id	sid	tid	token	lemma	pos
ejpam-3399	1	1	european	european	PROPN
ejpam-3399	1	2	journal	journal	PROPN
ejpam-3399	1	3	of	of	ADP
ejpam-3399	1	4	pure	pure	ADJ
ejpam-3399	1	5	and	and	CCONJ
ejpam-3399	1	6	applied	apply	VERB
ejpam-3399	1	7	mathematics	mathematic	NOUN
ejpam-3399	1	8	vol	vol	NOUN
ejpam-3399	1	9	.	.	PROPN
ejpam-3399	2	1	12	12	NUM
ejpam-3399	2	2	,	,	PUNCT
ejpam-3399	2	3	no	no	INTJ
ejpam-3399	2	4	.	.	NOUN
ejpam-3399	2	5	2	2	NUM
ejpam-3399	2	6	,	,	PUNCT
ejpam-3399	2	7	2019	2019	NUM
ejpam-3399	2	8	,	,	PUNCT
ejpam-3399	2	9	571	571	NUM
ejpam-3399	2	10	-	-	SYM
ejpam-3399	2	11	576	576	NUM
ejpam-3399	2	12	issn	issn	PROPN
ejpam-3399	2	13	1307	1307	NUM
ejpam-3399	2	14	-	-	SYM
ejpam-3399	2	15	5543	5543	NUM
ejpam-3399	2	16	–	–	PUNCT
ejpam-3399	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3399	2	18	published	publish	VERB
ejpam-3399	2	19	by	by	ADP
ejpam-3399	2	20	new	new	PROPN
ejpam-3399	2	21	york	york	PROPN
ejpam-3399	2	22	business	business	PROPN
ejpam-3399	2	23	global	global	ADJ
ejpam-3399	2	24	finite	finite	ADJ
ejpam-3399	2	25	groups	group	NOUN
ejpam-3399	2	26	with	with	ADP
ejpam-3399	2	27	certain	certain	ADJ
ejpam-3399	2	28	permutability	permutability	NOUN
ejpam-3399	2	29	criteria	criterion	NOUN
ejpam-3399	2	30	rola	rola	PROPN
ejpam-3399	2	31	a.	a.	PROPN
ejpam-3399	2	32	hijazi1	hijazi1	PROPN
ejpam-3399	2	33	,	,	PUNCT
ejpam-3399	2	34	fatme	fatme	NOUN
ejpam-3399	2	35	m.	m.	NOUN
ejpam-3399	2	36	charaf1,∗	charaf1,∗	NOUN
ejpam-3399	2	37	1	1	NUM
ejpam-3399	2	38	department	department	NOUN
ejpam-3399	2	39	of	of	ADP
ejpam-3399	2	40	mathematics	mathematic	NOUN
ejpam-3399	2	41	,	,	PUNCT
ejpam-3399	2	42	faculty	faculty	NOUN
ejpam-3399	2	43	of	of	ADP
ejpam-3399	2	44	science	science	NOUN
ejpam-3399	2	45	,	,	PUNCT
ejpam-3399	2	46	king	king	PROPN
ejpam-3399	2	47	abdulaziz	abdulaziz	PROPN
ejpam-3399	2	48	university	university	PROPN
ejpam-3399	2	49	,	,	PUNCT
ejpam-3399	2	50	jeddah	jeddah	PROPN
ejpam-3399	2	51	,	,	PUNCT
ejpam-3399	2	52	saudi	saudi	PROPN
ejpam-3399	2	53	arabia	arabia	PROPN
ejpam-3399	2	54	abstract	abstract	NOUN
ejpam-3399	2	55	.	.	PUNCT
ejpam-3399	3	1	let	let	VERB
ejpam-3399	3	2	g	g	PRON
ejpam-3399	3	3	be	be	AUX
ejpam-3399	3	4	a	a	DET
ejpam-3399	3	5	finite	finite	ADJ
ejpam-3399	3	6	group	group	NOUN
ejpam-3399	3	7	.	.	PUNCT
ejpam-3399	4	1	a	a	DET
ejpam-3399	4	2	subgroup	subgroup	NOUN
ejpam-3399	4	3	h	h	NOUN
ejpam-3399	4	4	of	of	ADP
ejpam-3399	4	5	g	g	PROPN
ejpam-3399	4	6	is	be	AUX
ejpam-3399	4	7	said	say	VERB
ejpam-3399	4	8	to	to	PART
ejpam-3399	4	9	be	be	AUX
ejpam-3399	4	10	s	s	NOUN
ejpam-3399	4	11	-	-	NOUN
ejpam-3399	4	12	permutable	permutable	ADJ
ejpam-3399	4	13	in	in	ADP
ejpam-3399	4	14	g	g	PROPN
ejpam-3399	4	15	if	if	SCONJ
ejpam-3399	4	16	it	it	PRON
ejpam-3399	4	17	permutes	permute	VERB
ejpam-3399	4	18	with	with	ADP
ejpam-3399	4	19	all	all	DET
ejpam-3399	4	20	sylow	sylow	NOUN
ejpam-3399	4	21	subgroups	subgroup	NOUN
ejpam-3399	4	22	of	of	ADP
ejpam-3399	4	23	g.	g.	PROPN
ejpam-3399	4	24	in	in	ADP
ejpam-3399	4	25	this	this	DET
ejpam-3399	4	26	note	note	NOUN
ejpam-3399	4	27	we	we	PRON
ejpam-3399	4	28	prove	prove	VERB
ejpam-3399	4	29	that	that	SCONJ
ejpam-3399	4	30	if	if	SCONJ
ejpam-3399	4	31	p	p	X
ejpam-3399	4	32	,	,	PUNCT
ejpam-3399	4	33	the	the	DET
ejpam-3399	4	34	sylow	sylow	NOUN
ejpam-3399	4	35	p	p	NOUN
ejpam-3399	4	36	-	-	PUNCT
ejpam-3399	4	37	subgroup	subgroup	NOUN
ejpam-3399	4	38	of	of	ADP
ejpam-3399	4	39	g	g	PROPN
ejpam-3399	4	40	(	(	PUNCT
ejpam-3399	4	41	p	p	X
ejpam-3399	4	42	>	>	X
ejpam-3399	4	43	2	2	NUM
ejpam-3399	4	44	)	)	PUNCT
ejpam-3399	4	45	,	,	PUNCT
ejpam-3399	4	46	has	have	VERB
ejpam-3399	4	47	a	a	DET
ejpam-3399	4	48	subgroup	subgroup	NOUN
ejpam-3399	4	49	d	d	NOUN
ejpam-3399	4	50	such	such	ADJ
ejpam-3399	4	51	that	that	SCONJ
ejpam-3399	4	52	1	1	NUM
ejpam-3399	4	53	<	<	X
ejpam-3399	4	54	|d|	|d|	PROPN
ejpam-3399	4	55	<	<	X
ejpam-3399	4	56	|p	|p	PROPN
ejpam-3399	5	1	|	|	ADV
ejpam-3399	5	2	and	and	CCONJ
ejpam-3399	5	3	all	all	DET
ejpam-3399	5	4	subgroups	subgroup	NOUN
ejpam-3399	5	5	h	h	VERB
ejpam-3399	5	6	of	of	ADP
ejpam-3399	5	7	p	p	NOUN
ejpam-3399	5	8	with	with	ADP
ejpam-3399	5	9	|h|	|h|	PROPN
ejpam-3399	5	10	=	=	SYM
ejpam-3399	5	11	|d|	|d|	PROPN
ejpam-3399	5	12	are	be	AUX
ejpam-3399	5	13	s	s	NOUN
ejpam-3399	5	14	-	-	NOUN
ejpam-3399	5	15	permutable	permutable	ADJ
ejpam-3399	5	16	in	in	ADP
ejpam-3399	5	17	g	g	NOUN
ejpam-3399	5	18	,	,	PUNCT
ejpam-3399	5	19	then	then	ADV
ejpam-3399	5	20	g′	g′	NOUN
ejpam-3399	5	21	is	be	AUX
ejpam-3399	5	22	p	p	NOUN
ejpam-3399	5	23	-	-	PUNCT
ejpam-3399	5	24	nilpotent	nilpotent	ADJ
ejpam-3399	5	25	.	.	PUNCT
ejpam-3399	6	1	2010	2010	NUM
ejpam-3399	6	2	mathematics	mathematic	NOUN
ejpam-3399	6	3	subject	subject	NOUN
ejpam-3399	6	4	classifications	classification	NOUN
ejpam-3399	6	5	:	:	PUNCT
ejpam-3399	6	6	20d10	20d10	NUM
ejpam-3399	6	7	,	,	PUNCT
ejpam-3399	6	8	20d20	20d20	NUM
ejpam-3399	6	9	key	key	ADJ
ejpam-3399	6	10	words	word	NOUN
ejpam-3399	6	11	and	and	CCONJ
ejpam-3399	6	12	phrases	phrase	NOUN
ejpam-3399	6	13	:	:	PUNCT
ejpam-3399	6	14	s	s	VERB
ejpam-3399	6	15	-permutable	-permutable	ADJ
ejpam-3399	6	16	subgroup	subgroup	NOUN
ejpam-3399	6	17	,	,	PUNCT
ejpam-3399	6	18	p	p	NOUN
ejpam-3399	6	19	-	-	PUNCT
ejpam-3399	6	20	nilpotent	nilpotent	ADJ
ejpam-3399	6	21	group	group	NOUN
ejpam-3399	6	22	,	,	PUNCT
ejpam-3399	6	23	solvable	solvable	ADJ
ejpam-3399	6	24	group	group	NOUN
ejpam-3399	6	25	,	,	PUNCT
ejpam-3399	6	26	supersolvable	supersolvable	ADJ
ejpam-3399	6	27	group	group	NOUN
ejpam-3399	6	28	.	.	PUNCT
ejpam-3399	7	1	1	1	X
ejpam-3399	7	2	.	.	X
ejpam-3399	7	3	introduction	introduction	NOUN
ejpam-3399	7	4	throughout	throughout	ADP
ejpam-3399	7	5	this	this	DET
ejpam-3399	7	6	note	note	NOUN
ejpam-3399	7	7	,	,	PUNCT
ejpam-3399	7	8	g	g	PROPN
ejpam-3399	7	9	denotes	denote	VERB
ejpam-3399	7	10	a	a	DET
ejpam-3399	7	11	finite	finite	ADJ
ejpam-3399	7	12	group	group	NOUN
ejpam-3399	7	13	.	.	PUNCT
ejpam-3399	8	1	the	the	DET
ejpam-3399	8	2	relationship	relationship	NOUN
ejpam-3399	8	3	between	between	ADP
ejpam-3399	8	4	the	the	DET
ejpam-3399	8	5	properties	property	NOUN
ejpam-3399	8	6	of	of	ADP
ejpam-3399	8	7	the	the	DET
ejpam-3399	8	8	sylow	sylow	NOUN
ejpam-3399	8	9	subgroups	subgroup	NOUN
ejpam-3399	8	10	of	of	ADP
ejpam-3399	8	11	a	a	DET
ejpam-3399	8	12	group	group	NOUN
ejpam-3399	8	13	g	g	NOUN
ejpam-3399	8	14	and	and	CCONJ
ejpam-3399	8	15	its	its	PRON
ejpam-3399	8	16	structure	structure	NOUN
ejpam-3399	8	17	has	have	AUX
ejpam-3399	8	18	been	be	AUX
ejpam-3399	8	19	investigated	investigate	VERB
ejpam-3399	8	20	by	by	ADP
ejpam-3399	8	21	many	many	ADJ
ejpam-3399	8	22	authors	author	NOUN
ejpam-3399	8	23	.	.	PUNCT
ejpam-3399	9	1	starting	start	VERB
ejpam-3399	9	2	from	from	ADP
ejpam-3399	9	3	gaschűtz	gaschűtz	NOUN
ejpam-3399	9	4	and	and	CCONJ
ejpam-3399	9	5	itő	itő	NOUN
ejpam-3399	9	6	(	(	PUNCT
ejpam-3399	9	7	[	[	X
ejpam-3399	9	8	10	10	NUM
ejpam-3399	9	9	]	]	PUNCT
ejpam-3399	9	10	,	,	PUNCT
ejpam-3399	9	11	satz	satz	PROPN
ejpam-3399	9	12	5.7	5.7	NUM
ejpam-3399	9	13	,	,	PUNCT
ejpam-3399	9	14	p.436	p.436	NUM
ejpam-3399	9	15	)	)	PUNCT
ejpam-3399	9	16	who	who	PRON
ejpam-3399	9	17	proved	prove	VERB
ejpam-3399	9	18	that	that	SCONJ
ejpam-3399	9	19	a	a	DET
ejpam-3399	9	20	group	group	NOUN
ejpam-3399	9	21	g	g	NOUN
ejpam-3399	9	22	is	be	AUX
ejpam-3399	9	23	solvable	solvable	ADJ
ejpam-3399	9	24	if	if	SCONJ
ejpam-3399	9	25	all	all	DET
ejpam-3399	9	26	its	its	PRON
ejpam-3399	9	27	minimal	minimal	ADJ
ejpam-3399	9	28	subgroups	subgroup	NOUN
ejpam-3399	9	29	are	be	AUX
ejpam-3399	9	30	normal	normal	ADJ
ejpam-3399	9	31	.	.	PUNCT
ejpam-3399	10	1	in	in	ADP
ejpam-3399	10	2	1970	1970	NUM
ejpam-3399	10	3	,	,	PUNCT
ejpam-3399	10	4	buckely	buckely	ADV
ejpam-3399	10	5	[	[	X
ejpam-3399	10	6	4	4	X
ejpam-3399	10	7	]	]	PUNCT
ejpam-3399	10	8	proved	prove	VERB
ejpam-3399	10	9	that	that	SCONJ
ejpam-3399	10	10	a	a	DET
ejpam-3399	10	11	group	group	NOUN
ejpam-3399	10	12	of	of	ADP
ejpam-3399	10	13	odd	odd	ADJ
ejpam-3399	10	14	order	order	NOUN
ejpam-3399	10	15	is	be	AUX
ejpam-3399	10	16	supersolvable	supersolvable	ADJ
ejpam-3399	10	17	if	if	SCONJ
ejpam-3399	10	18	all	all	DET
ejpam-3399	10	19	its	its	PRON
ejpam-3399	10	20	minimal	minimal	ADJ
ejpam-3399	10	21	subgroups	subgroup	NOUN
ejpam-3399	10	22	are	be	AUX
ejpam-3399	10	23	normal	normal	ADJ
ejpam-3399	10	24	(	(	PUNCT
ejpam-3399	10	25	a	a	DET
ejpam-3399	10	26	subgroup	subgroup	NOUN
ejpam-3399	10	27	of	of	ADP
ejpam-3399	10	28	prime	prime	ADJ
ejpam-3399	10	29	order	order	NOUN
ejpam-3399	10	30	is	be	AUX
ejpam-3399	10	31	called	call	VERB
ejpam-3399	10	32	a	a	DET
ejpam-3399	10	33	minimal	minimal	ADJ
ejpam-3399	10	34	subgroup	subgroup	NOUN
ejpam-3399	10	35	)	)	PUNCT
ejpam-3399	10	36	.	.	PUNCT
ejpam-3399	11	1	recall	recall	VERB
ejpam-3399	11	2	that	that	SCONJ
ejpam-3399	11	3	a	a	DET
ejpam-3399	11	4	subgroup	subgroup	NOUN
ejpam-3399	11	5	is	be	AUX
ejpam-3399	11	6	said	say	VERB
ejpam-3399	11	7	to	to	PART
ejpam-3399	11	8	be	be	AUX
ejpam-3399	11	9	s	s	NOUN
ejpam-3399	11	10	-	-	NOUN
ejpam-3399	11	11	permutable	permutable	ADJ
ejpam-3399	11	12	in	in	ADP
ejpam-3399	11	13	g	g	PROPN
ejpam-3399	11	14	if	if	SCONJ
ejpam-3399	11	15	it	it	PRON
ejpam-3399	11	16	permutes	permute	VERB
ejpam-3399	11	17	with	with	ADP
ejpam-3399	11	18	all	all	DET
ejpam-3399	11	19	sylow	sylow	NOUN
ejpam-3399	11	20	subgroup	subgroup	NOUN
ejpam-3399	11	21	of	of	ADP
ejpam-3399	11	22	g.	g.	PROPN
ejpam-3399	11	23	this	this	DET
ejpam-3399	11	24	concept	concept	NOUN
ejpam-3399	11	25	,	,	PUNCT
ejpam-3399	11	26	as	as	ADP
ejpam-3399	11	27	a	a	DET
ejpam-3399	11	28	generalization	generalization	NOUN
ejpam-3399	11	29	of	of	ADP
ejpam-3399	11	30	normality	normality	NOUN
ejpam-3399	11	31	,	,	PUNCT
ejpam-3399	11	32	was	be	AUX
ejpam-3399	11	33	introduced	introduce	VERB
ejpam-3399	11	34	by	by	ADP
ejpam-3399	11	35	kegel	kegel	PROPN
ejpam-3399	12	1	[	[	X
ejpam-3399	12	2	11	11	NUM
ejpam-3399	12	3	]	]	PUNCT
ejpam-3399	12	4	in	in	ADP
ejpam-3399	12	5	1962	1962	NUM
ejpam-3399	12	6	and	and	CCONJ
ejpam-3399	12	7	has	have	AUX
ejpam-3399	12	8	been	be	AUX
ejpam-3399	12	9	studied	study	VERB
ejpam-3399	12	10	extensively	extensively	ADV
ejpam-3399	12	11	in	in	ADP
ejpam-3399	12	12	many	many	ADJ
ejpam-3399	12	13	notes	note	NOUN
ejpam-3399	12	14	.	.	PUNCT
ejpam-3399	13	1	for	for	ADP
ejpam-3399	13	2	example	example	NOUN
ejpam-3399	13	3	,	,	PUNCT
ejpam-3399	13	4	srinivasan	srinivasan	NOUN
ejpam-3399	13	5	[	[	X
ejpam-3399	13	6	15	15	NUM
ejpam-3399	13	7	]	]	PUNCT
ejpam-3399	13	8	in	in	ADP
ejpam-3399	13	9	1980	1980	NUM
ejpam-3399	13	10	obtained	obtain	VERB
ejpam-3399	13	11	the	the	DET
ejpam-3399	13	12	supersolvability	supersolvability	NOUN
ejpam-3399	13	13	of	of	ADP
ejpam-3399	13	14	g	g	PROPN
ejpam-3399	13	15	under	under	ADP
ejpam-3399	13	16	the	the	DET
ejpam-3399	13	17	assumption	assumption	NOUN
ejpam-3399	13	18	that	that	SCONJ
ejpam-3399	13	19	the	the	DET
ejpam-3399	13	20	maximal	maximal	ADJ
ejpam-3399	13	21	subgroups	subgroup	NOUN
ejpam-3399	13	22	of	of	ADP
ejpam-3399	13	23	all	all	DET
ejpam-3399	13	24	sylow	sylow	NOUN
ejpam-3399	13	25	subgroups	subgroup	NOUN
ejpam-3399	13	26	are	be	AUX
ejpam-3399	13	27	s	s	NOUN
ejpam-3399	13	28	-	-	NOUN
ejpam-3399	13	29	permutable	permutable	ADJ
ejpam-3399	13	30	in	in	ADP
ejpam-3399	13	31	g.	g.	PROPN
ejpam-3399	13	32	in	in	ADP
ejpam-3399	13	33	2000	2000	NUM
ejpam-3399	13	34	,	,	PUNCT
ejpam-3399	13	35	ballester	ballester	NOUN
ejpam-3399	13	36	-	-	PUNCT
ejpam-3399	13	37	bolinches	bolinche	NOUN
ejpam-3399	13	38	et	et	PROPN
ejpam-3399	13	39	al	al	PROPN
ejpam-3399	13	40	.	.	PUNCT
ejpam-3399	14	1	[	[	X
ejpam-3399	14	2	3	3	X
ejpam-3399	14	3	]	]	PUNCT
ejpam-3399	14	4	introduced	introduce	VERB
ejpam-3399	14	5	the	the	DET
ejpam-3399	14	6	c	c	NOUN
ejpam-3399	14	7	-	-	PUNCT
ejpam-3399	14	8	supplementation	supplementation	NOUN
ejpam-3399	14	9	concept	concept	NOUN
ejpam-3399	14	10	of	of	ADP
ejpam-3399	14	11	a	a	DET
ejpam-3399	14	12	finite	finite	ADJ
ejpam-3399	14	13	group	group	NOUN
ejpam-3399	14	14	:	:	PUNCT
ejpam-3399	14	15	a	a	DET
ejpam-3399	14	16	subgroup	subgroup	NOUN
ejpam-3399	14	17	h	h	NOUN
ejpam-3399	14	18	of	of	ADP
ejpam-3399	14	19	a	a	DET
ejpam-3399	14	20	group	group	NOUN
ejpam-3399	14	21	g	g	NOUN
ejpam-3399	14	22	is	be	AUX
ejpam-3399	14	23	said	say	VERB
ejpam-3399	14	24	to	to	PART
ejpam-3399	14	25	be	be	AUX
ejpam-3399	14	26	c	c	NOUN
ejpam-3399	14	27	-	-	PUNCT
ejpam-3399	14	28	supplemented	supplement	VERB
ejpam-3399	14	29	in	in	ADP
ejpam-3399	14	30	g	g	PROPN
ejpam-3399	14	31	if	if	SCONJ
ejpam-3399	14	32	there	there	PRON
ejpam-3399	14	33	exists	exist	VERB
ejpam-3399	14	34	a	a	DET
ejpam-3399	14	35	subgroup	subgroup	NOUN
ejpam-3399	14	36	k	k	PROPN
ejpam-3399	14	37	of	of	ADP
ejpam-3399	14	38	g	g	PROPN
ejpam-3399	15	1	such	such	ADJ
ejpam-3399	15	2	that	that	SCONJ
ejpam-3399	15	3	g	g	PROPN
ejpam-3399	15	4	=	=	PUNCT
ejpam-3399	15	5	hk	hk	PROPN
ejpam-3399	15	6	and	and	CCONJ
ejpam-3399	15	7	h	h	NOUN
ejpam-3399	15	8	∩k	∩k	PROPN
ejpam-3399	15	9	≤	≤	NUM
ejpam-3399	15	10	hg	hg	NOUN
ejpam-3399	15	11	,	,	PUNCT
ejpam-3399	15	12	where	where	SCONJ
ejpam-3399	15	13	hg	hg	PROPN
ejpam-3399	15	14	=	=	PROPN
ejpam-3399	15	15	coreg(h	coreg(h	PROPN
ejpam-3399	15	16	)	)	PUNCT
ejpam-3399	15	17	is	be	AUX
ejpam-3399	15	18	the	the	DET
ejpam-3399	15	19	largest	large	ADJ
ejpam-3399	15	20	normal	normal	ADJ
ejpam-3399	15	21	subgroup	subgroup	NOUN
ejpam-3399	15	22	of	of	ADP
ejpam-3399	15	23	g	g	PROPN
ejpam-3399	15	24	contained	contain	VERB
ejpam-3399	15	25	in	in	ADP
ejpam-3399	15	26	h.	h.	NOUN
ejpam-3399	15	27	by	by	ADP
ejpam-3399	15	28	using	use	VERB
ejpam-3399	15	29	this	this	DET
ejpam-3399	15	30	concept	concept	NOUN
ejpam-3399	15	31	they	they	PRON
ejpam-3399	15	32	were	be	AUX
ejpam-3399	15	33	able	able	ADJ
ejpam-3399	15	34	to	to	PART
ejpam-3399	15	35	prove	prove	VERB
ejpam-3399	15	36	that	that	SCONJ
ejpam-3399	15	37	a	a	DET
ejpam-3399	15	38	group	group	NOUN
ejpam-3399	15	39	g	g	NOUN
ejpam-3399	15	40	is	be	AUX
ejpam-3399	15	41	solvable	solvable	ADJ
ejpam-3399	15	42	if	if	SCONJ
ejpam-3399	15	43	and	and	CCONJ
ejpam-3399	16	1	only	only	ADV
ejpam-3399	16	2	if	if	SCONJ
ejpam-3399	16	3	every	every	DET
ejpam-3399	16	4	sylow	sylow	NOUN
ejpam-3399	16	5	subgroup	subgroup	NOUN
ejpam-3399	16	6	of	of	ADP
ejpam-3399	16	7	g	g	PROPN
ejpam-3399	16	8	is	be	AUX
ejpam-3399	16	9	c	c	NOUN
ejpam-3399	16	10	-	-	PUNCT
ejpam-3399	16	11	supplemented	supplement	VERB
ejpam-3399	16	12	in	in	ADP
ejpam-3399	16	13	g.	g.	PROPN
ejpam-3399	16	14	moreover	moreover	ADV
ejpam-3399	16	15	,	,	PUNCT
ejpam-3399	16	16	as	as	ADP
ejpam-3399	16	17	an	an	DET
ejpam-3399	16	18	application	application	NOUN
ejpam-3399	16	19	,	,	PUNCT
ejpam-3399	16	20	they	they	PRON
ejpam-3399	16	21	got	get	VERB
ejpam-3399	16	22	the	the	DET
