	30	68	permutable	permutable	ADJ
ejpam-6033	30	69	in	in	ADP
ejpam-6033	30	70	g.	g.	PROPN
ejpam-6033	30	71	definition	definition	NOUN
ejpam-6033	30	72	2	2	NUM
ejpam-6033	30	73	.	.	PUNCT
ejpam-6033	31	1	[	[	X
ejpam-6033	31	2	11	11	NUM
ejpam-6033	31	3	]	]	X
ejpam-6033	31	4	a	a	DET
ejpam-6033	31	5	group	group	NOUN
ejpam-6033	31	6	g	g	NOUN
ejpam-6033	31	7	is	be	AUX
ejpam-6033	31	8	referred	refer	VERB
ejpam-6033	31	9	to	to	ADP
ejpam-6033	31	10	as	as	ADP
ejpam-6033	31	11	an	an	DET
ejpam-6033	31	12	nspt	nspt	NOUN
ejpam-6033	31	13	-group	-group	NOUN
ejpam-6033	31	14	if	if	SCONJ
ejpam-6033	31	15	the	the	DET
ejpam-6033	31	16	property	property	NOUN
ejpam-6033	31	17	of	of	ADP
ejpam-6033	31	18	nearly	nearly	ADV
ejpam-6033	31	19	s	s	NOUN
ejpam-6033	31	20	-	-	NOUN
ejpam-6033	31	21	permutability	permutability	NOUN
ejpam-6033	31	22	is	be	AUX
ejpam-6033	31	23	transitive	transitive	ADJ
ejpam-6033	31	24	within	within	ADP
ejpam-6033	31	25	g.	g.	PROPN
ejpam-6033	31	26	specifically	specifically	ADV
ejpam-6033	31	27	,	,	PUNCT
ejpam-6033	31	28	g	g	PROPN
ejpam-6033	31	29	is	be	AUX
ejpam-6033	31	30	an	an	DET
ejpam-6033	31	31	nspt	nspt	ADJ
ejpam-6033	31	32	-group	-group	NOUN
ejpam-6033	31	33	if	if	SCONJ
ejpam-6033	31	34	,	,	PUNCT
ejpam-6033	31	35	for	for	ADP
ejpam-6033	31	36	any	any	DET
ejpam-6033	31	37	subgroups	subgroup	NOUN
ejpam-6033	31	38	h	h	NOUN
ejpam-6033	31	39	and	and	CCONJ
ejpam-6033	31	40	k	k	PROPN
ejpam-6033	31	41	of	of	ADP
ejpam-6033	31	42	g	g	PROPN
ejpam-6033	31	43	such	such	ADJ
ejpam-6033	31	44	that	that	SCONJ
ejpam-6033	31	45	his	his	PRON
ejpam-6033	31	46	nearly	nearly	ADV
ejpam-6033	31	47	s	s	NOUN
ejpam-6033	31	48	-	-	NOUN
ejpam-6033	31	49	permutable	permutable	ADJ
ejpam-6033	31	50	in	in	ADP
ejpam-6033	31	51	k	k	PROPN
ejpam-6033	31	52	and	and	CCONJ
ejpam-6033	31	53	k	k	PROPN
ejpam-6033	31	54	is	be	AUX
ejpam-6033	31	55	nearly	nearly	ADV
ejpam-6033	31	56	s	s	NOUN
ejpam-6033	31	57	-	-	NOUN
ejpam-6033	31	58	permutable	permutable	ADJ
ejpam-6033	31	59	in	in	ADP
ejpam-6033	31	60	g	g	PROPN
ejpam-6033	31	61	,	,	PUNCT
ejpam-6033	31	62	it	it	PRON
ejpam-6033	31	63	follows	follow	VERB
ejpam-6033	31	64	that	that	SCONJ
ejpam-6033	31	65	h	h	NOUN
ejpam-6033	31	66	is	be	AUX
ejpam-6033	31	67	nearly	nearly	ADV
ejpam-6033	31	68	s	s	NOUN
ejpam-6033	31	69	-	-	NOUN
ejpam-6033	31	70	permutable	permutable	ADJ
ejpam-6033	31	71	in	in	ADP
ejpam-6033	31	72	g.	g.	PROPN
ejpam-6033	31	73	lemma	lemma	PROPN
ejpam-6033	32	1	1	1	NUM
ejpam-6033	32	2	.	.	PUNCT
ejpam-6033	33	1	[	[	X
ejpam-6033	33	2	12	12	NUM
ejpam-6033	33	3	]	]	PUNCT
ejpam-6033	33	4	let	let	VERB
ejpam-6033	33	5	n	n	PRON
ejpam-6033	33	6	⊴g	⊴g	ADJ
ejpam-6033	33	7	and	and	CCONJ
ejpam-6033	33	8	suppose	suppose	VERB
ejpam-6033	33	9	that	that	SCONJ
ejpam-6033	33	10	p	p	PROPN
ejpam-6033	33	11	∈	∈	PROPN
ejpam-6033	33	12	sylp(n	sylp(n	PROPN
ejpam-6033	33	13	)	)	PUNCT
ejpam-6033	33	14	,	,	PUNCT
ejpam-6033	33	15	then	then	ADV
ejpam-6033	33	16	g	g	PROPN
ejpam-6033	33	17	=	=	NOUN
ejpam-6033	33	18	ng(p	ng(p	X
ejpam-6033	33	19	)	)	PUNCT
ejpam-6033	33	20	n	n	X
ejpam-6033	33	21	.	.	PUNCT
ejpam-6033	34	1	definition	definition	NOUN
ejpam-6033	34	2	3	3	NUM
ejpam-6033	34	3	.	.	PUNCT
ejpam-6033	35	1	[	[	X
ejpam-6033	35	2	8	8	NUM
ejpam-6033	35	3	]	]	X
ejpam-6033	35	4	a	a	DET
ejpam-6033	35	5	subgroup	subgroup	NOUN
ejpam-6033	35	6	h	h	NOUN
ejpam-6033	35	7	of	of	ADP
ejpam-6033	35	8	g	g	PROPN
ejpam-6033	35	9	is	be	AUX
ejpam-6033	35	10	said	say	VERB
ejpam-6033	35	11	to	to	PART
ejpam-6033	35	12	be	be	AUX
ejpam-6033	35	13	s	s	NOUN
ejpam-6033	35	14	-	-	NOUN
ejpam-6033	35	15	permutable	permutable	ADJ
ejpam-6033	35	16	in	in	ADP
ejpam-6033	35	17	g	g	PROPN
ejpam-6033	35	18	if	if	SCONJ
ejpam-6033	35	19	hp	hp	ADJ
ejpam-6033	35	20	=	=	PUNCT
ejpam-6033	35	21	ph	ph	NOUN
ejpam-6033	35	22	holds	hold	VERB
ejpam-6033	35	23	for	for	ADP
ejpam-6033	35	24	every	every	DET
ejpam-6033	35	25	sylow	sylow	NOUN
ejpam-6033	35	26	p	p	PROPN
ejpam-6033	35	27	-	-	PUNCT
ejpam-6033	35	28	subgroup	subgroup	NOUN
ejpam-6033	35	29	of	of	ADP
ejpam-6033	35	30	g	g	PROPN
ejpam-6033	35	31	and	and	CCONJ
ejpam-6033	35	32	for	for	ADP
ejpam-6033	35	33	every	every	DET
ejpam-6033	35	34	prime	prime	NOUN
ejpam-6033	35	35	p	p	NOUN
ejpam-6033	35	36	in	in	ADP
ejpam-6033	35	37	the	the	DET
ejpam-6033	35	38	set	set	NOUN
ejpam-6033	35	39	of	of	ADP
ejpam-6033	35	40	prime	prime	ADJ
ejpam-6033	35	41	divisors	divisor	NOUN
ejpam-6033	35	42	of	of	ADP
ejpam-6033	35	43	the	the	DET
ejpam-6033	35	44	order	order	NOUN
ejpam-6033	35	45	of	of	ADP
ejpam-6033	35	46	g	g	NOUN
ejpam-6033	35	47	,	,	PUNCT
ejpam-6033	35	48	denoted	denote	VERB
ejpam-6033	35	49	by	by	ADP
ejpam-6033	35	50	σ(g	σ(g	NOUN
ejpam-6033	35	51	)	)	PUNCT
ejpam-6033	35	52	.	.	PUNCT
ejpam-6033	36	1	proposition	proposition	NOUN
ejpam-6033	36	2	1	1	NUM
ejpam-6033	36	3	.	.	PUNCT
ejpam-6033	37	1	[	[	X
ejpam-6033	37	2	13	13	NUM
ejpam-6033	37	3	]	]	PUNCT
ejpam-6033	37	4	let	let	VERB
ejpam-6033	37	5	g	g	PRON
ejpam-6033	37	6	be	be	AUX
ejpam-6033	37	7	a	a	DET
ejpam-6033	37	8	group	group	NOUN
ejpam-6033	37	9	.	.	PUNCT
ejpam-6033	38	1	then	then	ADV
ejpam-6033	38	2	the	the	DET
ejpam-6033	38	3	following	follow	VERB
ejpam-6033	38	4	properties	property	NOUN
ejpam-6033	38	5	hold	hold	VERB
ejpam-6033	38	6	:	:	PUNCT
ejpam-6033	38	7	(	(	PUNCT
ejpam-6033	38	8	i	i	NOUN
ejpam-6033	38	9	)	)	PUNCT
ejpam-6033	38	10	if	if	SCONJ
ejpam-6033	38	11	h	h	NOUN
ejpam-6033	38	12	is	be	AUX
ejpam-6033	38	13	normal	normal	ADJ
ejpam-6033	38	14	in	in	ADP
ejpam-6033	38	15	g	g	PROPN
ejpam-6033	38	16	,	,	PUNCT
ejpam-6033	38	17	then	then	ADV
ejpam-6033	38	18	h	h	NOUN
ejpam-6033	38	19	is	be	AUX
ejpam-6033	38	20	c	c	NOUN
ejpam-6033	38	21	-	-	ADJ
ejpam-6033	38	22	normal	normal	ADJ
ejpam-6033	38	23	in	in	ADP
ejpam-6033	38	24	g.	g.	PROPN
ejpam-6033	38	25	(	(	PUNCT
ejpam-6033	38	26	ii	ii	PROPN
ejpam-6033	38	27	)	)	PUNCT
ejpam-6033	38	28	the	the	DET
ejpam-6033	38	29	group	group	NOUN
ejpam-6033	38	30	g	g	PROPN
ejpam-6033	38	31	is	be	AUX
ejpam-6033	38	32	c	c	NOUN
ejpam-6033	38	33	-	-	NOUN
ejpam-6033	38	34	simple	simple	ADJ
ejpam-6033	38	35	if	if	SCONJ
ejpam-6033	39	1	and	and	CCONJ
ejpam-6033	39	2	only	only	ADV
ejpam-6033	39	3	if	if	SCONJ
ejpam-6033	39	4	g	g	PROPN
ejpam-6033	39	5	is	be	AUX
ejpam-6033	39	6	simple	simple	ADJ
ejpam-6033	39	7	.	.	PUNCT
ejpam-6033	40	1	(	(	PUNCT
ejpam-6033	40	2	iii	iii	X
ejpam-6033	40	3	)	)	PUNCT
ejpam-6033	40	4	if	if	SCONJ
ejpam-6033	40	5	h	h	NOUN
ejpam-6033	40	6	is	be	AUX
ejpam-6033	40	7	c	c	NOUN
ejpam-6033	40	8	-	-	ADJ
ejpam-6033	40	9	normal	normal	ADJ
ejpam-6033	40	10	in	in	ADP
ejpam-6033	40	11	g	g	PROPN
ejpam-6033	40	12	and	and	CCONJ
ejpam-6033	40	13	h	h	NOUN
ejpam-6033	40	14	≤	≤	NUM
ejpam-6033	40	15	k	k	NOUN
ejpam-6033	40	16	≤	≤	PROPN
ejpam-6033	40	17	g	g	NOUN
ejpam-6033	40	18	,	,	PUNCT
ejpam-6033	40	19	then	then	ADV
ejpam-6033	40	20	h	h	NOUN
ejpam-6033	40	21	is	be	AUX
ejpam-6033	40	22	c	c	NOUN
ejpam-6033	40	23	-	-	ADJ
ejpam-6033	40	24	normal	normal	ADJ
ejpam-6033	40	25	in	in	ADP
ejpam-6033	40	26	k.	k.	PROPN
ejpam-6033	40	27	(	(	PUNCT
ejpam-6033	40	28	iv	iv	X
ejpam-6033	40	29	)	)	PUNCT
ejpam-6033	40	30	let	let	VERB
ejpam-6033	40	31	k	k	PRON
ejpam-6033	40	32	be	be	AUX
ejpam-6033	40	33	a	a	DET
ejpam-6033	40	34	normal	normal	ADJ
ejpam-6033	40	35	subgroup	subgroup	NOUN
ejpam-6033	40	36	of	of	ADP
ejpam-6033	40	37	g	g	PROPN
ejpam-6033	40	38	such	such	ADJ
ejpam-6033	40	39	that	that	SCONJ
ejpam-6033	40	40	k	k	PROPN
ejpam-6033	40	41	≤	≤	PROPN
ejpam-6033	40	42	h.	h.	NOUN
ejpam-6033	41	1	then	then	ADV
ejpam-6033	41	2	h	h	PROPN
ejpam-6033	41	3	is	be	AUX
ejpam-6033	41	4	c	c	NOUN
ejpam-6033	41	5	-	-	ADJ
ejpam-6033	41	6	normal	normal	ADJ
ejpam-6033	41	7	in	in	ADP
ejpam-6033	41	8	g	g	PROPN
ejpam-6033	41	9	if	if	SCONJ
ejpam-6033	42	1	and	and	CCONJ
ejpam-6033	42	2	only	only	ADV
ejpam-6033	42	3	if	if	SCONJ
ejpam-6033	42	4	h	h	PROPN
ejpam-6033	42	5	/	/	SYM
ejpam-6033	42	6	k	k	PROPN
ejpam-6033	42	7	is	be	AUX
ejpam-6033	42	8	c	c	NOUN
ejpam-6033	42	9	-	-	ADJ
ejpam-6033	42	10	normal	normal	ADJ
ejpam-6033	42	11	in	in	ADP
ejpam-6033	42	12	g	g	PROPN
ejpam-6033	42	13	/	/	SYM
ejpam-6033	42	14	k.	k.	NOUN
ejpam-6033	42	15	definition	definition	NOUN
ejpam-6033	42	16	4	4	NUM
ejpam-6033	42	17	.	.	PUNCT
ejpam-6033	43	1	[	[	X
ejpam-6033	43	2	9	9	NUM
ejpam-6033	43	3	]	]	SYM
ejpam-6033	43	4	a	a	DET
ejpam-6033	43	5	t	t	NOUN
ejpam-6033	43	6	-group	-group	NOUN
ejpam-6033	43	7	is	be	AUX
ejpam-6033	43	8	a	a	DET
ejpam-6033	43	9	group	group	NOUN
ejpam-6033	43	10	where	where	SCONJ
ejpam-6033	43	11	normality	normality	NOUN
ejpam-6033	43	12	is	be	AUX
ejpam-6033	43	13	a	a	DET
ejpam-6033	43	14	transitive	transitive	ADJ
ejpam-6033	43	15	property	property	NOUN
ejpam-6033	43	16	,	,	PUNCT
ejpam-6033	43	17	meaning	mean	VERB
ejpam-6033	43	18	that	that	SCONJ
ejpam-6033	43	19	every	every	DET
ejpam-6033	43	20	subnormal	subnormal	ADJ
ejpam-6033	43	21	subgroup	subgroup	NOUN
ejpam-6033	43	22	is	be	AUX
ejpam-6033	43	23	normal	normal	ADJ
ejpam-6033	43	24	.	.	PUNCT
ejpam-6033	44	1	specifically	specifically	ADV
ejpam-6033	44	2	,	,	PUNCT
ejpam-6033	44	3	if	if	SCONJ
ejpam-6033	44	4	h	h	NOUN
ejpam-6033	44	5	⊴k	⊴k	VERB
ejpam-6033	44	6	and	and	CCONJ
ejpam-6033	44	7	k	k	PROPN
ejpam-6033	44	8	⊴g	⊴g	PROPN
ejpam-6033	44	9	,	,	PUNCT
ejpam-6033	44	10	then	then	ADV
ejpam-6033	44	11	h	h	PROPN
ejpam-6033	44	12	⊴g	⊴g	PROPN
ejpam-6033	44	13	.	.	PUNCT
ejpam-6033	44	14	a.	a.	PROPN
ejpam-6033	44	15	m.	m.	PROPN
ejpam-6033	44	16	alotaibiang	alotaibiang	PROPN
ejpam-6033	44	17	,	,	PUNCT
ejpam-6033	44	18	k.	k.	PROPN
ejpam-6033	44	19	al	al	PROPN
ejpam-6033	44	20	-	-	PROPN
ejpam-6033	44	21	tahat	tahat	PROPN
ejpam-6033	44	22	,	,	PUNCT
ejpam-6033	44	23	k.	k.	PROPN
ejpam-6033	44	24	m.	m.	PROPN
ejpam-6033	44	25	al	al	PROPN
ejpam-6033	44	26	-	-	PROPN
ejpam-6033	44	27	jamal	jamal	PROPN
ejpam-6033	44	28	/	/	SYM
ejpam-6033	44	29	eur	eur	PROPN
ejpam-6033	44	30	.	.	PUNCT
ejpam-6033	45	1	j.	j.	PROPN
ejpam-6033	45	2	pure	pure	PROPN
ejpam-6033	45	3	appl	appl	PROPN
ejpam-6033	45	4	.	.	PROPN
ejpam-6033	45	5	math	math	PROPN
ejpam-6033	45	6	,	,	PUNCT
ejpam-6033	45	7	18	18	NUM
ejpam-6033	45	8	(	(	PUNCT
ejpam-6033	45	9	3	3	NUM
ejpam-6033	45	10	)	)	PUNCT
ejpam-6033	45	11	(	(	PUNCT
ejpam-6033	45	12	2025	2025	NUM
ejpam-6033	45	13	)	)	PUNCT
ejpam-6033	45	14	,	,	PUNCT
ejpam-6033	45	15	6033	6033	NUM
ejpam-6033	45	16	3	3	NUM
ejpam-6033	45	17	of	of	ADP
ejpam-6033	45	18	8	8	NUM
ejpam-6033	45	19	lemma	lemma	PROPN
ejpam-6033	45	20	2	2	NUM
ejpam-6033	45	21	.	.	PUNCT
ejpam-6033	46	1	every	every	DET
ejpam-6033	46	2	normal	normal	ADJ
ejpam-6033	46	3	subgroup	subgroup	NOUN
ejpam-6033	46	4	is	be	AUX
ejpam-6033	46	5	nearly	nearly	ADV
ejpam-6033	46	6	s	s	NOUN
ejpam-6033	46	7	-	-	PUNCT
ejpam-6033	46	8	permutability	permutability	NOUN
ejpam-6033	46	9	subgroup	subgroup	NOUN
ejpam-6033	46	10	.	.	PUNCT
ejpam-6033	47	1	proof	proof	NOUN
ejpam-6033	47	2	.	.	PUNCT
ejpam-6033	48	1	see	see	VERB
ejpam-6033	48	2	[	[	X
ejpam-6033	48	3	11	11	NUM
ejpam-6033	48	4	]	]	PUNCT
ejpam-6033	48	5	examples	example	NOUN
ejpam-6033	48	6	of	of	ADP
ejpam-6033	48	7	t	t	PROPN
ejpam-6033	48	8	-groups	-group	NOUN
ejpam-6033	48	9	include	include	VERB
ejpam-6033	48	10	abelian	abelian	ADJ
ejpam-6033	48	11	groups	group	NOUN
ejpam-6033	48	12	,	,	PUNCT
ejpam-6033	48	13	dedekind	dedekind	ADJ
ejpam-6033	48	14	groups	group	NOUN
ejpam-6033	48	15	,	,	PUNCT
ejpam-6033	48	16	and	and	CCONJ
ejpam-6033	48	17	simple	simple	ADJ
ejpam-6033	48	18	groups	group	NOUN
ejpam-6033	48	19	.	.	PUNCT
ejpam-6033	49	1	definition	definition	NOUN
ejpam-6033	49	2	5	5	NUM
ejpam-6033	49	3	.	.	PUNCT
ejpam-6033	50	1	[	[	X
ejpam-6033	50	2	14	14	NUM
ejpam-6033	50	3	]	]	PUNCT
ejpam-6033	50	4	let	let	VERB
ejpam-6033	50	5	g	g	PRON
ejpam-6033	50	6	be	be	AUX
ejpam-6033	50	7	a	a	DET
ejpam-6033	50	8	group	group	NOUN
ejpam-6033	50	9	we	we	PRON
ejpam-6033	50	10	called	call	VERB
ejpam-6033	50	11	a	a	DET
ejpam-6033	50	12	ct	ct	NUM
ejpam-6033	50	13	-group	-group	NOUN
ejpam-6033	50	14	if	if	SCONJ
ejpam-6033	50	15	the	the	DET
ejpam-6033	50	16	property	property	NOUN
ejpam-6033	50	17	of	of	ADP
ejpam-6033	50	18	c	c	NOUN
ejpam-6033	50	19	-	-	PUNCT
ejpam-6033	50	20	normality	normality	NOUN
ejpam-6033	50	21	is	be	AUX
ejpam-6033	50	22	transitive	transitive	ADJ
ejpam-6033	50	23	in	in	ADP
ejpam-6033	50	24	g.	g.	PROPN
ejpam-6033	50	25	specifically	specifically	ADV
ejpam-6033	50	26	,	,	PUNCT
ejpam-6033	50	27	g	g	PROPN
ejpam-6033	50	28	is	be	AUX
ejpam-6033	50	29	a	a	DET
ejpam-6033	50	30	ct	ct	NUM
ejpam-6033	50	31	-group	-group	NOUN
ejpam-6033	50	32	if	if	SCONJ
ejpam-6033	50	33	for	for	ADP
ejpam-6033	50	34	all	all	DET
ejpam-6033	50	35	subgroups	subgroup	NOUN
ejpam-6033	50	36	h	h	PROPN
ejpam-6033	50	37	and	and	CCONJ
ejpam-6033	50	38	k	k	PROPN
ejpam-6033	50	39	of	of	ADP
ejpam-6033	50	40	g	g	PROPN
ejpam-6033	50	41	,	,	PUNCT
ejpam-6033	50	42	whenever	whenever	SCONJ
ejpam-6033	50	43	h	h	NOUN
ejpam-6033	50	44	is	be	AUX
ejpam-6033	50	45	c	c	NOUN
ejpam-6033	50	46	-	-	ADJ
ejpam-6033	50	47	normal	normal	ADJ
ejpam-6033	50	48	in	in	ADP
ejpam-6033	50	49	k	k	PROPN
ejpam-6033	50	50	and	and	CCONJ
ejpam-6033	50	51	k	k	PROPN
ejpam-6033	50	52	is	be	AUX
ejpam-6033	50	53	c	c	NOUN
ejpam-6033	50	54	-	-	ADJ
ejpam-6033	50	55	normal	normal	ADJ
ejpam-6033	50	56	in	in	ADP
ejpam-6033	50	57	g	g	PROPN
ejpam-6033	50	58	,	,	PUNCT
ejpam-6033	50	59	it	it	PRON
ejpam-6033	50	60	follows	follow	VERB
ejpam-6033	50	61	that	that	SCONJ
ejpam-6033	50	62	h	h	NOUN
ejpam-6033	50	63	is	be	AUX
ejpam-6033	50	64	c	c	NOUN
ejpam-6033	50	65	-	-	ADJ
ejpam-6033	50	66	normal	normal	ADJ
ejpam-6033	50	67	in	in	ADP
ejpam-6033	50	68	g.	g.	PROPN
ejpam-6033	50	69	corollary	corollary	NOUN
ejpam-6033	50	70	1	1	NUM
ejpam-6033	50	71	.	.	PUNCT
ejpam-6033	51	1	[	[	X
ejpam-6033	51	2	15	15	NUM
ejpam-6033	51	3	]	]	X
ejpam-6033	51	4	all	all	DET
ejpam-6033	51	5	maximal	maximal	ADJ
ejpam-6033	51	6	subgroups	subgroup	NOUN
ejpam-6033	51	7	of	of	ADP
ejpam-6033	51	8	a	a	DET
ejpam-6033	51	9	solvable	solvable	ADJ
ejpam-6033	51	10	ct	ct	NUM
ejpam-6033	51	11	-group	-group	NOUN
ejpam-6033	51	12	is	be	AUX
ejpam-6033	51	13	a	a	DET
ejpam-6033	51	14	ct	ct	NUM
