id	sid	tid	token	lemma	pos
ejpam-5645	1	1	european	european	PROPN
ejpam-5645	1	2	journal	journal	PROPN
ejpam-5645	1	3	of	of	ADP
ejpam-5645	1	4	pure	pure	ADJ
ejpam-5645	1	5	and	and	CCONJ
ejpam-5645	1	6	applied	applied	ADJ
ejpam-5645	1	7	mathematics	mathematic	NOUN
ejpam-5645	1	8	2025	2025	NUM
ejpam-5645	1	9	,	,	PUNCT
ejpam-5645	1	10	vol	vol	NOUN
ejpam-5645	1	11	.	.	PROPN
ejpam-5645	1	12	18	18	NUM
ejpam-5645	1	13	,	,	PUNCT
ejpam-5645	1	14	issue	issue	NOUN
ejpam-5645	1	15	1	1	NUM
ejpam-5645	1	16	,	,	PUNCT
ejpam-5645	1	17	article	article	NOUN
ejpam-5645	1	18	number	number	NOUN
ejpam-5645	1	19	5645	5645	NUM
ejpam-5645	1	20	issn	issn	PROPN
ejpam-5645	1	21	1307	1307	NUM
ejpam-5645	1	22	-	-	SYM
ejpam-5645	1	23	5543	5543	NUM
ejpam-5645	1	24	–	–	PUNCT
ejpam-5645	1	25	ejpam.com	ejpam.com	X
ejpam-5645	1	26	published	publish	VERB
ejpam-5645	1	27	by	by	ADP
ejpam-5645	1	28	new	new	PROPN
ejpam-5645	1	29	york	york	PROPN
ejpam-5645	1	30	business	business	PROPN
ejpam-5645	1	31	global	global	PROPN
ejpam-5645	1	32	the	the	DET
ejpam-5645	1	33	superfluous	superfluous	ADJ
ejpam-5645	1	34	kernel	kernel	NOUN
ejpam-5645	1	35	property	property	NOUN
ejpam-5645	1	36	in	in	ADP
ejpam-5645	1	37	first	first	ADJ
ejpam-5645	1	38	theorems	theorem	NOUN
ejpam-5645	1	39	on	on	ADP
ejpam-5645	1	40	generalized	generalized	ADJ
ejpam-5645	1	41	hopficity	hopficity	NOUN
ejpam-5645	1	42	through	through	ADP
ejpam-5645	1	43	hereditarily	hereditarily	ADJ
ejpam-5645	1	44	hopfian	hopfian	ADJ
ejpam-5645	1	45	groups	group	NOUN
ejpam-5645	1	46	abderrahim	abderrahim	PROPN
ejpam-5645	1	47	bouzendaga1	bouzendaga1	PROPN
ejpam-5645	1	48	,	,	PUNCT
ejpam-5645	1	49	,	,	PUNCT
ejpam-5645	1	50	seddik	seddik	ADJ
ejpam-5645	1	51	abdelalim1	abdelalim1	PROPN
ejpam-5645	1	52	,	,	PUNCT
ejpam-5645	1	53	ilias	ilias	PROPN
ejpam-5645	1	54	elmouki1,∗	elmouki1,∗	NOUN
ejpam-5645	1	55	1	1	NUM
ejpam-5645	1	56	laboratory	laboratory	NOUN
ejpam-5645	1	57	of	of	ADP
ejpam-5645	1	58	fundamental	fundamental	ADJ
ejpam-5645	1	59	and	and	CCONJ
ejpam-5645	1	60	applied	applied	ADJ
ejpam-5645	1	61	mathematics	mathematic	NOUN
ejpam-5645	1	62	(	(	PUNCT
ejpam-5645	1	63	lmfa	lmfa	NOUN
ejpam-5645	1	64	)	)	PUNCT
ejpam-5645	1	65	,	,	PUNCT
ejpam-5645	1	66	faculty	faculty	NOUN
ejpam-5645	1	67	of	of	ADP
ejpam-5645	1	68	sciences	science	NOUN
ejpam-5645	1	69	ain	ain	PROPN
ejpam-5645	1	70	chock	chock	PROPN
ejpam-5645	1	71	(	(	PUNCT
ejpam-5645	1	72	fsac	fsac	NOUN
ejpam-5645	1	73	)	)	PUNCT
ejpam-5645	1	74	,	,	PUNCT
ejpam-5645	1	75	university	university	PROPN
ejpam-5645	1	76	hassan	hassan	PROPN
ejpam-5645	1	77	ii	ii	PROPN
ejpam-5645	1	78	of	of	ADP
ejpam-5645	1	79	casablanca	casablanca	PROPN
ejpam-5645	1	80	(	(	PUNCT
ejpam-5645	1	81	univh2c	univh2c	PROPN
ejpam-5645	1	82	)	)	PUNCT
ejpam-5645	1	83	,	,	PUNCT
ejpam-5645	1	84	morocco	morocco	PROPN
ejpam-5645	1	85	abstract	abstract	NOUN
ejpam-5645	1	86	.	.	PUNCT
ejpam-5645	2	1	in	in	ADP
ejpam-5645	2	2	this	this	DET
ejpam-5645	2	3	paper	paper	NOUN
ejpam-5645	2	4	,	,	PUNCT
ejpam-5645	2	5	we	we	PRON
ejpam-5645	2	6	introduce	introduce	VERB
ejpam-5645	2	7	the	the	DET
ejpam-5645	2	8	superfluous	superfluous	ADJ
ejpam-5645	2	9	kernel	kernel	NOUN
ejpam-5645	2	10	property	property	NOUN
ejpam-5645	2	11	in	in	ADP
ejpam-5645	2	12	order	order	NOUN
ejpam-5645	2	13	to	to	PART
ejpam-5645	2	14	characterize	characterize	VERB
ejpam-5645	2	15	generalized	generalized	ADJ
ejpam-5645	2	16	hereditarily	hereditarily	ADJ
ejpam-5645	2	17	hopfian	hopfian	ADJ
ejpam-5645	2	18	groups	group	NOUN
ejpam-5645	2	19	.	.	PUNCT
ejpam-5645	3	1	then	then	ADV
ejpam-5645	3	2	,	,	PUNCT
ejpam-5645	3	3	we	we	PRON
ejpam-5645	3	4	state	state	VERB
ejpam-5645	3	5	our	our	PRON
ejpam-5645	3	6	first	first	ADJ
ejpam-5645	3	7	theorems	theorem	NOUN
ejpam-5645	3	8	in	in	ADP
ejpam-5645	3	9	this	this	DET
ejpam-5645	3	10	regard	regard	NOUN
ejpam-5645	3	11	,	,	PUNCT
ejpam-5645	3	12	through	through	ADP
ejpam-5645	3	13	the	the	DET
ejpam-5645	3	14	study	study	NOUN
ejpam-5645	3	15	of	of	ADP
ejpam-5645	3	16	two	two	NUM
ejpam-5645	3	17	categories	category	NOUN
ejpam-5645	3	18	of	of	ADP
ejpam-5645	3	19	abelian	abelian	ADJ
ejpam-5645	3	20	groups	group	NOUN
ejpam-5645	3	21	,	,	PUNCT
ejpam-5645	3	22	namely	namely	ADV
ejpam-5645	3	23	the	the	DET
ejpam-5645	3	24	reduced	reduced	ADJ
ejpam-5645	3	25	p−groups	p−group	NOUN
ejpam-5645	3	26	and	and	CCONJ
ejpam-5645	3	27	the	the	DET
ejpam-5645	3	28	reduced	reduced	ADJ
ejpam-5645	3	29	torsion	torsion	NOUN
ejpam-5645	3	30	groups	group	NOUN
ejpam-5645	3	31	.	.	PUNCT
ejpam-5645	4	1	in	in	ADP
ejpam-5645	4	2	fact	fact	NOUN
ejpam-5645	4	3	,	,	PUNCT
ejpam-5645	4	4	we	we	PRON
ejpam-5645	4	5	answer	answer	VERB
ejpam-5645	4	6	to	to	ADP
ejpam-5645	4	7	the	the	DET
ejpam-5645	4	8	open	open	ADJ
ejpam-5645	4	9	question	question	NOUN
ejpam-5645	4	10	about	about	ADP
ejpam-5645	4	11	the	the	DET
ejpam-5645	4	12	implication	implication	NOUN
ejpam-5645	4	13	from	from	ADP
ejpam-5645	4	14	generalized	generalized	ADJ
ejpam-5645	4	15	hereditarily	hereditarily	ADJ
ejpam-5645	4	16	hopficity	hopficity	NOUN
ejpam-5645	4	17	to	to	ADP
ejpam-5645	4	18	finiteness	finiteness	NOUN
ejpam-5645	4	19	.	.	PUNCT
ejpam-5645	5	1	additionally	additionally	ADV
ejpam-5645	5	2	,	,	PUNCT
ejpam-5645	5	3	we	we	PRON
ejpam-5645	5	4	succeed	succeed	VERB
ejpam-5645	5	5	to	to	PART
ejpam-5645	5	6	prove	prove	VERB
ejpam-5645	5	7	a	a	DET
ejpam-5645	5	8	third	third	ADJ
ejpam-5645	5	9	theorem	theorem	NOUN
ejpam-5645	5	10	for	for	ADP
ejpam-5645	5	11	the	the	DET
ejpam-5645	5	12	category	category	NOUN
ejpam-5645	5	13	of	of	ADP
ejpam-5645	5	14	the	the	DET
ejpam-5645	5	15	divisible	divisible	ADJ
ejpam-5645	5	16	p−groups	p−group	NOUN
ejpam-5645	5	17	.	.	PUNCT
ejpam-5645	6	1	along	along	ADP
ejpam-5645	6	2	all	all	DET
ejpam-5645	6	3	these	these	DET
ejpam-5645	6	4	results	result	NOUN
ejpam-5645	6	5	,	,	PUNCT
ejpam-5645	6	6	we	we	PRON
ejpam-5645	6	7	also	also	ADV
ejpam-5645	6	8	try	try	VERB
ejpam-5645	6	9	to	to	PART
ejpam-5645	6	10	benefit	benefit	VERB
ejpam-5645	6	11	from	from	ADP
ejpam-5645	6	12	the	the	DET
ejpam-5645	6	13	properties	property	NOUN
ejpam-5645	6	14	of	of	ADP
ejpam-5645	6	15	hereditarily	hereditarily	ADJ
ejpam-5645	6	16	hopfian	hopfian	ADJ
ejpam-5645	6	17	groups	group	NOUN
ejpam-5645	6	18	to	to	PART
ejpam-5645	6	19	easily	easily	ADV
ejpam-5645	6	20	reach	reach	VERB
ejpam-5645	6	21	the	the	DET
ejpam-5645	6	22	generalized	generalized	ADJ
ejpam-5645	6	23	hopficity	hopficity	NOUN
ejpam-5645	6	24	property	property	NOUN
ejpam-5645	6	25	.	.	PUNCT
ejpam-5645	7	1	2020	2020	NUM
ejpam-5645	7	2	mathematics	mathematic	NOUN
ejpam-5645	7	3	subject	subject	NOUN
ejpam-5645	7	4	classifications	classification	NOUN
ejpam-5645	7	5	:	:	PUNCT
ejpam-5645	7	6	20k10	20k10	NUM
ejpam-5645	7	7	,	,	PUNCT
ejpam-5645	7	8	20k25	20k25	NUM
ejpam-5645	7	9	,	,	PUNCT
ejpam-5645	7	10	20f24	20f24	NUM
ejpam-5645	7	11	,	,	PUNCT
ejpam-5645	7	12	20e10	20e10	NUM
ejpam-5645	7	13	key	key	ADJ
ejpam-5645	7	14	words	word	NOUN
ejpam-5645	7	15	and	and	CCONJ
ejpam-5645	7	16	phrases	phrase	NOUN
ejpam-5645	7	17	:	:	PUNCT
ejpam-5645	7	18	superfluous	superfluous	ADJ
ejpam-5645	7	19	kernel	kernel	NOUN
ejpam-5645	7	20	,	,	PUNCT
ejpam-5645	7	21	abelian	abelian	PROPN
ejpam-5645	7	22	group	group	NOUN
ejpam-5645	7	23	,	,	PUNCT
ejpam-5645	7	24	hopfian	hopfian	ADJ
ejpam-5645	7	25	group	group	NOUN
ejpam-5645	7	26	,	,	PUNCT
ejpam-5645	7	27	p−group	p−group	PROPN
ejpam-5645	7	28	,	,	PUNCT
ejpam-5645	7	29	torsion	torsion	NOUN
ejpam-5645	7	30	group	group	NOUN
ejpam-5645	7	31	,	,	PUNCT
ejpam-5645	7	32	divisible	divisible	ADJ
ejpam-5645	7	33	group	group	NOUN
ejpam-5645	7	34	,	,	PUNCT
ejpam-5645	7	35	hereditarily	hereditarily	ADJ
ejpam-5645	7	36	hopfian	hopfian	ADJ
ejpam-5645	7	37	group	group	NOUN
ejpam-5645	7	38	,	,	PUNCT
ejpam-5645	7	39	generalized	generalized	ADJ
ejpam-5645	7	40	hopfian	hopfian	ADJ
ejpam-5645	7	41	group	group	NOUN
ejpam-5645	7	42	.	.	PUNCT
ejpam-5645	8	1	1	1	X
ejpam-5645	8	2	.	.	X
ejpam-5645	8	3	introduction	introduction	NOUN
ejpam-5645	8	4	in	in	ADP
ejpam-5645	8	5	modern	modern	ADJ
ejpam-5645	8	6	algebra	algebra	NOUN
ejpam-5645	8	7	,	,	PUNCT
ejpam-5645	8	8	the	the	DET
ejpam-5645	8	9	concept	concept	NOUN
ejpam-5645	8	10	of	of	ADP
ejpam-5645	8	11	hopficity	hopficity	NOUN
ejpam-5645	8	12	plays	play	VERB
ejpam-5645	8	13	an	an	DET
ejpam-5645	8	14	interesting	interesting	ADJ
ejpam-5645	8	15	role	role	NOUN
ejpam-5645	8	16	as	as	SCONJ
ejpam-5645	8	17	it	it	PRON
ejpam-5645	8	18	has	have	AUX
ejpam-5645	8	19	been	be	AUX
ejpam-5645	8	20	introduced	introduce	VERB
ejpam-5645	8	21	to	to	ADP
ejpam-5645	8	22	various	various	ADJ
ejpam-5645	8	23	algebraic	algebraic	ADJ
ejpam-5645	8	24	systems	system	NOUN
ejpam-5645	8	25	,	,	PUNCT
ejpam-5645	8	26	including	include	VERB
ejpam-5645	8	27	abelian	abelian	ADJ
ejpam-5645	8	28	groups	group	NOUN
ejpam-5645	8	29	,	,	PUNCT
ejpam-5645	8	30	modules	module	NOUN
ejpam-5645	8	31	,	,	PUNCT
ejpam-5645	8	32	rings	ring	NOUN
ejpam-5645	8	33	,	,	PUNCT
ejpam-5645	8	34	topological	topological	ADJ
ejpam-5645	8	35	spaces	space	NOUN
ejpam-5645	8	36	,	,	PUNCT
ejpam-5645	8	37	and	and	CCONJ
ejpam-5645	8	38	functional	functional	ADJ
ejpam-5645	8	39	spaces	space	NOUN
ejpam-5645	8	40	[	[	X
ejpam-5645	8	41	18	18	NUM
ejpam-5645	8	42	]	]	PUNCT
ejpam-5645	8	43	.	.	PUNCT
ejpam-5645	9	1	nielsen	nielsen	PROPN
ejpam-5645	9	2	used	use	VERB
ejpam-5645	9	3	in	in	ADP
ejpam-5645	9	4	1921	1921	NUM
ejpam-5645	9	5	[	[	X
ejpam-5645	9	6	16	16	NUM
ejpam-5645	9	7	]	]	X
ejpam-5645	9	8	,	,	PUNCT
ejpam-5645	9	9	a	a	DET
ejpam-5645	9	10	purely	purely	ADV
ejpam-5645	9	11	algebraic	algebraic	ADJ
ejpam-5645	9	12	method	method	NOUN
ejpam-5645	9	13	to	to	PART
ejpam-5645	9	14	show	show	VERB
ejpam-5645	9	15	that	that	SCONJ
ejpam-5645	9	16	a	a	DET
ejpam-5645	9	17	finitely	finitely	ADV
ejpam-5645	9	18	generated	generate	VERB
ejpam-5645	9	19	free	free	ADJ
ejpam-5645	9	20	group	group	NOUN
ejpam-5645	9	21	can	can	AUX
ejpam-5645	9	22	not	not	PART
ejpam-5645	9	23	be	be	AUX
ejpam-5645	9	24	isomorphic	isomorphic	ADJ
ejpam-5645	9	25	to	to	ADP
ejpam-5645	9	26	its	its	PRON
ejpam-5645	9	27	proper	proper	ADJ
ejpam-5645	9	28	factor	factor	NOUN
ejpam-5645	9	29	group	group	NOUN
ejpam-5645	9	30	.	.	PUNCT
ejpam-5645	10	1	eleven	eleven	NUM
ejpam-5645	10	2	years	year	NOUN
ejpam-5645	10	3	later	later	ADV
ejpam-5645	10	4	,	,	PUNCT
ejpam-5645	10	5	hopf	hopf	PROPN
ejpam-5645	10	6	showed	show	VERB
ejpam-5645	10	7	the	the	DET
ejpam-5645	10	8	same	same	ADJ
ejpam-5645	10	9	result	result	NOUN
ejpam-5645	10	10	through	through	ADP
ejpam-5645	10	11	a	a	DET
ejpam-5645	10	12	topological	topological	ADJ
ejpam-5645	10	13	method	method	NOUN
ejpam-5645	10	14	[	[	X
ejpam-5645	10	15	2	2	NUM
ejpam-5645	10	16	]	]	PUNCT
ejpam-5645	10	17	.	.	PUNCT
ejpam-5645	11	1	then	then	ADV
ejpam-5645	11	2	,	,	PUNCT
ejpam-5645	11	3	in	in	ADP
ejpam-5645	11	4	1944	1944	NUM
ejpam-5645	11	5	,	,	PUNCT
ejpam-5645	11	6	baer	baer	PROPN
ejpam-5645	11	7	extended	extend	VERB
ejpam-5645	11	8	the	the	DET
ejpam-5645	11	9	study	study	NOUN
ejpam-5645	11	10	of	of	ADP
ejpam-5645	11	11	hopfian	hopfian	ADJ
ejpam-5645	11	12	groups	group	NOUN
ejpam-5645	11	13	through	through	ADP
ejpam-5645	11	14	the	the	DET
ejpam-5645	11	15	names	name	NOUN
ejpam-5645	11	16	of	of	ADP
ejpam-5645	11	17	q	q	NOUN
ejpam-5645	11	18	-	-	NOUN
ejpam-5645	11	19	group	group	NOUN
ejpam-5645	11	20	and	and	CCONJ
ejpam-5645	11	21	s	s	NOUN
ejpam-5645	11	22	-	-	NOUN
ejpam-5645	11	23	group	group	NOUN
ejpam-5645	11	24	[	[	X
ejpam-5645	11	25	17	17	NUM
ejpam-5645	11	26	]	]	PUNCT
ejpam-5645	11	27	.	.	PUNCT
ejpam-5645	12	1	in	in	ADP
ejpam-5645	12	2	relation	relation	NOUN
ejpam-5645	12	3	to	to	ADP
ejpam-5645	12	4	abelian	abelian	ADJ
ejpam-5645	12	5	groups	group	NOUN
ejpam-5645	12	6	,	,	PUNCT
ejpam-5645	12	7	baumslag	baumslag	PROPN
ejpam-5645	12	8	showed	show	VERB
ejpam-5645	12	9	in	in	ADP
ejpam-5645	12	10	1962	1962	NUM
ejpam-5645	12	11	,	,	PUNCT
ejpam-5645	12	12	how	how	SCONJ
ejpam-5645	12	13	the	the	DET
ejpam-5645	12	14	property	property	NOUN
ejpam-5645	12	15	of	of	ADP
ejpam-5645	12	16	hopficity	hopficity	NOUN
ejpam-5645	12	17	can	can	AUX
ejpam-5645	12	18	be	be	AUX
ejpam-5645	12	19	applied	apply	VERB
ejpam-5645	12	20	to	to	PART
ejpam-5645	12	21	gain	gain	VERB
ejpam-5645	12	22	a	a	DET
ejpam-5645	12	23	deeper	deep	ADJ
ejpam-5645	12	24	understanding	understanding	NOUN
ejpam-5645	12	25	of	of	ADP
ejpam-5645	12	26	such	such	ADJ
ejpam-5645	12	27	groups	group	NOUN
ejpam-5645	13	1	[	[	X
ejpam-5645	13	2	3	3	NUM
ejpam-5645	13	3	]	]	PUNCT
ejpam-5645	13	4	.	.	PUNCT
ejpam-5645	14	1	three	three	NUM
ejpam-5645	14	2	years	year	NOUN
ejpam-5645	14	3	later	later	ADV
ejpam-5645	14	4	,	,	PUNCT
ejpam-5645	14	5	corner	corner	NOUN
ejpam-5645	14	6	presented	present	VERB
ejpam-5645	14	7	concrete	concrete	ADJ
ejpam-5645	14	8	examples	example	NOUN
ejpam-5645	14	9	that	that	PRON
ejpam-5645	14	10	illustrate	illustrate	VERB
ejpam-5645	14	11	that	that	DET
ejpam-5645	14	12	concept	concept	NOUN
ejpam-5645	14	13	in	in	ADP
ejpam-5645	14	14	the	the	DET
ejpam-5645	14	15	context	context	NOUN
ejpam-5645	14	16	of	of	ADP
ejpam-5645	14	17	torsion	torsion	NOUN
ejpam-5645	14	18	-	-	PUNCT
ejpam-5645	14	19	free	free	ADJ
ejpam-5645	14	20	abelian	abelian	ADJ
ejpam-5645	14	21	groups	group	NOUN
ejpam-5645	14	22	[	[	X
ejpam-5645	14	23	4	4	NUM
ejpam-5645	14	24	]	]	PUNCT
ejpam-5645	14	25	.	.	PUNCT
ejpam-5645	15	1	then	then	ADV
ejpam-5645	15	2	,	,	PUNCT
ejpam-5645	15	3	in	in	ADP
ejpam-5645	15	4	1969	1969	NUM
ejpam-5645	15	5	,	,	PUNCT
ejpam-5645	15	6	irwin	irwin	PROPN
ejpam-5645	15	7	and	and	CCONJ
ejpam-5645	15	8	takashi	takashi	PROPN
ejpam-5645	15	9	presented	present	VERB
ejpam-5645	15	10	a	a	DET
ejpam-5645	15	11	∗corresponding	∗corresponding	NOUN
ejpam-5645	15	12	author	author	NOUN
ejpam-5645	15	13	.	.	PUNCT
ejpam-5645	16	1	doi	doi	NOUN
ejpam-5645	16	2	:	:	PUNCT
ejpam-5645	16	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5645	https://doi.org/10.29020/nybg.ejpam.v18i1.5645	ADJ
ejpam-5645	16	4	email	email	NOUN
ejpam-5645	16	5	addresses	address	NOUN
ejpam-5645	16	6	:	:	PUNCT
ejpam-5645	16	7	bouzendaga1978@gmail.com	bouzendaga1978@gmail.com	X
ejpam-5645	16	8	(	(	PUNCT
ejpam-5645	16	9	a.	a.	NOUN
ejpam-5645	16	10	bouzendaga	bouzendaga	PROPN
ejpam-5645	16	11	)	)	PUNCT
ejpam-5645	16	12	,	,	PUNCT
ejpam-5645	16	13	seddikabd@hotmail.com	seddikabd@hotmail.com	X
ejpam-5645	16	14	(	(	PUNCT
ejpam-5645	16	15	s.	s.	PROPN
ejpam-5645	16	16	abdelalim	abdelalim	PROPN
ejpam-5645	16	17	)	)	PUNCT
ejpam-5645	16	18	,	,	PUNCT
ejpam-5645	16	19	i.elmouki@gmail.com	i.elmouki@gmail.com	X
ejpam-5645	16	20	(	(	PUNCT
ejpam-5645	16	21	i.	i.	PROPN
ejpam-5645	16	22	elmouki	elmouki	PROPN
ejpam-5645	16	23	)	)	PUNCT
ejpam-5645	16	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5645	16	25	1	1	NUM
ejpam-5645	16	26	copyright	copyright	NOUN
ejpam-5645	16	27	:	:	PUNCT
ejpam-5645	16	28	©	©	PROPN
ejpam-5645	16	29	2025	2025	NUM
ejpam-5645	16	30	the	the	DET
ejpam-5645	16	31	author(s	author(s	NOUN
ejpam-5645	16	32	)	)	PUNCT
ejpam-5645	16	33	.	.	PUNCT
ejpam-5645	17	1	(	(	PUNCT
ejpam-5645	17	2	cc	cc	NOUN
ejpam-5645	17	3	by	by	ADP
ejpam-5645	17	4	-	-	PUNCT
ejpam-5645	17	5	nc	nc	PROPN
ejpam-5645	17	6	4.0	4.0	NUM
ejpam-5645	17	7	)	)	PUNCT
ejpam-5645	17	8	2	2	NUM
ejpam-5645	17	9	of	of	ADP
ejpam-5645	17	10	13	13	NUM
ejpam-5645	17	11	specific	specific	ADJ
ejpam-5645	17	12	case	case	NOUN
ejpam-5645	17	13	of	of	ADP
ejpam-5645	17	14	a	a	DET
ejpam-5645	17	15	quasi	quasi	ADJ
ejpam-5645	17	16	-	-	ADJ
ejpam-5645	17	17	decomposable	decomposable	ADJ
ejpam-5645	17	18	abelian	abelian	ADJ
ejpam-5645	17	19	group	group	NOUN
ejpam-5645	17	20	that	that	PRON
ejpam-5645	17	21	possesses	possess	VERB
ejpam-5645	17	22	neither	neither	CCONJ
ejpam-5645	17	23	distinct	distinct	ADJ
ejpam-5645	17	24	isomorphic	isomorphic	ADJ
ejpam-5645	17	25	subgroups	subgroup	NOUN
ejpam-5645	17	26	nor	nor	CCONJ
ejpam-5645	17	27	distinct	distinct	ADJ
ejpam-5645	17	28	isomorphic	isomorphic	ADJ
ejpam-5645	17	29	quotient	quotient	NOUN
ejpam-5645	17	30	groups	group	NOUN
ejpam-5645	17	31	[	[	X
ejpam-5645	17	32	14	14	NUM
ejpam-5645	17	33	]	]	PUNCT
ejpam-5645	17	34	.	.	PUNCT
ejpam-5645	18	1	in	in	ADP
ejpam-5645	18	2	the	the	DET
ejpam-5645	18	3	80	80	NUM
ejpam-5645	18	4	’s	’s	NOUN
ejpam-5645	18	5	,	,	PUNCT
ejpam-5645	18	6	hirmath	hirmath	NOUN
ejpam-5645	18	7	in	in	ADP
ejpam-5645	18	8	1986	1986	NUM
ejpam-5645	18	9	,	,	PUNCT
ejpam-5645	18	10	studied	study	VERB
ejpam-5645	18	11	the	the	DET
ejpam-5645	18	12	hopficity	hopficity	NOUN
ejpam-5645	18	13	in	in	ADP
ejpam-5645	18	14	the	the	DET
ejpam-5645	18	15	context	context	NOUN
ejpam-5645	18	16	of	of	ADP
ejpam-5645	18	17	rings	ring	NOUN
ejpam-5645	18	18	and	and	CCONJ
ejpam-5645	18	19	modules	module	NOUN
ejpam-5645	18	20	[	[	X
ejpam-5645	18	21	13	13	NUM
ejpam-5645	18	22	]	]	PUNCT
ejpam-5645	18	23	,	,	PUNCT
ejpam-5645	18	24	then	then	ADV
ejpam-5645	18	25	,	,	PUNCT
ejpam-5645	18	26	after	after	ADP
ejpam-5645	18	27	two	two	NUM
ejpam-5645	18	28	years	year	NOUN
ejpam-5645	18	29	,	,	PUNCT
ejpam-5645	18	30	kaidi	kaidi	NOUN
ejpam-5645	18	31	and	and	CCONJ
ejpam-5645	18	32	mamadou	mamadou	PROPN
ejpam-5645	18	33	provided	provide	VERB
ejpam-5645	18	34	a	a	DET
ejpam-5645	18	35	characterization	characterization	NOUN
ejpam-5645	18	36	of	of	ADP
ejpam-5645	18	37	artinian	artinian	ADJ
ejpam-5645	18	38	rings	ring	NOUN
ejpam-5645	18	39	with	with	ADP
ejpam-5645	18	40	principal	principal	ADJ
ejpam-5645	18	41	ideals	ideal	NOUN
ejpam-5645	18	42	[	[	X
ejpam-5645	18	43	15	15	NUM
ejpam-5645	18	44	]	]	PUNCT
ejpam-5645	18	45	.	.	PUNCT
ejpam-5645	19	1	we	we	PRON
ejpam-5645	19	2	can	can	AUX
ejpam-5645	19	3	also	also	ADV
ejpam-5645	19	4	find	find	VERB
ejpam-5645	19	5	the	the	DET
ejpam-5645	19	6	work	work	NOUN
ejpam-5645	19	7	of	of	ADP
ejpam-5645	19	8	haghany	haghany	NOUN
ejpam-5645	19	9	who	who	PRON
ejpam-5645	19	10	explored	explore	VERB
ejpam-5645	19	11	in	in	ADP
ejpam-5645	19	12	1999	1999	NUM
ejpam-5645	19	13	,	,	PUNCT
ejpam-5645	19	14	both	both	DET
ejpam-5645	19	15	hopficity	hopficity	NOUN
ejpam-5645	19	16	and	and	CCONJ
ejpam-5645	19	17	co	co	NOUN
ejpam-5645	19	18	-	-	NOUN
ejpam-5645	19	19	hopficity	hopficity	NOUN
ejpam-5645	19	20	within	within	ADP
ejpam-5645	19	21	the	the	DET
ejpam-5645	19	22	context	context	NOUN
ejpam-5645	19	23	of	of	ADP
ejpam-5645	19	24	morita	morita	PROPN
ejpam-5645	19	25	and	and	CCONJ
ejpam-5645	19	26	which	which	PRON
ejpam-5645	19	27	play	play	VERB
ejpam-5645	19	28	a	a	DET
ejpam-5645	19	29	significant	significant	ADJ
ejpam-5645	19	30	construction	construction	NOUN
ejpam-5645	19	31	in	in	ADP
ejpam-5645	19	32	category	category	NOUN
ejpam-5645	19	33	theory	theory	NOUN
ejpam-5645	19	34	as	as	SCONJ
ejpam-5645	19	35	it	it	PRON
ejpam-5645	19	36	establishes	establish	VERB
ejpam-5645	19	37	equivalences	equivalence	NOUN
ejpam-5645	19	38	between	between	ADP
ejpam-5645	19	39	categories	category	NOUN
ejpam-5645	19	40	of	of	ADP
ejpam-5645	19	41	rings	ring	NOUN
ejpam-5645	19	42	[	[	X
ejpam-5645	19	43	11	11	NUM
ejpam-5645	19	44	]	]	PUNCT
ejpam-5645	19	45	.	.	PUNCT
ejpam-5645	20	1	ghorbani	ghorbani	NOUN
ejpam-5645	20	2	and	and	CCONJ
ejpam-5645	20	3	haghany	haghany	NOUN
ejpam-5645	20	4	also	also	ADV
ejpam-5645	20	5	extended	extend	VERB
ejpam-5645	20	6	this	this	DET
ejpam-5645	20	7	work	work	NOUN
ejpam-5645	20	8	in	in	ADP
ejpam-5645	20	9	the	the	DET
ejpam-5645	20	10	context	context	NOUN
ejpam-5645	20	11	of	of	ADP
ejpam-5645	20	12	modules	module	NOUN
ejpam-5645	20	13	by	by	ADP
ejpam-5645	20	14	introducing	introduce	VERB
ejpam-5645	20	15	generalized	generalize	VERB
ejpam-5645	20	16	hopfian	hopfian	ADJ
ejpam-5645	20	17	modules	module	NOUN
ejpam-5645	20	18	[	[	X
ejpam-5645	20	19	12	12	NUM
ejpam-5645	20	20	]	]	PUNCT
ejpam-5645	20	21	.	.	PUNCT
ejpam-5645	21	1	as	as	ADP
ejpam-5645	21	2	for	for	ADP
ejpam-5645	21	3	the	the	DET
ejpam-5645	21	4	21st	21st	ADJ
ejpam-5645	21	5	century	century	NOUN
ejpam-5645	21	6	,	,	PUNCT
ejpam-5645	21	7	gang	gang	NOUN
ejpam-5645	21	8	and	and	CCONJ
ejpam-5645	21	9	zhongkui	zhongkui	NOUN
ejpam-5645	21	10	also	also	ADV
ejpam-5645	21	11	explored	explore	VERB
ejpam-5645	21	12	in	in	ADP
ejpam-5645	21	13	2007	2007	NUM
ejpam-5645	21	14	,	,	PUNCT
ejpam-5645	21	15	new	new	ADJ
ejpam-5645	21	16	criteria	criterion	NOUN
ejpam-5645	21	17	on	on	ADP
ejpam-5645	21	18	hopfian	hopfian	NOUN
ejpam-5645	21	19	and	and	CCONJ
ejpam-5645	21	20	co	co	ADJ
ejpam-5645	21	21	-	-	ADJ
ejpam-5645	21	22	hopfian	hopfian	ADJ
ejpam-5645	21	23	modules	module	NOUN
ejpam-5645	21	24	[	[	X
ejpam-5645	21	25	19	19	NUM
ejpam-5645	21	26	]	]	PUNCT
ejpam-5645	21	27	,	,	PUNCT
ejpam-5645	21	28	then	then	ADV
ejpam-5645	21	29	published	publish	VERB
ejpam-5645	21	30	a	a	DET
ejpam-5645	21	31	note	note	NOUN
ejpam-5645	21	32	in	in	ADP
ejpam-5645	21	33	2010	2010	NUM
ejpam-5645	21	34	where	where	SCONJ
ejpam-5645	21	35	they	they	PRON
ejpam-5645	21	36	provided	provide	VERB
ejpam-5645	21	37	generalizations	generalization	NOUN
ejpam-5645	21	38	on	on	ADP
ejpam-5645	21	39	these	these	DET
ejpam-5645	21	40	concepts	concept	NOUN
ejpam-5645	21	41	[	[	X
ejpam-5645	21	42	20	20	NUM
ejpam-5645	21	43	]	]	PUNCT
ejpam-5645	21	44	.	.	PUNCT
ejpam-5645	22	1	more	more	ADV
ejpam-5645	22	2	recently	recently	ADV
ejpam-5645	22	3	,	,	PUNCT
ejpam-5645	22	4	abdelalim	abdelalim	PROPN
ejpam-5645	22	5	et	et	PROPN
ejpam-5645	22	6	al	al	PROPN
ejpam-5645	22	7	.	.	PROPN
ejpam-5645	22	8	provided	provide	VERB
ejpam-5645	22	9	a	a	DET
ejpam-5645	22	10	characterization	characterization	NOUN
ejpam-5645	22	11	of	of	ADP
ejpam-5645	22	12	strongly	strongly	ADV
ejpam-5645	22	13	hopfian	hopfian	ADJ
ejpam-5645	22	14	abelian	abelian	ADJ
ejpam-5645	22	15	groups	group	NOUN
ejpam-5645	23	1	[	[	X
ejpam-5645	23	2	1	1	NUM
ejpam-5645	23	3	,	,	PUNCT
ejpam-5645	23	4	5	5	NUM
ejpam-5645	23	5	]	]	PUNCT
ejpam-5645	23	6	using	use	VERB
ejpam-5645	23	7	background	background	NOUN
ejpam-5645	23	8	from	from	ADP
ejpam-5645	23	9	[	[	X
ejpam-5645	23	10	6	6	NUM
ejpam-5645	23	11	,	,	PUNCT
ejpam-5645	23	12	7	7	NUM
ejpam-5645	23	13	]	]	PUNCT
ejpam-5645	23	14	.	.	PUNCT
ejpam-5645	24	1	in	in	ADP
ejpam-5645	24	2	our	our	PRON
ejpam-5645	24	3	present	present	ADJ
ejpam-5645	24	4	paper	paper	NOUN
ejpam-5645	24	5	,	,	PUNCT
ejpam-5645	24	6	we	we	PRON
ejpam-5645	24	7	characterize	characterize	VERB
ejpam-5645	24	8	generalized	generalized	ADJ
ejpam-5645	24	9	hopfian	hopfian	ADJ
ejpam-5645	24	10	groups	group	NOUN
ejpam-5645	24	11	within	within	ADP
ejpam-5645	24	12	the	the	DET
ejpam-5645	24	13	category	category	NOUN
ejpam-5645	24	14	of	of	ADP
ejpam-5645	24	15	abelian	abelian	ADJ
ejpam-5645	24	16	groups	group	NOUN
ejpam-5645	24	17	,	,	PUNCT
ejpam-5645	24	18	based	base	VERB
ejpam-5645	24	19	on	on	ADP
ejpam-5645	24	20	a	a	DET
ejpam-5645	24	21	series	series	NOUN
ejpam-5645	24	22	of	of	ADP
ejpam-5645	24	23	results	result	NOUN
ejpam-5645	24	24	in	in	ADP
ejpam-5645	24	25	the	the	DET
ejpam-5645	24	26	context	context	NOUN
ejpam-5645	24	27	of	of	ADP
ejpam-5645	24	28	hopfian	hopfian	ADJ
ejpam-5645	24	29	hereditation	hereditation	NOUN
ejpam-5645	24	30	.	.	PUNCT
ejpam-5645	25	1	for	for	ADP
ejpam-5645	25	2	that	that	PRON
ejpam-5645	25	3	,	,	PUNCT
ejpam-5645	25	4	we	we	PRON
ejpam-5645	25	5	first	first	ADV
ejpam-5645	25	6	demonstrate	demonstrate	VERB
ejpam-5645	25	7	that	that	SCONJ
ejpam-5645	25	8	generalized	generalize	VERB
ejpam-5645	25	9	hereditarily	hereditarily	ADJ
ejpam-5645	25	10	hopfian	hopfian	NOUN
ejpam-5645	25	11	reduced	reduce	VERB
ejpam-5645	25	12	p−groups	p−group	NOUN
ejpam-5645	25	13	are	be	AUX
ejpam-5645	25	14	finite	finite	ADJ
ejpam-5645	25	15	.	.	PUNCT
ejpam-5645	26	1	next	next	ADJ
ejpam-5645	26	2	,	,	PUNCT
ejpam-5645	26	3	we	we	PRON
ejpam-5645	26	4	prove	prove	VERB
ejpam-5645	26	5	that	that	SCONJ
ejpam-5645	26	6	reduced	reduce	VERB
ejpam-5645	26	7	torsion	torsion	NOUN
ejpam-5645	26	8	groups	group	NOUN
ejpam-5645	26	9	are	be	AUX
ejpam-5645	26	10	generalized	generalize	VERB
ejpam-5645	26	11	hereditarily	hereditarily	ADJ
ejpam-5645	26	12	hopfian	hopfian	ADJ
ejpam-5645	26	13	if	if	SCONJ
ejpam-5645	26	14	and	and	CCONJ
ejpam-5645	26	15	only	only	ADV
ejpam-5645	26	16	if	if	SCONJ
ejpam-5645	26	17	their	their	PRON
ejpam-5645	26	18	p	p	NOUN
ejpam-5645	26	19	-	-	PUNCT
ejpam-5645	26	20	components	component	NOUN
ejpam-5645	26	21	are	be	AUX
ejpam-5645	26	22	finite	finite	ADJ
ejpam-5645	26	23	.	.	PUNCT
ejpam-5645	27	1	finally	finally	ADV
ejpam-5645	27	2	,	,	PUNCT
ejpam-5645	27	3	we	we	PRON
ejpam-5645	27	4	prove	prove	VERB
ejpam-5645	27	5	that	that	SCONJ
ejpam-5645	27	6	a	a	DET
ejpam-5645	27	7	divisible	divisible	ADJ
ejpam-5645	27	8	group	group	NOUN
ejpam-5645	27	9	is	be	AUX
ejpam-5645	27	10	generalized	generalize	VERB
ejpam-5645	27	11	hereditarily	hereditarily	ADJ
ejpam-5645	27	12	hopfian	hopfian	ADJ
ejpam-5645	27	13	group	group	NOUN
ejpam-5645	27	14	if	if	SCONJ
ejpam-5645	27	15	it	it	PRON
ejpam-5645	27	16	is	be	AUX
ejpam-5645	27	17	a	a	DET