ejpam-3399	16	23	supersolvability	supersolvability	NOUN
ejpam-3399	16	24	of	of	ADP
ejpam-3399	16	25	a	a	DET
ejpam-3399	16	26	group	group	NOUN
ejpam-3399	16	27	g	g	NOUN
ejpam-3399	16	28	if	if	SCONJ
ejpam-3399	16	29	all	all	DET
ejpam-3399	16	30	its	its	PRON
ejpam-3399	16	31	minimal	minimal	ADJ
ejpam-3399	16	32	subgroups	subgroup	NOUN
ejpam-3399	16	33	and	and	CCONJ
ejpam-3399	16	34	the	the	DET
ejpam-3399	16	35	cyclic	cyclic	ADJ
ejpam-3399	16	36	subgroups	subgroup	NOUN
ejpam-3399	16	37	of	of	ADP
ejpam-3399	16	38	order	order	NOUN
ejpam-3399	16	39	4	4	NUM
ejpam-3399	16	40	are	be	AUX
ejpam-3399	16	41	c	c	NOUN
ejpam-3399	16	42	-	-	PUNCT
ejpam-3399	16	43	supplemented	supplement	VERB
ejpam-3399	16	44	in	in	ADP
ejpam-3399	16	45	g.	g.	NOUN
ejpam-3399	16	46	∗corresponding	∗corresponde	VERB
ejpam-3399	16	47	author	author	NOUN
ejpam-3399	16	48	.	.	PUNCT
ejpam-3399	17	1	doi	doi	NOUN
ejpam-3399	17	2	:	:	PUNCT
ejpam-3399	17	3	https://doi.org/10.29020/nybg.ejpam.v12i2.3399	https://doi.org/10.29020/nybg.ejpam.v12i2.3399	NOUN
ejpam-3399	17	4	email	email	NOUN
ejpam-3399	17	5	addresses	address	NOUN
ejpam-3399	17	6	:	:	PUNCT
ejpam-3399	17	7	rhijazi@kau.edu.sa	rhijazi@kau.edu.sa	NOUN
ejpam-3399	17	8	(	(	PUNCT
ejpam-3399	17	9	r.	r.	PROPN
ejpam-3399	17	10	hijazi	hijazi	PROPN
ejpam-3399	17	11	)	)	PUNCT
ejpam-3399	17	12	,	,	PUNCT
ejpam-3399	17	13	fa-sharaf@hotmail.com	fa-sharaf@hotmail.com	X
ejpam-3399	17	14	(	(	PUNCT
ejpam-3399	17	15	f.	f.	PROPN
ejpam-3399	17	16	charaf	charaf	PROPN
ejpam-3399	17	17	)	)	PUNCT
ejpam-3399	17	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3399	18	1	571	571	NUM
ejpam-3399	18	2	c	c	NOUN
ejpam-3399	18	3	©	©	NOUN
ejpam-3399	18	4	2019	2019	NUM
ejpam-3399	18	5	ejpam	ejpam	NOUN
ejpam-3399	18	6	all	all	DET
ejpam-3399	18	7	rights	right	NOUN
ejpam-3399	18	8	reserved	reserve	VERB
ejpam-3399	18	9	.	.	PUNCT
ejpam-3399	19	1	r.	r.	PROPN
ejpam-3399	19	2	hijazi	hijazi	PROPN
ejpam-3399	19	3	,	,	PUNCT
ejpam-3399	19	4	f.	f.	PROPN
ejpam-3399	19	5	charaf	charaf	PROPN
ejpam-3399	19	6	/	/	SYM
ejpam-3399	19	7	eur	eur	PROPN
ejpam-3399	19	8	.	.	PUNCT
ejpam-3399	20	1	j.	j.	PROPN
ejpam-3399	20	2	pure	pure	PROPN
ejpam-3399	20	3	appl	appl	PROPN
ejpam-3399	20	4	.	.	PROPN
ejpam-3399	20	5	math	math	PROPN
ejpam-3399	20	6	,	,	PUNCT
ejpam-3399	20	7	12	12	NUM
ejpam-3399	20	8	(	(	PUNCT
ejpam-3399	20	9	2	2	NUM
ejpam-3399	20	10	)	)	PUNCT
ejpam-3399	20	11	(	(	PUNCT
ejpam-3399	20	12	2019	2019	NUM
ejpam-3399	20	13	)	)	PUNCT
ejpam-3399	20	14	,	,	PUNCT
ejpam-3399	20	15	571	571	NUM
ejpam-3399	20	16	-	-	SYM
ejpam-3399	20	17	576	576	NUM
ejpam-3399	20	18	572	572	NUM
ejpam-3399	20	19	in	in	ADP
ejpam-3399	20	20	2014	2014	NUM
ejpam-3399	20	21	,	,	PUNCT
ejpam-3399	20	22	heliel	heliel	PROPN
ejpam-3399	21	1	[	[	X
ejpam-3399	21	2	8	8	NUM
ejpam-3399	21	3	]	]	PUNCT
ejpam-3399	21	4	proved	prove	VERB
ejpam-3399	21	5	that	that	SCONJ
ejpam-3399	21	6	g	g	PROPN
ejpam-3399	21	7	is	be	AUX
ejpam-3399	21	8	solvable	solvable	ADJ
ejpam-3399	21	9	if	if	SCONJ
ejpam-3399	21	10	each	each	DET
ejpam-3399	21	11	subgroup	subgroup	NOUN
ejpam-3399	21	12	of	of	ADP
ejpam-3399	21	13	prime	prime	ADJ
ejpam-3399	21	14	odd	odd	ADJ
ejpam-3399	21	15	order	order	NOUN
ejpam-3399	21	16	of	of	ADP
ejpam-3399	21	17	g	g	PROPN
ejpam-3399	21	18	is	be	AUX
ejpam-3399	21	19	c	c	NOUN
ejpam-3399	21	20	-	-	PUNCT
ejpam-3399	21	21	supplemented	supplement	VERB
ejpam-3399	21	22	in	in	ADP
ejpam-3399	21	23	g.	g.	PROPN
ejpam-3399	21	24	also	also	ADV
ejpam-3399	21	25	he	he	PRON
ejpam-3399	21	26	proved	prove	VERB
ejpam-3399	21	27	that	that	SCONJ
ejpam-3399	21	28	g	g	PROPN
ejpam-3399	21	29	is	be	AUX
ejpam-3399	21	30	solvable	solvable	ADJ
ejpam-3399	21	31	if	if	SCONJ
ejpam-3399	21	32	and	and	CCONJ
ejpam-3399	21	33	only	only	ADV
ejpam-3399	21	34	if	if	SCONJ
ejpam-3399	21	35	every	every	DET
ejpam-3399	21	36	sylow	sylow	NOUN
ejpam-3399	21	37	subgroup	subgroup	NOUN
ejpam-3399	21	38	of	of	ADP
ejpam-3399	21	39	odd	odd	ADJ
ejpam-3399	21	40	order	order	NOUN
ejpam-3399	21	41	of	of	ADP
ejpam-3399	21	42	g	g	PROPN
ejpam-3399	21	43	is	be	AUX
ejpam-3399	21	44	c	c	NOUN
ejpam-3399	21	45	-	-	PUNCT
ejpam-3399	21	46	supplemented	supplement	VERB
ejpam-3399	21	47	in	in	ADP
ejpam-3399	21	48	g.	g.	PROPN
ejpam-3399	21	49	this	this	PRON
ejpam-3399	21	50	improved	improve	VERB
ejpam-3399	21	51	and	and	CCONJ
ejpam-3399	21	52	generalized	generalize	VERB
ejpam-3399	21	53	the	the	DET
ejpam-3399	21	54	results	result	NOUN
ejpam-3399	21	55	of	of	ADP
ejpam-3399	21	56	hall	hall	NOUN
ejpam-3399	22	1	[	[	X
ejpam-3399	22	2	6	6	NUM
ejpam-3399	22	3	,	,	PUNCT
ejpam-3399	22	4	7	7	NUM
ejpam-3399	22	5	]	]	PUNCT
ejpam-3399	22	6	,	,	PUNCT
ejpam-3399	22	7	ballester	ballester	NOUN
ejpam-3399	22	8	-	-	PUNCT
ejpam-3399	22	9	bolinches	bolinche	NOUN
ejpam-3399	22	10	and	and	CCONJ
ejpam-3399	22	11	guo	guo	X
ejpam-3399	23	1	[	[	X
ejpam-3399	23	2	2	2	NUM
ejpam-3399	23	3	]	]	PUNCT
ejpam-3399	23	4	,	,	PUNCT
ejpam-3399	23	5	and	and	CCONJ
ejpam-3399	23	6	ballester	ballester	NOUN
ejpam-3399	23	7	-	-	PUNCT
ejpam-3399	23	8	bolinches	bolinche	NOUN
ejpam-3399	23	9	et	et	PROPN
ejpam-3399	23	10	al	al	PROPN
ejpam-3399	23	11	.	.	PUNCT
ejpam-3399	24	1	[	[	X
ejpam-3399	24	2	3	3	NUM
ejpam-3399	24	3	]	]	PUNCT
ejpam-3399	24	4	.	.	PUNCT
ejpam-3399	25	1	heliel	heliel	PROPN
ejpam-3399	25	2	also	also	ADV
ejpam-3399	25	3	posted	post	VERB
ejpam-3399	25	4	the	the	DET
ejpam-3399	25	5	following	follow	VERB
ejpam-3399	25	6	conjecture	conjecture	NOUN
ejpam-3399	25	7	:	:	PUNCT
ejpam-3399	25	8	let	let	VERB
ejpam-3399	25	9	g	g	PRON
ejpam-3399	25	10	be	be	AUX
ejpam-3399	25	11	a	a	DET
ejpam-3399	25	12	finite	finite	ADJ
ejpam-3399	25	13	group	group	NOUN
ejpam-3399	25	14	such	such	ADJ
ejpam-3399	25	15	that	that	SCONJ
ejpam-3399	25	16	every	every	DET
ejpam-3399	25	17	non	non	ADJ
ejpam-3399	25	18	-	-	ADJ
ejpam-3399	25	19	cyclic	cyclic	ADJ
ejpam-3399	25	20	sylow	sylow	NOUN
ejpam-3399	25	21	subgroup	subgroup	NOUN
ejpam-3399	25	22	p	p	PROPN
ejpam-3399	25	23	of	of	ADP
ejpam-3399	25	24	odd	odd	ADJ
ejpam-3399	25	25	order	order	NOUN
ejpam-3399	25	26	of	of	ADP
ejpam-3399	25	27	g	g	PROPN
ejpam-3399	25	28	has	have	VERB
ejpam-3399	25	29	a	a	DET
ejpam-3399	25	30	subgroup	subgroup	NOUN
ejpam-3399	25	31	d	d	NOUN
ejpam-3399	25	32	such	such	ADJ
ejpam-3399	25	33	that	that	SCONJ
ejpam-3399	25	34	1	1	NUM
ejpam-3399	25	35	<	<	X
ejpam-3399	25	36	|d|	|d|	PROPN
ejpam-3399	25	37	≤	≤	PROPN
ejpam-3399	25	38	|p	|p	PROPN
ejpam-3399	26	1	|	|	ADV
ejpam-3399	26	2	and	and	CCONJ
ejpam-3399	26	3	all	all	DET
ejpam-3399	26	4	subgroups	subgroup	NOUN
ejpam-3399	26	5	h	h	VERB
ejpam-3399	26	6	of	of	ADP
ejpam-3399	26	7	p	p	NOUN
ejpam-3399	26	8	with	with	ADP
ejpam-3399	26	9	|h|	|h|	PROPN
ejpam-3399	26	10	=	=	SYM
ejpam-3399	26	11	|d|	|d|	PROPN
ejpam-3399	26	12	are	be	AUX
ejpam-3399	26	13	c	c	NOUN
ejpam-3399	26	14	-	-	PUNCT
ejpam-3399	26	15	supplemented	supplement	VERB
ejpam-3399	26	16	in	in	ADP
ejpam-3399	26	17	g.	g.	PROPN
ejpam-3399	26	18	is	be	AUX
ejpam-3399	26	19	g	g	NOUN
ejpam-3399	26	20	solvable	solvable	ADJ
ejpam-3399	26	21	?	?	PUNCT
ejpam-3399	27	1	in	in	ADP
ejpam-3399	27	2	the	the	DET
ejpam-3399	27	3	same	same	ADJ
ejpam-3399	27	4	year	year	NOUN
ejpam-3399	27	5	,	,	PUNCT
ejpam-3399	27	6	li	li	PROPN
ejpam-3399	27	7	et	et	PROPN
ejpam-3399	27	8	al	al	PROPN
ejpam-3399	27	9	.	.	PUNCT
ejpam-3399	28	1	[	[	X
ejpam-3399	28	2	12	12	NUM
ejpam-3399	28	3	]	]	PUNCT
ejpam-3399	28	4	presented	present	VERB
ejpam-3399	28	5	a	a	DET
ejpam-3399	28	6	counterexample	counterexample	NOUN
ejpam-3399	28	7	to	to	PART
ejpam-3399	28	8	show	show	VERB
ejpam-3399	28	9	that	that	SCONJ
ejpam-3399	28	10	the	the	DET
ejpam-3399	28	11	answer	answer	NOUN
ejpam-3399	28	12	of	of	ADP
ejpam-3399	28	13	this	this	DET
ejpam-3399	28	14	conjecture	conjecture	NOUN
ejpam-3399	28	15	is	be	AUX
ejpam-3399	28	16	negative	negative	ADJ
ejpam-3399	28	17	in	in	ADP
ejpam-3399	28	18	general	general	ADJ
ejpam-3399	28	19	and	and	CCONJ
ejpam-3399	28	20	then	then	ADV
ejpam-3399	28	21	gave	give	VERB
ejpam-3399	28	22	a	a	DET
ejpam-3399	28	23	generalization	generalization	NOUN
ejpam-3399	28	24	of	of	ADP
ejpam-3399	28	25	heliel	heliel	PROPN
ejpam-3399	28	26	’s	’s	PART
ejpam-3399	28	27	theorems	theorem	NOUN
ejpam-3399	28	28	.	.	PUNCT
ejpam-3399	28	29	example	example	NOUN
ejpam-3399	29	1	1	1	NUM
ejpam-3399	29	2	.	.	PUNCT
ejpam-3399	29	3	let	let	VERB
ejpam-3399	29	4	g	g	PROPN
ejpam-3399	29	5	=	=	VERB
ejpam-3399	29	6	a5	a5	PROPN
ejpam-3399	29	7	×h	×h	PROPN
ejpam-3399	29	8	,	,	PUNCT
ejpam-3399	29	9	where	where	SCONJ
ejpam-3399	29	10	a5	a5	PROPN
ejpam-3399	29	11	is	be	AUX
ejpam-3399	29	12	the	the	DET
ejpam-3399	29	13	alternating	alternate	VERB
ejpam-3399	29	14	group	group	NOUN
ejpam-3399	29	15	of	of	ADP
ejpam-3399	29	16	degree	degree	NOUN
ejpam-3399	29	17	5	5	NUM
ejpam-3399	29	18	and	and	CCONJ
ejpam-3399	29	19	h	h	NOUN
ejpam-3399	29	20	is	be	AUX
ejpam-3399	29	21	an	an	DET
ejpam-3399	29	22	elementary	elementary	ADJ
ejpam-3399	29	23	group	group	NOUN
ejpam-3399	29	24	of	of	ADP
ejpam-3399	29	25	order	order	NOUN
ejpam-3399	29	26	pn	pn	VERB
ejpam-3399	29	27	with	with	ADP
ejpam-3399	29	28	p	p	PROPN
ejpam-3399	29	29	>	>	X
ejpam-3399	29	30	5	5	NUM
ejpam-3399	29	31	and	and	CCONJ
ejpam-3399	29	32	n	n	PRON
ejpam-3399	29	33	≥	≥	NOUN
ejpam-3399	29	34	2	2	NUM
ejpam-3399	29	35	.	.	PUNCT
ejpam-3399	30	1	then	then	ADV
ejpam-3399	30	2	g	g	PROPN
ejpam-3399	30	3	satisfies	satisfy	VERB
ejpam-3399	30	4	the	the	DET
ejpam-3399	30	5	condition	condition	NOUN
ejpam-3399	30	6	of	of	ADP
ejpam-3399	30	7	the	the	DET
ejpam-3399	30	8	preceding	precede	VERB
ejpam-3399	30	9	conjecture	conjecture	NOUN
ejpam-3399	30	10	,	,	PUNCT
ejpam-3399	30	11	but	but	CCONJ
ejpam-3399	30	12	g	g	NOUN
ejpam-3399	30	13	is	be	AUX
ejpam-3399	30	14	not	not	PART
ejpam-3399	30	15	solvable	solvable	ADJ
ejpam-3399	30	16	.	.	PUNCT
ejpam-3399	31	1	in	in	ADP
ejpam-3399	31	2	2015	2015	NUM
ejpam-3399	31	3	,	,	PUNCT
ejpam-3399	31	4	hijazi	hijazi	PROPN
ejpam-3399	32	1	[	[	X
ejpam-3399	32	2	9	9	X
ejpam-3399	32	3	]	]	PUNCT
ejpam-3399	32	4	continued	continue	VERB
ejpam-3399	32	5	the	the	DET
ejpam-3399	32	6	above	above	ADV
ejpam-3399	32	7	mentioned	mention	VERB
ejpam-3399	32	8	investigations	investigation	NOUN
ejpam-3399	32	9	and	and	CCONJ
ejpam-3399	32	10	proved	prove	VERB
ejpam-3399	32	11	the	the	DET
ejpam-3399	32	12	following	following	NOUN
ejpam-3399	32	13	:	:	PUNCT
ejpam-3399	32	14	suppose	suppose	VERB
ejpam-3399	32	15	that	that	SCONJ
ejpam-3399	32	16	each	each	DET
ejpam-3399	32	17	sylow	sylow	NOUN
ejpam-3399	32	18	subgroup	subgroup	NOUN
ejpam-3399	32	19	p	p	PROPN
ejpam-3399	32	20	of	of	ADP
ejpam-3399	32	21	g	g	PROPN
ejpam-3399	32	22	has	have	VERB
ejpam-3399	32	23	a	a	DET
ejpam-3399	32	24	subgroup	subgroup	NOUN
ejpam-3399	32	25	d	d	NOUN
ejpam-3399	32	26	such	such	ADJ
ejpam-3399	32	27	that	that	SCONJ
ejpam-3399	32	28	1	1	NUM
ejpam-3399	32	29	<	<	X
ejpam-3399	32	30	|d|	|d|	PROPN
ejpam-3399	32	31	<	<	X
ejpam-3399	32	32	|p	|p	PROPN
ejpam-3399	33	1	|	|	ADV
ejpam-3399	33	2	and	and	CCONJ
ejpam-3399	33	3	all	all	DET
ejpam-3399	33	4	subgroups	subgroup	NOUN
ejpam-3399	33	5	h	h	VERB
ejpam-3399	33	6	of	of	ADP
ejpam-3399	33	7	p	p	NOUN
ejpam-3399	33	8	with	with	ADP
ejpam-3399	33	9	|h|	|h|	PROPN
ejpam-3399	33	10	=	=	SYM
ejpam-3399	33	11	|d|	|d|	PROPN
ejpam-3399	33	12	are	be	AUX
ejpam-3399	33	13	s	s	NOUN
ejpam-3399	33	14	-	-	NOUN
ejpam-3399	33	15	permutable	permutable	ADJ
ejpam-3399	33	16	in	in	ADP
ejpam-3399	33	17	g.	g.	PROPN
ejpam-3399	33	18	then	then	ADV
ejpam-3399	33	19	g	g	PROPN
ejpam-3399	33	20	is	be	AUX
ejpam-3399	33	21	solvable	solvable	ADJ
ejpam-3399	33	22	.	.	PUNCT
ejpam-3399	34	1	the	the	DET
ejpam-3399	34	2	main	main	ADJ
ejpam-3399	34	3	goal	goal	NOUN
ejpam-3399	34	4	of	of	ADP
ejpam-3399	34	5	this	this	DET
ejpam-3399	34	6	note	note	NOUN
ejpam-3399	34	7	is	be	AUX
ejpam-3399	34	8	to	to	PART
ejpam-3399	34	9	prove	prove	VERB
ejpam-3399	34	10	the	the	DET
ejpam-3399	34	11	following	follow	VERB
ejpam-3399	34	12	main	main	ADJ
ejpam-3399	34	13	theorem	theorem	NOUN
ejpam-3399	34	14	:	:	PUNCT
ejpam-3399	34	15	main	main	ADJ
ejpam-3399	34	16	theorem	theorem	NOUN
ejpam-3399	34	17	1	1	X
ejpam-3399	34	18	.	.	PUNCT
ejpam-3399	35	1	let	let	VERB
ejpam-3399	35	2	p	p	PRON
ejpam-3399	35	3	be	be	AUX
ejpam-3399	35	4	a	a	DET
ejpam-3399	35	5	sylow	sylow	NOUN
ejpam-3399	35	6	p	p	NOUN
ejpam-3399	35	7	-	-	PUNCT
ejpam-3399	35	8	subgroup	subgroup	NOUN
ejpam-3399	35	9	of	of	ADP
ejpam-3399	35	10	g	g	PROPN
ejpam-3399	35	11	(	(	PUNCT
ejpam-3399	35	12	p	p	X
ejpam-3399	35	13	>	>	X
ejpam-3399	35	14	2	2	NUM
ejpam-3399	35	15	)	)	PUNCT
ejpam-3399	35	16	.	.	PUNCT
ejpam-3399	36	1	suppose	suppose	VERB
ejpam-3399	36	2	that	that	SCONJ
ejpam-3399	36	3	p	p	PROPN
ejpam-3399	36	4	has	have	VERB
ejpam-3399	36	5	a	a	DET
ejpam-3399	36	6	subgroup	subgroup	NOUN
ejpam-3399	36	7	d	d	NOUN
ejpam-3399	36	8	such	such	ADJ
ejpam-3399	36	9	that	that	SCONJ
ejpam-3399	36	10	1	1	NUM
ejpam-3399	36	11	<	<	X
ejpam-3399	36	12	|d|	|d|	PROPN
ejpam-3399	36	13	<	<	X
ejpam-3399	36	14	|p	|p	PROPN
ejpam-3399	37	1	|	|	ADV
ejpam-3399	37	2	and	and	CCONJ
ejpam-3399	37	3	all	all	DET
ejpam-3399	37	4	subgroups	subgroup	NOUN
ejpam-3399	37	5	h	h	VERB
ejpam-3399	37	6	of	of	ADP
ejpam-3399	37	7	p	p	NOUN
ejpam-3399	37	8	with	with	ADP
ejpam-3399	37	9	|h|	|h|	PROPN
ejpam-3399	37	10	=	=	SYM
ejpam-3399	37	11	|d|	|d|	PROPN
ejpam-3399	37	12	are	be	AUX
ejpam-3399	37	13	s	s	NOUN
ejpam-3399	37	14	-	-	NOUN
ejpam-3399	37	15	permutable	permutable	ADJ
ejpam-3399	37	16	in	in	ADP
ejpam-3399	37	17	g.	g.	PROPN
ejpam-3399	37	18	then	then	ADV
ejpam-3399	37	19	g′	g′	PROPN
ejpam-3399	37	20	is	be	AUX
ejpam-3399	37	21	p	p	NOUN
ejpam-3399	37	22	-	-	PUNCT
ejpam-3399	37	23	nilpotent	nilpotent	ADJ
ejpam-3399	37	24	.	.	PUNCT
ejpam-3399	38	1	as	as	SCONJ
ejpam-3399	38	2	immediate	immediate	ADJ
ejpam-3399	38	3	consequences	consequence	NOUN
ejpam-3399	38	4	of	of	ADP
ejpam-3399	38	5	the	the	DET
ejpam-3399	38	6	main	main	ADJ
ejpam-3399	38	7	theorem	theorem	NOUN
ejpam-3399	38	8	we	we	PRON
ejpam-3399	38	9	have	have	VERB
ejpam-3399	38	10	:	:	PUNCT
ejpam-3399	38	11	corollary	corollary	ADJ
ejpam-3399	38	12	1	1	X
ejpam-3399	38	13	.	.	PUNCT
ejpam-3399	38	14	let	let	VERB
ejpam-3399	38	15	p	p	PRON
ejpam-3399	38	16	be	be	AUX
ejpam-3399	38	17	a	a	DET
ejpam-3399	38	18	sylow	sylow	NOUN
ejpam-3399	38	19	p	p	NOUN
ejpam-3399	38	20	-	-	PUNCT
ejpam-3399	38	21	subgroup	subgroup	NOUN
ejpam-3399	38	22	of	of	ADP
ejpam-3399	38	23	g	g	PROPN
ejpam-3399	38	24	(	(	PUNCT
ejpam-3399	38	25	p	p	X
ejpam-3399	38	26	>	>	X
ejpam-3399	38	27	2	2	NUM
ejpam-3399	38	28	)	)	PUNCT
ejpam-3399	38	29	.	.	PUNCT
ejpam-3399	39	1	suppose	suppose	VERB
ejpam-3399	39	2	that	that	SCONJ
ejpam-3399	39	3	p	p	PROPN
ejpam-3399	39	4	has	have	VERB
ejpam-3399	39	5	a	a	DET