ejpam-6033	51	15	-group	-group	NOUN
ejpam-6033	51	16	.	.	PUNCT
ejpam-6033	52	1	3	3	X
ejpam-6033	52	2	.	.	X
ejpam-6033	52	3	main	main	ADJ
ejpam-6033	52	4	results	result	NOUN
ejpam-6033	52	5	nilpotent	nilpotent	ADJ
ejpam-6033	52	6	groups	group	NOUN
ejpam-6033	52	7	can	can	AUX
ejpam-6033	52	8	be	be	AUX
ejpam-6033	52	9	viewed	view	VERB
ejpam-6033	52	10	as	as	ADP
ejpam-6033	52	11	an	an	DET
ejpam-6033	52	12	extension	extension	NOUN
ejpam-6033	52	13	of	of	ADP
ejpam-6033	52	14	the	the	DET
ejpam-6033	52	15	concept	concept	NOUN
ejpam-6033	52	16	of	of	ADP
ejpam-6033	52	17	p	p	PROPN
ejpam-6033	52	18	-groups	-groups	PROPN
ejpam-6033	52	19	.	.	PUNCT
ejpam-6033	53	1	this	this	DET
ejpam-6033	53	2	section	section	NOUN
ejpam-6033	53	3	explores	explore	VERB
ejpam-6033	53	4	finite	finite	VERB
ejpam-6033	53	5	groups	group	NOUN
ejpam-6033	53	6	where	where	SCONJ
ejpam-6033	53	7	the	the	DET
ejpam-6033	53	8	property	property	NOUN
ejpam-6033	53	9	of	of	ADP
ejpam-6033	53	10	nearly	nearly	ADV
ejpam-6033	53	11	s	s	NOUN
ejpam-6033	53	12	-	-	NOUN
ejpam-6033	53	13	permutability	permutability	NOUN
ejpam-6033	53	14	is	be	AUX
ejpam-6033	53	15	transitive	transitive	ADJ
ejpam-6033	53	16	,	,	PUNCT
ejpam-6033	53	17	some	some	DET
ejpam-6033	53	18	results	result	NOUN
ejpam-6033	53	19	and	and	CCONJ
ejpam-6033	53	20	theorems	theorem	NOUN
ejpam-6033	53	21	of	of	ADP
ejpam-6033	53	22	finite	finite	PROPN
ejpam-6033	53	23	solvable	solvable	ADJ
ejpam-6033	53	24	nspt	nspt	PROPN
ejpam-6033	53	25	-groups	-group	NOUN
ejpam-6033	53	26	were	be	AUX
ejpam-6033	53	27	proven	prove	VERB
ejpam-6033	53	28	.	.	PUNCT
ejpam-6033	54	1	it	it	PRON
ejpam-6033	54	2	is	be	AUX
ejpam-6033	54	3	clear	clear	ADJ
ejpam-6033	54	4	that	that	SCONJ
ejpam-6033	54	5	all	all	DET
ejpam-6033	54	6	abelian	abelian	ADJ
ejpam-6033	54	7	groups	group	NOUN
ejpam-6033	54	8	and	and	CCONJ
ejpam-6033	54	9	all	all	DET
ejpam-6033	54	10	nilpotent	nilpotent	ADJ
ejpam-6033	54	11	groups	group	NOUN
ejpam-6033	54	12	are	be	AUX
ejpam-6033	54	13	examples	example	NOUN
ejpam-6033	54	14	of	of	ADP
ejpam-6033	54	15	groups	group	NOUN
ejpam-6033	54	16	with	with	ADP
ejpam-6033	54	17	nearly	nearly	ADV
ejpam-6033	54	18	s	s	NOUN
ejpam-6033	54	19	-	-	ADJ
ejpam-6033	54	20	permutable	permutable	ADJ
ejpam-6033	54	21	groups	group	NOUN
ejpam-6033	54	22	.	.	PUNCT
ejpam-6033	55	1	but	but	CCONJ
ejpam-6033	55	2	not	not	PART
ejpam-6033	55	3	all	all	DET
ejpam-6033	55	4	groups	group	NOUN
ejpam-6033	55	5	satisfies	satisfy	VERB
ejpam-6033	55	6	this	this	DET
ejpam-6033	55	7	property	property	NOUN
ejpam-6033	55	8	as	as	ADP
ejpam-6033	55	9	the	the	DET
ejpam-6033	55	10	following	follow	VERB
ejpam-6033	55	11	example	example	NOUN
ejpam-6033	55	12	shows	show	VERB
ejpam-6033	55	13	:	:	PUNCT
ejpam-6033	55	14	example	example	NOUN
ejpam-6033	56	1	1	1	NUM
ejpam-6033	56	2	.	.	PUNCT
ejpam-6033	57	1	the	the	DET
ejpam-6033	57	2	alternating	alternate	VERB
ejpam-6033	57	3	group	group	NOUN
ejpam-6033	57	4	on	on	ADP
ejpam-6033	57	5	4	4	NUM
ejpam-6033	57	6	-	-	PUNCT
ejpam-6033	57	7	letters	letter	NOUN
ejpam-6033	57	8	a4	a4	NOUN
ejpam-6033	57	9	does	do	AUX
ejpam-6033	57	10	not	not	PART
ejpam-6033	57	11	satisfiy	satisfiy	VERB
ejpam-6033	57	12	the	the	DET
ejpam-6033	57	13	nearly	nearly	ADV
ejpam-6033	57	14	s	s	NOUN
ejpam-6033	57	15	-	-	NOUN
ejpam-6033	57	16	permutable	permutable	ADJ
ejpam-6033	57	17	.	.	PUNCT
ejpam-6033	58	1	specifically	specifically	ADV
ejpam-6033	58	2	,	,	PUNCT
ejpam-6033	58	3	any	any	PRON
ejpam-6033	58	4	of	of	ADP
ejpam-6033	58	5	the	the	DET
ejpam-6033	58	6	sylow	sylow	NOUN
ejpam-6033	58	7	3	3	NUM
ejpam-6033	58	8	-	-	NOUN
ejpam-6033	58	9	subgroups	subgroup	NOUN
ejpam-6033	58	10	in	in	ADP
ejpam-6033	58	11	a4	a4	NOUN
ejpam-6033	58	12	will	will	AUX
ejpam-6033	58	13	not	not	PART
ejpam-6033	58	14	be	be	AUX
ejpam-6033	58	15	a	a	DET
ejpam-6033	58	16	nearly	nearly	ADV
ejpam-6033	58	17	s	s	NOUN
ejpam-6033	58	18	-	-	NOUN
ejpam-6033	58	19	permutable	permutable	ADJ
ejpam-6033	58	20	in	in	ADP
ejpam-6033	58	21	a4	a4	NUM
ejpam-6033	58	22	.	.	PUNCT
ejpam-6033	59	1	remark	remark	NOUN
ejpam-6033	59	2	1	1	NUM
ejpam-6033	59	3	.	.	PUNCT
ejpam-6033	59	4	transitive	transitive	ADJ
ejpam-6033	59	5	realation	realation	NOUN
ejpam-6033	59	6	of	of	ADP
ejpam-6033	59	7	nearly	nearly	ADV
ejpam-6033	59	8	s	s	NOUN
ejpam-6033	59	9	-	-	ADJ
ejpam-6033	59	10	permutable	permutable	ADJ
ejpam-6033	59	11	is	be	AUX
ejpam-6033	59	12	not	not	PART
ejpam-6033	59	13	true	true	ADJ
ejpam-6033	59	14	for	for	ADP
ejpam-6033	59	15	all	all	DET
ejpam-6033	59	16	groups	group	NOUN
ejpam-6033	59	17	.	.	PUNCT
ejpam-6033	60	1	lemma	lemma	PROPN
ejpam-6033	60	2	3	3	NUM
ejpam-6033	60	3	.	.	PUNCT
ejpam-6033	61	1	every	every	DET
ejpam-6033	61	2	normal	normal	ADJ
ejpam-6033	61	3	subgroup	subgroup	NOUN
ejpam-6033	61	4	is	be	AUX
ejpam-6033	61	5	nearly	nearly	ADV
ejpam-6033	61	6	s	s	NOUN
ejpam-6033	61	7	-	-	NOUN
ejpam-6033	61	8	permutable	permutable	ADJ
ejpam-6033	61	9	.	.	PUNCT
ejpam-6033	62	1	proof	proof	NOUN
ejpam-6033	62	2	.	.	PUNCT
ejpam-6033	63	1	let	let	VERB
ejpam-6033	63	2	g	g	NOUN
ejpam-6033	63	3	be	be	AUX
ejpam-6033	63	4	agroup	agroup	ADV
ejpam-6033	63	5	and	and	CCONJ
ejpam-6033	63	6	h	h	NOUN
ejpam-6033	63	7	is	be	AUX
ejpam-6033	63	8	normal	normal	ADJ
ejpam-6033	63	9	subgroup	subgroup	NOUN
ejpam-6033	63	10	of	of	ADP
ejpam-6033	63	11	g	g	PROPN
ejpam-6033	63	12	and	and	CCONJ
ejpam-6033	63	13	let	let	VERB
ejpam-6033	63	14	h	h	NOUN
ejpam-6033	63	15	≤	≤	NOUN
ejpam-6033	64	1	k	k	NOUN
ejpam-6033	64	2	≤	≤	NUM
ejpam-6033	64	3	g	g	NOUN
ejpam-6033	64	4	for	for	ADP
ejpam-6033	64	5	every	every	DET
ejpam-6033	64	6	prime	prime	ADJ
ejpam-6033	64	7	number	number	NOUN
ejpam-6033	64	8	p	p	NOUN
ejpam-6033	64	9	∈	∈	PROPN
ejpam-6033	64	10	p	p	NOUN
ejpam-6033	64	11	with	with	ADP
ejpam-6033	64	12	(	(	PUNCT
ejpam-6033	64	13	p	p	X
ejpam-6033	64	14	,	,	PUNCT
ejpam-6033	64	15	|h|	|h|	PROPN
ejpam-6033	64	16	)	)	PUNCT
ejpam-6033	64	17	,	,	PUNCT
ejpam-6033	64	18	since	since	SCONJ
ejpam-6033	64	19	h	h	NOUN
ejpam-6033	64	20	⊴	⊴	NOUN
ejpam-6033	64	21	g	g	PROPN
ejpam-6033	64	22	implies	imply	VERB
ejpam-6033	64	23	h	h	NOUN
ejpam-6033	64	24	⊴	⊴	PROPN
ejpam-6033	64	25	k.	k.	PROPN
ejpam-6033	64	26	then	then	ADV
ejpam-6033	64	27	nk(h	nk(h	PUNCT
ejpam-6033	64	28	)	)	PUNCT
ejpam-6033	64	29	=	=	PUNCT
ejpam-6033	65	1	k.if	k.if	PROPN
ejpam-6033	65	2	p	p	NOUN
ejpam-6033	65	3	∈	∈	PROPN
ejpam-6033	65	4	sylp(k	sylp(k	PROPN
ejpam-6033	65	5	)	)	PUNCT
ejpam-6033	65	6	that	that	PRON
ejpam-6033	65	7	implies	imply	VERB
ejpam-6033	65	8	p	p	NOUN
ejpam-6033	65	9	≤	≤	NUM
ejpam-6033	65	10	k	k	X
ejpam-6033	65	11	=	=	PUNCT
ejpam-6033	65	12	nk(h	nk(h	PROPN
ejpam-6033	65	13	)	)	PUNCT
ejpam-6033	65	14	,	,	PUNCT
ejpam-6033	65	15	that	that	PRON
ejpam-6033	65	16	mean	mean	VERB
ejpam-6033	65	17	h	h	NOUN
ejpam-6033	65	18	is	be	AUX
ejpam-6033	65	19	nearly	nearly	ADV
ejpam-6033	65	20	s-permutable.the	s-permutable.the	DET
ejpam-6033	65	21	proof	proof	NOUN
ejpam-6033	65	22	is	be	AUX
ejpam-6033	65	23	complete	complete	ADJ
ejpam-6033	65	24	.	.	PUNCT
ejpam-6033	66	1	proposition	proposition	NOUN
ejpam-6033	66	2	2	2	NUM
ejpam-6033	66	3	.	.	PUNCT
ejpam-6033	67	1	the	the	DET
ejpam-6033	67	2	intersection	intersection	NOUN
ejpam-6033	67	3	of	of	ADP
ejpam-6033	67	4	two	two	NUM
ejpam-6033	67	5	nearly	nearly	ADV
ejpam-6033	67	6	s	s	NOUN
ejpam-6033	67	7	-	-	PUNCT
ejpam-6033	67	8	permutable	permutable	ADJ
ejpam-6033	67	9	subgroups	subgroup	NOUN
ejpam-6033	67	10	does	do	AUX
ejpam-6033	67	11	not	not	PART
ejpam-6033	67	12	necessarily	necessarily	ADV
ejpam-6033	67	13	imply	imply	VERB
ejpam-6033	67	14	that	that	SCONJ
ejpam-6033	67	15	the	the	DET
ejpam-6033	67	16	intersection	intersection	NOUN
ejpam-6033	67	17	is	be	AUX
ejpam-6033	67	18	nearly	nearly	ADV
ejpam-6033	67	19	s	s	NOUN
ejpam-6033	67	20	-	-	NOUN
ejpam-6033	67	21	permutable	permutable	ADJ
ejpam-6033	67	22	,	,	PUNCT
ejpam-6033	67	23	and	and	CCONJ
ejpam-6033	67	24	a	a	DET
ejpam-6033	67	25	subgroup	subgroup	NOUN
ejpam-6033	67	26	being	be	AUX
ejpam-6033	67	27	nearly	nearly	ADV
ejpam-6033	67	28	s	s	NOUN
ejpam-6033	67	29	-	-	PUNCT
ejpam-6033	67	30	permutable	permutable	ADJ
ejpam-6033	67	31	does	do	AUX
ejpam-6033	67	32	not	not	PART
ejpam-6033	67	33	imply	imply	VERB
ejpam-6033	67	34	that	that	SCONJ
ejpam-6033	67	35	all	all	PRON
ejpam-6033	67	36	of	of	ADP
ejpam-6033	67	37	its	its	PRON
ejpam-6033	67	38	subgroups	subgroup	NOUN
ejpam-6033	67	39	are	be	AUX
ejpam-6033	67	40	nearly	nearly	ADV
ejpam-6033	67	41	s	s	NOUN
ejpam-6033	67	42	-	-	NOUN
ejpam-6033	67	43	permutable	permutable	ADJ
ejpam-6033	67	44	.	.	PUNCT
ejpam-6033	68	1	proof	proof	NOUN
ejpam-6033	68	2	.	.	PUNCT
ejpam-6033	69	1	let	let	VERB
ejpam-6033	69	2	g	g	PRON
ejpam-6033	69	3	be	be	AUX
ejpam-6033	69	4	a	a	DET
ejpam-6033	69	5	group	group	NOUN
ejpam-6033	69	6	of	of	ADP
ejpam-6033	69	7	order	order	NOUN
ejpam-6033	69	8	18	18	NUM
ejpam-6033	69	9	defined	define	VERB
ejpam-6033	69	10	as	as	ADP
ejpam-6033	69	11	the	the	DET
ejpam-6033	69	12	direct	direct	ADJ
ejpam-6033	69	13	product	product	NOUN
ejpam-6033	69	14	of	of	ADP
ejpam-6033	69	15	the	the	DET
ejpam-6033	69	16	symmetric	symmetric	ADJ
ejpam-6033	69	17	group	group	NOUN
ejpam-6033	69	18	s3	s3	PROPN
ejpam-6033	69	19	and	and	CCONJ
ejpam-6033	69	20	the	the	DET
ejpam-6033	69	21	cyclic	cyclic	ADJ
ejpam-6033	69	22	group	group	NOUN
ejpam-6033	69	23	z3	z3	PROPN
ejpam-6033	69	24	,	,	PUNCT
ejpam-6033	69	25	i.e.	i.e.	X
ejpam-6033	69	26	,	,	PUNCT
ejpam-6033	69	27	g	g	PROPN
ejpam-6033	69	28	=	=	SYM
ejpam-6033	69	29	s3	s3	PROPN
ejpam-6033	69	30	×	×	PROPN
ejpam-6033	69	31	z3	z3	PROPN
ejpam-6033	69	32	.	.	PUNCT
ejpam-6033	70	1	g	g	PROPN
ejpam-6033	70	2	=	=	PRON
ejpam-6033	70	3	{	{	PUNCT
ejpam-6033	70	4	(	(	PUNCT
ejpam-6033	70	5	e	e	NOUN
ejpam-6033	70	6	,	,	PUNCT
ejpam-6033	70	7	0	0	NUM
ejpam-6033	70	8	)	)	PUNCT
ejpam-6033	70	9	,	,	PUNCT
ejpam-6033	70	10	(	(	PUNCT
ejpam-6033	70	11	(	(	PUNCT
ejpam-6033	70	12	12	12	NUM
ejpam-6033	70	13	)	)	PUNCT
ejpam-6033	70	14	,	,	PUNCT
ejpam-6033	70	15	0	0	NUM
ejpam-6033	70	16	)	)	PUNCT
ejpam-6033	70	17	,	,	PUNCT
ejpam-6033	70	18	(	(	PUNCT
ejpam-6033	70	19	(	(	PUNCT
ejpam-6033	70	20	13	13	NUM
ejpam-6033	70	21	)	)	PUNCT
ejpam-6033	70	22	,	,	PUNCT
ejpam-6033	70	23	0	0	NUM
ejpam-6033	70	24	)	)	PUNCT
ejpam-6033	70	25	,	,	PUNCT
ejpam-6033	70	26	(	(	PUNCT
ejpam-6033	70	27	(	(	PUNCT
ejpam-6033	70	28	23	23	NUM
ejpam-6033	70	29	)	)	PUNCT
ejpam-6033	70	30	,	,	PUNCT
ejpam-6033	70	31	0	0	NUM
ejpam-6033	70	32	)	)	PUNCT
ejpam-6033	70	33	,	,	PUNCT
ejpam-6033	70	34	(	(	PUNCT
ejpam-6033	70	35	(	(	PUNCT
ejpam-6033	70	36	132	132	NUM
ejpam-6033	70	37	)	)	PUNCT
ejpam-6033	70	38	,	,	PUNCT
ejpam-6033	70	39	0)((123	0)((123	NOUN
ejpam-6033	70	40	)	)	PUNCT
ejpam-6033	70	41	,	,	PUNCT
ejpam-6033	70	42	0	0	NUM
ejpam-6033	70	43	)	)	PUNCT
ejpam-6033	70	44	,	,	PUNCT
ejpam-6033	70	45	(	(	PUNCT
ejpam-6033	70	46	e	e	NOUN
ejpam-6033	70	47	,	,	PUNCT
ejpam-6033	70	48	1	1	NUM
ejpam-6033	70	49	)	)	PUNCT
ejpam-6033	70	50	,	,	PUNCT
ejpam-6033	70	51	(	(	PUNCT
ejpam-6033	70	52	(	(	PUNCT
ejpam-6033	70	53	12	12	NUM
ejpam-6033	70	54	)	)	PUNCT
ejpam-6033	70	55	,	,	PUNCT
ejpam-6033	70	56	1	1	NUM
ejpam-6033	70	57	)	)	PUNCT
ejpam-6033	70	58	,	,	PUNCT
ejpam-6033	70	59	(	(	PUNCT
ejpam-6033	70	60	(	(	PUNCT
ejpam-6033	70	61	13	13	NUM
ejpam-6033	70	62	)	)	PUNCT
ejpam-6033	70	63	,	,	PUNCT
ejpam-6033	70	64	1	1	NUM
ejpam-6033	70	65	)	)	PUNCT
ejpam-6033	70	66	,	,	PUNCT
ejpam-6033	70	67	(	(	PUNCT
ejpam-6033	70	68	(	(	PUNCT
ejpam-6033	70	69	23	23	NUM
ejpam-6033	70	70	)	)	PUNCT
ejpam-6033	70	71	,	,	PUNCT
ejpam-6033	70	72	1	1	NUM
ejpam-6033	70	73	)	)	PUNCT
ejpam-6033	70	74	,	,	PUNCT
ejpam-6033	70	75	(	(	PUNCT
ejpam-6033	70	76	(	(	PUNCT
ejpam-6033	70	77	132	132	NUM
ejpam-6033	70	78	)	)	PUNCT
ejpam-6033	70	79	,	,	PUNCT
ejpam-6033	70	80	1	1	NUM
ejpam-6033	70	81	)	)	PUNCT
ejpam-6033	70	82	,	,	PUNCT
ejpam-6033	70	83	(	(	PUNCT
ejpam-6033	70	84	(	(	PUNCT
ejpam-6033	70	85	123	123	NUM
ejpam-6033	70	86	)	)	PUNCT
ejpam-6033	70	87	,	,	PUNCT
ejpam-6033	70	88	1	1	NUM
ejpam-6033	70	89	)	)	PUNCT
ejpam-6033	70	90	,	,	PUNCT
ejpam-6033	70	91	(	(	PUNCT
ejpam-6033	70	92	e	e	NOUN
ejpam-6033	70	93	,	,	PUNCT
ejpam-6033	70	94	2	2	NUM
ejpam-6033	70	95	)	)	PUNCT
ejpam-6033	70	96	,	,	PUNCT
ejpam-6033	70	97	(	(	PUNCT
ejpam-6033	70	98	(	(	PUNCT
ejpam-6033	70	99	12	12	NUM
ejpam-6033	70	100	)	)	PUNCT
ejpam-6033	70	101	,	,	PUNCT
ejpam-6033	70	102	2	2	NUM
ejpam-6033	70	103	)	)	PUNCT
ejpam-6033	70	104	,	,	PUNCT
ejpam-6033	70	105	(	(	PUNCT
ejpam-6033	70	106	(	(	PUNCT
ejpam-6033	70	107	13	13	NUM
ejpam-6033	70	108	)	)	PUNCT
ejpam-6033	70	109	,	,	PUNCT
ejpam-6033	70	110	2	2	NUM
ejpam-6033	70	111	)	)	PUNCT
ejpam-6033	70	112	,	,	PUNCT
ejpam-6033	70	113	(	(	PUNCT
ejpam-6033	70	114	(	(	PUNCT
ejpam-6033	70	115	23	23	NUM
ejpam-6033	70	116	)	)	PUNCT
ejpam-6033	70	117	,	,	PUNCT
ejpam-6033	70	118	2	2	NUM
ejpam-6033	70	119	)	)	PUNCT
ejpam-6033	70	120	,	,	PUNCT
ejpam-6033	70	121	(	(	PUNCT
ejpam-6033	70	122	(	(	PUNCT
ejpam-6033	70	123	132	132	NUM
ejpam-6033	70	124	)	)	PUNCT
ejpam-6033	70	125	,	,	PUNCT
ejpam-6033	70	126	2	2	NUM
ejpam-6033	70	127	)	)	PUNCT
ejpam-6033	70	128	,	,	PUNCT
ejpam-6033	70	129	(	(	PUNCT
ejpam-6033	70	130	(	(	PUNCT
ejpam-6033	70	131	123	123	NUM
ejpam-6033	70	132	)	)	PUNCT
ejpam-6033	70	133	,	,	PUNCT
ejpam-6033	70	134	2	2	NUM
ejpam-6033	70	135	)	)	PUNCT
ejpam-6033	70	136	}	}	PUNCT
ejpam-6033	70	137	.	.	PUNCT
ejpam-6033	71	1	the	the	DET
ejpam-6033	71	2	normal	normal	ADJ
ejpam-6033	71	3	subgroups	subgroup	NOUN
ejpam-6033	71	4	in	in	ADP
ejpam-6033	71	5	g	g	PROPN
ejpam-6033	71	6	are	be	AUX
ejpam-6033	71	7	:	:	PUNCT
ejpam-6033	71	8	order	order	NOUN
ejpam-6033	71	9	9	9	NUM
ejpam-6033	71	10	:	:	PUNCT
ejpam-6033	71	11	⟨((132	⟨((132	PROPN
ejpam-6033	71	12	)	)	PUNCT
ejpam-6033	71	13	,	,	PUNCT
ejpam-6033	71	14	0	0	NUM
ejpam-6033	71	15	)	)	PUNCT
ejpam-6033	71	16	,	,	PUNCT
ejpam-6033	71	17	(	(	PUNCT
ejpam-6033	71	18	e	e	NOUN
ejpam-6033	71	19	,	,	PUNCT
ejpam-6033	71	20	1)⟩.	1)⟩.	NUM
ejpam-6033	71	21	order	order	NOUN
ejpam-6033	71	22	6	6	NUM
ejpam-6033	71	23	:	:	PUNCT
ejpam-6033	71	24	⟨((12	⟨((12	NUM
ejpam-6033	71	25	)	)	PUNCT