ejpam-5645	27	18	finite	finite	ADJ
ejpam-5645	27	19	direct	direct	ADJ
ejpam-5645	27	20	sum	sum	NOUN
ejpam-5645	27	21	of	of	ADP
ejpam-5645	27	22	quasi	quasi	ADJ
ejpam-5645	27	23	-	-	ADJ
ejpam-5645	27	24	cyclic	cyclic	ADJ
ejpam-5645	27	25	group	group	NOUN
ejpam-5645	27	26	z	z	PROPN
ejpam-5645	27	27	(	(	PUNCT
ejpam-5645	27	28	p∞	p∞	PROPN
ejpam-5645	27	29	)	)	PUNCT
ejpam-5645	27	30	.	.	PUNCT
ejpam-5645	28	1	the	the	DET
ejpam-5645	28	2	paper	paper	NOUN
ejpam-5645	28	3	is	be	AUX
ejpam-5645	28	4	organized	organize	VERB
ejpam-5645	28	5	as	as	SCONJ
ejpam-5645	28	6	follows	follow	VERB
ejpam-5645	28	7	.	.	PUNCT
ejpam-5645	29	1	in	in	ADP
ejpam-5645	29	2	section	section	NOUN
ejpam-5645	29	3	2	2	NUM
ejpam-5645	29	4	,	,	PUNCT
ejpam-5645	29	5	our	our	PRON
ejpam-5645	29	6	first	first	ADJ
ejpam-5645	29	7	theorem	theorem	ADJ
ejpam-5645	29	8	states	state	NOUN
ejpam-5645	29	9	that	that	PRON
ejpam-5645	29	10	generalized	generalize	VERB
ejpam-5645	29	11	hereditarily	hereditarily	ADJ
ejpam-5645	29	12	hopfian	hopfian	NOUN
ejpam-5645	29	13	reduced	reduce	VERB
ejpam-5645	29	14	p−groups	p−group	NOUN
ejpam-5645	29	15	are	be	AUX
ejpam-5645	29	16	finite	finite	ADJ
ejpam-5645	29	17	,	,	PUNCT
ejpam-5645	29	18	while	while	SCONJ
ejpam-5645	29	19	the	the	DET
ejpam-5645	29	20	proof	proof	NOUN
ejpam-5645	29	21	uses	use	VERB
ejpam-5645	29	22	properties	property	NOUN
ejpam-5645	29	23	of	of	ADP
ejpam-5645	29	24	pure	pure	ADJ
ejpam-5645	29	25	subgroups	subgroup	NOUN
ejpam-5645	29	26	,	,	PUNCT
ejpam-5645	29	27	basic	basic	ADJ
ejpam-5645	29	28	subgroups	subgroup	NOUN
ejpam-5645	29	29	,	,	PUNCT
ejpam-5645	29	30	bounded	bound	VERB
ejpam-5645	29	31	groups	group	NOUN
ejpam-5645	29	32	and	and	CCONJ
ejpam-5645	29	33	direct	direct	ADJ
ejpam-5645	29	34	summand	summand	NOUN
ejpam-5645	29	35	.	.	PUNCT
ejpam-5645	30	1	as	as	ADP
ejpam-5645	30	2	for	for	ADP
ejpam-5645	30	3	section	section	NOUN
ejpam-5645	30	4	3	3	NUM
ejpam-5645	30	5	,	,	PUNCT
ejpam-5645	30	6	our	our	PRON
ejpam-5645	30	7	second	second	ADJ
ejpam-5645	30	8	theorem	theorem	ADJ
ejpam-5645	30	9	states	state	NOUN
ejpam-5645	30	10	that	that	PRON
ejpam-5645	30	11	reduced	reduce	VERB
ejpam-5645	30	12	torsion	torsion	NOUN
ejpam-5645	30	13	groups	group	NOUN
ejpam-5645	30	14	are	be	AUX
ejpam-5645	30	15	generalized	generalize	VERB
ejpam-5645	30	16	hereditarily	hereditarily	ADJ
ejpam-5645	30	17	hopfian	hopfian	ADJ
ejpam-5645	30	18	if	if	SCONJ
ejpam-5645	30	19	and	and	CCONJ
ejpam-5645	30	20	only	only	ADV
ejpam-5645	30	21	if	if	SCONJ
ejpam-5645	30	22	their	their	PRON
ejpam-5645	30	23	p	p	NOUN
ejpam-5645	30	24	-	-	PUNCT
ejpam-5645	30	25	components	component	NOUN
ejpam-5645	30	26	are	be	AUX
ejpam-5645	30	27	finite	finite	ADJ
ejpam-5645	30	28	,	,	PUNCT
ejpam-5645	30	29	while	while	SCONJ
ejpam-5645	30	30	the	the	DET
ejpam-5645	30	31	proof	proof	NOUN
ejpam-5645	30	32	uses	use	VERB
ejpam-5645	30	33	the	the	DET
ejpam-5645	30	34	previous	previous	ADJ
ejpam-5645	30	35	result	result	NOUN
ejpam-5645	30	36	in	in	ADP
ejpam-5645	30	37	addition	addition	NOUN
ejpam-5645	30	38	to	to	ADP
ejpam-5645	30	39	the	the	DET
ejpam-5645	30	40	fact	fact	NOUN
ejpam-5645	30	41	that	that	SCONJ
ejpam-5645	30	42	a	a	DET
ejpam-5645	30	43	torsion	torsion	NOUN
ejpam-5645	30	44	group	group	NOUN
ejpam-5645	30	45	is	be	AUX
ejpam-5645	30	46	a	a	DET
ejpam-5645	30	47	direct	direct	ADJ
ejpam-5645	30	48	sum	sum	NOUN
ejpam-5645	30	49	of	of	ADP
ejpam-5645	30	50	p	p	NOUN
ejpam-5645	30	51	-	-	PUNCT
ejpam-5645	30	52	components	component	NOUN
ejpam-5645	30	53	.	.	PUNCT
ejpam-5645	31	1	then	then	ADV
ejpam-5645	31	2	,	,	PUNCT
ejpam-5645	31	3	in	in	ADP
ejpam-5645	31	4	section	section	NOUN
ejpam-5645	31	5	4	4	NUM
ejpam-5645	31	6	,	,	PUNCT
ejpam-5645	31	7	our	our	PRON
ejpam-5645	31	8	third	third	ADJ
ejpam-5645	31	9	theorem	theorem	NOUN
ejpam-5645	31	10	provides	provide	VERB
ejpam-5645	31	11	the	the	DET
ejpam-5645	31	12	condition	condition	NOUN
ejpam-5645	31	13	to	to	PART
ejpam-5645	31	14	characterize	characterize	VERB
ejpam-5645	31	15	a	a	DET
ejpam-5645	31	16	divisible	divisible	ADJ
ejpam-5645	31	17	p−group	p−group	NOUN
ejpam-5645	31	18	as	as	ADP
ejpam-5645	31	19	a	a	DET
ejpam-5645	31	20	generalized	generalized	ADJ
ejpam-5645	31	21	hereditarily	hereditarily	ADJ
ejpam-5645	31	22	hopfian	hopfian	ADJ
ejpam-5645	31	23	group	group	NOUN
ejpam-5645	31	24	.	.	PUNCT
ejpam-5645	31	25	,	,	PUNCT
ejpam-5645	31	26	and	and	CCONJ
ejpam-5645	31	27	this	this	PRON
ejpam-5645	31	28	has	have	AUX
ejpam-5645	31	29	been	be	AUX
ejpam-5645	31	30	reached	reach	VERB
ejpam-5645	31	31	by	by	ADP
ejpam-5645	31	32	using	use	VERB
ejpam-5645	31	33	a	a	DET
ejpam-5645	31	34	characterization	characterization	NOUN
ejpam-5645	31	35	of	of	ADP
ejpam-5645	31	36	divisible	divisible	ADJ
ejpam-5645	31	37	p−groups	p−group	NOUN
ejpam-5645	31	38	.	.	PUNCT
ejpam-5645	32	1	for	for	ADP
ejpam-5645	32	2	the	the	DET
ejpam-5645	32	3	convenience	convenience	NOUN
ejpam-5645	32	4	of	of	ADP
ejpam-5645	32	5	reading	reading	NOUN
ejpam-5645	32	6	,	,	PUNCT
ejpam-5645	32	7	here	here	ADV
ejpam-5645	32	8	is	be	AUX
ejpam-5645	32	9	some	some	DET
ejpam-5645	32	10	information	information	NOUN
ejpam-5645	32	11	regarding	regard	VERB
ejpam-5645	32	12	the	the	DET
ejpam-5645	32	13	notation	notation	NOUN
ejpam-5645	32	14	and	and	CCONJ
ejpam-5645	32	15	terminology.throughout	terminology.throughout	ADP
ejpam-5645	32	16	the	the	DET
ejpam-5645	32	17	paper	paper	NOUN
ejpam-5645	32	18	,	,	PUNCT
ejpam-5645	32	19	when	when	SCONJ
ejpam-5645	32	20	we	we	PRON
ejpam-5645	32	21	refer	refer	VERB
ejpam-5645	32	22	to	to	ADP
ejpam-5645	32	23	a	a	DET
ejpam-5645	32	24	group	group	NOUN
ejpam-5645	32	25	,	,	PUNCT
ejpam-5645	32	26	we	we	PRON
ejpam-5645	32	27	are	be	AUX
ejpam-5645	32	28	referring	refer	VERB
ejpam-5645	32	29	to	to	ADP
ejpam-5645	32	30	an	an	DET
ejpam-5645	32	31	abelian	abelian	ADJ
ejpam-5645	32	32	group	group	NOUN
ejpam-5645	32	33	with	with	ADP
ejpam-5645	32	34	additive	additive	ADJ
ejpam-5645	32	35	notation	notation	NOUN
ejpam-5645	32	36	,	,	PUNCT
ejpam-5645	32	37	also	also	ADV
ejpam-5645	32	38	we	we	PRON
ejpam-5645	32	39	use	use	VERB
ejpam-5645	32	40	the	the	DET
ejpam-5645	32	41	following	following	ADJ
ejpam-5645	32	42	notations	notation	NOUN
ejpam-5645	32	43	:	:	PUNCT
ejpam-5645	32	44	p	p	PRON
ejpam-5645	32	45	is	be	AUX
ejpam-5645	32	46	a	a	DET
ejpam-5645	32	47	prime	prime	ADJ
ejpam-5645	32	48	number	number	NOUN
ejpam-5645	32	49	,	,	PUNCT
ejpam-5645	32	50	q	q	PUNCT
ejpam-5645	32	51	is	be	AUX
ejpam-5645	32	52	a	a	DET
ejpam-5645	32	53	group	group	NOUN
ejpam-5645	32	54	of	of	ADP
ejpam-5645	32	55	rational	rational	ADJ
ejpam-5645	32	56	number	number	NOUN
ejpam-5645	32	57	,	,	PUNCT
ejpam-5645	32	58	z	z	PROPN
ejpam-5645	32	59	is	be	AUX
ejpam-5645	32	60	a	a	DET
ejpam-5645	32	61	group	group	NOUN
ejpam-5645	32	62	of	of	ADP
ejpam-5645	32	63	integer	integer	NOUN
ejpam-5645	32	64	number	number	NOUN
ejpam-5645	32	65	,	,	PUNCT
ejpam-5645	32	66	d	d	PRON
ejpam-5645	32	67	is	be	AUX
ejpam-5645	32	68	a	a	DET
ejpam-5645	32	69	divisible	divisible	ADJ
ejpam-5645	32	70	group	group	NOUN
ejpam-5645	32	71	,	,	PUNCT
ejpam-5645	32	72	r	r	NOUN
ejpam-5645	32	73	is	be	AUX
ejpam-5645	32	74	a	a	DET
ejpam-5645	32	75	reduced	reduced	ADJ
ejpam-5645	32	76	group	group	NOUN
ejpam-5645	32	77	,	,	PUNCT
ejpam-5645	32	78	gp	gp	PROPN
ejpam-5645	32	79	is	be	AUX
ejpam-5645	32	80	a	a	DET
ejpam-5645	32	81	p	p	NOUN
ejpam-5645	32	82	-	-	PUNCT
ejpam-5645	32	83	component	component	NOUN
ejpam-5645	32	84	of	of	ADP
ejpam-5645	32	85	g	g	NOUN
ejpam-5645	32	86	,	,	PUNCT
ejpam-5645	32	87	z	z	PROPN
ejpam-5645	32	88	(	(	PUNCT
ejpam-5645	32	89	p∞	p∞	PROPN
ejpam-5645	32	90	)	)	PUNCT
ejpam-5645	32	91	is	be	AUX
ejpam-5645	32	92	a	a	DET
ejpam-5645	32	93	quasi	quasi	ADJ
ejpam-5645	32	94	-	-	ADJ
ejpam-5645	32	95	cyclic	cyclic	ADJ
ejpam-5645	32	96	group	group	NOUN
ejpam-5645	32	97	,	,	PUNCT
ejpam-5645	32	98	g	g	PROPN
ejpam-5645	32	99	/	/	SYM
ejpam-5645	32	100	h	h	NOUN
ejpam-5645	32	101	is	be	AUX
ejpam-5645	32	102	a	a	DET
ejpam-5645	32	103	quotient	quotient	NOUN
ejpam-5645	32	104	group	group	NOUN
ejpam-5645	32	105	,	,	PUNCT
ejpam-5645	32	106	b	b	PROPN
ejpam-5645	32	107	is	be	AUX
ejpam-5645	32	108	a	a	DET
ejpam-5645	32	109	p	p	ADJ
ejpam-5645	32	110	-	-	PUNCT
ejpam-5645	32	111	basic	basic	ADJ
ejpam-5645	32	112	subgroup	subgroup	NOUN
ejpam-5645	32	113	,	,	PUNCT
ejpam-5645	32	114	⟨x⟩	⟨x⟩	PROPN
ejpam-5645	32	115	is	be	AUX
ejpam-5645	32	116	a	a	DET
ejpam-5645	32	117	cyclic	cyclic	NOUN
ejpam-5645	32	118	group,⊕	group,⊕	ADJ
ejpam-5645	32	119	is	be	AUX
ejpam-5645	32	120	a	a	DET
ejpam-5645	32	121	direct	direct	ADJ
ejpam-5645	32	122	sum	sum	NOUN
ejpam-5645	32	123	,	,	PUNCT
ejpam-5645	32	124	φ	φ	PROPN
ejpam-5645	32	125	,	,	PUNCT
ejpam-5645	32	126	α	α	PROPN
ejpam-5645	32	127	and	and	CCONJ
ejpam-5645	32	128	ϕ	ϕ	PROPN
ejpam-5645	32	129	are	be	AUX
ejpam-5645	32	130	groups	group	NOUN
ejpam-5645	32	131	homomorphisms	homomorphism	NOUN
ejpam-5645	32	132	.	.	PUNCT
ejpam-5645	33	1	2	2	X
ejpam-5645	33	2	.	.	X
ejpam-5645	33	3	on	on	ADP
ejpam-5645	33	4	generalized	generalized	ADJ
ejpam-5645	33	5	hereditarily	hereditarily	ADJ
ejpam-5645	33	6	hopfian	hopfian	ADJ
ejpam-5645	33	7	p−groups	p−group	NOUN
ejpam-5645	33	8	in	in	ADP
ejpam-5645	33	9	this	this	DET
ejpam-5645	33	10	section	section	NOUN
ejpam-5645	33	11	,	,	PUNCT
ejpam-5645	33	12	we	we	PRON
ejpam-5645	33	13	state	state	VERB
ejpam-5645	33	14	our	our	PRON
ejpam-5645	33	15	first	first	ADJ
ejpam-5645	33	16	theorem	theorem	NOUN
ejpam-5645	33	17	which	which	PRON
ejpam-5645	33	18	says	say	VERB
ejpam-5645	33	19	that	that	SCONJ
ejpam-5645	33	20	every	every	DET
ejpam-5645	33	21	reduced	reduce	VERB
ejpam-5645	33	22	generalized	generalized	ADJ
ejpam-5645	33	23	hereditarily	hereditarily	ADJ
ejpam-5645	33	24	hopfian	hopfian	ADJ
ejpam-5645	33	25	p−group	p−group	X
ejpam-5645	33	26	is	be	AUX
ejpam-5645	33	27	a	a	DET
ejpam-5645	33	28	finite	finite	ADJ
ejpam-5645	33	29	group	group	NOUN
ejpam-5645	33	30	.	.	PUNCT
ejpam-5645	34	1	but	but	CCONJ
ejpam-5645	34	2	before	before	ADP
ejpam-5645	34	3	that	that	PRON
ejpam-5645	34	4	,	,	PUNCT
ejpam-5645	34	5	we	we	PRON
ejpam-5645	34	6	use	use	VERB
ejpam-5645	34	7	three	three	NUM
ejpam-5645	34	8	lemmas	lemmas	ADJ
ejpam-5645	34	9	and	and	CCONJ
ejpam-5645	34	10	one	one	NUM
ejpam-5645	34	11	proposition	proposition	NOUN
ejpam-5645	34	12	to	to	PART
ejpam-5645	34	13	achieve	achieve	VERB
ejpam-5645	34	14	the	the	DET
ejpam-5645	34	15	proof	proof	NOUN
ejpam-5645	34	16	of	of	ADP
ejpam-5645	34	17	this	this	DET
ejpam-5645	34	18	result	result	NOUN
ejpam-5645	34	19	.	.	PUNCT
ejpam-5645	35	1	3	3	NUM
ejpam-5645	35	2	of	of	ADP
ejpam-5645	35	3	13	13	NUM
ejpam-5645	35	4	we	we	PRON
ejpam-5645	35	5	recall	recall	VERB
ejpam-5645	35	6	that	that	SCONJ
ejpam-5645	35	7	a	a	DET
ejpam-5645	35	8	group	group	NOUN
ejpam-5645	35	9	g	g	NOUN
ejpam-5645	35	10	is	be	AUX
ejpam-5645	35	11	hopfian	hopfian	ADJ
ejpam-5645	35	12	if	if	SCONJ
ejpam-5645	35	13	every	every	DET
ejpam-5645	35	14	surjective	surjective	ADJ
ejpam-5645	35	15	endomorphism	endomorphism	NOUN
ejpam-5645	35	16	α	α	NOUN
ejpam-5645	35	17	:	:	PUNCT
ejpam-5645	35	18	g	g	NOUN
ejpam-5645	35	19	→	→	SYM
ejpam-5645	35	20	g	g	PROPN
ejpam-5645	35	21	is	be	AUX
ejpam-5645	35	22	an	an	DET
ejpam-5645	35	23	automorphism	automorphism	NOUN
ejpam-5645	35	24	.	.	PUNCT
ejpam-5645	36	1	this	this	PRON
ejpam-5645	36	2	is	be	AUX
ejpam-5645	36	3	also	also	ADV
ejpam-5645	36	4	equivalent	equivalent	ADJ
ejpam-5645	36	5	to	to	PART
ejpam-5645	36	6	say	say	VERB
ejpam-5645	36	7	that	that	SCONJ
ejpam-5645	36	8	g	g	PROPN
ejpam-5645	36	9	is	be	AUX
ejpam-5645	36	10	not	not	PART
ejpam-5645	36	11	isomorphic	isomorphic	ADJ
ejpam-5645	36	12	to	to	ADP
ejpam-5645	36	13	any	any	PRON
ejpam-5645	36	14	of	of	ADP
ejpam-5645	36	15	its	its	PRON
ejpam-5645	36	16	proper	proper	ADJ
ejpam-5645	36	17	quotient	quotient	NOUN
ejpam-5645	36	18	groups	group	NOUN
ejpam-5645	36	19	.	.	PUNCT
ejpam-5645	37	1	some	some	DET
ejpam-5645	37	2	examples	example	NOUN
ejpam-5645	37	3	of	of	ADP
ejpam-5645	37	4	such	such	ADJ
ejpam-5645	37	5	groups	group	NOUN
ejpam-5645	37	6	are	be	AUX
ejpam-5645	37	7	finite	finite	ADJ
ejpam-5645	37	8	groups	group	NOUN
ejpam-5645	37	9	,	,	PUNCT
ejpam-5645	37	10	finitely	finitely	ADV
ejpam-5645	37	11	generated	generate	VERB
ejpam-5645	37	12	free	free	ADJ
ejpam-5645	37	13	groups	group	NOUN
ejpam-5645	37	14	,	,	PUNCT
ejpam-5645	37	15	finitely	finitely	ADV
ejpam-5645	37	16	generated	generate	VERB
ejpam-5645	37	17	residually	residually	ADV
ejpam-5645	37	18	finite	finite	ADJ
ejpam-5645	37	19	groups	group	NOUN
ejpam-5645	37	20	,	,	PUNCT
ejpam-5645	37	21	and	and	CCONJ
ejpam-5645	37	22	torsion	torsion	NOUN
ejpam-5645	37	23	-	-	PUNCT
ejpam-5645	37	24	free	free	ADJ
ejpam-5645	37	25	groups	group	NOUN
ejpam-5645	37	26	of	of	ADP
ejpam-5645	37	27	finite	finite	PROPN
ejpam-5645	37	28	rank	rank	PROPN
ejpam-5645	37	29	.	.	PUNCT
ejpam-5645	38	1	we	we	PRON
ejpam-5645	38	2	recall	recall	VERB
ejpam-5645	38	3	that	that	SCONJ
ejpam-5645	38	4	groups	group	NOUN
ejpam-5645	38	5	needed	need	VERB
ejpam-5645	38	6	in	in	ADP
ejpam-5645	38	7	the	the	DET
ejpam-5645	38	8	proof	proof	NOUN
ejpam-5645	38	9	of	of	ADP
ejpam-5645	38	10	our	our	PRON
ejpam-5645	38	11	theorems	theorem	NOUN
ejpam-5645	38	12	thereafter	thereafter	ADV
ejpam-5645	38	13	are	be	AUX
ejpam-5645	38	14	about	about	ADP
ejpam-5645	38	15	the	the	DET
ejpam-5645	38	16	following	follow	VERB
ejpam-5645	38	17	types	type	NOUN
ejpam-5645	38	18	.	.	PUNCT
ejpam-5645	39	1	definition	definition	NOUN
ejpam-5645	39	2	1	1	NUM
ejpam-5645	39	3	.	.	PUNCT
ejpam-5645	40	1	(	(	PUNCT
ejpam-5645	40	2	i	i	NOUN
ejpam-5645	40	3	)	)	PUNCT
ejpam-5645	40	4	torsion	torsion	NOUN
ejpam-5645	40	5	group	group	NOUN
ejpam-5645	40	6	(	(	PUNCT
ejpam-5645	40	7	an	an	DET
ejpam-5645	40	8	abelian	abelian	ADJ
ejpam-5645	40	9	group	group	NOUN
ejpam-5645	40	10	g	g	PROPN
ejpam-5645	40	11	is	be	AUX
ejpam-5645	40	12	a	a	DET
ejpam-5645	40	13	torsion	torsion	NOUN
ejpam-5645	40	14	group	group	NOUN
ejpam-5645	40	15	if	if	SCONJ
ejpam-5645	40	16	∀x	∀x	X
ejpam-5645	40	17	∈	∈	PROPN
ejpam-5645	40	18	g	g	NOUN
ejpam-5645	40	19	:	:	PUNCT
ejpam-5645	40	20	◦	◦	NOUN
ejpam-5645	40	21	(	(	PUNCT
ejpam-5645	40	22	x	x	X
ejpam-5645	40	23	)	)	PUNCT
ejpam-5645	40	24	<	<	X
ejpam-5645	40	25	∞	∞	PROPN
ejpam-5645	40	26	)	)	PUNCT
ejpam-5645	40	27	.	.	PUNCT
ejpam-5645	41	1	(	(	PUNCT
ejpam-5645	41	2	ii	ii	NOUN
ejpam-5645	41	3	)	)	PUNCT
ejpam-5645	41	4	p−group	p−group	NOUN
ejpam-5645	41	5	(	(	PUNCT
ejpam-5645	41	6	a	a	DET
ejpam-5645	41	7	group	group	NOUN
ejpam-5645	41	8	g	g	NOUN
ejpam-5645	41	9	is	be	AUX
ejpam-5645	41	10	said	say	VERB
ejpam-5645	41	11	to	to	PART
ejpam-5645	41	12	be	be	AUX
ejpam-5645	41	13	a	a	DET
ejpam-5645	41	14	p−group	p−group	NOUN
ejpam-5645	41	15	when	when	SCONJ
ejpam-5645	41	16	the	the	DET
ejpam-5645	41	17	order	order	NOUN
ejpam-5645	41	18	of	of	ADP
ejpam-5645	41	19	every	every	DET
ejpam-5645	41	20	element	element	NOUN
ejpam-5645	41	21	is	be	AUX
ejpam-5645	41	22	a	a	DET
ejpam-5645	41	23	power	power	NOUN
ejpam-5645	41	24	of	of	ADP
ejpam-5645	41	25	p	p	NOUN
ejpam-5645	41	26	,	,	PUNCT
ejpam-5645	41	27	with	with	ADP
ejpam-5645	41	28	p	p	PRON
ejpam-5645	41	29	a	a	DET
ejpam-5645	41	30	prime	prime	ADJ
ejpam-5645	41	31	number	number	NOUN
ejpam-5645	41	32	)	)	PUNCT
ejpam-5645	41	33	.	.	PUNCT
ejpam-5645	42	1	(	(	PUNCT
ejpam-5645	42	2	iii	iii	X
ejpam-5645	42	3	)	)	PUNCT
ejpam-5645	42	4	bounded	bounded	ADJ
ejpam-5645	42	5	group	group	NOUN
ejpam-5645	42	6	(	(	PUNCT
ejpam-5645	42	7	a	a	DET
ejpam-5645	42	8	group	group	NOUN
ejpam-5645	42	9	g	g	NOUN
ejpam-5645	42	10	is	be	AUX
ejpam-5645	42	11	bounded	bound	VERB
ejpam-5645	42	12	if	if	SCONJ
ejpam-5645	42	13	there	there	PRON
ejpam-5645	42	14	is	be	VERB
ejpam-5645	42	15	n	n	DET
ejpam-5645	42	16	∈	∈	NOUN
ejpam-5645	42	17	n∗	n∗	NOUN
ejpam-5645	42	18	such	such	ADJ
ejpam-5645	42	19	that	that	PRON
ejpam-5645	42	20	ng	ng	PROPN
ejpam-5645	42	21	=	=	SYM
ejpam-5645	42	22	0	0	NUM
ejpam-5645	42	23	)	)	PUNCT
ejpam-5645	42	24	.	.	PUNCT
ejpam-5645	43	1	(	(	PUNCT
ejpam-5645	43	2	iv	iv	X
ejpam-5645	43	3	)	)	PUNCT
ejpam-5645	43	4	divisible	divisible	ADJ
ejpam-5645	43	5	group	group	NOUN
ejpam-5645	43	6	(	(	PUNCT
ejpam-5645	43	7	an	an	DET
ejpam-5645	43	8	abelian	abelian	ADJ
ejpam-5645	43	9	group	group	NOUN
ejpam-5645	43	10	g	g	PROPN
ejpam-5645	43	11	is	be	AUX
ejpam-5645	43	12	a	a	DET
ejpam-5645	43	13	divisible	divisible	ADJ
ejpam-5645	43	14	group	group	NOUN
ejpam-5645	43	15	if	if	SCONJ
ejpam-5645	43	16	for	for	ADP
ejpam-5645	43	17	any	any	DET
ejpam-5645	43	18	a	a	DET
ejpam-5645	43	19	∈	∈	NOUN
ejpam-5645	43	20	g	g	NOUN
ejpam-5645	43	21	and	and	CCONJ
ejpam-5645	43	22	integer	integer	PROPN
ejpam-5645	43	23	n	n	DET
ejpam-5645	43	24	≥	≥	NUM
ejpam-5645	43	25	1	1	NUM
ejpam-5645	43	26	there	there	PRON
ejpam-5645	43	27	exists	exist	VERB
ejpam-5645	43	28	b	b	PROPN
ejpam-5645	43	29	∈	∈	PROPN
ejpam-5645	43	30	g	g	NOUN
ejpam-5645	43	31	such	such	DET
ejpam-5645	43	32	that	that	SCONJ
ejpam-5645	43	33	a	a	DET
ejpam-5645	43	34	=	=	X
ejpam-5645	43	35	nb	nb	PROPN
ejpam-5645	43	36	.	.	PROPN
ejpam-5645	43	37	otherwise	otherwise	ADV
ejpam-5645	43	38	expressed	express	VERB
ejpam-5645	43	39	,	,	PUNCT
ejpam-5645	43	40	g	g	PROPN
ejpam-5645	43	41	is	be	AUX
ejpam-5645	43	42	divisible	divisible	ADJ
ejpam-5645	43	43	if	if	SCONJ
ejpam-5645	43	44	ng	ng	PROPN
ejpam-5645	43	45	=	=	SYM
ejpam-5645	43	46	g	g	PROPN
ejpam-5645	43	47	holds	hold	VERB
ejpam-5645	43	48	for	for	ADP
ejpam-5645	43	49	every	every	DET
ejpam-5645	43	50	natural	natural	ADJ
ejpam-5645	43	51	integer	integer	NOUN
ejpam-5645	43	52	n	n	CCONJ
ejpam-5645	43	53	)	)	PUNCT
ejpam-5645	43	54	.	.	PUNCT
ejpam-5645	44	1	(	(	PUNCT
ejpam-5645	44	2	v	v	NOUN
ejpam-5645	44	3	)	)	PUNCT
ejpam-5645	44	4	reduced	reduce	VERB
ejpam-5645	44	5	group	group	NOUN
ejpam-5645	44	6	a	a	DET
ejpam-5645	44	7	group	group	NOUN
ejpam-5645	44	8	(	(	PUNCT
ejpam-5645	44	9	g	g	PROPN
ejpam-5645	44	10	is	be	AUX
ejpam-5645	44	11	said	say	VERB
ejpam-5645	44	12	to	to	PART
ejpam-5645	44	13	be	be	AUX
ejpam-5645	44	14	a	a	DET
ejpam-5645	44	15	reduced	reduce	VERB
ejpam-5645	44	16	group	group	NOUN
ejpam-5645	44	17	if	if	SCONJ
ejpam-5645	44	18	it	it	PRON
ejpam-5645	44	19	does	do	AUX
ejpam-5645	44	20	not	not	PART
ejpam-5645	44	21	contain	contain	VERB
ejpam-5645	44	22	any	any	DET
ejpam-5645	44	23	proper	proper	ADJ
ejpam-5645	44	24	divisible	divisible	ADJ
ejpam-5645	44	25	subgroups	subgroup	NOUN
ejpam-5645	44	26	)	)	PUNCT
ejpam-5645	44	27	.	.	PUNCT
ejpam-5645	45	1	(	(	PUNCT
ejpam-5645	45	2	vi	vi	X
ejpam-5645	45	3	)	)	PUNCT
ejpam-5645	45	4	direct	direct	ADJ
ejpam-5645	45	5	summand	summand	NOUN
ejpam-5645	45	6	(	(	PUNCT
ejpam-5645	45	7	a	a	DET
ejpam-5645	45	8	subgroup	subgroup	PROPN
ejpam-5645	45	9	b	b	PROPN
ejpam-5645	45	10	of	of	ADP
ejpam-5645	45	11	a	a	PRON
ejpam-5645	45	12	is	be	AUX
ejpam-5645	45	13	called	call	VERB
ejpam-5645	45	14	a	a	DET
ejpam-5645	45	15	direct	direct	ADJ
ejpam-5645	45	16	summand	summand	NOUN
ejpam-5645	45	17	of	of	ADP
ejpam-5645	45	18	a	a	PRON
ejpam-5645	45	19	,	,	PUNCT
ejpam-5645	45	20	if	if	SCONJ
ejpam-5645	45	21	there	there	PRON
ejpam-5645	45	22	is	be	VERB
ejpam-5645	45	23	a	a	DET
ejpam-5645	45	24	c	c	NOUN
ejpam-5645	45	25	≤	≤	NOUN
ejpam-5645	45	26	a	a	DET
ejpam-5645	45	27	such	such	ADJ
ejpam-5645	45	28	that	that	SCONJ
ejpam-5645	45	29	a	a	DET
ejpam-5645	45	30	=	=	SYM
ejpam-5645	45	31	b	b	PROPN
ejpam-5645	45	32	⊕	⊕	PROPN
ejpam-5645	45	33	c.	c.	PROPN
ejpam-5645	45	34	in	in	ADP
ejpam-5645	45	35	this	this	DET
ejpam-5645	45	36	case	case	NOUN
ejpam-5645	45	37	,	,	PUNCT
ejpam-5645	45	38	c	c	PROPN
ejpam-5645	45	39	is	be	AUX
ejpam-5645	45	40	a	a	DET
ejpam-5645	45	41	complementaray	complementaray	ADJ
ejpam-5645	45	42	direct	direct	ADJ
ejpam-5645	45	43	summand	summand	NOUN
ejpam-5645	45	44	,	,	PUNCT
ejpam-5645	45	45	or	or	CCONJ
ejpam-5645	45	46	simply	simply	ADV
ejpam-5645	45	47	a	a	DET
ejpam-5645	45	48	complement	complement	NOUN
ejpam-5645	45	49	of	of	ADP
ejpam-5645	45	50	b	b	NOUN
ejpam-5645	45	51	in	in	ADP
ejpam-5645	45	52	a	a	PRON
ejpam-5645	45	53	)	)	PUNCT
ejpam-5645	45	54	.	.	PUNCT
ejpam-5645	46	1	(	(	PUNCT
ejpam-5645	46	2	vii	vii	PROPN
ejpam-5645	46	3	)	)	PUNCT
ejpam-5645	46	4	basic	basic	ADJ
ejpam-5645	46	5	subgroup	subgroup	NOUN
ejpam-5645	46	6	(	(	PUNCT
ejpam-5645	46	7	a	a	DET
ejpam-5645	46	8	subgroup	subgroup	NOUN
ejpam-5645	46	9	h	h	NOUN
ejpam-5645	46	10	of	of	ADP
ejpam-5645	46	11	a	a	DET
ejpam-5645	46	12	torsion	torsion	NOUN
ejpam-5645	46	13	group	group	NOUN
ejpam-5645	46	14	g	g	PROPN
ejpam-5645	46	15	is	be	AUX
ejpam-5645	46	16	basic	basic	ADJ
ejpam-5645	46	17	if	if	SCONJ
ejpam-5645	46	18	h	h	NOUN
ejpam-5645	46	19	is	be	AUX
ejpam-5645	46	20	a	a	DET
ejpam-5645	46	21	direct	direct	ADJ
ejpam-5645	46	22	sum	sum	NOUN
ejpam-5645	46	23	of	of	ADP
ejpam-5645	46	24	cyclic	cyclic	ADJ
ejpam-5645	46	25	p−groups	p−groups	PROPN
ejpam-5645	46	26	and	and	CCONJ
ejpam-5645	46	27	it	it	PRON
ejpam-5645	46	28	is	be	AUX
ejpam-5645	46	29	pure	pure	ADJ
ejpam-5645	46	30	in	in	ADP
ejpam-5645	46	31	g	g	PROPN
ejpam-5645	46	32	,	,	PUNCT
ejpam-5645	46	33	and	and	CCONJ
ejpam-5645	46	34	g	g	NOUN
ejpam-5645	46	35	/	/	SYM
ejpam-5645	46	36	h	h	NOUN
ejpam-5645	46	37	is	be	AUX
ejpam-5645	46	38	divisible	divisible	ADJ
ejpam-5645	46	39	.	.	PUNCT
ejpam-5645	46	40	)	)	PUNCT
ejpam-5645	47	1	(	(	PUNCT
ejpam-5645	47	2	viii	viii	NOUN
ejpam-5645	47	3	)	)	PUNCT
ejpam-5645	47	4	pure	pure	ADJ
ejpam-5645	47	5	subgroup	subgroup	NOUN
ejpam-5645	47	6	(	(	PUNCT
ejpam-5645	47	7	a	a	DET
ejpam-5645	47	8	subgroup	subgroup	NOUN
ejpam-5645	47	9	h	h	NOUN
ejpam-5645	47	10	of	of	ADP
ejpam-5645	47	11	a	a	DET
ejpam-5645	47	12	group	group	NOUN
ejpam-5645	47	13	g	g	NOUN
ejpam-5645	47	14	is	be	AUX
ejpam-5645	47	15	said	say	VERB
ejpam-5645	47	16	to	to	PART
ejpam-5645	47	17	be	be	AUX
ejpam-5645	47	18	a	a	DET
ejpam-5645	47	19	pure	pure	ADJ
ejpam-5645	47	20	subgroup	subgroup	NOUN
ejpam-5645	47	21	if	if	SCONJ
ejpam-5645	47	22	∀n	∀n	NUM
ejpam-5645	47	23	∈	∈	VERB
ejpam-5645	47	24	n	n	PRON
ejpam-5645	47	25	h	h	NOUN
ejpam-5645	47	26	∩	∩	PROPN
ejpam-5645	47	27	ng	ng	PROPN
ejpam-5645	47	28	=	=	SYM
ejpam-5645	47	29	nh	nh	PROPN
ejpam-5645	47	30	)	)	PUNCT
ejpam-5645	47	31	.	.	PUNCT
ejpam-5645	48	1	(	(	PUNCT
ejpam-5645	48	2	ix	ix	CCONJ
ejpam-5645	48	3	)	)	PUNCT
ejpam-5645	48	4	small	small	ADJ
ejpam-5645	48	5	or	or	CCONJ
ejpam-5645	48	6	superfluous	superfluous	ADJ
ejpam-5645	48	7	subgroup	subgroup	NOUN
ejpam-5645	48	8	(	(	PUNCT
ejpam-5645	48	9	a	a	DET
ejpam-5645	48	10	subgroup	subgroup	NOUN
ejpam-5645	48	11	h	h	NOUN
ejpam-5645	48	12	of	of	ADP
ejpam-5645	48	13	a	a	DET
ejpam-5645	48	14	group	group	NOUN
ejpam-5645	48	15	g	g	NOUN
ejpam-5645	48	16	is	be	AUX
ejpam-5645	48	17	called	call	VERB
ejpam-5645	48	18	small	small	ADJ
ejpam-5645	48	19	or	or	CCONJ
ejpam-5645	48	20	superfluous	superfluous	ADJ
ejpam-5645	48	21	(	(	PUNCT
ejpam-5645	48	22	denoted	denote	VERB
ejpam-5645	48	23	h	h	NOUN
ejpam-5645	48	24	≪	≪	NOUN
ejpam-5645	48	25	g	g	NOUN
ejpam-5645	48	26	)	)	PUNCT
ejpam-5645	48	27	if	if	SCONJ
ejpam-5645	48	28	,	,	PUNCT
ejpam-5645	48	29	for	for	ADP
ejpam-5645	48	30	every	every	DET
ejpam-5645	48	31	subgroup	subgroup	NOUN
ejpam-5645	48	32	k	k	PROPN
ejpam-5645	48	33	of	of	ADP
ejpam-5645	48	34	g	g	PROPN
ejpam-5645	48	35	,	,	PUNCT
ejpam-5645	48	36	the	the	DET
ejpam-5645	48	37	condition	condition	NOUN
ejpam-5645	48	38	h	h	NOUN
ejpam-5645	49	1	+	+	NOUN
ejpam-5645	49	2	k	k	NOUN
ejpam-5645	49	3	=	=	SYM
ejpam-5645	49	4	g	g	PROPN
ejpam-5645	49	5	implies	imply	VERB
ejpam-5645	49	6	k	k	PROPN
ejpam-5645	49	7	=	=	SYM
ejpam-5645	49	8	g	g	NOUN
ejpam-5645	49	9	)	)	PUNCT
ejpam-5645	49	10	.	.	PUNCT
ejpam-5645	50	1	(	(	PUNCT
ejpam-5645	50	2	x	x	X
ejpam-5645	50	3	)	)	PUNCT
ejpam-5645	50	4	small	small	ADJ
ejpam-5645	50	5	or	or	CCONJ
ejpam-5645	50	6	superfluous	superfluous	ADJ
ejpam-5645	50	7	homomorphism	homomorphism	NOUN
ejpam-5645	50	8	(	(	PUNCT
ejpam-5645	50	9	an	an	DET
ejpam-5645	50	10	homomorphism	homomorphism	PROPN
ejpam-5645	50	11	φ	φ	NOUN
ejpam-5645	50	12	of	of	ADP
ejpam-5645	50	13	g	g	PROPN
ejpam-5645	50	14	is	be	AUX
ejpam-5645	50	15	called	call	VERB
ejpam-5645	50	16	small	small	ADJ
ejpam-5645	50	17	or	or	CCONJ
ejpam-5645	50	18	superfluous	superfluous	ADJ
ejpam-5645	50	19	if	if	SCONJ
ejpam-5645	50	20	ker(φ	ker(φ	X
ejpam-5645	50	21	)	)	PUNCT
ejpam-5645	50	22	is	be	AUX
ejpam-5645	50	23	superfluous	superfluous	ADJ
ejpam-5645	50	24	in	in	ADP
ejpam-5645	50	25	g	g	NOUN
ejpam-5645	50	26	)	)	PUNCT
ejpam-5645	50	27	.	.	PUNCT
ejpam-5645	51	1	(	(	PUNCT
ejpam-5645	51	2	xi	xi	X
ejpam-5645	51	3	)	)	PUNCT
ejpam-5645	51	4	a	a	DET
ejpam-5645	51	5	hopfian	hopfian	ADJ
ejpam-5645	51	6	group	group	NOUN
ejpam-5645	51	7	(	(	PUNCT
ejpam-5645	51	8	a	a	DET
ejpam-5645	51	9	group	group	NOUN
ejpam-5645	51	10	g	g	NOUN
ejpam-5645	51	11	is	be	AUX
ejpam-5645	51	12	called	call	VERB
ejpam-5645	51	13	a	a	DET
ejpam-5645	51	14	hopfian	hopfian	ADJ