ejpam-3399	39	6	subgroup	subgroup	NOUN
ejpam-3399	39	7	d	d	NOUN
ejpam-3399	39	8	such	such	ADJ
ejpam-3399	39	9	that	that	SCONJ
ejpam-3399	39	10	1	1	NUM
ejpam-3399	39	11	<	<	X
ejpam-3399	39	12	|d|	|d|	PROPN
ejpam-3399	39	13	<	<	X
ejpam-3399	39	14	|p	|p	PROPN
ejpam-3399	40	1	|	|	ADV
ejpam-3399	40	2	and	and	CCONJ
ejpam-3399	40	3	all	all	DET
ejpam-3399	40	4	subgroups	subgroup	NOUN
ejpam-3399	40	5	h	h	VERB
ejpam-3399	40	6	of	of	ADP
ejpam-3399	40	7	p	p	NOUN
ejpam-3399	40	8	with	with	ADP
ejpam-3399	40	9	|h|	|h|	PROPN
ejpam-3399	40	10	=	=	SYM
ejpam-3399	40	11	|d|	|d|	PROPN
ejpam-3399	40	12	are	be	AUX
ejpam-3399	40	13	permutable	permutable	ADJ
ejpam-3399	40	14	in	in	ADP
ejpam-3399	40	15	g.	g.	PROPN
ejpam-3399	40	16	then	then	ADV
ejpam-3399	40	17	g′	g′	PROPN
ejpam-3399	40	18	is	be	AUX
ejpam-3399	40	19	p	p	NOUN
ejpam-3399	40	20	-	-	PUNCT
ejpam-3399	40	21	nilpotent	nilpotent	ADJ
ejpam-3399	40	22	.	.	PUNCT
ejpam-3399	41	1	corollary	corollary	ADJ
ejpam-3399	41	2	2	2	NUM
ejpam-3399	41	3	(	(	PUNCT
ejpam-3399	41	4	[	[	X
ejpam-3399	41	5	9	9	NUM
ejpam-3399	41	6	]	]	PUNCT
ejpam-3399	41	7	,	,	PUNCT
ejpam-3399	41	8	theorem	theorem	VERB
ejpam-3399	41	9	3.1	3.1	NUM
ejpam-3399	41	10	)	)	PUNCT
ejpam-3399	41	11	.	.	PUNCT
ejpam-3399	42	1	suppose	suppose	VERB
ejpam-3399	42	2	that	that	SCONJ
ejpam-3399	42	3	each	each	DET
ejpam-3399	42	4	sylow	sylow	NOUN
ejpam-3399	42	5	subgroup	subgroup	NOUN
ejpam-3399	42	6	p	p	PROPN
ejpam-3399	42	7	of	of	ADP
ejpam-3399	42	8	g	g	PROPN
ejpam-3399	42	9	has	have	VERB
ejpam-3399	42	10	a	a	DET
ejpam-3399	42	11	subgroup	subgroup	NOUN
ejpam-3399	42	12	d	d	NOUN
ejpam-3399	42	13	such	such	ADJ
ejpam-3399	42	14	that	that	SCONJ
ejpam-3399	42	15	1	1	NUM
ejpam-3399	42	16	<	<	X
ejpam-3399	42	17	|d|	|d|	PROPN
ejpam-3399	42	18	<	<	X
ejpam-3399	42	19	|p	|p	PROPN
ejpam-3399	43	1	|	|	ADV
ejpam-3399	43	2	and	and	CCONJ
ejpam-3399	43	3	all	all	DET
ejpam-3399	43	4	subgroups	subgroup	NOUN
ejpam-3399	43	5	h	h	VERB
ejpam-3399	43	6	of	of	ADP
ejpam-3399	43	7	p	p	NOUN
ejpam-3399	43	8	with	with	ADP
ejpam-3399	43	9	|h|	|h|	PROPN
ejpam-3399	43	10	=	=	SYM
ejpam-3399	43	11	|d|	|d|	PROPN
ejpam-3399	43	12	are	be	AUX
ejpam-3399	43	13	s	s	NOUN
ejpam-3399	43	14	-	-	NOUN
ejpam-3399	43	15	permutable	permutable	ADJ
ejpam-3399	43	16	in	in	ADP
ejpam-3399	43	17	g.	g.	PROPN
ejpam-3399	43	18	then	then	ADV
ejpam-3399	43	19	g	g	PROPN
ejpam-3399	43	20	is	be	AUX
ejpam-3399	43	21	solvable	solvable	ADJ
ejpam-3399	43	22	.	.	PUNCT
ejpam-3399	44	1	corollary	corollary	ADJ
ejpam-3399	44	2	3	3	NUM
ejpam-3399	44	3	(	(	PUNCT
ejpam-3399	44	4	gaschűtz	gaschűtz	NOUN
ejpam-3399	44	5	and	and	CCONJ
ejpam-3399	44	6	itő	itő	NOUN
ejpam-3399	45	1	[	[	X
ejpam-3399	45	2	10	10	NUM
ejpam-3399	45	3	]	]	PUNCT
ejpam-3399	45	4	,	,	PUNCT
ejpam-3399	45	5	satz	satz	PROPN
ejpam-3399	45	6	5.7	5.7	NUM
ejpam-3399	45	7	,	,	PUNCT
ejpam-3399	45	8	p.436	p.436	NOUN
ejpam-3399	45	9	)	)	PUNCT
ejpam-3399	45	10	.	.	PUNCT
ejpam-3399	46	1	a	a	DET
ejpam-3399	46	2	group	group	NOUN
ejpam-3399	46	3	g	g	NOUN
ejpam-3399	46	4	is	be	AUX
ejpam-3399	46	5	solvable	solvable	ADJ
ejpam-3399	46	6	if	if	SCONJ
ejpam-3399	46	7	all	all	DET
ejpam-3399	46	8	its	its	PRON
ejpam-3399	46	9	minimal	minimal	ADJ
ejpam-3399	46	10	subgroups	subgroup	NOUN
ejpam-3399	46	11	are	be	AUX
ejpam-3399	46	12	normal	normal	ADJ
ejpam-3399	46	13	.	.	PUNCT
ejpam-3399	47	1	2	2	X
ejpam-3399	47	2	.	.	X
ejpam-3399	47	3	proofs	proof	NOUN
ejpam-3399	47	4	we	we	PRON
ejpam-3399	47	5	first	first	ADV
ejpam-3399	47	6	prove	prove	VERB
ejpam-3399	47	7	the	the	DET
ejpam-3399	47	8	following	follow	VERB
ejpam-3399	47	9	theorems	theorem	NOUN
ejpam-3399	47	10	:	:	PUNCT
ejpam-3399	47	11	theorem	theorem	NOUN
ejpam-3399	47	12	2	2	NUM
ejpam-3399	47	13	.	.	PUNCT
ejpam-3399	47	14	let	let	VERB
ejpam-3399	47	15	p	p	PRON
ejpam-3399	47	16	be	be	AUX
ejpam-3399	47	17	a	a	DET
ejpam-3399	47	18	sylow	sylow	NOUN
ejpam-3399	47	19	p	p	NOUN
ejpam-3399	47	20	-	-	PUNCT
ejpam-3399	47	21	subgroup	subgroup	NOUN
ejpam-3399	47	22	of	of	ADP
ejpam-3399	47	23	a	a	DET
ejpam-3399	47	24	group	group	NOUN
ejpam-3399	47	25	g	g	NOUN
ejpam-3399	47	26	,	,	PUNCT
ejpam-3399	47	27	where	where	SCONJ
ejpam-3399	47	28	p	p	NOUN
ejpam-3399	47	29	is	be	AUX
ejpam-3399	47	30	an	an	DET
ejpam-3399	47	31	odd	odd	ADJ
ejpam-3399	47	32	prime	prime	NOUN
ejpam-3399	47	33	.	.	PUNCT
ejpam-3399	48	1	if	if	SCONJ
ejpam-3399	48	2	each	each	DET
ejpam-3399	48	3	subgroup	subgroup	NOUN
ejpam-3399	48	4	of	of	ADP
ejpam-3399	48	5	p	p	NOUN
ejpam-3399	48	6	of	of	ADP
ejpam-3399	48	7	order	order	NOUN
ejpam-3399	48	8	p	p	NOUN
ejpam-3399	48	9	is	be	AUX
ejpam-3399	48	10	s	s	NOUN
ejpam-3399	48	11	-	-	NOUN
ejpam-3399	48	12	permutable	permutable	ADJ
ejpam-3399	48	13	in	in	ADP
ejpam-3399	48	14	g	g	PROPN
ejpam-3399	48	15	,	,	PUNCT
ejpam-3399	48	16	then	then	ADV
ejpam-3399	48	17	g′is	g′is	VERB
ejpam-3399	48	18	p	p	NOUN
ejpam-3399	48	19	-	-	PUNCT
ejpam-3399	48	20	nilpotent	nilpotent	ADJ
ejpam-3399	48	21	.	.	PUNCT
ejpam-3399	49	1	proof	proof	NOUN
ejpam-3399	49	2	.	.	PUNCT
ejpam-3399	50	1	we	we	PRON
ejpam-3399	50	2	prove	prove	VERB
ejpam-3399	50	3	the	the	DET
ejpam-3399	50	4	theorem	theorem	NOUN
ejpam-3399	50	5	by	by	ADP
ejpam-3399	50	6	induction	induction	NOUN
ejpam-3399	50	7	on	on	ADP
ejpam-3399	50	8	|g|	|g|	PROPN
ejpam-3399	50	9	.	.	PUNCT
ejpam-3399	51	1	hence	hence	ADV
ejpam-3399	51	2	if	if	SCONJ
ejpam-3399	51	3	each	each	DET
ejpam-3399	51	4	subgroup	subgroup	NOUN
ejpam-3399	51	5	of	of	ADP
ejpam-3399	51	6	p	p	NOUN
ejpam-3399	51	7	of	of	ADP
ejpam-3399	51	8	order	order	NOUN
ejpam-3399	51	9	p	p	NOUN
ejpam-3399	51	10	is	be	AUX
ejpam-3399	51	11	normal	normal	ADJ
ejpam-3399	51	12	in	in	ADP
ejpam-3399	51	13	g	g	PROPN
ejpam-3399	51	14	,	,	PUNCT
ejpam-3399	51	15	then	then	ADV
ejpam-3399	51	16	each	each	DET
ejpam-3399	51	17	subgroup	subgroup	NOUN
ejpam-3399	51	18	of	of	ADP
ejpam-3399	51	19	g	g	PROPN
ejpam-3399	51	20	′	′	NUM
ejpam-3399	51	21	of	of	ADP
ejpam-3399	51	22	order	order	NOUN
ejpam-3399	51	23	p	p	NOUN
ejpam-3399	51	24	is	be	AUX
ejpam-3399	51	25	normal	normal	ADJ
ejpam-3399	51	26	in	in	ADP
ejpam-3399	51	27	g′.	g′.	NOUN
ejpam-3399	51	28	let	let	VERB
ejpam-3399	51	29	l	l	NOUN
ejpam-3399	51	30	be	be	AUX
ejpam-3399	51	31	a	a	DET
ejpam-3399	51	32	r.	r.	PROPN
ejpam-3399	51	33	hijazi	hijazi	PROPN
ejpam-3399	51	34	,	,	PUNCT
ejpam-3399	51	35	f.	f.	PROPN
ejpam-3399	51	36	charaf	charaf	PROPN
ejpam-3399	51	37	/	/	SYM
ejpam-3399	51	38	eur	eur	PROPN
ejpam-3399	51	39	.	.	PUNCT
ejpam-3399	52	1	j.	j.	PROPN
ejpam-3399	52	2	pure	pure	PROPN
ejpam-3399	52	3	appl	appl	PROPN
ejpam-3399	52	4	.	.	PROPN
ejpam-3399	52	5	math	math	PROPN
ejpam-3399	52	6	,	,	PUNCT
ejpam-3399	52	7	12	12	NUM
ejpam-3399	52	8	(	(	PUNCT
ejpam-3399	52	9	2	2	NUM
ejpam-3399	52	10	)	)	PUNCT
ejpam-3399	52	11	(	(	PUNCT
ejpam-3399	52	12	2019	2019	NUM
ejpam-3399	52	13	)	)	PUNCT
ejpam-3399	52	14	,	,	PUNCT
ejpam-3399	52	15	571	571	NUM
ejpam-3399	52	16	-	-	SYM
ejpam-3399	52	17	576	576	NUM
ejpam-3399	52	18	573	573	NUM
ejpam-3399	52	19	subgroup	subgroup	NOUN
ejpam-3399	52	20	of	of	ADP
ejpam-3399	52	21	g′	g′	NOUN
ejpam-3399	52	22	such	such	ADJ
ejpam-3399	52	23	that	that	DET
ejpam-3399	52	24	|l|	|l|	NOUN
ejpam-3399	52	25	=	=	SYM
ejpam-3399	53	1	p.	p.	NOUN
ejpam-3399	53	2	then	then	ADV
ejpam-3399	53	3	g	g	NOUN
ejpam-3399	53	4	/	/	SYM
ejpam-3399	53	5	cg(l	cg(l	NOUN
ejpam-3399	53	6	)	)	PUNCT
ejpam-3399	53	7	⊆	⊆	NUM
ejpam-3399	53	8	aut(l	aut(l	PROPN
ejpam-3399	53	9	)	)	PUNCT
ejpam-3399	53	10	and	and	CCONJ
ejpam-3399	53	11	,	,	PUNCT
ejpam-3399	53	12	since	since	SCONJ
ejpam-3399	53	13	aut(l	aut(l	PROPN
ejpam-3399	53	14	)	)	PUNCT
ejpam-3399	53	15	is	be	AUX
ejpam-3399	53	16	cyclic	cyclic	ADJ
ejpam-3399	53	17	of	of	ADP
ejpam-3399	53	18	order	order	NOUN
ejpam-3399	53	19	p−	p−	NOUN
ejpam-3399	53	20	1	1	NUM
ejpam-3399	53	21	,	,	PUNCT
ejpam-3399	53	22	we	we	PRON
ejpam-3399	53	23	have	have	VERB
ejpam-3399	53	24	g	g	NOUN
ejpam-3399	53	25	/	/	SYM
ejpam-3399	53	26	cg(l	cg(l	NOUN
ejpam-3399	53	27	)	)	PUNCT
ejpam-3399	53	28	is	be	AUX
ejpam-3399	53	29	abelian	abelian	ADJ
ejpam-3399	53	30	.	.	PUNCT
ejpam-3399	54	1	thus	thus	ADV
ejpam-3399	54	2	g′	g′	NOUN
ejpam-3399	54	3	≤	≤	PROPN
ejpam-3399	54	4	cg(l	cg(l	NOUN
ejpam-3399	54	5	)	)	PUNCT
ejpam-3399	54	6	and	and	CCONJ
ejpam-3399	54	7	so	so	ADV
ejpam-3399	54	8	l	l	PROPN
ejpam-3399	54	9	≤	≤	NUM
ejpam-3399	54	10	z(g′	z(g′	NUM
ejpam-3399	54	11	)	)	PUNCT
ejpam-3399	54	12	.	.	PUNCT
ejpam-3399	55	1	by	by	ADP
ejpam-3399	55	2	(	(	PUNCT
ejpam-3399	55	3	[	[	X
ejpam-3399	55	4	10	10	NUM
ejpam-3399	55	5	]	]	PUNCT
ejpam-3399	55	6	,	,	PUNCT
ejpam-3399	55	7	satz	satz	PROPN
ejpam-3399	55	8	5.5(a	5.5(a	NUM
ejpam-3399	55	9	)	)	PUNCT
ejpam-3399	55	10	,	,	PUNCT
ejpam-3399	55	11	p.	p.	NOUN
ejpam-3399	55	12	435	435	NUM
ejpam-3399	55	13	)	)	PUNCT
ejpam-3399	55	14	,	,	PUNCT
ejpam-3399	55	15	g′is	g′is	X
ejpam-3399	55	16	p	p	NOUN
ejpam-3399	55	17	-	-	PUNCT
ejpam-3399	55	18	nilpotent	nilpotent	ADJ
ejpam-3399	55	19	.	.	PUNCT
ejpam-3399	56	1	thus	thus	ADV
ejpam-3399	56	2	we	we	PRON
ejpam-3399	56	3	may	may	AUX
ejpam-3399	56	4	assume	assume	VERB
ejpam-3399	56	5	that	that	SCONJ
ejpam-3399	56	6	there	there	PRON
ejpam-3399	56	7	exists	exist	VERB
ejpam-3399	56	8	a	a	DET
ejpam-3399	56	9	subgroup	subgroup	NOUN
ejpam-3399	56	10	h	h	NOUN
ejpam-3399	56	11	of	of	ADP
ejpam-3399	56	12	p	p	NOUN
ejpam-3399	56	13	of	of	ADP
ejpam-3399	56	14	order	order	NOUN
ejpam-3399	56	15	p	p	NOUN
ejpam-3399	56	16	such	such	ADJ
ejpam-3399	56	17	that	that	DET
ejpam-3399	56	18	h	h	NOUN
ejpam-3399	56	19	is	be	AUX
ejpam-3399	56	20	not	not	PART
ejpam-3399	56	21	normal	normal	ADJ
ejpam-3399	56	22	in	in	ADP
ejpam-3399	56	23	g.	g.	PROPN
ejpam-3399	56	24	by	by	ADP
ejpam-3399	56	25	the	the	DET
ejpam-3399	56	26	hypothesis	hypothesis	NOUN
ejpam-3399	56	27	,	,	PUNCT
ejpam-3399	56	28	h	h	PROPN
ejpam-3399	56	29	is	be	AUX
ejpam-3399	56	30	s	s	NOUN
ejpam-3399	56	31	-	-	NOUN
ejpam-3399	56	32	permutable	permutable	ADJ
ejpam-3399	56	33	in	in	ADP
ejpam-3399	56	34	g	g	NOUN
ejpam-3399	56	35	and	and	CCONJ
ejpam-3399	56	36	hence	hence	ADV
ejpam-3399	56	37	by	by	ADP
ejpam-3399	56	38	(	(	PUNCT
ejpam-3399	56	39	[	[	X
ejpam-3399	56	40	13	13	NUM
ejpam-3399	56	41	]	]	PUNCT
ejpam-3399	56	42	,	,	PUNCT
ejpam-3399	56	43	lemma	lemma	PROPN
ejpam-3399	56	44	a	a	PRON
ejpam-3399	56	45	)	)	PUNCT
ejpam-3399	56	46	,	,	PUNCT
ejpam-3399	56	47	op(g	op(g	NUM
ejpam-3399	56	48	)	)	PUNCT
ejpam-3399	56	49	≤	≤	NOUN
ejpam-3399	57	1	ng(h	ng(h	ADV
ejpam-3399	57	2	)	)	PUNCT
ejpam-3399	57	3	<	<	X
ejpam-3399	57	4	g.	g.	PROPN
ejpam-3399	57	5	let	let	VERB
ejpam-3399	57	6	m	m	PRON
ejpam-3399	57	7	be	be	AUX
ejpam-3399	57	8	a	a	DET
ejpam-3399	57	9	maximal	maximal	ADJ
ejpam-3399	57	10	subgroup	subgroup	NOUN
ejpam-3399	57	11	of	of	ADP
ejpam-3399	57	12	g	g	PROPN
ejpam-3399	57	13	such	such	ADJ
ejpam-3399	57	14	that	that	PRON
ejpam-3399	57	15	ng(h	ng(h	NOUN
ejpam-3399	57	16	)	)	PUNCT
ejpam-3399	57	17	≤m	≤m	NOUN
ejpam-3399	57	18	<	<	X
ejpam-3399	57	19	g.	g.	PROPN
ejpam-3399	58	1	then	then	ADV
ejpam-3399	58	2	m	m	VERB
ejpam-3399	58	3	cg	cg	NOUN
ejpam-3399	59	1	and	and	CCONJ
ejpam-3399	59	2	|	|	ADV
ejpam-3399	59	3	g	g	NOUN
ejpam-3399	59	4	/	/	SYM
ejpam-3399	59	5	m	m	VERB
ejpam-3399	59	6	|=	|=	NOUN
ejpam-3399	59	7	p.	p.	VERB
ejpam-3399	59	8	by	by	ADP
ejpam-3399	59	9	induction	induction	NOUN
ejpam-3399	59	10	on	on	ADP
ejpam-3399	59	11	|g|	|g|	PROPN
ejpam-3399	59	12	,	,	PUNCT
ejpam-3399	59	13	m	m	VERB
ejpam-3399	59	14	′	′	NOUN
ejpam-3399	59	15	is	be	AUX
ejpam-3399	59	16	p	p	NOUN
ejpam-3399	59	17	-	-	PUNCT
ejpam-3399	59	18	nilpotent	nilpotent	ADJ
ejpam-3399	59	19	.	.	PUNCT
ejpam-3399	60	1	hence	hence	ADV
ejpam-3399	60	2	if	if	SCONJ
ejpam-3399	60	3	op′(g	op′(g	PROPN
ejpam-3399	60	4	)	)	PUNCT
ejpam-3399	61	1	6=	6=	ADP
ejpam-3399	61	2	1	1	NUM
ejpam-3399	61	3	,	,	PUNCT
ejpam-3399	61	4	g/	g/	NOUN
ejpam-3399	61	5	op′(g	op′(g	PROPN
ejpam-3399	61	6	)	)	PUNCT
ejpam-3399	61	7	satisfies	satisfy	VERB
ejpam-3399	61	8	the	the	DET
ejpam-3399	61	9	hypothesis	hypothesis	NOUN
ejpam-3399	61	10	of	of	ADP
ejpam-3399	61	11	the	the	DET
ejpam-3399	61	12	theorem	theorem	NOUN
ejpam-3399	61	13	and	and	CCONJ
ejpam-3399	61	14	so	so	ADV
ejpam-3399	61	15	(	(	PUNCT
ejpam-3399	61	16	g/	g/	NOUN
ejpam-3399	61	17	op′(g))′	op′(g))′	PROPN
ejpam-3399	61	18	=	=	SYM
ejpam-3399	61	19	g′op′(g)/op′(g	g′op′(g)/op′(g	PROPN
ejpam-3399	61	20	)	)	PUNCT
ejpam-3399	61	21	∼=	∼=	PROPN
ejpam-3399	61	22	g′/(g8	g′/(g8	PROPN
ejpam-3399	61	23	∩op′(g	∩op′(g	NUM
ejpam-3399	61	24	)	)	PUNCT
ejpam-3399	61	25	)	)	PUNCT
ejpam-3399	61	26	is	be	AUX
ejpam-3399	61	27	p	p	NOUN
ejpam-3399	61	28	-	-	PUNCT
ejpam-3399	61	29	nilpotent	nilpotent	NOUN
ejpam-3399	61	30	which	which	PRON
ejpam-3399	61	31	implies	imply	VERB
ejpam-3399	61	32	that	that	SCONJ
ejpam-3399	61	33	g′is	g′is	X
ejpam-3399	61	34	p	p	X
ejpam-3399	61	35	-	-	PUNCT
ejpam-3399	61	36	nilpotent	nilpotent	ADJ
ejpam-3399	61	37	.	.	PUNCT
ejpam-3399	62	1	thus	thus	ADV
ejpam-3399	62	2	assume	assume	VERB
ejpam-3399	62	3	that	that	SCONJ
ejpam-3399	62	4	op′(g	op′(g	PROPN
ejpam-3399	62	5	)	)	PUNCT
ejpam-3399	62	6	=	=	PUNCT
ejpam-3399	63	1	1	1	X
ejpam-3399	63	2	.	.	PUNCT
ejpam-3399	63	3	since	since	SCONJ
ejpam-3399	63	4	m	m	PROPN
ejpam-3399	63	5	′	′	NUM
ejpam-3399	63	6	char	char	NOUN
ejpam-3399	63	7	m	m	PROPN
ejpam-3399	63	8	and	and	CCONJ
ejpam-3399	63	9	m	m	PROPN
ejpam-3399	63	10	cg	cg	NOUN
ejpam-3399	63	11	,	,	PUNCT
ejpam-3399	63	12	we	we	PRON
ejpam-3399	63	13	have	have	VERB
ejpam-3399	63	14	m	m	NOUN
ejpam-3399	63	15	′	′	NUM
ejpam-3399	63	16	c	c	PROPN
ejpam-3399	63	17	g.	g.	PROPN
ejpam-3399	63	18	as	as	SCONJ
ejpam-3399	63	19	m	m	PROPN
ejpam-3399	63	20	′	′	NUM
ejpam-3399	63	21	is	be	AUX
ejpam-3399	63	22	p	p	NOUN
ejpam-3399	63	23	-	-	PUNCT
ejpam-3399	63	24	nilpotent	nilpotent	NOUN
ejpam-3399	63	25	and	and	CCONJ
ejpam-3399	63	26	op′(g	op′(g	PROPN
ejpam-3399	63	27	)	)	PUNCT
ejpam-3399	64	1	=	=	SYM
ejpam-3399	64	2	1	1	NUM
ejpam-3399	64	3	,	,	PUNCT
ejpam-3399	64	4	we	we	PRON
ejpam-3399	64	5	have	have	AUX
ejpam-3399	64	6	m	m	VERB
ejpam-3399	64	7	′	′	NUM
ejpam-3399	64	8	is	be	AUX
ejpam-3399	64	9	a	a	DET
ejpam-3399	64	10	p	p	NOUN
ejpam-3399	64	11	-	-	PUNCT
ejpam-3399	64	12	group	group	NOUN
ejpam-3399	64	13	.	.	PUNCT
ejpam-3399	65	1	then	then	ADV
ejpam-3399	65	2	p1	p1	PROPN
ejpam-3399	65	3	cm	cm	PROPN
ejpam-3399	65	4	where	where	SCONJ
ejpam-3399	65	5	p1	p1	PROPN
ejpam-3399	65	6	is	be	AUX
ejpam-3399	65	7	a	a	DET
ejpam-3399	65	8	sylow	sylow	NOUN
ejpam-3399	65	9	p	p	NOUN
ejpam-3399	65	10	-	-	PUNCT
ejpam-3399	65	11	subgroup	subgroup	NOUN
ejpam-3399	65	12	of	of	ADP
ejpam-3399	65	13	m	m	PROPN
ejpam-3399	65	14	.	.	PUNCT
ejpam-3399	66	1	by	by	ADP
ejpam-3399	66	2	schur	schur	NOUN
ejpam-3399	66	3	-	-	PUNCT
ejpam-3399	66	4	zassenhaus	zassenhaus	NOUN