ejpam-6033	71	26	,	,	PUNCT
ejpam-6033	71	27	0	0	NUM
ejpam-6033	71	28	)	)	PUNCT
ejpam-6033	71	29	,	,	PUNCT
ejpam-6033	71	30	(	(	PUNCT
ejpam-6033	71	31	(	(	PUNCT
ejpam-6033	71	32	13	13	NUM
ejpam-6033	71	33	)	)	PUNCT
ejpam-6033	71	34	,	,	PUNCT
ejpam-6033	71	35	0)⟩.	0)⟩.	PRON
ejpam-6033	71	36	order	order	NOUN
ejpam-6033	71	37	3	3	NUM
ejpam-6033	71	38	:	:	PUNCT
ejpam-6033	71	39	⟨(e	⟨(e	PROPN
ejpam-6033	71	40	,	,	PUNCT
ejpam-6033	71	41	1)⟩	1)⟩	NUM
ejpam-6033	71	42	and	and	CCONJ
ejpam-6033	71	43	order	order	NOUN
ejpam-6033	71	44	1	1	NUM
ejpam-6033	71	45	in	in	ADP
ejpam-6033	71	46	this	this	DET
ejpam-6033	71	47	case	case	NOUN
ejpam-6033	71	48	,	,	PUNCT
ejpam-6033	71	49	every	every	DET
ejpam-6033	71	50	normal	normal	ADJ
ejpam-6033	71	51	subgroup	subgroup	NOUN
ejpam-6033	71	52	is	be	AUX
ejpam-6033	71	53	nearly	nearly	ADV
ejpam-6033	71	54	s	s	NOUN
ejpam-6033	71	55	-	-	NOUN
ejpam-6033	71	56	permutable	permutable	ADJ
ejpam-6033	71	57	.	.	PUNCT
ejpam-6033	72	1	a.	a.	PROPN
ejpam-6033	72	2	m.	m.	PROPN
ejpam-6033	72	3	alotaibiang	alotaibiang	PROPN
ejpam-6033	72	4	,	,	PUNCT
ejpam-6033	72	5	k.	k.	PROPN
ejpam-6033	72	6	al	al	PROPN
ejpam-6033	72	7	-	-	PROPN
ejpam-6033	72	8	tahat	tahat	PROPN
ejpam-6033	72	9	,	,	PUNCT
ejpam-6033	72	10	k.	k.	PROPN
ejpam-6033	72	11	m.	m.	PROPN
ejpam-6033	72	12	al	al	PROPN
ejpam-6033	72	13	-	-	PROPN
ejpam-6033	72	14	jamal	jamal	PROPN
ejpam-6033	72	15	/	/	SYM
ejpam-6033	72	16	eur	eur	PROPN
ejpam-6033	72	17	.	.	PUNCT
ejpam-6033	73	1	j.	j.	PROPN
ejpam-6033	73	2	pure	pure	PROPN
ejpam-6033	73	3	appl	appl	PROPN
ejpam-6033	73	4	.	.	PROPN
ejpam-6033	73	5	math	math	PROPN
ejpam-6033	73	6	,	,	PUNCT
ejpam-6033	73	7	18	18	NUM
ejpam-6033	73	8	(	(	PUNCT
ejpam-6033	73	9	3	3	NUM
ejpam-6033	73	10	)	)	PUNCT
ejpam-6033	73	11	(	(	PUNCT
ejpam-6033	73	12	2025	2025	NUM
ejpam-6033	73	13	)	)	PUNCT
ejpam-6033	73	14	,	,	PUNCT
ejpam-6033	73	15	6033	6033	NUM
ejpam-6033	73	16	4	4	NUM
ejpam-6033	73	17	of	of	ADP
ejpam-6033	73	18	8	8	NUM
ejpam-6033	73	19	however	however	ADV
ejpam-6033	73	20	,	,	PUNCT
ejpam-6033	73	21	the	the	DET
ejpam-6033	73	22	intersection	intersection	NOUN
ejpam-6033	73	23	of	of	ADP
ejpam-6033	73	24	two	two	NUM
ejpam-6033	73	25	nearly	nearly	ADV
ejpam-6033	73	26	s	s	NOUN
ejpam-6033	73	27	-	-	PUNCT
ejpam-6033	73	28	permutable	permutable	ADJ
ejpam-6033	73	29	subgroups	subgroup	NOUN
ejpam-6033	73	30	does	do	AUX
ejpam-6033	73	31	not	not	PART
ejpam-6033	73	32	necessarily	necessarily	ADV
ejpam-6033	73	33	maintain	maintain	VERB
ejpam-6033	73	34	the	the	DET
ejpam-6033	73	35	nearly	nearly	ADV
ejpam-6033	73	36	s	s	NOUN
ejpam-6033	73	37	-	-	ADJ
ejpam-6033	73	38	permutable	permutable	ADJ
ejpam-6033	73	39	property	property	NOUN
ejpam-6033	73	40	.	.	PUNCT
ejpam-6033	74	1	moreover	moreover	ADV
ejpam-6033	74	2	,	,	PUNCT
ejpam-6033	74	3	a	a	DET
ejpam-6033	74	4	subgroup	subgroup	NOUN
ejpam-6033	74	5	being	be	AUX
ejpam-6033	74	6	nearly	nearly	ADV
ejpam-6033	74	7	spermutable	spermutable	ADJ
ejpam-6033	74	8	does	do	AUX
ejpam-6033	74	9	not	not	PART
ejpam-6033	74	10	guarantee	guarantee	VERB
ejpam-6033	74	11	that	that	SCONJ
ejpam-6033	74	12	all	all	PRON
ejpam-6033	74	13	its	its	PRON
ejpam-6033	74	14	subgroups	subgroup	NOUN
ejpam-6033	74	15	will	will	AUX
ejpam-6033	74	16	also	also	ADV
ejpam-6033	74	17	be	be	AUX
ejpam-6033	74	18	nearly	nearly	ADV
ejpam-6033	74	19	s	s	NOUN
ejpam-6033	74	20	-	-	NOUN
ejpam-6033	74	21	permutable	permutable	ADJ
ejpam-6033	74	22	.	.	PUNCT
ejpam-6033	75	1	for	for	ADP
ejpam-6033	75	2	the	the	DET
ejpam-6033	75	3	subgroups	subgroup	NOUN
ejpam-6033	75	4	of	of	ADP
ejpam-6033	75	5	order	order	NOUN
ejpam-6033	75	6	6	6	NUM
ejpam-6033	75	7	,	,	PUNCT
ejpam-6033	75	8	(	(	PUNCT
ejpam-6033	75	9	non	non	ADJ
ejpam-6033	75	10	-	-	ADJ
ejpam-6033	75	11	normal	normal	ADJ
ejpam-6033	75	12	subgroup	subgroup	NOUN
ejpam-6033	75	13	)	)	PUNCT
ejpam-6033	75	14	there	there	PRON
ejpam-6033	75	15	are	be	VERB
ejpam-6033	75	16	3	3	NUM
ejpam-6033	75	17	conjugacy	conjugacy	ADJ
ejpam-6033	75	18	classes	class	NOUN
ejpam-6033	75	19	are	be	AUX
ejpam-6033	75	20	nearly	nearly	ADV
ejpam-6033	75	21	s	s	NOUN
ejpam-6033	75	22	-	-	ADJ
ejpam-6033	75	23	permutable	permutable	ADJ
ejpam-6033	75	24	:	:	PUNCT
ejpam-6033	75	25	h1	h1	NOUN
ejpam-6033	75	26	=	=	PUNCT
ejpam-6033	75	27	⟨(13	⟨(13	PROPN
ejpam-6033	75	28	)	)	PUNCT
ejpam-6033	75	29	,	,	PUNCT
ejpam-6033	75	30	1)⟩.	1)⟩.	NUM
ejpam-6033	75	31	h2	h2	NOUN
ejpam-6033	75	32	=	=	SYM
ejpam-6033	75	33	⟨(23	⟨(23	NOUN
ejpam-6033	75	34	)	)	PUNCT
ejpam-6033	75	35	,	,	PUNCT
ejpam-6033	75	36	1)⟩.	1)⟩.	NUM
ejpam-6033	75	37	h3	h3	NOUN
ejpam-6033	75	38	=	=	SYM
ejpam-6033	75	39	⟨(12	⟨(12	PROPN
ejpam-6033	75	40	,	,	PUNCT
ejpam-6033	75	41	1)⟩.	1)⟩.	ADP
ejpam-6033	75	42	now	now	ADV
ejpam-6033	75	43	in	in	ADP
ejpam-6033	75	44	this	this	DET
ejpam-6033	75	45	group	group	NOUN
ejpam-6033	75	46	g	g	NOUN
ejpam-6033	75	47	we	we	PRON
ejpam-6033	75	48	have	have	VERB
ejpam-6033	75	49	9	9	NUM
ejpam-6033	75	50	subgroups	subgroup	NOUN
ejpam-6033	75	51	that	that	PRON
ejpam-6033	75	52	are	be	AUX
ejpam-6033	75	53	nearly	nearly	ADV
ejpam-6033	75	54	s	s	NOUN
ejpam-6033	75	55	-	-	ADJ
ejpam-6033	75	56	permutable	permutable	ADJ
ejpam-6033	75	57	.	.	PUNCT
ejpam-6033	76	1	take	take	VERB
ejpam-6033	76	2	h1	h1	NOUN
ejpam-6033	76	3	with	with	ADP
ejpam-6033	76	4	n	n	CCONJ
ejpam-6033	76	5	a	a	DET
ejpam-6033	76	6	normal	normal	ADJ
ejpam-6033	76	7	subgroup	subgroup	NOUN
ejpam-6033	76	8	of	of	ADP
ejpam-6033	76	9	order	order	NOUN
ejpam-6033	76	10	6	6	NUM
ejpam-6033	76	11	,	,	PUNCT
ejpam-6033	76	12	we	we	PRON
ejpam-6033	76	13	have	have	VERB
ejpam-6033	76	14	h1	h1	NOUN
ejpam-6033	76	15	∩n	∩n	NOUN
ejpam-6033	76	16	=	=	PUNCT
ejpam-6033	76	17	⟨(12	⟨(12	PROPN
ejpam-6033	76	18	)	)	PUNCT
ejpam-6033	76	19	,	,	PUNCT
ejpam-6033	76	20	0)⟩	0)⟩	NUM
ejpam-6033	76	21	,	,	PUNCT
ejpam-6033	76	22	now	now	ADV
ejpam-6033	76	23	h1	h1	NOUN
ejpam-6033	76	24	is	be	AUX
ejpam-6033	76	25	nsp	nsp	ADJ
ejpam-6033	76	26	and	and	CCONJ
ejpam-6033	76	27	n	n	ADV
ejpam-6033	76	28	is	be	AUX
ejpam-6033	76	29	nsp	nsp	ADJ
ejpam-6033	76	30	but	but	CCONJ
ejpam-6033	76	31	the	the	DET
ejpam-6033	76	32	intersection	intersection	NOUN
ejpam-6033	76	33	does	do	AUX
ejpam-6033	76	34	nt	not	PART
ejpam-6033	76	35	nearly	nearly	ADV
ejpam-6033	76	36	s	s	VERB
ejpam-6033	76	37	-	-	NOUN
ejpam-6033	76	38	permutable	permutable	ADJ
ejpam-6033	76	39	.	.	PUNCT
ejpam-6033	77	1	now	now	ADV
ejpam-6033	77	2	takeh2,the	takeh2,the	DET
ejpam-6033	77	3	subgroup	subgroup	NOUN
ejpam-6033	77	4	of	of	ADP
ejpam-6033	77	5	h2	h2	PROPN
ejpam-6033	77	6	is⟨(23	is⟨(23	NOUN
ejpam-6033	77	7	,	,	PUNCT
ejpam-6033	77	8	0)⟩	0)⟩	NUM
ejpam-6033	77	9	,	,	PUNCT
ejpam-6033	77	10	its	its	PRON
ejpam-6033	77	11	clear	clear	ADJ
ejpam-6033	77	12	that	that	SCONJ
ejpam-6033	77	13	h2	h2	NOUN
ejpam-6033	77	14	is	be	AUX
ejpam-6033	77	15	nsp	nsp	ADJ
ejpam-6033	77	16	.	.	PUNCT
ejpam-6033	78	1	but	but	CCONJ
ejpam-6033	78	2	the	the	DET
ejpam-6033	78	3	subgroup	subgroup	NOUN
ejpam-6033	78	4	from	from	ADP
ejpam-6033	78	5	h2	h2	PROPN
ejpam-6033	78	6	is	be	AUX
ejpam-6033	78	7	not	not	PART
ejpam-6033	78	8	nsp	nsp	ADJ
ejpam-6033	78	9	.	.	PUNCT
ejpam-6033	79	1	the	the	DET
ejpam-6033	79	2	proof	proof	NOUN
ejpam-6033	79	3	is	be	AUX
ejpam-6033	79	4	complete	complete	ADJ
ejpam-6033	79	5	.	.	PUNCT
ejpam-6033	80	1	lemma	lemma	PROPN
ejpam-6033	80	2	4	4	X
ejpam-6033	80	3	.	.	PUNCT
ejpam-6033	81	1	if	if	SCONJ
ejpam-6033	81	2	h	h	NOUN
ejpam-6033	81	3	is	be	AUX
ejpam-6033	81	4	a	a	DET
ejpam-6033	81	5	p	p	NOUN
ejpam-6033	81	6	-	-	PUNCT
ejpam-6033	81	7	subgroup	subgroup	NOUN
ejpam-6033	81	8	of	of	ADP
ejpam-6033	81	9	g	g	PROPN
ejpam-6033	81	10	,	,	PUNCT
ejpam-6033	81	11	then	then	ADV
ejpam-6033	81	12	h	h	NOUN
ejpam-6033	81	13	is	be	AUX
ejpam-6033	81	14	contained	contain	VERB
ejpam-6033	81	15	in	in	ADP
ejpam-6033	81	16	some	some	DET
ejpam-6033	81	17	sylow	sylow	NOUN
ejpam-6033	81	18	a	a	DET
ejpam-6033	81	19	p	p	NOUN
ejpam-6033	81	20	-	-	PUNCT
ejpam-6033	81	21	subgroup	subgroup	NOUN
ejpam-6033	81	22	of	of	ADP
ejpam-6033	81	23	g.	g.	PROPN
ejpam-6033	81	24	proof	proof	PROPN
ejpam-6033	81	25	.	.	PUNCT
ejpam-6033	82	1	let	let	VERB
ejpam-6033	82	2	l	l	NOUN
ejpam-6033	82	3	=	=	SYM
ejpam-6033	82	4	sylp(g	sylp(g	PROPN
ejpam-6033	82	5	)	)	PUNCT
ejpam-6033	82	6	,	,	PUNCT
ejpam-6033	82	7	and	and	CCONJ
ejpam-6033	82	8	h	h	NOUN
ejpam-6033	82	9	be	be	VERB
ejpam-6033	82	10	p	p	NOUN
ejpam-6033	82	11	-	-	PUNCT
ejpam-6033	82	12	subgroup	subgroup	NOUN
ejpam-6033	82	13	of	of	ADP
ejpam-6033	82	14	g.	g.	PROPN
ejpam-6033	82	15	consider	consider	VERB
ejpam-6033	83	1	the	the	DET
ejpam-6033	83	2	action	action	NOUN
ejpam-6033	83	3	h	h	NOUN
ejpam-6033	83	4	×	×	NOUN
ejpam-6033	83	5	l	l	NOUN
ejpam-6033	83	6	→	→	X
ejpam-6033	83	7	l	l	NOUN
ejpam-6033	83	8	,	,	PUNCT
ejpam-6033	83	9	h(p	h(p	NOUN
ejpam-6033	83	10	)	)	PUNCT
ejpam-6033	84	1	=	=	SYM
ejpam-6033	84	2	h−1ph	h−1ph	NOUN
ejpam-6033	84	3	,	,	PUNCT
ejpam-6033	84	4	then	then	ADV
ejpam-6033	84	5	l	l	NOUN
ejpam-6033	84	6	is	be	AUX
ejpam-6033	84	7	a	a	DET
ejpam-6033	84	8	g	g	NOUN
ejpam-6033	84	9	-	-	PUNCT
ejpam-6033	84	10	set	set	VERB
ejpam-6033	84	11	so	so	SCONJ
ejpam-6033	84	12	|l|∼=	|l|∼=	NOUN
ejpam-6033	84	13	|lh	|lh	PROPN
ejpam-6033	84	14	|(modp	|(modp	PROPN
ejpam-6033	84	15	)	)	PUNCT
ejpam-6033	84	16	.	.	PUNCT
ejpam-6033	85	1	but|l|	but|l|	PROPN
ejpam-6033	85	2	=	=	PROPN
ejpam-6033	85	3	|sylp(g)|	|sylp(g)|	PROPN
ejpam-6033	85	4	=	=	PRON
ejpam-6033	85	5	ηp	ηp	ADP
ejpam-6033	85	6	≡	≡	PROPN
ejpam-6033	85	7	1(mod	1(mod	NUM
ejpam-6033	85	8	p	p	X
ejpam-6033	85	9	)	)	PUNCT
ejpam-6033	85	10	.	.	PUNCT
ejpam-6033	85	11	.	.	PUNCT
ejpam-6033	85	12	.	.	PUNCT
ejpam-6033	86	1	(	(	PUNCT
ejpam-6033	86	2	1	1	X
ejpam-6033	86	3	)	)	PUNCT
ejpam-6033	86	4	let	let	VERB
ejpam-6033	86	5	us	we	PRON
ejpam-6033	86	6	examine	examine	VERB
ejpam-6033	86	7	lh	lh	PROPN
ejpam-6033	86	8	.	.	PUNCT
ejpam-6033	87	1	p	p	PROPN
ejpam-6033	87	2	∈	∈	PROPN
ejpam-6033	87	3	lh	lh	NOUN
ejpam-6033	87	4	if	if	SCONJ
ejpam-6033	87	5	and	and	CCONJ
ejpam-6033	87	6	only	only	ADV
ejpam-6033	87	7	if	if	SCONJ
ejpam-6033	87	8	hp	hp	ADJ
ejpam-6033	87	9	=	=	SYM
ejpam-6033	87	10	p	p	X
ejpam-6033	87	11	∀h	∀h	PROPN
ejpam-6033	87	12	∈	∈	PROPN
ejpam-6033	87	13	h	h	NOUN
ejpam-6033	87	14	and	and	CCONJ
ejpam-6033	87	15	h−1ph∀h	h−1ph∀h	ADJ
ejpam-6033	87	16	∈	∈	PROPN
ejpam-6033	87	17	h.ifh	h.ifh	VERB
ejpam-6033	87	18	≤	≤	NOUN
ejpam-6033	87	19	ng(p	ng(p	PUNCT
ejpam-6033	87	20	)	)	PUNCT
ejpam-6033	87	21	,	,	PUNCT
ejpam-6033	87	22	from	from	ADP
ejpam-6033	87	23	(	(	PUNCT
ejpam-6033	87	24	1	1	X
ejpam-6033	87	25	)	)	PUNCT
ejpam-6033	87	26	there	there	PRON
ejpam-6033	87	27	exist	exist	VERB
ejpam-6033	87	28	at	at	ADV
ejpam-6033	87	29	least	least	ADJ
ejpam-6033	87	30	one	one	NUM
ejpam-6033	87	31	p	p	NOUN
ejpam-6033	87	32	∈	∈	PROPN
ejpam-6033	87	33	l	l	NOUN
ejpam-6033	87	34	,	,	PUNCT
ejpam-6033	87	35	such	such	ADJ
ejpam-6033	87	36	that	that	SCONJ
ejpam-6033	87	37	h	h	NOUN
ejpam-6033	87	38	≤	≤	NOUN
ejpam-6033	87	39	ng(p	ng(p	PUNCT
ejpam-6033	87	40	)	)	PUNCT
ejpam-6033	87	41	,	,	PUNCT
ejpam-6033	87	42	then	then	ADV
ejpam-6033	87	43	hp	hp	PROPN
ejpam-6033	87	44	=	=	PUNCT
ejpam-6033	87	45	ph	ph	PROPN
ejpam-6033	87	46	,	,	PUNCT
ejpam-6033	87	47	it	it	PRON
ejpam-6033	87	48	can	can	AUX
ejpam-6033	87	49	be	be	AUX
ejpam-6033	87	50	seen	see	VERB
ejpam-6033	87	51	that	that	SCONJ
ejpam-6033	87	52	hp	hp	PROPN
ejpam-6033	87	53	is	be	AUX
ejpam-6033	87	54	a	a	DET
ejpam-6033	87	55	subgroup	subgroup	NOUN
ejpam-6033	87	56	of	of	ADP
ejpam-6033	87	57	ng(p	ng(p	NOUN
ejpam-6033	87	58	)	)	PUNCT
ejpam-6033	87	59	.	.	PUNCT
ejpam-6033	88	1	note	note	VERB
ejpam-6033	88	2	hp	hp	PROPN
ejpam-6033	88	3	is	be	AUX
ejpam-6033	88	4	sylow	sylow	ADJ
ejpam-6033	88	5	p	p	PROPN
ejpam-6033	88	6	-	-	PUNCT
ejpam-6033	88	7	subgroup	subgroup	NOUN
ejpam-6033	88	8	ng(p	ng(p	PUNCT
ejpam-6033	88	9	)	)	PUNCT
ejpam-6033	88	10	.	.	PUNCT
ejpam-6033	89	1	hence	hence	ADV
ejpam-6033	89	2	,	,	PUNCT
ejpam-6033	89	3	hp	hp	NOUN
ejpam-6033	89	4	=	=	SYM
ejpam-6033	89	5	p	p	X
ejpam-6033	89	6	;	;	PUNCT
ejpam-6033	89	7	thus	thus	ADV
ejpam-6033	89	8	,	,	PUNCT
ejpam-6033	89	9	h	h	PROPN
ejpam-6033	89	10	≤	≤	PROPN
ejpam-6033	89	11	p	p	X
ejpam-6033	89	12	.	.	PUNCT
ejpam-6033	90	1	remark	remark	NOUN
ejpam-6033	90	2	2	2	NUM
ejpam-6033	90	3	.	.	PUNCT
ejpam-6033	91	1	there	there	PRON
ejpam-6033	91	2	exists	exist	VERB
ejpam-6033	91	3	a	a	DET
ejpam-6033	91	4	ct	ct	NUM
ejpam-6033	91	5	-group	-group	NOUN
ejpam-6033	91	6	which	which	PRON
ejpam-6033	91	7	is	be	AUX
ejpam-6033	91	8	not	not	PART
ejpam-6033	91	9	an	an	DET
ejpam-6033	91	10	nspt	nspt	ADJ
ejpam-6033	91	11	-group	-group	NOUN
ejpam-6033	91	12	.	.	PUNCT
ejpam-6033	92	1	proof	proof	NOUN
ejpam-6033	92	2	.	.	PUNCT
ejpam-6033	93	1	let	let	VERB
ejpam-6033	93	2	g	g	PRON
ejpam-6033	93	3	be	be	AUX
ejpam-6033	93	4	a	a	DET
ejpam-6033	93	5	finite	finite	ADJ
ejpam-6033	93	6	group	group	NOUN
ejpam-6033	93	7	of	of	ADP
ejpam-6033	93	8	order	order	NOUN
ejpam-6033	93	9	18	18	NUM
ejpam-6033	93	10	,	,	PUNCT
ejpam-6033	93	11	given	give	VERB
ejpam-6033	93	12	by	by	ADP
ejpam-6033	93	13	g	g	PROPN
ejpam-6033	93	14	=	=	PROPN
ejpam-6033	93	15	s3	s3	PROPN
ejpam-6033	93	16	×z3	×z3	PROPN
ejpam-6033	93	17	.	.	PUNCT
ejpam-6033	94	1	the	the	DET
ejpam-6033	94	2	elements	element	NOUN
ejpam-6033	94	3	of	of	ADP
ejpam-6033	94	4	g	g	NOUN
ejpam-6033	94	5	are	be	AUX
ejpam-6033	94	6	:	:	PUNCT
ejpam-6033	94	7	g	g	PROPN
ejpam-6033	94	8	=	=	PRON
ejpam-6033	94	9	{	{	PUNCT
ejpam-6033	94	10	(	(	PUNCT
ejpam-6033	94	11	e	e	NOUN
ejpam-6033	94	12	,	,	PUNCT
ejpam-6033	94	13	0	0	NUM
ejpam-6033	94	14	)	)	PUNCT
ejpam-6033	94	15	,	,	PUNCT
ejpam-6033	94	16	(	(	PUNCT
ejpam-6033	94	17	(	(	PUNCT
ejpam-6033	94	18	12	12	NUM
ejpam-6033	94	19	)	)	PUNCT
ejpam-6033	94	20	,	,	PUNCT
ejpam-6033	94	21	0	0	NUM
ejpam-6033	94	22	)	)	PUNCT
ejpam-6033	94	23	,	,	PUNCT
ejpam-6033	94	24	(	(	PUNCT
ejpam-6033	94	25	(	(	PUNCT
ejpam-6033	94	26	13	13	NUM
ejpam-6033	94	27	)	)	PUNCT
ejpam-6033	94	28	,	,	PUNCT
ejpam-6033	94	29	0	0	NUM
ejpam-6033	94	30	)	)	PUNCT
ejpam-6033	94	31	,	,	PUNCT
ejpam-6033	94	32	(	(	PUNCT
ejpam-6033	94	33	(	(	PUNCT