ejpam-5645	51	15	group	group	NOUN
ejpam-5645	51	16	if	if	SCONJ
ejpam-5645	51	17	,	,	PUNCT
ejpam-5645	51	18	every	every	DET
ejpam-5645	51	19	surjective	surjective	ADJ
ejpam-5645	51	20	endomorphism	endomorphism	NOUN
ejpam-5645	51	21	is	be	AUX
ejpam-5645	51	22	an	an	DET
ejpam-5645	51	23	automorphism	automorphism	NOUN
ejpam-5645	51	24	)	)	PUNCT
ejpam-5645	51	25	.	.	PUNCT
ejpam-5645	52	1	(	(	PUNCT
ejpam-5645	52	2	xii	xii	NOUN
ejpam-5645	52	3	)	)	PUNCT
ejpam-5645	52	4	generalized	generalized	ADJ
ejpam-5645	52	5	hopfian	hopfian	ADJ
ejpam-5645	52	6	group	group	NOUN
ejpam-5645	52	7	(	(	PUNCT
ejpam-5645	52	8	a	a	DET
ejpam-5645	52	9	group	group	NOUN
ejpam-5645	52	10	g	g	NOUN
ejpam-5645	52	11	is	be	AUX
ejpam-5645	52	12	called	call	VERB
ejpam-5645	52	13	a	a	DET
ejpam-5645	52	14	generalized	generalized	ADJ
ejpam-5645	52	15	hopfian	hopfian	ADJ
ejpam-5645	52	16	group	group	NOUN
ejpam-5645	52	17	if	if	SCONJ
ejpam-5645	52	18	,	,	PUNCT
ejpam-5645	52	19	for	for	ADP
ejpam-5645	52	20	every	every	DET
ejpam-5645	52	21	surjective	surjective	ADJ
ejpam-5645	52	22	endomorphism	endomorphism	PROPN
ejpam-5645	52	23	φ	φ	PROPN
ejpam-5645	52	24	,	,	PUNCT
ejpam-5645	52	25	ker(φ	ker(φ	X
ejpam-5645	52	26	)	)	PUNCT
ejpam-5645	52	27	is	be	AUX
ejpam-5645	52	28	superfluous	superfluous	ADJ
ejpam-5645	52	29	subgroup	subgroup	NOUN
ejpam-5645	52	30	.	.	PUNCT
ejpam-5645	53	1	4	4	NUM
ejpam-5645	53	2	of	of	ADP
ejpam-5645	53	3	13	13	NUM
ejpam-5645	53	4	(	(	PUNCT
ejpam-5645	53	5	xiii	xiii	PROPN
ejpam-5645	53	6	)	)	PUNCT
ejpam-5645	53	7	hereditarily	hereditarily	ADV
ejpam-5645	53	8	hopfian	hopfian	PROPN
ejpam-5645	53	9	group	group	NOUN
ejpam-5645	53	10	(	(	PUNCT
ejpam-5645	53	11	a	a	DET
ejpam-5645	53	12	group	group	NOUN
ejpam-5645	53	13	g	g	NOUN
ejpam-5645	53	14	is	be	AUX
ejpam-5645	53	15	said	say	VERB
ejpam-5645	53	16	to	to	PART
ejpam-5645	53	17	be	be	AUX
ejpam-5645	53	18	a	a	DET
ejpam-5645	53	19	hereditarily	hereditarily	ADJ
ejpam-5645	53	20	hopfian	hopfian	ADJ
ejpam-5645	53	21	group	group	NOUN
ejpam-5645	53	22	if	if	SCONJ
ejpam-5645	53	23	every	every	DET
ejpam-5645	53	24	subgroup	subgroup	NOUN
ejpam-5645	53	25	h	h	NOUN
ejpam-5645	53	26	of	of	ADP
ejpam-5645	53	27	g	g	PROPN
ejpam-5645	53	28	is	be	AUX
ejpam-5645	53	29	hopfian	hopfian	ADJ
ejpam-5645	53	30	group	group	NOUN
ejpam-5645	53	31	)	)	PUNCT
ejpam-5645	53	32	.	.	PUNCT
ejpam-5645	54	1	for	for	ADP
ejpam-5645	54	2	more	more	ADJ
ejpam-5645	54	3	information	information	NOUN
ejpam-5645	54	4	about	about	ADP
ejpam-5645	54	5	other	other	ADJ
ejpam-5645	54	6	properties	property	NOUN
ejpam-5645	54	7	of	of	ADP
ejpam-5645	54	8	these	these	DET
ejpam-5645	54	9	groups	group	NOUN
ejpam-5645	54	10	,	,	PUNCT
ejpam-5645	54	11	the	the	DET
ejpam-5645	54	12	reader	reader	NOUN
ejpam-5645	54	13	could	could	AUX
ejpam-5645	54	14	check	check	VERB
ejpam-5645	54	15	the	the	DET
ejpam-5645	54	16	books	book	NOUN
ejpam-5645	54	17	[	[	X
ejpam-5645	54	18	8	8	NUM
ejpam-5645	54	19	,	,	PUNCT
ejpam-5645	54	20	9	9	NUM
ejpam-5645	54	21	]	]	PUNCT
ejpam-5645	54	22	.	.	PUNCT
ejpam-5645	55	1	we	we	PRON
ejpam-5645	55	2	start	start	VERB
ejpam-5645	55	3	with	with	ADP
ejpam-5645	55	4	the	the	DET
ejpam-5645	55	5	following	follow	VERB
ejpam-5645	55	6	two	two	NUM
ejpam-5645	55	7	remarks	remark	NOUN
ejpam-5645	55	8	that	that	PRON
ejpam-5645	55	9	are	be	AUX
ejpam-5645	55	10	important	important	ADJ
ejpam-5645	55	11	thereafter	thereafter	ADV
ejpam-5645	55	12	.	.	PUNCT
ejpam-5645	56	1	remark	remark	NOUN
ejpam-5645	56	2	1	1	NUM
ejpam-5645	56	3	.	.	PUNCT
ejpam-5645	57	1	if	if	SCONJ
ejpam-5645	57	2	g	g	PROPN
ejpam-5645	57	3	is	be	AUX
ejpam-5645	57	4	a	a	DET
ejpam-5645	57	5	finite	finite	ADJ
ejpam-5645	57	6	group	group	NOUN
ejpam-5645	57	7	,	,	PUNCT
ejpam-5645	57	8	then	then	ADV
ejpam-5645	57	9	g	g	PROPN
ejpam-5645	57	10	is	be	AUX
ejpam-5645	57	11	hopfian	hopfian	ADJ
ejpam-5645	57	12	and	and	CCONJ
ejpam-5645	57	13	hereditarily	hereditarily	ADJ
ejpam-5645	57	14	hopfian	hopfian	ADJ
ejpam-5645	57	15	group	group	NOUN
ejpam-5645	57	16	.	.	PUNCT
ejpam-5645	58	1	in	in	ADP
ejpam-5645	58	2	fact	fact	NOUN
ejpam-5645	58	3	,	,	PUNCT
ejpam-5645	58	4	if	if	SCONJ
ejpam-5645	58	5	we	we	PRON
ejpam-5645	58	6	consider	consider	VERB
ejpam-5645	58	7	a	a	DET
ejpam-5645	58	8	finite	finite	ADJ
ejpam-5645	58	9	group	group	NOUN
ejpam-5645	58	10	g	g	NOUN
ejpam-5645	58	11	,	,	PUNCT
ejpam-5645	58	12	and	and	CCONJ
ejpam-5645	58	13	φ	φ	PROPN
ejpam-5645	58	14	∈	∈	PROPN
ejpam-5645	58	15	end(g	end(g	PROPN
ejpam-5645	58	16	)	)	PUNCT
ejpam-5645	58	17	an	an	DET
ejpam-5645	58	18	epimorphism	epimorphism	NOUN
ejpam-5645	58	19	,	,	PUNCT
ejpam-5645	58	20	then	then	ADV
ejpam-5645	58	21	g	g	PROPN
ejpam-5645	58	22	/	/	SYM
ejpam-5645	58	23	ker(φ	ker(φ	NOUN
ejpam-5645	58	24	)	)	PUNCT
ejpam-5645	58	25	and	and	CCONJ
ejpam-5645	58	26	g	g	PROPN
ejpam-5645	58	27	are	be	AUX
ejpam-5645	58	28	isomorphic	isomorphic	ADJ
ejpam-5645	58	29	.	.	PUNCT
ejpam-5645	59	1	by	by	ADP
ejpam-5645	59	2	uing	ue	VERB
ejpam-5645	59	3	the	the	DET
ejpam-5645	59	4	lagrange	lagrange	NOUN
ejpam-5645	59	5	theorem	theorem	NOUN
ejpam-5645	59	6	,	,	PUNCT
ejpam-5645	59	7	we	we	PRON
ejpam-5645	59	8	get	get	VERB
ejpam-5645	59	9	|g	|g	NOUN
ejpam-5645	59	10	/	/	SYM
ejpam-5645	59	11	kerφ|	kerφ|	NOUN
ejpam-5645	59	12	.	.	PUNCT
ejpam-5645	60	1	|kerφ|	|kerφ|	X
ejpam-5645	61	1	=	=	PUNCT
ejpam-5645	61	2	|g|	|g|	PROPN
ejpam-5645	61	3	.	.	PUNCT
ejpam-5645	62	1	therefore	therefore	ADV
ejpam-5645	62	2	,	,	PUNCT
ejpam-5645	62	3	|kerφ|	|kerφ|	X
ejpam-5645	63	1	=	=	SYM
ejpam-5645	63	2	1	1	NUM
ejpam-5645	63	3	,	,	PUNCT
ejpam-5645	63	4	and	and	CCONJ
ejpam-5645	63	5	then	then	ADV
ejpam-5645	63	6	φ	φ	PROPN
ejpam-5645	63	7	is	be	AUX
ejpam-5645	63	8	a	a	DET
ejpam-5645	63	9	monomorphism	monomorphism	NOUN
ejpam-5645	63	10	,	,	PUNCT
ejpam-5645	63	11	thus	thus	ADV
ejpam-5645	63	12	g	g	PROPN
ejpam-5645	63	13	is	be	AUX
ejpam-5645	63	14	a	a	DET
ejpam-5645	63	15	hopfian	hopfian	ADJ
ejpam-5645	63	16	group	group	NOUN
ejpam-5645	63	17	.	.	PUNCT
ejpam-5645	64	1	finally	finally	ADV
ejpam-5645	64	2	,	,	PUNCT
ejpam-5645	64	3	since	since	SCONJ
ejpam-5645	64	4	all	all	DET
ejpam-5645	64	5	subgroups	subgroup	NOUN
ejpam-5645	64	6	of	of	ADP
ejpam-5645	64	7	g	g	PROPN
ejpam-5645	64	8	are	be	AUX
ejpam-5645	64	9	finite	finite	ADJ
ejpam-5645	64	10	,	,	PUNCT
ejpam-5645	64	11	so	so	SCONJ
ejpam-5645	64	12	they	they	PRON
ejpam-5645	64	13	are	be	AUX
ejpam-5645	64	14	hopfian	hopfian	ADJ
ejpam-5645	64	15	,	,	PUNCT
ejpam-5645	64	16	hence	hence	ADV
ejpam-5645	64	17	,	,	PUNCT
ejpam-5645	64	18	g	g	PROPN
ejpam-5645	64	19	is	be	AUX
ejpam-5645	64	20	hereditarily	hereditarily	ADV
ejpam-5645	64	21	hopfian	hopfian	ADJ
ejpam-5645	64	22	.	.	PUNCT
ejpam-5645	65	1	if	if	SCONJ
ejpam-5645	65	2	we	we	PRON
ejpam-5645	65	3	consider	consider	VERB
ejpam-5645	65	4	just	just	ADV
ejpam-5645	65	5	the	the	DET
ejpam-5645	65	6	case	case	NOUN
ejpam-5645	65	7	of	of	ADP
ejpam-5645	65	8	reduced	reduced	ADJ
ejpam-5645	65	9	p−groups	p−group	NOUN
ejpam-5645	65	10	,	,	PUNCT
ejpam-5645	65	11	our	our	PRON
ejpam-5645	65	12	motivation	motivation	NOUN
ejpam-5645	65	13	arises	arise	VERB
ejpam-5645	65	14	from	from	ADP
ejpam-5645	65	15	the	the	DET
ejpam-5645	65	16	fact	fact	NOUN
ejpam-5645	65	17	that	that	SCONJ
ejpam-5645	65	18	goldsmith	goldsmith	VERB
ejpam-5645	65	19	in	in	ADP
ejpam-5645	65	20	[	[	X
ejpam-5645	65	21	10	10	NUM
ejpam-5645	65	22	]	]	PUNCT
ejpam-5645	65	23	proved	prove	VERB
ejpam-5645	65	24	that	that	SCONJ
ejpam-5645	65	25	there	there	PRON
ejpam-5645	65	26	is	be	VERB
ejpam-5645	65	27	an	an	DET
ejpam-5645	65	28	equivalence	equivalence	NOUN
ejpam-5645	65	29	between	between	ADP
ejpam-5645	65	30	the	the	DET
ejpam-5645	65	31	hereditarily	hereditarily	ADJ
ejpam-5645	65	32	hopficity	hopficity	NOUN
ejpam-5645	65	33	(	(	PUNCT
ejpam-5645	65	34	co	co	NOUN
ejpam-5645	65	35	-	-	NOUN
ejpam-5645	65	36	hopficity	hopficity	NOUN
ejpam-5645	65	37	as	as	ADV
ejpam-5645	65	38	well	well	ADV
ejpam-5645	65	39	)	)	PUNCT
ejpam-5645	65	40	and	and	CCONJ
ejpam-5645	65	41	finiteness	finiteness	NOUN
ejpam-5645	65	42	,	,	PUNCT
ejpam-5645	65	43	but	but	CCONJ
ejpam-5645	65	44	could	could	AUX
ejpam-5645	65	45	we	we	PRON
ejpam-5645	65	46	claim	claim	VERB
ejpam-5645	65	47	that	that	SCONJ
ejpam-5645	65	48	a	a	DET
ejpam-5645	65	49	generalized	generalized	ADJ
ejpam-5645	65	50	hereditarily	hereditarily	ADJ
ejpam-5645	65	51	hopfian	hopfian	ADJ
ejpam-5645	65	52	group	group	NOUN
ejpam-5645	65	53	is	be	AUX
ejpam-5645	65	54	finite	finite	ADJ
ejpam-5645	65	55	?	?	PUNCT
ejpam-5645	66	1	one	one	PRON
ejpam-5645	66	2	could	could	AUX
ejpam-5645	66	3	just	just	ADV
ejpam-5645	66	4	take	take	VERB
ejpam-5645	66	5	z(p∞	z(p∞	PROPN
ejpam-5645	66	6	)	)	PUNCT
ejpam-5645	66	7	as	as	ADP
ejpam-5645	66	8	a	a	DET
ejpam-5645	66	9	counterexample	counterexample	NOUN
ejpam-5645	66	10	.	.	PUNCT
ejpam-5645	67	1	we	we	PRON
ejpam-5645	67	2	need	need	VERB
ejpam-5645	67	3	this	this	DET
ejpam-5645	67	4	following	follow	VERB
ejpam-5645	67	5	proposition	proposition	NOUN
ejpam-5645	67	6	as	as	ADV
ejpam-5645	67	7	well	well	ADV
ejpam-5645	67	8	.	.	PUNCT
ejpam-5645	68	1	proposition	proposition	NOUN
ejpam-5645	68	2	1	1	NUM
ejpam-5645	68	3	.	.	PUNCT
ejpam-5645	69	1	let	let	VERB
ejpam-5645	69	2	g	g	PRON
ejpam-5645	69	3	be	be	AUX
ejpam-5645	69	4	a	a	DET
ejpam-5645	69	5	hereditarily	hereditarily	ADJ
ejpam-5645	69	6	hopfian	hopfian	ADJ
ejpam-5645	69	7	group	group	NOUN
ejpam-5645	69	8	.	.	PUNCT
ejpam-5645	70	1	if	if	SCONJ
ejpam-5645	70	2	h	h	NOUN
ejpam-5645	70	3	is	be	AUX
ejpam-5645	70	4	a	a	DET
ejpam-5645	70	5	subgroup	subgroup	NOUN
ejpam-5645	70	6	of	of	ADP
ejpam-5645	70	7	g	g	PROPN
ejpam-5645	70	8	,	,	PUNCT
ejpam-5645	70	9	then	then	ADV
ejpam-5645	70	10	h	h	NOUN
ejpam-5645	70	11	is	be	AUX
ejpam-5645	70	12	hereditarily	hereditarily	ADV
ejpam-5645	70	13	hopfian	hopfian	ADJ
ejpam-5645	70	14	.	.	PUNCT
ejpam-5645	71	1	proof	proof	NOUN
ejpam-5645	71	2	.	.	PUNCT
ejpam-5645	72	1	let	let	VERB
ejpam-5645	72	2	g	g	PRON
ejpam-5645	72	3	be	be	AUX
ejpam-5645	72	4	a	a	DET
ejpam-5645	72	5	hereditarily	hereditarily	ADJ
ejpam-5645	72	6	hopfian	hopfian	ADJ
ejpam-5645	72	7	group	group	NOUN
ejpam-5645	72	8	.	.	PUNCT
ejpam-5645	73	1	suppose	suppose	VERB
ejpam-5645	73	2	h	h	NOUN
ejpam-5645	73	3	is	be	AUX
ejpam-5645	73	4	a	a	DET
ejpam-5645	73	5	subgroup	subgroup	NOUN
ejpam-5645	73	6	of	of	ADP
ejpam-5645	73	7	g.	g.	PROPN
ejpam-5645	73	8	then	then	ADV
ejpam-5645	73	9	,	,	PUNCT
ejpam-5645	73	10	h	h	NOUN
ejpam-5645	73	11	is	be	AUX
ejpam-5645	73	12	a	a	DET
ejpam-5645	73	13	hopfian	hopfian	ADJ
ejpam-5645	73	14	group	group	NOUN
ejpam-5645	73	15	.	.	PUNCT
ejpam-5645	74	1	now	now	ADV
ejpam-5645	74	2	,	,	PUNCT
ejpam-5645	74	3	let	let	VERB
ejpam-5645	74	4	k	k	PRON
ejpam-5645	74	5	be	be	AUX
ejpam-5645	74	6	a	a	DET
ejpam-5645	74	7	subgroup	subgroup	NOUN
ejpam-5645	74	8	of	of	ADP
ejpam-5645	74	9	h.	h.	PROPN
ejpam-5645	74	10	since	since	SCONJ
ejpam-5645	74	11	k	k	PROPN
ejpam-5645	74	12	is	be	AUX
ejpam-5645	74	13	a	a	DET
ejpam-5645	74	14	subgroup	subgroup	NOUN
ejpam-5645	74	15	of	of	ADP
ejpam-5645	74	16	g	g	PROPN
ejpam-5645	74	17	,	,	PUNCT
ejpam-5645	74	18	it	it	PRON
ejpam-5645	74	19	follows	follow	VERB
ejpam-5645	74	20	that	that	SCONJ
ejpam-5645	74	21	k	k	PROPN
ejpam-5645	74	22	is	be	AUX
ejpam-5645	74	23	hopfian	hopfian	ADJ
ejpam-5645	74	24	.	.	PUNCT
ejpam-5645	75	1	therefore	therefore	ADV
ejpam-5645	75	2	,	,	PUNCT
ejpam-5645	75	3	every	every	DET
ejpam-5645	75	4	subgroup	subgroup	NOUN
ejpam-5645	75	5	of	of	ADP
ejpam-5645	75	6	h	h	PROPN
ejpam-5645	75	7	is	be	AUX
ejpam-5645	75	8	hopfian	hopfian	ADJ
ejpam-5645	75	9	,	,	PUNCT
ejpam-5645	75	10	which	which	PRON
ejpam-5645	75	11	shows	show	VERB
ejpam-5645	75	12	that	that	SCONJ
ejpam-5645	75	13	h	h	NOUN
ejpam-5645	75	14	is	be	AUX
ejpam-5645	75	15	hereditarily	hereditarily	ADV
ejpam-5645	75	16	hopfian	hopfian	ADJ
ejpam-5645	75	17	.	.	PUNCT
ejpam-5645	76	1	remark	remark	PROPN
ejpam-5645	76	2	2	2	NUM
ejpam-5645	76	3	.	.	PUNCT
ejpam-5645	77	1	if	if	SCONJ
ejpam-5645	77	2	g	g	PROPN
ejpam-5645	77	3	is	be	AUX
ejpam-5645	77	4	hereditarily	hereditarily	ADV
ejpam-5645	77	5	hopfian	hopfian	ADJ
ejpam-5645	77	6	group	group	NOUN
ejpam-5645	77	7	,	,	PUNCT
ejpam-5645	77	8	then	then	ADV
ejpam-5645	77	9	g	g	PROPN
ejpam-5645	77	10	is	be	AUX
ejpam-5645	77	11	generalized	generalize	VERB
ejpam-5645	77	12	hereditarily	hereditarily	ADJ
ejpam-5645	77	13	hopfian	hopfian	ADJ
ejpam-5645	77	14	group	group	NOUN
ejpam-5645	77	15	.	.	PUNCT
ejpam-5645	78	1	in	in	ADP
ejpam-5645	78	2	fact	fact	NOUN
ejpam-5645	78	3	,	,	PUNCT
ejpam-5645	78	4	if	if	SCONJ
ejpam-5645	78	5	we	we	PRON
ejpam-5645	78	6	consider	consider	VERB
ejpam-5645	78	7	a	a	DET
ejpam-5645	78	8	subgroup	subgroup	NOUN
ejpam-5645	78	9	k	k	PROPN
ejpam-5645	78	10	of	of	ADP
ejpam-5645	78	11	g	g	PROPN
ejpam-5645	78	12	,	,	PUNCT
ejpam-5645	78	13	then	then	ADV
ejpam-5645	78	14	k	k	PROPN
ejpam-5645	78	15	is	be	AUX
ejpam-5645	78	16	hereditarily	hereditarily	ADV
ejpam-5645	78	17	hopfian	hopfian	ADJ
ejpam-5645	78	18	by	by	ADP
ejpam-5645	78	19	proposition	proposition	NOUN
ejpam-5645	78	20	1	1	NUM
ejpam-5645	78	21	,	,	PUNCT
ejpam-5645	78	22	thus	thus	ADV
ejpam-5645	78	23	k	k	PROPN
ejpam-5645	78	24	is	be	AUX
ejpam-5645	78	25	generalized	generalize	VERB
ejpam-5645	78	26	hopfian	hopfian	ADJ
ejpam-5645	78	27	subgroup	subgroup	NOUN
ejpam-5645	78	28	,	,	PUNCT
ejpam-5645	78	29	and	and	CCONJ
ejpam-5645	78	30	therefore	therefore	ADV
ejpam-5645	78	31	g	g	PROPN
ejpam-5645	78	32	is	be	AUX
ejpam-5645	78	33	generalized	generalize	VERB
ejpam-5645	78	34	hereditarily	hereditarily	ADJ
ejpam-5645	78	35	hopfian	hopfian	ADJ
ejpam-5645	78	36	group	group	NOUN
ejpam-5645	78	37	.	.	PUNCT
ejpam-5645	79	1	lemma	lemma	PROPN
ejpam-5645	79	2	1	1	NUM
ejpam-5645	79	3	.	.	PUNCT
ejpam-5645	80	1	if	if	SCONJ
ejpam-5645	80	2	g	g	PROPN
ejpam-5645	80	3	is	be	AUX
ejpam-5645	80	4	a	a	DET
ejpam-5645	80	5	generalized	generalized	ADJ
ejpam-5645	80	6	hereditarily	hereditarily	ADJ
ejpam-5645	80	7	hopfian	hopfian	ADJ
ejpam-5645	80	8	group	group	NOUN
ejpam-5645	80	9	,	,	PUNCT
ejpam-5645	80	10	and	and	CCONJ
ejpam-5645	80	11	h	h	NOUN
ejpam-5645	80	12	is	be	AUX
ejpam-5645	80	13	a	a	DET
ejpam-5645	80	14	subgroup	subgroup	NOUN
ejpam-5645	80	15	of	of	ADP
ejpam-5645	80	16	g	g	PROPN
ejpam-5645	80	17	,	,	PUNCT
ejpam-5645	80	18	then	then	ADV
ejpam-5645	80	19	h	h	PROPN
ejpam-5645	80	20	is	be	AUX
ejpam-5645	80	21	a	a	DET
ejpam-5645	80	22	generalized	generalized	ADJ
ejpam-5645	80	23	hereditarily	hereditarily	ADJ
ejpam-5645	80	24	hopfian	hopfian	PROPN
ejpam-5645	80	25	subgroup	subgroup	NOUN
ejpam-5645	80	26	.	.	PUNCT
ejpam-5645	81	1	proof	proof	NOUN
ejpam-5645	81	2	.	.	PUNCT
ejpam-5645	82	1	since	since	SCONJ
ejpam-5645	82	2	g	g	PROPN
ejpam-5645	82	3	is	be	AUX
ejpam-5645	82	4	a	a	DET
ejpam-5645	82	5	generalized	generalized	ADJ
ejpam-5645	82	6	hereditarily	hereditarily	ADJ
ejpam-5645	82	7	hopfian	hopfian	ADJ
ejpam-5645	82	8	group	group	NOUN
ejpam-5645	82	9	,	,	PUNCT
ejpam-5645	82	10	then	then	ADV
ejpam-5645	82	11	h	h	PROPN
ejpam-5645	82	12	is	be	AUX
ejpam-5645	82	13	a	a	DET
ejpam-5645	82	14	generalized	generalized	ADJ
ejpam-5645	82	15	hopfian	hopfian	ADJ
ejpam-5645	82	16	group	group	NOUN
ejpam-5645	82	17	.	.	PUNCT
ejpam-5645	83	1	and	and	CCONJ
ejpam-5645	83	2	again	again	ADV
ejpam-5645	83	3	,	,	PUNCT
ejpam-5645	83	4	using	use	VERB
ejpam-5645	83	5	the	the	DET
ejpam-5645	83	6	same	same	ADJ
ejpam-5645	83	7	method	method	NOUN
ejpam-5645	83	8	as	as	ADP
ejpam-5645	83	9	in	in	ADP
ejpam-5645	83	10	the	the	DET
ejpam-5645	83	11	proof	proof	NOUN
ejpam-5645	83	12	of	of	ADP
ejpam-5645	83	13	proposition	proposition	NOUN
ejpam-5645	83	14	1	1	NUM
ejpam-5645	83	15	,	,	PUNCT
ejpam-5645	83	16	we	we	PRON
ejpam-5645	83	17	conclude	conclude	VERB
ejpam-5645	83	18	that	that	SCONJ
ejpam-5645	83	19	h	h	NOUN
ejpam-5645	83	20	is	be	AUX
ejpam-5645	83	21	a	a	DET
ejpam-5645	83	22	generalized	generalized	ADJ
ejpam-5645	83	23	hereditarily	hereditarily	ADJ
ejpam-5645	83	24	hopfian	hopfian	ADJ
ejpam-5645	83	25	group	group	NOUN
ejpam-5645	83	26	.	.	PUNCT
ejpam-5645	84	1	theorem	theorem	NOUN
ejpam-5645	84	2	1	1	X
ejpam-5645	84	3	.	.	PUNCT
ejpam-5645	85	1	let	let	VERB
ejpam-5645	85	2	g	g	PRON
ejpam-5645	85	3	be	be	AUX
ejpam-5645	85	4	a	a	DET
ejpam-5645	85	5	abelian	abelian	NOUN
ejpam-5645	85	6	reduced	reduce	VERB
ejpam-5645	85	7	p−group	p−group	NOUN
ejpam-5645	85	8	.	.	PUNCT
ejpam-5645	86	1	then	then	ADV
ejpam-5645	86	2	the	the	DET
ejpam-5645	86	3	following	follow	VERB
ejpam-5645	86	4	properties	property	NOUN
ejpam-5645	86	5	are	be	AUX
ejpam-5645	86	6	equivalent	equivalent	ADJ
ejpam-5645	86	7	,	,	PUNCT
ejpam-5645	86	8	•	•	PRON
ejpam-5645	86	9	(	(	PUNCT
ejpam-5645	86	10	a	a	NOUN
ejpam-5645	86	11	)	)	PUNCT
ejpam-5645	86	12	g	g	NOUN
ejpam-5645	86	13	is	be	AUX
ejpam-5645	86	14	finite	finite	ADJ
ejpam-5645	86	15	group	group	NOUN
ejpam-5645	86	16	,	,	PUNCT
ejpam-5645	86	17	5	5	NUM
ejpam-5645	86	18	of	of	ADP
ejpam-5645	86	19	13	13	NUM
ejpam-5645	86	20	•	•	NOUN
ejpam-5645	86	21	(	(	PUNCT
ejpam-5645	86	22	b	b	NOUN
ejpam-5645	86	23	)	)	PUNCT
ejpam-5645	86	24	g	g	NOUN
ejpam-5645	86	25	is	be	AUX
ejpam-5645	86	26	hereditarily	hereditarily	ADV
ejpam-5645	86	27	hopfian	hopfian	ADJ
ejpam-5645	86	28	group	group	NOUN
ejpam-5645	86	29	,	,	PUNCT
ejpam-5645	86	30	•	•	X
ejpam-5645	86	31	(	(	PUNCT
ejpam-5645	86	32	c	c	NOUN
ejpam-5645	86	33	)	)	PUNCT
ejpam-5645	86	34	g	g	NOUN
ejpam-5645	86	35	is	be	AUX
ejpam-5645	86	36	generalized	generalize	VERB
ejpam-5645	86	37	hereditarily	hereditarily	ADJ
ejpam-5645	86	38	hopfian	hopfian	ADJ
ejpam-5645	86	39	group	group	NOUN
ejpam-5645	86	40	.	.	PUNCT
ejpam-5645	87	1	proof	proof	NOUN
ejpam-5645	87	2	.	.	PUNCT
ejpam-5645	88	1	•	•	NUM
ejpam-5645	88	2	(	(	PUNCT
ejpam-5645	88	3	a	a	NOUN
ejpam-5645	88	4	)	)	PUNCT
ejpam-5645	88	5	⇒	⇒	NOUN
ejpam-5645	88	6	(	(	PUNCT
ejpam-5645	88	7	b	b	X
ejpam-5645	88	8	)	)	PUNCT
ejpam-5645	88	9	is	be	AUX
ejpam-5645	88	10	obvious	obvious	ADJ
ejpam-5645	88	11	due	due	ADJ
ejpam-5645	88	12	to	to	PART
ejpam-5645	88	13	remark	remark	VERB
ejpam-5645	88	14	1	1	NUM
ejpam-5645	88	15	.	.	NOUN
ejpam-5645	88	16	•	•	NUM
ejpam-5645	88	17	(	(	PUNCT
ejpam-5645	88	18	b	b	NOUN
ejpam-5645	88	19	)	)	PUNCT
ejpam-5645	88	20	⇒	⇒	NOUN
ejpam-5645	88	21	(	(	PUNCT
ejpam-5645	88	22	c	c	X
ejpam-5645	88	23	)	)	PUNCT
ejpam-5645	88	24	is	be	AUX
ejpam-5645	88	25	obvious	obvious	ADJ
ejpam-5645	88	26	due	due	ADJ
ejpam-5645	88	27	to	to	PART
ejpam-5645	88	28	remark	remark	VERB
ejpam-5645	88	29	2	2	NUM
ejpam-5645	88	30	.	.	NOUN
ejpam-5645	88	31	•	•	NUM
ejpam-5645	88	32	(	(	PUNCT
ejpam-5645	88	33	c	c	NOUN
ejpam-5645	88	34	)	)	PUNCT
ejpam-5645	88	35	⇒	⇒	NOUN
ejpam-5645	88	36	(	(	PUNCT
ejpam-5645	88	37	a	a	NOUN
ejpam-5645	88	38	)	)	PUNCT
ejpam-5645	88	39	.	.	PUNCT
ejpam-5645	89	1	in	in	ADP
ejpam-5645	89	2	fact	fact	NOUN
ejpam-5645	89	3	,	,	PUNCT
ejpam-5645	89	4	this	this	PRON
ejpam-5645	89	5	is	be	AUX
ejpam-5645	89	6	the	the	DET
ejpam-5645	89	7	right	right	ADJ
ejpam-5645	89	8	remaining	remain	VERB
ejpam-5645	89	9	question	question	NOUN
ejpam-5645	89	10	that	that	PRON
ejpam-5645	89	11	is	be	AUX
ejpam-5645	89	12	still	still	ADV
ejpam-5645	89	13	open	open	ADJ
ejpam-5645	89	14	.	.	PUNCT
ejpam-5645	90	1	let	let	VERB
ejpam-5645	90	2	g	g	PRON
ejpam-5645	90	3	be	be	AUX
ejpam-5645	90	4	a	a	DET
ejpam-5645	90	5	generalized	generalized	ADJ
ejpam-5645	90	6	hereditary	hereditary	ADJ
ejpam-5645	90	7	hopfian	hopfian	ADJ
ejpam-5645	90	8	group	group	NOUN
ejpam-5645	90	9	.	.	PUNCT
ejpam-5645	91	1	according	accord	VERB
ejpam-5645	91	2	to	to	ADP
ejpam-5645	91	3	theorem	theorem	VERB
ejpam-5645	91	4	32.3	32.3	NUM
ejpam-5645	91	5	[	[	NOUN
ejpam-5645	91	6	8	8	NUM
ejpam-5645	91	7	]	]	PUNCT
ejpam-5645	91	8	,	,	PUNCT
ejpam-5645	91	9	g	g	PROPN
ejpam-5645	91	10	contains	contain	VERB
ejpam-5645	91	11	a	a	DET
ejpam-5645	91	12	basic	basic	ADJ
ejpam-5645	91	13	subgroup	subgroup	NOUN
ejpam-5645	91	14	b	b	NOUN
ejpam-5645	91	15	,	,	PUNCT
ejpam-5645	91	16	and	and	CCONJ
ejpam-5645	91	17	since	since	SCONJ
ejpam-5645	91	18	g	g	PROPN
ejpam-5645	91	19	is	be	AUX
ejpam-5645	91	20	a	a	DET
ejpam-5645	91	21	p−group	p−group	NOUN
ejpam-5645	91	22	(	(	PUNCT
ejpam-5645	91	23	then	then	ADV
ejpam-5645	91	24	of	of	ADP
ejpam-5645	91	25	torsion	torsion	NOUN
ejpam-5645	91	26	)	)	PUNCT
ejpam-5645	91	27	,	,	PUNCT
ejpam-5645	91	28	then	then	ADV
ejpam-5645	91	29	b	b	X
ejpam-5645	91	30	=	=	SYM
ejpam-5645	91	31	∞⊕	∞⊕	PROPN
ejpam-5645	91	32	n=1	n=1	PROPN
ejpam-5645	91	33	bn	bn	PROPN
ejpam-5645	91	34	,	,	PUNCT
ejpam-5645	91	35	bn	bn	NOUN
ejpam-5645	91	36	=	=	PROPN
ejpam-5645	91	37	⊕	⊕	PROPN
ejpam-5645	91	38	i∈in	i∈in	PROPN
ejpam-5645	91	39	⟨xi	⟨xi	PROPN
ejpam-5645	91	40	,	,	PUNCT
ejpam-5645	91	41	n⟩	n⟩	PROPN
ejpam-5645	91	42	,	,	PUNCT
ejpam-5645	91	43	in	in	ADP
ejpam-5645	91	44	⊆	⊆	NUM
ejpam-5645	91	45	n	n	CCONJ
ejpam-5645	91	46	,	,	PUNCT
ejpam-5645	91	47	ord(xi	ord(xi	NUM
ejpam-5645	91	48	,	,	PUNCT
ejpam-5645	91	49	n	n	CCONJ
ejpam-5645	91	50	)	)	PUNCT
ejpam-5645	91	51	=	=	SYM
ejpam-5645	91	52	pn	pn	PROPN
ejpam-5645	91	53	.	.	PROPN
ejpam-5645	91	54	to	to	PART
ejpam-5645	91	55	prove	prove	VERB
ejpam-5645	91	56	that	that	SCONJ
ejpam-5645	91	57	g	g	PROPN
ejpam-5645	91	58	is	be	AUX
ejpam-5645	91	59	finite	finite	ADJ
ejpam-5645	91	60	,	,	PUNCT
ejpam-5645	91	61	it	it	PRON
ejpam-5645	91	62	suffices	suffice	VERB
ejpam-5645	91	63	to	to	PART
ejpam-5645	91	64	show	show	VERB
ejpam-5645	91	65	that	that	SCONJ
ejpam-5645	91	66	g	g	PROPN
ejpam-5645	91	67	=	=	SYM
ejpam-5645	91	68	b	b	PROPN
ejpam-5645	91	69	and	and	CCONJ
ejpam-5645	91	70	b	b	PROPN
ejpam-5645	91	71	is	be	AUX
ejpam-5645	91	72	finite	finite	ADJ
ejpam-5645	91	73	.	.	PUNCT
ejpam-5645	92	1	since	since	SCONJ
ejpam-5645	92	2	g	g	PROPN
ejpam-5645	92	3	is	be	AUX
ejpam-5645	92	4	reduced	reduce	VERB
ejpam-5645	92	5	,	,	PUNCT
ejpam-5645	92	6	it	it	PRON
ejpam-5645	92	7	is	be	AUX
ejpam-5645	92	8	necessary	necessary	ADJ
ejpam-5645	92	9	to	to	PART
ejpam-5645	92	10	prove	prove	VERB
ejpam-5645	92	11	that	that	SCONJ
ejpam-5645	92	12	b	b	NOUN
ejpam-5645	92	13	is	be	AUX
ejpam-5645	92	14	a	a	DET
ejpam-5645	92	15	direct	direct	ADJ
ejpam-5645	92	16	summand	summand	NOUN
ejpam-5645	92	17	of	of	ADP
ejpam-5645	92	18	g.	g.	PROPN
ejpam-5645	92	19	being	be	AUX
ejpam-5645	92	20	b	b	NOUN
ejpam-5645	92	21	is	be	AUX
ejpam-5645	92	22	a	a	DET
ejpam-5645	92	23	basic	basic	ADJ
ejpam-5645	92	24	subgroup	subgroup	NOUN
ejpam-5645	92	25	of	of	ADP
ejpam-5645	92	26	g	g	PROPN
ejpam-5645	92	27	,	,	PUNCT
ejpam-5645	92	28	it	it	PRON
ejpam-5645	92	29	implies	imply	VERB
ejpam-5645	92	30	that	that	PRON
ejpam-5645	92	31	is	be	AUX
ejpam-5645	92	32	pure	pure	ADJ
ejpam-5645	92	33	.	.	PUNCT
ejpam-5645	93	1	but	but	CCONJ
ejpam-5645	93	2	according	accord	VERB
ejpam-5645	93	3	to	to	ADP
ejpam-5645	93	4	theorem	theorem	ADJ
ejpam-5645	93	5	27.5	27.5	NUM
ejpam-5645	93	6	(	(	PUNCT
ejpam-5645	93	7	kulikov	kulikov	PROPN
ejpam-5645	93	8	,	,	PUNCT
ejpam-5645	93	9	[	[	X
ejpam-5645	93	10	8	8	NUM
ejpam-5645	93	11	]	]	NUM
ejpam-5645	93	12	)	)	PUNCT
ejpam-5645	93	13	,	,	PUNCT
ejpam-5645	93	14	it	it	PRON
ejpam-5645	93	15	remains	remain	VERB
ejpam-5645	93	16	to	to	PART
ejpam-5645	93	17	prove	prove	VERB
ejpam-5645	93	18	that	that	SCONJ
ejpam-5645	93	19	b	b	NOUN
ejpam-5645	93	20	is	be	AUX
ejpam-5645	93	21	bounded	bound	VERB
ejpam-5645	93	22	to	to	PART
ejpam-5645	93	23	become	become	VERB
ejpam-5645	93	24	a	a	DET
ejpam-5645	93	25	direct	direct	ADJ
ejpam-5645	93	26	summand	summand	NOUN
ejpam-5645	93	27	,	,	PUNCT
ejpam-5645	93	28	which	which	PRON
ejpam-5645	93	29	will	will	AUX
ejpam-5645	93	30	be	be	AUX
ejpam-5645	93	31	shown	show	VERB
ejpam-5645	93	32	hereafter	hereafter	ADV
ejpam-5645	93	33	by	by	ADP
ejpam-5645	93	34	contradiction	contradiction	NOUN
ejpam-5645	93	35	.	.	PUNCT
ejpam-5645	94	1	assume	assume	VERB
ejpam-5645	94	2	that	that	SCONJ
ejpam-5645	94	3	b	b	NOUN
ejpam-5645	94	4	is	be	AUX
ejpam-5645	94	5	not	not	PART
ejpam-5645	94	6	bounded	bound	VERB
ejpam-5645	94	7	.	.	PUNCT
ejpam-5645	95	1	then	then	ADV
ejpam-5645	95	2	,	,	PUNCT
ejpam-5645	95	3	for	for	ADP
ejpam-5645	95	4	every	every	DET
ejpam-5645	95	5	integer	integer	NOUN
ejpam-5645	95	6	n	n	PRON
ejpam-5645	95	7	≥	≥	NOUN
ejpam-5645	95	8	1	1	NUM
ejpam-5645	95	9	and	and	CCONJ
ejpam-5645	95	10	prime	prime	ADJ
ejpam-5645	95	11	p	p	NOUN
ejpam-5645	95	12	,	,	PUNCT
ejpam-5645	95	13	we	we	PRON
ejpam-5645	95	14	have	have	AUX
ejpam-5645	95	15	:	:	PUNCT
ejpam-5645	95	16	pnb	pnb	PROPN
ejpam-5645	95	17	̸=	̸=	PROPN
ejpam-5645	95	18	0	0	NUM
ejpam-5645	96	1	⇐	⇐	ADJ
ejpam-5645	96	2	⇒	⇒	NOUN
ejpam-5645	96	3	pn(b1	pn(b1	VERB
ejpam-5645	96	4	⊕b2	⊕b2	PROPN
ejpam-5645	96	5	⊕	⊕	PROPN
ejpam-5645	96	6	·	·	PUNCT
ejpam-5645	96	7	·	·	PUNCT
ejpam-5645	96	8	·	·	PUNCT
ejpam-5645	96	9	⊕bn	⊕bn	NOUN
ejpam-5645	96	10	⊕bn+1	⊕bn+1	PROPN
ejpam-5645	96	11	⊕	⊕	PROPN
ejpam-5645	96	12	.	.	PUNCT
ejpam-5645	96	13	.	.	PUNCT
ejpam-5645	96	14	.	.	PUNCT
ejpam-5645	96	15	)	)	PUNCT
ejpam-5645	97	1	̸=	̸=	NOUN