ejpam-3399	66	5	theorem	theorem	NOUN
ejpam-3399	66	6	[	[	X
ejpam-3399	66	7	5	5	NUM
ejpam-3399	66	8	,	,	PUNCT
ejpam-3399	66	9	theorem	theorem	VERB
ejpam-3399	66	10	6.2.1	6.2.1	NOUN
ejpam-3399	66	11	,	,	PUNCT
ejpam-3399	66	12	p.	p.	NOUN
ejpam-3399	66	13	221	221	NUM
ejpam-3399	67	1	]	]	PUNCT
ejpam-3399	67	2	,	,	PUNCT
ejpam-3399	67	3	m	m	VERB
ejpam-3399	67	4	=	=	ADJ
ejpam-3399	67	5	p1k	p1k	PROPN
ejpam-3399	67	6	,	,	PUNCT
ejpam-3399	67	7	where	where	SCONJ
ejpam-3399	67	8	k	k	PROPN
ejpam-3399	67	9	is	be	AUX
ejpam-3399	67	10	a	a	DET
ejpam-3399	67	11	p′-hall	p′-hall	NUM
ejpam-3399	67	12	subgroup	subgroup	NOUN
ejpam-3399	67	13	of	of	ADP
ejpam-3399	67	14	m	m	PROPN
ejpam-3399	67	15	.	.	PUNCT
ejpam-3399	68	1	hence	hence	ADV
ejpam-3399	68	2	if	if	SCONJ
ejpam-3399	68	3	cg(p1	cg(p1	NOUN
ejpam-3399	68	4	)	)	PUNCT
ejpam-3399	68	5	≤	≤	NOUN
ejpam-3399	68	6	p1	p1	PROPN
ejpam-3399	68	7	,	,	PUNCT
ejpam-3399	68	8	k	k	PROPN
ejpam-3399	68	9	is	be	AUX
ejpam-3399	68	10	a	a	DET
ejpam-3399	68	11	p′-group	p′-group	PROPN
ejpam-3399	68	12	of	of	ADP
ejpam-3399	68	13	automorphisms	automorphism	NOUN
ejpam-3399	68	14	of	of	ADP
ejpam-3399	68	15	p1	p1	PROPN
ejpam-3399	68	16	,	,	PUNCT
ejpam-3399	68	17	and	and	CCONJ
ejpam-3399	68	18	since	since	SCONJ
ejpam-3399	68	19	k	k	PROPN
ejpam-3399	68	20	leaves	leave	VERB
ejpam-3399	68	21	each	each	DET
ejpam-3399	68	22	subgroup	subgroup	NOUN
ejpam-3399	68	23	of	of	ADP
ejpam-3399	68	24	p1	p1	PROPN
ejpam-3399	68	25	invariant	invariant	ADJ
ejpam-3399	68	26	because	because	SCONJ
ejpam-3399	68	27	every	every	DET
ejpam-3399	68	28	subgroup	subgroup	NOUN
ejpam-3399	68	29	of	of	ADP
ejpam-3399	68	30	p	p	NOUN
ejpam-3399	68	31	of	of	ADP
ejpam-3399	68	32	prime	prime	ADJ
ejpam-3399	68	33	order	order	NOUN
ejpam-3399	68	34	is	be	AUX
ejpam-3399	68	35	s	s	NOUN
ejpam-3399	68	36	-	-	ADJ
ejpam-3399	68	37	permutable	permutable	ADJ
ejpam-3399	68	38	,	,	PUNCT
ejpam-3399	68	39	then	then	ADV
ejpam-3399	68	40	by	by	ADP
ejpam-3399	68	41	(	(	PUNCT
ejpam-3399	68	42	[	[	X
ejpam-3399	68	43	14	14	NUM
ejpam-3399	68	44	]	]	X
ejpam-3399	68	45	,	,	PUNCT
ejpam-3399	68	46	lemma	lemma	PROPN
ejpam-3399	68	47	2.20	2.20	NUM
ejpam-3399	68	48	)	)	PUNCT
ejpam-3399	68	49	,	,	PUNCT
ejpam-3399	68	50	k	k	PROPN
ejpam-3399	68	51	is	be	AUX
ejpam-3399	68	52	cyclic	cyclic	ADJ
ejpam-3399	68	53	.	.	PUNCT
ejpam-3399	69	1	let	let	VERB
ejpam-3399	69	2	q	q	PRON
ejpam-3399	69	3	be	be	AUX
ejpam-3399	69	4	a	a	DET
ejpam-3399	69	5	sylow	sylow	NOUN
ejpam-3399	69	6	q	q	NOUN
ejpam-3399	69	7	-	-	NOUN
ejpam-3399	69	8	subgroup	subgroup	NOUN
ejpam-3399	69	9	of	of	ADP
ejpam-3399	69	10	k	k	NOUN
ejpam-3399	69	11	,	,	PUNCT
ejpam-3399	69	12	where	where	SCONJ
ejpam-3399	69	13	q	q	NOUN
ejpam-3399	69	14	is	be	AUX
ejpam-3399	69	15	a	a	DET
ejpam-3399	69	16	prime	prime	ADJ
ejpam-3399	69	17	divisor	divisor	NOUN
ejpam-3399	69	18	of	of	ADP
ejpam-3399	69	19	the	the	DET
ejpam-3399	69	20	order	order	NOUN
ejpam-3399	69	21	of	of	ADP
ejpam-3399	69	22	k.	k.	NOUN
ejpam-3399	70	1	hence	hence	ADV
ejpam-3399	70	2	if	if	SCONJ
ejpam-3399	70	3	p	p	X
ejpam-3399	70	4	<	<	X
ejpam-3399	70	5	q	q	X
ejpam-3399	70	6	,	,	PUNCT
ejpam-3399	70	7	then	then	ADV
ejpam-3399	70	8	p1q	p1q	PROPN
ejpam-3399	70	9	=	=	PUNCT
ejpam-3399	70	10	p1×q	p1×q	PROPN
ejpam-3399	70	11	and	and	CCONJ
ejpam-3399	70	12	this	this	PRON
ejpam-3399	70	13	means	mean	VERB
ejpam-3399	70	14	that	that	SCONJ
ejpam-3399	70	15	q	q	PROPN
ejpam-3399	70	16	≤	≤	PROPN
ejpam-3399	70	17	cg(p1	cg(p1	NOUN
ejpam-3399	70	18	)	)	PUNCT
ejpam-3399	70	19	,	,	PUNCT
ejpam-3399	70	20	a	a	DET
ejpam-3399	70	21	contradiction	contradiction	NOUN
ejpam-3399	70	22	.	.	PUNCT
ejpam-3399	71	1	thus	thus	ADV
ejpam-3399	71	2	p	p	X
ejpam-3399	71	3	is	be	AUX
ejpam-3399	71	4	the	the	DET
ejpam-3399	71	5	largest	large	ADJ
ejpam-3399	71	6	prime	prime	ADJ
ejpam-3399	71	7	dividing	dividing	NOUN
ejpam-3399	71	8	|g|	|g|	PROPN
ejpam-3399	71	9	and	and	CCONJ
ejpam-3399	71	10	since	since	SCONJ
ejpam-3399	71	11	k	k	PROPN
ejpam-3399	71	12	is	be	AUX
ejpam-3399	71	13	cyclic	cyclic	ADJ
ejpam-3399	71	14	,	,	PUNCT
ejpam-3399	71	15	it	it	PRON
ejpam-3399	71	16	follows	follow	VERB
ejpam-3399	71	17	,	,	PUNCT
ejpam-3399	71	18	by	by	ADP
ejpam-3399	71	19	burnside′s	burnside′s	NOUN
ejpam-3399	71	20	p	p	NOUN
ejpam-3399	71	21	-	-	PUNCT
ejpam-3399	71	22	nilpotent	nilpotent	NOUN
ejpam-3399	71	23	theorem	theorem	NOUN
ejpam-3399	71	24	(	(	PUNCT
ejpam-3399	71	25	[	[	X
ejpam-3399	71	26	10	10	NUM
ejpam-3399	71	27	]	]	PUNCT
ejpam-3399	71	28	,	,	PUNCT
ejpam-3399	71	29	satz	satz	PROPN
ejpam-3399	71	30	2.8	2.8	NUM
ejpam-3399	71	31	,	,	PUNCT
ejpam-3399	71	32	p.420	p.420	NOUN
ejpam-3399	71	33	)	)	PUNCT
ejpam-3399	71	34	,	,	PUNCT
ejpam-3399	72	1	that	that	SCONJ
ejpam-3399	72	2	p	p	PROPN
ejpam-3399	72	3	c	c	X
ejpam-3399	72	4	g.	g.	PROPN
ejpam-3399	73	1	but	but	CCONJ
ejpam-3399	73	2	g	g	NOUN
ejpam-3399	73	3	/	/	SYM
ejpam-3399	73	4	p	p	NOUN
ejpam-3399	73	5	∼=	∼=	PROPN
ejpam-3399	73	6	k	k	NOUN
ejpam-3399	73	7	,	,	PUNCT
ejpam-3399	73	8	therefore	therefore	ADV
ejpam-3399	73	9	g	g	PROPN
ejpam-3399	73	10	/	/	SYM
ejpam-3399	73	11	p	p	NOUN
ejpam-3399	73	12	is	be	AUX
ejpam-3399	73	13	cyclic	cyclic	ADJ
ejpam-3399	73	14	and	and	CCONJ
ejpam-3399	73	15	so	so	ADV
ejpam-3399	73	16	abelian	abelian	ADJ
ejpam-3399	73	17	,	,	PUNCT
ejpam-3399	73	18	then	then	ADV
ejpam-3399	73	19	g′	g′	NOUN
ejpam-3399	73	20	≤	≤	PROPN
ejpam-3399	73	21	p	p	NOUN
ejpam-3399	73	22	.	.	PUNCT
ejpam-3399	74	1	this	this	PRON
ejpam-3399	74	2	completes	complete	VERB
ejpam-3399	74	3	the	the	DET
ejpam-3399	74	4	proof	proof	NOUN
ejpam-3399	74	5	of	of	ADP
ejpam-3399	74	6	the	the	DET
ejpam-3399	74	7	theorem	theorem	NOUN
ejpam-3399	74	8	.	.	PROPN
ejpam-3399	75	1	as	as	ADP
ejpam-3399	75	2	a	a	DET
ejpam-3399	75	3	corollary	corollary	NOUN
ejpam-3399	75	4	of	of	ADP
ejpam-3399	75	5	theorem	theorem	ADJ
ejpam-3399	75	6	2.1	2.1	NUM
ejpam-3399	75	7	:	:	PUNCT
ejpam-3399	75	8	corollary	corollary	ADJ
ejpam-3399	75	9	4	4	NUM
ejpam-3399	75	10	.	.	PUNCT
ejpam-3399	76	1	if	if	SCONJ
ejpam-3399	76	2	each	each	DET
ejpam-3399	76	3	subgroup	subgroup	NOUN
ejpam-3399	76	4	of	of	ADP
ejpam-3399	76	5	prime	prime	ADJ
ejpam-3399	76	6	order	order	NOUN
ejpam-3399	76	7	of	of	ADP
ejpam-3399	76	8	g	g	PROPN
ejpam-3399	76	9	is	be	AUX
ejpam-3399	76	10	s	s	NOUN
ejpam-3399	76	11	-	-	NOUN
ejpam-3399	76	12	permutable	permutable	ADJ
ejpam-3399	76	13	in	in	ADP
ejpam-3399	76	14	g	g	PROPN
ejpam-3399	76	15	,	,	PUNCT
ejpam-3399	76	16	then	then	ADV
ejpam-3399	76	17	g	g	PROPN
ejpam-3399	76	18	is	be	AUX
ejpam-3399	76	19	solvable	solvable	ADJ
ejpam-3399	76	20	,	,	PUNCT
ejpam-3399	76	21	s	s	PART
ejpam-3399	76	22	cg′and	cg′and	CCONJ
ejpam-3399	76	23	g′/s	g′/s	NOUN
ejpam-3399	76	24	is	be	AUX
ejpam-3399	76	25	nilpotent	nilpotent	ADJ
ejpam-3399	76	26	,	,	PUNCT
ejpam-3399	76	27	where	where	SCONJ
ejpam-3399	76	28	s	s	NOUN
ejpam-3399	76	29	is	be	AUX
ejpam-3399	76	30	a	a	DET
ejpam-3399	76	31	sylow	sylow	NOUN
ejpam-3399	76	32	2	2	NUM
ejpam-3399	76	33	-	-	PUNCT
ejpam-3399	76	34	subgroup	subgroup	NOUN
ejpam-3399	76	35	of	of	ADP
ejpam-3399	76	36	g′.	g′.	NOUN
ejpam-3399	76	37	proof	proof	NOUN
ejpam-3399	76	38	.	.	PUNCT
ejpam-3399	77	1	by	by	ADP
ejpam-3399	77	2	theorem	theorem	NOUN
ejpam-3399	77	3	2.1	2.1	NUM
ejpam-3399	77	4	,	,	PUNCT
ejpam-3399	77	5	g′	g′	NOUN
ejpam-3399	77	6	is	be	AUX
ejpam-3399	77	7	p	p	NOUN
ejpam-3399	77	8	-	-	PUNCT
ejpam-3399	77	9	nilpotent	nilpotent	ADJ
ejpam-3399	77	10	for	for	ADP
ejpam-3399	77	11	each	each	DET
ejpam-3399	77	12	odd	odd	ADJ
ejpam-3399	77	13	prime	prime	ADJ
ejpam-3399	77	14	p	p	NOUN
ejpam-3399	77	15	dividing	divide	VERB
ejpam-3399	77	16	|g|	|g|	ADJ
ejpam-3399	77	17	.	.	PUNCT
ejpam-3399	78	1	so	so	ADV
ejpam-3399	78	2	g′	g′	NOUN
ejpam-3399	78	3	/s	/s	PUNCT
ejpam-3399	78	4	is	be	AUX
ejpam-3399	78	5	nilpotent	nilpotent	ADJ
ejpam-3399	78	6	,	,	PUNCT
ejpam-3399	78	7	s	s	X
ejpam-3399	78	8	is	be	AUX
ejpam-3399	78	9	a	a	DET
ejpam-3399	78	10	sylow	sylow	NOUN
ejpam-3399	78	11	2	2	NUM
ejpam-3399	78	12	-	-	PUNCT
ejpam-3399	78	13	subgroup	subgroup	NOUN
ejpam-3399	78	14	of	of	ADP
ejpam-3399	78	15	g′and	g′and	PROPN
ejpam-3399	78	16	hence	hence	ADV
ejpam-3399	78	17	g	g	PROPN
ejpam-3399	78	18	is	be	AUX
ejpam-3399	78	19	solvable	solvable	ADJ
ejpam-3399	78	20	.	.	PUNCT
ejpam-3399	79	1	theorem	theorem	NOUN
ejpam-3399	79	2	3	3	X
ejpam-3399	79	3	.	.	PUNCT
ejpam-3399	80	1	let	let	VERB
ejpam-3399	80	2	p	p	PRON
ejpam-3399	80	3	be	be	AUX
ejpam-3399	80	4	an	an	DET
ejpam-3399	80	5	odd	odd	ADJ
ejpam-3399	80	6	prime	prime	NOUN
ejpam-3399	80	7	and	and	CCONJ
ejpam-3399	80	8	let	let	VERB
ejpam-3399	80	9	p	p	PRON
ejpam-3399	80	10	be	be	AUX
ejpam-3399	80	11	a	a	DET
ejpam-3399	80	12	sylow	sylow	NOUN
ejpam-3399	80	13	p	p	NOUN
ejpam-3399	80	14	-	-	PUNCT
ejpam-3399	80	15	subgroup	subgroup	NOUN
ejpam-3399	80	16	of	of	ADP
ejpam-3399	80	17	g.	g.	PROPN
ejpam-3399	80	18	suppose	suppose	VERB
ejpam-3399	80	19	that	that	SCONJ
ejpam-3399	80	20	p	p	PROPN
ejpam-3399	80	21	has	have	VERB
ejpam-3399	80	22	a	a	DET
ejpam-3399	80	23	subgroup	subgroup	NOUN
ejpam-3399	80	24	d	d	NOUN
ejpam-3399	80	25	such	such	ADJ
ejpam-3399	80	26	that	that	SCONJ
ejpam-3399	80	27	1	1	NUM
ejpam-3399	80	28	<	<	X
ejpam-3399	80	29	|d|	|d|	PROPN
ejpam-3399	80	30	<	<	X
ejpam-3399	80	31	|p	|p	PROPN
ejpam-3399	81	1	|	|	ADV
ejpam-3399	81	2	and	and	CCONJ
ejpam-3399	81	3	all	all	DET
ejpam-3399	81	4	subgroups	subgroup	NOUN
ejpam-3399	81	5	h	h	VERB
ejpam-3399	81	6	of	of	ADP
ejpam-3399	81	7	p	p	NOUN
ejpam-3399	81	8	with	with	ADP
ejpam-3399	81	9	|h|	|h|	PROPN
ejpam-3399	81	10	=	=	SYM
ejpam-3399	81	11	|d|	|d|	PROPN
ejpam-3399	81	12	are	be	AUX
ejpam-3399	81	13	normal	normal	ADJ
ejpam-3399	81	14	in	in	ADP
ejpam-3399	81	15	g.	g.	PROPN
ejpam-3399	81	16	then	then	ADV
ejpam-3399	81	17	g′is	g′is	VERB
ejpam-3399	81	18	p	p	NOUN
ejpam-3399	81	19	-	-	PUNCT
ejpam-3399	81	20	nilpotent	nilpotent	ADJ
ejpam-3399	81	21	.	.	PUNCT
ejpam-3399	82	1	proof	proof	NOUN
ejpam-3399	82	2	.	.	PUNCT
ejpam-3399	83	1	we	we	PRON
ejpam-3399	83	2	prove	prove	VERB
ejpam-3399	83	3	the	the	DET
ejpam-3399	83	4	theorem	theorem	NOUN
ejpam-3399	83	5	by	by	ADP
ejpam-3399	83	6	induction	induction	NOUN
ejpam-3399	83	7	on	on	ADP
ejpam-3399	83	8	|g|	|g|	PROPN
ejpam-3399	83	9	.	.	PUNCT
ejpam-3399	84	1	clearly	clearly	ADV
ejpam-3399	84	2	,	,	PUNCT
ejpam-3399	84	3	p∩g′	p∩g′	PROPN
ejpam-3399	84	4	is	be	AUX
ejpam-3399	84	5	a	a	DET
ejpam-3399	84	6	sylow	sylow	NOUN
ejpam-3399	84	7	p	p	NOUN
ejpam-3399	84	8	-	-	PUNCT
ejpam-3399	84	9	subgroup	subgroup	NOUN
ejpam-3399	84	10	of	of	ADP
ejpam-3399	84	11	g′.	g′.	NOUN
ejpam-3399	84	12	set	set	VERB
ejpam-3399	84	13	p1	p1	NOUN
ejpam-3399	84	14	=	=	PUNCT
ejpam-3399	85	1	p	p	NOUN
ejpam-3399	85	2	∩g′.	∩g′.	NOUN
ejpam-3399	85	3	we	we	PRON
ejpam-3399	85	4	deal	deal	VERB
ejpam-3399	85	5	with	with	ADP
ejpam-3399	85	6	the	the	DET
ejpam-3399	85	7	following	follow	VERB
ejpam-3399	85	8	two	two	NUM
ejpam-3399	85	9	cases	case	NOUN
ejpam-3399	85	10	:	:	PUNCT
ejpam-3399	85	11	case	case	NOUN
ejpam-3399	85	12	1	1	NUM
ejpam-3399	85	13	.	.	X
ejpam-3399	85	14	|p1|	|p1|	PROPN
ejpam-3399	85	15	≤	≤	ADJ
ejpam-3399	85	16	|d|	|d|	PROPN
ejpam-3399	85	17	.	.	PUNCT
ejpam-3399	86	1	hence	hence	ADV
ejpam-3399	86	2	if	if	SCONJ
ejpam-3399	86	3	|d|	|d|	PROPN
ejpam-3399	86	4	=	=	SYM
ejpam-3399	86	5	p	p	PROPN
ejpam-3399	86	6	,	,	PUNCT
ejpam-3399	86	7	|p1|	|p1|	NOUN
ejpam-3399	86	8	=	=	PROPN
ejpam-3399	86	9	p	p	X
ejpam-3399	86	10	,	,	PUNCT
ejpam-3399	86	11	and	and	CCONJ
ejpam-3399	86	12	p1	p1	PROPN
ejpam-3399	86	13	c	c	PROPN
ejpam-3399	86	14	g.	g.	PROPN
ejpam-3399	86	15	then	then	ADV
ejpam-3399	86	16	g′	g′	PROPN
ejpam-3399	86	17	≤	≤	PROPN
ejpam-3399	86	18	cg(p1	cg(p1	NOUN
ejpam-3399	86	19	)	)	PUNCT
ejpam-3399	86	20	and	and	CCONJ
ejpam-3399	86	21	so	so	ADV
ejpam-3399	86	22	p1	p1	PROPN
ejpam-3399	86	23	≤	≤	NUM
ejpam-3399	86	24	z(g′	z(g′	NUM
ejpam-3399	86	25	)	)	PUNCT
ejpam-3399	86	26	.	.	PUNCT
ejpam-3399	87	1	hence	hence	ADV
ejpam-3399	87	2	,	,	PUNCT
ejpam-3399	87	3	by	by	ADP
ejpam-3399	87	4	schur	schur	NOUN
ejpam-3399	87	5	-	-	PUNCT
ejpam-3399	87	6	zassenhaus	zassenhaus	NOUN
ejpam-3399	87	7	theorem	theorem	NOUN
ejpam-3399	87	8	,	,	PUNCT
ejpam-3399	87	9	g′	g′	NOUN
ejpam-3399	87	10	=	=	SYM
ejpam-3399	87	11	p1	p1	PROPN
ejpam-3399	87	12	×k	×k	NOUN
ejpam-3399	87	13	,	,	PUNCT
ejpam-3399	87	14	where	where	SCONJ
ejpam-3399	87	15	k	k	PROPN
ejpam-3399	87	16	is	be	AUX
ejpam-3399	87	17	a	a	DET
ejpam-3399	87	18	p′-hall	p′-hall	NUM
ejpam-3399	87	19	subgroup	subgroup	NOUN
ejpam-3399	87	20	of	of	ADP
ejpam-3399	87	21	g′.	g′.	NOUN
ejpam-3399	87	22	in	in	ADP
ejpam-3399	87	23	particular	particular	ADJ
ejpam-3399	87	24	,	,	PUNCT
ejpam-3399	87	25	g′	g′	NOUN
ejpam-3399	87	26	is	be	AUX
ejpam-3399	87	27	p	p	NOUN
ejpam-3399	87	28	-	-	PUNCT
ejpam-3399	87	29	nilpotent	nilpotent	ADJ
ejpam-3399	87	30	.	.	PUNCT
ejpam-3399	88	1	thus	thus	ADV
ejpam-3399	88	2	we	we	PRON
ejpam-3399	88	3	may	may	AUX
ejpam-3399	88	4	assume	assume	VERB
ejpam-3399	88	5	that	that	SCONJ
ejpam-3399	88	6	|d|	|d|	PROPN
ejpam-3399	88	7	=	=	SYM
ejpam-3399	88	8	pn	pn	PROPN
ejpam-3399	88	9	(	(	PUNCT
ejpam-3399	88	10	n	n	X
ejpam-3399	88	11	≥	≥	NOUN
ejpam-3399	88	12	2	2	NUM
ejpam-3399	88	13	)	)	PUNCT
ejpam-3399	88	14	.	.	PUNCT
ejpam-3399	89	1	let	let	VERB
ejpam-3399	89	2	h	h	PRON
ejpam-3399	89	3	be	be	AUX
ejpam-3399	89	4	a	a	DET
ejpam-3399	89	5	subgroup	subgroup	NOUN
ejpam-3399	89	6	of	of	ADP
ejpam-3399	89	7	p	p	NOUN
ejpam-3399	89	8	with	with	ADP
ejpam-3399	89	9	|h|	|h|	PROPN
ejpam-3399	89	10	=	=	PUNCT
ejpam-3399	89	11	|d|	|d|	PROPN
ejpam-3399	89	12	such	such	ADJ
ejpam-3399	89	13	that	that	SCONJ
ejpam-3399	89	14	p1	p1	PROPN
ejpam-3399	90	1	≤	≤	NUM
ejpam-3399	90	2	h	h	NOUN
ejpam-3399	90	3	<	<	X
ejpam-3399	90	4	p	p	X
ejpam-3399	90	5	.	.	PUNCT
ejpam-3399	91	1	by	by	ADP
ejpam-3399	91	2	the	the	DET
ejpam-3399	91	3	hypothesis	hypothesis	NOUN
ejpam-3399	91	4	,	,	PUNCT
ejpam-3399	91	5	h	h	NOUN
ejpam-3399	91	6	cg	cg	PROPN
ejpam-3399	91	7	.	.	PUNCT
ejpam-3399	91	8	assume	assume	VERB
ejpam-3399	91	9	that	that	SCONJ
ejpam-3399	91	10	φ(h	φ(h	NOUN
ejpam-3399	91	11	)	)	PUNCT
ejpam-3399	91	12	6=	6=	ADP
ejpam-3399	91	13	1	1	NUM
ejpam-3399	91	14	and	and	CCONJ
ejpam-3399	91	15	consider	consider	VERB
ejpam-3399	91	16	the	the	DET
ejpam-3399	91	17	factor	factor	NOUN
ejpam-3399	91	18	group	group	NOUN
ejpam-3399	91	19	g	g	PROPN
ejpam-3399	91	20	/	/	SYM
ejpam-3399	91	21	φ(h	φ(h	NOUN
ejpam-3399	91	22	)	)	PUNCT
ejpam-3399	91	23	.	.	PUNCT
ejpam-3399	92	1	obviously	obviously	ADV
ejpam-3399	92	2	,	,	PUNCT
ejpam-3399	92	3	g	g	NOUN
ejpam-3399	92	4	/	/	SYM
ejpam-3399	92	5	φ(h	φ(h	NOUN
ejpam-3399	92	6	)	)	PUNCT
ejpam-3399	92	7	satisfies	satisfy	VERB
ejpam-3399	92	8	the	the	DET
ejpam-3399	92	9	theorem	theorem	ADJ
ejpam-3399	92	10	hypothesis	hypothesis	NOUN