ejpam-6033	94	34	23	23	NUM
ejpam-6033	94	35	)	)	PUNCT
ejpam-6033	94	36	,	,	PUNCT
ejpam-6033	94	37	0	0	NUM
ejpam-6033	94	38	)	)	PUNCT
ejpam-6033	94	39	,	,	PUNCT
ejpam-6033	94	40	(	(	PUNCT
ejpam-6033	94	41	(	(	PUNCT
ejpam-6033	94	42	13	13	NUM
ejpam-6033	94	43	)	)	PUNCT
ejpam-6033	94	44	,	,	PUNCT
ejpam-6033	94	45	2	2	NUM
ejpam-6033	94	46	)	)	PUNCT
ejpam-6033	94	47	,	,	PUNCT
ejpam-6033	94	48	(	(	PUNCT
ejpam-6033	94	49	(	(	PUNCT
ejpam-6033	94	50	23	23	NUM
ejpam-6033	94	51	)	)	PUNCT
ejpam-6033	94	52	,	,	PUNCT
ejpam-6033	94	53	2	2	NUM
ejpam-6033	94	54	)	)	PUNCT
ejpam-6033	94	55	,	,	PUNCT
ejpam-6033	94	56	(	(	PUNCT
ejpam-6033	94	57	(	(	PUNCT
ejpam-6033	94	58	132	132	NUM
ejpam-6033	94	59	)	)	PUNCT
ejpam-6033	94	60	,	,	PUNCT
ejpam-6033	94	61	2	2	NUM
ejpam-6033	94	62	)	)	PUNCT
ejpam-6033	94	63	,	,	PUNCT
ejpam-6033	94	64	(	(	PUNCT
ejpam-6033	94	65	(	(	PUNCT
ejpam-6033	94	66	123	123	NUM
ejpam-6033	94	67	)	)	PUNCT
ejpam-6033	94	68	,	,	PUNCT
ejpam-6033	94	69	2	2	NUM
ejpam-6033	94	70	)	)	PUNCT
ejpam-6033	94	71	}	}	PUNCT
ejpam-6033	94	72	.	.	PUNCT
ejpam-6033	95	1	normal	normal	ADJ
ejpam-6033	95	2	subgroups	subgroup	NOUN
ejpam-6033	95	3	in	in	ADP
ejpam-6033	95	4	g	g	PROPN
ejpam-6033	95	5	are	be	AUX
ejpam-6033	95	6	:	:	PUNCT
ejpam-6033	95	7	order	order	NOUN
ejpam-6033	95	8	9	9	NUM
ejpam-6033	95	9	:	:	PUNCT
ejpam-6033	95	10	⟨((132	⟨((132	PROPN
ejpam-6033	95	11	)	)	PUNCT
ejpam-6033	95	12	,	,	PUNCT
ejpam-6033	95	13	0	0	NUM
ejpam-6033	95	14	)	)	PUNCT
ejpam-6033	95	15	,	,	PUNCT
ejpam-6033	95	16	(	(	PUNCT
ejpam-6033	95	17	e	e	NOUN
ejpam-6033	95	18	,	,	PUNCT
ejpam-6033	95	19	1)⟩.	1)⟩.	NUM
ejpam-6033	95	20	order	order	NOUN
ejpam-6033	95	21	6	6	NUM
ejpam-6033	95	22	:	:	PUNCT
ejpam-6033	95	23	⟨((12	⟨((12	NUM
ejpam-6033	95	24	)	)	PUNCT
ejpam-6033	95	25	,	,	PUNCT
ejpam-6033	95	26	0	0	NUM
ejpam-6033	95	27	)	)	PUNCT
ejpam-6033	95	28	,	,	PUNCT
ejpam-6033	95	29	(	(	PUNCT
ejpam-6033	95	30	(	(	PUNCT
ejpam-6033	95	31	13	13	NUM
ejpam-6033	95	32	)	)	PUNCT
ejpam-6033	95	33	,	,	PUNCT
ejpam-6033	95	34	0)⟩.	0)⟩.	PRON
ejpam-6033	95	35	order	order	NOUN
ejpam-6033	95	36	3	3	NUM
ejpam-6033	95	37	:	:	PUNCT
ejpam-6033	95	38	⟨(e	⟨(e	PROPN
ejpam-6033	95	39	,	,	PUNCT
ejpam-6033	95	40	1)⟩	1)⟩	NUM
ejpam-6033	95	41	and	and	CCONJ
ejpam-6033	95	42	order1	order1	NOUN
ejpam-6033	95	43	.	.	PUNCT
ejpam-6033	96	1	all	all	DET
ejpam-6033	96	2	normal	normal	ADJ
ejpam-6033	96	3	subgroups	subgroup	NOUN
ejpam-6033	96	4	of	of	ADP
ejpam-6033	96	5	g	g	NOUN
ejpam-6033	96	6	satisfy	satisfy	VERB
ejpam-6033	96	7	the	the	DET
ejpam-6033	96	8	c	c	NOUN
ejpam-6033	96	9	-	-	PUNCT
ejpam-6033	96	10	normality	normality	NOUN
ejpam-6033	96	11	condition	condition	NOUN
ejpam-6033	96	12	.	.	PUNCT
ejpam-6033	97	1	additionally	additionally	ADV
ejpam-6033	97	2	,	,	PUNCT
ejpam-6033	97	3	subgroups	subgroup	NOUN
ejpam-6033	97	4	with	with	ADP
ejpam-6033	97	5	order	order	NOUN
ejpam-6033	97	6	6	6	NUM
ejpam-6033	97	7	are	be	AUX
ejpam-6033	97	8	distributed	distribute	VERB
ejpam-6033	97	9	across	across	ADP
ejpam-6033	97	10	3	3	NUM
ejpam-6033	97	11	conjugacy	conjugacy	ADJ
ejpam-6033	97	12	classes	class	NOUN
ejpam-6033	97	13	:	:	PUNCT
ejpam-6033	97	14	h1	h1	PROPN
ejpam-6033	97	15	=	=	PRON
ejpam-6033	97	16	{	{	PUNCT
ejpam-6033	97	17	(	(	PUNCT
ejpam-6033	97	18	e	e	NOUN
ejpam-6033	97	19	,	,	PUNCT
ejpam-6033	97	20	0	0	NUM
ejpam-6033	97	21	)	)	PUNCT
ejpam-6033	97	22	,	,	PUNCT
ejpam-6033	97	23	(	(	PUNCT
ejpam-6033	97	24	e	e	NOUN
ejpam-6033	97	25	,	,	PUNCT
ejpam-6033	97	26	1	1	NUM
ejpam-6033	97	27	)	)	PUNCT
ejpam-6033	97	28	,	,	PUNCT
ejpam-6033	97	29	(	(	PUNCT
ejpam-6033	97	30	e	e	NOUN
ejpam-6033	97	31	,	,	PUNCT
ejpam-6033	97	32	2	2	NUM
ejpam-6033	97	33	)	)	PUNCT
ejpam-6033	97	34	,	,	PUNCT
ejpam-6033	97	35	(	(	PUNCT
ejpam-6033	97	36	(	(	PUNCT
ejpam-6033	97	37	23	23	NUM
ejpam-6033	97	38	)	)	PUNCT
ejpam-6033	97	39	,	,	PUNCT
ejpam-6033	97	40	0	0	NUM
ejpam-6033	97	41	)	)	PUNCT
ejpam-6033	97	42	,	,	PUNCT
ejpam-6033	97	43	(	(	PUNCT
ejpam-6033	97	44	(	(	PUNCT
ejpam-6033	97	45	23	23	NUM
ejpam-6033	97	46	)	)	PUNCT
ejpam-6033	97	47	,	,	PUNCT
ejpam-6033	97	48	1	1	NUM
ejpam-6033	97	49	)	)	PUNCT
ejpam-6033	97	50	,	,	PUNCT
ejpam-6033	97	51	(	(	PUNCT
ejpam-6033	97	52	(	(	PUNCT
ejpam-6033	97	53	23	23	NUM
ejpam-6033	97	54	)	)	PUNCT
ejpam-6033	97	55	,	,	PUNCT
ejpam-6033	97	56	2	2	NUM
ejpam-6033	97	57	)	)	PUNCT
ejpam-6033	97	58	}	}	PUNCT
ejpam-6033	97	59	.	.	PUNCT
ejpam-6033	98	1	h2	h2	NOUN
ejpam-6033	98	2	=	=	PRON
ejpam-6033	98	3	{	{	PUNCT
ejpam-6033	98	4	(	(	PUNCT
ejpam-6033	98	5	e	e	NOUN
ejpam-6033	98	6	,	,	PUNCT
ejpam-6033	98	7	0	0	NUM
ejpam-6033	98	8	)	)	PUNCT
ejpam-6033	98	9	,	,	PUNCT
ejpam-6033	98	10	(	(	PUNCT
ejpam-6033	98	11	e	e	NOUN
ejpam-6033	98	12	,	,	PUNCT
ejpam-6033	98	13	1	1	NUM
ejpam-6033	98	14	)	)	PUNCT
ejpam-6033	98	15	,	,	PUNCT
ejpam-6033	98	16	(	(	PUNCT
ejpam-6033	98	17	e	e	NOUN
ejpam-6033	98	18	,	,	PUNCT
ejpam-6033	98	19	2	2	NUM
ejpam-6033	98	20	)	)	PUNCT
ejpam-6033	98	21	,	,	PUNCT
ejpam-6033	98	22	(	(	PUNCT
ejpam-6033	98	23	(	(	PUNCT
ejpam-6033	98	24	13	13	NUM
ejpam-6033	98	25	)	)	PUNCT
ejpam-6033	98	26	,	,	PUNCT
ejpam-6033	98	27	0	0	NUM
ejpam-6033	98	28	)	)	PUNCT
ejpam-6033	98	29	,	,	PUNCT
ejpam-6033	98	30	(	(	PUNCT
ejpam-6033	98	31	(	(	PUNCT
ejpam-6033	98	32	13	13	NUM
ejpam-6033	98	33	)	)	PUNCT
ejpam-6033	98	34	,	,	PUNCT
ejpam-6033	98	35	1	1	NUM
ejpam-6033	98	36	)	)	PUNCT
ejpam-6033	98	37	,	,	PUNCT
ejpam-6033	98	38	(	(	PUNCT
ejpam-6033	98	39	(	(	PUNCT
ejpam-6033	98	40	13	13	NUM
ejpam-6033	98	41	)	)	PUNCT
ejpam-6033	98	42	,	,	PUNCT
ejpam-6033	98	43	2	2	NUM
ejpam-6033	98	44	)	)	PUNCT
ejpam-6033	98	45	.	.	PUNCT
ejpam-6033	99	1	h3	h3	NOUN
ejpam-6033	99	2	=	=	SYM
ejpam-6033	99	3	{	{	PUNCT
ejpam-6033	99	4	(	(	PUNCT
ejpam-6033	99	5	e	e	NOUN
ejpam-6033	99	6	,	,	PUNCT
ejpam-6033	99	7	0	0	NUM
ejpam-6033	99	8	)	)	PUNCT
ejpam-6033	99	9	,	,	PUNCT
ejpam-6033	99	10	(	(	PUNCT
ejpam-6033	99	11	e	e	NOUN
ejpam-6033	99	12	,	,	PUNCT
ejpam-6033	99	13	1	1	NUM
ejpam-6033	99	14	)	)	PUNCT
ejpam-6033	99	15	,	,	PUNCT
ejpam-6033	99	16	(	(	PUNCT
ejpam-6033	99	17	e	e	NOUN
ejpam-6033	99	18	,	,	PUNCT
ejpam-6033	99	19	2	2	NUM
ejpam-6033	99	20	)	)	PUNCT
ejpam-6033	99	21	,	,	PUNCT
ejpam-6033	99	22	(	(	PUNCT
ejpam-6033	99	23	(	(	PUNCT
ejpam-6033	99	24	12	12	NUM
ejpam-6033	99	25	)	)	PUNCT
ejpam-6033	99	26	,	,	PUNCT
ejpam-6033	99	27	0	0	NUM
ejpam-6033	99	28	)	)	PUNCT
ejpam-6033	99	29	,	,	PUNCT
ejpam-6033	99	30	(	(	PUNCT
ejpam-6033	99	31	(	(	PUNCT
ejpam-6033	99	32	12	12	NUM
ejpam-6033	99	33	)	)	PUNCT
ejpam-6033	99	34	,	,	PUNCT
ejpam-6033	99	35	1	1	NUM
ejpam-6033	99	36	)	)	PUNCT
ejpam-6033	99	37	,	,	PUNCT
ejpam-6033	99	38	(	(	PUNCT
ejpam-6033	99	39	(	(	PUNCT
ejpam-6033	99	40	12	12	NUM
ejpam-6033	99	41	)	)	PUNCT
ejpam-6033	99	42	,	,	PUNCT
ejpam-6033	99	43	2	2	NUM
ejpam-6033	99	44	)	)	PUNCT
ejpam-6033	99	45	}	}	PUNCT
ejpam-6033	99	46	.	.	PUNCT
ejpam-6033	100	1	for	for	ADP
ejpam-6033	100	2	each	each	DET
ejpam-6033	100	3	hi	hi	ADJ
ejpam-6033	100	4	,	,	PUNCT
ejpam-6033	100	5	we	we	PRON
ejpam-6033	100	6	find	find	VERB
ejpam-6033	100	7	that	that	SCONJ
ejpam-6033	100	8	:	:	PUNCT
ejpam-6033	100	9	if	if	SCONJ
ejpam-6033	100	10	h1	h1	PROPN
ejpam-6033	100	11	is	be	AUX
ejpam-6033	100	12	paired	pair	VERB
ejpam-6033	100	13	with	with	ADP
ejpam-6033	100	14	n	n	PROPN
ejpam-6033	100	15	,	,	PUNCT
ejpam-6033	100	16	a	a	DET
ejpam-6033	100	17	normal	normal	ADJ
ejpam-6033	100	18	subgroup	subgroup	NOUN
ejpam-6033	100	19	of	of	ADP
ejpam-6033	100	20	order	order	NOUN
ejpam-6033	100	21	9	9	NUM
ejpam-6033	100	22	,	,	PUNCT
ejpam-6033	100	23	then	then	ADV
ejpam-6033	100	24	g	g	PROPN
ejpam-6033	100	25	=	=	PUNCT
ejpam-6033	100	26	h1n	h1n	PROPN
ejpam-6033	100	27	and	and	CCONJ
ejpam-6033	100	28	h1	h1	VERB
ejpam-6033	100	29	∩n	∩n	NOUN
ejpam-6033	100	30	=	=	SYM
ejpam-6033	100	31	⟨(e	⟨(e	PROPN
ejpam-6033	100	32	,	,	PUNCT
ejpam-6033	100	33	1)⟩.	1)⟩.	AUX
ejpam-6033	100	34	this	this	DET
ejpam-6033	100	35	ensures	ensure	VERB
ejpam-6033	100	36	h1	h1	PROPN
ejpam-6033	100	37	∩n	∩n	PROPN
ejpam-6033	100	38	⊆	⊆	NUM
ejpam-6033	100	39	(	(	PUNCT
ejpam-6033	100	40	h1	h1	PROPN
ejpam-6033	100	41	)	)	PUNCT
ejpam-6033	100	42	,	,	PUNCT
ejpam-6033	100	43	making	make	VERB
ejpam-6033	100	44	subgroups	subgroup	NOUN
ejpam-6033	100	45	of	of	ADP
ejpam-6033	100	46	order	order	NOUN
ejpam-6033	100	47	6	6	NUM
ejpam-6033	100	48	are	be	AUX
ejpam-6033	100	49	c	c	NOUN
ejpam-6033	100	50	-	-	NOUN
ejpam-6033	100	51	normal	normal	ADJ
ejpam-6033	100	52	.	.	PUNCT
ejpam-6033	101	1	for	for	ADP
ejpam-6033	101	2	subgroups	subgroup	NOUN
ejpam-6033	101	3	of	of	ADP
ejpam-6033	101	4	order	order	NOUN
ejpam-6033	101	5	3	3	X
ejpam-6033	101	6	,	,	PUNCT
ejpam-6033	101	7	there	there	PRON
ejpam-6033	101	8	are	be	VERB
ejpam-6033	101	9	two	two	NUM
ejpam-6033	101	10	distinct	distinct	ADJ
ejpam-6033	101	11	conjugacy	conjugacy	ADJ
ejpam-6033	101	12	classes	class	NOUN
ejpam-6033	101	13	:	:	PUNCT
ejpam-6033	101	14	h1	h1	PROPN
ejpam-6033	101	15	=	=	PRON
ejpam-6033	101	16	{	{	PUNCT
ejpam-6033	101	17	(	(	PUNCT
ejpam-6033	101	18	e	e	NOUN
ejpam-6033	101	19	,	,	PUNCT
ejpam-6033	101	20	0	0	NUM
ejpam-6033	101	21	)	)	PUNCT
ejpam-6033	101	22	,	,	PUNCT
ejpam-6033	101	23	(	(	PUNCT
ejpam-6033	101	24	(	(	PUNCT
ejpam-6033	101	25	123	123	NUM
ejpam-6033	101	26	)	)	PUNCT
ejpam-6033	101	27	,	,	PUNCT
ejpam-6033	101	28	1	1	NUM
ejpam-6033	101	29	)	)	PUNCT
ejpam-6033	101	30	,	,	PUNCT
ejpam-6033	101	31	(	(	PUNCT
ejpam-6033	101	32	(	(	PUNCT
ejpam-6033	101	33	132	132	NUM
ejpam-6033	101	34	)	)	PUNCT
ejpam-6033	101	35	,	,	PUNCT
ejpam-6033	101	36	2	2	NUM
ejpam-6033	101	37	}	}	PUNCT
ejpam-6033	101	38	.	.	PUNCT
ejpam-6033	102	1	a.	a.	PROPN
ejpam-6033	102	2	m.	m.	PROPN
ejpam-6033	102	3	alotaibiang	alotaibiang	PROPN
ejpam-6033	102	4	,	,	PUNCT
ejpam-6033	102	5	k.	k.	PROPN
ejpam-6033	102	6	al	al	PROPN
ejpam-6033	102	7	-	-	PROPN
ejpam-6033	102	8	tahat	tahat	PROPN
ejpam-6033	102	9	,	,	PUNCT
ejpam-6033	102	10	k.	k.	PROPN
ejpam-6033	102	11	m.	m.	PROPN
ejpam-6033	102	12	al	al	PROPN
ejpam-6033	102	13	-	-	PROPN
ejpam-6033	102	14	jamal	jamal	PROPN
ejpam-6033	102	15	/	/	SYM
ejpam-6033	102	16	eur	eur	PROPN
ejpam-6033	102	17	.	.	PUNCT
ejpam-6033	103	1	j.	j.	PROPN
ejpam-6033	103	2	pure	pure	PROPN
ejpam-6033	103	3	appl	appl	PROPN
ejpam-6033	103	4	.	.	PROPN
ejpam-6033	103	5	math	math	PROPN
ejpam-6033	103	6	,	,	PUNCT
ejpam-6033	103	7	18	18	NUM
ejpam-6033	103	8	(	(	PUNCT
ejpam-6033	103	9	3	3	NUM
ejpam-6033	103	10	)	)	PUNCT
ejpam-6033	103	11	(	(	PUNCT
ejpam-6033	103	12	2025	2025	NUM
ejpam-6033	103	13	)	)	PUNCT
ejpam-6033	103	14	,	,	PUNCT
ejpam-6033	103	15	6033	6033	NUM
ejpam-6033	103	16	5	5	NUM
ejpam-6033	103	17	of	of	ADP
ejpam-6033	103	18	8	8	NUM
ejpam-6033	103	19	h2	h2	NOUN
ejpam-6033	103	20	=	=	SYM
ejpam-6033	103	21	{	{	PUNCT
ejpam-6033	103	22	(	(	PUNCT
ejpam-6033	103	23	e	e	NOUN
ejpam-6033	103	24	,	,	PUNCT
ejpam-6033	103	25	0	0	NUM
ejpam-6033	103	26	)	)	PUNCT
ejpam-6033	103	27	,	,	PUNCT
ejpam-6033	103	28	(	(	PUNCT
ejpam-6033	103	29	(	(	PUNCT
ejpam-6033	103	30	132	132	NUM
ejpam-6033	103	31	)	)	PUNCT
ejpam-6033	103	32	,	,	PUNCT
ejpam-6033	103	33	1	1	NUM
ejpam-6033	103	34	)	)	PUNCT
ejpam-6033	103	35	,	,	PUNCT
ejpam-6033	103	36	(	(	PUNCT
ejpam-6033	103	37	(	(	PUNCT
ejpam-6033	103	38	123	123	NUM
ejpam-6033	103	39	)	)	PUNCT
ejpam-6033	103	40	,	,	PUNCT
ejpam-6033	103	41	2	2	NUM
ejpam-6033	103	42	}	}	PUNCT
ejpam-6033	103	43	.	.	PUNCT
ejpam-6033	104	1	similarly	similarly	ADV
ejpam-6033	104	2	,	,	PUNCT
ejpam-6033	104	3	when	when	SCONJ
ejpam-6033	104	4	h1	h1	PROPN
ejpam-6033	104	5	is	be	AUX
ejpam-6033	104	6	paired	pair	VERB
ejpam-6033	104	7	with	with	ADP
ejpam-6033	104	8	n	n	PROPN
ejpam-6033	104	9	,	,	PUNCT
ejpam-6033	104	10	a	a	DET
ejpam-6033	104	11	normal	normal	ADJ
ejpam-6033	104	12	subgroup	subgroup	NOUN
ejpam-6033	104	13	of	of	ADP
ejpam-6033	104	14	order	order	NOUN
ejpam-6033	104	15	6	6	NUM
ejpam-6033	104	16	,	,	PUNCT
ejpam-6033	104	17	we	we	PRON
ejpam-6033	104	18	have	have	VERB
ejpam-6033	104	19	g	g	NOUN
ejpam-6033	104	20	=	=	PUNCT
ejpam-6033	104	21	h1n	h1n	PROPN
ejpam-6033	104	22	and	and	CCONJ
ejpam-6033	104	23	h1	h1	VERB
ejpam-6033	104	24	∩	∩	ADJ
ejpam-6033	104	25	n	n	NOUN
ejpam-6033	104	26	=	=	SYM
ejpam-6033	104	27	⟨(e	⟨(e	PROPN
ejpam-6033	104	28	,	,	PUNCT
ejpam-6033	104	29	0)⟩h1	0)⟩h1	NUM
ejpam-6033	104	30	∩	∩	PROPN
ejpam-6033	104	31	n	n	NOUN
ejpam-6033	104	32	=	=	SYM
ejpam-6033	104	33	⟨(e	⟨(e	PROPN
ejpam-6033	104	34	,	,	PUNCT
ejpam-6033	104	35	0)⟩.	0)⟩.	NUM
ejpam-6033	104	36	this	this	DET
ejpam-6033	104	37	guarantees	guarantee	VERB
ejpam-6033	104	38	that	that	SCONJ
ejpam-6033	104	39	subgroups	subgroup	NOUN
ejpam-6033	104	40	of	of	ADP
ejpam-6033	104	41	order	order	NOUN
ejpam-6033	104	42	3	3	NUM
ejpam-6033	104	43	are	be	AUX
ejpam-6033	104	44	c	c	NOUN
ejpam-6033	104	45	-	-	NOUN
ejpam-6033	104	46	normal	normal	ADJ
ejpam-6033	104	47	.	.	PUNCT
ejpam-6033	105	1	for	for	ADP
ejpam-6033	105	2	subgroups	subgroup	NOUN
ejpam-6033	105	3	of	of	ADP
ejpam-6033	105	4	order	order	NOUN
ejpam-6033	105	5	2	2	NUM
ejpam-6033	105	6	,	,	PUNCT
ejpam-6033	105	7	there	there	PRON
ejpam-6033	105	8	are	be	VERB
ejpam-6033	105	9	3	3	NUM
ejpam-6033	105	10	conjugacy	conjugacy	ADJ
ejpam-6033	105	11	classes	class	NOUN
ejpam-6033	105	12	:	:	PUNCT
ejpam-6033	105	13	h1	h1	PROPN
ejpam-6033	105	14	=	=	PRON
ejpam-6033	105	15	{	{	PUNCT
ejpam-6033	105	16	(	(	PUNCT
ejpam-6033	105	17	e	e	NOUN
ejpam-6033	105	18	,	,	PUNCT
ejpam-6033	105	19	0	0	NUM
ejpam-6033	105	20	)	)	PUNCT
ejpam-6033	105	21	,	,	PUNCT
ejpam-6033	105	22	(	(	PUNCT
ejpam-6033	105	23	(	(	PUNCT
ejpam-6033	105	24	23	23	NUM
ejpam-6033	105	25	)	)	PUNCT
ejpam-6033	105	26	,	,	PUNCT
ejpam-6033	105	27	0	0	NUM
ejpam-6033	105	28	)	)	PUNCT
ejpam-6033	105	29	}	}	PUNCT
ejpam-6033	105	30	.	.	PUNCT
ejpam-6033	106	1	h2	h2	NOUN
ejpam-6033	106	2	=	=	PRON
ejpam-6033	106	3	{	{	PUNCT
ejpam-6033	106	4	(	(	PUNCT
ejpam-6033	106	5	e	e	NOUN
ejpam-6033	106	6	,	,	PUNCT
ejpam-6033	106	7	0	0	NUM
ejpam-6033	106	8	)	)	PUNCT
ejpam-6033	106	9	,	,	PUNCT
ejpam-6033	106	10	(	(	PUNCT
ejpam-6033	106	11	(	(	PUNCT
ejpam-6033	106	12	13	13	NUM
ejpam-6033	106	13	)	)	PUNCT
ejpam-6033	106	14	,	,	PUNCT
ejpam-6033	106	15	0	0	NUM