ejpam-5645	97	2	0	0	NUM
ejpam-5645	97	3	⇐	⇐	ADJ
ejpam-5645	97	4	⇒	⇒	NOUN
ejpam-5645	97	5	pn(bn+1	pn(bn+1	VERB
ejpam-5645	97	6	⊕bn+2	⊕bn+2	PROPN
ejpam-5645	97	7	⊕	⊕	PROPN
ejpam-5645	97	8	.	.	PUNCT
ejpam-5645	97	9	.	.	PUNCT
ejpam-5645	97	10	.	.	PUNCT
ejpam-5645	97	11	)	)	PUNCT
ejpam-5645	98	1	̸=	̸=	PROPN
ejpam-5645	98	2	0	0	NUM
ejpam-5645	98	3	,	,	PUNCT
ejpam-5645	98	4	.	.	PUNCT
ejpam-5645	99	1	then	then	ADV
ejpam-5645	99	2	there	there	PRON
ejpam-5645	99	3	exists	exist	VERB
ejpam-5645	99	4	increasing	increase	VERB
ejpam-5645	99	5	sequence	sequence	NOUN
ejpam-5645	99	6	mk	mk	X
ejpam-5645	99	7	>	>	X
ejpam-5645	99	8	n	n	CCONJ
ejpam-5645	99	9	with	with	ADP
ejpam-5645	99	10	k	k	PROPN
ejpam-5645	99	11	>	>	X
ejpam-5645	99	12	0	0	PROPN
ejpam-5645	99	13	,	,	PUNCT
ejpam-5645	99	14	such	such	ADJ
ejpam-5645	99	15	that	that	SCONJ
ejpam-5645	99	16	bmk	bmk	PROPN
ejpam-5645	99	17	̸=	̸=	PROPN
ejpam-5645	99	18	0	0	NUM
ejpam-5645	99	19	,	,	PUNCT
ejpam-5645	99	20	and	and	CCONJ
ejpam-5645	99	21	also	also	ADV
ejpam-5645	99	22	we	we	PRON
ejpam-5645	99	23	can	can	AUX
ejpam-5645	99	24	write	write	VERB
ejpam-5645	99	25	bmk	bmk	PROPN
ejpam-5645	99	26	=	=	PROPN
ejpam-5645	99	27	⟨xmk	⟨xmk	PROPN
ejpam-5645	99	28	⟩	⟩	PROPN
ejpam-5645	99	29	)	)	PUNCT
ejpam-5645	99	30	⊕	⊕	PROPN
ejpam-5645	99	31	b′	b′	NUM
ejpam-5645	99	32	with	with	ADP
ejpam-5645	99	33	ord(xmk	ord(xmk	PROPN
ejpam-5645	99	34	)	)	PUNCT
ejpam-5645	100	1	=	=	PROPN
ejpam-5645	100	2	pmk	pmk	PROPN
ejpam-5645	100	3	and	and	CCONJ
ejpam-5645	100	4	b′	b′	NUM
ejpam-5645	100	5	=	=	NOUN
ejpam-5645	100	6	⊕∞	⊕∞	PROPN
ejpam-5645	100	7	k=1⟨xmk	k=1⟨xmk	PROPN
ejpam-5645	100	8	⟩.	⟩.	PROPN
ejpam-5645	100	9	it	it	PRON
ejpam-5645	100	10	is	be	AUX
ejpam-5645	100	11	clear	clear	ADJ
ejpam-5645	100	12	that	that	SCONJ
ejpam-5645	100	13	b′	b′	NOUN
ejpam-5645	100	14	is	be	AUX
ejpam-5645	100	15	generalized	generalize	VERB
ejpam-5645	100	16	hereditary	hereditary	ADJ
ejpam-5645	100	17	hopfian	hopfian	ADJ
ejpam-5645	100	18	subgroup	subgroup	NOUN
ejpam-5645	100	19	of	of	ADP
ejpam-5645	100	20	g	g	PROPN
ejpam-5645	100	21	,	,	PUNCT
ejpam-5645	100	22	by	by	ADP
ejpam-5645	100	23	lemma	lemma	PROPN
ejpam-5645	100	24	1	1	NUM
ejpam-5645	100	25	,	,	PUNCT
ejpam-5645	100	26	because	because	SCONJ
ejpam-5645	100	27	b′	b′	NUM
ejpam-5645	100	28	is	be	AUX
ejpam-5645	100	29	subgroup	subgroup	NOUN
ejpam-5645	100	30	of	of	ADP
ejpam-5645	100	31	g.	g.	PROPN
ejpam-5645	100	32	let	let	VERB
ejpam-5645	100	33	φ	φ	PROPN
ejpam-5645	100	34	the	the	DET
ejpam-5645	100	35	following	follow	VERB
ejpam-5645	100	36	map	map	NOUN
ejpam-5645	100	37	defined	define	VERB
ejpam-5645	100	38	by	by	ADP
ejpam-5645	100	39	b′	b′	NUM
ejpam-5645	100	40	−→	−→	NOUN
ejpam-5645	100	41	b′∑n0	b′∑n0	VERB
ejpam-5645	100	42	k=1mkxmk	k=1mkxmk	PROPN
ejpam-5645	100	43	7−→	7−→	NUM
ejpam-5645	100	44	∑n0−1	∑n0−1	PROPN
ejpam-5645	101	1	k=1	k=1	X
ejpam-5645	101	2	mk+1xmk	mk+1xmk	PROPN
ejpam-5645	101	3	.	.	PUNCT
ejpam-5645	102	1	it	it	PRON
ejpam-5645	102	2	is	be	AUX
ejpam-5645	102	3	clear	clear	ADJ
ejpam-5645	102	4	that	that	SCONJ
ejpam-5645	102	5	φ	φ	PROPN
ejpam-5645	102	6	is	be	AUX
ejpam-5645	102	7	a	a	DET
ejpam-5645	102	8	surjective	surjective	ADJ
ejpam-5645	102	9	endomorphism	endomorphism	NOUN
ejpam-5645	102	10	,	,	PUNCT
ejpam-5645	102	11	and	and	CCONJ
ejpam-5645	102	12	we	we	PRON
ejpam-5645	102	13	can	can	AUX
ejpam-5645	102	14	write	write	VERB
ejpam-5645	102	15	b′	b′	NOUN
ejpam-5645	102	16	as	as	ADP
ejpam-5645	102	17	:	:	PUNCT
ejpam-5645	102	18	b′	b′	NUM
ejpam-5645	102	19	=	=	NOUN
ejpam-5645	102	20	⟨xm1⟩	⟨xm1⟩	PROPN
ejpam-5645	102	21	⊕	⊕	PROPN
ejpam-5645	102	22	⊕∞	⊕∞	PROPN
ejpam-5645	102	23	k=2⟨xmk	k=2⟨xmk	PROPN
ejpam-5645	102	24	⟩	⟩	PROPN
ejpam-5645	102	25	⊂	⊂	PROPN
ejpam-5645	102	26	ker(φ)⊕	ker(φ)⊕	PROPN
ejpam-5645	102	27	⊕∞	⊕∞	PROPN
ejpam-5645	102	28	k=2⟨xmk	k=2⟨xmk	PROPN
ejpam-5645	102	29	⟩	⟩	PROPN
ejpam-5645	102	30	⊂	⊂	PROPN
ejpam-5645	103	1	b′	b′	NUM
ejpam-5645	104	1	thus	thus	ADV
ejpam-5645	104	2	,	,	PUNCT
ejpam-5645	104	3	b′	b′	NOUN
ejpam-5645	104	4	=	=	SYM
ejpam-5645	104	5	ker(φ	ker(φ	X
ejpam-5645	104	6	)	)	PUNCT
ejpam-5645	104	7	⊕	⊕	PROPN
ejpam-5645	104	8	⊕∞	⊕∞	PROPN
ejpam-5645	104	9	k=2⟨xmk	k=2⟨xmk	PROPN
ejpam-5645	104	10	⟩	⟩	PROPN
ejpam-5645	104	11	and	and	CCONJ
ejpam-5645	104	12	consequently	consequently	ADV
ejpam-5645	104	13	b′	b′	NUM
ejpam-5645	104	14	=	=	PUNCT
ejpam-5645	104	15	⊕∞	⊕∞	PROPN
ejpam-5645	104	16	k=2⟨xmk	k=2⟨xmk	PROPN
ejpam-5645	104	17	⟩	⟩	PROPN
ejpam-5645	104	18	,	,	PUNCT
ejpam-5645	104	19	which	which	PRON
ejpam-5645	104	20	is	be	AUX
ejpam-5645	104	21	absurd	absurd	ADJ
ejpam-5645	104	22	.	.	PUNCT
ejpam-5645	105	1	consequently	consequently	ADV
ejpam-5645	105	2	,	,	PUNCT
ejpam-5645	105	3	b	b	PROPN
ejpam-5645	105	4	is	be	AUX
ejpam-5645	105	5	bounded	bounded	ADJ
ejpam-5645	105	6	group	group	NOUN
ejpam-5645	105	7	.	.	PUNCT
ejpam-5645	106	1	since	since	SCONJ
ejpam-5645	106	2	also	also	ADV
ejpam-5645	106	3	b	b	PROPN
ejpam-5645	106	4	is	be	AUX
ejpam-5645	106	5	a	a	DET
ejpam-5645	106	6	pure	pure	ADJ
ejpam-5645	106	7	subgroup	subgroup	NOUN
ejpam-5645	106	8	of	of	ADP
ejpam-5645	106	9	g	g	PROPN
ejpam-5645	106	10	,	,	PUNCT
ejpam-5645	106	11	then	then	ADV
ejpam-5645	106	12	b	b	PROPN
ejpam-5645	106	13	is	be	AUX
ejpam-5645	106	14	a	a	DET
ejpam-5645	106	15	direct	direct	ADJ
ejpam-5645	106	16	summand	summand	NOUN
ejpam-5645	106	17	of	of	ADP
ejpam-5645	106	18	g.	g.	PROPN
ejpam-5645	106	19	therefore	therefore	ADV
ejpam-5645	106	20	,	,	PUNCT
ejpam-5645	106	21	g	g	PROPN
ejpam-5645	106	22	=	=	SYM
ejpam-5645	106	23	b⊕c	b⊕c	PROPN
ejpam-5645	106	24	by	by	ADP
ejpam-5645	106	25	property	property	NOUN
ejpam-5645	106	26	(	(	PUNCT
ejpam-5645	106	27	a	a	NOUN
ejpam-5645	106	28	)	)	PUNCT
ejpam-5645	106	29	of	of	ADP
ejpam-5645	106	30	page	page	NOUN
ejpam-5645	106	31	38	38	NUM
ejpam-5645	106	32	in	in	ADP
ejpam-5645	106	33	[	[	X
ejpam-5645	106	34	8	8	NUM
ejpam-5645	106	35	]	]	PUNCT
ejpam-5645	106	36	,	,	PUNCT
ejpam-5645	106	37	and	and	CCONJ
ejpam-5645	106	38	thus	thus	ADV
ejpam-5645	106	39	g	g	PROPN
ejpam-5645	106	40	/	/	SYM
ejpam-5645	106	41	b	b	PROPN
ejpam-5645	106	42	is	be	AUX
ejpam-5645	106	43	isomorphic	isomorphic	ADJ
ejpam-5645	106	44	6	6	NUM
ejpam-5645	106	45	of	of	ADP
ejpam-5645	106	46	13	13	NUM
ejpam-5645	106	47	to	to	PART
ejpam-5645	106	48	c	c	NOUN
ejpam-5645	106	49	,	,	PUNCT
ejpam-5645	106	50	and	and	CCONJ
ejpam-5645	106	51	also	also	ADV
ejpam-5645	106	52	g	g	PROPN
ejpam-5645	106	53	/	/	SYM
ejpam-5645	106	54	b	b	NOUN
ejpam-5645	106	55	is	be	AUX
ejpam-5645	106	56	divisible	divisible	ADJ
ejpam-5645	106	57	.	.	PUNCT
ejpam-5645	107	1	hence	hence	ADV
ejpam-5645	107	2	,	,	PUNCT
ejpam-5645	107	3	c	c	PROPN
ejpam-5645	107	4	is	be	AUX
ejpam-5645	107	5	a	a	DET
ejpam-5645	107	6	divisible	divisible	ADJ
ejpam-5645	107	7	subgroup	subgroup	NOUN
ejpam-5645	107	8	of	of	ADP
ejpam-5645	107	9	g	g	PROPN
ejpam-5645	107	10	,	,	PUNCT
ejpam-5645	107	11	by	by	ADP
ejpam-5645	107	12	property	property	NOUN
ejpam-5645	107	13	(	(	PUNCT
ejpam-5645	107	14	d	d	NOUN
ejpam-5645	107	15	)	)	PUNCT
ejpam-5645	107	16	of	of	ADP
ejpam-5645	107	17	page	page	NOUN
ejpam-5645	107	18	98	98	NUM
ejpam-5645	107	19	[	[	SYM
ejpam-5645	107	20	8	8	NUM
ejpam-5645	107	21	]	]	PUNCT
ejpam-5645	107	22	.	.	PUNCT
ejpam-5645	108	1	since	since	SCONJ
ejpam-5645	108	2	g	g	PROPN
ejpam-5645	108	3	is	be	AUX
ejpam-5645	108	4	reduced	reduce	VERB
ejpam-5645	108	5	,	,	PUNCT
ejpam-5645	108	6	then	then	ADV
ejpam-5645	108	7	g	g	PROPN
ejpam-5645	108	8	contains	contain	VERB
ejpam-5645	108	9	no	no	DET
ejpam-5645	108	10	proper	proper	ADJ
ejpam-5645	108	11	divisible	divisible	ADJ
ejpam-5645	108	12	subgroup	subgroup	NOUN
ejpam-5645	108	13	,	,	PUNCT
ejpam-5645	108	14	which	which	PRON
ejpam-5645	108	15	implies	imply	VERB
ejpam-5645	108	16	that	that	SCONJ
ejpam-5645	108	17	c	c	NOUN
ejpam-5645	108	18	=	=	SYM
ejpam-5645	108	19	0	0	NUM
ejpam-5645	108	20	,	,	PUNCT
ejpam-5645	108	21	and	and	CCONJ
ejpam-5645	108	22	consequently	consequently	ADV
ejpam-5645	108	23	g	g	PROPN
ejpam-5645	108	24	=	=	PROPN
ejpam-5645	108	25	b.	b.	PROPN
ejpam-5645	109	1	it	it	PRON
ejpam-5645	109	2	remains	remain	VERB
ejpam-5645	109	3	to	to	PART
ejpam-5645	109	4	prove	prove	VERB
ejpam-5645	109	5	that	that	SCONJ
ejpam-5645	109	6	g	g	PROPN
ejpam-5645	109	7	is	be	AUX
ejpam-5645	109	8	finite	finite	ADJ
ejpam-5645	109	9	.	.	PUNCT
ejpam-5645	110	1	to	to	PART
ejpam-5645	110	2	do	do	VERB
ejpam-5645	110	3	this	this	PRON
ejpam-5645	110	4	,	,	PUNCT
ejpam-5645	110	5	we	we	PRON
ejpam-5645	110	6	will	will	AUX
ejpam-5645	110	7	show	show	VERB
ejpam-5645	110	8	that	that	SCONJ
ejpam-5645	110	9	b	b	NOUN
ejpam-5645	110	10	is	be	AUX
ejpam-5645	110	11	finite	finite	ADJ
ejpam-5645	110	12	and	and	CCONJ
ejpam-5645	110	13	this	this	PRON
ejpam-5645	110	14	holds	hold	VERB
ejpam-5645	110	15	true	true	ADJ
ejpam-5645	110	16	when	when	SCONJ
ejpam-5645	110	17	card(bk	card(bk	NOUN
ejpam-5645	110	18	)	)	PUNCT
ejpam-5645	110	19	<	<	X
ejpam-5645	110	20	∞	∞	PROPN
ejpam-5645	110	21	,	,	PUNCT
ejpam-5645	110	22	with	with	ADP
ejpam-5645	110	23	1	1	NUM
ejpam-5645	110	24	≤	≤	NUM
ejpam-5645	110	25	k	k	PROPN
ejpam-5645	110	26	≤	≤	PROPN
ejpam-5645	110	27	n.	n.	NOUN
ejpam-5645	110	28	to	to	PART
ejpam-5645	110	29	achieve	achieve	VERB
ejpam-5645	110	30	this	this	PRON
ejpam-5645	110	31	,	,	PUNCT
ejpam-5645	110	32	let	let	VERB
ejpam-5645	110	33	us	we	PRON
ejpam-5645	110	34	suppose	suppose	VERB
ejpam-5645	110	35	that	that	SCONJ
ejpam-5645	110	36	there	there	PRON
ejpam-5645	110	37	exists	exist	VERB
ejpam-5645	110	38	a	a	DET
ejpam-5645	110	39	nonzero	nonzero	ADJ
ejpam-5645	110	40	positive	positive	ADJ
ejpam-5645	110	41	integer	integer	NOUN
ejpam-5645	110	42	k0	k0	PROPN
ejpam-5645	110	43	such	such	ADJ
ejpam-5645	110	44	that	that	DET
ejpam-5645	110	45	card	card	NOUN
ejpam-5645	110	46	(	(	PUNCT
ejpam-5645	110	47	bk0	bk0	NOUN
ejpam-5645	110	48	)	)	PUNCT
ejpam-5645	111	1	=	=	SYM
ejpam-5645	111	2	∞	∞	PROPN
ejpam-5645	111	3	,	,	PUNCT
ejpam-5645	111	4	and	and	CCONJ
ejpam-5645	111	5	bk0	bk0	NOUN
ejpam-5645	111	6	=	=	PUNCT
ejpam-5645	111	7	⊕ik∈ik0	⊕ik∈ik0	NOUN
ejpam-5645	111	8	⟨xik	⟨xik	PROPN
ejpam-5645	111	9	,	,	PUNCT
ejpam-5645	111	10	k0⟩	k0⟩	NOUN
ejpam-5645	111	11	with	with	ADP
ejpam-5645	111	12	card	card	NOUN
ejpam-5645	111	13	(	(	PUNCT
ejpam-5645	111	14	ik0	ik0	NOUN
ejpam-5645	111	15	)	)	PUNCT
ejpam-5645	111	16	=	=	SYM
ejpam-5645	112	1	∞	∞	PROPN
ejpam-5645	112	2	,	,	PUNCT
ejpam-5645	112	3	then	then	ADV
ejpam-5645	112	4	bk0	bk0	NOUN
ejpam-5645	113	1	=	=	SYM
ejpam-5645	113	2	⊕k∈n	⊕k∈n	PROPN
ejpam-5645	113	3	⟨xik	⟨xik	PROPN
ejpam-5645	113	4	,	,	PUNCT
ejpam-5645	113	5	k0⟩	k0⟩	PUNCT
ejpam-5645	113	6	⊕	⊕	PROPN
ejpam-5645	113	7	⊕ik∈t	⊕ik∈t	PROPN
ejpam-5645	113	8	⟨xik	⟨xik	PROPN
ejpam-5645	113	9	,	,	PUNCT
ejpam-5645	113	10	k0⟩	k0⟩	NOUN
ejpam-5645	113	11	with	with	ADP
ejpam-5645	113	12	t	t	PROPN
ejpam-5645	113	13	=	=	PUNCT
ejpam-5645	113	14	ik0	ik0	VERB
ejpam-5645	113	15	\	\	PROPN
ejpam-5645	113	16	{	{	PUNCT
ejpam-5645	113	17	ik	ik	PROPN
ejpam-5645	113	18	,	,	PUNCT
ejpam-5645	113	19	k	k	PROPN
ejpam-5645	113	20	∈	∈	PROPN
ejpam-5645	113	21	n	n	CCONJ
ejpam-5645	113	22	}	}	PUNCT
ejpam-5645	113	23	let	let	VERB
ejpam-5645	113	24	h	h	NOUN
ejpam-5645	113	25	=	=	NOUN
ejpam-5645	113	26	⊕k∈n	⊕k∈n	PROPN
ejpam-5645	114	1	⟨xik	⟨xik	PROPN
ejpam-5645	114	2	,	,	PUNCT
ejpam-5645	114	3	k0⟩	k0⟩	PROPN
ejpam-5645	114	4	,	,	PUNCT
ejpam-5645	114	5	we	we	PRON
ejpam-5645	114	6	remark	remark	VERB
ejpam-5645	114	7	that	that	SCONJ
ejpam-5645	114	8	h	h	NOUN
ejpam-5645	114	9	is	be	AUX
ejpam-5645	114	10	generalized	generalize	VERB
ejpam-5645	114	11	hereditarily	hereditarily	ADJ
ejpam-5645	114	12	hopfian	hopfian	ADJ
ejpam-5645	114	13	group	group	NOUN
ejpam-5645	114	14	according	accord	VERB
ejpam-5645	114	15	to	to	ADP
ejpam-5645	114	16	lemma	lemma	PROPN
ejpam-5645	114	17	1	1	NUM
ejpam-5645	114	18	,	,	PUNCT
ejpam-5645	114	19	and	and	CCONJ
ejpam-5645	114	20	we	we	PRON
ejpam-5645	114	21	define	define	VERB
ejpam-5645	114	22	the	the	DET
ejpam-5645	114	23	following	follow	VERB
ejpam-5645	114	24	surjective	surjective	ADJ
ejpam-5645	114	25	endomorphism	endomorphism	NOUN
ejpam-5645	114	26	of	of	ADP
ejpam-5645	114	27	h	h	NOUN
ejpam-5645	114	28	,	,	PUNCT
ejpam-5645	114	29	ϕ	ϕ	X
ejpam-5645	114	30	:	:	PUNCT
ejpam-5645	114	31	h	h	PROPN
ejpam-5645	114	32	−→	−→	NOUN
ejpam-5645	114	33	h∑n0	h∑n0	ADP
ejpam-5645	114	34	k=1mkxik	k=1mkxik	PROPN
ejpam-5645	114	35	,	,	PUNCT
ejpam-5645	114	36	k0	k0	PROPN
ejpam-5645	114	37	7−→	7−→	PROPN
ejpam-5645	114	38	∑n0−1	∑n0−1	PROPN
ejpam-5645	115	1	k=1	k=1	PROPN
ejpam-5645	115	2	mk+1xik	mk+1xik	PROPN
ejpam-5645	115	3	,	,	PUNCT
ejpam-5645	115	4	k0	k0	PROPN
ejpam-5645	115	5	we	we	PRON
ejpam-5645	115	6	haveh	haveh	NOUN
ejpam-5645	115	7	=	=	PUNCT
ejpam-5645	115	8	⊕k∈n	⊕k∈n	NOUN
ejpam-5645	115	9	⟨xik	⟨xik	PROPN
ejpam-5645	115	10	,	,	PUNCT
ejpam-5645	115	11	k0⟩	k0⟩	NOUN
ejpam-5645	115	12	or	or	CCONJ
ejpam-5645	115	13	h	h	NOUN
ejpam-5645	115	14	=	=	SYM
ejpam-5645	115	15	⟨xi0,k0⟩	⟨xi0,k0⟩	PROPN
ejpam-5645	115	16	⊕	⊕	PROPN
ejpam-5645	115	17	⊕k∈n∗	⊕k∈n∗	PUNCT
ejpam-5645	116	1	⟨xik	⟨xik	PROPN
ejpam-5645	116	2	,	,	PUNCT
ejpam-5645	116	3	k0⟩	k0⟩	PUNCT
ejpam-5645	117	1	⊂	⊂	PROPN
ejpam-5645	117	2	kerϕ	kerϕ	PROPN
ejpam-5645	117	3	⊕	⊕	PROPN
ejpam-5645	117	4	⊕k∈n∗	⊕k∈n∗	PUNCT
ejpam-5645	118	1	⟨xik	⟨xik	PROPN
ejpam-5645	118	2	,	,	PUNCT
ejpam-5645	118	3	k0⟩	k0⟩	PUNCT
ejpam-5645	119	1	⊂	⊂	PROPN
ejpam-5645	119	2	h	h	NOUN
ejpam-5645	119	3	,	,	PUNCT
ejpam-5645	119	4	then	then	ADV
ejpam-5645	119	5	h	h	PROPN
ejpam-5645	119	6	=	=	PUNCT
ejpam-5645	119	7	kerϕ	kerϕ	PROPN
ejpam-5645	119	8	⊕	⊕	PROPN
ejpam-5645	119	9	⊕k∈n∗	⊕k∈n∗	PUNCT
ejpam-5645	120	1	⟨xik	⟨xik	PROPN
ejpam-5645	120	2	,	,	PUNCT
ejpam-5645	120	3	k0⟩	k0⟩	NOUN
ejpam-5645	120	4	,	,	PUNCT
ejpam-5645	120	5	and	and	CCONJ
ejpam-5645	120	6	since	since	SCONJ
ejpam-5645	120	7	h	h	NOUN
ejpam-5645	120	8	is	be	AUX
ejpam-5645	120	9	generalized	generalize	VERB
ejpam-5645	120	10	hereditarily	hereditarily	ADJ
ejpam-5645	120	11	hopfian	hopfian	ADJ
ejpam-5645	120	12	group	group	NOUN
ejpam-5645	120	13	,	,	PUNCT
ejpam-5645	120	14	then	then	ADV
ejpam-5645	120	15	h	h	PROPN
ejpam-5645	120	16	=	=	SYM
ejpam-5645	120	17	⊕k∈n∗	⊕k∈n∗	PROPN
ejpam-5645	121	1	⟨xik	⟨xik	PROPN
ejpam-5645	121	2	,	,	PUNCT
ejpam-5645	121	3	k0⟩	k0⟩	PROPN
ejpam-5645	121	4	,	,	PUNCT
ejpam-5645	121	5	witch	witch	NOUN
ejpam-5645	121	6	is	be	AUX
ejpam-5645	121	7	absurd	absurd	ADJ
ejpam-5645	121	8	.	.	PUNCT
ejpam-5645	122	1	therefore	therefore	ADV
ejpam-5645	122	2	,	,	PUNCT
ejpam-5645	122	3	b	b	PROPN
ejpam-5645	122	4	is	be	AUX
ejpam-5645	122	5	finite	finite	ADJ
ejpam-5645	122	6	,	,	PUNCT
ejpam-5645	122	7	and	and	CCONJ
ejpam-5645	122	8	consequently	consequently	ADV
ejpam-5645	122	9	,	,	PUNCT
ejpam-5645	122	10	g	g	PROPN
ejpam-5645	122	11	is	be	AUX
ejpam-5645	122	12	finite	finite	ADJ
ejpam-5645	122	13	.	.	PUNCT
ejpam-5645	123	1	we	we	PRON
ejpam-5645	123	2	have	have	AUX
ejpam-5645	123	3	just	just	ADV
ejpam-5645	123	4	showed	show	VERB
ejpam-5645	123	5	that	that	SCONJ
ejpam-5645	123	6	an	an	DET
ejpam-5645	123	7	abelian	abelian	NOUN
ejpam-5645	123	8	reduced	reduce	VERB
ejpam-5645	123	9	p−group	p−group	NOUN
ejpam-5645	123	10	,	,	PUNCT
ejpam-5645	123	11	is	be	AUX
ejpam-5645	123	12	generalized	generalize	VERB
ejpam-5645	123	13	hereditarily	hereditarily	ADJ
ejpam-5645	123	14	hopfian	hopfian	ADJ
ejpam-5645	123	15	,	,	PUNCT
ejpam-5645	123	16	when	when	SCONJ
ejpam-5645	123	17	it	it	PRON
ejpam-5645	123	18	is	be	AUX
ejpam-5645	123	19	finite	finite	ADJ
ejpam-5645	123	20	.	.	PUNCT
ejpam-5645	124	1	now	now	ADV
ejpam-5645	124	2	,	,	PUNCT
ejpam-5645	124	3	let	let	VERB
ejpam-5645	124	4	us	we	PRON
ejpam-5645	124	5	expand	expand	VERB
ejpam-5645	124	6	our	our	PRON
ejpam-5645	124	7	research	research	NOUN
ejpam-5645	124	8	and	and	CCONJ
ejpam-5645	124	9	ask	ask	VERB
ejpam-5645	124	10	the	the	DET
ejpam-5645	124	11	question	question	NOUN
ejpam-5645	124	12	:	:	PUNCT
ejpam-5645	124	13	what	what	PRON
ejpam-5645	124	14	are	be	AUX
ejpam-5645	124	15	the	the	DET
ejpam-5645	124	16	generalized	generalized	ADJ
ejpam-5645	124	17	hereditarily	hereditarily	ADJ
ejpam-5645	124	18	hopfian	hopfian	ADJ
ejpam-5645	124	19	groups	group	NOUN
ejpam-5645	124	20	within	within	ADP
ejpam-5645	124	21	the	the	DET
ejpam-5645	124	22	category	category	NOUN
ejpam-5645	124	23	of	of	ADP
ejpam-5645	124	24	reduced	reduce	VERB
ejpam-5645	124	25	torsion	torsion	NOUN
ejpam-5645	124	26	groups	group	NOUN
ejpam-5645	124	27	?	?	PUNCT
ejpam-5645	125	1	the	the	DET
ejpam-5645	125	2	answer	answer	NOUN
ejpam-5645	125	3	to	to	ADP
ejpam-5645	125	4	this	this	DET
ejpam-5645	125	5	question	question	NOUN
ejpam-5645	125	6	will	will	AUX
ejpam-5645	125	7	be	be	AUX
ejpam-5645	125	8	provided	provide	VERB
ejpam-5645	125	9	in	in	ADP
ejpam-5645	125	10	the	the	DET
ejpam-5645	125	11	following	follow	VERB
ejpam-5645	125	12	section	section	NOUN
ejpam-5645	125	13	.	.	PUNCT
ejpam-5645	126	1	3	3	X
ejpam-5645	126	2	.	.	X
ejpam-5645	126	3	on	on	ADP
ejpam-5645	126	4	reduced	reduce	VERB
ejpam-5645	126	5	torsion	torsion	NOUN
ejpam-5645	126	6	generalized	generalize	VERB
ejpam-5645	126	7	hereditarily	hereditarily	ADJ
ejpam-5645	126	8	hopfian	hopfian	ADJ
ejpam-5645	126	9	groups	group	NOUN
ejpam-5645	126	10	we	we	PRON
ejpam-5645	126	11	recall	recall	VERB
ejpam-5645	126	12	that	that	SCONJ
ejpam-5645	126	13	groups	group	NOUN
ejpam-5645	126	14	needed	need	VERB
ejpam-5645	126	15	in	in	ADP
ejpam-5645	126	16	the	the	DET
ejpam-5645	126	17	proof	proof	NOUN
ejpam-5645	126	18	of	of	ADP
ejpam-5645	126	19	our	our	PRON
ejpam-5645	126	20	next	next	ADJ
ejpam-5645	126	21	theorem	theorem	NOUN
ejpam-5645	126	22	hereafter	hereafter	ADV
ejpam-5645	126	23	are	be	AUX
ejpam-5645	126	24	about	about	ADP
ejpam-5645	126	25	the	the	DET
ejpam-5645	126	26	following	follow	VERB
ejpam-5645	126	27	types	type	NOUN
ejpam-5645	126	28	,	,	PUNCT
ejpam-5645	126	29	•	•	NUM
ejpam-5645	126	30	group	group	NOUN
ejpam-5645	126	31	gp	gp	NOUN
ejpam-5645	126	32	(	(	PUNCT
ejpam-5645	126	33	let	let	VERB
ejpam-5645	126	34	p	p	PRON
ejpam-5645	126	35	be	be	AUX
ejpam-5645	126	36	a	a	DET
ejpam-5645	126	37	prime	prime	ADJ
ejpam-5645	126	38	number	number	NOUN
ejpam-5645	126	39	,	,	PUNCT
ejpam-5645	126	40	the	the	DET
ejpam-5645	126	41	p	p	NOUN
ejpam-5645	126	42	-	-	PUNCT
ejpam-5645	126	43	component	component	NOUN
ejpam-5645	126	44	of	of	ADP
ejpam-5645	126	45	an	an	DET
ejpam-5645	126	46	abelian	abelian	ADJ
ejpam-5645	126	47	group	group	NOUN
ejpam-5645	126	48	g	g	PROPN
ejpam-5645	126	49	is	be	AUX
ejpam-5645	126	50	the	the	DET
ejpam-5645	126	51	group	group	NOUN
ejpam-5645	126	52	gp	gp	NOUN
ejpam-5645	126	53	defined	define	VERB
ejpam-5645	126	54	as	as	ADP
ejpam-5645	126	55	,	,	PUNCT
ejpam-5645	126	56	gp	gp	NOUN
ejpam-5645	126	57	=	=	SYM
ejpam-5645	126	58	{	{	PUNCT
ejpam-5645	126	59	a	a	DET
ejpam-5645	126	60	∈	∈	PROPN
ejpam-5645	126	61	g/	g/	NOUN
ejpam-5645	126	62	◦	◦	NOUN
ejpam-5645	126	63	(	(	PUNCT
ejpam-5645	126	64	a	a	X
ejpam-5645	126	65	)	)	PUNCT
ejpam-5645	126	66	=	=	SYM
ejpam-5645	126	67	pn	pn	PROPN
ejpam-5645	126	68	,	,	PUNCT
ejpam-5645	126	69	n	n	PROPN
ejpam-5645	126	70	∈	∈	PROPN
ejpam-5645	126	71	n	n	CCONJ
ejpam-5645	126	72	}	}	PUNCT
ejpam-5645	126	73	)	)	PUNCT
ejpam-5645	126	74	.	.	PUNCT
ejpam-5645	127	1	lemma	lemma	PROPN
ejpam-5645	127	2	2	2	X
ejpam-5645	127	3	.	.	PUNCT
ejpam-5645	128	1	let	let	VERB
ejpam-5645	128	2	g	g	NOUN
ejpam-5645	128	3	be	be	AUX
ejpam-5645	128	4	an	an	DET
ejpam-5645	128	5	abelian	abelian	ADJ
ejpam-5645	128	6	group	group	NOUN
ejpam-5645	128	7	.	.	PUNCT
ejpam-5645	129	1	if	if	SCONJ
ejpam-5645	129	2	g	g	PROPN
ejpam-5645	129	3	is	be	AUX
ejpam-5645	129	4	a	a	DET
ejpam-5645	129	5	generalized	generalized	ADJ
ejpam-5645	129	6	hereditarily	hereditarily	ADJ
ejpam-5645	129	7	hopfian	hopfian	ADJ
ejpam-5645	129	8	group	group	NOUN
ejpam-5645	129	9	then	then	ADV
ejpam-5645	129	10	the	the	DET
ejpam-5645	129	11	direct	direct	ADJ
ejpam-5645	129	12	summand	summand	NOUN
ejpam-5645	129	13	of	of	ADP
ejpam-5645	129	14	g	g	PROPN
ejpam-5645	129	15	is	be	AUX
ejpam-5645	129	16	a	a	DET
ejpam-5645	129	17	generalized	generalized	ADJ
ejpam-5645	129	18	hereditarily	hereditarily	ADJ
ejpam-5645	129	19	hopfian	hopfian	ADJ
ejpam-5645	129	20	group	group	NOUN
ejpam-5645	129	21	.	.	PUNCT
ejpam-5645	130	1	proof	proof	NOUN
ejpam-5645	130	2	.	.	PUNCT
ejpam-5645	131	1	let	let	VERB
ejpam-5645	131	2	g	g	NOUN
ejpam-5645	131	3	=	=	SYM
ejpam-5645	131	4	a⊕b	a⊕b	PROPN
ejpam-5645	131	5	,	,	PUNCT
ejpam-5645	131	6	let	let	VERB
ejpam-5645	131	7	φ1	φ1	NOUN
ejpam-5645	131	8	:	:	PUNCT
ejpam-5645	131	9	a	a	DET
ejpam-5645	131	10	−→	−→	NOUN
ejpam-5645	131	11	a	a	DET
ejpam-5645	131	12	be	be	AUX
ejpam-5645	131	13	a	a	DET
ejpam-5645	131	14	surjective	surjective	ADJ
ejpam-5645	131	15	endomorphismand	endomorphismand	NOUN
ejpam-5645	131	16	let	let	VERB
ejpam-5645	131	17	ϕ	ϕ	NOUN
ejpam-5645	131	18	:	:	PUNCT
ejpam-5645	131	19	ϕ	ϕ	NOUN
ejpam-5645	131	20	:	:	PUNCT
ejpam-5645	131	21	g	g	NOUN
ejpam-5645	131	22	=	=	PUNCT
ejpam-5645	131	23	a⊕b	a⊕b	PROPN
ejpam-5645	131	24	−→	−→	NOUN
ejpam-5645	131	25	a⊕b	a⊕b	PROPN
ejpam-5645	131	26	x1	x1	PROPN
ejpam-5645	132	1	+	+	CCONJ
ejpam-5645	132	2	x2	x2	PROPN
ejpam-5645	132	3	7−→	7−→	PROPN
ejpam-5645	132	4	φ1	φ1	NOUN
ejpam-5645	132	5	(	(	PUNCT
ejpam-5645	132	6	x1	x1	PROPN
ejpam-5645	132	7	)	)	PUNCT
ejpam-5645	133	1	+	+	CCONJ
ejpam-5645	133	2	x2	x2	PROPN
ejpam-5645	133	3	7	7	NUM
ejpam-5645	133	4	of	of	ADP
ejpam-5645	133	5	13	13	NUM
ejpam-5645	133	6	it	it	PRON
ejpam-5645	133	7	is	be	AUX
ejpam-5645	133	8	clear	clear	ADJ
ejpam-5645	133	9	that	that	SCONJ
ejpam-5645	133	10	ϕ	ϕ	NOUN
ejpam-5645	133	11	is	be	AUX
ejpam-5645	133	12	a	a	DET
ejpam-5645	133	13	surjective	surjective	ADJ
ejpam-5645	133	14	endomorphism	endomorphism	NOUN
ejpam-5645	133	15	because	because	SCONJ
ejpam-5645	133	16	for	for	ADP
ejpam-5645	133	17	all	all	PRON
ejpam-5645	133	18	x	x	PUNCT
ejpam-5645	133	19	=	=	PUNCT
ejpam-5645	133	20	x1+x2	x1+x2	PROPN
ejpam-5645	133	21	and	and	CCONJ
ejpam-5645	133	22	y	y	PROPN
ejpam-5645	133	23	=	=	SYM
ejpam-5645	133	24	y1+y2	y1+y2	PROPN
ejpam-5645	133	25	,	,	PUNCT
ejpam-5645	133	26	where	where	SCONJ
ejpam-5645	133	27	x1	x1	X
ejpam-5645	133	28	,	,	PUNCT
ejpam-5645	133	29	y1	y1	PROPN
ejpam-5645	133	30	∈	∈	PROPN
ejpam-5645	133	31	a	a	PRON
ejpam-5645	133	32	and	and	CCONJ
ejpam-5645	133	33	y1	y1	NOUN
ejpam-5645	134	1	+	+	CCONJ
ejpam-5645	134	2	y2	y2	PROPN
ejpam-5645	134	3	∈	∈	PROPN
ejpam-5645	134	4	b	b	NOUN
ejpam-5645	134	5	,	,	PUNCT
ejpam-5645	134	6	we	we	PRON
ejpam-5645	134	7	have	have	VERB
ejpam-5645	134	8	,	,	PUNCT
ejpam-5645	134	9	ϕ(x+	ϕ(x+	INTJ
ejpam-5645	134	10	y	y	X
ejpam-5645	134	11	)	)	PUNCT
ejpam-5645	135	1	=	=	SYM
ejpam-5645	136	1	ϕ(x1	ϕ(x1	PROPN
ejpam-5645	137	1	+	+	CCONJ
ejpam-5645	137	2	x2	x2	PROPN
ejpam-5645	138	1	+	+	CCONJ
ejpam-5645	138	2	y1	y1	NOUN
ejpam-5645	138	3	+	+	CCONJ
ejpam-5645	138	4	y2	y2	NOUN
ejpam-5645	138	5	)	)	PUNCT
ejpam-5645	139	1	=	=	SYM
ejpam-5645	139	2	ϕ(x1	ϕ(x1	PROPN
ejpam-5645	140	1	+	+	CCONJ
ejpam-5645	140	2	y1	y1	PROPN
ejpam-5645	141	1	+	+	CCONJ
ejpam-5645	141	2	x2	x2	PROPN
ejpam-5645	141	3	+	+	CCONJ
ejpam-5645	141	4	y2	y2	NOUN
ejpam-5645	141	5	)	)	PUNCT
ejpam-5645	142	1	=	=	PUNCT
ejpam-5645	143	1	φ1(x1	φ1(x1	PRON
ejpam-5645	143	2	+	+	NUM
ejpam-5645	143	3	y1	y1	NOUN
ejpam-5645	143	4	)	)	PUNCT
ejpam-5645	143	5	+	+	CCONJ
ejpam-5645	143	6	x2	x2	PROPN
ejpam-5645	144	1	+	+	CCONJ
ejpam-5645	144	2	y2	y2	NOUN
ejpam-5645	144	3	=	=	SYM
ejpam-5645	144	4	φ1(x1	φ1(x1	PROPN
ejpam-5645	144	5	)	)	PUNCT
ejpam-5645	144	6	+	+	NUM
ejpam-5645	144	7	x2	x2	PROPN
ejpam-5645	145	1	+	+	CCONJ
ejpam-5645	145	2	φ1(y1	φ1(y1	ADP
ejpam-5645	145	3	)	)	PUNCT
ejpam-5645	145	4	+	+	NUM
ejpam-5645	145	5	y2	y2	NOUN
ejpam-5645	145	6	=	=	SYM
ejpam-5645	145	7	ϕ(x	ϕ(x	X
ejpam-5645	145	8	)	)	PUNCT
ejpam-5645	145	9	+	+	CCONJ
ejpam-5645	146	1	ϕ(y	ϕ(y	PROPN
ejpam-5645	146	2	)	)	PUNCT
ejpam-5645	146	3	.	.	PUNCT
ejpam-5645	147	1	then	then	ADV
ejpam-5645	147	2	ϕ	ϕ	PROPN
ejpam-5645	147	3	is	be	AUX
ejpam-5645	147	4	an	an	DET
ejpam-5645	147	5	endomorphism.and	endomorphism.and	X
ejpam-5645	147	6	we	we	PRON
ejpam-5645	147	7	haveϕ(g	haveϕ(g	PROPN
ejpam-5645	147	8	)	)	PUNCT
ejpam-5645	148	1	⊂	⊂	PROPN
ejpam-5645	148	2	g.	g.	PROPN
ejpam-5645	148	3	let	let	VERB
ejpam-5645	148	4	us	we	PRON
ejpam-5645	148	5	check	check	VERB
ejpam-5645	148	6	that	that	SCONJ
ejpam-5645	148	7	g	g	PROPN
ejpam-5645	148	8	⊂	⊂	PROPN
ejpam-5645	148	9	ϕ(g	ϕ(g	PROPN
ejpam-5645	148	10	)	)	PUNCT
ejpam-5645	148	11	.	.	PUNCT
ejpam-5645	149	1	let	let	VERB
ejpam-5645	149	2	x	x	PUNCT
ejpam-5645	149	3	∈	∈	PROPN
ejpam-5645	149	4	g	g	PROPN
ejpam-5645	149	5	,	,	PUNCT
ejpam-5645	149	6	there	there	PRON
ejpam-5645	149	7	exists	exist	VERB
ejpam-5645	149	8	(	(	PUNCT
ejpam-5645	149	9	x1	x1	PROPN
ejpam-5645	149	10	,	,	PUNCT
ejpam-5645	149	11	x2	x2	PROPN
ejpam-5645	149	12	)	)	PUNCT
ejpam-5645	149	13	∈	∈	PROPN
ejpam-5645	149	14	a	a	DET
ejpam-5645	149	15	×	×	NOUN