ejpam-3399	92	11	and	and	CCONJ
ejpam-3399	92	12	so	so	ADV
ejpam-3399	92	13	(	(	PUNCT
ejpam-3399	92	14	g	g	NOUN
ejpam-3399	92	15	/	/	SYM
ejpam-3399	92	16	φ(h))′	φ(h))′	PROPN
ejpam-3399	92	17	=	=	PUNCT
ejpam-3399	92	18	g′φ(h)/φ(h	g′φ(h)/φ(h	PROPN
ejpam-3399	92	19	)	)	PUNCT
ejpam-3399	92	20	is	be	AUX
ejpam-3399	92	21	p	p	NOUN
ejpam-3399	92	22	-	-	PUNCT
ejpam-3399	92	23	nilpotent	nilpotent	ADJ
ejpam-3399	92	24	by	by	ADP
ejpam-3399	92	25	the	the	DET
ejpam-3399	92	26	induction	induction	NOUN
ejpam-3399	92	27	on	on	ADP
ejpam-3399	92	28	|g|	|g|	PROPN
ejpam-3399	92	29	.	.	PUNCT
ejpam-3399	93	1	but	but	CCONJ
ejpam-3399	93	2	g′φ(h)/φ(h	g′φ(h)/φ(h	PROPN
ejpam-3399	93	3	)	)	PUNCT
ejpam-3399	93	4	∼=	∼=	PROPN
ejpam-3399	93	5	g′/g′	g′/g′	ADJ
ejpam-3399	93	6	∩	∩	NOUN
ejpam-3399	93	7	φ(h	φ(h	NOUN
ejpam-3399	93	8	)	)	PUNCT
ejpam-3399	93	9	and	and	CCONJ
ejpam-3399	93	10	φ(h	φ(h	NOUN
ejpam-3399	93	11	)	)	PUNCT
ejpam-3399	93	12	≤	≤	NOUN
ejpam-3399	93	13	φ(g	φ(g	PROPN
ejpam-3399	93	14	)	)	PUNCT
ejpam-3399	93	15	,	,	PUNCT
ejpam-3399	93	16	then	then	ADV
ejpam-3399	93	17	we	we	PRON
ejpam-3399	93	18	have	have	VERB
ejpam-3399	93	19	g′	g′	NOUN
ejpam-3399	93	20	∩	∩	NOUN
ejpam-3399	93	21	φ(h	φ(h	NOUN
ejpam-3399	93	22	)	)	PUNCT
ejpam-3399	93	23	≤	≤	NUM
ejpam-3399	93	24	g′	g′	NOUN
ejpam-3399	93	25	∩	∩	NOUN
ejpam-3399	93	26	φ(g	φ(g	PROPN
ejpam-3399	93	27	)	)	PUNCT
ejpam-3399	93	28	and	and	CCONJ
ejpam-3399	93	29	therefore	therefore	ADV
ejpam-3399	93	30	r.	r.	PROPN
ejpam-3399	93	31	hijazi	hijazi	PROPN
ejpam-3399	93	32	,	,	PUNCT
ejpam-3399	93	33	f.	f.	PROPN
ejpam-3399	93	34	charaf	charaf	PROPN
ejpam-3399	93	35	/	/	SYM
ejpam-3399	93	36	eur	eur	PROPN
ejpam-3399	93	37	.	.	PUNCT
ejpam-3399	94	1	j.	j.	PROPN
ejpam-3399	94	2	pure	pure	PROPN
ejpam-3399	94	3	appl	appl	PROPN
ejpam-3399	94	4	.	.	PROPN
ejpam-3399	94	5	math	math	PROPN
ejpam-3399	94	6	,	,	PUNCT
ejpam-3399	94	7	12	12	NUM
ejpam-3399	94	8	(	(	PUNCT
ejpam-3399	94	9	2	2	NUM
ejpam-3399	94	10	)	)	PUNCT
ejpam-3399	94	11	(	(	PUNCT
ejpam-3399	94	12	2019	2019	NUM
ejpam-3399	94	13	)	)	PUNCT
ejpam-3399	94	14	,	,	PUNCT
ejpam-3399	94	15	571	571	NUM
ejpam-3399	94	16	-	-	SYM
ejpam-3399	94	17	576	576	NUM
ejpam-3399	94	18	574	574	NUM
ejpam-3399	94	19	g′/g′	g′/g′	ADJ
ejpam-3399	94	20	∩	∩	NOUN
ejpam-3399	94	21	φ(g	φ(g	PROPN
ejpam-3399	94	22	)	)	PUNCT
ejpam-3399	94	23	is	be	AUX
ejpam-3399	94	24	p	p	NOUN
ejpam-3399	94	25	-	-	PUNCT
ejpam-3399	94	26	nilpotent	nilpotent	ADJ
ejpam-3399	94	27	.	.	PUNCT
ejpam-3399	95	1	now	now	ADV
ejpam-3399	95	2	g′φ(g)/φ(g	g′φ(g)/φ(g	PROPN
ejpam-3399	95	3	)	)	PUNCT
ejpam-3399	95	4	∼=	∼=	PROPN
ejpam-3399	95	5	g′/g′	g′/g′	ADJ
ejpam-3399	95	6	∩	∩	NOUN
ejpam-3399	95	7	φ(g	φ(g	PROPN
ejpam-3399	95	8	)	)	PUNCT
ejpam-3399	95	9	is	be	AUX
ejpam-3399	95	10	p	p	ADJ
ejpam-3399	95	11	-	-	PUNCT
ejpam-3399	95	12	nilpotent	nilpotent	NOUN
ejpam-3399	95	13	implies	imply	VERB
ejpam-3399	95	14	that	that	SCONJ
ejpam-3399	95	15	g′φ(g	g′φ(g	NOUN
ejpam-3399	95	16	)	)	PUNCT
ejpam-3399	95	17	is	be	AUX
ejpam-3399	95	18	p	p	NOUN
ejpam-3399	95	19	-	-	PUNCT
ejpam-3399	95	20	nilpotent	nilpotent	ADJ
ejpam-3399	95	21	and	and	CCONJ
ejpam-3399	95	22	consequently	consequently	ADV
ejpam-3399	95	23	g′	g′	NOUN
ejpam-3399	95	24	is	be	AUX
ejpam-3399	95	25	p	p	NOUN
ejpam-3399	95	26	-	-	PUNCT
ejpam-3399	95	27	nilpotent	nilpotent	ADJ
ejpam-3399	95	28	.	.	PUNCT
ejpam-3399	96	1	thus	thus	ADV
ejpam-3399	96	2	we	we	PRON
ejpam-3399	96	3	may	may	AUX
ejpam-3399	96	4	assume	assume	VERB
ejpam-3399	96	5	that	that	SCONJ
ejpam-3399	96	6	φ(h	φ(h	NOUN
ejpam-3399	96	7	)	)	PUNCT
ejpam-3399	96	8	=	=	SYM
ejpam-3399	96	9	1	1	NUM
ejpam-3399	97	1	and	and	CCONJ
ejpam-3399	97	2	so	so	ADV
ejpam-3399	97	3	h	h	NOUN
ejpam-3399	97	4	is	be	AUX
ejpam-3399	97	5	elementary	elementary	ADJ
ejpam-3399	97	6	abelian	abelian	NOUN
ejpam-3399	97	7	p	p	PROPN
ejpam-3399	97	8	-	-	PUNCT
ejpam-3399	97	9	group	group	NOUN
ejpam-3399	97	10	of	of	ADP
ejpam-3399	97	11	order	order	NOUN
ejpam-3399	97	12	pn	pn	X
ejpam-3399	97	13	(	(	PUNCT
ejpam-3399	97	14	n	n	CCONJ
ejpam-3399	97	15	≥	≥	NOUN
ejpam-3399	97	16	2	2	NUM
ejpam-3399	97	17	)	)	PUNCT
ejpam-3399	97	18	.	.	PUNCT
ejpam-3399	98	1	let	let	VERB
ejpam-3399	98	2	l	l	NOUN
ejpam-3399	98	3	be	be	AUX
ejpam-3399	98	4	a	a	DET
ejpam-3399	98	5	subgroup	subgroup	NOUN
ejpam-3399	98	6	of	of	ADP
ejpam-3399	98	7	p	p	PROPN
ejpam-3399	98	8	contains	contain	VERB
ejpam-3399	98	9	h	h	NOUN
ejpam-3399	98	10	such	such	ADJ
ejpam-3399	98	11	that	that	SCONJ
ejpam-3399	98	12	h	h	NOUN
ejpam-3399	98	13	is	be	AUX
ejpam-3399	98	14	maximal	maximal	ADJ
ejpam-3399	98	15	in	in	ADP
ejpam-3399	98	16	l.	l.	PROPN
ejpam-3399	98	17	clearly	clearly	ADV
ejpam-3399	98	18	,	,	PUNCT
ejpam-3399	98	19	l	l	NOUN
ejpam-3399	98	20	is	be	AUX
ejpam-3399	98	21	not	not	PART
ejpam-3399	98	22	cyclic	cyclic	ADJ
ejpam-3399	98	23	because	because	SCONJ
ejpam-3399	98	24	h	h	NOUN
ejpam-3399	98	25	is	be	AUX
ejpam-3399	98	26	elementary	elementary	ADJ
ejpam-3399	98	27	abelian	abelian	PROPN
ejpam-3399	98	28	group	group	NOUN
ejpam-3399	98	29	of	of	ADP
ejpam-3399	98	30	order	order	NOUN
ejpam-3399	98	31	pn	pn	X
ejpam-3399	98	32	(	(	PUNCT
ejpam-3399	98	33	n	n	CCONJ
ejpam-3399	98	34	≥	≥	NOUN
ejpam-3399	98	35	2	2	NUM
ejpam-3399	98	36	)	)	PUNCT
ejpam-3399	98	37	.	.	PUNCT
ejpam-3399	99	1	then	then	ADV
ejpam-3399	99	2	l	l	PROPN
ejpam-3399	99	3	contains	contain	VERB
ejpam-3399	99	4	a	a	DET
ejpam-3399	99	5	subgroup	subgroup	NOUN
ejpam-3399	99	6	h1	h1	NOUN
ejpam-3399	99	7	such	such	ADJ
ejpam-3399	99	8	that	that	SCONJ
ejpam-3399	99	9	|h1|	|h1|	PROPN
ejpam-3399	99	10	=	=	SYM
ejpam-3399	99	11	|d|	|d|	PROPN
ejpam-3399	99	12	and	and	CCONJ
ejpam-3399	99	13	h1	h1	PROPN
ejpam-3399	99	14	6=	6=	PROPN
ejpam-3399	99	15	h.	h.	PROPN
ejpam-3399	99	16	by	by	ADP
ejpam-3399	99	17	the	the	DET
ejpam-3399	99	18	hypothesis	hypothesis	NOUN
ejpam-3399	99	19	,	,	PUNCT
ejpam-3399	99	20	h1cg	h1cg	NOUN
ejpam-3399	99	21	and	and	CCONJ
ejpam-3399	99	22	since	since	SCONJ
ejpam-3399	99	23	hcg	hcg	PROPN
ejpam-3399	99	24	,	,	PUNCT
ejpam-3399	99	25	we	we	PRON
ejpam-3399	99	26	have	have	VERB
ejpam-3399	100	1	l	l	NOUN
ejpam-3399	100	2	=	=	SYM
ejpam-3399	100	3	h1h	h1h	PROPN
ejpam-3399	100	4	c	c	NOUN
ejpam-3399	100	5	g	g	NOUN
ejpam-3399	100	6	and	and	CCONJ
ejpam-3399	100	7	so	so	ADV
ejpam-3399	100	8	φ(l	φ(l	PROPN
ejpam-3399	100	9	)	)	PUNCT
ejpam-3399	100	10	≤	≤	NOUN
ejpam-3399	100	11	φ(g	φ(g	NOUN
ejpam-3399	100	12	)	)	PUNCT
ejpam-3399	100	13	.	.	PUNCT
ejpam-3399	101	1	hence	hence	ADV
ejpam-3399	101	2	if	if	SCONJ
ejpam-3399	101	3	φ(l	φ(l	NOUN
ejpam-3399	101	4	)	)	PUNCT
ejpam-3399	101	5	6=	6=	ADP
ejpam-3399	101	6	1	1	NUM
ejpam-3399	101	7	,	,	PUNCT
ejpam-3399	101	8	φ(l	φ(l	PROPN
ejpam-3399	101	9	)	)	PUNCT
ejpam-3399	101	10	≤	≤	PUNCT
ejpam-3399	101	11	h1	h1	VERB
ejpam-3399	101	12	<	<	X
ejpam-3399	101	13	l	l	NOUN
ejpam-3399	101	14	≤	≤	ADJ
ejpam-3399	101	15	p	p	NOUN
ejpam-3399	101	16	.	.	PUNCT
ejpam-3399	102	1	since	since	SCONJ
ejpam-3399	102	2	l	l	NOUN
ejpam-3399	102	3	is	be	AUX
ejpam-3399	102	4	not	not	PART
ejpam-3399	102	5	cyclic	cyclic	ADJ
ejpam-3399	102	6	,	,	PUNCT
ejpam-3399	102	7	we	we	PRON
ejpam-3399	102	8	have	have	VERB
ejpam-3399	102	9	φ(l	φ(l	NOUN
ejpam-3399	102	10	)	)	PUNCT
ejpam-3399	102	11	is	be	AUX
ejpam-3399	102	12	contained	contain	VERB
ejpam-3399	102	13	properly	properly	ADV
ejpam-3399	102	14	in	in	ADP
ejpam-3399	102	15	h1	h1	PROPN
ejpam-3399	102	16	.	.	PUNCT
ejpam-3399	103	1	now	now	ADV
ejpam-3399	103	2	it	it	PRON
ejpam-3399	103	3	is	be	AUX
ejpam-3399	103	4	easy	easy	ADJ
ejpam-3399	103	5	to	to	PART
ejpam-3399	103	6	notice	notice	VERB
ejpam-3399	103	7	that	that	SCONJ
ejpam-3399	103	8	the	the	DET
ejpam-3399	103	9	factor	factor	NOUN
ejpam-3399	103	10	group	group	NOUN
ejpam-3399	103	11	g	g	PROPN
ejpam-3399	103	12	/	/	SYM
ejpam-3399	103	13	φ(l	φ(l	PROPN
ejpam-3399	103	14	)	)	PUNCT
ejpam-3399	103	15	satisfies	satisfy	VERB
ejpam-3399	103	16	the	the	DET
ejpam-3399	103	17	hypothesis	hypothesis	NOUN
ejpam-3399	103	18	of	of	ADP
ejpam-3399	103	19	the	the	DET
ejpam-3399	103	20	theorem	theorem	NOUN
ejpam-3399	103	21	,	,	PUNCT
ejpam-3399	103	22	so	so	ADV
ejpam-3399	103	23	by	by	ADP
ejpam-3399	103	24	induction	induction	NOUN
ejpam-3399	103	25	on	on	ADP
ejpam-3399	103	26	|g|	|g|	ADJ
ejpam-3399	103	27	,	,	PUNCT
ejpam-3399	103	28	g′	g′	NOUN
ejpam-3399	103	29	is	be	AUX
ejpam-3399	103	30	p	p	NOUN
ejpam-3399	103	31	-	-	PUNCT
ejpam-3399	103	32	nilpotent	nilpotent	ADJ
ejpam-3399	103	33	.	.	PUNCT
ejpam-3399	104	1	thus	thus	ADV
ejpam-3399	104	2	we	we	PRON
ejpam-3399	104	3	may	may	AUX
ejpam-3399	104	4	assume	assume	VERB
ejpam-3399	104	5	that	that	SCONJ
ejpam-3399	104	6	φ(l	φ(l	PROPN
ejpam-3399	104	7	)	)	PUNCT
ejpam-3399	104	8	=	=	SYM
ejpam-3399	104	9	1	1	NUM
ejpam-3399	104	10	and	and	CCONJ
ejpam-3399	104	11	so	so	ADV
ejpam-3399	104	12	p1	p1	PROPN
ejpam-3399	104	13	is	be	AUX
ejpam-3399	104	14	elementary	elementary	ADJ
ejpam-3399	104	15	abelian	abelian	NOUN
ejpam-3399	104	16	p	p	PROPN
ejpam-3399	104	17	-	-	PUNCT
ejpam-3399	104	18	group	group	NOUN
ejpam-3399	104	19	.	.	PUNCT
ejpam-3399	105	1	since	since	SCONJ
ejpam-3399	105	2	p1	p1	PROPN
ejpam-3399	105	3	≤	≤	NUM
ejpam-3399	106	1	h	h	NOUN
ejpam-3399	106	2	<	<	X
ejpam-3399	106	3	l	l	NOUN
ejpam-3399	106	4	≤	≤	ADJ
ejpam-3399	106	5	p	p	NOUN
ejpam-3399	106	6	and	and	CCONJ
ejpam-3399	106	7	h	h	NOUN
ejpam-3399	106	8	is	be	AUX
ejpam-3399	106	9	maximal	maximal	ADJ
ejpam-3399	106	10	in	in	ADP
ejpam-3399	106	11	l	l	NOUN
ejpam-3399	106	12	,	,	PUNCT
ejpam-3399	106	13	it	it	PRON
ejpam-3399	106	14	follows	follow	VERB
ejpam-3399	106	15	that	that	SCONJ
ejpam-3399	106	16	|l|	|l|	NOUN
ejpam-3399	106	17	=	=	SYM
ejpam-3399	106	18	pn+1	pn+1	PROPN
ejpam-3399	106	19	.	.	PUNCT
ejpam-3399	107	1	let	let	VERB
ejpam-3399	107	2	l1	l1	PROPN
ejpam-3399	108	1	=	=	PROPN
ejpam-3399	108	2	<	<	X
ejpam-3399	108	3	x1	x1	X
ejpam-3399	108	4	>	>	X
ejpam-3399	108	5	be	be	AUX
ejpam-3399	108	6	a	a	DET
ejpam-3399	108	7	subgroup	subgroup	NOUN
ejpam-3399	108	8	of	of	ADP
ejpam-3399	108	9	p1	p1	PROPN
ejpam-3399	108	10	of	of	ADP
ejpam-3399	108	11	order	order	NOUN
ejpam-3399	109	1	p.	p.	NOUN
ejpam-3399	109	2	then	then	ADV
ejpam-3399	109	3	l	l	X
ejpam-3399	110	1	=	=	X
ejpam-3399	110	2	<	<	X
ejpam-3399	110	3	x1	x1	X
ejpam-3399	110	4	>	>	X
ejpam-3399	110	5	×	×	X
ejpam-3399	110	6	<	<	X
ejpam-3399	110	7	x2	x2	X
ejpam-3399	110	8	>	>	X
ejpam-3399	110	9	×	×	NOUN
ejpam-3399	110	10	.	.	PUNCT
ejpam-3399	110	11	.	.	PUNCT
ejpam-3399	111	1	.×	.×	NOUN
ejpam-3399	111	2	<	<	X
ejpam-3399	111	3	xn+1	xn+1	PROPN
ejpam-3399	111	4	>	>	PUNCT
ejpam-3399	111	5	.	.	PUNCT
ejpam-3399	112	1	by	by	ADP
ejpam-3399	112	2	the	the	DET
ejpam-3399	112	3	hypothesis	hypothesis	NOUN
ejpam-3399	112	4	,	,	PUNCT
ejpam-3399	112	5	each	each	DET
ejpam-3399	112	6	maximal	maximal	ADJ
ejpam-3399	112	7	subgroup	subgroup	NOUN
ejpam-3399	112	8	of	of	ADP
ejpam-3399	112	9	l	l	NOUN
ejpam-3399	112	10	is	be	AUX
ejpam-3399	112	11	normal	normal	ADJ
ejpam-3399	112	12	in	in	ADP
ejpam-3399	112	13	g.	g.	NOUN
ejpam-3399	112	14	applying	apply	VERB
ejpam-3399	112	15	(	(	PUNCT
ejpam-3399	112	16	[	[	X
ejpam-3399	112	17	1	1	NUM
ejpam-3399	112	18	]	]	PUNCT
ejpam-3399	112	19	,	,	PUNCT
ejpam-3399	112	20	lemma	lemma	PROPN
ejpam-3399	112	21	2.9	2.9	NUM
ejpam-3399	112	22	)	)	PUNCT
ejpam-3399	112	23	implies	imply	VERB
ejpam-3399	112	24	that	that	SCONJ
ejpam-3399	112	25	each	each	DET
ejpam-3399	112	26	subgroup	subgroup	NOUN
ejpam-3399	112	27	of	of	ADP
ejpam-3399	112	28	l	l	NOUN
ejpam-3399	112	29	of	of	ADP
ejpam-3399	112	30	order	order	NOUN
ejpam-3399	112	31	p	p	NOUN
ejpam-3399	112	32	is	be	AUX
ejpam-3399	112	33	normal	normal	ADJ
ejpam-3399	112	34	in	in	ADP
ejpam-3399	112	35	g	g	NOUN
ejpam-3399	112	36	;	;	PUNCT
ejpam-3399	112	37	in	in	ADP
ejpam-3399	112	38	particular	particular	ADJ
ejpam-3399	112	39	each	each	DET
ejpam-3399	112	40	subgroup	subgroup	PROPN
ejpam-3399	112	41	l1	l1	PROPN
ejpam-3399	112	42	of	of	ADP
ejpam-3399	112	43	p1	p1	PROPN
ejpam-3399	112	44	of	of	ADP
ejpam-3399	112	45	order	order	NOUN
ejpam-3399	112	46	p	p	NOUN
ejpam-3399	112	47	is	be	AUX
ejpam-3399	112	48	normal	normal	ADJ
ejpam-3399	112	49	in	in	ADP
ejpam-3399	112	50	g.	g.	PROPN
ejpam-3399	112	51	so	so	ADV
ejpam-3399	112	52	,	,	PUNCT
ejpam-3399	112	53	g8	g8	PROPN
ejpam-3399	112	54	≤	≤	PROPN
ejpam-3399	112	55	cg(l1	cg(l1	PROPN
ejpam-3399	112	56	)	)	PUNCT
ejpam-3399	112	57	and	and	CCONJ
ejpam-3399	112	58	consequently	consequently	ADV
ejpam-3399	112	59	p1	p1	VERB
ejpam-3399	112	60	≤	≤	NUM
ejpam-3399	112	61	z(g′	z(g′	NUM
ejpam-3399	112	62	)	)	PUNCT
ejpam-3399	112	63	.	.	PUNCT
ejpam-3399	113	1	by	by	ADP
ejpam-3399	113	2	schur	schur	NOUN
ejpam-3399	113	3	-	-	PUNCT
ejpam-3399	113	4	zassenhaus	zassenhaus	NOUN
ejpam-3399	113	5	theorem	theorem	NOUN
ejpam-3399	113	6	,	,	PUNCT
ejpam-3399	113	7	g′	g′	NOUN
ejpam-3399	113	8	=	=	SYM
ejpam-3399	113	9	p1	p1	PROPN
ejpam-3399	113	10	×	×	PROPN
ejpam-3399	113	11	k1	k1	NOUN
ejpam-3399	113	12	,	,	PUNCT
ejpam-3399	113	13	where	where	SCONJ
ejpam-3399	113	14	k1	k1	PROPN
ejpam-3399	113	15	is	be	AUX
ejpam-3399	113	16	a	a	DET
ejpam-3399	113	17	p′-hall	p′-hall	NUM
ejpam-3399	113	18	subgroup	subgroup	NOUN
ejpam-3399	113	19	of	of	ADP
ejpam-3399	113	20	g	g	NOUN
ejpam-3399	113	21	;	;	PUNCT
ejpam-3399	113	22	in	in	ADP
ejpam-3399	113	23	particular	particular	ADJ
ejpam-3399	113	24	g′	g′	NOUN
ejpam-3399	113	25	is	be	AUX
ejpam-3399	113	26	p	p	NOUN
ejpam-3399	113	27	-	-	PUNCT
ejpam-3399	113	28	nilpotent	nilpotent	ADJ
ejpam-3399	113	29	.	.	PUNCT
ejpam-3399	114	1	case	case	NOUN
ejpam-3399	114	2	2	2	NUM
ejpam-3399	114	3	.	.	PUNCT
ejpam-3399	114	4	|p1|	|p1|	PROPN
ejpam-3399	114	5	>	>	X
ejpam-3399	114	6	|d|	|d|	PROPN
ejpam-3399	114	7	.	.	PUNCT
ejpam-3399	115	1	hence	hence	ADV
ejpam-3399	115	2	if	if	SCONJ
ejpam-3399	115	3	|d|	|d|	PROPN
ejpam-3399	115	4	=	=	SYM
ejpam-3399	115	5	p	p	PROPN
ejpam-3399	115	6	,	,	PUNCT
ejpam-3399	115	7	then	then	ADV
ejpam-3399	115	8	every	every	DET
ejpam-3399	115	9	subgroup	subgroup	NOUN
ejpam-3399	115	10	of	of	ADP
ejpam-3399	115	11	p1	p1	PROPN
ejpam-3399	115	12	of	of	ADP
ejpam-3399	115	13	order	order	NOUN
ejpam-3399	115	14	p	p	NOUN
ejpam-3399	115	15	is	be	AUX
ejpam-3399	115	16	normal	normal	ADJ
ejpam-3399	115	17	in	in	ADP
ejpam-3399	115	18	g	g	PROPN
ejpam-3399	115	19	,	,	PUNCT
ejpam-3399	115	20	so	so	ADV
ejpam-3399	115	21	ω1(p1	ω1(p1	NOUN
ejpam-3399	115	22	)	)	PUNCT
ejpam-3399	115	23	≤	≤	NOUN
ejpam-3399	115	24	z(g′	z(g′	NUM
ejpam-3399	115	25	)	)	PUNCT
ejpam-3399	115	26	which	which	PRON
ejpam-3399	115	27	implies	imply	VERB
ejpam-3399	115	28	that	that	SCONJ
ejpam-3399	115	29	g′	g′	NOUN
ejpam-3399	115	30	is	be	AUX
ejpam-3399	115	31	p	p	NOUN
ejpam-3399	115	32	-	-	PUNCT
ejpam-3399	115	33	nilpotent	nilpotent	ADJ
ejpam-3399	115	34	by	by	ADP
ejpam-3399	115	35	(	(	PUNCT