ejpam-6033	106	16	)	)	PUNCT
ejpam-6033	106	17	}	}	PUNCT
ejpam-6033	106	18	.	.	PUNCT
ejpam-6033	107	1	h3	h3	NOUN
ejpam-6033	107	2	=	=	SYM
ejpam-6033	107	3	{	{	PUNCT
ejpam-6033	107	4	(	(	PUNCT
ejpam-6033	107	5	e	e	NOUN
ejpam-6033	107	6	,	,	PUNCT
ejpam-6033	107	7	0	0	NUM
ejpam-6033	107	8	)	)	PUNCT
ejpam-6033	107	9	,	,	PUNCT
ejpam-6033	107	10	(	(	PUNCT
ejpam-6033	107	11	(	(	PUNCT
ejpam-6033	107	12	12	12	NUM
ejpam-6033	107	13	)	)	PUNCT
ejpam-6033	107	14	,	,	PUNCT
ejpam-6033	107	15	0	0	NUM
ejpam-6033	107	16	)	)	PUNCT
ejpam-6033	107	17	}	}	PUNCT
ejpam-6033	107	18	.	.	PUNCT
ejpam-6033	108	1	subgroups	subgroup	NOUN
ejpam-6033	108	2	of	of	ADP
ejpam-6033	108	3	order	order	NOUN
ejpam-6033	108	4	2	2	NUM
ejpam-6033	108	5	are	be	AUX
ejpam-6033	108	6	c	c	NOUN
ejpam-6033	108	7	-	-	ADJ
ejpam-6033	108	8	normal	normal	ADJ
ejpam-6033	108	9	,	,	PUNCT
ejpam-6033	108	10	as	as	SCONJ
ejpam-6033	108	11	demonstrated	demonstrate	VERB
ejpam-6033	108	12	by	by	ADP
ejpam-6033	108	13	similar	similar	ADJ
ejpam-6033	108	14	reasoning	reasoning	NOUN
ejpam-6033	108	15	.	.	PUNCT
ejpam-6033	109	1	now	now	ADV
ejpam-6033	109	2	the	the	DET
ejpam-6033	109	3	sylow	sylow	NOUN
ejpam-6033	109	4	3	3	NUM
ejpam-6033	109	5	-	-	PUNCT
ejpam-6033	109	6	subgroup	subgroup	NOUN
ejpam-6033	109	7	of	of	ADP
ejpam-6033	109	8	g	g	PROPN
ejpam-6033	109	9	is	be	AUX
ejpam-6033	109	10	⟨((132	⟨((132	PROPN
ejpam-6033	109	11	)	)	PUNCT
ejpam-6033	109	12	,	,	PUNCT
ejpam-6033	109	13	(	(	PUNCT
ejpam-6033	109	14	e	e	NOUN
ejpam-6033	109	15	,	,	PUNCT
ejpam-6033	109	16	1)⟩	1)⟩	NUM
ejpam-6033	109	17	≃	≃	ADJ
ejpam-6033	109	18	z3	z3	PROPN
ejpam-6033	109	19	×	×	PROPN
ejpam-6033	109	20	a3	a3	NOUN
ejpam-6033	109	21	=	=	PROPN
ejpam-6033	109	22	p	p	PROPN
ejpam-6033	109	23	,	,	PUNCT
ejpam-6033	109	24	the	the	DET
ejpam-6033	109	25	indexed	indexed	NOUN
ejpam-6033	110	1	[	[	X
ejpam-6033	110	2	g	g	NOUN
ejpam-6033	110	3	:	:	PUNCT
ejpam-6033	110	4	p	p	X
ejpam-6033	110	5	]	]	X
ejpam-6033	110	6	=	=	SYM
ejpam-6033	110	7	2	2	X
ejpam-6033	110	8	.	.	PUNCT
ejpam-6033	111	1	now	now	ADV
ejpam-6033	111	2	p	p	X
ejpam-6033	111	3	is	be	AUX
ejpam-6033	111	4	normal	normal	ADJ
ejpam-6033	111	5	in	in	ADP
ejpam-6033	111	6	g	g	PROPN
ejpam-6033	111	7	,	,	PUNCT
ejpam-6033	111	8	such	such	ADJ
ejpam-6033	111	9	that	that	SCONJ
ejpam-6033	111	10	ng(h	ng(h	ADV
ejpam-6033	111	11	)	)	PUNCT
ejpam-6033	112	1	=	=	SYM
ejpam-6033	112	2	g	g	NOUN
ejpam-6033	112	3	;	;	PUNCT
ejpam-6033	112	4	take	take	VERB
ejpam-6033	112	5	h	h	NOUN
ejpam-6033	112	6	of	of	ADP
ejpam-6033	112	7	order	order	NOUN
ejpam-6033	112	8	3	3	X
ejpam-6033	112	9	.	.	PUNCT
ejpam-6033	113	1	now	now	ADV
ejpam-6033	113	2	h	h	NOUN
ejpam-6033	113	3	is	be	AUX
ejpam-6033	113	4	nearly	nearly	ADV
ejpam-6033	113	5	s	s	NOUN
ejpam-6033	113	6	-	-	ADJ
ejpam-6033	113	7	permutable	permutable	ADJ
ejpam-6033	113	8	,	,	PUNCT
ejpam-6033	113	9	since	since	SCONJ
ejpam-6033	113	10	ng(h	ng(h	ADV
ejpam-6033	113	11	)	)	PUNCT
ejpam-6033	114	1	=	=	SYM
ejpam-6033	114	2	p	p	NOUN
ejpam-6033	114	3	and	and	CCONJ
ejpam-6033	114	4	p	p	NOUN
ejpam-6033	114	5	is	be	AUX
ejpam-6033	114	6	nearly	nearly	ADV
ejpam-6033	114	7	s	s	NOUN
ejpam-6033	114	8	-	-	NOUN
ejpam-6033	114	9	permutable	permutable	ADJ
ejpam-6033	114	10	in	in	ADP
ejpam-6033	114	11	g	g	NOUN
ejpam-6033	114	12	,	,	PUNCT
ejpam-6033	114	13	but	but	CCONJ
ejpam-6033	114	14	h	h	NOUN
ejpam-6033	114	15	is	be	AUX
ejpam-6033	114	16	not	not	PART
ejpam-6033	114	17	nearly	nearly	ADV
ejpam-6033	114	18	s	s	NOUN
ejpam-6033	114	19	-	-	NOUN
ejpam-6033	114	20	permutable	permutable	ADJ
ejpam-6033	114	21	in	in	ADP
ejpam-6033	114	22	g	g	NOUN
ejpam-6033	114	23	,	,	PUNCT
ejpam-6033	114	24	hence	hence	ADV
ejpam-6033	114	25	,	,	PUNCT
ejpam-6033	114	26	g	g	PROPN
ejpam-6033	114	27	is	be	AUX
ejpam-6033	114	28	not	not	PART
ejpam-6033	114	29	nspt	nspt	PROPN
ejpam-6033	114	30	-group	-group	NOUN
ejpam-6033	114	31	.	.	PUNCT
ejpam-6033	115	1	thus	thus	ADV
ejpam-6033	115	2	,	,	PUNCT
ejpam-6033	115	3	g	g	PROPN
ejpam-6033	115	4	is	be	AUX
ejpam-6033	115	5	not	not	PART
ejpam-6033	115	6	an	an	DET
ejpam-6033	115	7	nspt	nspt	PROPN
ejpam-6033	115	8	-group	-group	NOUN
ejpam-6033	115	9	,	,	PUNCT
ejpam-6033	115	10	demonstrating	demonstrate	VERB
ejpam-6033	115	11	that	that	SCONJ
ejpam-6033	115	12	a	a	DET
ejpam-6033	115	13	ct	ct	NUM
ejpam-6033	115	14	-group	-group	NOUN
ejpam-6033	115	15	need	need	AUX
ejpam-6033	115	16	not	not	PART
ejpam-6033	115	17	be	be	AUX
ejpam-6033	115	18	an	an	DET
ejpam-6033	115	19	nspt	nspt	PROPN
ejpam-6033	115	20	-group	-group	NOUN
ejpam-6033	115	21	.	.	PUNCT
ejpam-6033	116	1	remark	remark	PROPN
ejpam-6033	116	2	3	3	NUM
ejpam-6033	116	3	.	.	PUNCT
ejpam-6033	117	1	there	there	PRON
ejpam-6033	117	2	exists	exist	VERB
ejpam-6033	117	3	a	a	DET
ejpam-6033	117	4	finite	finite	ADJ
ejpam-6033	117	5	group	group	NOUN
ejpam-6033	117	6	which	which	PRON
ejpam-6033	117	7	is	be	AUX
ejpam-6033	117	8	an	an	DET
ejpam-6033	117	9	nspt	nspt	ADJ
ejpam-6033	117	10	-group	-group	NOUN
ejpam-6033	117	11	but	but	CCONJ
ejpam-6033	117	12	not	not	PART
ejpam-6033	117	13	a	a	DET
ejpam-6033	117	14	ct	ct	NUM
ejpam-6033	117	15	-group	-group	NOUN
ejpam-6033	117	16	.	.	PUNCT
ejpam-6033	118	1	proof	proof	NOUN
ejpam-6033	118	2	.	.	PUNCT
ejpam-6033	119	1	let	let	VERB
ejpam-6033	119	2	e8	e8	PROPN
ejpam-6033	119	3	=	=	PROPN
ejpam-6033	119	4	z2	z2	PROPN
ejpam-6033	119	5	×	×	PROPN
ejpam-6033	119	6	z2	z2	PROPN
ejpam-6033	119	7	×	×	PROPN
ejpam-6033	119	8	z2	z2	PROPN
ejpam-6033	119	9	,	,	PUNCT
ejpam-6033	119	10	(	(	PUNCT
ejpam-6033	119	11	e	e	NOUN
ejpam-6033	119	12	:	:	PUNCT
ejpam-6033	119	13	elementary	elementary	ADJ
ejpam-6033	119	14	2	2	NUM
ejpam-6033	119	15	-	-	PUNCT
ejpam-6033	119	16	group	group	NOUN
ejpam-6033	119	17	of	of	ADP
ejpam-6033	119	18	order	order	NOUN
ejpam-6033	119	19	8)	8)	NUM
ejpam-6033	119	20	.	.	PUNCT
ejpam-6033	120	1	now	now	ADV
ejpam-6033	120	2	aut	aut	PROPN
ejpam-6033	120	3	(	(	PUNCT
ejpam-6033	120	4	e8	e8	PROPN
ejpam-6033	120	5	)	)	PUNCT
ejpam-6033	120	6	≃	≃	NOUN
ejpam-6033	120	7	psl(3	psl(3	NOUN
ejpam-6033	120	8	,	,	PUNCT
ejpam-6033	120	9	2)-simple	2)-simple	NUM
ejpam-6033	120	10	group	group	NOUN
ejpam-6033	120	11	of	of	ADP
ejpam-6033	120	12	order	order	NOUN
ejpam-6033	120	13	168	168	NUM
ejpam-6033	120	14	and	and	CCONJ
ejpam-6033	120	15	it	it	PRON
ejpam-6033	120	16	has	have	VERB
ejpam-6033	120	17	179	179	NUM
ejpam-6033	120	18	subgroups	subgroup	NOUN
ejpam-6033	120	19	,	,	PUNCT
ejpam-6033	120	20	35	35	NUM
ejpam-6033	120	21	-	-	PUNCT
ejpam-6033	120	22	subgroups	subgroup	NOUN
ejpam-6033	120	23	of	of	ADP
ejpam-6033	120	24	which	which	PRON
ejpam-6033	120	25	are	be	AUX
ejpam-6033	120	26	of	of	ADP
ejpam-6033	120	27	order	order	NOUN
ejpam-6033	120	28	4	4	NUM
ejpam-6033	120	29	.	.	PUNCT
ejpam-6033	121	1	if	if	SCONJ
ejpam-6033	121	2	h	h	NOUN
ejpam-6033	121	3	≃	≃	NOUN
ejpam-6033	121	4	z4	z4	PROPN
ejpam-6033	121	5	≤	≤	PROPN
ejpam-6033	121	6	aut(e8	aut(e8	PROPN
ejpam-6033	121	7	)	)	PUNCT
ejpam-6033	121	8	=	=	SYM
ejpam-6033	121	9	psl(3	psl(3	NOUN
ejpam-6033	121	10	,	,	PUNCT
ejpam-6033	121	11	2	2	NUM
ejpam-6033	121	12	)	)	PUNCT
ejpam-6033	121	13	and	and	CCONJ
ejpam-6033	121	14	g	g	PROPN
ejpam-6033	121	15	=	=	PROPN
ejpam-6033	121	16	e8	e8	PROPN
ejpam-6033	121	17	⋊	⋊	PROPN
ejpam-6033	121	18	h(z2	h(z2	NOUN
ejpam-6033	121	19	×	×	PROPN
ejpam-6033	121	20	z2	z2	PROPN
ejpam-6033	121	21	×	×	PROPN
ejpam-6033	121	22	z2	z2	PROPN
ejpam-6033	121	23	)	)	PUNCT
ejpam-6033	121	24	⋊	⋊	NUM
ejpam-6033	121	25	z4	z4	X
ejpam-6033	121	26	,	,	PUNCT
ejpam-6033	121	27	then	then	ADV
ejpam-6033	121	28	g	g	PROPN
ejpam-6033	121	29	is	be	AUX
ejpam-6033	121	30	example	example	NOUN
ejpam-6033	121	31	of	of	ADP
ejpam-6033	121	32	an	an	DET
ejpam-6033	121	33	nspt	nspt	PROPN
ejpam-6033	121	34	-group	-group	NOUN
ejpam-6033	121	35	that	that	PRON
ejpam-6033	121	36	is	be	AUX
ejpam-6033	121	37	not	not	PART
ejpam-6033	121	38	a	a	DET
ejpam-6033	121	39	ct	ct	NUM
ejpam-6033	121	40	-group	-group	NOUN
ejpam-6033	121	41	.	.	PUNCT
ejpam-6033	122	1	g	g	NOUN
ejpam-6033	122	2	is	be	AUX
ejpam-6033	122	3	not	not	PART
ejpam-6033	122	4	ct	ct	NUM
ejpam-6033	122	5	-group	-group	NOUN
ejpam-6033	122	6	,	,	PUNCT
ejpam-6033	122	7	g	g	NOUN
ejpam-6033	122	8	=	=	SYM
ejpam-6033	122	9	e8×z4	e8×z4	PROPN
ejpam-6033	122	10	.	.	PUNCT
ejpam-6033	123	1	more	more	ADV
ejpam-6033	123	2	specifically	specifically	ADV
ejpam-6033	123	3	,	,	PUNCT
ejpam-6033	123	4	g	g	NOUN
ejpam-6033	123	5	=	=	SYM
ejpam-6033	123	6	(	(	PUNCT
ejpam-6033	123	7	z2×z2×z2)⋊h	z2×z2×z2)⋊h	NOUN
ejpam-6033	123	8	·	·	SYM
ejpam-6033	123	9	h	h	NOUN
ejpam-6033	123	10	=	=	SYM
ejpam-6033	123	11	⟨d⟩	⟨d⟩	PROPN
ejpam-6033	123	12	,	,	PUNCT
ejpam-6033	123	13	note	note	VERB
ejpam-6033	123	14	h	h	NOUN
ejpam-6033	123	15	is	be	AUX
ejpam-6033	123	16	a	a	DET
ejpam-6033	123	17	c	c	NOUN
ejpam-6033	123	18	-	-	NOUN
ejpam-6033	123	19	normal	normal	ADJ
ejpam-6033	123	20	in	in	ADP
ejpam-6033	123	21	g	g	NOUN
ejpam-6033	123	22	,	,	PUNCT
ejpam-6033	123	23	since	since	SCONJ
ejpam-6033	123	24	there	there	PRON
ejpam-6033	123	25	exist	exist	VERB
ejpam-6033	123	26	k	k	PROPN
ejpam-6033	123	27	≤	≤	PROPN
ejpam-6033	123	28	g;k	g;k	PUNCT
ejpam-6033	123	29	⊴	⊴	ADP
ejpam-6033	123	30	g	g	PROPN
ejpam-6033	123	31	and	and	CCONJ
ejpam-6033	123	32	k	k	PROPN
ejpam-6033	123	33	∩	∩	ADJ
ejpam-6033	123	34	h	h	NOUN
ejpam-6033	123	35	≤	≤	NUM
ejpam-6033	123	36	hg	hg	NOUN
ejpam-6033	123	37	=	=	SYM
ejpam-6033	123	38	1	1	NUM
ejpam-6033	123	39	and	and	CCONJ
ejpam-6033	123	40	hk	hk	PROPN
ejpam-6033	123	41	=	=	SYM
ejpam-6033	123	42	g	g	NOUN
ejpam-6033	123	43	;	;	PUNCT
ejpam-6033	123	44	since	since	ADV
ejpam-6033	123	45	,	,	PUNCT
ejpam-6033	123	46	|h|	|h|	PROPN
ejpam-6033	123	47	=	=	SYM
ejpam-6033	123	48	4every	4every	NUM
ejpam-6033	123	49	subgroup	subgroup	NOUN
ejpam-6033	123	50	of	of	ADP
ejpam-6033	123	51	h	h	NOUN
ejpam-6033	123	52	is	be	AUX
ejpam-6033	123	53	normal	normal	ADJ
ejpam-6033	123	54	.	.	PUNCT
ejpam-6033	124	1	but	but	CCONJ
ejpam-6033	124	2	h1	h1	PROPN
ejpam-6033	124	3	=	=	PUNCT
ejpam-6033	124	4	⟨d2⟩⊴h	⟨d2⟩⊴h	NOUN
ejpam-6033	124	5	,	,	PUNCT
ejpam-6033	124	6	c	c	NOUN
ejpam-6033	124	7	-	-	ADJ
ejpam-6033	124	8	normal	normal	ADJ
ejpam-6033	124	9	in	in	ADP
ejpam-6033	124	10	g	g	NOUN
ejpam-6033	124	11	,	,	PUNCT
ejpam-6033	124	12	h1{1	h1{1	PROPN
ejpam-6033	124	13	,	,	PUNCT
ejpam-6033	124	14	d2	d2	PROPN
ejpam-6033	124	15	}	}	PUNCT
ejpam-6033	124	16	≃	≃	NOUN
ejpam-6033	124	17	z2	z2	NOUN
ejpam-6033	124	18	and	and	CCONJ
ejpam-6033	124	19	note	note	VERB
ejpam-6033	124	20	h1	h1	NOUN
ejpam-6033	124	21	≤	≤	NUM
ejpam-6033	124	22	m	m	VERB
ejpam-6033	124	23	for	for	ADP
ejpam-6033	124	24	any	any	DET
ejpam-6033	124	25	subgroup	subgroup	NOUN
ejpam-6033	124	26	m	m	NOUN
ejpam-6033	124	27	of	of	ADP
ejpam-6033	124	28	g	g	NOUN
ejpam-6033	124	29	with	with	ADP
ejpam-6033	124	30	|m	|m	NOUN
ejpam-6033	124	31	|	|	ADV
ejpam-6033	124	32	=	=	SYM
ejpam-6033	124	33	16	16	NUM
ejpam-6033	124	34	implies	imply	VERB
ejpam-6033	124	35	m	m	VERB
ejpam-6033	124	36	⊴g	⊴g	ADJ
ejpam-6033	124	37	,	,	PUNCT
ejpam-6033	124	38	there	there	PRON
ejpam-6033	124	39	are	be	VERB
ejpam-6033	124	40	3	3	NUM
ejpam-6033	124	41	such	such	ADJ
ejpam-6033	124	42	m.mg	m.mg	NOUN
ejpam-6033	124	43	=	=	SYM
ejpam-6033	124	44	1	1	NUM
ejpam-6033	124	45	-	-	PUNCT
ejpam-6033	124	46	identity	identity	NOUN
ejpam-6033	124	47	.	.	PUNCT
ejpam-6033	125	1	if	if	SCONJ
ejpam-6033	125	2	kh1	kh1	PROPN
ejpam-6033	125	3	=	=	VERB
ejpam-6033	125	4	g	g	NOUN
ejpam-6033	125	5	with	with	ADP
ejpam-6033	125	6	k	k	PROPN
ejpam-6033	125	7	⊴	⊴	ADP
ejpam-6033	125	8	g	g	PROPN
ejpam-6033	125	9	implies	imply	VERB
ejpam-6033	125	10	|k|	|k|	NOUN
ejpam-6033	125	11	=	=	SYM
ejpam-6033	125	12	16	16	NUM
ejpam-6033	125	13	,	,	PUNCT
ejpam-6033	125	14	but	but	CCONJ
ejpam-6033	125	15	h	h	NOUN
ejpam-6033	125	16	≤	≤	PROPN
ejpam-6033	125	17	k	k	NOUN
ejpam-6033	125	18	for	for	ADP
ejpam-6033	125	19	any	any	DET
ejpam-6033	125	20	k.	k.	PROPN
ejpam-6033	125	21	nspt	nspt	PROPN
ejpam-6033	125	22	-group	-group	PROPN
ejpam-6033	125	23	follows	follow	VERB
ejpam-6033	125	24	from	from	ADP
ejpam-6033	125	25	|g|	|g|	PROPN
ejpam-6033	125	26	=	=	PROPN
ejpam-6033	125	27	25	25	NUM
ejpam-6033	125	28	and	and	CCONJ
ejpam-6033	125	29	g	g	PROPN
ejpam-6033	125	30	is	be	AUX
ejpam-6033	125	31	p	p	NOUN
ejpam-6033	125	32	-	-	PUNCT
ejpam-6033	125	33	group	group	NOUN
ejpam-6033	125	34	that	that	PRON
ejpam-6033	125	35	implies	imply	VERB
ejpam-6033	125	36	,	,	PUNCT
ejpam-6033	125	37	every	every	DET
ejpam-6033	125	38	subgroup	subgroup	NOUN
ejpam-6033	125	39	is	be	AUX
ejpam-6033	125	40	nearly	nearly	ADV
ejpam-6033	125	41	s	s	NOUN
ejpam-6033	125	42	-	-	NOUN
ejpam-6033	125	43	permutable	permutable	ADJ
ejpam-6033	125	44	.	.	PUNCT
ejpam-6033	126	1	from	from	ADP
ejpam-6033	126	2	remark	remark	NOUN
ejpam-6033	126	3	2	2	NUM
ejpam-6033	126	4	and	and	CCONJ
ejpam-6033	126	5	remark	remark	NOUN
ejpam-6033	126	6	3	3	NUM
ejpam-6033	126	7	,	,	PUNCT
ejpam-6033	126	8	we	we	PRON
ejpam-6033	126	9	conclude	conclude	VERB
ejpam-6033	126	10	that	that	SCONJ
ejpam-6033	126	11	the	the	DET
ejpam-6033	126	12	classes	class	NOUN
ejpam-6033	126	13	of	of	ADP
ejpam-6033	126	14	ct	ct	PROPN
ejpam-6033	126	15	-groups	-groups	PROPN
ejpam-6033	126	16	and	and	CCONJ
ejpam-6033	126	17	nspt	nspt	NOUN
ejpam-6033	126	18	groups	group	NOUN
ejpam-6033	126	19	are	be	AUX
ejpam-6033	126	20	incomparable	incomparable	ADJ
ejpam-6033	126	21	.	.	PUNCT
ejpam-6033	127	1	that	that	PRON
ejpam-6033	127	2	is	be	AUX
ejpam-6033	127	3	,	,	PUNCT
ejpam-6033	127	4	a	a	DET
ejpam-6033	127	5	ct	ct	NUM
ejpam-6033	127	6	-group	-group	NOUN
ejpam-6033	127	7	need	need	VERB
ejpam-6033	127	8	not	not	PART
ejpam-6033	127	9	benspt	benspt	VERB
ejpam-6033	127	10	,	,	PUNCT
ejpam-6033	127	11	and	and	CCONJ
ejpam-6033	127	12	an	an	DET
ejpam-6033	127	13	nspt	nspt	ADJ
ejpam-6033	127	14	-group	-group	NOUN
ejpam-6033	127	15	need	need	AUX
ejpam-6033	127	16	not	not	PART
ejpam-6033	127	17	be	be	AUX
ejpam-6033	127	18	ct	ct	PROPN
ejpam-6033	127	19	-groups	-groups	PROPN
ejpam-6033	127	20	.	.	PUNCT
ejpam-6033	128	1	lemma	lemma	PROPN
ejpam-6033	128	2	5	5	X
ejpam-6033	128	3	.	.	PUNCT
ejpam-6033	129	1	let	let	VERB
ejpam-6033	129	2	g	g	PRON