ejpam-5645	149	16	b	b	NOUN
ejpam-5645	149	17	such	such	ADJ
ejpam-5645	149	18	that	that	PRON
ejpam-5645	149	19	x	x	X
ejpam-5645	150	1	=	=	SYM
ejpam-5645	150	2	x1	x1	PROPN
ejpam-5645	151	1	+	+	CCONJ
ejpam-5645	151	2	x2	x2	ADJ
ejpam-5645	151	3	,	,	PUNCT
ejpam-5645	151	4	then	then	ADV
ejpam-5645	151	5	x	x	PUNCT
ejpam-5645	151	6	=	=	PUNCT
ejpam-5645	152	1	φ1(x	φ1(x	NOUN
ejpam-5645	152	2	′	′	NUM
ejpam-5645	152	3	1	1	NUM
ejpam-5645	152	4	)	)	PUNCT
ejpam-5645	153	1	+	+	CCONJ
ejpam-5645	153	2	x2	x2	INTJ
ejpam-5645	153	3	(	(	PUNCT
ejpam-5645	153	4	because	because	SCONJ
ejpam-5645	153	5	φ1	φ1	PROPN
ejpam-5645	153	6	is	be	AUX
ejpam-5645	153	7	surjective	surjective	ADJ
ejpam-5645	153	8	)	)	PUNCT
ejpam-5645	153	9	and	and	CCONJ
ejpam-5645	153	10	also	also	ADV
ejpam-5645	153	11	x	x	X
ejpam-5645	153	12	=	=	PUNCT
ejpam-5645	153	13	ϕ(x′1	ϕ(x′1	X
ejpam-5645	154	1	+	+	CCONJ
ejpam-5645	154	2	x2	x2	PROPN
ejpam-5645	154	3	)	)	PUNCT
ejpam-5645	155	1	,	,	PUNCT
ejpam-5645	155	2	then	then	ADV
ejpam-5645	155	3	x	x	X
ejpam-5645	155	4	∈	∈	PROPN
ejpam-5645	155	5	ϕ(g	ϕ(g	PROPN
ejpam-5645	155	6	)	)	PUNCT
ejpam-5645	155	7	,	,	PUNCT
ejpam-5645	155	8	therefore	therefore	ADV
ejpam-5645	155	9	g	g	PROPN
ejpam-5645	155	10	⊂	⊂	PROPN
ejpam-5645	155	11	ϕ(g	ϕ(g	PROPN
ejpam-5645	155	12	)	)	PUNCT
ejpam-5645	155	13	,	,	PUNCT
ejpam-5645	155	14	and	and	CCONJ
ejpam-5645	155	15	thus	thus	ADV
ejpam-5645	155	16	g	g	PROPN
ejpam-5645	155	17	=	=	PROPN
ejpam-5645	155	18	ϕ(g	ϕ(g	PROPN
ejpam-5645	155	19	)	)	PUNCT
ejpam-5645	155	20	,	,	PUNCT
ejpam-5645	155	21	hence	hence	ADV
ejpam-5645	155	22	ϕ	ϕ	PROPN
ejpam-5645	155	23	is	be	AUX
ejpam-5645	155	24	surjective	surjective	ADJ
ejpam-5645	155	25	.	.	PUNCT
ejpam-5645	156	1	let	let	VERB
ejpam-5645	156	2	us	we	PRON
ejpam-5645	156	3	now	now	ADV
ejpam-5645	156	4	show	show	VERB
ejpam-5645	156	5	that	that	SCONJ
ejpam-5645	156	6	a	a	PRON
ejpam-5645	156	7	is	be	AUX
ejpam-5645	156	8	generalized	generalize	VERB
ejpam-5645	156	9	hereditarily	hereditarily	ADJ
ejpam-5645	156	10	hopfian	hopfian	PROPN
ejpam-5645	156	11	.	.	PUNCT
ejpam-5645	157	1	assume	assume	VERB
ejpam-5645	157	2	that	that	SCONJ
ejpam-5645	157	3	h	h	PROPN
ejpam-5645	157	4	as	as	ADP
ejpam-5645	157	5	a	a	DET
ejpam-5645	157	6	subgroup	subgroup	NOUN
ejpam-5645	157	7	of	of	ADP
ejpam-5645	157	8	a	a	DET
ejpam-5645	157	9	such	such	ADJ
ejpam-5645	157	10	that	that	DET
ejpam-5645	157	11	h+ker(φ1	h+ker(φ1	NOUN
ejpam-5645	157	12	)	)	PUNCT
ejpam-5645	157	13	=	=	SYM
ejpam-5645	158	1	a	a	NOUN
ejpam-5645	158	2	,	,	PUNCT
ejpam-5645	158	3	then	then	ADV
ejpam-5645	158	4	g	g	PROPN
ejpam-5645	158	5	=	=	PROPN
ejpam-5645	158	6	h+ker(φ1)⊕b	h+ker(φ1)⊕b	PROPN
ejpam-5645	158	7	.	.	PUNCT
ejpam-5645	159	1	since	since	SCONJ
ejpam-5645	159	2	ker(φ1	ker(φ1	PROPN
ejpam-5645	159	3	)	)	PUNCT
ejpam-5645	159	4	⊂	⊂	PROPN
ejpam-5645	159	5	ker(ϕ	ker(ϕ	PROPN
ejpam-5645	159	6	)	)	PUNCT
ejpam-5645	159	7	,	,	PUNCT
ejpam-5645	159	8	and	and	CCONJ
ejpam-5645	159	9	g	g	NOUN
ejpam-5645	159	10	is	be	AUX
ejpam-5645	159	11	a	a	DET
ejpam-5645	159	12	generalized	generalized	ADJ
ejpam-5645	159	13	hereditarily	hereditarily	ADJ
ejpam-5645	159	14	hopfian	hopfian	ADJ
ejpam-5645	159	15	group	group	NOUN
ejpam-5645	159	16	,	,	PUNCT
ejpam-5645	159	17	it	it	PRON
ejpam-5645	159	18	follows	follow	VERB
ejpam-5645	159	19	that	that	SCONJ
ejpam-5645	159	20	g	g	PROPN
ejpam-5645	159	21	=	=	NOUN
ejpam-5645	159	22	h	h	NOUN
ejpam-5645	159	23	⊕b	⊕b	NOUN
ejpam-5645	159	24	.	.	PUNCT
ejpam-5645	160	1	since	since	SCONJ
ejpam-5645	160	2	h	h	PROPN
ejpam-5645	160	3	<	<	X
ejpam-5645	160	4	a	a	PROPN
ejpam-5645	160	5	and	and	CCONJ
ejpam-5645	160	6	g	g	NOUN
ejpam-5645	160	7	=	=	PUNCT
ejpam-5645	160	8	a⊕b	a⊕b	PROPN
ejpam-5645	160	9	,	,	PUNCT
ejpam-5645	160	10	we	we	PRON
ejpam-5645	160	11	conclude	conclude	VERB
ejpam-5645	160	12	that	that	DET
ejpam-5645	160	13	h	h	NOUN
ejpam-5645	161	1	=	=	PUNCT
ejpam-5645	161	2	a	a	NOUN
ejpam-5645	161	3	,	,	PUNCT
ejpam-5645	161	4	hence	hence	ADV
ejpam-5645	161	5	a	a	DET
ejpam-5645	161	6	is	be	AUX
ejpam-5645	161	7	generalized	generalize	VERB
ejpam-5645	161	8	hereditarily	hereditarily	ADJ
ejpam-5645	161	9	hopfian	hopfian	ADJ
ejpam-5645	161	10	group	group	NOUN
ejpam-5645	161	11	.	.	PUNCT
ejpam-5645	162	1	theorem	theorem	NOUN
ejpam-5645	162	2	2	2	NUM
ejpam-5645	162	3	.	.	PUNCT
ejpam-5645	163	1	let	let	VERB
ejpam-5645	163	2	g	g	PROPN
ejpam-5645	163	3	a	a	DET
ejpam-5645	163	4	reduced	reduced	ADJ
ejpam-5645	163	5	torsion	torsion	NOUN
ejpam-5645	163	6	group	group	NOUN
ejpam-5645	163	7	,	,	PUNCT
ejpam-5645	163	8	then	then	ADV
ejpam-5645	163	9	g	g	PROPN
ejpam-5645	163	10	is	be	AUX
ejpam-5645	163	11	generalized	generalize	VERB
ejpam-5645	163	12	hereditarily	hereditarily	ADJ
ejpam-5645	163	13	hopfian	hopfian	ADJ
ejpam-5645	163	14	if	if	SCONJ
ejpam-5645	163	15	and	and	CCONJ
ejpam-5645	163	16	only	only	ADV
ejpam-5645	163	17	if	if	SCONJ
ejpam-5645	163	18	gp	gp	NOUN
ejpam-5645	163	19	is	be	AUX
ejpam-5645	163	20	finite	finite	ADJ
ejpam-5645	163	21	for	for	ADP
ejpam-5645	163	22	every	every	DET
ejpam-5645	163	23	prime	prime	ADJ
ejpam-5645	163	24	number	number	NOUN
ejpam-5645	163	25	p.	p.	NOUN
ejpam-5645	163	26	proof	proof	NOUN
ejpam-5645	163	27	.	.	PUNCT
ejpam-5645	164	1	⇒	⇒	NOUN
ejpam-5645	164	2	)	)	PUNCT
ejpam-5645	164	3	let	let	VERB
ejpam-5645	164	4	g	g	NOUN
ejpam-5645	164	5	be	be	AUX
ejpam-5645	164	6	a	a	DET
ejpam-5645	164	7	reduced	reduced	ADJ
ejpam-5645	164	8	torsion	torsion	NOUN
ejpam-5645	164	9	group	group	NOUN
ejpam-5645	164	10	.	.	PUNCT
ejpam-5645	165	1	suppose	suppose	VERB
ejpam-5645	165	2	that	that	SCONJ
ejpam-5645	165	3	g	g	PROPN
ejpam-5645	165	4	is	be	AUX
ejpam-5645	165	5	generalized	generalize	VERB
ejpam-5645	165	6	hereditarily	hereditarily	ADJ
ejpam-5645	165	7	hopfian	hopfian	ADJ
ejpam-5645	165	8	,	,	PUNCT
ejpam-5645	165	9	and	and	CCONJ
ejpam-5645	165	10	let	let	VERB
ejpam-5645	165	11	us	we	PRON
ejpam-5645	165	12	show	show	VERB
ejpam-5645	165	13	that	that	SCONJ
ejpam-5645	165	14	gp	gp	NOUN
ejpam-5645	165	15	is	be	AUX
ejpam-5645	165	16	finite	finite	ADJ
ejpam-5645	165	17	for	for	ADP
ejpam-5645	165	18	every	every	DET
ejpam-5645	165	19	prime	prime	ADJ
ejpam-5645	165	20	number	number	NOUN
ejpam-5645	165	21	p.	p.	NOUN
ejpam-5645	165	22	since	since	SCONJ
ejpam-5645	165	23	g	g	PROPN
ejpam-5645	165	24	is	be	AUX
ejpam-5645	165	25	a	a	DET
ejpam-5645	165	26	reduced	reduced	ADJ
ejpam-5645	165	27	torsion	torsion	NOUN
ejpam-5645	165	28	group	group	NOUN
ejpam-5645	165	29	,	,	PUNCT
ejpam-5645	165	30	then	then	ADV
ejpam-5645	165	31	according	accord	VERB
ejpam-5645	165	32	to	to	ADP
ejpam-5645	165	33	theorem	theorem	NOUN
ejpam-5645	165	34	8.4	8.4	NUM
ejpam-5645	165	35	of	of	ADP
ejpam-5645	165	36	page	page	NOUN
ejpam-5645	165	37	43	43	NUM
ejpam-5645	165	38	in	in	ADP
ejpam-5645	165	39	[	[	X
ejpam-5645	165	40	8	8	NUM
ejpam-5645	165	41	]	]	PUNCT
ejpam-5645	165	42	,	,	PUNCT
ejpam-5645	165	43	g	g	PROPN
ejpam-5645	165	44	=	=	PROPN
ejpam-5645	165	45	⊕	⊕	PROPN
ejpam-5645	165	46	pgp	pgp	NOUN
ejpam-5645	165	47	and	and	CCONJ
ejpam-5645	165	48	with	with	ADP
ejpam-5645	165	49	lemma	lemma	PROPN
ejpam-5645	165	50	2	2	NUM
ejpam-5645	165	51	,	,	PUNCT
ejpam-5645	165	52	we	we	PRON
ejpam-5645	165	53	therefore	therefore	ADV
ejpam-5645	165	54	have	have	AUX
ejpam-5645	165	55	,	,	PUNCT
ejpam-5645	165	56	gp	gp	NOUN
ejpam-5645	165	57	is	be	AUX
ejpam-5645	165	58	a	a	DET
ejpam-5645	165	59	p−group	p−group	NOUN
ejpam-5645	165	60	that	that	PRON
ejpam-5645	165	61	is	be	AUX
ejpam-5645	165	62	generalized	generalize	VERB
ejpam-5645	165	63	hereditarily	hereditarily	ADJ
ejpam-5645	165	64	hopfian	hopfian	ADJ
ejpam-5645	165	65	,	,	PUNCT
ejpam-5645	165	66	and	and	CCONJ
ejpam-5645	165	67	also	also	ADV
ejpam-5645	165	68	a	a	DET
ejpam-5645	165	69	reduced	reduced	ADJ
ejpam-5645	165	70	group	group	NOUN
ejpam-5645	165	71	,	,	PUNCT
ejpam-5645	165	72	which	which	PRON
ejpam-5645	165	73	implies	imply	VERB
ejpam-5645	165	74	by	by	ADP
ejpam-5645	165	75	theorem	theorem	NOUN
ejpam-5645	165	76	1	1	NUM
ejpam-5645	165	77	,	,	PUNCT
ejpam-5645	165	78	that	that	DET
ejpam-5645	165	79	gp	gp	NOUN
ejpam-5645	165	80	is	be	AUX
ejpam-5645	165	81	finite	finite	ADJ
ejpam-5645	165	82	.	.	PUNCT
ejpam-5645	166	1	therefore	therefore	ADV
ejpam-5645	166	2	,	,	PUNCT
ejpam-5645	166	3	gp	gp	NOUN
ejpam-5645	166	4	is	be	AUX
ejpam-5645	166	5	finite	finite	ADJ
ejpam-5645	166	6	for	for	ADP
ejpam-5645	166	7	every	every	DET
ejpam-5645	166	8	prime	prime	ADJ
ejpam-5645	166	9	number	number	NOUN
ejpam-5645	166	10	p.	p.	NOUN
ejpam-5645	166	11	conversely	conversely	ADV
ejpam-5645	166	12	:	:	PUNCT
ejpam-5645	166	13	⇐	⇐	ADJ
ejpam-5645	166	14	)	)	PUNCT
ejpam-5645	166	15	let	let	VERB
ejpam-5645	166	16	us	we	PRON
ejpam-5645	166	17	assume	assume	VERB
ejpam-5645	166	18	that	that	SCONJ
ejpam-5645	166	19	gp	gp	NOUN
ejpam-5645	166	20	is	be	AUX
ejpam-5645	166	21	finite	finite	ADJ
ejpam-5645	166	22	for	for	ADP
ejpam-5645	166	23	every	every	DET
ejpam-5645	166	24	prime	prime	ADJ
ejpam-5645	166	25	number	number	NOUN
ejpam-5645	166	26	p.	p.	NOUN
ejpam-5645	166	27	let	let	VERB
ejpam-5645	166	28	g1	g1	PROPN
ejpam-5645	166	29	<	<	X
ejpam-5645	166	30	g	g	PROPN
ejpam-5645	166	31	,	,	PUNCT
ejpam-5645	166	32	g1	g1	PROPN
ejpam-5645	167	1	=	=	SYM
ejpam-5645	167	2	⊕	⊕	PROPN
ejpam-5645	167	3	pg1p	pg1p	PROPN
ejpam-5645	167	4	,	,	PUNCT
ejpam-5645	167	5	g1p	g1p	VERB
ejpam-5645	167	6	<	<	X
ejpam-5645	167	7	gp	gp	X
ejpam-5645	167	8	,	,	PUNCT
ejpam-5645	167	9	φ	φ	PROPN
ejpam-5645	167	10	:	:	PUNCT
ejpam-5645	167	11	g1	g1	PROPN
ejpam-5645	167	12	−→	−→	NOUN
ejpam-5645	167	13	g1	g1	NOUN
ejpam-5645	167	14	be	be	VERB
ejpam-5645	167	15	a	a	DET
ejpam-5645	167	16	surjective	surjective	ADJ
ejpam-5645	167	17	endomorphism	endomorphism	NOUN
ejpam-5645	167	18	,	,	PUNCT
ejpam-5645	167	19	and	and	CCONJ
ejpam-5645	167	20	let	let	VERB
ejpam-5645	167	21	φp	φp	NOUN
ejpam-5645	167	22	:	:	PUNCT
ejpam-5645	167	23	g1p	g1p	AUX
ejpam-5645	167	24	−→	−→	ADJ
ejpam-5645	167	25	g1p	g1p	NOUN
ejpam-5645	167	26	be	be	AUX
ejpam-5645	167	27	the	the	DET
ejpam-5645	167	28	restriction	restriction	NOUN
ejpam-5645	167	29	of	of	ADP
ejpam-5645	167	30	φ	φ	PROPN
ejpam-5645	167	31	.	.	PUNCT
ejpam-5645	168	1	let	let	VERB
ejpam-5645	168	2	us	we	PRON
ejpam-5645	168	3	check	check	VERB
ejpam-5645	168	4	that	that	PRON
ejpam-5645	168	5	φp	φp	ADP
ejpam-5645	168	6	is	be	AUX
ejpam-5645	168	7	surjective	surjective	ADJ
ejpam-5645	168	8	for	for	SCONJ
ejpam-5645	168	9	every	every	DET
ejpam-5645	168	10	prime	prime	ADJ
ejpam-5645	168	11	p.	p.	NOUN
ejpam-5645	168	12	suppose	suppose	VERB
ejpam-5645	168	13	that	that	SCONJ
ejpam-5645	168	14	y	y	PROPN
ejpam-5645	168	15	∈	∈	PROPN
ejpam-5645	168	16	g1p	g1p	VERB
ejpam-5645	168	17	,	,	PUNCT
ejpam-5645	168	18	then	then	ADV
ejpam-5645	168	19	y	y	PROPN
ejpam-5645	168	20	∈	∈	PROPN
ejpam-5645	168	21	g1	g1	PROPN
ejpam-5645	168	22	,	,	PUNCT
ejpam-5645	168	23	implying	imply	VERB
ejpam-5645	168	24	the	the	DET
ejpam-5645	168	25	existence	existence	NOUN
ejpam-5645	168	26	of	of	ADP
ejpam-5645	168	27	x	x	PROPN
ejpam-5645	168	28	∈	∈	PROPN
ejpam-5645	168	29	g1	g1	NOUN
ejpam-5645	168	30	such	such	ADJ
ejpam-5645	168	31	that	that	SCONJ
ejpam-5645	168	32	φ(x	φ(x	NOUN
ejpam-5645	168	33	)	)	PUNCT
ejpam-5645	168	34	=	=	PUNCT
ejpam-5645	169	1	y.	y.	NOUN
ejpam-5645	169	2	since	since	SCONJ
ejpam-5645	169	3	g1	g1	PROPN
ejpam-5645	169	4	=	=	PROPN
ejpam-5645	169	5	⊕	⊕	PROPN
ejpam-5645	169	6	pg1p	pg1p	PROPN
ejpam-5645	169	7	=	=	PUNCT
ejpam-5645	169	8	g1p	g1p	PROPN
ejpam-5645	169	9	⊕	⊕	PROPN
ejpam-5645	169	10	g	g	NOUN
ejpam-5645	169	11	′	′	NUM
ejpam-5645	169	12	where	where	SCONJ
ejpam-5645	169	13	g	g	NOUN
ejpam-5645	169	14	′	′	NOUN
ejpam-5645	169	15	=	=	PUNCT
ejpam-5645	169	16	⊕	⊕	PROPN
ejpam-5645	169	17	q∈p	q∈p	NOUN
ejpam-5645	169	18	g1q	g1q	NOUN
ejpam-5645	169	19	with	with	ADP
ejpam-5645	169	20	p	p	PROPN
ejpam-5645	169	21	̸=	̸=	PROPN
ejpam-5645	169	22	q	q	NOUN
ejpam-5645	169	23	,	,	PUNCT
ejpam-5645	169	24	we	we	PRON
ejpam-5645	169	25	have	have	VERB
ejpam-5645	169	26	x	x	PART
ejpam-5645	169	27	∈	∈	PROPN
ejpam-5645	169	28	g1	g1	NOUN
ejpam-5645	169	29	implies	imply	VERB
ejpam-5645	169	30	x	x	NOUN
ejpam-5645	169	31	=	=	SYM
ejpam-5645	169	32	xp	xp	PROPN
ejpam-5645	170	1	+	+	CCONJ
ejpam-5645	170	2	x	x	SYM
ejpam-5645	170	3	′	′	INTJ
ejpam-5645	170	4	where	where	SCONJ
ejpam-5645	170	5	xp	xp	ADV
ejpam-5645	170	6	∈	∈	PROPN
ejpam-5645	170	7	g1p	g1p	PROPN
ejpam-5645	170	8	and	and	CCONJ
ejpam-5645	170	9	x	x	SYM
ejpam-5645	170	10	′	′	NUM
ejpam-5645	170	11	∈	∈	NOUN
ejpam-5645	170	12	g	g	NOUN
ejpam-5645	170	13	′	′	NOUN
ejpam-5645	170	14	.	.	PUNCT
ejpam-5645	171	1	therefore	therefore	ADV
ejpam-5645	171	2	,	,	PUNCT
ejpam-5645	171	3	φ(xp	φ(xp	ADP
ejpam-5645	171	4	+	+	NOUN
ejpam-5645	171	5	x	x	NOUN
ejpam-5645	171	6	′	′	NUM
ejpam-5645	171	7	)	)	PUNCT
ejpam-5645	172	1	=	=	SYM
ejpam-5645	172	2	y	y	PROPN
ejpam-5645	172	3	implies	imply	VERB
ejpam-5645	172	4	φ(xp	φ(xp	NOUN
ejpam-5645	172	5	)	)	PUNCT
ejpam-5645	172	6	+	+	CCONJ
ejpam-5645	172	7	φ(x	φ(x	PROPN
ejpam-5645	172	8	′	′	NUM
ejpam-5645	172	9	)	)	PUNCT
ejpam-5645	173	1	=	=	SYM
ejpam-5645	173	2	y	y	PROPN
ejpam-5645	173	3	,	,	PUNCT
ejpam-5645	173	4	and	and	CCONJ
ejpam-5645	173	5	thus	thus	ADV
ejpam-5645	173	6	φp(xp	φp(xp	ADV
ejpam-5645	173	7	)	)	PUNCT
ejpam-5645	174	1	+	+	CCONJ
ejpam-5645	174	2	φ(x	φ(x	PROPN
ejpam-5645	174	3	′	′	NUM
ejpam-5645	174	4	)	)	PUNCT
ejpam-5645	175	1	=	=	PUNCT
ejpam-5645	175	2	y.	y.	NOUN
ejpam-5645	175	3	since	since	SCONJ
ejpam-5645	175	4	φp(xp	φp(xp	ADJ
ejpam-5645	175	5	)	)	PUNCT
ejpam-5645	175	6	∈	∈	PROPN
ejpam-5645	175	7	g1p	g1p	NOUN
ejpam-5645	175	8	and	and	CCONJ
ejpam-5645	175	9	y	y	PROPN
ejpam-5645	175	10	∈	∈	PROPN
ejpam-5645	175	11	g1p	g1p	NOUN
ejpam-5645	175	12	,	,	PUNCT
ejpam-5645	175	13	then	then	ADV
ejpam-5645	175	14	φ(x	φ(x	PROPN
ejpam-5645	175	15	′	′	NUM
ejpam-5645	175	16	)	)	PUNCT
ejpam-5645	176	1	=	=	SYM
ejpam-5645	176	2	0	0	NUM
ejpam-5645	176	3	,	,	PUNCT
ejpam-5645	176	4	leading	lead	VERB
ejpam-5645	176	5	to	to	ADP
ejpam-5645	176	6	φ(xp	φ(xp	NOUN
ejpam-5645	176	7	)	)	PUNCT
ejpam-5645	176	8	=	=	VERB
ejpam-5645	177	1	y.	y.	NOUN
ejpam-5645	177	2	this	this	PRON
ejpam-5645	177	3	implies	imply	VERB
ejpam-5645	177	4	that	that	SCONJ
ejpam-5645	177	5	φp(xp	φp(xp	ADV
ejpam-5645	177	6	)	)	PUNCT
ejpam-5645	177	7	=	=	PUNCT
ejpam-5645	178	1	y.	y.	NOUN
ejpam-5645	178	2	8	8	NUM
ejpam-5645	178	3	of	of	ADP
ejpam-5645	178	4	13	13	NUM
ejpam-5645	178	5	therefore	therefore	ADV
ejpam-5645	178	6	,	,	PUNCT
ejpam-5645	178	7	we	we	PRON
ejpam-5645	178	8	have	have	VERB
ejpam-5645	178	9	the	the	DET
ejpam-5645	178	10	existence	existence	NOUN
ejpam-5645	178	11	of	of	ADP
ejpam-5645	178	12	xp	xp	PROPN
ejpam-5645	178	13	∈	∈	PROPN
ejpam-5645	178	14	g1p	g1p	PROPN
ejpam-5645	178	15	and	and	CCONJ
ejpam-5645	178	16	then	then	ADV
ejpam-5645	178	17	φp	φp	ADP
ejpam-5645	178	18	is	be	AUX
ejpam-5645	178	19	surjective	surjective	ADJ
ejpam-5645	178	20	for	for	ADP
ejpam-5645	178	21	every	every	DET
ejpam-5645	178	22	prime	prime	ADJ
ejpam-5645	178	23	p.	p.	NOUN
ejpam-5645	178	24	since	since	SCONJ
ejpam-5645	178	25	g1p	g1p	PROPN
ejpam-5645	178	26	is	be	AUX
ejpam-5645	178	27	finite	finite	ADJ
ejpam-5645	178	28	because	because	SCONJ
ejpam-5645	178	29	it	it	PRON
ejpam-5645	178	30	is	be	AUX
ejpam-5645	178	31	a	a	DET
ejpam-5645	178	32	subgroup	subgroup	NOUN
ejpam-5645	178	33	of	of	ADP
ejpam-5645	178	34	a	a	DET
ejpam-5645	178	35	finite	finite	ADJ
ejpam-5645	178	36	group	group	NOUN
ejpam-5645	178	37	gp	gp	NOUN
ejpam-5645	178	38	,	,	PUNCT
ejpam-5645	178	39	then	then	ADV
ejpam-5645	178	40	φp	φp	ADP
ejpam-5645	178	41	is	be	AUX
ejpam-5645	178	42	bijective	bijective	ADJ
ejpam-5645	178	43	,	,	PUNCT
ejpam-5645	178	44	and	and	CCONJ
ejpam-5645	178	45	therefore	therefore	ADV
ejpam-5645	178	46	,	,	PUNCT
ejpam-5645	178	47	g1p	g1p	NOUN
ejpam-5645	178	48	is	be	AUX
ejpam-5645	178	49	hopfian	hopfian	ADJ
ejpam-5645	178	50	for	for	ADP
ejpam-5645	178	51	every	every	DET
ejpam-5645	178	52	prime	prime	ADJ
ejpam-5645	178	53	p.	p.	NOUN
ejpam-5645	178	54	hence	hence	ADV
ejpam-5645	178	55	,	,	PUNCT
ejpam-5645	178	56	all	all	DET
ejpam-5645	178	57	subgroups	subgroup	NOUN
ejpam-5645	178	58	of	of	ADP
ejpam-5645	178	59	g1	g1	NOUN
ejpam-5645	178	60	are	be	AUX
ejpam-5645	178	61	hopfian	hopfian	ADJ
ejpam-5645	178	62	,	,	PUNCT
ejpam-5645	178	63	and	and	CCONJ
ejpam-5645	178	64	then	then	ADV
ejpam-5645	178	65	g1	g1	PROPN
ejpam-5645	178	66	is	be	AUX
ejpam-5645	178	67	hereditarily	hereditarily	ADV
ejpam-5645	178	68	hopfian	hopfian	ADJ
ejpam-5645	178	69	group	group	NOUN
ejpam-5645	178	70	.	.	PUNCT
ejpam-5645	179	1	thus	thus	ADV
ejpam-5645	179	2	,	,	PUNCT
ejpam-5645	179	3	according	accord	VERB
ejpam-5645	179	4	to	to	ADP
ejpam-5645	179	5	remark	remark	NOUN
ejpam-5645	179	6	2	2	NUM
ejpam-5645	179	7	,	,	PUNCT
ejpam-5645	179	8	g1	g1	PROPN
ejpam-5645	179	9	is	be	AUX
ejpam-5645	179	10	generalized	generalized	ADJ
ejpam-5645	179	11	hopfian	hopfian	ADJ
ejpam-5645	179	12	group	group	NOUN
ejpam-5645	179	13	,	,	PUNCT
ejpam-5645	179	14	and	and	CCONJ
ejpam-5645	179	15	therefore	therefore	ADV
ejpam-5645	179	16	g	g	PROPN
ejpam-5645	179	17	is	be	AUX
ejpam-5645	179	18	generalized	generalize	VERB
ejpam-5645	179	19	hereditarily	hereditarily	ADJ
ejpam-5645	179	20	hopfian	hopfian	ADJ
ejpam-5645	179	21	group	group	NOUN
ejpam-5645	179	22	.	.	PUNCT
ejpam-5645	180	1	in	in	ADP
ejpam-5645	180	2	the	the	DET
ejpam-5645	180	3	previous	previous	ADJ
ejpam-5645	180	4	sections	section	NOUN
ejpam-5645	180	5	,	,	PUNCT
ejpam-5645	180	6	we	we	PRON
ejpam-5645	180	7	have	have	AUX
ejpam-5645	180	8	examined	examine	VERB
ejpam-5645	180	9	the	the	DET
ejpam-5645	180	10	property	property	NOUN
ejpam-5645	180	11	of	of	ADP
ejpam-5645	180	12	generalized	generalized	ADJ
ejpam-5645	180	13	hereditarily	hereditarily	ADJ
ejpam-5645	180	14	hopficity	hopficity	NOUN
ejpam-5645	180	15	within	within	ADP
ejpam-5645	180	16	the	the	DET
ejpam-5645	180	17	categories	category	NOUN
ejpam-5645	180	18	of	of	ADP
ejpam-5645	180	19	reduced	reduce	VERB
ejpam-5645	180	20	p−groups	p−group	NOUN
ejpam-5645	180	21	and	and	CCONJ
ejpam-5645	180	22	reduced	reduce	VERB
ejpam-5645	180	23	torsion	torsion	NOUN
ejpam-5645	180	24	groups	group	NOUN
ejpam-5645	180	25	.	.	PUNCT
ejpam-5645	181	1	now	now	ADV
ejpam-5645	181	2	,	,	PUNCT
ejpam-5645	181	3	we	we	PRON
ejpam-5645	181	4	expand	expand	VERB
ejpam-5645	181	5	upon	upon	SCONJ
ejpam-5645	181	6	those	those	DET
ejpam-5645	181	7	findings	finding	NOUN
ejpam-5645	181	8	to	to	PART
ejpam-5645	181	9	study	study	VERB
ejpam-5645	181	10	the	the	DET
ejpam-5645	181	11	case	case	NOUN
ejpam-5645	181	12	of	of	ADP
ejpam-5645	181	13	divisible	divisible	ADJ
ejpam-5645	181	14	p−groups	p−group	NOUN
ejpam-5645	181	15	.	.	PUNCT
ejpam-5645	182	1	4	4	X
ejpam-5645	182	2	.	.	X
ejpam-5645	182	3	on	on	ADP
ejpam-5645	182	4	generalized	generalized	ADJ
ejpam-5645	182	5	hopfian	hopfian	ADJ
ejpam-5645	182	6	divisible	divisible	ADJ
ejpam-5645	182	7	p−groups	p−group	NOUN
ejpam-5645	182	8	in	in	ADP
ejpam-5645	182	9	this	this	DET
ejpam-5645	182	10	section	section	NOUN
ejpam-5645	182	11	,	,	PUNCT
ejpam-5645	182	12	we	we	PRON
ejpam-5645	182	13	characterize	characterize	VERB
ejpam-5645	182	14	generalized	generalized	ADJ
ejpam-5645	182	15	hopfian	hopfian	ADJ
ejpam-5645	182	16	groups	group	NOUN
ejpam-5645	182	17	in	in	ADP
ejpam-5645	182	18	the	the	DET
ejpam-5645	182	19	category	category	NOUN
ejpam-5645	182	20	of	of	ADP
ejpam-5645	182	21	divisible	divisible	ADJ
ejpam-5645	182	22	p−groups	p−group	NOUN
ejpam-5645	182	23	.	.	PUNCT
ejpam-5645	183	1	we	we	PRON
ejpam-5645	183	2	note	note	VERB
ejpam-5645	183	3	that	that	SCONJ
ejpam-5645	183	4	the	the	DET
ejpam-5645	183	5	group	group	NOUN
ejpam-5645	183	6	needed	need	VERB
ejpam-5645	183	7	in	in	ADP
ejpam-5645	183	8	the	the	DET
ejpam-5645	183	9	proof	proof	NOUN
ejpam-5645	183	10	of	of	ADP
ejpam-5645	183	11	our	our	PRON
ejpam-5645	183	12	final	final	ADJ
ejpam-5645	183	13	theorem	theorem	NOUN
ejpam-5645	183	14	hereafter	hereafter	NOUN
ejpam-5645	183	15	is	be	AUX
ejpam-5645	183	16	about	about	ADP
ejpam-5645	183	17	the	the	DET
ejpam-5645	183	18	divisible	divisible	ADJ
ejpam-5645	183	19	group	group	NOUN
ejpam-5645	183	20	as	as	SCONJ
ejpam-5645	183	21	recalled	recall	VERB
ejpam-5645	183	22	among	among	ADP
ejpam-5645	183	23	the	the	DET
ejpam-5645	183	24	classical	classical	ADJ
ejpam-5645	183	25	definitions	definition	NOUN
ejpam-5645	183	26	listed	list	VERB
ejpam-5645	183	27	in	in	ADP
ejpam-5645	183	28	section	section	NOUN
ejpam-5645	183	29	2	2	NUM
ejpam-5645	183	30	.	.	PUNCT
ejpam-5645	184	1	in	in	ADP
ejpam-5645	184	2	addition	addition	NOUN
ejpam-5645	184	3	,	,	PUNCT
ejpam-5645	184	4	we	we	PRON
ejpam-5645	184	5	will	will	AUX
ejpam-5645	184	6	also	also	ADV
ejpam-5645	184	7	need	need	VERB
ejpam-5645	184	8	the	the	DET
ejpam-5645	184	9	following	follow	VERB
ejpam-5645	184	10	property	property	NOUN
ejpam-5645	184	11	,	,	PUNCT
ejpam-5645	184	12	see	see	VERB
ejpam-5645	184	13	[	[	X
ejpam-5645	184	14	8	8	NUM
ejpam-5645	184	15	]	]	PUNCT
ejpam-5645	184	16	and	and	CCONJ
ejpam-5645	184	17	which	which	PRON
ejpam-5645	184	18	states	state	VERB
ejpam-5645	184	19	that	that	SCONJ
ejpam-5645	184	20	g	g	PROPN
ejpam-5645	184	21	is	be	AUX
ejpam-5645	184	22	a	a	DET
ejpam-5645	184	23	divisible	divisible	ADJ
ejpam-5645	184	24	group	group	NOUN
ejpam-5645	184	25	if	if	SCONJ
ejpam-5645	184	26	and	and	CCONJ
ejpam-5645	184	27	only	only	ADV
ejpam-5645	184	28	ifg	ifg	NOUN
ejpam-5645	184	29	can	can	AUX
ejpam-5645	184	30	be	be	AUX
ejpam-5645	184	31	expressed	express	VERB
ejpam-5645	184	32	asg	asg	PROPN
ejpam-5645	184	33	=	=	SYM
ejpam-5645	184	34	(	(	PUNCT
ejpam-5645	184	35	⊕r0(g)q	⊕r0(g)q	PROPN
ejpam-5645	184	36	)	)	PUNCT
ejpam-5645	184	37	⊕[⊕	⊕[⊕	NOUN
ejpam-5645	184	38	p∈p	p∈p	NOUN
ejpam-5645	184	39	(	(	PUNCT
ejpam-5645	184	40	⊕rp(g)z	⊕rp(g)z	PROPN
ejpam-5645	184	41	(	(	PUNCT
ejpam-5645	184	42	p∞	p∞	PROPN
ejpam-5645	184	43	)	)	PUNCT
ejpam-5645	184	44	)	)	PUNCT
ejpam-5645	184	45	]	]	PUNCT
ejpam-5645	184	46	,	,	PUNCT
ejpam-5645	184	47	such	such	ADJ
ejpam-5645	184	48	that	that	DET
ejpam-5645	184	49	q	q	NOUN
ejpam-5645	184	50	is	be	AUX
ejpam-5645	184	51	the	the	DET
ejpam-5645	184	52	rational	rational	ADJ
ejpam-5645	184	53	group	group	NOUN
ejpam-5645	184	54	,	,	PUNCT
ejpam-5645	184	55	while	while	SCONJ
ejpam-5645	184	56	we	we	PRON
ejpam-5645	184	57	recall	recall	VERB
ejpam-5645	184	58	z	z	PROPN
ejpam-5645	184	59	(	(	PUNCT
ejpam-5645	184	60	p∞	p∞	PROPN
ejpam-5645	184	61	)	)	PUNCT
ejpam-5645	184	62	is	be	AUX
ejpam-5645	184	63	the	the	DET
ejpam-5645	184	64	prufer	prufer	NOUN
ejpam-5645	184	65	group	group	NOUN
ejpam-5645	184	66	to	to	PART
ejpam-5645	184	67	be	be	AUX
ejpam-5645	184	68	defined	define	VERB
ejpam-5645	184	69	as	as	ADP
ejpam-5645	184	70	follows	follow	VERB
ejpam-5645	184	71	.	.	PUNCT
ejpam-5645	185	1	z(p∞	z(p∞	PROPN
ejpam-5645	185	2	)	)	PUNCT
ejpam-5645	185	3	is	be	AUX
ejpam-5645	185	4	a	a	DET
ejpam-5645	185	5	fundamental	fundamental	ADJ
ejpam-5645	185	6	example	example	NOUN
ejpam-5645	185	7	of	of	ADP
ejpam-5645	185	8	a	a	DET
ejpam-5645	185	9	quasi	quasi	ADJ
ejpam-5645	185	10	-	-	ADJ
ejpam-5645	185	11	cyclic	cyclic	ADJ
ejpam-5645	185	12	group	group	NOUN
ejpam-5645	185	13	or	or	CCONJ
ejpam-5645	185	14	a	a	DET
ejpam-5645	185	15	group	group	NOUN
ejpam-5645	185	16	of	of	ADP
ejpam-5645	185	17	type	type	NOUN
ejpam-5645	185	18	p∞.	p∞.	SCONJ
ejpam-5645	185	19	it	it	PRON
ejpam-5645	185	20	is	be	AUX
ejpam-5645	185	21	commonly	commonly	ADV
ejpam-5645	185	22	used	use	VERB
ejpam-5645	185	23	in	in	ADP
ejpam-5645	185	24	the	the	DET
ejpam-5645	185	25	theory	theory	NOUN
ejpam-5645	185	26	of	of	ADP
ejpam-5645	185	27	abelian	abelian	ADJ
ejpam-5645	185	28	groups	group	NOUN
ejpam-5645	185	29	and	and	CCONJ
ejpam-5645	185	30	the	the	DET
ejpam-5645	185	31	classification	classification	NOUN
ejpam-5645	185	32	of	of	ADP
ejpam-5645	185	33	finite	finite	ADJ
ejpam-5645	185	34	groups	group	NOUN
ejpam-5645	185	35	.	.	PUNCT
ejpam-5645	186	1	it	it	PRON
ejpam-5645	186	2	is	be	AUX
ejpam-5645	186	3	generated	generate	VERB
ejpam-5645	186	4	by	by	ADP
ejpam-5645	186	5	a	a	DET
ejpam-5645	186	6	sequence	sequence	NOUN
ejpam-5645	186	7	of	of	ADP
ejpam-5645	186	8	elements	element	NOUN
ejpam-5645	186	9	a1	a1	NOUN
ejpam-5645	186	10	,	,	PUNCT
ejpam-5645	186	11	a2	a2	PROPN
ejpam-5645	186	12	,	,	PUNCT
ejpam-5645	186	13	a3	a3	NOUN
ejpam-5645	186	14	,	,	PUNCT
ejpam-5645	186	15	.	.	PUNCT
ejpam-5645	186	16	.	.	PUNCT
ejpam-5645	187	1	.	.	PUNCT
ejpam-5645	188	1	,	,	PUNCT
ejpam-5645	188	2	an	an	PRON
ejpam-5645	188	3	,	,	PUNCT
ejpam-5645	188	4	.	.	PUNCT
ejpam-5645	188	5	.	.	PUNCT
ejpam-5645	189	1	.	.	PUNCT
ejpam-5645	189	2	,	,	PUNCT
ejpam-5645	189	3	or	or	CCONJ
ejpam-5645	189	4	z(p∞	z(p∞	NUM
ejpam-5645	189	5	)	)	PUNCT
ejpam-5645	190	1	=	=	NOUN
ejpam-5645	190	2	⋃∞	⋃∞	X
ejpam-5645	190	3	i=1	i=1	PROPN
ejpam-5645	190	4	⟨ai⟩	⟨ai⟩	NOUN
ejpam-5645	190	5	where	where	SCONJ