ejpam-3399	115	36	[	[	X
ejpam-3399	115	37	10	10	NUM
ejpam-3399	115	38	]	]	PUNCT
ejpam-3399	115	39	,	,	PUNCT
ejpam-3399	115	40	satz	satz	PROPN
ejpam-3399	115	41	5.5(a	5.5(a	NUM
ejpam-3399	115	42	)	)	PUNCT
ejpam-3399	115	43	,	,	PUNCT
ejpam-3399	115	44	p	p	NOUN
ejpam-3399	115	45	435	435	NUM
ejpam-3399	115	46	)	)	PUNCT
ejpam-3399	115	47	.	.	PUNCT
ejpam-3399	116	1	thus	thus	ADV
ejpam-3399	116	2	assume	assume	VERB
ejpam-3399	116	3	that	that	SCONJ
ejpam-3399	116	4	|d|	|d|	PROPN
ejpam-3399	116	5	=	=	SYM
ejpam-3399	116	6	pn	pn	PROPN
ejpam-3399	116	7	(	(	PUNCT
ejpam-3399	116	8	n	n	X
ejpam-3399	116	9	≥	≥	NOUN
ejpam-3399	116	10	2	2	NUM
ejpam-3399	116	11	)	)	PUNCT
ejpam-3399	116	12	.	.	PUNCT
ejpam-3399	117	1	hence	hence	ADV
ejpam-3399	117	2	if	if	SCONJ
ejpam-3399	117	3	φ(d	φ(d	NUM
ejpam-3399	117	4	)	)	PUNCT
ejpam-3399	117	5	6=	6=	ADP
ejpam-3399	117	6	1	1	NUM
ejpam-3399	117	7	,	,	PUNCT
ejpam-3399	117	8	g	g	NOUN
ejpam-3399	117	9	/	/	SYM
ejpam-3399	117	10	φ(d	φ(d	NUM
ejpam-3399	117	11	)	)	PUNCT
ejpam-3399	117	12	satisfies	satisfy	VERB
ejpam-3399	117	13	the	the	DET
ejpam-3399	117	14	hypothesis	hypothesis	NOUN
ejpam-3399	117	15	of	of	ADP
ejpam-3399	117	16	the	the	DET
ejpam-3399	117	17	theorem	theorem	NOUN
ejpam-3399	117	18	and	and	CCONJ
ejpam-3399	117	19	so	so	ADV
ejpam-3399	117	20	(	(	PUNCT
ejpam-3399	117	21	g	g	NOUN
ejpam-3399	117	22	/	/	SYM
ejpam-3399	117	23	φ(d))′	φ(d))′	NOUN
ejpam-3399	117	24	=	=	SYM
ejpam-3399	117	25	g′φ(d)/φ(d	g′φ(d)/φ(d	PROPN
ejpam-3399	117	26	)	)	PUNCT
ejpam-3399	117	27	is	be	AUX
ejpam-3399	117	28	p	p	NOUN
ejpam-3399	117	29	-	-	PUNCT
ejpam-3399	117	30	nilpotent	nilpotent	ADJ
ejpam-3399	117	31	by	by	ADP
ejpam-3399	117	32	induction	induction	NOUN
ejpam-3399	117	33	on	on	ADP
ejpam-3399	117	34	|g|	|g|	PROPN
ejpam-3399	117	35	which	which	PRON
ejpam-3399	117	36	implies	imply	VERB
ejpam-3399	117	37	that	that	SCONJ
ejpam-3399	117	38	g′/g′	g′/g′	NOUN
ejpam-3399	117	39	∩	∩	NOUN
ejpam-3399	117	40	φ(g	φ(g	PROPN
ejpam-3399	117	41	)	)	PUNCT
ejpam-3399	117	42	is	be	AUX
ejpam-3399	117	43	p	p	NOUN
ejpam-3399	117	44	-	-	PUNCT
ejpam-3399	117	45	nilpotent	nilpotent	ADJ
ejpam-3399	117	46	;	;	PUNCT
ejpam-3399	117	47	in	in	ADP
ejpam-3399	117	48	particular	particular	ADJ
ejpam-3399	117	49	g′	g′	NOUN
ejpam-3399	117	50	is	be	AUX
ejpam-3399	117	51	p	p	NOUN
ejpam-3399	117	52	-	-	PUNCT
ejpam-3399	117	53	nilpotent	nilpotent	ADJ
ejpam-3399	117	54	.	.	PUNCT
ejpam-3399	118	1	thus	thus	ADV
ejpam-3399	118	2	we	we	PRON
ejpam-3399	118	3	may	may	AUX
ejpam-3399	118	4	assume	assume	VERB
ejpam-3399	118	5	that	that	SCONJ
ejpam-3399	118	6	φ(d	φ(d	PRON
ejpam-3399	118	7	)	)	PUNCT
ejpam-3399	118	8	=	=	SYM
ejpam-3399	119	1	1	1	X
ejpam-3399	119	2	.	.	PUNCT
ejpam-3399	119	3	let	let	VERB
ejpam-3399	119	4	l	l	NOUN
ejpam-3399	119	5	≤	≤	NOUN
ejpam-3399	119	6	p1	p1	NOUN
ejpam-3399	119	7	such	such	ADJ
ejpam-3399	119	8	that	that	SCONJ
ejpam-3399	119	9	d	d	NOUN
ejpam-3399	119	10	is	be	AUX
ejpam-3399	119	11	maximal	maximal	ADJ
ejpam-3399	119	12	in	in	ADP
ejpam-3399	119	13	l.	l.	PROPN
ejpam-3399	119	14	then	then	ADV
ejpam-3399	119	15	|l|	|l|	VERB
ejpam-3399	119	16	=	=	PUNCT
ejpam-3399	120	1	pn+1(n	pn+1(n	VERB
ejpam-3399	120	2	>	>	X
ejpam-3399	120	3	2	2	NUM
ejpam-3399	120	4	)	)	PUNCT
ejpam-3399	120	5	.	.	PUNCT
ejpam-3399	121	1	clearly	clearly	ADV
ejpam-3399	121	2	l	l	NOUN
ejpam-3399	121	3	is	be	AUX
ejpam-3399	121	4	not	not	PART
ejpam-3399	121	5	cyclic	cyclic	ADJ
ejpam-3399	121	6	.	.	PUNCT
ejpam-3399	122	1	then	then	ADV
ejpam-3399	122	2	there	there	PRON
ejpam-3399	122	3	exists	exist	VERB
ejpam-3399	122	4	a	a	DET
ejpam-3399	122	5	maximal	maximal	ADJ
ejpam-3399	122	6	subgroup	subgroup	NOUN
ejpam-3399	122	7	l1	l1	PROPN
ejpam-3399	122	8	6=	6=	PROPN
ejpam-3399	123	1	d	d	PROPN
ejpam-3399	123	2	in	in	ADP
ejpam-3399	123	3	l.	l.	NOUN
ejpam-3399	123	4	by	by	ADP
ejpam-3399	123	5	the	the	DET
ejpam-3399	123	6	hypothesis	hypothesis	NOUN
ejpam-3399	123	7	l1	l1	PROPN
ejpam-3399	123	8	c	c	PROPN
ejpam-3399	123	9	g	g	PROPN
ejpam-3399	123	10	and	and	CCONJ
ejpam-3399	123	11	d	d	PROPN
ejpam-3399	123	12	c	c	PROPN
ejpam-3399	123	13	g	g	NOUN
ejpam-3399	123	14	which	which	PRON
ejpam-3399	123	15	implies	imply	VERB
ejpam-3399	123	16	that	that	SCONJ
ejpam-3399	123	17	l	l	NOUN
ejpam-3399	123	18	=	=	PUNCT
ejpam-3399	123	19	l1d	l1d	PROPN
ejpam-3399	124	1	c	c	NOUN
ejpam-3399	124	2	g.	g.	NOUN
ejpam-3399	124	3	hence	hence	ADV
ejpam-3399	124	4	if	if	SCONJ
ejpam-3399	124	5	φ(l	φ(l	NOUN
ejpam-3399	124	6	)	)	PUNCT
ejpam-3399	124	7	6=	6=	ADP
ejpam-3399	124	8	1	1	NUM
ejpam-3399	124	9	,	,	PUNCT
ejpam-3399	124	10	φ(l	φ(l	PROPN
ejpam-3399	124	11	)	)	PUNCT
ejpam-3399	124	12	≤	≤	PUNCT
ejpam-3399	125	1	d	d	ADP
ejpam-3399	125	2	<	<	X
ejpam-3399	125	3	l	l	NOUN
ejpam-3399	125	4	≤	≤	NOUN
ejpam-3399	125	5	p1	p1	NOUN
ejpam-3399	125	6	and	and	CCONJ
ejpam-3399	125	7	since	since	SCONJ
ejpam-3399	125	8	l	l	NOUN
ejpam-3399	125	9	is	be	AUX
ejpam-3399	125	10	not	not	PART
ejpam-3399	125	11	cyclic	cyclic	ADJ
ejpam-3399	125	12	,	,	PUNCT
ejpam-3399	125	13	it	it	PRON
ejpam-3399	125	14	follows	follow	VERB
ejpam-3399	125	15	that	that	SCONJ
ejpam-3399	125	16	φ(l	φ(l	PROPN
ejpam-3399	125	17	)	)	PUNCT
ejpam-3399	125	18	<	<	X
ejpam-3399	125	19	d.	d.	PROPN
ejpam-3399	125	20	by	by	ADP
ejpam-3399	125	21	induction	induction	NOUN
ejpam-3399	125	22	on	on	ADP
ejpam-3399	125	23	|g|	|g|	ADJ
ejpam-3399	125	24	,	,	PUNCT
ejpam-3399	125	25	g′φ(l)/φ(l	g′φ(l)/φ(l	PROPN
ejpam-3399	125	26	)	)	PUNCT
ejpam-3399	125	27	∼=	∼=	PROPN
ejpam-3399	125	28	g′/g′	g′/g′	NOUN
ejpam-3399	125	29	∩	∩	NOUN
ejpam-3399	125	30	φ(l	φ(l	NOUN
ejpam-3399	125	31	)	)	PUNCT
ejpam-3399	125	32	is	be	AUX
ejpam-3399	125	33	p	p	NOUN
ejpam-3399	125	34	-	-	PUNCT
ejpam-3399	125	35	nilpotent	nilpotent	ADJ
ejpam-3399	125	36	.	.	PUNCT
ejpam-3399	126	1	in	in	ADP
ejpam-3399	126	2	particular	particular	ADJ
ejpam-3399	126	3	,	,	PUNCT
ejpam-3399	126	4	g′φ(g)/φ(g	g′φ(g)/φ(g	PROPN
ejpam-3399	126	5	)	)	PUNCT
ejpam-3399	126	6	is	be	AUX
ejpam-3399	126	7	pnilpotent	pnilpotent	NOUN
ejpam-3399	126	8	and	and	CCONJ
ejpam-3399	126	9	it	it	PRON
ejpam-3399	126	10	follows	follow	VERB
ejpam-3399	126	11	easily	easily	ADV
ejpam-3399	126	12	that	that	SCONJ
ejpam-3399	126	13	g′	g′	NOUN
ejpam-3399	126	14	is	be	AUX
ejpam-3399	126	15	p	p	NOUN
ejpam-3399	126	16	-	-	PUNCT
ejpam-3399	126	17	nilpotent	nilpotent	ADJ
ejpam-3399	126	18	.	.	PUNCT
ejpam-3399	127	1	so	so	ADV
ejpam-3399	127	2	we	we	PRON
ejpam-3399	127	3	may	may	AUX
ejpam-3399	127	4	assume	assume	VERB
ejpam-3399	127	5	that	that	SCONJ
ejpam-3399	127	6	φ(l	φ(l	PROPN
ejpam-3399	127	7	)	)	PUNCT
ejpam-3399	127	8	=	=	SYM
ejpam-3399	127	9	1	1	NUM
ejpam-3399	127	10	and	and	CCONJ
ejpam-3399	127	11	so	so	ADV
ejpam-3399	127	12	l	l	NOUN
ejpam-3399	127	13	is	be	AUX
ejpam-3399	127	14	elementary	elementary	ADJ
ejpam-3399	127	15	abelian	abelian	NOUN
ejpam-3399	127	16	.	.	PUNCT
ejpam-3399	128	1	let	let	VERB
ejpam-3399	128	2	l1	l1	PROPN
ejpam-3399	128	3	<	<	X
ejpam-3399	128	4	p	p	X
ejpam-3399	128	5	such	such	ADJ
ejpam-3399	128	6	that	that	DET
ejpam-3399	128	7	|l1|	|l1|	NOUN
ejpam-3399	128	8	=	=	PUNCT
ejpam-3399	129	1	p.	p.	NOUN
ejpam-3399	129	2	then	then	ADV
ejpam-3399	129	3	l1	l1	PROPN
ejpam-3399	129	4	<	<	X
ejpam-3399	129	5	l	l	PROPN
ejpam-3399	129	6	≤	≤	PROPN
ejpam-3399	129	7	p1	p1	NOUN
ejpam-3399	129	8	and	and	CCONJ
ejpam-3399	129	9	so	so	ADV
ejpam-3399	129	10	l1	l1	PROPN
ejpam-3399	129	11	cg	cg	PROPN
ejpam-3399	129	12	by	by	ADP
ejpam-3399	129	13	(	(	PUNCT
ejpam-3399	129	14	[	[	X
ejpam-3399	129	15	1	1	NUM
ejpam-3399	129	16	]	]	PUNCT
ejpam-3399	129	17	,	,	PUNCT
ejpam-3399	129	18	lemma	lemma	PROPN
ejpam-3399	129	19	2.9	2.9	NUM
ejpam-3399	129	20	)	)	PUNCT
ejpam-3399	129	21	.	.	PUNCT
ejpam-3399	130	1	in	in	ADP
ejpam-3399	130	2	particular	particular	ADJ
ejpam-3399	130	3	,	,	PUNCT
ejpam-3399	130	4	ω1(p1	ω1(p1	NUM
ejpam-3399	130	5	)	)	PUNCT
ejpam-3399	130	6	≤	≤	NOUN
ejpam-3399	130	7	z(g′	z(g′	NUM
ejpam-3399	130	8	)	)	PUNCT
ejpam-3399	130	9	.	.	PUNCT
ejpam-3399	131	1	again	again	ADV
ejpam-3399	131	2	by	by	ADP
ejpam-3399	131	3	(	(	PUNCT
ejpam-3399	131	4	[	[	X
ejpam-3399	131	5	10	10	NUM
ejpam-3399	131	6	]	]	PUNCT
ejpam-3399	131	7	,	,	PUNCT
ejpam-3399	131	8	satz	satz	PROPN
ejpam-3399	131	9	5.5(a	5.5(a	NUM
ejpam-3399	131	10	)	)	PUNCT
ejpam-3399	131	11	,	,	PUNCT
ejpam-3399	131	12	p	p	NOUN
ejpam-3399	131	13	435	435	NUM
ejpam-3399	131	14	)	)	PUNCT
ejpam-3399	131	15	,	,	PUNCT
ejpam-3399	131	16	g′	g′	NOUN
ejpam-3399	131	17	is	be	AUX
ejpam-3399	131	18	p	p	NOUN
ejpam-3399	131	19	-	-	PUNCT
ejpam-3399	131	20	nilpotent	nilpotent	ADJ
ejpam-3399	131	21	.	.	PUNCT
ejpam-3399	132	1	this	this	PRON
ejpam-3399	132	2	completes	complete	VERB
ejpam-3399	132	3	the	the	DET
ejpam-3399	132	4	proof	proof	NOUN
ejpam-3399	132	5	of	of	ADP
ejpam-3399	132	6	the	the	DET
ejpam-3399	132	7	theorem	theorem	NOUN
ejpam-3399	132	8	.	.	PUNCT
ejpam-3399	133	1	now	now	ADV
ejpam-3399	133	2	we	we	PRON
ejpam-3399	133	3	can	can	AUX
ejpam-3399	133	4	move	move	VERB
ejpam-3399	133	5	forward	forward	ADV
ejpam-3399	133	6	to	to	PART
ejpam-3399	133	7	prove	prove	VERB
ejpam-3399	133	8	our	our	PRON
ejpam-3399	133	9	main	main	ADJ
ejpam-3399	133	10	theorem	theorem	NOUN
ejpam-3399	133	11	:	:	PUNCT
ejpam-3399	133	12	proof	proof	NOUN
ejpam-3399	133	13	.	.	PUNCT
ejpam-3399	134	1	we	we	PRON
ejpam-3399	134	2	prove	prove	VERB
ejpam-3399	134	3	the	the	DET
ejpam-3399	134	4	theorem	theorem	NOUN
ejpam-3399	134	5	by	by	ADP
ejpam-3399	134	6	induction	induction	NOUN
ejpam-3399	134	7	on	on	ADP
ejpam-3399	134	8	|g|	|g|	PROPN
ejpam-3399	134	9	.	.	PUNCT
ejpam-3399	135	1	hence	hence	ADV
ejpam-3399	135	2	if	if	SCONJ
ejpam-3399	135	3	op′(g	op′(g	PROPN
ejpam-3399	135	4	)	)	PUNCT
ejpam-3399	136	1	6=	6=	ADP
ejpam-3399	136	2	1	1	NUM
ejpam-3399	136	3	,	,	PUNCT
ejpam-3399	136	4	g	g	NOUN
ejpam-3399	136	5	/	/	SYM
ejpam-3399	136	6	op′(g	op′(g	PROPN
ejpam-3399	136	7	)	)	PUNCT
ejpam-3399	136	8	satisfies	satisfy	VERB
ejpam-3399	136	9	the	the	DET
ejpam-3399	136	10	hypothesis	hypothesis	NOUN
ejpam-3399	136	11	of	of	ADP
ejpam-3399	136	12	the	the	DET
ejpam-3399	136	13	theorem	theorem	NOUN
ejpam-3399	136	14	and	and	CCONJ
ejpam-3399	136	15	so	so	ADV
ejpam-3399	136	16	(	(	PUNCT
ejpam-3399	136	17	g	g	NOUN
ejpam-3399	136	18	/	/	SYM
ejpam-3399	136	19	op′(g))′	op′(g))′	PROPN
ejpam-3399	136	20	is	be	AUX
ejpam-3399	136	21	p	p	NOUN
ejpam-3399	136	22	-	-	PUNCT
ejpam-3399	136	23	nilpotent	nilpotent	ADJ
ejpam-3399	136	24	by	by	ADP
ejpam-3399	136	25	induction	induction	NOUN
ejpam-3399	136	26	on	on	ADP
ejpam-3399	136	27	|g|	|g|	PROPN
ejpam-3399	136	28	;	;	PUNCT
ejpam-3399	136	29	in	in	ADP
ejpam-3399	136	30	particular	particular	ADJ
ejpam-3399	136	31	,	,	PUNCT
ejpam-3399	136	32	g′	g′	NOUN
ejpam-3399	136	33	is	be	AUX
ejpam-3399	136	34	p	p	NOUN
ejpam-3399	136	35	-	-	PUNCT
ejpam-3399	136	36	nilpotent	nilpotent	ADJ
ejpam-3399	136	37	.	.	PUNCT
ejpam-3399	137	1	thus	thus	ADV
ejpam-3399	137	2	we	we	PRON
ejpam-3399	137	3	may	may	AUX
ejpam-3399	137	4	assume	assume	VERB
ejpam-3399	137	5	that	that	SCONJ
ejpam-3399	137	6	op′(g	op′(g	PROPN
ejpam-3399	137	7	)	)	PUNCT
ejpam-3399	137	8	=	=	PUNCT
ejpam-3399	138	1	1	1	X
ejpam-3399	138	2	.	.	PUNCT
ejpam-3399	139	1	if	if	SCONJ
ejpam-3399	139	2	each	each	DET
ejpam-3399	139	3	subgroup	subgroup	NOUN
ejpam-3399	139	4	h	h	NOUN
ejpam-3399	139	5	of	of	ADP
ejpam-3399	139	6	p	p	NOUN
ejpam-3399	139	7	with	with	ADP
ejpam-3399	139	8	|h|	|h|	PROPN
ejpam-3399	139	9	=	=	PUNCT
ejpam-3399	139	10	|d|	|d|	PROPN
ejpam-3399	139	11	is	be	AUX
ejpam-3399	139	12	normal	normal	ADJ
ejpam-3399	139	13	in	in	ADP
ejpam-3399	139	14	g	g	PROPN
ejpam-3399	139	15	,	,	PUNCT
ejpam-3399	139	16	then	then	ADV
ejpam-3399	139	17	g′	g′	NOUN
ejpam-3399	139	18	is	be	AUX
ejpam-3399	139	19	p	p	NOUN
ejpam-3399	139	20	-	-	PUNCT
ejpam-3399	139	21	nilpotent	nilpotent	ADJ
ejpam-3399	139	22	by	by	ADP
ejpam-3399	139	23	theorem	theorem	NOUN
ejpam-3399	139	24	2.2	2.2	NUM
ejpam-3399	139	25	.	.	PUNCT
ejpam-3399	140	1	so	so	ADV
ejpam-3399	140	2	we	we	PRON
ejpam-3399	140	3	may	may	AUX
ejpam-3399	140	4	assume	assume	VERB
ejpam-3399	140	5	that	that	SCONJ
ejpam-3399	140	6	there	there	PRON
ejpam-3399	140	7	exists	exist	VERB
ejpam-3399	140	8	a	a	DET
ejpam-3399	140	9	subgroup	subgroup	NOUN
ejpam-3399	140	10	h	h	NOUN
ejpam-3399	140	11	of	of	ADP
ejpam-3399	140	12	p	p	NOUN
ejpam-3399	140	13	with	with	ADP
ejpam-3399	140	14	|h|	|h|	PROPN
ejpam-3399	140	15	=	=	SYM
ejpam-3399	140	16	|d|	|d|	PROPN
ejpam-3399	140	17	and	and	CCONJ
ejpam-3399	140	18	h	h	NOUN
ejpam-3399	140	19	is	be	AUX
ejpam-3399	140	20	not	not	PART
ejpam-3399	140	21	normal	normal	ADJ
ejpam-3399	140	22	in	in	ADP
ejpam-3399	140	23	g.	g.	PROPN
ejpam-3399	140	24	by	by	ADP
ejpam-3399	140	25	hypothesis	hypothesis	NOUN
ejpam-3399	140	26	,	,	PUNCT
ejpam-3399	140	27	h	h	PROPN
ejpam-3399	140	28	is	be	AUX
ejpam-3399	140	29	s	s	NOUN
ejpam-3399	140	30	-	-	NOUN
ejpam-3399	140	31	permutable	permutable	ADJ
ejpam-3399	140	32	in	in	ADP
ejpam-3399	140	33	g.	g.	PROPN
ejpam-3399	140	34	since	since	SCONJ
ejpam-3399	140	35	h	h	PROPN
ejpam-3399	140	36	6	6	NUM
ejpam-3399	140	37	g	g	NOUN
ejpam-3399	140	38	and	and	CCONJ
ejpam-3399	140	39	h	h	NOUN
ejpam-3399	140	40	is	be	AUX
ejpam-3399	140	41	s	s	NOUN
ejpam-3399	140	42	-	-	NOUN
ejpam-3399	140	43	permutable	permutable	ADJ
ejpam-3399	140	44	in	in	ADP
ejpam-3399	140	45	g	g	PROPN
ejpam-3399	140	46	,	,	PUNCT
ejpam-3399	140	47	we	we	PRON
ejpam-3399	140	48	have	have	VERB
ejpam-3399	140	49	by	by	ADP
ejpam-3399	140	50	(	(	PUNCT
ejpam-3399	140	51	[	[	X
ejpam-3399	140	52	13	13	NUM
ejpam-3399	140	53	]	]	PUNCT
ejpam-3399	140	54	,	,	PUNCT
ejpam-3399	140	55	lemma	lemma	PROPN
ejpam-3399	140	56	a	a	PRON
ejpam-3399	140	57	)	)	PUNCT
ejpam-3399	140	58	that	that	PRON
ejpam-3399	140	59	op(g	op(g	X
ejpam-3399	140	60	)	)	PUNCT
ejpam-3399	140	61	≤	≤	NOUN
ejpam-3399	140	62	ng(h	ng(h	ADV
ejpam-3399	140	63	)	)	PUNCT
ejpam-3399	141	1	<	<	X
ejpam-3399	142	1	g.	g.	PROPN
ejpam-3399	143	1	let	let	VERB
ejpam-3399	143	2	m	m	PRON
ejpam-3399	143	3	be	be	AUX
ejpam-3399	143	4	a	a	DET
ejpam-3399	143	5	maximal	maximal	ADJ
ejpam-3399	143	6	subgroup	subgroup	NOUN
ejpam-3399	143	7	of	of	ADP
ejpam-3399	143	8	g	g	PROPN
ejpam-3399	143	9	contains	contain	VERB
ejpam-3399	143	10	ng(h	ng(h	ADV
ejpam-3399	143	11	)	)	PUNCT
ejpam-3399	143	12	properly	properly	ADV
ejpam-3399	143	13	.	.	PUNCT
ejpam-3399	144	1	then	then	ADV
ejpam-3399	144	2	m	m	VERB
ejpam-3399	144	3	cg	cg	NOUN
ejpam-3399	144	4	and	and	CCONJ
ejpam-3399	144	5	|g	|g	NOUN
ejpam-3399	144	6	/	/	SYM
ejpam-3399	144	7	m	m	PROPN
ejpam-3399	144	8	|	|	NOUN
ejpam-3399	144	9	=	=	SYM
ejpam-3399	145	1	p.	p.	NOUN
ejpam-3399	145	2	let	let	VERB
ejpam-3399	145	3	p1	p1	PROPN
ejpam-3399	145	4	=	=	PROPN
ejpam-3399	146	1	p	p	X
ejpam-3399	146	2	∩m	∩m	PROPN