ejpam-6033	129	3	be	be	AUX
ejpam-6033	129	4	a	a	DET
ejpam-6033	129	5	finite	finite	ADJ
ejpam-6033	129	6	group	group	NOUN
ejpam-6033	129	7	and	and	CCONJ
ejpam-6033	129	8	let	let	VERB
ejpam-6033	129	9	p	p	PRON
ejpam-6033	129	10	be	be	AUX
ejpam-6033	129	11	a	a	DET
ejpam-6033	129	12	sylow	sylow	NOUN
ejpam-6033	129	13	p	p	NOUN
ejpam-6033	129	14	-	-	PUNCT
ejpam-6033	129	15	subgroup	subgroup	NOUN
ejpam-6033	129	16	of	of	ADP
ejpam-6033	129	17	g	g	PROPN
ejpam-6033	129	18	,	,	PUNCT
ejpam-6033	129	19	it	it	PRON
ejpam-6033	129	20	follows	follow	VERB
ejpam-6033	129	21	that	that	SCONJ
ejpam-6033	129	22	ng(ng(p	ng(ng(p	NOUN
ejpam-6033	129	23	)	)	PUNCT
ejpam-6033	130	1	=	=	NOUN
ejpam-6033	130	2	ng(p	ng(p	NOUN
ejpam-6033	130	3	)	)	PUNCT
ejpam-6033	130	4	.	.	PUNCT
ejpam-6033	131	1	proof	proof	NOUN
ejpam-6033	131	2	.	.	PUNCT
ejpam-6033	132	1	since	since	SCONJ
ejpam-6033	132	2	p	p	NOUN
ejpam-6033	132	3	⊆	⊆	NUM
ejpam-6033	132	4	ng(p	ng(p	NOUN
ejpam-6033	132	5	)	)	PUNCT
ejpam-6033	132	6	⊆	⊆	NUM
ejpam-6033	132	7	g	g	NOUN
ejpam-6033	132	8	and	and	CCONJ
ejpam-6033	132	9	p	p	NOUN
ejpam-6033	132	10	is	be	AUX
ejpam-6033	132	11	a	a	DET
ejpam-6033	132	12	sylow	sylow	NOUN
ejpam-6033	132	13	p	p	NOUN
ejpam-6033	132	14	-	-	PUNCT
ejpam-6033	132	15	subgroup	subgroup	NOUN
ejpam-6033	132	16	of	of	ADP
ejpam-6033	132	17	g	g	PROPN
ejpam-6033	132	18	therefore	therefore	ADV
ejpam-6033	132	19	,	,	PUNCT
ejpam-6033	132	20	p	p	NOUN
ejpam-6033	132	21	is	be	AUX
ejpam-6033	132	22	a	a	DET
ejpam-6033	132	23	sylow	sylow	NOUN
ejpam-6033	132	24	p	p	NOUN
ejpam-6033	132	25	-	-	PUNCT
ejpam-6033	132	26	subgroup	subgroup	NOUN
ejpam-6033	132	27	of	of	ADP
ejpam-6033	132	28	ng(p	ng(p	NOUN
ejpam-6033	132	29	)	)	PUNCT
ejpam-6033	132	30	.	.	PUNCT
ejpam-6033	133	1	furthermore	furthermore	ADV
ejpam-6033	133	2	,	,	PUNCT
ejpam-6033	133	3	p	p	NOUN
ejpam-6033	133	4	is	be	AUX
ejpam-6033	133	5	normal	normal	ADJ
ejpam-6033	133	6	in	in	ADP
ejpam-6033	133	7	ng(p	ng(p	PUNCT
ejpam-6033	133	8	)	)	PUNCT
ejpam-6033	133	9	,	,	PUNCT
ejpam-6033	133	10	making	make	VERB
ejpam-6033	133	11	p	p	NOUN
ejpam-6033	133	12	is	be	AUX
ejpam-6033	133	13	unique	unique	ADJ
ejpam-6033	133	14	sylow	sylow	NOUN
ejpam-6033	133	15	p	p	NOUN
ejpam-6033	133	16	-	-	PUNCT
ejpam-6033	133	17	subgroup	subgroup	NOUN
ejpam-6033	133	18	of	of	ADP
ejpam-6033	133	19	g.	g.	PROPN
ejpam-6033	133	20	now	now	ADV
ejpam-6033	133	21	let	let	VERB
ejpam-6033	133	22	a	a	DET
ejpam-6033	133	23	∈	∈	NOUN
ejpam-6033	133	24	ng(ng(p	ng(ng(p	NOUN
ejpam-6033	133	25	)	)	PUNCT
ejpam-6033	133	26	)	)	PUNCT
ejpam-6033	133	27	.	.	PUNCT
ejpam-6033	134	1	a.	a.	PROPN
ejpam-6033	134	2	m.	m.	PROPN
ejpam-6033	134	3	alotaibiang	alotaibiang	PROPN
ejpam-6033	134	4	,	,	PUNCT
ejpam-6033	134	5	k.	k.	PROPN
ejpam-6033	134	6	al	al	PROPN
ejpam-6033	134	7	-	-	PROPN
ejpam-6033	134	8	tahat	tahat	PROPN
ejpam-6033	134	9	,	,	PUNCT
ejpam-6033	134	10	k.	k.	PROPN
ejpam-6033	134	11	m.	m.	PROPN
ejpam-6033	134	12	al	al	PROPN
ejpam-6033	134	13	-	-	PROPN
ejpam-6033	134	14	jamal	jamal	PROPN
ejpam-6033	134	15	/	/	SYM
ejpam-6033	134	16	eur	eur	PROPN
ejpam-6033	134	17	.	.	PUNCT
ejpam-6033	135	1	j.	j.	PROPN
ejpam-6033	135	2	pure	pure	PROPN
ejpam-6033	135	3	appl	appl	PROPN
ejpam-6033	135	4	.	.	PROPN
ejpam-6033	135	5	math	math	PROPN
ejpam-6033	135	6	,	,	PUNCT
ejpam-6033	135	7	18	18	NUM
ejpam-6033	135	8	(	(	PUNCT
ejpam-6033	135	9	3	3	NUM
ejpam-6033	135	10	)	)	PUNCT
ejpam-6033	135	11	(	(	PUNCT
ejpam-6033	135	12	2025	2025	NUM
ejpam-6033	135	13	)	)	PUNCT
ejpam-6033	135	14	,	,	PUNCT
ejpam-6033	135	15	6033	6033	NUM
ejpam-6033	135	16	6	6	NUM
ejpam-6033	135	17	of	of	ADP
ejpam-6033	135	18	8	8	NUM
ejpam-6033	135	19	we	we	PRON
ejpam-6033	135	20	will	will	AUX
ejpam-6033	135	21	aim	aim	VERB
ejpam-6033	135	22	show	show	VERB
ejpam-6033	135	23	that	that	SCONJ
ejpam-6033	135	24	a	a	DET
ejpam-6033	135	25	∈	∈	NOUN
ejpam-6033	135	26	ng(p	ng(p	PUNCT
ejpam-6033	135	27	)	)	PUNCT
ejpam-6033	135	28	.	.	PUNCT
ejpam-6033	136	1	observe	observe	VERB
ejpam-6033	136	2	that	that	SCONJ
ejpam-6033	136	3	:	:	PUNCT
ejpam-6033	136	4	apa	apa	PROPN
ejpam-6033	136	5	−1	−1	NOUN
ejpam-6033	136	6	⊆	⊆	NUM
ejpam-6033	136	7	ang	ang	NOUN
ejpam-6033	136	8	(	(	PUNCT
ejpam-6033	136	9	p	p	NOUN
ejpam-6033	136	10	)	)	PUNCT
ejpam-6033	136	11	a−1	a−1	PROPN
ejpam-6033	136	12	=	=	PUNCT
ejpam-6033	136	13	ng(p	ng(p	NOUN
ejpam-6033	136	14	)	)	PUNCT
ejpam-6033	136	15	.	.	PUNCT
ejpam-6033	137	1	this	this	PRON
ejpam-6033	137	2	implies	imply	VERB
ejpam-6033	137	3	that	that	SCONJ
ejpam-6033	137	4	,	,	PUNCT
ejpam-6033	137	5	apa−1	apa−1	PROPN
ejpam-6033	137	6	is	be	AUX
ejpam-6033	137	7	a	a	DET
ejpam-6033	137	8	sylow	sylow	NOUN
ejpam-6033	137	9	p	p	NOUN
ejpam-6033	137	10	-	-	PUNCT
ejpam-6033	137	11	subgroup	subgroup	NOUN
ejpam-6033	137	12	of	of	ADP
ejpam-6033	137	13	ng(p	ng(p	NOUN
ejpam-6033	137	14	)	)	PUNCT
ejpam-6033	137	15	,	,	PUNCT
ejpam-6033	137	16	we	we	PRON
ejpam-6033	137	17	have	have	VERB
ejpam-6033	137	18	apa−1	apa−1	X
ejpam-6033	137	19	=	=	PUNCT
ejpam-6033	137	20	p	p	PROPN
ejpam-6033	137	21	.	.	PUNCT
ejpam-6033	138	1	this	this	PRON
ejpam-6033	138	2	means	mean	VERB
ejpam-6033	138	3	a	a	DET
ejpam-6033	138	4	∈	∈	NOUN
ejpam-6033	138	5	ng(p	ng(p	PUNCT
ejpam-6033	138	6	)	)	PUNCT
ejpam-6033	138	7	.	.	PUNCT
ejpam-6033	139	1	theorem	theorem	NOUN
ejpam-6033	139	2	1	1	X
ejpam-6033	139	3	.	.	PUNCT
ejpam-6033	140	1	let	let	VERB
ejpam-6033	140	2	g	g	PROPN
ejpam-6033	140	3	is	be	AUX
ejpam-6033	140	4	a	a	DET
ejpam-6033	140	5	nilpotent	nilpotent	ADJ
ejpam-6033	140	6	group	group	NOUN
ejpam-6033	140	7	and	and	CCONJ
ejpam-6033	140	8	let	let	VERB
ejpam-6033	140	9	h	h	PROPN
ejpam-6033	140	10	subgroup	subgroup	PROPN
ejpam-6033	140	11	of	of	ADP
ejpam-6033	140	12	g.	g.	PROPN
ejpam-6033	141	1	then	then	ADV
ejpam-6033	141	2	h	h	PROPN
ejpam-6033	141	3	≤	≤	PROPN
ejpam-6033	141	4	ng(h	ng(h	ADV
ejpam-6033	141	5	)	)	PUNCT
ejpam-6033	141	6	.	.	PUNCT
ejpam-6033	142	1	proof	proof	NOUN
ejpam-6033	142	2	.	.	PUNCT
ejpam-6033	143	1	since	since	SCONJ
ejpam-6033	143	2	g	g	PROPN
ejpam-6033	143	3	is	be	AUX
ejpam-6033	143	4	nilpotent	nilpotent	ADJ
ejpam-6033	143	5	,	,	PUNCT
ejpam-6033	143	6	it	it	PRON
ejpam-6033	143	7	has	have	VERB
ejpam-6033	143	8	a	a	DET
ejpam-6033	143	9	central	central	ADJ
ejpam-6033	143	10	series{ni	series{ni	NOUN
ejpam-6033	143	11	|	|	ADV
ejpam-6033	143	12	0	0	NUM
ejpam-6033	143	13	<	<	X
ejpam-6033	144	1	i	i	X
ejpam-6033	144	2	<	<	X
ejpam-6033	144	3	r	r	NOUN
ejpam-6033	144	4	}	}	PUNCT
ejpam-6033	144	5	,	,	PUNCT
ejpam-6033	144	6	and	and	CCONJ
ejpam-6033	144	7	we	we	PRON
ejpam-6033	144	8	have	have	VERB
ejpam-6033	144	9	n0	n0	NOUN
ejpam-6033	144	10	=	=	SYM
ejpam-6033	145	1	1	1	NUM
ejpam-6033	145	2	⊆	⊆	NUM
ejpam-6033	145	3	h	h	NOUN
ejpam-6033	145	4	and	and	CCONJ
ejpam-6033	145	5	nr	nr	NOUN
ejpam-6033	145	6	=	=	NOUN
ejpam-6033	145	7	g	g	PROPN
ejpam-6033	145	8	⊈	⊈	PROPN
ejpam-6033	145	9	h.	h.	NOUN
ejpam-6033	145	10	consequently	consequently	ADV
ejpam-6033	145	11	,	,	PUNCT
ejpam-6033	145	12	there	there	PRON
ejpam-6033	145	13	exists	exist	VERB
ejpam-6033	145	14	an	an	DET
ejpam-6033	145	15	index	index	NOUN
ejpam-6033	145	16	k	k	NOUN
ejpam-6033	145	17	with	with	ADP
ejpam-6033	145	18	0	0	NUM
ejpam-6033	145	19	<	<	X
ejpam-6033	145	20	k	k	X
ejpam-6033	145	21	<	<	X
ejpam-6033	145	22	r	r	NOUN
ejpam-6033	145	23	,	,	PUNCT
ejpam-6033	145	24	such	such	ADJ
ejpam-6033	145	25	that	that	SCONJ
ejpam-6033	145	26	nk	nk	PROPN
ejpam-6033	145	27	⊆	⊆	NUM
ejpam-6033	145	28	h	h	NOUN
ejpam-6033	145	29	,	,	PUNCT
ejpam-6033	145	30	butnk+1	butnk+1	NOUN
ejpam-6033	145	31	⊊	⊊	VERB
ejpam-6033	145	32	h.	h.	NOUN
ejpam-6033	145	33	we	we	PRON
ejpam-6033	145	34	will	will	AUX
ejpam-6033	145	35	show	show	VERB
ejpam-6033	145	36	that	that	SCONJ
ejpam-6033	145	37	in	in	ADP
ejpam-6033	145	38	fact	fact	NOUN
ejpam-6033	145	39	,	,	PUNCT
ejpam-6033	145	40	nk+1	nk+1	NUM
ejpam-6033	145	41	⊆	⊆	NUM
ejpam-6033	145	42	ng(h	ng(h	NUM
ejpam-6033	145	43	)	)	PUNCT
ejpam-6033	145	44	,	,	PUNCT
ejpam-6033	145	45	and	and	CCONJ
ejpam-6033	145	46	it	it	PRON
ejpam-6033	145	47	will	will	AUX
ejpam-6033	145	48	follow	follow	VERB
ejpam-6033	145	49	that	that	DET
ejpam-6033	145	50	h	h	NOUN
ejpam-6033	145	51	≤	≤	NOUN
ejpam-6033	145	52	ng(h	ng(h	ADV
ejpam-6033	145	53	)	)	PUNCT
ejpam-6033	145	54	,	,	PUNCT
ejpam-6033	145	55	as	as	SCONJ
ejpam-6033	145	56	required	require	VERB
ejpam-6033	145	57	.	.	PUNCT
ejpam-6033	146	1	theorem	theorem	NOUN
ejpam-6033	146	2	2	2	NUM
ejpam-6033	146	3	.	.	PUNCT
ejpam-6033	147	1	let	let	VERB
ejpam-6033	147	2	g	g	PRON
ejpam-6033	147	3	be	be	AUX
ejpam-6033	147	4	a	a	DET
ejpam-6033	147	5	finite	finite	ADJ
ejpam-6033	147	6	group	group	NOUN
ejpam-6033	147	7	.	.	PUNCT
ejpam-6033	148	1	then	then	ADV
ejpam-6033	148	2	the	the	DET
ejpam-6033	148	3	following	following	NOUN
ejpam-6033	148	4	are	be	AUX
ejpam-6033	148	5	equivalent	equivalent	ADJ
ejpam-6033	148	6	.	.	PUNCT
ejpam-6033	149	1	(	(	PUNCT
ejpam-6033	149	2	i	i	NOUN
ejpam-6033	149	3	)	)	PUNCT
ejpam-6033	149	4	g	g	PROPN
ejpam-6033	149	5	is	be	AUX
ejpam-6033	149	6	nilpotent	nilpotent	ADJ
ejpam-6033	149	7	.	.	PUNCT
ejpam-6033	150	1	(	(	PUNCT
ejpam-6033	150	2	ii	ii	NOUN
ejpam-6033	150	3	)	)	PUNCT
ejpam-6033	150	4	h	h	NOUN
ejpam-6033	150	5	≤	≤	NOUN
ejpam-6033	150	6	ng(h	ng(h	ADV
ejpam-6033	150	7	)	)	PUNCT
ejpam-6033	150	8	for	for	ADP
ejpam-6033	150	9	every	every	DET
ejpam-6033	150	10	subgroup	subgroup	NOUN
ejpam-6033	150	11	h	h	PROPN
ejpam-6033	150	12	≤	≤	PROPN
ejpam-6033	150	13	g.	g.	PROPN
ejpam-6033	150	14	(	(	PUNCT
ejpam-6033	150	15	iii	iii	X
ejpam-6033	150	16	)	)	PUNCT
ejpam-6033	150	17	all	all	DET
ejpam-6033	150	18	maximal	maximal	ADJ
ejpam-6033	150	19	subgroups	subgroup	NOUN
ejpam-6033	150	20	of	of	ADP
ejpam-6033	150	21	g	g	NOUN
ejpam-6033	150	22	are	be	AUX
ejpam-6033	150	23	nearly	nearly	ADV
ejpam-6033	150	24	s	s	NOUN
ejpam-6033	150	25	-	-	NOUN
ejpam-6033	150	26	permutable	permutable	ADJ
ejpam-6033	150	27	.	.	PUNCT
ejpam-6033	151	1	proof	proof	NOUN
ejpam-6033	151	2	.	.	PUNCT
ejpam-6033	152	1	we	we	PRON
ejpam-6033	152	2	saw	see	VERB
ejpam-6033	152	3	that	that	SCONJ
ejpam-6033	152	4	(	(	PUNCT
ejpam-6033	152	5	i	i	NOUN
ejpam-6033	152	6	)	)	PUNCT
ejpam-6033	152	7	implies	imply	VERB
ejpam-6033	152	8	(	(	PUNCT
ejpam-6033	152	9	ii	ii	NOUN
ejpam-6033	152	10	)	)	PUNCT
ejpam-6033	152	11	in	in	ADP
ejpam-6033	152	12	theorem	theorem	NOUN
ejpam-6033	152	13	1	1	NUM
ejpam-6033	152	14	that	that	PRON
ejpam-6033	152	15	(	(	PUNCT
ejpam-6033	152	16	ii	ii	NOUN
ejpam-6033	152	17	)	)	PUNCT
ejpam-6033	152	18	implies	imply	VERB
ejpam-6033	152	19	(	(	PUNCT
ejpam-6033	152	20	iii	iii	X
ejpam-6033	152	21	)	)	PUNCT
ejpam-6033	152	22	is	be	AUX
ejpam-6033	152	23	clear	clear	ADJ
ejpam-6033	152	24	,	,	PUNCT
ejpam-6033	152	25	since	since	SCONJ
ejpam-6033	152	26	every	every	DET
ejpam-6033	152	27	maximal	maximal	ADJ
ejpam-6033	152	28	subgroup	subgroup	NOUN
ejpam-6033	152	29	m	m	VERB
ejpam-6033	152	30	in	in	ADP
ejpam-6033	152	31	g	g	PROPN
ejpam-6033	152	32	satisfies	satisfie	NOUN
ejpam-6033	152	33	ng(m	ng(m	NOUN
ejpam-6033	152	34	)	)	PUNCT
ejpam-6033	152	35	≥	≥	NUM
ejpam-6033	152	36	m	m	NOUN
ejpam-6033	152	37	.	.	PUNCT
ejpam-6033	153	1	it	it	PRON
ejpam-6033	153	2	follows	follow	VERB
ejpam-6033	153	3	that	that	PRON
ejpam-6033	153	4	ng(m	ng(m	PUNCT
ejpam-6033	153	5	)	)	PUNCT
ejpam-6033	153	6	=	=	SYM
ejpam-6033	154	1	g.	g.	PROPN
ejpam-6033	154	2	now	now	ADV
ejpam-6033	154	3	assume	assume	VERB
ejpam-6033	154	4	condition	condition	NOUN
ejpam-6033	154	5	(	(	PUNCT
ejpam-6033	154	6	iii	iii	NOUN
ejpam-6033	154	7	)	)	PUNCT
ejpam-6033	154	8	holds	hold	VERB
ejpam-6033	154	9	and	and	CCONJ
ejpam-6033	154	10	let	let	VERB
ejpam-6033	154	11	p	p	PROPN
ejpam-6033	154	12	∈	∈	PROPN
ejpam-6033	154	13	sylp(g	sylp(g	NOUN
ejpam-6033	154	14	)	)	PUNCT
ejpam-6033	154	15	for	for	ADP
ejpam-6033	154	16	some	some	DET
ejpam-6033	154	17	prime	prime	ADJ
ejpam-6033	154	18	p.	p.	NOUN
ejpam-6033	154	19	if	if	SCONJ
ejpam-6033	154	20	ng(p	ng(p	NOUN
ejpam-6033	154	21	)	)	PUNCT
ejpam-6033	154	22	is	be	AUX
ejpam-6033	154	23	proper	proper	ADJ
ejpam-6033	154	24	in	in	ADP
ejpam-6033	154	25	g	g	PROPN
ejpam-6033	154	26	,	,	PUNCT
ejpam-6033	154	27	it	it	PRON
ejpam-6033	154	28	must	must	AUX
ejpam-6033	154	29	be	be	AUX
ejpam-6033	154	30	contained	contain	VERB
ejpam-6033	154	31	in	in	ADP
ejpam-6033	154	32	some	some	DET
ejpam-6033	154	33	maximal	maximal	ADJ
ejpam-6033	154	34	subgroup	subgroup	NOUN
ejpam-6033	154	35	m	m	PROPN
ejpam-6033	154	36	,	,	PUNCT
ejpam-6033	154	37	and	and	CCONJ
ejpam-6033	154	38	we	we	PRON
ejpam-6033	154	39	have	have	VERB
ejpam-6033	154	40	m	m	PROPN
ejpam-6033	154	41	≤	≤	VERB
ejpam-6033	154	42	g.	g.	NOUN
ejpam-6033	154	43	since	since	SCONJ
ejpam-6033	154	44	p	p	PROPN
ejpam-6033	154	45	∈	∈	PROPN
ejpam-6033	154	46	sylp(m	sylp(m	NOUN
ejpam-6033	154	47	)	)	PUNCT
ejpam-6033	154	48	,	,	PUNCT
ejpam-6033	154	49	it	it	PRON
ejpam-6033	154	50	follows	follow	VERB
ejpam-6033	154	51	by	by	ADP
ejpam-6033	154	52	lemma	lemma	PROPN
ejpam-6033	154	53	1	1	NUM
ejpam-6033	154	54	and	and	CCONJ
ejpam-6033	154	55	lemma	lemma	PROPN
ejpam-6033	154	56	5	5	NUM
ejpam-6033	154	57	,	,	PUNCT
ejpam-6033	155	1	that	that	PRON
ejpam-6033	155	2	g	g	NOUN
ejpam-6033	155	3	=	=	NOUN
ejpam-6033	155	4	ng(p	ng(p	X
ejpam-6033	155	5	)	)	PUNCT
ejpam-6033	155	6	m	m	PROPN
ejpam-6033	155	7	⊆	⊆	NUM
ejpam-6033	155	8	m	m	NOUN
ejpam-6033	155	9	,	,	PUNCT
ejpam-6033	155	10	and	and	CCONJ
ejpam-6033	155	11	this	this	PRON
ejpam-6033	155	12	is	be	AUX
ejpam-6033	155	13	a	a	DET
ejpam-6033	155	14	contradiction	contradiction	NOUN
ejpam-6033	155	15	.	.	PUNCT
ejpam-6033	156	1	thus	thus	ADV
ejpam-6033	156	2	p	p	X
ejpam-6033	156	3	is	be	AUX
ejpam-6033	156	4	normal	normal	ADJ
ejpam-6033	156	5	in	in	ADP
ejpam-6033	156	6	g	g	PROPN
ejpam-6033	156	7	and	and	CCONJ
ejpam-6033	156	8	by	by	ADP
ejpam-6033	156	9	lemma	lemma	PROPN
ejpam-6033	156	10	3	3	NUM
ejpam-6033	156	11	,	,	PUNCT
ejpam-6033	156	12	p	p	PRON
ejpam-6033	156	13	is	be	AUX
ejpam-6033	156	14	nearly	nearly	ADV
ejpam-6033	156	15	s	s	NOUN
ejpam-6033	156	16	-	-	ADJ
ejpam-6033	156	17	permutable	permutable	ADJ
ejpam-6033	156	18	.	.	PUNCT
