id	sid	tid	token	lemma	pos
ejpam-5118	1	1	european	european	PROPN
ejpam-5118	1	2	journal	journal	PROPN
ejpam-5118	1	3	of	of	ADP
ejpam-5118	1	4	pure	pure	ADJ
ejpam-5118	1	5	and	and	CCONJ
ejpam-5118	1	6	applied	apply	VERB
ejpam-5118	1	7	mathematics	mathematic	NOUN
ejpam-5118	1	8	vol	vol	NOUN
ejpam-5118	1	9	.	.	PROPN
ejpam-5118	2	1	17	17	NUM
ejpam-5118	2	2	,	,	PUNCT
ejpam-5118	2	3	no	no	INTJ
ejpam-5118	2	4	.	.	NOUN
ejpam-5118	2	5	2	2	NUM
ejpam-5118	2	6	,	,	PUNCT
ejpam-5118	2	7	2024	2024	NUM
ejpam-5118	2	8	,	,	PUNCT
ejpam-5118	2	9	956	956	NUM
ejpam-5118	2	10	-	-	SYM
ejpam-5118	2	11	968	968	NUM
ejpam-5118	2	12	issn	issn	PROPN
ejpam-5118	2	13	1307	1307	NUM
ejpam-5118	2	14	-	-	SYM
ejpam-5118	2	15	5543	5543	NUM
ejpam-5118	2	16	–	–	PUNCT
ejpam-5118	3	1	ejpam.com	ejpam.com	X
ejpam-5118	3	2	published	publish	VERB
ejpam-5118	3	3	by	by	ADP
ejpam-5118	3	4	new	new	PROPN
ejpam-5118	3	5	york	york	PROPN
ejpam-5118	3	6	business	business	PROPN
ejpam-5118	3	7	global	global	PROPN
ejpam-5118	3	8	on	on	ADP
ejpam-5118	3	9	the	the	DET
ejpam-5118	3	10	isomorphism	isomorphism	NOUN
ejpam-5118	3	11	problem	problem	NOUN
ejpam-5118	3	12	for	for	ADP
ejpam-5118	3	13	central	central	ADJ
ejpam-5118	3	14	extensions	extension	NOUN
ejpam-5118	3	15	ii	ii	PROPN
ejpam-5118	3	16	noureddine	noureddine	ADP
ejpam-5118	3	17	snanou	snanou	PROPN
ejpam-5118	3	18	department	department	PROPN
ejpam-5118	3	19	of	of	ADP
ejpam-5118	3	20	mathematics	mathematic	NOUN
ejpam-5118	3	21	,	,	PUNCT
ejpam-5118	3	22	faculty	faculty	NOUN
ejpam-5118	3	23	of	of	ADP
ejpam-5118	3	24	sciences	sciences	PROPN
ejpam-5118	3	25	dhar	dhar	PROPN
ejpam-5118	3	26	el	el	PROPN
ejpam-5118	3	27	mahraz	mahraz	PROPN
ejpam-5118	3	28	,	,	PUNCT
ejpam-5118	3	29	sidi	sidi	PROPN
ejpam-5118	3	30	mohamed	mohamed	PROPN
ejpam-5118	3	31	ben	ben	PROPN
ejpam-5118	3	32	abdellah	abdellah	PROPN
ejpam-5118	3	33	university	university	PROPN
ejpam-5118	3	34	,	,	PUNCT
ejpam-5118	3	35	fez	fez	PROPN
ejpam-5118	3	36	,	,	PUNCT
ejpam-5118	3	37	morocco	morocco	PROPN
ejpam-5118	3	38	abstract	abstract	NOUN
ejpam-5118	3	39	.	.	PUNCT
ejpam-5118	4	1	in	in	ADP
ejpam-5118	4	2	this	this	DET
ejpam-5118	4	3	paper	paper	NOUN
ejpam-5118	4	4	,	,	PUNCT
ejpam-5118	4	5	we	we	PRON
ejpam-5118	4	6	study	study	VERB
ejpam-5118	4	7	the	the	DET
ejpam-5118	4	8	isomorphism	isomorphism	NOUN
ejpam-5118	4	9	problem	problem	NOUN
ejpam-5118	4	10	for	for	ADP
ejpam-5118	4	11	central	central	ADJ
ejpam-5118	4	12	extensions	extension	NOUN
ejpam-5118	4	13	.	.	PUNCT
ejpam-5118	5	1	more	more	ADV
ejpam-5118	5	2	precisely	precisely	ADV
ejpam-5118	5	3	,	,	PUNCT
ejpam-5118	5	4	in	in	ADP