ejpam-5645	190	6	each	each	PRON
ejpam-5645	190	7	element	element	VERB
ejpam-5645	190	8	an	an	DET
ejpam-5645	190	9	satisfies	satisfie	NOUN
ejpam-5645	190	10	the	the	DET
ejpam-5645	190	11	condition	condition	NOUN
ejpam-5645	190	12	◦	◦	NOUN
ejpam-5645	190	13	(	(	PUNCT
ejpam-5645	190	14	an	an	X
ejpam-5645	190	15	)	)	PUNCT
ejpam-5645	190	16	=	=	SYM
ejpam-5645	191	1	pn	pn	PROPN
ejpam-5645	191	2	which	which	PRON
ejpam-5645	191	3	means	mean	VERB
ejpam-5645	191	4	that	that	SCONJ
ejpam-5645	191	5	an	an	PRON
ejpam-5645	191	6	has	have	VERB
ejpam-5645	191	7	order	order	NOUN
ejpam-5645	191	8	pn	pn	NOUN
ejpam-5645	191	9	with	with	ADP
ejpam-5645	191	10	p	p	X
ejpam-5645	191	11	a	a	DET
ejpam-5645	191	12	fixed	fix	VERB
ejpam-5645	191	13	prime	prime	ADJ
ejpam-5645	191	14	number	number	NOUN
ejpam-5645	191	15	.	.	PUNCT
ejpam-5645	192	1	the	the	DET
ejpam-5645	192	2	relations	relation	NOUN
ejpam-5645	192	3	between	between	ADP
ejpam-5645	192	4	these	these	DET
ejpam-5645	192	5	generators	generator	NOUN
ejpam-5645	192	6	are	be	AUX
ejpam-5645	192	7	given	give	VERB
ejpam-5645	192	8	by	by	ADP
ejpam-5645	192	9	the	the	DET
ejpam-5645	192	10	following	follow	VERB
ejpam-5645	192	11	equations	equation	NOUN
ejpam-5645	192	12	,	,	PUNCT
ejpam-5645	192	13	pa1	pa1	NOUN
ejpam-5645	192	14	=	=	SYM
ejpam-5645	192	15	0	0	PROPN
ejpam-5645	192	16	,	,	PUNCT
ejpam-5645	192	17	pa2	pa2	PROPN
ejpam-5645	192	18	=	=	PUNCT
ejpam-5645	192	19	a1	a1	PROPN
ejpam-5645	192	20	,	,	PUNCT
ejpam-5645	192	21	pan+1	pan+1	NOUN
ejpam-5645	192	22	=	=	SYM
ejpam-5645	192	23	an	an	DET
ejpam-5645	192	24	,	,	PUNCT
ejpam-5645	192	25	∀n	∀n	SYM
ejpam-5645	192	26	∈	∈	PROPN
ejpam-5645	192	27	n.	n.	NOUN
ejpam-5645	192	28	this	this	PRON
ejpam-5645	192	29	means	mean	VERB
ejpam-5645	192	30	that	that	SCONJ
ejpam-5645	192	31	a1	a1	NOUN
ejpam-5645	192	32	is	be	AUX
ejpam-5645	192	33	annihilated	annihilate	VERB
ejpam-5645	192	34	by	by	ADP
ejpam-5645	192	35	multiplication	multiplication	NOUN
ejpam-5645	192	36	by	by	ADP
ejpam-5645	192	37	p	p	NOUN
ejpam-5645	192	38	,	,	PUNCT
ejpam-5645	192	39	and	and	CCONJ
ejpam-5645	192	40	each	each	DET
ejpam-5645	192	41	subsequent	subsequent	ADJ
ejpam-5645	192	42	generator	generator	NOUN
ejpam-5645	192	43	an	an	PRON
ejpam-5645	192	44	is	be	AUX
ejpam-5645	192	45	related	relate	VERB
ejpam-5645	192	46	to	to	ADP
ejpam-5645	192	47	the	the	DET
ejpam-5645	192	48	previous	previous	ADJ
ejpam-5645	192	49	generator	generator	NOUN
ejpam-5645	192	50	an−1	an−1	ADV
ejpam-5645	192	51	by	by	ADP
ejpam-5645	192	52	multiplication	multiplication	NOUN
ejpam-5645	192	53	by	by	ADP
ejpam-5645	192	54	p.	p.	NOUN
ejpam-5645	192	55	the	the	DET
ejpam-5645	192	56	elements	element	NOUN
ejpam-5645	192	57	of	of	ADP
ejpam-5645	192	58	z(p∞	z(p∞	PROPN
ejpam-5645	192	59	)	)	PUNCT
ejpam-5645	192	60	are	be	AUX
ejpam-5645	192	61	of	of	ADP
ejpam-5645	192	62	order	order	NOUN
ejpam-5645	192	63	pn	pn	NOUN
ejpam-5645	192	64	for	for	ADP
ejpam-5645	192	65	increasingly	increasingly	ADV
ejpam-5645	192	66	larger	large	ADJ
ejpam-5645	192	67	values	value	NOUN
ejpam-5645	192	68	of	of	ADP
ejpam-5645	192	69	n	n	PRON
ejpam-5645	192	70	and	and	CCONJ
ejpam-5645	192	71	its	its	PRON
ejpam-5645	192	72	structure	structure	NOUN
ejpam-5645	192	73	is	be	AUX
ejpam-5645	192	74	such	such	ADJ
ejpam-5645	192	75	that	that	SCONJ
ejpam-5645	192	76	each	each	DET
ejpam-5645	192	77	subgroup	subgroup	NOUN
ejpam-5645	192	78	⟨an⟩	⟨an⟩	NOUN
ejpam-5645	192	79	is	be	AUX
ejpam-5645	192	80	contained	contain	VERB
ejpam-5645	192	81	in	in	ADP
ejpam-5645	192	82	the	the	DET
ejpam-5645	192	83	next	next	ADJ
ejpam-5645	192	84	as	as	ADP
ejpam-5645	192	85	,	,	PUNCT
ejpam-5645	192	86	⟨a1⟩	⟨a1⟩	X
ejpam-5645	192	87	⊆	⊆	NUM
ejpam-5645	192	88	⟨a2⟩	⟨a2⟩	NOUN
ejpam-5645	192	89	⊆	⊆	NUM
ejpam-5645	192	90	⟨a3⟩	⟨a3⟩	NOUN
ejpam-5645	192	91	⊆	⊆	NUM
ejpam-5645	192	92	·	·	PUNCT
ejpam-5645	192	93	·	·	PUNCT
ejpam-5645	192	94	·	·	PUNCT
ejpam-5645	193	1	⊆	⊆	NUM
ejpam-5645	193	2	z(p∞	z(p∞	NUM
ejpam-5645	193	3	)	)	PUNCT
ejpam-5645	193	4	.	.	PUNCT
ejpam-5645	194	1	this	this	PRON
ejpam-5645	194	2	means	mean	VERB
ejpam-5645	194	3	that	that	SCONJ
ejpam-5645	194	4	each	each	DET
ejpam-5645	194	5	subgroup	subgroup	NOUN
ejpam-5645	194	6	generated	generate	VERB
ejpam-5645	194	7	by	by	ADP
ejpam-5645	194	8	an	an	PRON
ejpam-5645	194	9	is	be	AUX
ejpam-5645	194	10	contained	contain	VERB
ejpam-5645	194	11	within	within	ADP
ejpam-5645	194	12	the	the	DET
ejpam-5645	194	13	subgroup	subgroup	NOUN
ejpam-5645	194	14	generated	generate	VERB
ejpam-5645	194	15	by	by	ADP
ejpam-5645	194	16	an+1	an+1	PROPN
ejpam-5645	194	17	,	,	PUNCT
ejpam-5645	194	18	and	and	CCONJ
ejpam-5645	194	19	every	every	DET
ejpam-5645	194	20	element	element	NOUN
ejpam-5645	194	21	of	of	ADP
ejpam-5645	194	22	z(p∞	z(p∞	PROPN
ejpam-5645	194	23	)	)	PUNCT
ejpam-5645	194	24	can	can	AUX
ejpam-5645	194	25	be	be	AUX
ejpam-5645	194	26	expressed	express	VERB
ejpam-5645	194	27	as	as	ADP
ejpam-5645	194	28	a	a	DET
ejpam-5645	194	29	linear	linear	ADJ
ejpam-5645	194	30	combination	combination	NOUN
ejpam-5645	194	31	of	of	ADP
ejpam-5645	194	32	the	the	DET
ejpam-5645	194	33	elements	element	NOUN
ejpam-5645	194	34	a1	a1	NOUN
ejpam-5645	194	35	,	,	PUNCT
ejpam-5645	194	36	a2	a2	PROPN
ejpam-5645	194	37	,	,	PUNCT
ejpam-5645	194	38	.	.	PUNCT
ejpam-5645	194	39	.	.	PUNCT
ejpam-5645	195	1	.	.	PUNCT
ejpam-5645	196	1	,	,	PUNCT
ejpam-5645	196	2	with	with	ADP
ejpam-5645	196	3	integer	integer	NOUN
ejpam-5645	196	4	coefficients	coefficient	NOUN
ejpam-5645	196	5	.	.	PUNCT
ejpam-5645	197	1	if	if	SCONJ
ejpam-5645	197	2	x	x	PROPN
ejpam-5645	197	3	∈	∈	PROPN
ejpam-5645	197	4	z(p∞	z(p∞	PROPN
ejpam-5645	197	5	)	)	PUNCT
ejpam-5645	197	6	,	,	PUNCT
ejpam-5645	197	7	then	then	ADV
ejpam-5645	197	8	x	x	PUNCT
ejpam-5645	197	9	is	be	AUX
ejpam-5645	197	10	a	a	DET
ejpam-5645	197	11	multiple	multiple	NOUN
ejpam-5645	197	12	of	of	ADP
ejpam-5645	197	13	some	some	DET
ejpam-5645	197	14	an	an	PRON
ejpam-5645	197	15	,	,	PUNCT
ejpam-5645	197	16	which	which	PRON
ejpam-5645	197	17	can	can	AUX
ejpam-5645	197	18	be	be	AUX
ejpam-5645	197	19	expressed	express	VERB
ejpam-5645	197	20	as	as	ADP
ejpam-5645	197	21	,	,	PUNCT
ejpam-5645	197	22	x	x	PROPN
ejpam-5645	197	23	∈	∈	PROPN
ejpam-5645	197	24	z(p∞	z(p∞	PROPN
ejpam-5645	197	25	)	)	PUNCT
ejpam-5645	197	26	⇐	⇐	ADJ
ejpam-5645	197	27	⇒	⇒	NOUN
ejpam-5645	197	28	∃m	∃m	PROPN
ejpam-5645	197	29	∈	∈	PROPN
ejpam-5645	197	30	z,∃ak	z,∃ak	PROPN
ejpam-5645	197	31	∈	∈	PROPN
ejpam-5645	197	32	{	{	PUNCT
ejpam-5645	197	33	a1	a1	PROPN
ejpam-5645	197	34	,	,	PUNCT
ejpam-5645	197	35	a2	a2	PROPN
ejpam-5645	197	36	,	,	PUNCT
ejpam-5645	197	37	a3	a3	NOUN
ejpam-5645	197	38	,	,	PUNCT
ejpam-5645	197	39	.	.	PUNCT
ejpam-5645	197	40	.	.	PUNCT
ejpam-5645	197	41	.	.	PUNCT
ejpam-5645	198	1	}	}	PUNCT
ejpam-5645	198	2	such	such	ADJ
ejpam-5645	198	3	that	that	SCONJ
ejpam-5645	198	4	x	x	X
ejpam-5645	198	5	=	=	SYM
ejpam-5645	198	6	mak	mak	PROPN
ejpam-5645	198	7	and	and	CCONJ
ejpam-5645	198	8	m	m	PROPN
ejpam-5645	198	9	∧	∧	NOUN
ejpam-5645	198	10	p	p	NOUN
ejpam-5645	198	11	=	=	NOUN
ejpam-5645	198	12	1	1	NUM
ejpam-5645	198	13	.	.	NOUN
ejpam-5645	198	14	9	9	NUM
ejpam-5645	198	15	of	of	ADP
ejpam-5645	198	16	13	13	NUM
ejpam-5645	198	17	this	this	PRON
ejpam-5645	198	18	means	mean	VERB
ejpam-5645	198	19	that	that	SCONJ
ejpam-5645	198	20	each	each	DET
ejpam-5645	198	21	element	element	NOUN
ejpam-5645	198	22	x	x	PUNCT
ejpam-5645	198	23	of	of	ADP
ejpam-5645	198	24	z(p∞	z(p∞	PROPN
ejpam-5645	198	25	)	)	PUNCT
ejpam-5645	198	26	can	can	AUX
ejpam-5645	198	27	be	be	AUX
ejpam-5645	198	28	written	write	VERB
ejpam-5645	198	29	as	as	ADP
ejpam-5645	198	30	a	a	DET
ejpam-5645	198	31	multiple	multiple	NOUN
ejpam-5645	198	32	of	of	ADP
ejpam-5645	198	33	ak	ak	NOUN
ejpam-5645	198	34	by	by	ADP
ejpam-5645	198	35	some	some	DET
ejpam-5645	198	36	integer	integer	NOUN
ejpam-5645	198	37	m	m	VERB
ejpam-5645	198	38	coprime	coprime	ADJ
ejpam-5645	198	39	with	with	ADP
ejpam-5645	198	40	p.	p.	PROPN
ejpam-5645	198	41	theorem	theorem	NOUN
ejpam-5645	198	42	3	3	X
ejpam-5645	198	43	.	.	PUNCT
ejpam-5645	199	1	let	let	VERB
ejpam-5645	199	2	g	g	NOUN
ejpam-5645	199	3	be	be	AUX
ejpam-5645	199	4	an	an	DET
ejpam-5645	199	5	abelian	abelian	ADJ
ejpam-5645	199	6	divisible	divisible	ADJ
ejpam-5645	199	7	p−group	p−group	NOUN
ejpam-5645	199	8	.	.	PUNCT
ejpam-5645	200	1	g	g	PROPN
ejpam-5645	200	2	is	be	AUX
ejpam-5645	200	3	generalized	generalize	VERB
ejpam-5645	200	4	hereditarily	hereditarily	ADJ
ejpam-5645	200	5	hopfian	hopfian	ADJ
ejpam-5645	200	6	group	group	NOUN
ejpam-5645	200	7	if	if	SCONJ
ejpam-5645	201	1	and	and	CCONJ
ejpam-5645	201	2	only	only	ADV
ejpam-5645	201	3	if	if	SCONJ
ejpam-5645	201	4	g	g	NOUN
ejpam-5645	201	5	=	=	SYM
ejpam-5645	201	6	⊕i∈ipz	⊕i∈ipz	PROPN
ejpam-5645	201	7	(	(	PUNCT
ejpam-5645	201	8	p∞	p∞	NOUN
ejpam-5645	201	9	)	)	PUNCT
ejpam-5645	201	10	such	such	ADJ
ejpam-5645	201	11	that	that	SCONJ
ejpam-5645	201	12	card(ip	card(ip	PROPN
ejpam-5645	201	13	)	)	PUNCT
ejpam-5645	201	14	<	<	X
ejpam-5645	201	15	∞.	∞.	PROPN
ejpam-5645	201	16	proof	proof	NOUN
ejpam-5645	201	17	.	.	PUNCT
ejpam-5645	202	1	•	•	NUM
ejpam-5645	202	2	⇒	⇒	NOUN
ejpam-5645	202	3	)	)	PUNCT
ejpam-5645	202	4	let	let	VERB
ejpam-5645	202	5	g	g	NOUN
ejpam-5645	202	6	be	be	AUX
ejpam-5645	202	7	a	a	DET
ejpam-5645	202	8	generalized	generalized	ADJ
ejpam-5645	202	9	hereditarily	hereditarily	ADJ
ejpam-5645	202	10	hopfian	hopfian	ADJ
ejpam-5645	202	11	group	group	NOUN
ejpam-5645	202	12	.	.	PUNCT
ejpam-5645	203	1	let	let	VERB
ejpam-5645	203	2	us	we	PRON
ejpam-5645	203	3	show	show	VERB
ejpam-5645	203	4	that	that	SCONJ
ejpam-5645	203	5	g	g	PROPN
ejpam-5645	203	6	=	=	SYM
ejpam-5645	203	7	⊕i∈ipz(p∞	⊕i∈ipz(p∞	PROPN
ejpam-5645	203	8	)	)	PUNCT
ejpam-5645	203	9	where	where	SCONJ
ejpam-5645	203	10	card(ip	card(ip	ADJ
ejpam-5645	203	11	)	)	PUNCT
ejpam-5645	203	12	<	<	X
ejpam-5645	203	13	∞.	∞.	PROPN
ejpam-5645	203	14	suppose	suppose	VERB
ejpam-5645	203	15	that	that	SCONJ
ejpam-5645	203	16	card(ip	card(ip	PROPN
ejpam-5645	203	17	)	)	PUNCT
ejpam-5645	203	18	=	=	SYM
ejpam-5645	203	19	∞	∞	PROPN
ejpam-5645	203	20	,	,	PUNCT
ejpam-5645	203	21	then	then	ADV
ejpam-5645	203	22	we	we	PRON
ejpam-5645	203	23	can	can	AUX
ejpam-5645	203	24	write	write	VERB
ejpam-5645	203	25	g	g	PROPN
ejpam-5645	203	26	=	=	SYM
ejpam-5645	203	27	g1	g1	PROPN
ejpam-5645	203	28	⊕	⊕	PROPN
ejpam-5645	203	29	g′	g′	NOUN
ejpam-5645	203	30	1	1	NUM
ejpam-5645	203	31	withg′	withg′	NOUN
ejpam-5645	203	32	1	1	NUM
ejpam-5645	203	33	=	=	SYM
ejpam-5645	203	34	(	(	PUNCT
ejpam-5645	203	35	⊕∞	⊕∞	X
ejpam-5645	203	36	i=1z(p∞))i	i=1z(p∞))i	NOUN
ejpam-5645	203	37	and	and	CCONJ
ejpam-5645	203	38	g1	g1	PROPN
ejpam-5645	203	39	=	=	SYM
ejpam-5645	203	40	(	(	PUNCT
ejpam-5645	203	41	⊕∞	⊕∞	PROPN
ejpam-5645	203	42	k=1z(p∞))k	k=1z(p∞))k	PROPN
ejpam-5645	203	43	and	and	CCONJ
ejpam-5645	203	44	we	we	PRON
ejpam-5645	203	45	consider	consider	VERB
ejpam-5645	203	46	now	now	ADV
ejpam-5645	203	47	,	,	PUNCT
ejpam-5645	203	48	ϕ	ϕ	PROPN
ejpam-5645	203	49	:	:	PUNCT
ejpam-5645	203	50	g1	g1	VERB
ejpam-5645	203	51	−→	−→	NOUN
ejpam-5645	203	52	g1	g1	PROPN
ejpam-5645	203	53	x	x	PUNCT
ejpam-5645	204	1	=	=	PUNCT
ejpam-5645	204	2	∑n0	∑n0	ADJ
ejpam-5645	205	1	k=1	k=1	PROPN
ejpam-5645	205	2	xk	xk	PROPN
ejpam-5645	206	1	7−→	7−→	PROPN
ejpam-5645	206	2	∑n0−1	∑n0−1	PROPN
ejpam-5645	206	3	k=1	k=1	PROPN
ejpam-5645	206	4	yk	yk	PROPN
ejpam-5645	206	5	with	with	ADP
ejpam-5645	206	6	xk	xk	PROPN
ejpam-5645	206	7	,	,	PUNCT
ejpam-5645	206	8	yk	yk	PROPN
ejpam-5645	206	9	∈	∈	PROPN
ejpam-5645	206	10	(	(	PUNCT
ejpam-5645	206	11	z(p∞))k	z(p∞))k	PROPN
ejpam-5645	206	12	,	,	PUNCT
ejpam-5645	206	13	yk	yk	PROPN
ejpam-5645	206	14	=	=	PUNCT
ejpam-5645	206	15	xk+1	xk+1	PROPN
ejpam-5645	206	16	,	,	PUNCT
ejpam-5645	206	17	yn0	yn0	NOUN
ejpam-5645	206	18	=	=	NOUN
ejpam-5645	206	19	0	0	X
ejpam-5645	206	20	.	.	PUNCT
ejpam-5645	207	1	it	it	PRON
ejpam-5645	207	2	is	be	AUX
ejpam-5645	207	3	clear	clear	ADJ
ejpam-5645	207	4	that	that	SCONJ
ejpam-5645	207	5	ϕ	ϕ	NOUN
ejpam-5645	207	6	is	be	AUX
ejpam-5645	207	7	a	a	DET
ejpam-5645	207	8	surjective	surjective	ADJ
ejpam-5645	207	9	endomorphism	endomorphism	NOUN
ejpam-5645	207	10	and	and	CCONJ
ejpam-5645	207	11	ker(ϕ	ker(ϕ	PROPN
ejpam-5645	207	12	)	)	PUNCT
ejpam-5645	207	13	=	=	SYM
ejpam-5645	207	14	z(p∞)1	z(p∞)1	X
ejpam-5645	207	15	=	=	SYM
ejpam-5645	207	16	z(p∞	z(p∞	PROPN
ejpam-5645	207	17	)	)	PUNCT
ejpam-5645	207	18	,	,	PUNCT
ejpam-5645	207	19	we	we	PRON
ejpam-5645	207	20	can	can	AUX
ejpam-5645	207	21	write	write	VERB
ejpam-5645	207	22	g1	g1	PROPN
ejpam-5645	207	23	=	=	SYM
ejpam-5645	207	24	z(p∞	z(p∞	PROPN
ejpam-5645	207	25	)	)	PUNCT
ejpam-5645	207	26	⊕	⊕	PROPN
ejpam-5645	207	27	(	(	PUNCT
ejpam-5645	207	28	⊕∞	⊕∞	PROPN
ejpam-5645	207	29	i=2z(p∞))i	i=2z(p∞))i	PROPN
ejpam-5645	207	30	⊂	⊂	PROPN
ejpam-5645	207	31	ker(ϕ	ker(ϕ	PROPN
ejpam-5645	207	32	)	)	PUNCT
ejpam-5645	207	33	⊕	⊕	PROPN
ejpam-5645	207	34	(	(	PUNCT
ejpam-5645	207	35	⊕∞	⊕∞	PROPN
ejpam-5645	207	36	i=2z(p∞))i	i=2z(p∞))i	PROPN
ejpam-5645	207	37	⊂	⊂	PROPN
ejpam-5645	207	38	g1	g1	PROPN
ejpam-5645	207	39	,	,	PUNCT
ejpam-5645	207	40	then	then	ADV
ejpam-5645	207	41	ker(ϕ	ker(ϕ	PROPN
ejpam-5645	207	42	)	)	PUNCT
ejpam-5645	207	43	⊕	⊕	PROPN
ejpam-5645	207	44	(	(	PUNCT
ejpam-5645	207	45	⊕∞	⊕∞	NOUN
ejpam-5645	207	46	i=2z(p∞)i	i=2z(p∞)i	NOUN
ejpam-5645	207	47	)	)	PUNCT
ejpam-5645	208	1	=	=	VERB
ejpam-5645	208	2	g1	g1	NOUN
ejpam-5645	208	3	and	and	CCONJ
ejpam-5645	208	4	since	since	SCONJ
ejpam-5645	208	5	g	g	PROPN
ejpam-5645	208	6	is	be	AUX
ejpam-5645	208	7	a	a	DET
ejpam-5645	208	8	generalized	generalized	ADJ
ejpam-5645	208	9	hereditarily	hereditarily	ADJ
ejpam-5645	208	10	hopfian	hopfian	ADJ
ejpam-5645	208	11	group	group	NOUN
ejpam-5645	208	12	,	,	PUNCT
ejpam-5645	208	13	then	then	ADV
ejpam-5645	208	14	by	by	ADP
ejpam-5645	208	15	lemma	lemma	PROPN
ejpam-5645	208	16	1	1	NUM
ejpam-5645	208	17	,	,	PUNCT
ejpam-5645	208	18	g1	g1	PROPN
ejpam-5645	208	19	is	be	AUX
ejpam-5645	208	20	also	also	ADV
ejpam-5645	208	21	generalized	generalize	VERB
ejpam-5645	208	22	hereditarily	hereditarily	ADJ
ejpam-5645	208	23	hopfian	hopfian	ADJ
ejpam-5645	208	24	group	group	NOUN
ejpam-5645	208	25	,	,	PUNCT
ejpam-5645	208	26	then	then	ADV
ejpam-5645	208	27	ker(ϕ	ker(ϕ	PROPN
ejpam-5645	208	28	)	)	PUNCT
ejpam-5645	208	29	≪	≪	VERB
ejpam-5645	208	30	g	g	NOUN
ejpam-5645	208	31	,	,	PUNCT
ejpam-5645	208	32	thus	thus	ADV
ejpam-5645	208	33	g1	g1	X
ejpam-5645	208	34	=	=	SYM
ejpam-5645	208	35	(	(	PUNCT
ejpam-5645	208	36	⊕∞	⊕∞	PROPN
ejpam-5645	208	37	i=2z(p∞))i	i=2z(p∞))i	PROPN
ejpam-5645	208	38	,	,	PUNCT
ejpam-5645	208	39	which	which	PRON
ejpam-5645	208	40	is	be	AUX
ejpam-5645	208	41	absurd	absurd	ADJ
ejpam-5645	208	42	,	,	PUNCT
ejpam-5645	208	43	therefore	therefore	ADV
ejpam-5645	208	44	card(ip	card(ip	ADJ
ejpam-5645	208	45	)	)	PUNCT
ejpam-5645	208	46	<	<	X
ejpam-5645	208	47	∞.	∞.	PROPN
ejpam-5645	208	48	•	•	ADV
ejpam-5645	208	49	conversely	conversely	ADV
ejpam-5645	208	50	:	:	PUNCT
ejpam-5645	208	51	⇐	⇐	ADJ
ejpam-5645	208	52	)	)	PUNCT
ejpam-5645	208	53	let	let	VERB
ejpam-5645	208	54	g	g	NOUN
ejpam-5645	208	55	=	=	VERB
ejpam-5645	208	56	⊕n	⊕n	NOUN
ejpam-5645	208	57	i=1	i=1	PROPN
ejpam-5645	208	58	z(p∞	z(p∞	PROPN
ejpam-5645	208	59	)	)	PUNCT
ejpam-5645	208	60	be	be	AUX
ejpam-5645	208	61	a	a	DET
ejpam-5645	208	62	divisible	divisible	ADJ
ejpam-5645	208	63	p−group	p−group	NOUN
ejpam-5645	208	64	,	,	PUNCT
ejpam-5645	208	65	and	and	CCONJ
ejpam-5645	208	66	let	let	VERB
ejpam-5645	208	67	g1	g1	PROPN
ejpam-5645	208	68	be	be	AUX
ejpam-5645	208	69	a	a	DET
ejpam-5645	208	70	subgroup	subgroup	NOUN
ejpam-5645	208	71	of	of	ADP
ejpam-5645	208	72	g.	g.	PROPN
ejpam-5645	208	73	now	now	ADV
ejpam-5645	208	74	,	,	PUNCT
ejpam-5645	208	75	we	we	PRON
ejpam-5645	208	76	aim	aim	VERB
ejpam-5645	208	77	to	to	PART
ejpam-5645	208	78	show	show	VERB
ejpam-5645	208	79	that	that	SCONJ
ejpam-5645	208	80	g1	g1	PROPN
ejpam-5645	208	81	is	be	AUX
ejpam-5645	208	82	generalized	generalized	ADJ
ejpam-5645	208	83	hopfian	hopfian	NOUN
ejpam-5645	208	84	,	,	PUNCT
ejpam-5645	208	85	and	and	CCONJ
ejpam-5645	208	86	for	for	ADP
ejpam-5645	208	87	this	this	PRON
ejpam-5645	208	88	,	,	PUNCT
ejpam-5645	208	89	we	we	PRON
ejpam-5645	208	90	need	need	VERB
ejpam-5645	208	91	to	to	PART
ejpam-5645	208	92	discuss	discuss	VERB
ejpam-5645	208	93	the	the	DET
ejpam-5645	208	94	two	two	NUM
ejpam-5645	208	95	possible	possible	ADJ
ejpam-5645	208	96	following	following	ADJ
ejpam-5645	208	97	cases	case	NOUN
ejpam-5645	208	98	.	.	PUNCT
ejpam-5645	209	1	first	first	ADJ
ejpam-5645	209	2	case	case	NOUN
ejpam-5645	209	3	.	.	PUNCT
ejpam-5645	210	1	let	let	AUX
ejpam-5645	210	2	assume	assume	VERB
ejpam-5645	210	3	that	that	SCONJ
ejpam-5645	210	4	g1	g1	PROPN
ejpam-5645	210	5	=	=	PROPN
ejpam-5645	210	6	⊕n0	⊕n0	PROPN
ejpam-5645	210	7	i=1	i=1	PROPN
ejpam-5645	210	8	z(p∞	z(p∞	PROPN
ejpam-5645	210	9	)	)	PUNCT
ejpam-5645	210	10	,	,	PUNCT
ejpam-5645	210	11	where	where	SCONJ
ejpam-5645	210	12	n0	n0	PROPN
ejpam-5645	210	13	≤	≤	PROPN
ejpam-5645	210	14	n.	n.	NOUN
ejpam-5645	210	15	consider	consider	VERB
ejpam-5645	210	16	the	the	DET
ejpam-5645	210	17	epimorphism	epimorphism	NOUN
ejpam-5645	210	18	φ	φ	NOUN
ejpam-5645	210	19	:	:	PUNCT
ejpam-5645	210	20	g1	g1	PROPN
ejpam-5645	210	21	→	→	SYM
ejpam-5645	210	22	g1	g1	PROPN
ejpam-5645	210	23	as	as	SCONJ
ejpam-5645	210	24	we	we	PRON
ejpam-5645	210	25	have	have	AUX
ejpam-5645	210	26	recalled	recall	VERB
ejpam-5645	210	27	in	in	ADP
ejpam-5645	210	28	the	the	DET
ejpam-5645	210	29	introduction	introduction	NOUN
ejpam-5645	210	30	of	of	ADP
ejpam-5645	210	31	this	this	DET
ejpam-5645	210	32	section	section	NOUN
ejpam-5645	210	33	,	,	PUNCT
ejpam-5645	210	34	it	it	PRON
ejpam-5645	210	35	is	be	AUX
ejpam-5645	210	36	known	know	VERB
ejpam-5645	210	37	that	that	SCONJ
ejpam-5645	210	38	z(p∞	z(p∞	PROPN
ejpam-5645	210	39	)	)	PUNCT
ejpam-5645	211	1	=	=	NOUN
ejpam-5645	211	2	⋃∞	⋃∞	ADP
ejpam-5645	211	3	n=1⟨ci	n=1⟨ci	PROPN
ejpam-5645	211	4	,	,	PUNCT
ejpam-5645	211	5	n⟩	n⟩	PROPN
ejpam-5645	211	6	,	,	PUNCT
ejpam-5645	211	7	where	where	SCONJ
ejpam-5645	211	8	ord(ci	ord(ci	NOUN
ejpam-5645	211	9	,	,	PUNCT
ejpam-5645	211	10	n	n	CCONJ
ejpam-5645	211	11	)	)	PUNCT
ejpam-5645	211	12	=	=	SYM
ejpam-5645	211	13	pn	pn	NOUN
ejpam-5645	211	14	,	,	PUNCT
ejpam-5645	211	15	and	and	CCONJ
ejpam-5645	211	16	p(ci	p(ci	NOUN
ejpam-5645	211	17	,	,	PUNCT
ejpam-5645	211	18	n+1	n+1	NOUN
ejpam-5645	211	19	)	)	PUNCT
ejpam-5645	211	20	=	=	SYM
ejpam-5645	211	21	ci	ci	PROPN
ejpam-5645	211	22	,	,	PUNCT
ejpam-5645	211	23	n.	n.	NOUN
ejpam-5645	211	24	for	for	ADP
ejpam-5645	211	25	ci,1	ci,1	PROPN
ejpam-5645	211	26	∈	∈	PROPN
ejpam-5645	211	27	g1	g1	NOUN
ejpam-5645	211	28	,	,	PUNCT
ejpam-5645	211	29	there	there	PRON
ejpam-5645	211	30	exists	exist	VERB
ejpam-5645	211	31	ti,1	ti,1	VERB
ejpam-5645	211	32	∈	∈	PROPN
ejpam-5645	211	33	g1	g1	NOUN
ejpam-5645	211	34	such	such	ADJ
ejpam-5645	211	35	that	that	DET
ejpam-5645	211	36	φ(ti,1	φ(ti,1	NOUN
ejpam-5645	211	37	)	)	PUNCT
ejpam-5645	211	38	=	=	SYM
ejpam-5645	212	1	ci,1	ci,1	PROPN
ejpam-5645	212	2	,	,	PUNCT
ejpam-5645	212	3	because	because	SCONJ
ejpam-5645	212	4	φ	φ	PROPN
ejpam-5645	212	5	is	be	AUX
ejpam-5645	212	6	an	an	DET
ejpam-5645	212	7	epimorphism	epimorphism	NOUN
ejpam-5645	212	8	of	of	ADP
ejpam-5645	212	9	g1	g1	PROPN
ejpam-5645	212	10	.	.	PUNCT
ejpam-5645	213	1	since	since	SCONJ
ejpam-5645	213	2	p(ti,2	p(ti,2	NUM
ejpam-5645	213	3	)	)	PUNCT
ejpam-5645	214	1	=	=	PRON
ejpam-5645	214	2	ti,1	ti,1	PROPN
ejpam-5645	214	3	,	,	PUNCT
ejpam-5645	214	4	the	the	DET
ejpam-5645	214	5	subgroup	subgroup	NOUN
ejpam-5645	214	6	⋃∞	⋃∞	PUNCT
ejpam-5645	214	7	k=1⟨ti	k=1⟨ti	PROPN
ejpam-5645	214	8	,	,	PUNCT
ejpam-5645	214	9	k⟩	k⟩	NOUN
ejpam-5645	214	10	is	be	AUX
ejpam-5645	214	11	a	a	DET
ejpam-5645	214	12	divisible	divisible	ADJ
ejpam-5645	214	13	p−group	p−group	NOUN
ejpam-5645	214	14	.	.	PUNCT
ejpam-5645	215	1	this	this	PRON
ejpam-5645	215	2	implies	imply	VERB
ejpam-5645	215	3	that	that	SCONJ
ejpam-5645	215	4	,	,	PUNCT
ejpam-5645	215	5	n0⊕	n0⊕	PROPN
ejpam-5645	215	6	i=1	i=1	PROPN
ejpam-5645	215	7	∞⋃	∞⋃	PROPN
ejpam-5645	215	8	k=1	k=1	PUNCT
ejpam-5645	215	9	⟨ti	⟨ti	X
ejpam-5645	215	10	,	,	PUNCT
ejpam-5645	215	11	k⟩	k⟩	NOUN
ejpam-5645	215	12	=	=	PUNCT
ejpam-5645	215	13	n0⊕	n0⊕	PROPN
ejpam-5645	215	14	i=1	i=1	PROPN
ejpam-5645	215	15	z(p∞	z(p∞	PROPN
ejpam-5645	215	16	)	)	PUNCT
ejpam-5645	215	17	=	=	SYM
ejpam-5645	215	18	g1	g1	PROPN
ejpam-5645	215	19	.	.	PUNCT
ejpam-5645	216	1	now	now	ADV
ejpam-5645	216	2	,	,	PUNCT
ejpam-5645	216	3	let	let	VERB
ejpam-5645	216	4	us	we	PRON
ejpam-5645	216	5	check	check	VERB
ejpam-5645	216	6	that	that	PRON
ejpam-5645	216	7	ker(φ	ker(φ	PROPN
ejpam-5645	216	8	)	)	PUNCT
ejpam-5645	216	9	≪	≪	VERB
ejpam-5645	216	10	g1	g1	NOUN
ejpam-5645	216	11	or	or	CCONJ
ejpam-5645	216	12	g1	g1	NOUN
ejpam-5645	216	13	=	=	SYM
ejpam-5645	216	14	g2	g2	PROPN
ejpam-5645	216	15	,	,	PUNCT
ejpam-5645	216	16	such	such	ADJ
ejpam-5645	216	17	that	that	SCONJ
ejpam-5645	216	18	g1	g1	PROPN
ejpam-5645	216	19	=	=	PUNCT
ejpam-5645	216	20	ker(φ	ker(φ	X
ejpam-5645	216	21	)	)	PUNCT
ejpam-5645	217	1	+	+	NOUN
ejpam-5645	218	1	g2	g2	PROPN
ejpam-5645	218	2	.	.	PUNCT
ejpam-5645	219	1	10	10	NUM
ejpam-5645	219	2	of	of	ADP
ejpam-5645	219	3	13	13	NUM
ejpam-5645	219	4	we	we	PRON
ejpam-5645	219	5	have	have	AUX
ejpam-5645	219	6	ker(φ	ker(φ	VERB
ejpam-5645	219	7	)	)	PUNCT
ejpam-5645	219	8	=	=	SYM
ejpam-5645	219	9	⊕n0	⊕n0	PROPN
ejpam-5645	219	10	i=1⟨pti,1⟩	i=1⟨pti,1⟩	INTJ
ejpam-5645	220	1	because	because	SCONJ
ejpam-5645	220	2	,	,	PUNCT
ejpam-5645	220	3	φ	φ	PROPN
ejpam-5645	220	4	(	(	PUNCT
ejpam-5645	220	5	n0∑	n0∑	PROPN
ejpam-5645	220	6	i=1	i=1	PROPN
ejpam-5645	220	7	miti	miti	PROPN
ejpam-5645	220	8	,	,	PUNCT
ejpam-5645	220	9	k	k	PROPN
ejpam-5645	220	10	)	)	PUNCT
ejpam-5645	221	1	=	=	SYM
ejpam-5645	221	2	n0∑	n0∑	PROPN
ejpam-5645	221	3	i=1	i=1	PROPN
ejpam-5645	221	4	miφ(ti	miφ(ti	PROPN
ejpam-5645	221	5	,	,	PUNCT
ejpam-5645	221	6	k	k	NOUN
ejpam-5645	221	7	)	)	PUNCT
ejpam-5645	222	1	=	=	SYM
ejpam-5645	222	2	n0∑	n0∑	PROPN
ejpam-5645	222	3	i=1	i=1	PROPN
ejpam-5645	222	4	mici	mici	PROPN
ejpam-5645	222	5	,	,	PUNCT
ejpam-5645	222	6	k	k	PROPN
ejpam-5645	222	7	=	=	PUNCT
ejpam-5645	222	8	0	0	PROPN
ejpam-5645	222	9	.	.	PUNCT
ejpam-5645	223	1	this	this	PRON
ejpam-5645	223	2	implies	imply	VERB
ejpam-5645	223	3	that	that	SCONJ
ejpam-5645	223	4	mici	mici	PROPN
ejpam-5645	223	5	,	,	PUNCT
ejpam-5645	223	6	k	k	PROPN
ejpam-5645	223	7	=	=	PUNCT
ejpam-5645	223	8	0	0	NUM
ejpam-5645	223	9	for	for	ADP
ejpam-5645	223	10	1	1	NUM
ejpam-5645	223	11	≤	≤	NUM
ejpam-5645	223	12	i	i	PROPN
ejpam-5645	223	13	≤	≤	PROPN
ejpam-5645	223	14	n0	n0	NUM
ejpam-5645	223	15	.	.	PUNCT
ejpam-5645	224	1	hence	hence	ADV
ejpam-5645	224	2	,	,	PUNCT
ejpam-5645	224	3	p	p	PROPN
ejpam-5645	224	4	k	k	PROPN
ejpam-5645	224	5	|	|	PROPN
ejpam-5645	224	6	mi	mi	PROPN
ejpam-5645	224	7	,	,	PUNCT
ejpam-5645	224	8	so	so	ADV
ejpam-5645	224	9	mi	mi	PROPN
ejpam-5645	224	10	=	=	PROPN
ejpam-5645	224	11	pkm′	pkm′	PROPN
ejpam-5645	224	12	i.	i.	NOUN
ejpam-5645	224	13	therefore	therefore	ADV
ejpam-5645	224	14	,	,	PUNCT
ejpam-5645	224	15	miti	miti	PROPN
ejpam-5645	224	16	,	,	PUNCT
ejpam-5645	224	17	k	k	PROPN
ejpam-5645	224	18	=	=	PUNCT
ejpam-5645	224	19	m′	m′	X
ejpam-5645	224	20	ip	ip	PRON
ejpam-5645	224	21	kti	kti	PROPN
ejpam-5645	224	22	,	,	PUNCT
ejpam-5645	224	23	k	k	NOUN
ejpam-5645	224	24	=	=	PUNCT
ejpam-5645	224	25	m′	m′	NOUN
ejpam-5645	224	26	ipti,1	ipti,1	NOUN
ejpam-5645	224	27	.	.	PUNCT
ejpam-5645	225	1	we	we	PRON
ejpam-5645	225	2	define	define	VERB
ejpam-5645	225	3	pm	pm	NOUN
ejpam-5645	225	4	=	=	SYM
ejpam-5645	225	5	max(ord(pti,1	max(ord(pti,1	NOUN
ejpam-5645	225	6	)	)	PUNCT
ejpam-5645	225	7	,	,	PUNCT
ejpam-5645	225	8	1	1	NUM
ejpam-5645	225	9	≤	≤	NUM
ejpam-5645	225	10	i	i	PROPN
ejpam-5645	225	11	≤	≤	NOUN
ejpam-5645	225	12	n0	n0	NUM
ejpam-5645	225	13	)	)	PUNCT
ejpam-5645	225	14	.	.	PUNCT
ejpam-5645	226	1	then	then	ADV
ejpam-5645	226	2	,	,	PUNCT
ejpam-5645	226	3	for	for	ADP
ejpam-5645	226	4	every	every	DET
ejpam-5645	226	5	element	element	NOUN
ejpam-5645	226	6	h	h	NOUN
ejpam-5645	226	7	∈	∈	PROPN
ejpam-5645	226	8	ker(φ	ker(φ	PROPN
ejpam-5645	226	9	)	)	PUNCT
ejpam-5645	226	10	,	,	PUNCT
ejpam-5645	226	11	we	we	PRON
ejpam-5645	226	12	have	have	VERB
ejpam-5645	226	13	pmh	pmh	NOUN
ejpam-5645	226	14	=	=	SYM
ejpam-5645	226	15	0	0	X
ejpam-5645	226	16	.	.	PUNCT
ejpam-5645	227	1	now	now	ADV
ejpam-5645	227	2	let	let	VERB
ejpam-5645	227	3	ti	ti	PRON
ejpam-5645	227	4	,	,	PUNCT
ejpam-5645	227	5	k	k	PROPN
ejpam-5645	227	6	∈	∈	PROPN
ejpam-5645	227	7	g1	g1	PROPN
ejpam-5645	227	8	,	,	PUNCT
ejpam-5645	227	9	then	then	ADV
ejpam-5645	227	10	ti	ti	NOUN
ejpam-5645	227	11	,	,	PUNCT
ejpam-5645	227	12	k	k	NOUN
ejpam-5645	227	13	=	=	PRON
ejpam-5645	227	14	pm	pm	NOUN
ejpam-5645	227	15	ti	ti	NOUN
ejpam-5645	227	16	,	,	PUNCT
ejpam-5645	227	17	k+m	k+m	PROPN
ejpam-5645	227	18	,	,	PUNCT