ejpam-6033	157	1	example	example	NOUN
ejpam-6033	158	1	2	2	NUM
ejpam-6033	158	2	.	.	PUNCT
ejpam-6033	158	3	let	let	VERB
ejpam-6033	158	4	g	g	PROPN
ejpam-6033	158	5	=	=	PROPN
ejpam-6033	158	6	z2×z2×z2	z2×z2×z2	PROPN
ejpam-6033	158	7	,	,	PUNCT
ejpam-6033	158	8	an	an	DET
ejpam-6033	158	9	abelian	abelian	ADJ
ejpam-6033	158	10	group	group	NOUN
ejpam-6033	158	11	of	of	ADP
ejpam-6033	158	12	order	order	NOUN
ejpam-6033	158	13	8	8	NUM
ejpam-6033	158	14	.	.	PUNCT
ejpam-6033	159	1	then	then	ADV
ejpam-6033	159	2	:	:	PUNCT
ejpam-6033	159	3	g	g	PROPN
ejpam-6033	159	4	is	be	AUX
ejpam-6033	159	5	nilpotent	nilpotent	ADJ
ejpam-6033	159	6	(	(	PUNCT
ejpam-6033	159	7	since	since	SCONJ
ejpam-6033	159	8	all	all	DET
ejpam-6033	159	9	abelian	abelian	ADJ
ejpam-6033	159	10	groups	group	NOUN
ejpam-6033	159	11	are	be	AUX
ejpam-6033	159	12	nilpotent	nilpotent	ADJ
ejpam-6033	159	13	)	)	PUNCT
ejpam-6033	159	14	.	.	PUNCT
ejpam-6033	160	1	every	every	DET
ejpam-6033	160	2	subgroup	subgroup	NOUN
ejpam-6033	160	3	h	h	NOUN
ejpam-6033	160	4	≤	≤	PROPN
ejpam-6033	160	5	g	g	PROPN
ejpam-6033	160	6	satisfies	satisfie	NOUN
ejpam-6033	160	7	h	h	NOUN
ejpam-6033	160	8	≤	≤	NUM
ejpam-6033	160	9	ng(h	ng(h	ADV
ejpam-6033	160	10	)	)	PUNCT
ejpam-6033	160	11	=	=	PUNCT
ejpam-6033	161	1	g.	g.	NOUN
ejpam-6033	162	1	every	every	DET
ejpam-6033	162	2	maximal	maximal	ADJ
ejpam-6033	162	3	subgroup	subgroup	NOUN
ejpam-6033	162	4	is	be	AUX
ejpam-6033	162	5	of	of	ADP
ejpam-6033	162	6	order	order	NOUN
ejpam-6033	162	7	4	4	NUM
ejpam-6033	162	8	and	and	CCONJ
ejpam-6033	162	9	is	be	AUX
ejpam-6033	162	10	normal	normal	ADJ
ejpam-6033	162	11	in	in	ADP
ejpam-6033	162	12	g	g	PROPN
ejpam-6033	162	13	,	,	PUNCT
ejpam-6033	162	14	and	and	CCONJ
ejpam-6033	162	15	hence	hence	ADV
ejpam-6033	162	16	nearly	nearly	ADV
ejpam-6033	162	17	s	s	NOUN
ejpam-6033	162	18	-	-	NOUN
ejpam-6033	162	19	permutable	permutable	ADJ
ejpam-6033	162	20	.	.	PUNCT
ejpam-6033	163	1	this	this	DET
ejpam-6033	163	2	example	example	NOUN
ejpam-6033	163	3	confirms	confirm	VERB
ejpam-6033	163	4	that	that	SCONJ
ejpam-6033	163	5	all	all	DET
ejpam-6033	163	6	three	three	NUM
ejpam-6033	163	7	conditions	condition	NOUN
ejpam-6033	163	8	hold	hold	VERB
ejpam-6033	163	9	simultaneously	simultaneously	ADV
ejpam-6033	163	10	,	,	PUNCT
ejpam-6033	163	11	illustrating	illustrate	VERB
ejpam-6033	163	12	the	the	DET
ejpam-6033	163	13	equivalence	equivalence	NOUN
ejpam-6033	163	14	.	.	PUNCT
ejpam-6033	164	1	4	4	X
ejpam-6033	164	2	.	.	X
ejpam-6033	164	3	conclusion	conclusion	VERB
ejpam-6033	164	4	new	new	ADJ
ejpam-6033	164	5	facts	fact	NOUN
ejpam-6033	164	6	on	on	ADP
ejpam-6033	164	7	sylow	sylow	NOUN
ejpam-6033	164	8	p	p	NOUN
ejpam-6033	164	9	-	-	PUNCT
ejpam-6033	164	10	subgroups	subgroup	NOUN
ejpam-6033	164	11	and	and	CCONJ
ejpam-6033	164	12	nearly	nearly	ADV
ejpam-6033	164	13	s	s	NOUN
ejpam-6033	164	14	-	-	PUNCT
ejpam-6033	164	15	permutable	permutable	ADJ
ejpam-6033	164	16	subgroups	subgroup	NOUN
ejpam-6033	164	17	were	be	AUX
ejpam-6033	164	18	discovered	discover	VERB
ejpam-6033	164	19	and	and	CCONJ
ejpam-6033	164	20	established	establish	VERB
ejpam-6033	164	21	.	.	PUNCT
ejpam-6033	165	1	the	the	DET
ejpam-6033	165	2	relationship	relationship	NOUN
ejpam-6033	165	3	between	between	ADP
ejpam-6033	165	4	ct	ct	PROPN
ejpam-6033	165	5	-groups	-group	NOUN
ejpam-6033	165	6	and	and	CCONJ
ejpam-6033	165	7	nspt	nspt	PROPN
ejpam-6033	165	8	-groups	-group	NOUN
ejpam-6033	165	9	was	be	AUX
ejpam-6033	165	10	clarified	clarify	VERB
ejpam-6033	165	11	.	.	PUNCT
ejpam-6033	166	1	it	it	PRON
ejpam-6033	166	2	was	be	AUX
ejpam-6033	166	3	demonstrated	demonstrate	VERB
ejpam-6033	166	4	that	that	SCONJ
ejpam-6033	166	5	every	every	DET
ejpam-6033	166	6	normal	normal	ADJ
ejpam-6033	166	7	subgroup	subgroup	NOUN
ejpam-6033	166	8	is	be	AUX
ejpam-6033	166	9	nearly	nearly	ADV
ejpam-6033	166	10	s	s	NOUN
ejpam-6033	166	11	-	-	ADJ
ejpam-6033	166	12	permutable	permutable	ADJ
ejpam-6033	166	13	,	,	PUNCT
ejpam-6033	166	14	whereas	whereas	SCONJ
ejpam-6033	166	15	a	a	DET
ejpam-6033	166	16	subnormal	subnormal	ADJ
ejpam-6033	166	17	subgroup	subgroup	NOUN
ejpam-6033	166	18	is	be	AUX
ejpam-6033	166	19	not	not	PART
ejpam-6033	166	20	necessarily	necessarily	ADV
ejpam-6033	166	21	nearly	nearly	ADV
ejpam-6033	166	22	s	s	NOUN
ejpam-6033	166	23	-	-	NOUN
ejpam-6033	166	24	permutable	permutable	ADJ
ejpam-6033	166	25	.	.	PUNCT
ejpam-6033	167	1	moreover	moreover	ADV
ejpam-6033	167	2	,	,	PUNCT
ejpam-6033	167	3	a	a	DET
ejpam-6033	167	4	new	new	ADJ
ejpam-6033	167	5	class	class	NOUN
ejpam-6033	167	6	of	of	ADP
ejpam-6033	167	7	groups	group	NOUN
ejpam-6033	167	8	,	,	PUNCT
ejpam-6033	167	9	termed	term	VERB
ejpam-6033	167	10	nspt	nspt	PROPN
ejpam-6033	167	11	-groups	-group	NOUN
ejpam-6033	167	12	,	,	PUNCT
ejpam-6033	167	13	was	be	AUX
ejpam-6033	167	14	introduced	introduce	VERB
ejpam-6033	167	15	,	,	PUNCT
ejpam-6033	167	16	characterized	characterize	VERB
ejpam-6033	167	17	by	by	ADP
ejpam-6033	167	18	the	the	DET
ejpam-6033	167	19	transitivity	transitivity	NOUN
ejpam-6033	167	20	of	of	ADP
ejpam-6033	167	21	nearly	nearly	ADV
ejpam-6033	167	22	s	s	NOUN
ejpam-6033	167	23	-	-	NOUN
ejpam-6033	167	24	permutability	permutability	NOUN
ejpam-6033	167	25	.	.	PUNCT
ejpam-6033	168	1	additionally	additionally	ADV
ejpam-6033	168	2	,	,	PUNCT
ejpam-6033	168	3	it	it	PRON
ejpam-6033	168	4	was	be	AUX
ejpam-6033	168	5	proven	prove	VERB
ejpam-6033	168	6	that	that	SCONJ
ejpam-6033	168	7	c	c	NOUN
ejpam-6033	168	8	-	-	PUNCT
ejpam-6033	168	9	normal	normal	ADJ
ejpam-6033	168	10	subgroups	subgroup	NOUN
ejpam-6033	168	11	do	do	AUX
ejpam-6033	168	12	not	not	PART
ejpam-6033	168	13	necessarily	necessarily	ADV
ejpam-6033	168	14	exhibit	exhibit	VERB
ejpam-6033	168	15	nearly	nearly	ADV
ejpam-6033	168	16	spermutability	spermutability	NOUN
ejpam-6033	168	17	,	,	PUNCT
ejpam-6033	168	18	and	and	CCONJ
ejpam-6033	168	19	conversely	conversely	ADV
ejpam-6033	168	20	,	,	PUNCT
ejpam-6033	168	21	nearly	nearly	ADV
ejpam-6033	168	22	s	s	NOUN
ejpam-6033	168	23	-	-	PUNCT
ejpam-6033	168	24	permutability	permutability	NOUN
ejpam-6033	168	25	does	do	AUX
ejpam-6033	168	26	not	not	PART
ejpam-6033	168	27	imply	imply	VERB
ejpam-6033	168	28	c	c	NOUN
ejpam-6033	168	29	-	-	NOUN
ejpam-6033	168	30	normality	normality	NOUN
ejpam-6033	168	31	.	.	PUNCT
ejpam-6033	169	1	future	future	ADJ
ejpam-6033	169	2	research	research	NOUN
ejpam-6033	169	3	may	may	AUX
ejpam-6033	169	4	focus	focus	VERB
ejpam-6033	169	5	on	on	ADP
ejpam-6033	169	6	the	the	DET
ejpam-6033	169	7	following	follow	VERB
ejpam-6033	169	8	directions	direction	NOUN
ejpam-6033	169	9	:	:	PUNCT
ejpam-6033	170	1	1	1	X
ejpam-6033	170	2	.	.	X
ejpam-6033	170	3	investigating	investigate	VERB
ejpam-6033	170	4	relationships	relationship	NOUN
ejpam-6033	170	5	between	between	ADP
ejpam-6033	170	6	nspt	nspt	PROPN
ejpam-6033	170	7	-groups	-group	NOUN
ejpam-6033	170	8	and	and	CCONJ
ejpam-6033	170	9	other	other	ADJ
ejpam-6033	170	10	group	group	NOUN
ejpam-6033	170	11	classes	class	NOUN
ejpam-6033	170	12	with	with	ADP
ejpam-6033	170	13	similar	similar	ADJ
ejpam-6033	170	14	subgroup	subgroup	NOUN
ejpam-6033	170	15	properties	property	NOUN
ejpam-6033	170	16	.	.	PUNCT
ejpam-6033	171	1	2	2	X
ejpam-6033	171	2	.	.	X
ejpam-6033	171	3	constructing	construct	VERB
ejpam-6033	171	4	new	new	ADJ
ejpam-6033	171	5	group	group	NOUN
ejpam-6033	171	6	classes	class	NOUN
ejpam-6033	171	7	inspired	inspire	VERB
ejpam-6033	171	8	by	by	ADP
ejpam-6033	171	9	nspt	nspt	PROPN
ejpam-6033	171	10	-groups	-group	NOUN
ejpam-6033	171	11	and	and	CCONJ
ejpam-6033	171	12	comparing	compare	VERB
ejpam-6033	171	13	them	they	PRON
ejpam-6033	171	14	with	with	ADP
ejpam-6033	171	15	nilpotent	nilpotent	ADJ
ejpam-6033	171	16	and	and	CCONJ
ejpam-6033	171	17	solvable	solvable	ADJ
ejpam-6033	171	18	groups	group	NOUN
ejpam-6033	171	19	.	.	PUNCT
ejpam-6033	172	1	a.	a.	PROPN
ejpam-6033	172	2	m.	m.	PROPN
ejpam-6033	172	3	alotaibiang	alotaibiang	PROPN
ejpam-6033	172	4	,	,	PUNCT
ejpam-6033	172	5	k.	k.	PROPN
ejpam-6033	172	6	al	al	PROPN
ejpam-6033	172	7	-	-	PROPN
ejpam-6033	172	8	tahat	tahat	PROPN
ejpam-6033	172	9	,	,	PUNCT
ejpam-6033	172	10	k.	k.	PROPN
ejpam-6033	172	11	m.	m.	PROPN
ejpam-6033	172	12	al	al	PROPN
ejpam-6033	172	13	-	-	PROPN
ejpam-6033	172	14	jamal	jamal	PROPN
ejpam-6033	172	15	/	/	SYM
ejpam-6033	172	16	eur	eur	PROPN
ejpam-6033	172	17	.	.	PUNCT
ejpam-6033	173	1	j.	j.	PROPN
ejpam-6033	173	2	pure	pure	PROPN
ejpam-6033	173	3	appl	appl	PROPN
ejpam-6033	173	4	.	.	PROPN
ejpam-6033	173	5	math	math	PROPN
ejpam-6033	173	6	,	,	PUNCT
ejpam-6033	173	7	18	18	NUM
ejpam-6033	173	8	(	(	PUNCT
ejpam-6033	173	9	3	3	NUM
ejpam-6033	173	10	)	)	PUNCT
ejpam-6033	173	11	(	(	PUNCT
ejpam-6033	173	12	2025	2025	NUM
ejpam-6033	173	13	)	)	PUNCT
ejpam-6033	173	14	,	,	PUNCT
ejpam-6033	173	15	6033	6033	NUM
ejpam-6033	173	16	7	7	NUM
ejpam-6033	173	17	of	of	ADP
ejpam-6033	173	18	8	8	NUM
ejpam-6033	173	19	acknowledgements	acknowledgement	NOUN
ejpam-6033	173	20	this	this	DET
ejpam-6033	173	21	study	study	NOUN
ejpam-6033	173	22	is	be	AUX
ejpam-6033	173	23	supported	support	VERB
ejpam-6033	173	24	via	via	ADP
ejpam-6033	173	25	funding	funding	NOUN
ejpam-6033	173	26	from	from	ADP
ejpam-6033	173	27	prince	prince	PROPN
ejpam-6033	173	28	sattam	sattam	PROPN
ejpam-6033	173	29	bin	bin	PROPN
ejpam-6033	173	30	abdulaziz	abdulaziz	PROPN
ejpam-6033	173	31	university	university	PROPN
ejpam-6033	173	32	project	project	NOUN
ejpam-6033	173	33	number	number	NOUN
ejpam-6033	173	34	(	(	PUNCT
ejpam-6033	173	35	psau/2025	psau/2025	NOUN
ejpam-6033	173	36	/	/	SYM
ejpam-6033	173	37	r/1447	r/1447	NOUN
ejpam-6033	173	38	)	)	PUNCT
ejpam-6033	173	39	.	.	PUNCT
ejpam-6033	174	1	references	reference	NOUN
ejpam-6033	174	2	[	[	X
ejpam-6033	174	3	1	1	X
ejpam-6033	174	4	]	]	PUNCT
ejpam-6033	174	5	o.	o.	PROPN
ejpam-6033	174	6	kegel	kegel	PROPN
ejpam-6033	174	7	.	.	PUNCT
ejpam-6033	175	1	sylow	sylow	NOUN
ejpam-6033	175	2	-	-	PUNCT
ejpam-6033	175	3	gruppen	gruppen	NOUN
ejpam-6033	175	4	und	und	NOUN
ejpam-6033	175	5	subnormalteiler	subnormalteiler	NOUN
ejpam-6033	175	6	endlicher	endlicher	PROPN
ejpam-6033	175	7	gruppen	gruppen	PROPN
ejpam-6033	175	8	.	.	PUNCT
ejpam-6033	176	1	mathematische	mathematische	PROPN
ejpam-6033	176	2	zeitschrift	zeitschrift	NOUN
ejpam-6033	176	3	,	,	PUNCT
ejpam-6033	176	4	78:205–221	78:205–221	PROPN
ejpam-6033	176	5	,	,	PUNCT
ejpam-6033	176	6	1962	1962	NUM
ejpam-6033	176	7	.	.	PUNCT
ejpam-6033	177	1	[	[	X
ejpam-6033	177	2	2	2	NUM
ejpam-6033	177	3	]	]	PUNCT
ejpam-6033	177	4	a.	a.	NOUN
ejpam-6033	177	5	m.	m.	NOUN
ejpam-6033	177	6	alotaibi	alotaibi	PROPN
ejpam-6033	177	7	and	and	CCONJ
ejpam-6033	177	8	k.	k.	PROPN
ejpam-6033	177	9	m.	m.	PROPN
ejpam-6033	177	10	aljamal	aljamal	PROPN
ejpam-6033	177	11	.	.	PUNCT
ejpam-6033	178	1	exploring	explore	VERB
ejpam-6033	178	2	the	the	DET
ejpam-6033	178	3	associated	associated	ADJ
ejpam-6033	178	4	groups	group	NOUN
ejpam-6033	178	5	of	of	ADP
ejpam-6033	178	6	quasi	quasi	ADJ
ejpam-6033	178	7	-	-	ADJ
ejpam-6033	178	8	free	free	ADJ
ejpam-6033	178	9	groups	group	NOUN
ejpam-6033	178	10	.	.	PUNCT
ejpam-6033	179	1	european	european	ADJ
ejpam-6033	179	2	journal	journal	PROPN
ejpam-6033	179	3	of	of	ADP
ejpam-6033	179	4	pure	pure	ADJ
ejpam-6033	179	5	and	and	CCONJ
ejpam-6033	179	6	applied	applied	ADJ
ejpam-6033	179	7	mathematics	mathematic	NOUN
ejpam-6033	179	8	,	,	PUNCT
ejpam-6033	179	9	17(3):2329–2335	17(3):2329–2335	NUM
ejpam-6033	179	10	,	,	PUNCT
ejpam-6033	179	11	2024	2024	NUM
ejpam-6033	179	12	.	.	PUNCT
ejpam-6033	180	1	[	[	X
ejpam-6033	180	2	3	3	X
ejpam-6033	180	3	]	]	PUNCT
ejpam-6033	180	4	k.	k.	PROPN
ejpam-6033	180	5	m.	m.	PROPN
ejpam-6033	180	6	aljamal	aljamal	PROPN
ejpam-6033	180	7	,	,	PUNCT
ejpam-6033	180	8	a.	a.	NOUN
ejpam-6033	180	9	t.	t.	PROPN
ejpam-6033	180	10	ab	ab	PROPN
ejpam-6033	180	11	ghani	ghani	PROPN
ejpam-6033	180	12	,	,	PUNCT
ejpam-6033	180	13	and	and	CCONJ
ejpam-6033	180	14	k.	k.	PROPN
ejpam-6033	180	15	a.	a.	PROPN
ejpam-6033	180	16	al	al	PROPN
ejpam-6033	180	17	-	-	PUNCT
ejpam-6033	180	18	sharo	sharo	NOUN
ejpam-6033	180	19	.	.	PUNCT
ejpam-6033	181	1	finite	finite	ADJ
ejpam-6033	181	2	groups	group	NOUN
ejpam-6033	181	3	in	in	ADP
ejpam-6033	181	4	which	which	PRON
ejpam-6033	181	5	maximal	maximal	ADJ
ejpam-6033	181	6	subgroups	subgroup	NOUN
ejpam-6033	181	7	of	of	ADP
ejpam-6033	181	8	sylow	sylow	NOUN
ejpam-6033	181	9	p	p	NOUN
ejpam-6033	181	10	-	-	PUNCT
ejpam-6033	181	11	subgroups	subgroup	NOUN
ejpam-6033	181	12	are	be	AUX
ejpam-6033	181	13	nearly	nearly	ADV
ejpam-6033	181	14	s	s	NOUN
ejpam-6033	181	15	-	-	ADJ
ejpam-6033	181	16	permutable	permutable	ADJ
ejpam-6033	181	17	.	.	PUNCT
ejpam-6033	182	1	international	international	ADJ
ejpam-6033	182	2	journal	journal	PROPN
ejpam-6033	182	3	of	of	ADP
ejpam-6033	182	4	mathematics	mathematic	NOUN
ejpam-6033	182	5	and	and	CCONJ
ejpam-6033	182	6	computer	computer	NOUN
ejpam-6033	182	7	science	science	NOUN
ejpam-6033	182	8	,	,	PUNCT
ejpam-6033	182	9	15(1):277–283	15(1):277–283	PROPN
ejpam-6033	182	10	,	,	PUNCT
ejpam-6033	182	11	2020	2020	NUM
ejpam-6033	182	12	.	.	PUNCT
ejpam-6033	183	1	[	[	X
ejpam-6033	183	2	4	4	X
ejpam-6033	183	3	]	]	PUNCT
ejpam-6033	183	4	k.	k.	PROPN
ejpam-6033	183	5	m.	m.	PROPN
ejpam-6033	183	6	aljamal	aljamal	PROPN
ejpam-6033	183	7	and	and	CCONJ
ejpam-6033	183	8	a.	a.	NOUN
ejpam-6033	183	9	t.	t.	PROPN
ejpam-6033	183	10	ab	ab	PROPN
ejpam-6033	183	11	ghani	ghani	PROPN
ejpam-6033	183	12	.	.	PUNCT
ejpam-6033	184	1	on	on	ADP
ejpam-6033	184	2	the	the	DET
ejpam-6033	184	3	relation	relation	NOUN
ejpam-6033	184	4	between	between	ADP
ejpam-6033	184	5	ct	ct	NOUN
ejpam-6033	184	6	-	-	PUNCT
ejpam-6033	184	7	groups	group	NOUN
ejpam-6033	184	8	and	and	CCONJ
ejpam-6033	184	9	nspgroups	nspgroup	NOUN
ejpam-6033	184	10	on	on	ADP
ejpam-6033	184	11	finite	finite	ADJ
ejpam-6033	184	12	groups	group	NOUN
ejpam-6033	184	13	.	.	PUNCT
ejpam-6033	185	1	in	in	ADP
ejpam-6033	185	2	2nd	2nd	ADJ
ejpam-6033	185	3	international	international	ADJ
ejpam-6033	185	4	conference	conference	NOUN
ejpam-6033	185	5	on	on	ADP
ejpam-6033	185	6	applied	apply	VERB