ejpam-3399	146	3	be	be	AUX
ejpam-3399	146	4	a	a	DET
ejpam-3399	146	5	sylow	sylow	NOUN
ejpam-3399	146	6	p	p	NOUN
ejpam-3399	146	7	-	-	PUNCT
ejpam-3399	146	8	subgroup	subgroup	NOUN
ejpam-3399	146	9	of	of	ADP
ejpam-3399	146	10	m	m	PROPN
ejpam-3399	146	11	.	.	PUNCT
ejpam-3399	147	1	by	by	ADP
ejpam-3399	147	2	the	the	DET
ejpam-3399	147	3	hypothesis	hypothesis	NOUN
ejpam-3399	147	4	,	,	PUNCT
ejpam-3399	147	5	|d|	|d|	PROPN
ejpam-3399	147	6	≤	≤	PROPN
ejpam-3399	147	7	|p1|	|p1|	ADV
ejpam-3399	147	8	.	.	PUNCT
ejpam-3399	148	1	if	if	SCONJ
ejpam-3399	148	2	|d|	|d|	PROPN
ejpam-3399	148	3	=	=	SYM
ejpam-3399	148	4	|p1|	|p1|	PROPN
ejpam-3399	148	5	,	,	PUNCT
ejpam-3399	148	6	then	then	ADV
ejpam-3399	148	7	|h|	|h|	PROPN
ejpam-3399	148	8	=	=	PUNCT
ejpam-3399	148	9	|p1|	|p1|	NOUN
ejpam-3399	148	10	and	and	CCONJ
ejpam-3399	148	11	so	so	ADV
ejpam-3399	148	12	references	reference	NOUN
ejpam-3399	148	13	575	575	NUM
ejpam-3399	148	14	p	p	NOUN
ejpam-3399	148	15	≤	≤	NUM
ejpam-3399	148	16	ng(h	ng(h	ADV
ejpam-3399	148	17	)	)	PUNCT
ejpam-3399	148	18	,	,	PUNCT
ejpam-3399	148	19	and	and	CCONJ
ejpam-3399	148	20	since	since	SCONJ
ejpam-3399	148	21	op(g	op(g	NUM
ejpam-3399	148	22	)	)	PUNCT
ejpam-3399	148	23	≤	≤	NOUN
ejpam-3399	148	24	ng(h	ng(h	ADV
ejpam-3399	148	25	)	)	PUNCT
ejpam-3399	148	26	,	,	PUNCT
ejpam-3399	148	27	we	we	PRON
ejpam-3399	148	28	have	have	VERB
ejpam-3399	148	29	pop(g	pop(g	NOUN
ejpam-3399	148	30	)	)	PUNCT
ejpam-3399	149	1	=	=	SYM
ejpam-3399	149	2	g	g	PROPN
ejpam-3399	149	3	≤	≤	NUM
ejpam-3399	149	4	ng(h	ng(h	ADV
ejpam-3399	149	5	)	)	PUNCT
ejpam-3399	149	6	<	<	X
ejpam-3399	149	7	m	m	VERB
ejpam-3399	149	8	which	which	PRON
ejpam-3399	149	9	is	be	AUX
ejpam-3399	149	10	impossible	impossible	ADJ
ejpam-3399	149	11	.	.	PUNCT
ejpam-3399	150	1	thus	thus	ADV
ejpam-3399	150	2	we	we	PRON
ejpam-3399	150	3	may	may	AUX
ejpam-3399	150	4	assume	assume	VERB
ejpam-3399	150	5	that	that	SCONJ
ejpam-3399	150	6	|d|	|d|	PROPN
ejpam-3399	150	7	<	<	X
ejpam-3399	150	8	|p1|	|p1|	PROPN
ejpam-3399	150	9	.	.	PUNCT
ejpam-3399	151	1	now	now	ADV
ejpam-3399	151	2	m	m	VERB
ejpam-3399	151	3	′	′	ADJ
ejpam-3399	151	4	is	be	AUX
ejpam-3399	151	5	p	p	NOUN
ejpam-3399	151	6	-	-	PUNCT
ejpam-3399	151	7	nilpotent	nilpotent	ADJ
ejpam-3399	151	8	,	,	PUNCT
ejpam-3399	151	9	by	by	ADP
ejpam-3399	151	10	the	the	DET
ejpam-3399	151	11	inductive	inductive	ADJ
ejpam-3399	151	12	hypothesis	hypothesis	NOUN
ejpam-3399	151	13	,	,	PUNCT
ejpam-3399	151	14	implies	imply	VERB
ejpam-3399	151	15	that	that	SCONJ
ejpam-3399	151	16	m	m	VERB
ejpam-3399	151	17	′	′	VERB
ejpam-3399	151	18	is	be	AUX
ejpam-3399	151	19	a	a	DET
ejpam-3399	151	20	p	p	NOUN
ejpam-3399	151	21	-	-	PUNCT
ejpam-3399	151	22	group	group	NOUN
ejpam-3399	151	23	because	because	SCONJ
ejpam-3399	151	24	op′(g	op′(g	PROPN
ejpam-3399	151	25	)	)	PUNCT
ejpam-3399	151	26	=	=	SYM
ejpam-3399	152	1	1	1	X
ejpam-3399	152	2	.	.	PUNCT
ejpam-3399	152	3	then	then	ADV
ejpam-3399	152	4	p1	p1	PROPN
ejpam-3399	152	5	is	be	AUX
ejpam-3399	152	6	characteristic	characteristic	ADJ
ejpam-3399	152	7	in	in	ADP
ejpam-3399	152	8	m	m	PROPN
ejpam-3399	152	9	and	and	CCONJ
ejpam-3399	152	10	since	since	SCONJ
ejpam-3399	152	11	mcg	mcg	PROPN
ejpam-3399	152	12	,	,	PUNCT
ejpam-3399	152	13	we	we	PRON
ejpam-3399	152	14	have	have	AUX
ejpam-3399	152	15	p1cg	p1cg	VERB
ejpam-3399	152	16	.	.	PUNCT
ejpam-3399	153	1	if	if	SCONJ
ejpam-3399	153	2	pcg	pcg	PROPN
ejpam-3399	153	3	,	,	PUNCT
ejpam-3399	153	4	then	then	ADV
ejpam-3399	153	5	g	g	PROPN
ejpam-3399	153	6	/	/	SYM
ejpam-3399	153	7	p	p	NOUN
ejpam-3399	153	8	is	be	AUX
ejpam-3399	153	9	abelian	abelian	ADJ
ejpam-3399	153	10	and	and	CCONJ
ejpam-3399	153	11	since	since	SCONJ
ejpam-3399	153	12	all	all	DET
ejpam-3399	153	13	subgroups	subgroup	NOUN
ejpam-3399	153	14	h	h	NOUN
ejpam-3399	153	15	of	of	ADP
ejpam-3399	153	16	p	p	NOUN
ejpam-3399	153	17	with	with	ADP
ejpam-3399	153	18	|h|	|h|	PROPN
ejpam-3399	153	19	=	=	SYM
ejpam-3399	153	20	|d|	|d|	PROPN
ejpam-3399	153	21	are	be	AUX
ejpam-3399	153	22	s	s	NOUN
ejpam-3399	153	23	-	-	NOUN
ejpam-3399	153	24	permutable	permutable	ADJ
ejpam-3399	153	25	in	in	ADP
ejpam-3399	153	26	g	g	PROPN
ejpam-3399	153	27	,	,	PUNCT
ejpam-3399	153	28	we	we	PRON
ejpam-3399	153	29	have	have	VERB
ejpam-3399	153	30	that	that	PRON
ejpam-3399	153	31	g	g	PROPN
ejpam-3399	153	32	is	be	AUX
ejpam-3399	153	33	supersolvable	supersolvable	ADJ
ejpam-3399	153	34	by	by	ADP
ejpam-3399	153	35	(	(	PUNCT
ejpam-3399	153	36	[	[	X
ejpam-3399	153	37	14	14	NUM
ejpam-3399	153	38	]	]	PUNCT
ejpam-3399	153	39	,	,	PUNCT
ejpam-3399	153	40	theorem	theorem	VERB
ejpam-3399	153	41	1.3	1.3	NUM
ejpam-3399	153	42	)	)	PUNCT
ejpam-3399	153	43	and	and	CCONJ
ejpam-3399	153	44	so	so	ADV
ejpam-3399	153	45	g′	g′	NOUN
ejpam-3399	153	46	is	be	AUX
ejpam-3399	153	47	nilpotent	nilpotent	ADJ
ejpam-3399	153	48	;	;	PUNCT
ejpam-3399	153	49	in	in	ADP
ejpam-3399	153	50	particular	particular	ADJ
ejpam-3399	153	51	g′	g′	NOUN
ejpam-3399	153	52	is	be	AUX
ejpam-3399	153	53	p	p	NOUN
ejpam-3399	153	54	-	-	PUNCT
ejpam-3399	153	55	nilpotent	nilpotent	ADJ
ejpam-3399	153	56	.	.	PUNCT
ejpam-3399	154	1	thus	thus	ADV
ejpam-3399	154	2	we	we	PRON
ejpam-3399	154	3	may	may	AUX
ejpam-3399	154	4	assume	assume	VERB
ejpam-3399	154	5	that	that	SCONJ
ejpam-3399	154	6	p	p	PROPN
ejpam-3399	154	7	6	6	NUM
ejpam-3399	154	8	g	g	NOUN
ejpam-3399	154	9	and	and	CCONJ
ejpam-3399	154	10	p1	p1	PROPN
ejpam-3399	154	11	=	=	SYM
ejpam-3399	154	12	f	f	PROPN
ejpam-3399	154	13	(	(	PUNCT
ejpam-3399	154	14	g	g	NOUN
ejpam-3399	154	15	)	)	PUNCT
ejpam-3399	154	16	the	the	DET
ejpam-3399	154	17	fitting	fitting	ADJ
ejpam-3399	154	18	subgroup	subgroup	NOUN
ejpam-3399	154	19	of	of	ADP
ejpam-3399	154	20	g	g	PROPN
ejpam-3399	154	21	(	(	PUNCT
ejpam-3399	154	22	recall	recall	VERB
ejpam-3399	154	23	that	that	PRON
ejpam-3399	154	24	op′(g	op′(g	PROPN
ejpam-3399	154	25	)	)	PUNCT
ejpam-3399	154	26	=	=	SYM
ejpam-3399	154	27	1	1	NUM
ejpam-3399	154	28	and	and	CCONJ
ejpam-3399	154	29	that	that	SCONJ
ejpam-3399	154	30	f	f	X
ejpam-3399	154	31	(	(	PUNCT
ejpam-3399	154	32	g	g	NOUN
ejpam-3399	154	33	)	)	PUNCT
ejpam-3399	155	1	=	=	NOUN
ejpam-3399	155	2	<	<	X
ejpam-3399	155	3	op(g	op(g	NUM
ejpam-3399	155	4	)	)	PUNCT
ejpam-3399	155	5	for	for	ADP
ejpam-3399	155	6	all	all	DET
ejpam-3399	155	7	p	p	NOUN
ejpam-3399	155	8	divides	divide	NOUN
ejpam-3399	155	9	|g|	|g|	PROPN
ejpam-3399	155	10	>	>	PUNCT
ejpam-3399	155	11	)	)	PUNCT
ejpam-3399	155	12	.	.	PUNCT
ejpam-3399	156	1	consider	consider	VERB
ejpam-3399	156	2	the	the	DET
ejpam-3399	156	3	subgroup	subgroup	NOUN
ejpam-3399	156	4	φ(p1	φ(p1	NOUN
ejpam-3399	156	5	)	)	PUNCT
ejpam-3399	156	6	and	and	CCONJ
ejpam-3399	156	7	assume	assume	VERB
ejpam-3399	156	8	that	that	SCONJ
ejpam-3399	156	9	φ(p1	φ(p1	NOUN
ejpam-3399	156	10	)	)	PUNCT
ejpam-3399	156	11	6=	6=	ADP
ejpam-3399	157	1	1	1	X
ejpam-3399	157	2	.	.	PUNCT
ejpam-3399	158	1	hence	hence	ADV
ejpam-3399	158	2	if	if	SCONJ
ejpam-3399	158	3	|φ(p1)|	|φ(p1)|	PROPN
ejpam-3399	158	4	<	<	X
ejpam-3399	158	5	|d|	|d|	PROPN
ejpam-3399	158	6	,	,	PUNCT
ejpam-3399	158	7	then	then	ADV
ejpam-3399	158	8	(	(	PUNCT
ejpam-3399	158	9	g	g	NOUN
ejpam-3399	158	10	/	/	SYM
ejpam-3399	158	11	φ(p1	φ(p1	NOUN
ejpam-3399	158	12	)	)	PUNCT
ejpam-3399	158	13	)	)	PUNCT
ejpam-3399	159	1	′	′	NUM
ejpam-3399	159	2	is	be	AUX
ejpam-3399	159	3	p	p	NOUN
ejpam-3399	159	4	-	-	PUNCT
ejpam-3399	159	5	nilpotent	nilpotent	ADJ
ejpam-3399	159	6	by	by	ADP
ejpam-3399	159	7	induction	induction	NOUN
ejpam-3399	159	8	on	on	ADP
ejpam-3399	159	9	|g|	|g|	PROPN
ejpam-3399	159	10	;	;	PUNCT
ejpam-3399	159	11	in	in	ADP
ejpam-3399	159	12	particular	particular	ADJ
ejpam-3399	159	13	g′	g′	NOUN
ejpam-3399	159	14	is	be	AUX
ejpam-3399	159	15	p	p	NOUN
ejpam-3399	159	16	-	-	PUNCT
ejpam-3399	159	17	nilpotent	nilpotent	ADJ
ejpam-3399	159	18	.	.	PUNCT
ejpam-3399	160	1	so	so	ADV
ejpam-3399	160	2	assume	assume	VERB
ejpam-3399	160	3	that	that	SCONJ
ejpam-3399	160	4	|φ(p1)|	|φ(p1)|	PROPN
ejpam-3399	160	5	≥	≥	NUM
ejpam-3399	160	6	|d|	|d|	NOUN
ejpam-3399	160	7	.	.	PUNCT
ejpam-3399	161	1	if	if	SCONJ
ejpam-3399	161	2	|φ(p1)|	|φ(p1)|	PROPN
ejpam-3399	161	3	=	=	SYM
ejpam-3399	161	4	|d|	|d|	PROPN
ejpam-3399	161	5	,	,	PUNCT
ejpam-3399	161	6	then	then	ADV
ejpam-3399	161	7	p	p	X
ejpam-3399	161	8	/	/	SYM
ejpam-3399	161	9	φ(p1	φ(p1	NOUN
ejpam-3399	161	10	)	)	PUNCT
ejpam-3399	161	11	is	be	AUX
ejpam-3399	161	12	not	not	PART
ejpam-3399	161	13	cyclic	cyclic	ADJ
ejpam-3399	161	14	.	.	PUNCT
ejpam-3399	162	1	let	let	VERB
ejpam-3399	162	2	l	l	NOUN
ejpam-3399	162	3	/	/	SYM
ejpam-3399	162	4	φ(p1	φ(p1	NOUN
ejpam-3399	162	5	)	)	PUNCT
ejpam-3399	162	6	be	be	VERB
ejpam-3399	162	7	a	a	DET
ejpam-3399	162	8	proper	proper	ADJ
ejpam-3399	162	9	subgroup	subgroup	NOUN
ejpam-3399	162	10	of	of	ADP
ejpam-3399	162	11	p	p	X
ejpam-3399	162	12	/	/	SYM
ejpam-3399	162	13	φ(p1	φ(p1	NOUN
ejpam-3399	162	14	)	)	PUNCT
ejpam-3399	163	1	such	such	ADJ
ejpam-3399	163	2	that	that	SCONJ
ejpam-3399	163	3	|l	|l	PROPN
ejpam-3399	163	4	/	/	SYM
ejpam-3399	163	5	φ(p1)|	φ(p1)|	PROPN
ejpam-3399	163	6	=	=	SYM
ejpam-3399	163	7	p	p	X
ejpam-3399	163	8	(	(	PUNCT
ejpam-3399	163	9	l	l	NOUN
ejpam-3399	163	10	is	be	AUX
ejpam-3399	163	11	not	not	PART
ejpam-3399	163	12	cyclic	cyclic	ADJ
ejpam-3399	163	13	;	;	PUNCT
ejpam-3399	163	14	otherwise	otherwise	ADV
ejpam-3399	163	15	φ(p1	φ(p1	NOUN
ejpam-3399	163	16	)	)	PUNCT
ejpam-3399	163	17	is	be	AUX
ejpam-3399	163	18	cyclic	cyclic	ADJ
ejpam-3399	163	19	and	and	CCONJ
ejpam-3399	163	20	this	this	PRON
ejpam-3399	163	21	implies	imply	VERB
ejpam-3399	163	22	that	that	SCONJ
ejpam-3399	163	23	there	there	PRON
ejpam-3399	163	24	exists	exist	VERB
ejpam-3399	163	25	l1	l1	PROPN
ejpam-3399	163	26	≤	≤	PROPN
ejpam-3399	163	27	φ(p1	φ(p1	NOUN
ejpam-3399	163	28	)	)	PUNCT
ejpam-3399	163	29	such	such	ADJ
ejpam-3399	163	30	that	that	SCONJ
ejpam-3399	163	31	l1cg	l1cg	ADV
ejpam-3399	163	32	;	;	PUNCT
ejpam-3399	163	33	in	in	ADP
ejpam-3399	163	34	particular	particular	ADJ
ejpam-3399	163	35	g	g	PROPN
ejpam-3399	163	36	/	/	SYM
ejpam-3399	163	37	cg(l1	cg(l1	NOUN
ejpam-3399	163	38	)	)	PUNCT
ejpam-3399	163	39	is	be	AUX
ejpam-3399	163	40	isomorphic	isomorphic	ADJ
ejpam-3399	163	41	to	to	ADP
ejpam-3399	163	42	a	a	DET
ejpam-3399	163	43	subgroup	subgroup	NOUN
ejpam-3399	163	44	of	of	ADP
ejpam-3399	163	45	aut(l1	aut(l1	PROPN
ejpam-3399	163	46	)	)	PUNCT
ejpam-3399	163	47	and	and	CCONJ
ejpam-3399	163	48	so	so	ADV
ejpam-3399	163	49	g′	g′	NOUN
ejpam-3399	163	50	≤	≤	PROPN
ejpam-3399	163	51	cg(l1	cg(l1	NOUN
ejpam-3399	163	52	)	)	PUNCT
ejpam-3399	163	53	and	and	CCONJ
ejpam-3399	163	54	we	we	PRON
ejpam-3399	163	55	conclude	conclude	VERB
ejpam-3399	163	56	then	then	ADV
ejpam-3399	163	57	that	that	SCONJ
ejpam-3399	163	58	g′	g′	NOUN
ejpam-3399	163	59	is	be	AUX
ejpam-3399	163	60	p	p	NOUN
ejpam-3399	163	61	-	-	PUNCT
ejpam-3399	163	62	nilpotent	nilpotent	ADJ
ejpam-3399	163	63	)	)	PUNCT
ejpam-3399	163	64	.	.	PUNCT
ejpam-3399	164	1	as	as	ADP
ejpam-3399	164	2	|l	|l	PROPN
ejpam-3399	164	3	/	/	SYM
ejpam-3399	164	4	φ(p1)|	φ(p1)|	PROPN
ejpam-3399	164	5	=	=	SYM
ejpam-3399	164	6	p	p	NOUN
ejpam-3399	164	7	,	,	PUNCT
ejpam-3399	164	8	then	then	ADV
ejpam-3399	164	9	there	there	PRON
ejpam-3399	164	10	exists	exist	VERB
ejpam-3399	164	11	a	a	DET
ejpam-3399	164	12	maximal	maximal	ADJ
ejpam-3399	164	13	subgroup	subgroup	NOUN
ejpam-3399	164	14	l1	l1	PROPN
ejpam-3399	164	15	of	of	ADP
ejpam-3399	164	16	l	l	PROPN
ejpam-3399	164	17	such	such	ADJ
ejpam-3399	164	18	that	that	DET
ejpam-3399	164	19	|l1|	|l1|	NOUN
ejpam-3399	164	20	=	=	SYM
ejpam-3399	164	21	|φ(p1)|	|φ(p1)|	PROPN
ejpam-3399	164	22	=	=	SYM
ejpam-3399	164	23	|d|	|d|	PROPN
ejpam-3399	164	24	and	and	CCONJ
ejpam-3399	164	25	l1	l1	PROPN
ejpam-3399	164	26	6=	6=	SYM
ejpam-3399	164	27	φ(p1	φ(p1	PROPN
ejpam-3399	164	28	)	)	PUNCT
ejpam-3399	164	29	.	.	PUNCT
ejpam-3399	165	1	but	but	CCONJ
ejpam-3399	165	2	l1φ(p1	l1φ(p1	NOUN
ejpam-3399	165	3	)	)	PUNCT
ejpam-3399	165	4	is	be	AUX
ejpam-3399	165	5	s	s	NOUN
ejpam-3399	165	6	-	-	NOUN
ejpam-3399	165	7	permutable	permutable	ADJ
ejpam-3399	165	8	in	in	ADP
ejpam-3399	165	9	g	g	PROPN
ejpam-3399	165	10	,	,	PUNCT
ejpam-3399	165	11	then	then	ADV
ejpam-3399	165	12	l1φ(p1)/φ(p1	l1φ(p1)/φ(p1	NOUN
ejpam-3399	165	13	)	)	PUNCT
ejpam-3399	166	1	=	=	PUNCT
ejpam-3399	166	2	l	l	NOUN
ejpam-3399	166	3	/	/	SYM
ejpam-3399	166	4	φ(p1	φ(p1	NOUN
ejpam-3399	166	5	)	)	PUNCT
ejpam-3399	166	6	is	be	AUX
ejpam-3399	166	7	s	s	NOUN
ejpam-3399	166	8	-	-	NOUN
ejpam-3399	166	9	permutable	permutable	ADJ
ejpam-3399	166	10	in	in	ADP
ejpam-3399	166	11	g	g	PROPN
ejpam-3399	166	12	/	/	SYM
ejpam-3399	166	13	φ(p1	φ(p1	NOUN
ejpam-3399	166	14	)	)	PUNCT
ejpam-3399	166	15	.	.	PUNCT
ejpam-3399	167	1	by	by	ADP
ejpam-3399	167	2	theorem	theorem	NOUN
ejpam-3399	167	3	2.1	2.1	NUM
ejpam-3399	167	4	,	,	PUNCT
ejpam-3399	167	5	(	(	PUNCT
ejpam-3399	167	6	g	g	NOUN
ejpam-3399	167	7	/	/	SYM
ejpam-3399	167	8	φ(p1	φ(p1	NOUN
ejpam-3399	167	9	)	)	PUNCT
ejpam-3399	167	10	)	)	PUNCT
ejpam-3399	167	11	′	′	NUM
ejpam-3399	168	1	=	=	PUNCT
ejpam-3399	168	2	g′φ(p1)/φ(p1	g′φ(p1)/φ(p1	NOUN
ejpam-3399	168	3	)	)	PUNCT
ejpam-3399	168	4	is	be	AUX
ejpam-3399	168	5	p	p	NOUN
ejpam-3399	168	6	-	-	PUNCT
ejpam-3399	168	7	nilpotent	nilpotent	ADJ
ejpam-3399	168	8	and	and	CCONJ
ejpam-3399	168	9	so	so	ADV
ejpam-3399	168	10	g′	g′	NOUN
ejpam-3399	168	11	is	be	AUX
ejpam-3399	168	12	p	p	NOUN
ejpam-3399	168	13	-	-	PUNCT
ejpam-3399	168	14	nilpotent	nilpotent	ADJ
ejpam-3399	168	15	.	.	PUNCT
ejpam-3399	169	1	thus	thus	ADV
ejpam-3399	169	2	we	we	PRON
ejpam-3399	169	3	may	may	AUX
ejpam-3399	169	4	assume	assume	VERB
ejpam-3399	169	5	that	that	SCONJ
ejpam-3399	169	6	φ(p1	φ(p1	NOUN
ejpam-3399	169	7	)	)	PUNCT
ejpam-3399	169	8	=	=	SYM
ejpam-3399	169	9	1	1	NUM
ejpam-3399	169	10	and	and	CCONJ
ejpam-3399	169	11	p1	p1	PROPN
ejpam-3399	169	12	is	be	AUX
ejpam-3399	169	13	elementary	elementary	ADJ
ejpam-3399	169	14	abelian	abelian	NOUN
ejpam-3399	169	15	.	.	PUNCT
ejpam-3399	170	1	since	since	SCONJ
ejpam-3399	170	2	all	all	DET
ejpam-3399	170	3	subgroups	subgroup	NOUN
ejpam-3399	170	4	h	h	NOUN
ejpam-3399	170	5	of	of	ADP
ejpam-3399	170	6	p1	p1	PROPN
ejpam-3399	170	7	with	with	ADP
ejpam-3399	170	8	|h|	|h|	PROPN
ejpam-3399	170	9	=	=	PUNCT
ejpam-3399	170	10	|d|	|d|	PROPN
ejpam-3399	170	11	are	be	AUX
ejpam-3399	170	12	normal	normal	ADJ
ejpam-3399	170	13	in	in	ADP
ejpam-3399	170	14	m	m	PROPN
ejpam-3399	170	15	,	,	PUNCT
ejpam-3399	170	16	we	we	PRON
ejpam-3399	170	17	have	have	VERB
ejpam-3399	170	18	by	by	ADP
ejpam-3399	170	19	(	(	PUNCT
ejpam-3399	170	20	[	[	X
ejpam-3399	170	21	1	1	NUM
ejpam-3399	170	22	]	]	PUNCT
ejpam-3399	170	23	,	,	PUNCT
ejpam-3399	170	24	lemma	lemma	PROPN
ejpam-3399	170	25	2.9	2.9	NUM
ejpam-3399	170	26	)	)	PUNCT
ejpam-3399	170	27	that	that	SCONJ