ejpam-5645	227	19	and	and	CCONJ
ejpam-5645	227	20	also	also	ADV
ejpam-5645	227	21	ti	ti	PROPN
ejpam-5645	227	22	,	,	PUNCT
ejpam-5645	227	23	k+m	k+m	PROPN
ejpam-5645	227	24	=	=	SYM
ejpam-5645	227	25	h+	h+	X
ejpam-5645	227	26	g2	g2	PROPN
ejpam-5645	227	27	,	,	PUNCT
ejpam-5645	227	28	where	where	SCONJ
ejpam-5645	227	29	h	h	NOUN
ejpam-5645	227	30	∈	∈	PROPN
ejpam-5645	227	31	ker(φ	ker(φ	NOUN
ejpam-5645	227	32	)	)	PUNCT
ejpam-5645	227	33	and	and	CCONJ
ejpam-5645	227	34	g2	g2	PROPN
ejpam-5645	227	35	∈	∈	PROPN
ejpam-5645	227	36	g2	g2	PROPN
ejpam-5645	227	37	.	.	PUNCT
ejpam-5645	228	1	substituting	substituting	NOUN
ejpam-5645	228	2	,	,	PUNCT
ejpam-5645	228	3	we	we	PRON
ejpam-5645	228	4	have	have	AUX
ejpam-5645	228	5	pm	pm	NOUN
ejpam-5645	228	6	ti	ti	NOUN
ejpam-5645	228	7	,	,	PUNCT
ejpam-5645	228	8	k+m	k+m	PROPN
ejpam-5645	228	9	=	=	SYM
ejpam-5645	229	1	pmh+	pmh+	PROPN
ejpam-5645	229	2	pmg2	pmg2	NOUN
ejpam-5645	229	3	.	.	PUNCT
ejpam-5645	230	1	which	which	PRON
ejpam-5645	230	2	implies	imply	VERB
ejpam-5645	230	3	that	that	SCONJ
ejpam-5645	230	4	ti	ti	NOUN
ejpam-5645	230	5	,	,	PUNCT
ejpam-5645	230	6	k	k	NOUN
ejpam-5645	230	7	=	=	PRON
ejpam-5645	230	8	pm	pm	NOUN
ejpam-5645	230	9	ti	ti	NOUN
ejpam-5645	230	10	,	,	PUNCT
ejpam-5645	230	11	k+m	k+m	PROPN
ejpam-5645	230	12	=	=	SYM
ejpam-5645	230	13	pmh+	pmh+	ADJ
ejpam-5645	230	14	pmg2	pmg2	NOUN
ejpam-5645	230	15	=	=	SYM
ejpam-5645	230	16	pmg2	pmg2	NOUN
ejpam-5645	230	17	∈	∈	PROPN
ejpam-5645	230	18	g2	g2	PROPN
ejpam-5645	230	19	,	,	PUNCT
ejpam-5645	230	20	because	because	SCONJ
ejpam-5645	230	21	pmh	pmh	NOUN
ejpam-5645	230	22	=	=	NOUN
ejpam-5645	230	23	0	0	X
ejpam-5645	230	24	.	.	PUNCT
ejpam-5645	231	1	therefore	therefore	ADV
ejpam-5645	231	2	ti	ti	X
ejpam-5645	231	3	,	,	PUNCT
ejpam-5645	231	4	k	k	PROPN
ejpam-5645	231	5	∈	∈	PROPN
ejpam-5645	231	6	g2	g2	PROPN
ejpam-5645	231	7	.	.	PUNCT
ejpam-5645	232	1	since	since	SCONJ
ejpam-5645	232	2	ti	ti	X
ejpam-5645	232	3	,	,	PUNCT
ejpam-5645	232	4	k	k	PROPN
ejpam-5645	232	5	∈	∈	PROPN
ejpam-5645	232	6	g2	g2	PROPN
ejpam-5645	232	7	,	,	PUNCT
ejpam-5645	232	8	it	it	PRON
ejpam-5645	232	9	follows	follow	VERB
ejpam-5645	232	10	that	that	SCONJ
ejpam-5645	232	11	g1	g1	PROPN
ejpam-5645	232	12	⊆	⊆	NUM
ejpam-5645	232	13	g2	g2	NOUN
ejpam-5645	232	14	.	.	PUNCT
ejpam-5645	233	1	conversely	conversely	ADV
ejpam-5645	233	2	,	,	PUNCT
ejpam-5645	233	3	by	by	ADP
ejpam-5645	233	4	construction	construction	NOUN
ejpam-5645	233	5	,	,	PUNCT
ejpam-5645	233	6	g2	g2	PROPN
ejpam-5645	233	7	⊆	⊆	NUM
ejpam-5645	233	8	g1	g1	PROPN
ejpam-5645	233	9	.	.	PUNCT
ejpam-5645	234	1	thus	thus	ADV
ejpam-5645	234	2	,	,	PUNCT
ejpam-5645	234	3	g1	g1	PROPN
ejpam-5645	234	4	=	=	SYM
ejpam-5645	234	5	g2	g2	PROPN
ejpam-5645	234	6	.	.	PUNCT
ejpam-5645	235	1	consequently	consequently	ADV
ejpam-5645	235	2	,	,	PUNCT
ejpam-5645	235	3	g1	g1	PROPN
ejpam-5645	235	4	is	be	AUX
ejpam-5645	235	5	generalized	generalized	ADJ
ejpam-5645	235	6	hopfian	hopfian	ADJ
ejpam-5645	235	7	.	.	PUNCT
ejpam-5645	236	1	second	second	ADJ
ejpam-5645	236	2	case	case	NOUN
ejpam-5645	236	3	:	:	PUNCT
ejpam-5645	236	4	g1	g1	PROPN
ejpam-5645	236	5	=	=	PUNCT
ejpam-5645	236	6	d	d	PROPN
ejpam-5645	236	7	⊕	⊕	PROPN
ejpam-5645	236	8	c.	c.	PROPN
ejpam-5645	236	9	now	now	ADV
ejpam-5645	236	10	assume	assume	VERB
ejpam-5645	236	11	g1	g1	PROPN
ejpam-5645	236	12	<	<	X
ejpam-5645	236	13	g.	g.	PROPN
ejpam-5645	236	14	then	then	ADV
ejpam-5645	236	15	,	,	PUNCT
ejpam-5645	236	16	by	by	ADP
ejpam-5645	236	17	theorem	theorem	NOUN
ejpam-5645	236	18	21.3	21.3	NUM
ejpam-5645	236	19	[	[	NOUN
ejpam-5645	236	20	8	8	NUM
ejpam-5645	236	21	]	]	PUNCT
ejpam-5645	236	22	,	,	PUNCT
ejpam-5645	236	23	we	we	PRON
ejpam-5645	236	24	can	can	AUX
ejpam-5645	236	25	write	write	VERB
ejpam-5645	236	26	:	:	PUNCT
ejpam-5645	236	27	g1	g1	PROPN
ejpam-5645	236	28	=	=	PUNCT
ejpam-5645	237	1	d	d	PROPN
ejpam-5645	237	2	⊕	⊕	PROPN
ejpam-5645	237	3	c	c	PROPN
ejpam-5645	237	4	,	,	PUNCT
ejpam-5645	237	5	where	where	SCONJ
ejpam-5645	237	6	d	d	NOUN
ejpam-5645	237	7	is	be	AUX
ejpam-5645	237	8	a	a	DET
ejpam-5645	237	9	maximal	maximal	ADJ
ejpam-5645	237	10	divisible	divisible	ADJ
ejpam-5645	237	11	subgroup	subgroup	NOUN
ejpam-5645	237	12	and	and	CCONJ
ejpam-5645	237	13	c	c	PROPN
ejpam-5645	237	14	is	be	AUX
ejpam-5645	237	15	a	a	DET
ejpam-5645	237	16	reduced	reduce	VERB
ejpam-5645	237	17	subgroup	subgroup	NOUN
ejpam-5645	237	18	.	.	PUNCT
ejpam-5645	238	1	consider	consider	VERB
ejpam-5645	238	2	the	the	DET
ejpam-5645	238	3	surjective	surjective	ADJ
ejpam-5645	238	4	endomorphism	endomorphism	PROPN
ejpam-5645	238	5	φ	φ	PROPN
ejpam-5645	238	6	:	:	PUNCT
ejpam-5645	238	7	g1	g1	PROPN
ejpam-5645	238	8	→	→	SYM
ejpam-5645	238	9	g1	g1	PROPN
ejpam-5645	238	10	denote	denote	VERB
ejpam-5645	238	11	ϕd	ϕd	ADP
ejpam-5645	238	12	as	as	ADP
ejpam-5645	238	13	the	the	DET
ejpam-5645	238	14	restriction	restriction	NOUN
ejpam-5645	238	15	of	of	ADP
ejpam-5645	238	16	φ	φ	PROPN
ejpam-5645	238	17	to	to	ADP
ejpam-5645	238	18	d	d	PROPN
ejpam-5645	238	19	,	,	PUNCT
ejpam-5645	238	20	that	that	ADV
ejpam-5645	238	21	is	is	ADV
ejpam-5645	238	22	,	,	PUNCT
ejpam-5645	238	23	φd	φd	PUNCT
ejpam-5645	238	24	:	:	PUNCT
ejpam-5645	238	25	d	d	X
ejpam-5645	238	26	→	→	SYM
ejpam-5645	238	27	g1	g1	PROPN
ejpam-5645	238	28	φc	φc	NOUN
ejpam-5645	238	29	as	as	ADP
ejpam-5645	238	30	the	the	DET
ejpam-5645	238	31	restriction	restriction	NOUN
ejpam-5645	238	32	of	of	ADP
ejpam-5645	238	33	φ	φ	PROPN
ejpam-5645	238	34	to	to	ADP
ejpam-5645	238	35	c	c	PROPN
ejpam-5645	238	36	,	,	PUNCT
ejpam-5645	238	37	namely	namely	ADV
ejpam-5645	238	38	φc	φc	VERB
ejpam-5645	238	39	:	:	PUNCT
ejpam-5645	238	40	c	c	PROPN
ejpam-5645	238	41	→	→	SYM
ejpam-5645	238	42	g1	g1	PROPN
ejpam-5645	238	43	take	take	VERB
ejpam-5645	238	44	the	the	DET
ejpam-5645	238	45	projection	projection	NOUN
ejpam-5645	238	46	p1	p1	NOUN
ejpam-5645	238	47	as	as	ADP
ejpam-5645	238	48	,	,	PUNCT
ejpam-5645	238	49	p1	p1	PROPN
ejpam-5645	238	50	:	:	PUNCT
ejpam-5645	238	51	g1	g1	PROPN
ejpam-5645	238	52	→	→	SYM
ejpam-5645	238	53	c	c	X
ejpam-5645	238	54	c+	c+	VERB
ejpam-5645	238	55	d	d	PROPN
ejpam-5645	238	56	7→	7→	NUM
ejpam-5645	238	57	c	c	NOUN
ejpam-5645	238	58	and	and	CCONJ
ejpam-5645	238	59	the	the	DET
ejpam-5645	238	60	projection	projection	NOUN
ejpam-5645	238	61	p2	p2	PROPN
ejpam-5645	238	62	as	as	ADP
ejpam-5645	238	63	,	,	PUNCT
ejpam-5645	238	64	p2	p2	PROPN
ejpam-5645	238	65	:	:	PUNCT
ejpam-5645	238	66	g1	g1	PROPN
ejpam-5645	238	67	→	→	PUNCT
ejpam-5645	239	1	d	d	X
ejpam-5645	239	2	c+	c+	NOUN
ejpam-5645	239	3	d	d	X
ejpam-5645	239	4	7→	7→	NUM
ejpam-5645	239	5	d	d	NOUN
ejpam-5645	239	6	11	11	NUM
ejpam-5645	239	7	of	of	ADP
ejpam-5645	239	8	13	13	NUM
ejpam-5645	239	9	we	we	PRON
ejpam-5645	239	10	have	have	VERB
ejpam-5645	239	11	p1φc	p1φc	NOUN
ejpam-5645	239	12	:	:	PUNCT
ejpam-5645	239	13	c	c	X
ejpam-5645	239	14	→	→	SYM
ejpam-5645	239	15	c	c	PROPN
ejpam-5645	239	16	is	be	AUX
ejpam-5645	239	17	bijective	bijective	ADJ
ejpam-5645	239	18	.	.	PUNCT
ejpam-5645	240	1	in	in	ADP
ejpam-5645	240	2	fact	fact	NOUN
ejpam-5645	240	3	,	,	PUNCT
ejpam-5645	240	4	for	for	ADP
ejpam-5645	240	5	y	y	PROPN
ejpam-5645	240	6	∈	∈	PROPN
ejpam-5645	240	7	c	c	X
ejpam-5645	240	8	,	,	PUNCT
ejpam-5645	240	9	there	there	PRON
ejpam-5645	240	10	exists	exist	VERB
ejpam-5645	240	11	x	x	X
ejpam-5645	240	12	=	=	PUNCT
ejpam-5645	241	1	c	c	X
ejpam-5645	241	2	+	+	CCONJ
ejpam-5645	241	3	d	d	PROPN
ejpam-5645	241	4	∈	∈	PROPN
ejpam-5645	241	5	g1	g1	NOUN
ejpam-5645	241	6	,	,	PUNCT
ejpam-5645	241	7	with	with	ADP
ejpam-5645	241	8	c	c	PROPN
ejpam-5645	241	9	∈	∈	PROPN
ejpam-5645	241	10	c	c	PROPN
ejpam-5645	241	11	and	and	CCONJ
ejpam-5645	241	12	d	d	PROPN
ejpam-5645	241	13	∈	∈	PROPN
ejpam-5645	242	1	d	d	NOUN
ejpam-5645	242	2	,	,	PUNCT
ejpam-5645	242	3	such	such	ADJ
ejpam-5645	242	4	that	that	SCONJ
ejpam-5645	242	5	φ(x	φ(x	NOUN
ejpam-5645	242	6	)	)	PUNCT
ejpam-5645	242	7	=	=	SYM
ejpam-5645	242	8	y	y	PROPN
ejpam-5645	242	9	(	(	PUNCT
ejpam-5645	242	10	∗	∗	PROPN
ejpam-5645	242	11	)	)	PUNCT
ejpam-5645	242	12	.	.	PUNCT
ejpam-5645	243	1	expanding	expand	VERB
ejpam-5645	243	2	,	,	PUNCT
ejpam-5645	243	3	we	we	PRON
ejpam-5645	243	4	have	have	VERB
ejpam-5645	243	5	φ(c+	φ(c+	NUM
ejpam-5645	243	6	d	d	NOUN
ejpam-5645	243	7	)	)	PUNCT
ejpam-5645	243	8	=	=	SYM
ejpam-5645	243	9	y	y	PROPN
ejpam-5645	243	10	,	,	PUNCT
ejpam-5645	243	11	so	so	ADV
ejpam-5645	243	12	φ(c	φ(c	NOUN
ejpam-5645	243	13	)	)	PUNCT
ejpam-5645	244	1	+	+	NUM
ejpam-5645	244	2	φ(d	φ(d	NUM
ejpam-5645	244	3	)	)	PUNCT
ejpam-5645	245	1	=	=	PUNCT
ejpam-5645	245	2	y.	y.	NOUN
ejpam-5645	245	3	applying	apply	VERB
ejpam-5645	245	4	the	the	DET
ejpam-5645	245	5	projection	projection	NOUN
ejpam-5645	245	6	p1	p1	NOUN
ejpam-5645	245	7	,	,	PUNCT
ejpam-5645	245	8	this	this	PRON
ejpam-5645	245	9	gives	give	VERB
ejpam-5645	245	10	p1(φ(c	p1(φ(c	NUM
ejpam-5645	245	11	)	)	PUNCT
ejpam-5645	245	12	)	)	PUNCT
ejpam-5645	246	1	+	+	CCONJ
ejpam-5645	246	2	p1(φ(d	p1(φ(d	X
ejpam-5645	246	3	)	)	PUNCT
ejpam-5645	246	4	)	)	PUNCT
ejpam-5645	247	1	=	=	PUNCT
ejpam-5645	247	2	p1(y	p1(y	PROPN
ejpam-5645	247	3	)	)	PUNCT
ejpam-5645	247	4	.	.	PUNCT
ejpam-5645	248	1	since	since	SCONJ
ejpam-5645	248	2	p1(φ(d	p1(φ(d	NOUN
ejpam-5645	248	3	)	)	PUNCT
ejpam-5645	248	4	)	)	PUNCT
ejpam-5645	249	1	=	=	SYM
ejpam-5645	249	2	0	0	PUNCT
ejpam-5645	249	3	(	(	PUNCT
ejpam-5645	249	4	as	as	ADP
ejpam-5645	249	5	φ(d	φ(d	NUM
ejpam-5645	249	6	)	)	PUNCT
ejpam-5645	249	7	∈	∈	PROPN
ejpam-5645	249	8	d	d	NOUN
ejpam-5645	249	9	and	and	CCONJ
ejpam-5645	249	10	p1	p1	PROPN
ejpam-5645	249	11	maps	map	NOUN
ejpam-5645	249	12	d	d	X
ejpam-5645	249	13	to	to	ADP
ejpam-5645	249	14	0	0	NUM
ejpam-5645	249	15	)	)	PUNCT
ejpam-5645	249	16	and	and	CCONJ
ejpam-5645	249	17	p1(y	p1(y	PROPN
ejpam-5645	249	18	)	)	PUNCT
ejpam-5645	249	19	=	=	SYM
ejpam-5645	249	20	y	y	PROPN
ejpam-5645	249	21	,	,	PUNCT
ejpam-5645	249	22	it	it	PRON
ejpam-5645	249	23	follows	follow	VERB
ejpam-5645	249	24	that	that	SCONJ
ejpam-5645	249	25	p1(φ(c	p1(φ(c	NUM
ejpam-5645	249	26	)	)	PUNCT
ejpam-5645	249	27	)	)	PUNCT
ejpam-5645	250	1	=	=	SYM
ejpam-5645	250	2	y	y	PROPN
ejpam-5645	250	3	or	or	CCONJ
ejpam-5645	250	4	p1(φc)(c	p1(φc)(c	NUM
ejpam-5645	250	5	)	)	PUNCT
ejpam-5645	250	6	=	=	SYM
ejpam-5645	251	1	y.	y.	PROPN
ejpam-5645	251	2	thus	thus	ADV
ejpam-5645	251	3	,	,	PUNCT
ejpam-5645	251	4	there	there	PRON
ejpam-5645	251	5	exists	exist	VERB
ejpam-5645	251	6	an	an	DET
ejpam-5645	251	7	element	element	NOUN
ejpam-5645	251	8	c	c	PROPN
ejpam-5645	251	9	∈	∈	PROPN
ejpam-5645	251	10	c	c	NOUN
ejpam-5645	251	11	such	such	ADJ
ejpam-5645	251	12	that	that	DET
ejpam-5645	251	13	p1φc(c	p1φc(c	PROPN
ejpam-5645	251	14	)	)	PUNCT
ejpam-5645	252	1	=	=	SYM
ejpam-5645	252	2	y	y	PROPN
ejpam-5645	252	3	,	,	PUNCT
ejpam-5645	252	4	showing	show	VERB
ejpam-5645	252	5	that	that	SCONJ
ejpam-5645	252	6	p1φc	p1φc	NOUN
ejpam-5645	252	7	is	be	AUX
ejpam-5645	252	8	surjective	surjective	ADJ
ejpam-5645	252	9	.	.	PUNCT
ejpam-5645	253	1	since	since	SCONJ
ejpam-5645	253	2	c	c	PROPN
ejpam-5645	253	3	is	be	AUX
ejpam-5645	253	4	reduced	reduce	VERB
ejpam-5645	253	5	p−group	p−group	NOUN
ejpam-5645	253	6	and	and	CCONJ
ejpam-5645	253	7	of	of	ADP
ejpam-5645	253	8	finite	finite	PROPN
ejpam-5645	253	9	rank	rank	PROPN
ejpam-5645	253	10	,	,	PUNCT
ejpam-5645	253	11	it	it	PRON
ejpam-5645	253	12	is	be	AUX
ejpam-5645	253	13	finite	finite	ADJ
ejpam-5645	253	14	,	,	PUNCT
ejpam-5645	253	15	and	and	CCONJ
ejpam-5645	253	16	hence	hence	ADV
ejpam-5645	253	17	,	,	PUNCT
ejpam-5645	253	18	p1φc	p1φc	PROPN
ejpam-5645	253	19	is	be	AUX
ejpam-5645	253	20	bijective	bijective	ADJ
ejpam-5645	253	21	.	.	PUNCT
ejpam-5645	254	1	we	we	PRON
ejpam-5645	254	2	have	have	VERB
ejpam-5645	254	3	p2φd	p2φd	NOUN
ejpam-5645	254	4	is	be	AUX
ejpam-5645	254	5	surjective	surjective	ADJ
ejpam-5645	254	6	,	,	PUNCT
ejpam-5645	254	7	because	because	SCONJ
ejpam-5645	254	8	if	if	SCONJ
ejpam-5645	254	9	we	we	PRON
ejpam-5645	254	10	take	take	VERB
ejpam-5645	254	11	y	y	PROPN
ejpam-5645	254	12	∈	∈	PROPN
ejpam-5645	255	1	d	d	NOUN
ejpam-5645	255	2	,	,	PUNCT
ejpam-5645	255	3	then	then	ADV
ejpam-5645	255	4	there	there	PRON
ejpam-5645	255	5	exists	exist	VERB
ejpam-5645	255	6	x	x	X
ejpam-5645	255	7	∈	∈	PROPN
ejpam-5645	255	8	g1	g1	NOUN
ejpam-5645	255	9	,	,	PUNCT
ejpam-5645	255	10	with	with	ADP
ejpam-5645	255	11	x	x	SYM
ejpam-5645	255	12	=	=	PRON
ejpam-5645	255	13	c+	c+	NOUN
ejpam-5645	255	14	d	d	NOUN
ejpam-5645	255	15	,	,	PUNCT
ejpam-5645	255	16	c	c	PROPN
ejpam-5645	255	17	∈	∈	PROPN
ejpam-5645	255	18	c	c	NOUN
ejpam-5645	255	19	,	,	PUNCT
ejpam-5645	255	20	and	and	CCONJ
ejpam-5645	256	1	d	d	ADP
ejpam-5645	256	2	∈	∈	PROPN
ejpam-5645	256	3	d	d	NOUN
ejpam-5645	256	4	,	,	PUNCT
ejpam-5645	256	5	such	such	ADJ
ejpam-5645	256	6	that	that	SCONJ
ejpam-5645	256	7	φ(x	φ(x	NOUN
ejpam-5645	256	8	)	)	PUNCT
ejpam-5645	256	9	=	=	PUNCT
ejpam-5645	256	10	y.	y.	NOUN
ejpam-5645	256	11	applying	apply	VERB
ejpam-5645	256	12	the	the	DET
ejpam-5645	256	13	projection	projection	NOUN
ejpam-5645	256	14	p1	p1	NOUN
ejpam-5645	256	15	,	,	PUNCT
ejpam-5645	256	16	we	we	PRON
ejpam-5645	256	17	get	get	VERB
ejpam-5645	256	18	p1(φ(c+	p1(φ(c+	NOUN
ejpam-5645	256	19	d	d	NOUN
ejpam-5645	256	20	)	)	PUNCT
ejpam-5645	256	21	)	)	PUNCT
ejpam-5645	257	1	=	=	PUNCT
ejpam-5645	257	2	p1(y	p1(y	PROPN
ejpam-5645	257	3	)	)	PUNCT
ejpam-5645	257	4	.	.	PUNCT
ejpam-5645	258	1	expanding	expand	VERB
ejpam-5645	258	2	,	,	PUNCT
ejpam-5645	258	3	this	this	PRON
ejpam-5645	258	4	gives	give	VERB
ejpam-5645	258	5	p1(φ(c	p1(φ(c	NUM
ejpam-5645	258	6	)	)	PUNCT
ejpam-5645	258	7	)	)	PUNCT
ejpam-5645	259	1	+	+	CCONJ
ejpam-5645	259	2	p1(φ(d	p1(φ(d	X
ejpam-5645	259	3	)	)	PUNCT
ejpam-5645	259	4	)	)	PUNCT
ejpam-5645	260	1	=	=	PUNCT
ejpam-5645	260	2	p1(y	p1(y	PROPN
ejpam-5645	260	3	)	)	PUNCT
ejpam-5645	260	4	.	.	PUNCT
ejpam-5645	261	1	since	since	SCONJ
ejpam-5645	261	2	p1(φ(d	p1(φ(d	NOUN
ejpam-5645	261	3	)	)	PUNCT
ejpam-5645	261	4	)	)	PUNCT
ejpam-5645	262	1	=	=	SYM
ejpam-5645	262	2	0	0	PUNCT
ejpam-5645	262	3	(	(	PUNCT
ejpam-5645	262	4	as	as	ADP
ejpam-5645	262	5	φ(d	φ(d	NUM
ejpam-5645	262	6	)	)	PUNCT
ejpam-5645	262	7	∈	∈	PROPN
ejpam-5645	262	8	d	d	NOUN
ejpam-5645	262	9	and	and	CCONJ
ejpam-5645	262	10	p1	p1	PROPN
ejpam-5645	262	11	maps	map	NOUN
ejpam-5645	262	12	d	d	X
ejpam-5645	262	13	to	to	ADP
ejpam-5645	262	14	0	0	NUM
ejpam-5645	262	15	)	)	PUNCT
ejpam-5645	262	16	,	,	PUNCT
ejpam-5645	262	17	and	and	CCONJ
ejpam-5645	262	18	p1(y	p1(y	PROPN
ejpam-5645	262	19	)	)	PUNCT
ejpam-5645	263	1	=	=	SYM
ejpam-5645	263	2	0	0	PUNCT
ejpam-5645	263	3	(	(	PUNCT
ejpam-5645	263	4	because	because	SCONJ
ejpam-5645	263	5	y	y	PROPN
ejpam-5645	263	6	∈	∈	PROPN
ejpam-5645	263	7	d	d	PROPN
ejpam-5645	263	8	)	)	PUNCT
ejpam-5645	263	9	,	,	PUNCT
ejpam-5645	263	10	it	it	PRON
ejpam-5645	263	11	follows	follow	VERB
ejpam-5645	263	12	that	that	SCONJ
ejpam-5645	263	13	p1(φ(c	p1(φ(c	NUM
ejpam-5645	263	14	)	)	PUNCT
ejpam-5645	263	15	)	)	PUNCT
ejpam-5645	264	1	=	=	SYM
ejpam-5645	264	2	0	0	NUM
ejpam-5645	264	3	or	or	CCONJ
ejpam-5645	264	4	p1(φc(c	p1(φc(c	NOUN
ejpam-5645	264	5	)	)	PUNCT
ejpam-5645	264	6	)	)	PUNCT
ejpam-5645	265	1	=	=	PUNCT
ejpam-5645	265	2	0	0	X
ejpam-5645	265	3	.	.	PUNCT
ejpam-5645	266	1	because	because	SCONJ
ejpam-5645	266	2	now	now	ADV
ejpam-5645	266	3	p1φc	p1φc	VERB
ejpam-5645	266	4	is	be	AUX
ejpam-5645	266	5	bijective	bijective	ADJ
ejpam-5645	266	6	,	,	PUNCT
ejpam-5645	266	7	p1(φc(c	p1(φc(c	NOUN
ejpam-5645	266	8	)	)	PUNCT
ejpam-5645	266	9	)	)	PUNCT
ejpam-5645	267	1	=	=	SYM
ejpam-5645	267	2	0	0	NUM
ejpam-5645	267	3	implies	imply	VERB
ejpam-5645	267	4	c	c	NOUN
ejpam-5645	267	5	=	=	SYM
ejpam-5645	267	6	0	0	PROPN
ejpam-5645	267	7	.	.	PUNCT
ejpam-5645	268	1	thus	thus	ADV
ejpam-5645	268	2	,	,	PUNCT
ejpam-5645	268	3	x	x	PUNCT
ejpam-5645	268	4	=	=	SYM
ejpam-5645	268	5	d	d	PROPN
ejpam-5645	268	6	,	,	PUNCT
ejpam-5645	268	7	and	and	CCONJ
ejpam-5645	268	8	applying	apply	VERB
ejpam-5645	268	9	the	the	DET
ejpam-5645	268	10	projection	projection	NOUN
ejpam-5645	268	11	p2	p2	NOUN
ejpam-5645	268	12	to	to	ADP
ejpam-5645	268	13	(	(	PUNCT
ejpam-5645	268	14	∗	∗	NOUN
ejpam-5645	268	15	)	)	PUNCT
ejpam-5645	268	16	,	,	PUNCT
ejpam-5645	268	17	we	we	PRON
ejpam-5645	268	18	obtain	obtain	VERB
ejpam-5645	268	19	p2φ(d	p2φ(d	PROPN
ejpam-5645	268	20	)	)	PUNCT
ejpam-5645	268	21	=	=	PUNCT
ejpam-5645	269	1	p2(y	p2(y	ADJ
ejpam-5645	269	2	)	)	PUNCT
ejpam-5645	269	3	,	,	PUNCT
ejpam-5645	269	4	or	or	CCONJ
ejpam-5645	269	5	p2φd(d	p2φd(d	PROPN
ejpam-5645	269	6	)	)	PUNCT
ejpam-5645	269	7	=	=	SYM
ejpam-5645	269	8	y	y	PROPN
ejpam-5645	269	9	,	,	PUNCT
ejpam-5645	269	10	so	so	SCONJ
ejpam-5645	269	11	there	there	PRON
ejpam-5645	269	12	exists	exist	VERB
ejpam-5645	269	13	x	x	X
ejpam-5645	269	14	=	=	SYM
ejpam-5645	269	15	d	d	SYM
ejpam-5645	269	16	∈	∈	PROPN
ejpam-5645	270	1	d	d	ADP
ejpam-5645	270	2	such	such	ADJ
ejpam-5645	270	3	that	that	PRON
ejpam-5645	270	4	p2φd(d	p2φd(d	PROPN
ejpam-5645	270	5	)	)	PUNCT
ejpam-5645	270	6	=	=	SYM
ejpam-5645	270	7	y	y	PROPN
ejpam-5645	270	8	,	,	PUNCT
ejpam-5645	270	9	therefore	therefore	ADV
ejpam-5645	270	10	p2φd	p2φd	NOUN
ejpam-5645	270	11	is	be	AUX
ejpam-5645	270	12	surjective	surjective	ADJ
ejpam-5645	270	13	.	.	PUNCT
ejpam-5645	271	1	let	let	VERB
ejpam-5645	271	2	x	x	PUNCT
ejpam-5645	271	3	∈	∈	PROPN
ejpam-5645	271	4	ker(φ	ker(φ	NOUN
ejpam-5645	271	5	)	)	PUNCT
ejpam-5645	271	6	,	,	PUNCT
ejpam-5645	271	7	with	with	ADP
ejpam-5645	271	8	x	x	X
ejpam-5645	271	9	=	=	SYM
ejpam-5645	271	10	c	c	PROPN
ejpam-5645	271	11	+	+	CCONJ
ejpam-5645	271	12	d.	d.	PROPN
ejpam-5645	271	13	then	then	ADV
ejpam-5645	271	14	φ(c	φ(c	NOUN
ejpam-5645	271	15	+	+	CCONJ
ejpam-5645	272	1	d	d	X
ejpam-5645	272	2	)	)	PUNCT
ejpam-5645	272	3	=	=	SYM
ejpam-5645	272	4	0	0	NUM
ejpam-5645	272	5	,	,	PUNCT
ejpam-5645	272	6	or	or	CCONJ
ejpam-5645	272	7	φ(c	φ(c	NOUN
ejpam-5645	272	8	)	)	PUNCT
ejpam-5645	273	1	+	+	NUM
ejpam-5645	273	2	φ(d	φ(d	NUM
ejpam-5645	273	3	)	)	PUNCT
ejpam-5645	274	1	=	=	SYM
ejpam-5645	274	2	0	0	NUM
ejpam-5645	274	3	,	,	PUNCT
ejpam-5645	274	4	also	also	ADV
ejpam-5645	274	5	φc(c	φc(c	NUM
ejpam-5645	274	6	)	)	PUNCT
ejpam-5645	275	1	+	+	CCONJ
ejpam-5645	275	2	φ(d	φ(d	NUM
ejpam-5645	275	3	)	)	PUNCT
ejpam-5645	276	1	=	=	SYM
ejpam-5645	276	2	0	0	NUM
ejpam-5645	276	3	and	and	CCONJ
ejpam-5645	276	4	applying	apply	VERB
ejpam-5645	276	5	p1	p1	NOUN
ejpam-5645	276	6	,	,	PUNCT
ejpam-5645	276	7	we	we	PRON
ejpam-5645	276	8	have	have	VERB
ejpam-5645	276	9	p1φc(c	p1φc(c	PROPN
ejpam-5645	276	10	)	)	PUNCT
ejpam-5645	277	1	+	+	NUM
ejpam-5645	277	2	p1φ(d	p1φ(d	NOUN
ejpam-5645	277	3	)	)	PUNCT
ejpam-5645	277	4	=	=	PUNCT
ejpam-5645	277	5	0	0	NUM
ejpam-5645	277	6	⇐	⇐	ADJ
ejpam-5645	277	7	⇒	⇒	PROPN
ejpam-5645	277	8	p1φc(c	p1φc(c	PROPN
ejpam-5645	277	9	)	)	PUNCT
ejpam-5645	277	10	=	=	SYM
ejpam-5645	278	1	0	0	NUM
ejpam-5645	278	2	⇐	⇐	ADJ
ejpam-5645	278	3	⇒	⇒	NOUN
ejpam-5645	278	4	c	c	NOUN
ejpam-5645	279	1	=	=	SYM
ejpam-5645	279	2	0	0	PROPN
ejpam-5645	279	3	,	,	PUNCT
ejpam-5645	279	4	then	then	ADV
ejpam-5645	279	5	x	x	X
ejpam-5645	279	6	=	=	SYM
ejpam-5645	279	7	d	d	PROPN
ejpam-5645	279	8	(	(	PUNCT
ejpam-5645	279	9	∗	∗	NOUN
ejpam-5645	279	10	)	)	PUNCT
ejpam-5645	279	11	let	let	VERB
ejpam-5645	279	12	x	x	X
ejpam-5645	279	13	∈	∈	PROPN
ejpam-5645	279	14	ker(φ	ker(φ	NOUN
ejpam-5645	279	15	)	)	PUNCT
ejpam-5645	279	16	,	,	PUNCT
ejpam-5645	279	17	then	then	ADV
ejpam-5645	279	18	φ(x	φ(x	NOUN
ejpam-5645	279	19	)	)	PUNCT
ejpam-5645	279	20	=	=	SYM
ejpam-5645	279	21	0	0	NUM
ejpam-5645	279	22	,	,	PUNCT
ejpam-5645	279	23	or	or	CCONJ
ejpam-5645	279	24	φ(d	φ(d	NUM
ejpam-5645	279	25	)	)	PUNCT
ejpam-5645	280	1	=	=	SYM
ejpam-5645	280	2	0	0	NUM
ejpam-5645	280	3	,	,	PUNCT
ejpam-5645	280	4	because	because	SCONJ
ejpam-5645	280	5	x	x	PROPN
ejpam-5645	280	6	=	=	SYM
ejpam-5645	280	7	d	d	X
ejpam-5645	280	8	by	by	ADP
ejpam-5645	280	9	(	(	PUNCT
ejpam-5645	280	10	∗	∗	NOUN
ejpam-5645	280	11	)	)	PUNCT
ejpam-5645	280	12	and	and	CCONJ
ejpam-5645	280	13	applying	apply	VERB
ejpam-5645	280	14	p2	p2	NOUN
ejpam-5645	280	15	,	,	PUNCT
ejpam-5645	280	16	we	we	PRON
ejpam-5645	280	17	have	have	VERB
ejpam-5645	280	18	p2φ(d	p2φ(d	PROPN
ejpam-5645	280	19	)	)	PUNCT
ejpam-5645	280	20	=	=	SYM
ejpam-5645	280	21	0	0	NUM
ejpam-5645	280	22	or	or	CCONJ
ejpam-5645	280	23	p2φ(x	p2φ(x	PROPN
ejpam-5645	280	24	)	)	PUNCT
ejpam-5645	280	25	=	=	SYM
ejpam-5645	281	1	0	0	X
ejpam-5645	281	2	.	.	PUNCT
ejpam-5645	282	1	thus	thus	ADV
ejpam-5645	282	2	x	x	X
ejpam-5645	282	3	∈	∈	PROPN
ejpam-5645	282	4	ker(p2φ	ker(p2φ	PROPN
ejpam-5645	282	5	)	)	PUNCT
ejpam-5645	282	6	,	,	PUNCT
ejpam-5645	282	7	and	and	CCONJ
ejpam-5645	282	8	therefore	therefore	ADV
ejpam-5645	282	9	ker(φ	ker(φ	PROPN
ejpam-5645	282	10	)	)	PUNCT
ejpam-5645	282	11	=	=	SYM
ejpam-5645	282	12	ker(p2ϕ	ker(p2ϕ	PROPN
ejpam-5645	282	13	)	)	PUNCT
ejpam-5645	282	14	⊆	⊆	NUM
ejpam-5645	282	15	d.	d.	PROPN
ejpam-5645	282	16	now	now	ADV
ejpam-5645	282	17	,	,	PUNCT
ejpam-5645	282	18	let	let	VERB
ejpam-5645	282	19	us	we	PRON
ejpam-5645	282	20	show	show	VERB
ejpam-5645	282	21	that	that	SCONJ
ejpam-5645	282	22	g1	g1	PROPN
ejpam-5645	282	23	is	be	AUX
ejpam-5645	282	24	generalized	generalized	ADJ
ejpam-5645	282	25	hopfian	hopfian	NOUN
ejpam-5645	282	26	.	.	PUNCT
ejpam-5645	283	1	for	for	ADP
ejpam-5645	283	2	this	this	PRON
ejpam-5645	283	3	,	,	PUNCT
ejpam-5645	283	4	let	let	VERB
ejpam-5645	283	5	g1	g1	PROPN
ejpam-5645	283	6	=	=	SYM
ejpam-5645	283	7	g′+kerφ	g′+kerφ	PROPN
ejpam-5645	283	8	,	,	PUNCT
ejpam-5645	283	9	where	where	SCONJ
ejpam-5645	283	10	g′	g′	NOUN
ejpam-5645	283	11	=	=	PUNCT
ejpam-5645	284	1	c	c	NOUN
ejpam-5645	285	1	′	′	NOUN
ejpam-5645	285	2	⊕d′.	⊕d′.	NOUN
ejpam-5645	285	3	we	we	PRON
ejpam-5645	285	4	have	have	VERB
ejpam-5645	285	5	pmc	pmc	PROPN
ejpam-5645	285	6	⊕	⊕	PROPN
ejpam-5645	285	7	pmd	pmd	PROPN
ejpam-5645	285	8	=	=	SYM
ejpam-5645	285	9	pmc	pmc	PROPN
ejpam-5645	285	10	′	′	NUM
ejpam-5645	285	11	⊕	⊕	PROPN
ejpam-5645	285	12	pmd′	pmd′	PROPN
ejpam-5645	286	1	+	+	CCONJ
ejpam-5645	286	2	pm	pm	PROPN
ejpam-5645	286	3	(	(	PUNCT
ejpam-5645	286	4	kerφ	kerφ	PROPN
ejpam-5645	286	5	)	)	PUNCT
ejpam-5645	286	6	.	.	PUNCT
ejpam-5645	287	1	since	since	SCONJ
ejpam-5645	287	2	pm	pm	PROPN
ejpam-5645	287	3	(	(	PUNCT
ejpam-5645	287	4	kerφ	kerφ	PROPN
ejpam-5645	287	5	)	)	PUNCT
ejpam-5645	287	6	=	=	SYM
ejpam-5645	287	7	0	0	NUM
ejpam-5645	287	8	,	,	PUNCT
ejpam-5645	287	9	and	and	CCONJ
ejpam-5645	287	10	d	d	NOUN
ejpam-5645	287	11	and	and	CCONJ
ejpam-5645	287	12	d′	d′	PRON
ejpam-5645	287	13	are	be	AUX
ejpam-5645	287	14	divisible	divisible	ADJ
ejpam-5645	287	15	subgroups	subgroup	NOUN
ejpam-5645	287	16	,	,	PUNCT
ejpam-5645	287	17	it	it	PRON
ejpam-5645	287	18	follows	follow	VERB
ejpam-5645	287	19	that	that	SCONJ
ejpam-5645	287	20	pmd	pmd	NOUN
ejpam-5645	287	21	=	=	PUNCT
ejpam-5645	287	22	d	d	PROPN
ejpam-5645	287	23	and	and	CCONJ
ejpam-5645	287	24	pmd′	pmd′	PROPN
ejpam-5645	287	25	=	=	PUNCT
ejpam-5645	287	26	d′.	d′.	VERB
ejpam-5645	287	27	thus	thus	ADV
ejpam-5645	287	28	,	,	PUNCT
ejpam-5645	287	29	pmc	pmc	PROPN
ejpam-5645	287	30	⊕d	⊕d	NOUN
ejpam-5645	287	31	=	=	SYM
ejpam-5645	287	32	pmc	pmc	PROPN
ejpam-5645	287	33	′	′	NUM
ejpam-5645	287	34	⊕d′.	⊕d′.	PUNCT
ejpam-5645	287	35	because	because	SCONJ
ejpam-5645	287	36	d	d	PROPN
ejpam-5645	287	37	and	and	CCONJ
ejpam-5645	287	38	d′	d′	PRON
ejpam-5645	287	39	are	be	AUX
ejpam-5645	287	40	maximal	maximal	ADJ
ejpam-5645	287	41	divisible	divisible	ADJ
ejpam-5645	287	42	subgroups	subgroup	NOUN
ejpam-5645	287	43	,	,	PUNCT
ejpam-5645	287	44	we	we	PRON
ejpam-5645	287	45	have	have	VERB
ejpam-5645	287	46	d	d	NOUN
ejpam-5645	287	47	=	=	PUNCT
ejpam-5645	287	48	d′.	d′.	VERB
ejpam-5645	287	49	therefore	therefore	ADV
ejpam-5645	287	50	,	,	PUNCT
ejpam-5645	287	51	g1	g1	NOUN
ejpam-5645	287	52	=	=	PUNCT
ejpam-5645	287	53	g′	g′	PROPN
ejpam-5645	287	54	+	+	CCONJ
ejpam-5645	287	55	kerφ	kerφ	PROPN
ejpam-5645	287	56	,	,	PUNCT
ejpam-5645	287	57	with	with	ADP
ejpam-5645	287	58	kerφ	kerφ	PROPN
ejpam-5645	287	59	⊆	⊆	PROPN
ejpam-5645	287	60	d.	d.	PROPN
ejpam-5645	287	61	12	12	NUM
ejpam-5645	287	62	of	of	ADP
ejpam-5645	287	63	13	13	NUM
ejpam-5645	287	64	this	this	PRON
ejpam-5645	287	65	implies	imply	VERB
ejpam-5645	287	66	g1	g1	NOUN
ejpam-5645	287	67	=	=	SYM
ejpam-5645	287	68	g′	g′	PROPN
ejpam-5645	287	69	+	+	CCONJ
ejpam-5645	287	70	kerφ	kerφ	PROPN
ejpam-5645	287	71	⊆	⊆	NUM
ejpam-5645	287	72	g′	g′	NOUN
ejpam-5645	288	1	+	+	CCONJ
ejpam-5645	288	2	d	d	PROPN
ejpam-5645	288	3	⊆	⊆	NUM
ejpam-5645	288	4	g′	g′	NOUN
ejpam-5645	288	5	,	,	PUNCT
ejpam-5645	288	6	as	as	SCONJ
ejpam-5645	288	7	d	d	X
ejpam-5645	288	8	=	=	PUNCT
ejpam-5645	288	9	d′	d′	NUM
ejpam-5645	288	10	⊆	⊆	NUM
ejpam-5645	288	11	g′.	g′.	NOUN
ejpam-5645	288	12	hence	hence	ADV
ejpam-5645	288	13	,	,	PUNCT
ejpam-5645	288	14	g1	g1	VERB
ejpam-5645	288	15	⊆	⊆	NUM
ejpam-5645	288	16	g′	g′	NOUN
ejpam-5645	288	17	,	,	PUNCT
ejpam-5645	288	18	which	which	PRON
ejpam-5645	288	19	implies	imply	VERB