ejpam-6033	185	7	&	&	CCONJ
ejpam-6033	185	8	industrial	industrial	ADJ
ejpam-6033	185	9	mathematics	mathematic	NOUN
ejpam-6033	185	10	and	and	CCONJ
ejpam-6033	185	11	statistics	statistic	NOUN
ejpam-6033	185	12	,	,	PUNCT
ejpam-6033	185	13	volume	volume	NOUN
ejpam-6033	185	14	1366	1366	NUM
ejpam-6033	185	15	of	of	ADP
ejpam-6033	185	16	journal	journal	PROPN
ejpam-6033	185	17	of	of	ADP
ejpam-6033	185	18	physics	physics	PROPN
ejpam-6033	185	19	:	:	PUNCT
ejpam-6033	185	20	conference	conference	NOUN
ejpam-6033	185	21	series	series	NOUN
ejpam-6033	185	22	,	,	PUNCT
ejpam-6033	185	23	page	page	NOUN
ejpam-6033	185	24	012069	012069	NUM
ejpam-6033	185	25	,	,	PUNCT
ejpam-6033	185	26	kuantan	kuantan	PROPN
ejpam-6033	185	27	,	,	PUNCT
ejpam-6033	185	28	pahang	pahang	PROPN
ejpam-6033	185	29	,	,	PUNCT
ejpam-6033	185	30	malaysia	malaysia	PROPN
ejpam-6033	185	31	,	,	PUNCT
ejpam-6033	185	32	2019	2019	NUM
ejpam-6033	185	33	.	.	PUNCT
ejpam-6033	186	1	23–25	23–25	NUM
ejpam-6033	186	2	july	july	NOUN
ejpam-6033	186	3	.	.	PUNCT
ejpam-6033	187	1	[	[	X
ejpam-6033	187	2	5	5	X
ejpam-6033	187	3	]	]	PUNCT
ejpam-6033	187	4	k.	k.	PROPN
ejpam-6033	187	5	m.	m.	PROPN
ejpam-6033	187	6	aljamal	aljamal	PROPN
ejpam-6033	187	7	,	,	PUNCT
ejpam-6033	187	8	a.	a.	NOUN
ejpam-6033	187	9	t.	t.	PROPN
ejpam-6033	187	10	ab	ab	PROPN
ejpam-6033	187	11	ghani	ghani	PROPN
ejpam-6033	187	12	,	,	PUNCT
ejpam-6033	187	13	and	and	CCONJ
ejpam-6033	187	14	k.	k.	PROPN
ejpam-6033	187	15	a.	a.	PROPN
ejpam-6033	187	16	al	al	PROPN
ejpam-6033	187	17	-	-	PUNCT
ejpam-6033	187	18	sharo	sharo	NOUN
ejpam-6033	187	19	.	.	PUNCT
ejpam-6033	188	1	finite	finite	PROPN
ejpam-6033	188	2	groups	group	NOUN
ejpam-6033	188	3	whose	whose	DET
ejpam-6033	188	4	every	every	DET
ejpam-6033	188	5	p	p	NOUN
ejpam-6033	188	6	-	-	PUNCT
ejpam-6033	188	7	subgroup	subgroup	NOUN
ejpam-6033	188	8	is	be	AUX
ejpam-6033	188	9	nearly	nearly	ADV
ejpam-6033	188	10	s	s	NOUN
ejpam-6033	188	11	-	-	PUNCT
ejpam-6033	188	12	permutably	permutably	ADV
ejpam-6033	188	13	embedded	embed	VERB
ejpam-6033	188	14	.	.	PUNCT
ejpam-6033	189	1	in	in	ADP
ejpam-6033	189	2	proceeding	proceeding	NOUN
ejpam-6033	189	3	of	of	ADP
ejpam-6033	189	4	the	the	DET
ejpam-6033	189	5	international	international	ADJ
ejpam-6033	189	6	conference	conference	NOUN
ejpam-6033	189	7	on	on	ADP
ejpam-6033	189	8	information	information	NOUN
ejpam-6033	189	9	technology	technology	NOUN
ejpam-6033	189	10	(	(	PUNCT
ejpam-6033	189	11	icit	icit	PROPN
ejpam-6033	189	12	)	)	PUNCT
ejpam-6033	189	13	,	,	PUNCT
ejpam-6033	189	14	pages	page	NOUN
ejpam-6033	189	15	89–91	89–91	NUM
ejpam-6033	189	16	,	,	PUNCT
ejpam-6033	189	17	amman	amman	PROPN
ejpam-6033	189	18	,	,	PUNCT
ejpam-6033	189	19	jordan	jordan	PROPN
ejpam-6033	189	20	,	,	PUNCT
ejpam-6033	189	21	2021	2021	NUM
ejpam-6033	189	22	.	.	PUNCT
ejpam-6033	190	1	14–15	14–15	NUM
ejpam-6033	190	2	july	july	NOUN
ejpam-6033	190	3	.	.	PUNCT
ejpam-6033	191	1	[	[	X
ejpam-6033	191	2	6	6	NUM
ejpam-6033	191	3	]	]	PUNCT
ejpam-6033	191	4	a.	a.	NOUN
ejpam-6033	191	5	alotaibi	alotaibi	NOUN
ejpam-6033	191	6	.	.	PUNCT
ejpam-6033	192	1	sign	sign	NOUN
ejpam-6033	192	2	-	-	PUNCT
ejpam-6033	192	3	symmetry	symmetry	NOUN
ejpam-6033	192	4	and	and	CCONJ
ejpam-6033	192	5	frustration	frustration	NOUN
ejpam-6033	192	6	index	index	NOUN
ejpam-6033	192	7	in	in	ADP
ejpam-6033	192	8	signed	sign	VERB
ejpam-6033	192	9	graphs	graph	NOUN
ejpam-6033	192	10	.	.	PUNCT
ejpam-6033	193	1	phd	phd	NOUN
ejpam-6033	193	2	thesis	thesis	PROPN
ejpam-6033	193	3	,	,	PUNCT
ejpam-6033	193	4	mississippi	mississippi	PROPN
ejpam-6033	193	5	state	state	PROPN
ejpam-6033	193	6	university	university	PROPN
ejpam-6033	193	7	,	,	PUNCT
ejpam-6033	193	8	2023	2023	NUM
ejpam-6033	193	9	.	.	PUNCT
ejpam-6033	194	1	[	[	X
ejpam-6033	194	2	7	7	X
ejpam-6033	194	3	]	]	X
ejpam-6033	194	4	w.	w.	PROPN
ejpam-6033	194	5	gaschütz	gaschütz	PROPN
ejpam-6033	194	6	.	.	PUNCT
ejpam-6033	194	7	gruppen	gruppen	PROPN
ejpam-6033	194	8	,	,	PUNCT
ejpam-6033	194	9	in	in	ADP
ejpam-6033	194	10	denen	denen	NOUN
ejpam-6033	194	11	das	das	PROPN
ejpam-6033	194	12	normalteilersein	normalteilersein	ADJ
ejpam-6033	194	13	transitiv	transitiv	PROPN
ejpam-6033	194	14	ist	ist	PROPN
ejpam-6033	194	15	.	.	PROPN
ejpam-6033	194	16	journal	journal	PROPN
ejpam-6033	194	17	für	für	AUX
ejpam-6033	194	18	die	die	VERB
ejpam-6033	194	19	reine	reine	PROPN
ejpam-6033	194	20	und	und	PROPN
ejpam-6033	194	21	angewandte	angewandte	PROPN
ejpam-6033	194	22	mathematik	mathematik	PROPN
ejpam-6033	194	23	,	,	PUNCT
ejpam-6033	194	24	198:87–92	198:87–92	NUM
ejpam-6033	194	25	,	,	PUNCT
ejpam-6033	194	26	1957	1957	NUM
ejpam-6033	194	27	.	.	PUNCT
ejpam-6033	195	1	[	[	X
ejpam-6033	195	2	8	8	NUM
ejpam-6033	195	3	]	]	X
ejpam-6033	195	4	r.	r.	PROPN
ejpam-6033	195	5	k.	k.	PROPN
ejpam-6033	195	6	agrawal	agrawal	PROPN
ejpam-6033	195	7	.	.	PUNCT
ejpam-6033	196	1	finite	finite	PROPN
ejpam-6033	196	2	groups	group	NOUN
ejpam-6033	196	3	whose	whose	DET
ejpam-6033	196	4	subnormal	subnormal	ADJ
ejpam-6033	196	5	subgroups	subgroup	NOUN
ejpam-6033	196	6	permute	permute	VERB
ejpam-6033	196	7	with	with	ADP
ejpam-6033	196	8	all	all	DET
ejpam-6033	196	9	sylow	sylow	NOUN
ejpam-6033	196	10	subgroups	subgroup	NOUN
ejpam-6033	196	11	.	.	PUNCT
ejpam-6033	197	1	proceedings	proceeding	NOUN
ejpam-6033	197	2	of	of	ADP
ejpam-6033	197	3	the	the	DET
ejpam-6033	197	4	american	american	PROPN
ejpam-6033	197	5	mathematical	mathematical	PROPN
ejpam-6033	197	6	society	society	NOUN
ejpam-6033	197	7	,	,	PUNCT
ejpam-6033	197	8	47:77–83	47:77–83	NUM
ejpam-6033	197	9	,	,	PUNCT
ejpam-6033	197	10	1975	1975	NUM
ejpam-6033	197	11	.	.	PUNCT
ejpam-6033	198	1	[	[	X
ejpam-6033	198	2	9	9	NUM
ejpam-6033	198	3	]	]	X
ejpam-6033	198	4	y.	y.	PROPN
ejpam-6033	198	5	wang	wang	PROPN
ejpam-6033	198	6	.	.	PUNCT
ejpam-6033	199	1	c	c	X
ejpam-6033	199	2	-	-	PUNCT
ejpam-6033	199	3	normality	normality	NOUN
ejpam-6033	199	4	of	of	ADP
ejpam-6033	199	5	groups	group	NOUN
ejpam-6033	199	6	and	and	CCONJ
ejpam-6033	199	7	its	its	PRON
ejpam-6033	199	8	properties	property	NOUN
ejpam-6033	199	9	.	.	PUNCT
ejpam-6033	200	1	journal	journal	NOUN
ejpam-6033	200	2	of	of	ADP
ejpam-6033	200	3	algebra	algebra	PROPN
ejpam-6033	200	4	,	,	PUNCT
ejpam-6033	200	5	180(3):954	180(3):954	NOUN
ejpam-6033	200	6	–	–	PUNCT
ejpam-6033	200	7	965	965	NUM
ejpam-6033	200	8	,	,	PUNCT
ejpam-6033	200	9	1996	1996	NUM
ejpam-6033	200	10	.	.	PUNCT
ejpam-6033	201	1	[	[	X
ejpam-6033	201	2	10	10	NUM
ejpam-6033	201	3	]	]	PUNCT
ejpam-6033	201	4	k.	k.	PROPN
ejpam-6033	201	5	a.	a.	PROPN
ejpam-6033	201	6	al	al	PROPN
ejpam-6033	201	7	-	-	PUNCT
ejpam-6033	201	8	sharo	sharo	NOUN
ejpam-6033	201	9	.	.	PUNCT
ejpam-6033	202	1	on	on	ADP
ejpam-6033	202	2	nearly	nearly	ADV
ejpam-6033	202	3	s	s	NOUN
ejpam-6033	202	4	-	-	ADJ
ejpam-6033	202	5	permutable	permutable	ADJ
ejpam-6033	202	6	subgroups	subgroup	NOUN
ejpam-6033	202	7	of	of	ADP
ejpam-6033	202	8	finite	finite	ADJ
ejpam-6033	202	9	groups	group	NOUN
ejpam-6033	202	10	.	.	PUNCT
ejpam-6033	203	1	communications	communication	NOUN
ejpam-6033	203	2	in	in	ADP
ejpam-6033	203	3	algebra	algebra	NOUN
ejpam-6033	203	4	,	,	PUNCT
ejpam-6033	203	5	40(1):315–326	40(1):315–326	PROPN
ejpam-6033	203	6	,	,	PUNCT
ejpam-6033	203	7	2012	2012	NUM
ejpam-6033	203	8	.	.	PUNCT
ejpam-6033	204	1	[	[	X
ejpam-6033	204	2	11	11	NUM
ejpam-6033	204	3	]	]	PUNCT
ejpam-6033	204	4	k.	k.	PROPN
ejpam-6033	204	5	m.	m.	PROPN
ejpam-6033	204	6	aljamal	aljamal	PROPN
ejpam-6033	204	7	,	,	PUNCT
ejpam-6033	204	8	a.	a.	NOUN
ejpam-6033	204	9	t.	t.	PROPN
ejpam-6033	204	10	ab	ab	PROPN
ejpam-6033	204	11	ghani	ghani	PROPN
ejpam-6033	204	12	,	,	PUNCT
ejpam-6033	204	13	and	and	CCONJ
ejpam-6033	204	14	k.	k.	PROPN
ejpam-6033	204	15	a.	a.	PROPN
ejpam-6033	204	16	al	al	PROPN
ejpam-6033	204	17	-	-	PUNCT
ejpam-6033	204	18	sharo	sharo	NOUN
ejpam-6033	204	19	.	.	PUNCT
ejpam-6033	205	1	finite	finite	ADJ
ejpam-6033	205	2	groups	group	NOUN
ejpam-6033	205	3	in	in	ADP
ejpam-6033	205	4	which	which	PRON
ejpam-6033	205	5	nearly	nearly	ADV
ejpam-6033	205	6	s	s	NOUN
ejpam-6033	205	7	-	-	NOUN
ejpam-6033	205	8	permutability	permutability	NOUN
ejpam-6033	205	9	is	be	AUX
ejpam-6033	205	10	a	a	DET
ejpam-6033	205	11	transitive	transitive	ADJ
ejpam-6033	205	12	relation	relation	NOUN
ejpam-6033	205	13	.	.	PUNCT
ejpam-6033	206	1	international	international	ADJ
ejpam-6033	206	2	journal	journal	PROPN
ejpam-6033	206	3	of	of	ADP
ejpam-6033	206	4	mathematics	mathematic	NOUN
ejpam-6033	206	5	and	and	CCONJ
ejpam-6033	206	6	computer	computer	NOUN
ejpam-6033	206	7	science	science	NOUN
ejpam-6033	206	8	,	,	PUNCT
ejpam-6033	206	9	14(2):493–499	14(2):493–499	NUM
ejpam-6033	206	10	,	,	PUNCT
ejpam-6033	206	11	2019	2019	NUM
ejpam-6033	206	12	.	.	PUNCT
ejpam-6033	207	1	[	[	X
ejpam-6033	207	2	12	12	NUM
ejpam-6033	207	3	]	]	X
ejpam-6033	207	4	i.	i.	PROPN
ejpam-6033	207	5	m.	m.	PROPN
ejpam-6033	207	6	isaacs	isaacs	PROPN
ejpam-6033	207	7	.	.	PUNCT
ejpam-6033	208	1	finite	finite	PROPN
ejpam-6033	208	2	group	group	PROPN
ejpam-6033	208	3	theory	theory	NOUN
ejpam-6033	208	4	.	.	PUNCT
ejpam-6033	209	1	american	american	PROPN
ejpam-6033	209	2	mathematical	mathematical	PROPN
ejpam-6033	209	3	society	society	NOUN
ejpam-6033	209	4	,	,	PUNCT
ejpam-6033	209	5	providence	providence	NOUN
ejpam-6033	209	6	,	,	PUNCT
ejpam-6033	209	7	rhode	rhode	NOUN
ejpam-6033	209	8	island	island	NOUN
ejpam-6033	209	9	,	,	PUNCT
ejpam-6033	209	10	2008	2008	NUM
ejpam-6033	209	11	.	.	PUNCT
ejpam-6033	210	1	[	[	X
ejpam-6033	210	2	13	13	NUM
ejpam-6033	210	3	]	]	X
ejpam-6033	210	4	d.	d.	PROPN
ejpam-6033	210	5	j.	j.	PROPN
ejpam-6033	210	6	s.	s.	PROPN
ejpam-6033	210	7	robinson	robinson	PROPN
ejpam-6033	210	8	.	.	PUNCT
ejpam-6033	211	1	a	a	DET
ejpam-6033	211	2	note	note	NOUN
ejpam-6033	211	3	on	on	ADP
ejpam-6033	211	4	finite	finite	ADJ
ejpam-6033	211	5	groups	group	NOUN
ejpam-6033	211	6	in	in	ADP
ejpam-6033	211	7	which	which	PRON
ejpam-6033	211	8	normality	normality	NOUN
ejpam-6033	211	9	is	be	AUX
ejpam-6033	211	10	transitive	transitive	ADJ
ejpam-6033	211	11	.	.	PUNCT
ejpam-6033	212	1	proceedings	proceeding	NOUN
ejpam-6033	212	2	of	of	ADP
ejpam-6033	212	3	the	the	DET
ejpam-6033	212	4	american	american	PROPN
ejpam-6033	212	5	mathematical	mathematical	PROPN
ejpam-6033	212	6	society	society	NOUN
ejpam-6033	212	7	,	,	PUNCT
ejpam-6033	212	8	19:933–937	19:933–937	PROPN
ejpam-6033	212	9	,	,	PUNCT
ejpam-6033	212	10	1968	1968	NUM
ejpam-6033	212	11	.	.	PUNCT
ejpam-6033	213	1	[	[	X
ejpam-6033	213	2	14	14	NUM
ejpam-6033	213	3	]	]	X
ejpam-6033	213	4	d.	d.	PROPN
ejpam-6033	213	5	m.	m.	PROPN
ejpam-6033	213	6	alsharo	alsharo	PROPN
ejpam-6033	213	7	,	,	PUNCT
ejpam-6033	213	8	h.	h.	PROPN
ejpam-6033	213	9	sulaiman	sulaiman	PROPN
ejpam-6033	213	10	,	,	PUNCT
ejpam-6033	213	11	k.	k.	PROPN
ejpam-6033	213	12	a.	a.	PROPN
ejpam-6033	213	13	al	al	PROPN
ejpam-6033	213	14	-	-	PUNCT
ejpam-6033	213	15	sharo	sharo	NOUN
ejpam-6033	213	16	,	,	PUNCT
ejpam-6033	213	17	and	and	CCONJ
ejpam-6033	213	18	i.	i.	PROPN
ejpam-6033	213	19	a.	a.	PROPN
ejpam-6033	213	20	i.	i.	PROPN
ejpam-6033	213	21	sulieman	sulieman	PROPN
ejpam-6033	213	22	.	.	PUNCT
ejpam-6033	214	1	a	a	DET
ejpam-6033	214	2	note	note	NOUN
ejpam-6033	214	3	on	on	ADP
ejpam-6033	214	4	finite	finite	ADJ
ejpam-6033	214	5	groups	group	NOUN
ejpam-6033	214	6	in	in	ADP
ejpam-6033	214	7	which	which	PRON
ejpam-6033	214	8	c	c	NOUN
ejpam-6033	214	9	-	-	PUNCT
ejpam-6033	214	10	normality	normality	NOUN
ejpam-6033	214	11	is	be	AUX
ejpam-6033	214	12	a	a	DET
ejpam-6033	214	13	transitive	transitive	ADJ
ejpam-6033	214	14	relation	relation	NOUN
ejpam-6033	214	15	.	.	PUNCT
ejpam-6033	215	1	international	international	ADJ
ejpam-6033	215	2	mathematical	mathematical	PROPN
ejpam-6033	215	3	forum	forum	PROPN
ejpam-6033	215	4	,	,	PUNCT
ejpam-6033	215	5	8(38):1881–1887	8(38):1881–1887	NUM
ejpam-6033	215	6	,	,	PUNCT
ejpam-6033	215	7	2013	2013	NUM
ejpam-6033	215	8	.	.	PUNCT
ejpam-6033	216	1	a.	a.	PROPN
ejpam-6033	216	2	m.	m.	PROPN
ejpam-6033	216	3	alotaibiang	alotaibiang	PROPN
ejpam-6033	216	4	,	,	PUNCT
ejpam-6033	216	5	k.	k.	PROPN
ejpam-6033	216	6	al	al	PROPN
ejpam-6033	216	7	-	-	PROPN
ejpam-6033	216	8	tahat	tahat	PROPN
ejpam-6033	216	9	,	,	PUNCT
ejpam-6033	216	10	k.	k.	PROPN
ejpam-6033	216	11	m.	m.	PROPN
ejpam-6033	216	12	al	al	PROPN
ejpam-6033	216	13	-	-	PROPN
ejpam-6033	216	14	jamal	jamal	PROPN
ejpam-6033	216	15	/	/	SYM
ejpam-6033	216	16	eur	eur	PROPN
ejpam-6033	216	17	.	.	PUNCT
ejpam-6033	217	1	j.	j.	PROPN
ejpam-6033	217	2	pure	pure	PROPN
ejpam-6033	217	3	appl	appl	PROPN
ejpam-6033	217	4	.	.	PROPN
ejpam-6033	217	5	math	math	PROPN
ejpam-6033	217	6	,	,	PUNCT
ejpam-6033	217	7	18	18	NUM
ejpam-6033	217	8	(	(	PUNCT
ejpam-6033	217	9	3	3	NUM
ejpam-6033	217	10	)	)	PUNCT
ejpam-6033	217	11	(	(	PUNCT
ejpam-6033	217	12	2025	2025	NUM
ejpam-6033	217	13	)	)	PUNCT
ejpam-6033	217	14	,	,	PUNCT
ejpam-6033	217	15	6033	6033	NUM
ejpam-6033	217	16	8	8	NUM
ejpam-6033	217	17	of	of	ADP
ejpam-6033	217	18	8	8	NUM
ejpam-6033	218	1	[	[	SYM
ejpam-6033	218	2	15	15	NUM
ejpam-6033	218	3	]	]	X
ejpam-6033	218	4	k.	k.	PROPN
ejpam-6033	218	5	a.	a.	PROPN
ejpam-6033	218	6	al	al	PROPN
ejpam-6033	218	7	-	-	PUNCT
ejpam-6033	218	8	sharo	sharo	PROPN
ejpam-6033	218	9	and	and	CCONJ
ejpam-6033	218	10	i.	i.	PROPN
ejpam-6033	218	11	a.	a.	PROPN
ejpam-6033	218	12	i.	i.	PROPN
ejpam-6033	218	13	suleiman	suleiman	PROPN
ejpam-6033	218	14	.	.	PUNCT
ejpam-6033	219	1	a	a	DET
ejpam-6033	219	2	note	note	NOUN
ejpam-6033	219	3	on	on	ADP
ejpam-6033	219	4	finite	finite	ADJ
ejpam-6033	219	5	groups	group	NOUN
ejpam-6033	219	6	in	in	ADP
ejpam-6033	219	7	which	which	PRON
ejpam-6033	219	8	c	c	NOUN
ejpam-6033	219	9	-	-	PUNCT
ejpam-6033	219	10	permutability	permutability	NOUN
ejpam-6033	219	11	is	be	AUX
ejpam-6033	219	12	transitive	transitive	ADJ
ejpam-6033	219	13	.	.	PUNCT
ejpam-6033	220	1	acta	acta	PROPN
ejpam-6033	220	2	mathematica	mathematica	PROPN
ejpam-6033	220	3	hungarica	hungarica	PROPN
ejpam-6033	220	4	,	,	PUNCT
ejpam-6033	220	5	134(1–2):162–168	134(1–2):162–168	NUM
ejpam-6033	220	6	,	,	PUNCT
ejpam-6033	220	7	2012	2012	NUM
ejpam-6033	220	8	.	.	PUNCT