ejpam-3399	170	28	all	all	DET
ejpam-3399	170	29	subgroups	subgroup	NOUN
ejpam-3399	170	30	of	of	ADP
ejpam-3399	170	31	p1	p1	NOUN
ejpam-3399	170	32	of	of	ADP
ejpam-3399	170	33	order	order	NOUN
ejpam-3399	170	34	p	p	NOUN
ejpam-3399	170	35	are	be	AUX
ejpam-3399	170	36	normal	normal	ADJ
ejpam-3399	170	37	in	in	ADP
ejpam-3399	170	38	m	m	PROPN
ejpam-3399	170	39	.	.	PUNCT
ejpam-3399	171	1	so	so	ADV
ejpam-3399	171	2	p1	p1	PROPN
ejpam-3399	171	3	∩	∩	NOUN
ejpam-3399	171	4	z(p	z(p	NOUN
ejpam-3399	171	5	)	)	PUNCT
ejpam-3399	172	1	6=	6=	ADP
ejpam-3399	172	2	1	1	X
ejpam-3399	172	3	.	.	PUNCT
ejpam-3399	173	1	let	let	VERB
ejpam-3399	173	2	l	l	NOUN
ejpam-3399	173	3	≤	≤	ADJ
ejpam-3399	173	4	p1	p1	NOUN
ejpam-3399	173	5	∩	∩	NOUN
ejpam-3399	173	6	z(p	z(p	NOUN
ejpam-3399	173	7	)	)	PUNCT
ejpam-3399	173	8	such	such	ADJ
ejpam-3399	173	9	that	that	DET
ejpam-3399	173	10	|l|	|l|	NOUN
ejpam-3399	173	11	=	=	SYM
ejpam-3399	174	1	p.	p.	NOUN
ejpam-3399	175	1	then	then	ADV
ejpam-3399	175	2	l	l	PROPN
ejpam-3399	175	3	c	c	PROPN
ejpam-3399	175	4	g	g	PROPN
ejpam-3399	175	5	and	and	CCONJ
ejpam-3399	175	6	since	since	SCONJ
ejpam-3399	175	7	g	g	PROPN
ejpam-3399	175	8	/	/	SYM
ejpam-3399	175	9	cg(l	cg(l	NOUN
ejpam-3399	175	10	)	)	PUNCT
ejpam-3399	175	11	is	be	AUX
ejpam-3399	175	12	isomorphic	isomorphic	ADJ
ejpam-3399	175	13	to	to	ADP
ejpam-3399	175	14	a	a	DET
ejpam-3399	175	15	subgroup	subgroup	NOUN
ejpam-3399	175	16	of	of	ADP
ejpam-3399	175	17	aut(l	aut(l	PROPN
ejpam-3399	175	18	)	)	PUNCT
ejpam-3399	175	19	,	,	PUNCT
ejpam-3399	175	20	we	we	PRON
ejpam-3399	175	21	have	have	VERB
ejpam-3399	175	22	that	that	DET
ejpam-3399	175	23	g′	g′	NOUN
ejpam-3399	175	24	≤	≤	PROPN
ejpam-3399	175	25	cg(l	cg(l	NOUN
ejpam-3399	175	26	)	)	PUNCT
ejpam-3399	175	27	,	,	PUNCT
ejpam-3399	175	28	in	in	ADP
ejpam-3399	175	29	particular	particular	ADJ
ejpam-3399	175	30	g′l	g′l	NOUN
ejpam-3399	175	31	/	/	SYM
ejpam-3399	175	32	l	l	NOUN
ejpam-3399	175	33	is	be	AUX
ejpam-3399	175	34	p	p	NOUN
ejpam-3399	175	35	-	-	PUNCT
ejpam-3399	175	36	nilpotent	nilpotent	ADJ
ejpam-3399	175	37	and	and	CCONJ
ejpam-3399	175	38	so	so	ADV
ejpam-3399	175	39	g′	g′	NOUN
ejpam-3399	175	40	is	be	AUX
ejpam-3399	175	41	p	p	NOUN
ejpam-3399	175	42	-	-	PUNCT
ejpam-3399	175	43	nilpotent	nilpotent	ADJ
ejpam-3399	175	44	.	.	PUNCT
ejpam-3399	176	1	this	this	PRON
ejpam-3399	176	2	completes	complete	VERB
ejpam-3399	176	3	the	the	DET
ejpam-3399	176	4	proof	proof	NOUN
ejpam-3399	176	5	of	of	ADP
ejpam-3399	176	6	the	the	DET
ejpam-3399	176	7	theorem	theorem	PROPN
ejpam-3399	176	8	.	.	PUNCT
ejpam-3399	177	1	references	reference	NOUN
ejpam-3399	177	2	[	[	X
ejpam-3399	177	3	1	1	NUM
ejpam-3399	177	4	]	]	PUNCT
ejpam-3399	177	5	m.	m.	NOUN
ejpam-3399	177	6	asaad	asaad	NOUN
ejpam-3399	177	7	and	and	CCONJ
ejpam-3399	177	8	a.	a.	NOUN
ejpam-3399	177	9	a.	a.	NOUN
ejpam-3399	177	10	heliel	heliel	PROPN
ejpam-3399	177	11	,	,	PUNCT
ejpam-3399	177	12	on	on	ADP
ejpam-3399	177	13	s	s	VERB
ejpam-3399	177	14	-	-	ADJ
ejpam-3399	177	15	quasinormally	quasinormally	ADV
ejpam-3399	177	16	embedded	embed	VERB
ejpam-3399	177	17	subgroups	subgroup	NOUN
ejpam-3399	177	18	of	of	ADP
ejpam-3399	177	19	finite	finite	ADJ
ejpam-3399	177	20	groups	group	NOUN
ejpam-3399	177	21	,	,	PUNCT
ejpam-3399	177	22	jpaa	jpaa	ADJ
ejpam-3399	177	23	165(2001	165(2001	NUM
ejpam-3399	177	24	)	)	PUNCT
ejpam-3399	177	25	129	129	NUM
ejpam-3399	177	26	-	-	SYM
ejpam-3399	177	27	135	135	NUM
ejpam-3399	177	28	.	.	PUNCT
ejpam-3399	178	1	[	[	X
ejpam-3399	178	2	2	2	NUM
ejpam-3399	178	3	]	]	PUNCT
ejpam-3399	178	4	a.	a.	NOUN
ejpam-3399	178	5	ballester	ballester	NOUN
ejpam-3399	178	6	-	-	PUNCT
ejpam-3399	178	7	bolinches	bolinches	PROPN
ejpam-3399	178	8	and	and	CCONJ
ejpam-3399	178	9	x.	x.	NOUN
ejpam-3399	178	10	guo	guo	PROPN
ejpam-3399	178	11	,	,	PUNCT
ejpam-3399	178	12	on	on	ADP
ejpam-3399	178	13	complemented	complemented	ADJ
ejpam-3399	178	14	subgroups	subgroup	NOUN
ejpam-3399	178	15	of	of	ADP
ejpam-3399	178	16	finite	finite	ADJ
ejpam-3399	178	17	groups	group	NOUN
ejpam-3399	178	18	,	,	PUNCT
ejpam-3399	178	19	arch	arch	NOUN
ejpam-3399	178	20	.	.	PUNCT
ejpam-3399	179	1	math	math	NOUN
ejpam-3399	179	2	.	.	PUNCT
ejpam-3399	180	1	72(1999	72(1999	NOUN
ejpam-3399	180	2	)	)	PUNCT
ejpam-3399	180	3	161	161	NUM
ejpam-3399	180	4	-	-	SYM
ejpam-3399	180	5	166	166	NUM
ejpam-3399	180	6	.	.	PUNCT
ejpam-3399	181	1	[	[	X
ejpam-3399	181	2	3	3	NUM
ejpam-3399	181	3	]	]	PUNCT
ejpam-3399	181	4	a.	a.	NOUN
ejpam-3399	181	5	ballester	ballester	NOUN
ejpam-3399	181	6	-	-	PUNCT
ejpam-3399	181	7	bolinches	bolinches	PROPN
ejpam-3399	181	8	,	,	PUNCT
ejpam-3399	181	9	y.	y.	PROPN
ejpam-3399	181	10	wang	wang	PROPN
ejpam-3399	181	11	and	and	CCONJ
ejpam-3399	181	12	x.	x.	PROPN
ejpam-3399	181	13	guo	guo	PROPN
ejpam-3399	181	14	(	(	PUNCT
ejpam-3399	181	15	2000	2000	NUM
ejpam-3399	181	16	)	)	PUNCT
ejpam-3399	181	17	,	,	PUNCT
ejpam-3399	181	18	c	c	X
ejpam-3399	181	19	-	-	PUNCT
ejpam-3399	181	20	supplemented	supplement	VERB
ejpam-3399	181	21	subgroups	subgroup	NOUN
ejpam-3399	181	22	of	of	ADP
ejpam-3399	181	23	finite	finite	ADJ
ejpam-3399	181	24	groups	group	NOUN
ejpam-3399	181	25	,	,	PUNCT
ejpam-3399	181	26	glasgow	glasgow	PROPN
ejpam-3399	181	27	math	math	NOUN
ejpam-3399	181	28	.	.	PUNCT
ejpam-3399	182	1	j.	j.	PROPN
ejpam-3399	182	2	42(2000	42(2000	PROPN
ejpam-3399	182	3	)	)	PUNCT
ejpam-3399	182	4	383	383	NUM
ejpam-3399	182	5	-	-	SYM
ejpam-3399	182	6	389	389	NUM
ejpam-3399	182	7	.	.	PUNCT
ejpam-3399	183	1	[	[	X
ejpam-3399	183	2	4	4	X
ejpam-3399	183	3	]	]	PUNCT
ejpam-3399	183	4	j.	j.	PROPN
ejpam-3399	183	5	buckely	buckely	ADV
ejpam-3399	183	6	,	,	PUNCT
ejpam-3399	183	7	finite	finite	ADJ
ejpam-3399	183	8	groups	group	NOUN
ejpam-3399	183	9	whose	whose	DET
ejpam-3399	183	10	minimal	minimal	ADJ
ejpam-3399	183	11	subgroups	subgroup	NOUN
ejpam-3399	183	12	are	be	AUX
ejpam-3399	183	13	normal	normal	ADJ
ejpam-3399	183	14	,	,	PUNCT
ejpam-3399	183	15	math	math	NOUN
ejpam-3399	183	16	.	.	PUNCT
ejpam-3399	184	1	z.	z.	PROPN
ejpam-3399	184	2	116(1970	116(1970	NUM
ejpam-3399	184	3	)	)	PUNCT
ejpam-3399	184	4	15	15	NUM
ejpam-3399	184	5	-	-	SYM
ejpam-3399	184	6	17	17	NUM
ejpam-3399	184	7	.	.	PUNCT
ejpam-3399	185	1	[	[	X
ejpam-3399	185	2	5	5	X
ejpam-3399	185	3	]	]	PUNCT
ejpam-3399	185	4	d.	d.	PROPN
ejpam-3399	185	5	gorenstein	gorenstein	PROPN
ejpam-3399	185	6	,	,	PUNCT
ejpam-3399	185	7	finite	finite	ADJ
ejpam-3399	185	8	groups	group	NOUN
ejpam-3399	185	9	,	,	PUNCT
ejpam-3399	185	10	american	american	PROPN
ejpam-3399	185	11	mathematical	mathematical	ADJ
ejpam-3399	185	12	society	society	NOUN
ejpam-3399	185	13	,	,	PUNCT
ejpam-3399	185	14	1980	1980	NUM
ejpam-3399	185	15	.	.	PUNCT
ejpam-3399	186	1	[	[	X
ejpam-3399	186	2	6	6	NUM
ejpam-3399	186	3	]	]	PUNCT
ejpam-3399	186	4	p.	p.	NOUN
ejpam-3399	186	5	hall	hall	PROPN
ejpam-3399	186	6	,	,	PUNCT
ejpam-3399	186	7	a	a	DET
ejpam-3399	186	8	characteristic	characteristic	ADJ
ejpam-3399	186	9	property	property	NOUN
ejpam-3399	186	10	of	of	ADP
ejpam-3399	186	11	solvable	solvable	ADJ
ejpam-3399	186	12	groups	group	NOUN
ejpam-3399	186	13	,	,	PUNCT
ejpam-3399	186	14	j.	j.	PROPN
ejpam-3399	186	15	london	london	PROPN
ejpam-3399	186	16	math	math	PROPN
ejpam-3399	186	17	.	.	PUNCT
ejpam-3399	187	1	soc	soc	PROPN
ejpam-3399	187	2	.	.	PUNCT
ejpam-3399	188	1	12(1937	12(1937	NUM
ejpam-3399	188	2	)	)	PUNCT
ejpam-3399	188	3	198	198	NUM
ejpam-3399	188	4	-	-	SYM
ejpam-3399	188	5	200	200	NUM
ejpam-3399	188	6	.	.	PUNCT
ejpam-3399	189	1	[	[	X
ejpam-3399	189	2	7	7	X
ejpam-3399	189	3	]	]	X
ejpam-3399	189	4	p.	p.	NOUN
ejpam-3399	189	5	hall	hall	PROPN
ejpam-3399	189	6	,	,	PUNCT
ejpam-3399	189	7	complemented	complemented	ADJ
ejpam-3399	189	8	groups	group	NOUN
ejpam-3399	189	9	,	,	PUNCT
ejpam-3399	189	10	j.	j.	PROPN
ejpam-3399	189	11	london	london	PROPN
ejpam-3399	189	12	math	math	PROPN
ejpam-3399	189	13	.	.	PUNCT
ejpam-3399	190	1	soc	soc	PROPN
ejpam-3399	190	2	.	.	PUNCT
ejpam-3399	191	1	12(1937	12(1937	NUM
ejpam-3399	191	2	)	)	PUNCT
ejpam-3399	191	3	201	201	NUM
ejpam-3399	191	4	-	-	SYM
ejpam-3399	191	5	204	204	NUM
ejpam-3399	191	6	.	.	PUNCT
ejpam-3399	192	1	references	reference	NOUN
ejpam-3399	192	2	576	576	NUM
ejpam-3399	193	1	[	[	NOUN
ejpam-3399	193	2	8	8	NUM
ejpam-3399	193	3	]	]	PUNCT
ejpam-3399	193	4	a.	a.	NOUN
ejpam-3399	193	5	a.	a.	NOUN
ejpam-3399	193	6	heliel	heliel	PROPN
ejpam-3399	193	7	,	,	PUNCT
ejpam-3399	193	8	a	a	DET
ejpam-3399	193	9	note	note	NOUN
ejpam-3399	193	10	on	on	ADP
ejpam-3399	193	11	c	c	NOUN
ejpam-3399	193	12	-	-	PUNCT
ejpam-3399	193	13	supplemented	supplement	VERB
ejpam-3399	193	14	subgroups	subgroup	NOUN
ejpam-3399	193	15	of	of	ADP
ejpam-3399	193	16	finite	finite	ADJ
ejpam-3399	193	17	groups	group	NOUN
ejpam-3399	193	18	,	,	PUNCT
ejpam-3399	193	19	comm	comm	NOUN
ejpam-3399	193	20	.	.	PUNCT
ejpam-3399	194	1	algebra	algebra	PROPN
ejpam-3399	194	2	42(2014	42(2014	NUM
ejpam-3399	194	3	)	)	PUNCT
ejpam-3399	194	4	1650	1650	NUM
ejpam-3399	194	5	-	-	SYM
ejpam-3399	194	6	1656	1656	NUM
ejpam-3399	194	7	.	.	PUNCT
ejpam-3399	195	1	[	[	X
ejpam-3399	195	2	9	9	NUM
ejpam-3399	195	3	]	]	X
ejpam-3399	195	4	r.	r.	PROPN
ejpam-3399	195	5	hijazi	hijazi	PROPN
ejpam-3399	195	6	,	,	PUNCT
ejpam-3399	195	7	a	a	DET
ejpam-3399	195	8	note	note	NOUN
ejpam-3399	195	9	on	on	ADP
ejpam-3399	195	10	solvability	solvability	NOUN
ejpam-3399	195	11	of	of	ADP
ejpam-3399	195	12	finite	finite	ADJ
ejpam-3399	195	13	groups	group	NOUN
ejpam-3399	195	14	,	,	PUNCT
ejpam-3399	195	15	journal	journal	NOUN
ejpam-3399	195	16	of	of	ADP
ejpam-3399	195	17	advances	advance	NOUN
ejpam-3399	195	18	in	in	ADP
ejpam-3399	195	19	mathematics	mathematic	NOUN
ejpam-3399	195	20	10(2015	10(2015	NUM
ejpam-3399	195	21	)	)	PUNCT
ejpam-3399	195	22	3639	3639	NUM
ejpam-3399	195	23	-	-	SYM
ejpam-3399	195	24	3642	3642	NUM
ejpam-3399	195	25	.	.	PUNCT
ejpam-3399	196	1	[	[	X
ejpam-3399	196	2	10	10	NUM
ejpam-3399	196	3	]	]	X
ejpam-3399	196	4	b.	b.	PROPN
ejpam-3399	196	5	huppert	huppert	PROPN
ejpam-3399	196	6	,	,	PUNCT
ejpam-3399	196	7	endliche	endliche	NOUN
ejpam-3399	196	8	gruppen	gruppen	VERB
ejpam-3399	196	9	i	i	PROPN
ejpam-3399	196	10	,	,	PUNCT
ejpam-3399	196	11	springer	springer	NOUN
ejpam-3399	196	12	,	,	PUNCT
ejpam-3399	196	13	berlin	berlin	PROPN
ejpam-3399	196	14	-	-	PUNCT
ejpam-3399	196	15	new	new	PROPN
ejpam-3399	196	16	york	york	PROPN
ejpam-3399	196	17	,	,	PUNCT
ejpam-3399	196	18	1979	1979	NUM
ejpam-3399	196	19	.	.	PUNCT
ejpam-3399	197	1	[	[	X
ejpam-3399	197	2	11	11	NUM
ejpam-3399	197	3	]	]	X
ejpam-3399	197	4	o.	o.	PROPN
ejpam-3399	197	5	h.	h.	PROPN
ejpam-3399	197	6	kegel	kegel	PROPN
ejpam-3399	197	7	,	,	PUNCT
ejpam-3399	197	8	sylow	sylow	NOUN
ejpam-3399	197	9	-	-	PUNCT
ejpam-3399	197	10	gruppen	gruppen	NOUN
ejpam-3399	197	11	und	und	NOUN
ejpam-3399	197	12	subnormalteiler	subnormalteiler	NOUN
ejpam-3399	197	13	endlicher	endlicher	PROPN
ejpam-3399	197	14	gruppen	gruppen	PROPN
ejpam-3399	197	15	,	,	PUNCT
ejpam-3399	197	16	math	math	NOUN
ejpam-3399	197	17	.	.	PUNCT
ejpam-3399	198	1	z.	z.	PROPN
ejpam-3399	198	2	78(1962	78(1962	NUM
ejpam-3399	198	3	)	)	PUNCT
ejpam-3399	198	4	205	205	NUM
ejpam-3399	198	5	-	-	SYM
ejpam-3399	198	6	221	221	NUM
ejpam-3399	198	7	.	.	PUNCT
ejpam-3399	199	1	[	[	X
ejpam-3399	199	2	12	12	NUM
ejpam-3399	199	3	]	]	PUNCT
ejpam-3399	199	4	j.	j.	PROPN
ejpam-3399	199	5	li	li	PROPN
ejpam-3399	199	6	,	,	PUNCT
ejpam-3399	199	7	w.	w.	PROPN
ejpam-3399	199	8	shi	shi	PROPN
ejpam-3399	199	9	,	,	PUNCT
ejpam-3399	199	10	g.	g.	PROPN
ejpam-3399	199	11	chen	chen	PROPN
ejpam-3399	199	12	and	and	CCONJ
ejpam-3399	199	13	d.	d.	PROPN
ejpam-3399	199	14	yu	yu	PROPN
ejpam-3399	199	15	,	,	PUNCT
ejpam-3399	199	16	new	new	ADJ
ejpam-3399	199	17	characterization	characterization	NOUN
ejpam-3399	199	18	of	of	ADP
ejpam-3399	199	19	solubility	solubility	NOUN
ejpam-3399	199	20	of	of	ADP
ejpam-3399	199	21	finite	finite	ADJ
ejpam-3399	199	22	groups	group	NOUN
ejpam-3399	199	23	,	,	PUNCT
ejpam-3399	199	24	italian	italian	ADJ
ejpam-3399	199	25	j.	j.	PROPN
ejpam-3399	199	26	pure	pure	PROPN
ejpam-3399	199	27	appl	appl	PROPN
ejpam-3399	199	28	.	.	PUNCT
ejpam-3399	199	29	math	math	PROPN
ejpam-3399	199	30	.	.	PUNCT
ejpam-3399	200	1	33(2014	33(2014	NUM
ejpam-3399	200	2	)	)	PUNCT
ejpam-3399	200	3	377	377	NUM
ejpam-3399	200	4	-	-	SYM
ejpam-3399	200	5	382	382	NUM
ejpam-3399	200	6	.	.	PUNCT
ejpam-3399	201	1	[	[	X
ejpam-3399	201	2	13	13	NUM
ejpam-3399	201	3	]	]	PUNCT
ejpam-3399	201	4	p.	p.	NOUN
ejpam-3399	201	5	schmid	schmid	PROPN
ejpam-3399	201	6	,	,	PUNCT
ejpam-3399	201	7	subgroups	subgroup	NOUN
ejpam-3399	201	8	permutable	permutable	ADJ
ejpam-3399	201	9	with	with	ADP
ejpam-3399	201	10	all	all	DET
ejpam-3399	201	11	sylow	sylow	NOUN
ejpam-3399	201	12	subgroups	subgroup	NOUN
ejpam-3399	201	13	,	,	PUNCT
ejpam-3399	201	14	j.	j.	PROPN
ejpam-3399	201	15	algebra	algebra	PROPN
ejpam-3399	201	16	,	,	PUNCT
ejpam-3399	201	17	207	207	NUM
ejpam-3399	201	18	(	(	PUNCT
ejpam-3399	201	19	1998	1998	NUM
ejpam-3399	201	20	)	)	PUNCT
ejpam-3399	201	21	285	285	NUM
ejpam-3399	201	22	-	-	SYM
ejpam-3399	201	23	293	293	NUM
ejpam-3399	201	24	.	.	PUNCT
ejpam-3399	202	1	[	[	X
ejpam-3399	202	2	14	14	NUM
ejpam-3399	202	3	]	]	PUNCT
ejpam-3399	202	4	a.	a.	PROPN
ejpam-3399	202	5	n.	n.	PROPN
ejpam-3399	202	6	skiba	skiba	PROPN
ejpam-3399	202	7	,	,	PUNCT
ejpam-3399	202	8	on	on	ADP
ejpam-3399	202	9	weakly	weakly	ADJ
ejpam-3399	202	10	s	s	NOUN
ejpam-3399	202	11	-	-	ADJ
ejpam-3399	202	12	permutable	permutable	ADJ
ejpam-3399	202	13	subgroups	subgroup	NOUN
ejpam-3399	202	14	of	of	ADP
ejpam-3399	202	15	finite	finite	ADJ
ejpam-3399	202	16	groups	group	NOUN
ejpam-3399	202	17	,	,	PUNCT
ejpam-3399	202	18	j.	j.	PROPN
ejpam-3399	202	19	algebra	algebra	PROPN
ejpam-3399	202	20	,	,	PUNCT
ejpam-3399	202	21	315(2007	315(2007	NUM
ejpam-3399	202	22	)	)	PUNCT
ejpam-3399	202	23	192	192	NUM
ejpam-3399	202	24	-	-	SYM
ejpam-3399	202	25	209	209	NUM
ejpam-3399	202	26	.	.	PUNCT
ejpam-3399	203	1	[	[	X
ejpam-3399	203	2	15	15	NUM
ejpam-3399	203	3	]	]	X
ejpam-3399	203	4	s.	s.	PROPN
ejpam-3399	203	5	srinivasan	srinivasan	PROPN
ejpam-3399	203	6	,	,	PUNCT
ejpam-3399	203	7	two	two	NUM
ejpam-3399	203	8	sufficient	sufficient	ADJ
ejpam-3399	203	9	conditions	condition	NOUN
ejpam-3399	203	10	for	for	ADP
ejpam-3399	203	11	supersolvability	supersolvability	NOUN
ejpam-3399	203	12	of	of	ADP
ejpam-3399	203	13	finite	finite	ADJ
ejpam-3399	203	14	groups	group	NOUN
ejpam-3399	203	15	,	,	PUNCT
ejpam-3399	203	16	israel	israel	PROPN
ejpam-3399	203	17	j.	j.	PROPN
ejpam-3399	203	18	math	math	PROPN
ejpam-3399	203	19	.	.	PUNCT
ejpam-3399	204	1	35(1980	35(1980	NUM
ejpam-3399	204	2	)	)	PUNCT
ejpam-3399	204	3	210	210	NUM
ejpam-3399	204	4	-	-	SYM
ejpam-3399	204	5	214	214	NUM
ejpam-3399	204	6	.	.	PUNCT