ejpam-5645	288	20	g1	g1	NOUN
ejpam-5645	288	21	=	=	SYM
ejpam-5645	288	22	g′.	g′.	PROPN
ejpam-5645	288	23	thus	thus	ADV
ejpam-5645	288	24	,	,	PUNCT
ejpam-5645	288	25	g1	g1	PROPN
ejpam-5645	288	26	is	be	AUX
ejpam-5645	288	27	generalized	generalized	ADJ
ejpam-5645	288	28	hopfian	hopfian	NOUN
ejpam-5645	288	29	.	.	PUNCT
ejpam-5645	289	1	finally	finally	ADV
ejpam-5645	289	2	,	,	PUNCT
ejpam-5645	289	3	g	g	PROPN
ejpam-5645	289	4	is	be	AUX
ejpam-5645	289	5	generalized	generalize	VERB
ejpam-5645	289	6	hereditarily	hereditarily	ADJ
ejpam-5645	289	7	hopfian	hopfian	ADJ
ejpam-5645	289	8	.	.	PUNCT
ejpam-5645	290	1	5	5	X
ejpam-5645	290	2	.	.	X
ejpam-5645	290	3	conclusion	conclusion	NOUN
ejpam-5645	290	4	in	in	ADP
ejpam-5645	290	5	the	the	DET
ejpam-5645	290	6	first	first	ADJ
ejpam-5645	290	7	two	two	NUM
ejpam-5645	290	8	theorems	theorem	NOUN
ejpam-5645	290	9	of	of	ADP
ejpam-5645	290	10	our	our	PRON
ejpam-5645	290	11	work	work	NOUN
ejpam-5645	290	12	,	,	PUNCT
ejpam-5645	290	13	we	we	PRON
ejpam-5645	290	14	extended	extend	VERB
ejpam-5645	290	15	the	the	DET
ejpam-5645	290	16	results	result	NOUN
ejpam-5645	290	17	of	of	ADP
ejpam-5645	290	18	the	the	DET
ejpam-5645	290	19	generalized	generalized	ADJ
ejpam-5645	290	20	hereditarily	hereditarily	ADJ
ejpam-5645	290	21	hopficity	hopficity	NOUN
ejpam-5645	290	22	property	property	NOUN
ejpam-5645	290	23	on	on	ADP
ejpam-5645	290	24	abelian	abelian	ADJ
ejpam-5645	290	25	groups	group	NOUN
ejpam-5645	290	26	within	within	ADP
ejpam-5645	290	27	the	the	DET
ejpam-5645	290	28	categories	category	NOUN
ejpam-5645	290	29	of	of	ADP
ejpam-5645	290	30	reduced	reduce	VERB
ejpam-5645	290	31	p−groups	p−group	NOUN
ejpam-5645	290	32	and	and	CCONJ
ejpam-5645	290	33	reduced	reduce	VERB
ejpam-5645	290	34	torsion	torsion	NOUN
ejpam-5645	290	35	groups	group	NOUN
ejpam-5645	290	36	.	.	PUNCT
ejpam-5645	291	1	as	as	ADP
ejpam-5645	291	2	for	for	ADP
ejpam-5645	291	3	the	the	DET
ejpam-5645	291	4	final	final	ADJ
ejpam-5645	291	5	part	part	NOUN
ejpam-5645	291	6	of	of	ADP
ejpam-5645	291	7	our	our	PRON
ejpam-5645	291	8	work	work	NOUN
ejpam-5645	291	9	,	,	PUNCT
ejpam-5645	291	10	we	we	PRON
ejpam-5645	291	11	succeeded	succeed	VERB
ejpam-5645	291	12	in	in	ADP
ejpam-5645	291	13	showing	show	VERB
ejpam-5645	291	14	in	in	ADP
ejpam-5645	291	15	a	a	DET
ejpam-5645	291	16	third	third	ADJ
ejpam-5645	291	17	theorem	theorem	NOUN
ejpam-5645	291	18	that	that	SCONJ
ejpam-5645	291	19	if	if	SCONJ
ejpam-5645	291	20	a	a	DET
ejpam-5645	291	21	group	group	NOUN
ejpam-5645	291	22	is	be	AUX
ejpam-5645	291	23	generalized	generalize	VERB
ejpam-5645	291	24	hereditarily	hereditarily	ADJ
ejpam-5645	291	25	hopfian	hopfian	NOUN
ejpam-5645	291	26	and	and	CCONJ
ejpam-5645	291	27	p	p	ADJ
ejpam-5645	291	28	-	-	PUNCT
ejpam-5645	291	29	divisible	divisible	ADJ
ejpam-5645	291	30	,	,	PUNCT
ejpam-5645	291	31	it	it	PRON
ejpam-5645	291	32	is	be	AUX
ejpam-5645	291	33	a	a	DET
ejpam-5645	291	34	finite	finite	ADJ
ejpam-5645	291	35	direct	direct	ADJ
ejpam-5645	291	36	sum	sum	NOUN
ejpam-5645	291	37	of	of	ADP
ejpam-5645	291	38	z(p∞	z(p∞	PROPN
ejpam-5645	291	39	)	)	PUNCT
ejpam-5645	291	40	.	.	PUNCT
ejpam-5645	292	1	as	as	ADP
ejpam-5645	292	2	a	a	DET
ejpam-5645	292	3	perspective	perspective	NOUN
ejpam-5645	292	4	,	,	PUNCT
ejpam-5645	292	5	one	one	PRON
ejpam-5645	292	6	would	would	AUX
ejpam-5645	292	7	think	think	VERB
ejpam-5645	292	8	about	about	ADP
ejpam-5645	292	9	the	the	DET
ejpam-5645	292	10	study	study	NOUN
ejpam-5645	292	11	of	of	ADP
ejpam-5645	292	12	such	such	ADJ
ejpam-5645	292	13	hopficity	hopficity	NOUN
ejpam-5645	292	14	properties	property	NOUN
ejpam-5645	292	15	but	but	CCONJ
ejpam-5645	292	16	now	now	ADV
ejpam-5645	292	17	in	in	ADP
ejpam-5645	292	18	the	the	DET
ejpam-5645	292	19	case	case	NOUN
ejpam-5645	292	20	of	of	ADP
ejpam-5645	292	21	torsion	torsion	NOUN
ejpam-5645	292	22	-	-	PUNCT
ejpam-5645	292	23	free	free	ADJ
ejpam-5645	292	24	group	group	NOUN
ejpam-5645	292	25	.	.	PUNCT
ejpam-5645	293	1	acknowledgements	acknowledgement	NOUN
ejpam-5645	293	2	a	a	DET
ejpam-5645	293	3	special	special	ADJ
ejpam-5645	293	4	thanks	thank	NOUN
ejpam-5645	293	5	to	to	ADP
ejpam-5645	293	6	the	the	DET
ejpam-5645	293	7	editors	editor	NOUN
ejpam-5645	293	8	professors	professor	NOUN
ejpam-5645	293	9	eyup	eyup	VERB
ejpam-5645	293	10	cetin	cetin	NOUN
ejpam-5645	293	11	and	and	CCONJ
ejpam-5645	293	12	baris	baris	PROPN
ejpam-5645	293	13	kiremitci	kiremitci	NOUN
ejpam-5645	293	14	.	.	PUNCT
ejpam-5645	294	1	we	we	PRON
ejpam-5645	294	2	would	would	AUX
ejpam-5645	294	3	also	also	ADV
ejpam-5645	294	4	like	like	VERB
ejpam-5645	294	5	to	to	PART
ejpam-5645	294	6	thank	thank	VERB
ejpam-5645	294	7	all	all	DET
ejpam-5645	294	8	the	the	DET
ejpam-5645	294	9	anonymous	anonymous	ADJ
ejpam-5645	294	10	referees	referee	NOUN
ejpam-5645	294	11	for	for	ADP
ejpam-5645	294	12	their	their	PRON
ejpam-5645	294	13	time	time	NOUN
ejpam-5645	294	14	,	,	PUNCT
ejpam-5645	294	15	effort	effort	NOUN
ejpam-5645	294	16	and	and	CCONJ
ejpam-5645	294	17	help	help	VERB
ejpam-5645	294	18	for	for	ADP
ejpam-5645	294	19	improving	improve	VERB
ejpam-5645	294	20	the	the	DET
ejpam-5645	294	21	content	content	NOUN
ejpam-5645	294	22	of	of	ADP
ejpam-5645	294	23	our	our	PRON
ejpam-5645	294	24	paper	paper	NOUN
ejpam-5645	294	25	.	.	PUNCT
ejpam-5645	295	1	references	reference	NOUN
ejpam-5645	295	2	[	[	X
ejpam-5645	295	3	1	1	X
ejpam-5645	295	4	]	]	PUNCT
ejpam-5645	295	5	s.	s.	PROPN
ejpam-5645	295	6	abdelalim	abdelalim	PROPN
ejpam-5645	295	7	.	.	PUNCT
ejpam-5645	296	1	characterization	characterization	NOUN
ejpam-5645	296	2	the	the	DET
ejpam-5645	296	3	strongly	strongly	ADV
ejpam-5645	296	4	co	co	ADJ
ejpam-5645	296	5	-	-	ADJ
ejpam-5645	296	6	hopfian	hopfian	ADJ
ejpam-5645	296	7	abelian	abelian	ADJ
ejpam-5645	296	8	groups	group	NOUN
ejpam-5645	296	9	in	in	ADP
ejpam-5645	296	10	the	the	DET
ejpam-5645	296	11	category	category	NOUN
ejpam-5645	296	12	of	of	ADP
ejpam-5645	296	13	abelian	abelian	ADJ
ejpam-5645	296	14	torsion	torsion	NOUN
ejpam-5645	296	15	groups	group	NOUN
ejpam-5645	296	16	.	.	PUNCT
ejpam-5645	297	1	journal	journal	PROPN
ejpam-5645	297	2	of	of	ADP
ejpam-5645	297	3	mathematical	mathematical	ADJ
ejpam-5645	297	4	analysis	analysis	NOUN
ejpam-5645	297	5	,	,	PUNCT
ejpam-5645	297	6	6(4	6(4	NUM
ejpam-5645	297	7	)	)	PUNCT
ejpam-5645	297	8	,	,	PUNCT
ejpam-5645	297	9	1	1	NUM
ejpam-5645	297	10	-	-	SYM
ejpam-5645	297	11	10	10	NUM
ejpam-5645	297	12	,	,	PUNCT
ejpam-5645	297	13	2015	2015	NUM
ejpam-5645	297	14	.	.	PUNCT
ejpam-5645	298	1	[	[	X
ejpam-5645	298	2	2	2	NUM
ejpam-5645	298	3	]	]	X
ejpam-5645	298	4	r.	r.	PROPN
ejpam-5645	298	5	baer	baer	PROPN
ejpam-5645	298	6	.	.	PUNCT
ejpam-5645	299	1	groups	group	NOUN
ejpam-5645	299	2	without	without	ADP
ejpam-5645	299	3	proper	proper	ADJ
ejpam-5645	299	4	isomorphic	isomorphic	ADJ
ejpam-5645	299	5	quotient	quotient	NOUN
ejpam-5645	299	6	groups	group	NOUN
ejpam-5645	299	7	.	.	PUNCT
ejpam-5645	300	1	bulletin	bulletin	NOUN
ejpam-5645	300	2	of	of	ADP
ejpam-5645	300	3	the	the	DET
ejpam-5645	300	4	american	american	PROPN
ejpam-5645	300	5	mathematical	mathematical	PROPN
ejpam-5645	300	6	society	society	NOUN
ejpam-5645	300	7	,	,	PUNCT
ejpam-5645	300	8	50(4	50(4	NUM
ejpam-5645	300	9	)	)	PUNCT
ejpam-5645	300	10	,	,	PUNCT
ejpam-5645	300	11	267	267	NUM
ejpam-5645	300	12	-	-	SYM
ejpam-5645	300	13	278	278	NUM
ejpam-5645	300	14	,	,	PUNCT
ejpam-5645	300	15	1944	1944	NUM
ejpam-5645	300	16	.	.	PUNCT
ejpam-5645	301	1	[	[	X
ejpam-5645	301	2	3	3	X
ejpam-5645	301	3	]	]	X
ejpam-5645	301	4	g.	g.	PROPN
ejpam-5645	301	5	baumslag	baumslag	PROPN
ejpam-5645	301	6	.	.	PUNCT
ejpam-5645	302	1	on	on	ADP
ejpam-5645	302	2	abelian	abelian	ADJ
ejpam-5645	302	3	hopfian	hopfian	ADJ
ejpam-5645	302	4	groups	group	NOUN
ejpam-5645	302	5	.	.	PUNCT
ejpam-5645	303	1	i.	i.	PROPN
ejpam-5645	303	2	mathematische	mathematische	PROPN
ejpam-5645	303	3	zeitschrift	zeitschrift	PROPN
ejpam-5645	303	4	,	,	PUNCT
ejpam-5645	303	5	78(1	78(1	NOUN
ejpam-5645	303	6	)	)	PUNCT
ejpam-5645	303	7	,	,	PUNCT
ejpam-5645	303	8	53	53	NUM
ejpam-5645	303	9	-	-	SYM
ejpam-5645	303	10	54	54	NUM
ejpam-5645	303	11	,	,	PUNCT
ejpam-5645	303	12	1962	1962	NUM
ejpam-5645	303	13	.	.	PUNCT
ejpam-5645	304	1	[	[	X
ejpam-5645	304	2	4	4	NUM
ejpam-5645	304	3	]	]	PUNCT
ejpam-5645	304	4	a.	a.	NOUN
ejpam-5645	304	5	corner	corner	NOUN
ejpam-5645	304	6	.	.	PUNCT
ejpam-5645	305	1	three	three	NUM
ejpam-5645	305	2	examples	example	NOUN
ejpam-5645	305	3	on	on	ADP
ejpam-5645	305	4	hopficity	hopficity	NOUN
ejpam-5645	305	5	in	in	ADP
ejpam-5645	305	6	torsion	torsion	NOUN
ejpam-5645	305	7	-	-	PUNCT
ejpam-5645	305	8	free	free	ADJ
ejpam-5645	305	9	abelian	abelian	ADJ
ejpam-5645	305	10	groups	group	NOUN
ejpam-5645	305	11	.	.	PUNCT
ejpam-5645	306	1	acta	acta	PROPN
ejpam-5645	306	2	mathematica	mathematica	PROPN
ejpam-5645	306	3	hungarica	hungarica	PROPN
ejpam-5645	306	4	,	,	PUNCT
ejpam-5645	306	5	16(3	16(3	PROPN
ejpam-5645	306	6	-	-	PUNCT
ejpam-5645	306	7	4	4	NUM
ejpam-5645	306	8	)	)	PUNCT
ejpam-5645	306	9	,	,	PUNCT
ejpam-5645	306	10	303	303	NUM
ejpam-5645	306	11	-	-	SYM
ejpam-5645	306	12	310	310	NUM
ejpam-5645	306	13	,	,	PUNCT
ejpam-5645	306	14	1965	1965	NUM
ejpam-5645	306	15	.	.	PUNCT
ejpam-5645	307	1	[	[	X
ejpam-5645	307	2	5	5	NUM
ejpam-5645	307	3	]	]	PUNCT
ejpam-5645	307	4	a.	a.	NOUN
ejpam-5645	307	5	chillali	chillali	PROPN
ejpam-5645	307	6	s.	s.	PROPN
ejpam-5645	307	7	abdelalim	abdelalim	PROPN
ejpam-5645	307	8	h.	h.	PROPN
ejpam-5645	307	9	essannouni	essannouni	PROPN
ejpam-5645	307	10	.	.	PUNCT
ejpam-5645	308	1	the	the	DET
ejpam-5645	308	2	strongly	strongly	ADV
ejpam-5645	308	3	hopfian	hopfian	ADJ
ejpam-5645	308	4	abelian	abelian	ADJ
ejpam-5645	308	5	groups	group	NOUN
ejpam-5645	308	6	.	.	PUNCT
ejpam-5645	309	1	ulf	ulf	PROPN
ejpam-5645	309	2	journal	journal	PROPN
ejpam-5645	309	3	of	of	ADP
ejpam-5645	309	4	mathematics	mathematic	NOUN
ejpam-5645	309	5	,	,	PUNCT
ejpam-5645	309	6	3(2	3(2	NUM
ejpam-5645	309	7	)	)	PUNCT
ejpam-5645	309	8	,	,	PUNCT
ejpam-5645	309	9	2015	2015	NUM
ejpam-5645	309	10	.	.	PUNCT
ejpam-5645	310	1	[	[	X
ejpam-5645	310	2	6	6	NUM
ejpam-5645	310	3	]	]	PUNCT
ejpam-5645	310	4	s.	s.	PROPN
ejpam-5645	310	5	abdelalim	abdelalim	PROPN
ejpam-5645	310	6	h.	h.	PROPN
ejpam-5645	310	7	essannouni	essannouni	PROPN
ejpam-5645	310	8	.	.	PUNCT
ejpam-5645	311	1	characterization	characterization	NOUN
ejpam-5645	311	2	of	of	ADP
ejpam-5645	311	3	the	the	DET
ejpam-5645	311	4	automorphisms	automorphism	NOUN
ejpam-5645	311	5	of	of	ADP
ejpam-5645	311	6	an	an	DET
ejpam-5645	311	7	abelian	abelian	ADJ
ejpam-5645	311	8	group	group	NOUN
ejpam-5645	311	9	having	have	VERB
ejpam-5645	311	10	the	the	DET
ejpam-5645	311	11	extension	extension	NOUN
ejpam-5645	311	12	property	property	NOUN
ejpam-5645	311	13	.	.	PUNCT
ejpam-5645	312	1	portugaliae	portugaliae	PROPN
ejpam-5645	312	2	math	math	PROPN
ejpam-5645	312	3	vol.59	vol.59	PROPN
ejpam-5645	312	4	,	,	PUNCT
ejpam-5645	312	5	p	p	ADJ
ejpam-5645	312	6	325	325	NUM
ejpam-5645	312	7	-	-	SYM
ejpam-5645	312	8	333	333	NUM
ejpam-5645	312	9	,	,	PUNCT
ejpam-5645	312	10	2002	2002	NUM
ejpam-5645	312	11	.	.	PUNCT
ejpam-5645	313	1	[	[	X
ejpam-5645	313	2	7	7	X
ejpam-5645	313	3	]	]	X
ejpam-5645	313	4	s.	s.	PROPN
ejpam-5645	313	5	abdelalim	abdelalim	PROPN
ejpam-5645	313	6	h.	h.	PROPN
ejpam-5645	313	7	essannouni	essannouni	PROPN
ejpam-5645	313	8	.	.	PUNCT
ejpam-5645	314	1	characterization	characterization	NOUN
ejpam-5645	314	2	of	of	ADP
ejpam-5645	314	3	the	the	DET
ejpam-5645	314	4	inessential	inessential	ADJ
ejpam-5645	314	5	endomorphisms	endomorphism	NOUN
ejpam-5645	314	6	in	in	ADP
ejpam-5645	314	7	the	the	DET
ejpam-5645	314	8	category	category	NOUN
ejpam-5645	314	9	of	of	ADP
ejpam-5645	314	10	abelian	abelian	ADJ
ejpam-5645	314	11	groups	group	NOUN
ejpam-5645	314	12	.	.	PUNCT
ejpam-5645	315	1	pub	pub	NOUN
ejpam-5645	315	2	.	.	PUNCT
ejpam-5645	316	1	mat	mat	NOUN
ejpam-5645	316	2	.	.	PROPN
ejpam-5645	317	1	47	47	NUM
ejpam-5645	317	2	(	(	PUNCT
ejpam-5645	317	3	2003	2003	NUM
ejpam-5645	317	4	)	)	PUNCT
ejpam-5645	317	5	359	359	NUM
ejpam-5645	317	6	-	-	SYM
ejpam-5645	317	7	372	372	NUM
ejpam-5645	317	8	,	,	PUNCT
ejpam-5645	317	9	2003	2003	NUM
ejpam-5645	317	10	.	.	PUNCT
ejpam-5645	318	1	[	[	X
ejpam-5645	318	2	8	8	NUM
ejpam-5645	318	3	]	]	PUNCT
ejpam-5645	318	4	l.	l.	PROPN
ejpam-5645	318	5	fuchs	fuchs	PROPN
ejpam-5645	318	6	.	.	PUNCT
ejpam-5645	319	1	infinite	infinite	ADJ
ejpam-5645	319	2	abelian	abelian	ADJ
ejpam-5645	319	3	groups	group	NOUN
ejpam-5645	319	4	.	.	PUNCT
ejpam-5645	320	1	vol	vol	NOUN
ejpam-5645	320	2	.	.	NOUN
ejpam-5645	320	3	1	1	NUM
ejpam-5645	320	4	academic	academic	ADJ
ejpam-5645	320	5	press	press	NOUN
ejpam-5645	320	6	.	.	PUNCT
ejpam-5645	320	7	,	,	PUNCT
ejpam-5645	320	8	1970	1970	NUM
ejpam-5645	320	9	.	.	PUNCT
ejpam-5645	321	1	[	[	X
ejpam-5645	321	2	9	9	NUM
ejpam-5645	321	3	]	]	PUNCT
ejpam-5645	321	4	l.	l.	PROPN
ejpam-5645	321	5	fuchs	fuchs	PROPN
ejpam-5645	321	6	.	.	PUNCT
ejpam-5645	322	1	infinite	infinite	ADJ
ejpam-5645	322	2	abelian	abelian	ADJ
ejpam-5645	322	3	groups	group	NOUN
ejpam-5645	322	4	.	.	PUNCT
ejpam-5645	323	1	vol	vol	NOUN
ejpam-5645	323	2	.	.	NOUN
ejpam-5645	323	3	2	2	NUM
ejpam-5645	323	4	academic	academic	ADJ
ejpam-5645	323	5	press	press	NOUN
ejpam-5645	323	6	.	.	PUNCT
ejpam-5645	323	7	,	,	PUNCT
ejpam-5645	323	8	1973	1973	NUM
ejpam-5645	323	9	.	.	PUNCT
ejpam-5645	324	1	[	[	X
ejpam-5645	324	2	10	10	NUM
ejpam-5645	324	3	]	]	X
ejpam-5645	324	4	b.	b.	PROPN
ejpam-5645	324	5	goldsmith	goldsmith	PROPN
ejpam-5645	324	6	k.	k.	PROPN
ejpam-5645	324	7	gong	gong	PROPN
ejpam-5645	324	8	.	.	PUNCT
ejpam-5645	325	1	on	on	ADP
ejpam-5645	325	2	super	super	ADJ
ejpam-5645	325	3	and	and	CCONJ
ejpam-5645	325	4	hereditarily	hereditarily	ADV
ejpam-5645	325	5	hopfian	hopfian	NOUN
ejpam-5645	325	6	and	and	CCONJ
ejpam-5645	325	7	co	co	ADJ
ejpam-5645	325	8	-	-	ADJ
ejpam-5645	325	9	hopfian	hopfian	ADJ
ejpam-5645	325	10	abelian	abelian	ADJ
ejpam-5645	325	11	groups	group	NOUN
ejpam-5645	325	12	.	.	PUNCT
ejpam-5645	326	1	archiv	archiv	PROPN
ejpam-5645	326	2	der	der	PROPN
ejpam-5645	326	3	mathematik	mathematik	PROPN
ejpam-5645	326	4	,	,	PUNCT
ejpam-5645	326	5	99	99	NUM
ejpam-5645	326	6	,	,	PUNCT
ejpam-5645	326	7	1	1	NUM
ejpam-5645	326	8	-	-	SYM
ejpam-5645	326	9	8	8	NUM
ejpam-5645	326	10	,	,	PUNCT
ejpam-5645	326	11	2012	2012	NUM
ejpam-5645	326	12	.	.	PUNCT
ejpam-5645	327	1	13	13	NUM
ejpam-5645	327	2	of	of	ADP
ejpam-5645	327	3	13	13	NUM
ejpam-5645	327	4	[	[	X
ejpam-5645	327	5	11	11	NUM
ejpam-5645	327	6	]	]	PUNCT
ejpam-5645	327	7	a.	a.	NOUN
ejpam-5645	327	8	haghany	haghany	NOUN
ejpam-5645	327	9	.	.	PUNCT
ejpam-5645	328	1	hopficity	hopficity	NOUN
ejpam-5645	328	2	and	and	CCONJ
ejpam-5645	328	3	co	co	NOUN
ejpam-5645	328	4	-	-	NOUN
ejpam-5645	328	5	hopficity	hopficity	NOUN
ejpam-5645	328	6	for	for	ADP
ejpam-5645	328	7	morita	morita	PROPN
ejpam-5645	328	8	contexts	contexts	PROPN
ejpam-5645	328	9	.	.	PUNCT
ejpam-5645	329	1	communications	communication	NOUN
ejpam-5645	329	2	in	in	ADP
ejpam-5645	329	3	algebra	algebra	NOUN
ejpam-5645	329	4	,	,	PUNCT
ejpam-5645	329	5	27(1	27(1	NUM
ejpam-5645	329	6	)	)	PUNCT
ejpam-5645	329	7	,	,	PUNCT
ejpam-5645	329	8	477	477	NUM
ejpam-5645	329	9	-	-	SYM
ejpam-5645	329	10	492	492	NUM
ejpam-5645	329	11	,	,	PUNCT
ejpam-5645	329	12	1999	1999	NUM
ejpam-5645	329	13	.	.	PUNCT
ejpam-5645	330	1	[	[	X
ejpam-5645	330	2	12	12	NUM
ejpam-5645	330	3	]	]	PUNCT
ejpam-5645	330	4	a.	a.	NOUN
ejpam-5645	330	5	ghorbani	ghorbani	PROPN
ejpam-5645	330	6	a.	a.	NOUN
ejpam-5645	330	7	haghany	haghany	PROPN
ejpam-5645	330	8	.	.	PUNCT
ejpam-5645	331	1	generalized	generalize	VERB
ejpam-5645	331	2	hopfian	hopfian	ADJ
ejpam-5645	331	3	modules	module	NOUN
ejpam-5645	331	4	.	.	PUNCT
ejpam-5645	332	1	journal	journal	NOUN
ejpam-5645	332	2	of	of	ADP
ejpam-5645	332	3	algebra	algebra	PROPN
ejpam-5645	332	4	,	,	PUNCT
ejpam-5645	332	5	255(2	255(2	NUM
ejpam-5645	332	6	)	)	PUNCT
ejpam-5645	332	7	,	,	PUNCT
ejpam-5645	332	8	324	324	NUM
ejpam-5645	332	9	-	-	SYM
ejpam-5645	332	10	341	341	NUM
ejpam-5645	332	11	,	,	PUNCT
ejpam-5645	332	12	2002	2002	NUM
ejpam-5645	332	13	.	.	PUNCT
ejpam-5645	333	1	[	[	X
ejpam-5645	333	2	13	13	NUM
ejpam-5645	333	3	]	]	X
ejpam-5645	333	4	v.a	v.a	PROPN
ejpam-5645	333	5	.	.	PROPN
ejpam-5645	333	6	hiremath	hiremath	PROPN
ejpam-5645	333	7	.	.	PUNCT
ejpam-5645	334	1	hopfian	hopfian	PROPN
ejpam-5645	334	2	rings	ring	NOUN
ejpam-5645	334	3	and	and	CCONJ
ejpam-5645	334	4	hopfian	hopfian	ADJ
ejpam-5645	334	5	modules	module	NOUN
ejpam-5645	334	6	.	.	PUNCT
ejpam-5645	335	1	indian	indian	PROPN
ejpam-5645	335	2	j.	j.	PROPN
ejpam-5645	335	3	pure	pure	PROPN
ejpam-5645	335	4	appl.math	appl.math	PROPN
ejpam-5645	335	5	.	.	PUNCT
ejpam-5645	335	6	17(7	17(7	NUM
ejpam-5645	335	7	)	)	PUNCT
ejpam-5645	335	8	,	,	PUNCT
ejpam-5645	335	9	895	895	NUM
ejpam-5645	335	10	-	-	SYM
ejpam-5645	335	11	900	900	NUM
ejpam-5645	335	12	,	,	PUNCT
ejpam-5645	335	13	1986	1986	NUM
ejpam-5645	335	14	.	.	PUNCT
ejpam-5645	336	1	[	[	X
ejpam-5645	336	2	14	14	NUM
ejpam-5645	336	3	]	]	X
ejpam-5645	336	4	j.	j.	PROPN
ejpam-5645	336	5	irwin	irwin	PROPN
ejpam-5645	336	6	i.	i.	PROPN
ejpam-5645	336	7	ito	ito	PROPN
ejpam-5645	336	8	.	.	PUNCT
ejpam-5645	337	1	a	a	DET
ejpam-5645	337	2	quasi	quasi	ADJ
ejpam-5645	337	3	-	-	ADJ
ejpam-5645	337	4	decomposable	decomposable	ADJ
ejpam-5645	337	5	abelian	abelian	ADJ
ejpam-5645	337	6	group	group	NOUN
ejpam-5645	337	7	without	without	ADP
ejpam-5645	337	8	proper	proper	ADJ
ejpam-5645	337	9	isomorphic	isomorphic	ADJ
ejpam-5645	337	10	quotient	quotient	NOUN
ejpam-5645	337	11	groups	group	NOUN
ejpam-5645	337	12	and	and	CCONJ
ejpam-5645	337	13	proper	proper	ADJ
ejpam-5645	337	14	isomorphic	isomorphic	ADJ
ejpam-5645	337	15	subgroups	subgroup	NOUN
ejpam-5645	337	16	.	.	PUNCT
ejpam-5645	338	1	pacific	pacific	PROPN
ejpam-5645	338	2	journal	journal	PROPN
ejpam-5645	338	3	of	of	ADP
ejpam-5645	338	4	mathematics	mathematic	NOUN
ejpam-5645	338	5	,	,	PUNCT
ejpam-5645	338	6	29(1	29(1	NUM
ejpam-5645	338	7	)	)	PUNCT
ejpam-5645	338	8	,	,	PUNCT
ejpam-5645	338	9	151	151	NUM
ejpam-5645	338	10	-	-	SYM
ejpam-5645	338	11	160	160	NUM
ejpam-5645	338	12	,	,	PUNCT
ejpam-5645	338	13	1969	1969	NUM
ejpam-5645	338	14	.	.	PUNCT
ejpam-5645	339	1	[	[	X
ejpam-5645	339	2	15	15	NUM
ejpam-5645	339	3	]	]	PUNCT
ejpam-5645	339	4	k.	k.	PROPN
ejpam-5645	339	5	el	el	PROPN
ejpam-5645	339	6	amin	amin	PROPN
ejpam-5645	339	7	mokhtar	mokhtar	PROPN
ejpam-5645	339	8	s.	s.	PROPN
ejpam-5645	339	9	mamadou	mamadou	PROPN
ejpam-5645	339	10	.	.	PROPN
ejpam-5645	339	11	une	une	PROPN
ejpam-5645	339	12	caracterisation	caracterisation	PROPN
ejpam-5645	339	13	des	des	PROPN
ejpam-5645	339	14	anneaux	anneaux	PROPN
ejpam-5645	339	15	artiniens	artinien	VERB
ejpam-5645	339	16	a	a	DET
ejpam-5645	339	17	ideaux	ideaux	ADJ
ejpam-5645	339	18	principaux	principaux	NOUN
ejpam-5645	339	19	.	.	PUNCT
ejpam-5645	340	1	in	in	ADP
ejpam-5645	340	2	ring	ring	NOUN
ejpam-5645	340	3	theory	theory	NOUN
ejpam-5645	340	4	:	:	PUNCT
ejpam-5645	340	5	proceedings	proceeding	NOUN
ejpam-5645	340	6	of	of	ADP
ejpam-5645	340	7	a	a	DET
ejpam-5645	340	8	conference	conference	NOUN
ejpam-5645	340	9	held	hold	VERB
ejpam-5645	340	10	in	in	ADP
ejpam-5645	340	11	granada	granada	PROPN
ejpam-5645	340	12	,	,	PUNCT
ejpam-5645	340	13	spain	spain	PROPN
ejpam-5645	340	14	,	,	PUNCT
ejpam-5645	340	15	sept	sept	PROPN
ejpam-5645	340	16	.	.	PROPN
ejpam-5645	340	17	1–6	1–6	NUM
ejpam-5645	340	18	,	,	PUNCT
ejpam-5645	340	19	1986	1986	NUM
ejpam-5645	340	20	(	(	PUNCT
ejpam-5645	340	21	pp	pp	ADJ
ejpam-5645	340	22	.	.	PUNCT
ejpam-5645	340	23	245	245	NUM
ejpam-5645	340	24	-	-	SYM
ejpam-5645	340	25	254	254	NUM
ejpam-5645	340	26	)	)	PUNCT
ejpam-5645	340	27	.	.	PUNCT
ejpam-5645	341	1	springer	springer	PROPN
ejpam-5645	341	2	berlin	berlin	PROPN
ejpam-5645	341	3	heidelberg	heidelberg	PROPN
ejpam-5645	341	4	.	.	PUNCT
ejpam-5645	341	5	,	,	PUNCT
ejpam-5645	341	6	1988	1988	NUM
ejpam-5645	341	7	.	.	PUNCT
ejpam-5645	342	1	[	[	X
ejpam-5645	342	2	16	16	NUM
ejpam-5645	342	3	]	]	X
ejpam-5645	342	4	j.	j.	PROPN
ejpam-5645	342	5	nielsen	nielsen	PROPN
ejpam-5645	342	6	.	.	PUNCT
ejpam-5645	343	1	om	om	PROPN
ejpam-5645	343	2	regning	regne	VERB
ejpam-5645	343	3	med	med	ADJ
ejpam-5645	343	4	ikkekommutative	ikkekommutative	ADJ
ejpam-5645	343	5	faktorer	faktorer	ADV
ejpam-5645	343	6	og	og	PROPN
ejpam-5645	343	7	dens	dens	ADP
ejpam-5645	343	8	anvendelse	anvendelse	PROPN
ejpam-5645	343	9	i	i	PROPN
ejpam-5645	343	10	gruppenteorien	gruppenteorien	PROPN
ejpam-5645	343	11	.	.	PUNCT
ejpam-5645	344	1	matematisk	matematisk	PROPN
ejpam-5645	344	2	tidsskrift	tidsskrift	PROPN
ejpam-5645	344	3	b	b	PROPN
ejpam-5645	344	4	pp	pp	ADJ
ejpam-5645	344	5	.	.	PUNCT
ejpam-5645	345	1	77	77	NUM
ejpam-5645	345	2	-	-	SYM
ejpam-5645	345	3	94	94	NUM
ejpam-5645	345	4	,	,	PUNCT
ejpam-5645	345	5	1921	1921	NUM
ejpam-5645	345	6	.	.	PUNCT
ejpam-5645	346	1	[	[	X
ejpam-5645	346	2	17	17	NUM
ejpam-5645	346	3	]	]	PUNCT
ejpam-5645	346	4	x.	x.	NOUN
ejpam-5645	346	5	magnus	magnus	PROPN
ejpam-5645	346	6	a.	a.	PROPN
ejpam-5645	346	7	karrass	karrass	PROPN
ejpam-5645	346	8	d.	d.	PROPN
ejpam-5645	346	9	solitar	solitar	PROPN
ejpam-5645	346	10	.	.	PUNCT
ejpam-5645	347	1	combinatorial	combinatorial	PROPN
ejpam-5645	347	2	group	group	NOUN
ejpam-5645	347	3	theory	theory	NOUN
ejpam-5645	347	4	:	:	PUNCT
ejpam-5645	347	5	presentations	presentation	NOUN
ejpam-5645	347	6	of	of	ADP
ejpam-5645	347	7	groups	group	NOUN
ejpam-5645	347	8	in	in	ADP
ejpam-5645	347	9	terms	term	NOUN
ejpam-5645	347	10	of	of	ADP
ejpam-5645	347	11	generators	generator	NOUN
ejpam-5645	347	12	and	and	CCONJ
ejpam-5645	347	13	relations	relation	NOUN
ejpam-5645	347	14	.	.	PUNCT
ejpam-5645	348	1	courier	courier	NOUN
ejpam-5645	348	2	corporation	corporation	NOUN
ejpam-5645	348	3	,	,	PUNCT
ejpam-5645	348	4	2004	2004	NUM
ejpam-5645	348	5	.	.	PUNCT
ejpam-5645	349	1	[	[	X
ejpam-5645	349	2	18	18	NUM
ejpam-5645	349	3	]	]	PUNCT
ejpam-5645	349	4	k.	k.	NOUN
ejpam-5645	349	5	varadarajan	varadarajan	PROPN
ejpam-5645	349	6	.	.	PUNCT
ejpam-5645	350	1	some	some	DET
ejpam-5645	350	2	recent	recent	ADJ
ejpam-5645	350	3	results	result	NOUN
ejpam-5645	350	4	on	on	ADP
ejpam-5645	350	5	hopficity	hopficity	NOUN
ejpam-5645	350	6	,	,	PUNCT
ejpam-5645	350	7	co	co	NOUN
ejpam-5645	350	8	-	-	NOUN
ejpam-5645	350	9	hopficity	hopficity	ADJ
ejpam-5645	350	10	and	and	CCONJ
ejpam-5645	350	11	related	related	ADJ
ejpam-5645	350	12	properties	property	NOUN
ejpam-5645	350	13	.	.	PUNCT
ejpam-5645	351	1	in	in	ADP
ejpam-5645	351	2	international	international	ADJ
ejpam-5645	351	3	symposium	symposium	NOUN
ejpam-5645	351	4	on	on	ADP
ejpam-5645	351	5	ring	ring	NOUN
ejpam-5645	351	6	theory	theory	NOUN
ejpam-5645	351	7	(	(	PUNCT
ejpam-5645	351	8	pp	pp	PROPN
ejpam-5645	351	9	.	.	PUNCT
ejpam-5645	351	10	371	371	NUM
ejpam-5645	351	11	-	-	SYM
ejpam-5645	351	12	392	392	NUM
ejpam-5645	351	13	)	)	PUNCT
ejpam-5645	351	14	,	,	PUNCT
ejpam-5645	351	15	2001	2001	NUM
ejpam-5645	351	16	.	.	PUNCT
ejpam-5645	352	1	[	[	X
ejpam-5645	352	2	19	19	NUM
ejpam-5645	352	3	]	]	X
ejpam-5645	352	4	y.	y.	PROPN
ejpam-5645	352	5	gang	gang	PROPN
ejpam-5645	352	6	l.	l.	PROPN
ejpam-5645	352	7	zhongkui	zhongkui	PROPN
ejpam-5645	352	8	.	.	PUNCT
ejpam-5645	353	1	on	on	ADP
ejpam-5645	353	2	hopfian	hopfian	PROPN
ejpam-5645	353	3	and	and	CCONJ
ejpam-5645	353	4	co	co	ADJ
ejpam-5645	353	5	-	-	ADJ
ejpam-5645	353	6	hopfian	hopfian	ADJ
ejpam-5645	353	7	modules	module	NOUN
ejpam-5645	353	8	.	.	PUNCT
ejpam-5645	354	1	vietnam	vietnam	PROPN
ejpam-5645	354	2	j.	j.	PROPN
ejpam-5645	354	3	math	math	PROPN
ejpam-5645	354	4	,	,	PUNCT
ejpam-5645	354	5	35(1	35(1	NUM
ejpam-5645	354	6	)	)	PUNCT
ejpam-5645	354	7	,	,	PUNCT
ejpam-5645	354	8	73	73	NUM
ejpam-5645	354	9	-	-	SYM
ejpam-5645	354	10	80	80	NUM
ejpam-5645	354	11	,	,	PUNCT
ejpam-5645	354	12	2007	2007	NUM
ejpam-5645	354	13	.	.	PUNCT
ejpam-5645	355	1	[	[	X
ejpam-5645	355	2	20	20	NUM
ejpam-5645	355	3	]	]	X
ejpam-5645	355	4	y.	y.	PROPN
ejpam-5645	355	5	gang	gang	PROPN
ejpam-5645	355	6	l.	l.	PROPN
ejpam-5645	355	7	zhongkui	zhongkui	PROPN
ejpam-5645	355	8	.	.	PUNCT
ejpam-5645	356	1	notes	note	NOUN
ejpam-5645	356	2	on	on	ADP
ejpam-5645	356	3	generalized	generalized	ADJ
ejpam-5645	356	4	hopfian	hopfian	NOUN
ejpam-5645	356	5	and	and	CCONJ
ejpam-5645	356	6	weakly	weakly	ADJ
ejpam-5645	356	7	co	co	ADJ
ejpam-5645	356	8	-	-	ADJ
ejpam-5645	356	9	hopfian	hopfian	ADJ
ejpam-5645	356	10	modules	module	NOUN
ejpam-5645	356	11	.	.	PUNCT
ejpam-5645	357	1	communications	communication	NOUN
ejpam-5645	357	2	in	in	ADP
ejpam-5645	357	3	algebra	algebra	NOUN
ejpam-5645	357	4	,	,	PUNCT
ejpam-5645	357	5	38(10	38(10	PROPN
ejpam-5645	357	6	)	)	PUNCT
ejpam-5645	357	7	,	,	PUNCT
ejpam-5645	357	8	3556	3556	NUM
ejpam-5645	357	9	-	-	SYM
ejpam-5645	357	10	3566	3566	NUM
ejpam-5645	357	11	,	,	PUNCT
ejpam-5645	357	12	2010	2010	NUM
ejpam-5645	357	13	.	.	PUNCT