ejpam-5118	5	5	some	some	DET
ejpam-5118	5	6	new	new	ADJ
ejpam-5118	5	7	situations	situation	NOUN
ejpam-5118	5	8	,	,	PUNCT
ejpam-5118	5	9	we	we	PRON
ejpam-5118	5	10	provide	provide	VERB
ejpam-5118	5	11	necessary	necessary	ADJ
ejpam-5118	5	12	and	and	CCONJ
ejpam-5118	5	13	sufficient	sufficient	ADJ
ejpam-5118	5	14	conditions	condition	NOUN
ejpam-5118	5	15	for	for	ADP
ejpam-5118	5	16	two	two	NUM
ejpam-5118	5	17	central	central	ADJ
ejpam-5118	5	18	extensions	extension	NOUN
ejpam-5118	5	19	to	to	PART
ejpam-5118	5	20	be	be	AUX
ejpam-5118	5	21	isomorphic	isomorphic	ADJ
ejpam-5118	5	22	.	.	PUNCT
ejpam-5118	6	1	we	we	PRON
ejpam-5118	6	2	investigate	investigate	VERB
ejpam-5118	6	3	the	the	DET
ejpam-5118	6	4	case	case	NOUN
ejpam-5118	6	5	when	when	SCONJ
ejpam-5118	6	6	the	the	DET
ejpam-5118	6	7	quotient	quotient	NOUN
ejpam-5118	6	8	group	group	NOUN
ejpam-5118	6	9	is	be	AUX
ejpam-5118	6	10	simple	simple	ADJ
ejpam-5118	6	11	or	or	CCONJ
ejpam-5118	6	12	purely	purely	ADV
ejpam-5118	6	13	nonabelian	nonabelian	ADJ
ejpam-5118	6	14	.	.	PUNCT
ejpam-5118	7	1	furthermore	furthermore	ADV
ejpam-5118	7	2	,	,	PUNCT
ejpam-5118	7	3	we	we	PRON
ejpam-5118	7	4	characterize	characterize	VERB
ejpam-5118	7	5	isomorphisms	isomorphism	NOUN
ejpam-5118	7	6	leaving	leave	VERB
ejpam-5118	7	7	the	the	DET
ejpam-5118	7	8	quotient	quotient	NOUN
ejpam-5118	7	9	group	group	NOUN
ejpam-5118	7	10	invariant	invariant	PROPN
ejpam-5118	7	11	.	.	PUNCT
ejpam-5118	8	1	finally	finally	ADV
ejpam-5118	8	2	,	,	PUNCT
ejpam-5118	8	3	we	we	PRON
ejpam-5118	8	4	deal	deal	VERB
ejpam-5118	8	5	with	with	ADP
ejpam-5118	8	6	isomorphisms	isomorphism	NOUN
ejpam-5118	8	7	of	of	ADP
ejpam-5118	8	8	central	central	ADJ
ejpam-5118	8	9	extensions	extension	NOUN
ejpam-5118	8	10	where	where	SCONJ
ejpam-5118	8	11	the	the	DET
ejpam-5118	8	12	kernel	kernel	PROPN
ejpam-5118	8	13	group	group	NOUN
ejpam-5118	8	14	and	and	CCONJ
ejpam-5118	8	15	the	the	DET
ejpam-5118	8	16	quotient	quotient	NOUN
ejpam-5118	8	17	group	group	NOUN
ejpam-5118	8	18	are	be	AUX
ejpam-5118	8	19	isomorphic	isomorphic	ADJ
ejpam-5118	8	20	.	.	PUNCT
ejpam-5118	9	1	2020	2020	NUM
ejpam-5118	9	2	mathematics	mathematic	NOUN
ejpam-5118	9	3	subject	subject	NOUN
ejpam-5118	9	4	classifications	classification	NOUN
ejpam-5118	9	5	:	:	PUNCT
ejpam-5118	9	6	20j05	20j05	NUM
ejpam-5118	9	7	,	,	PUNCT
ejpam-5118	9	8	20e22	20e22	NUM
ejpam-5118	9	9	,	,	PUNCT
ejpam-5118	9	10	20j06	20j06	NUM
ejpam-5118	9	11	key	key	ADJ
ejpam-5118	9	12	words	word	NOUN
ejpam-5118	9	13	and	and	CCONJ
ejpam-5118	9	14	phrases	phrase	NOUN
ejpam-5118	9	15	:	:	PUNCT
ejpam-5118	9	16	central	central	ADJ
ejpam-5118	9	17	extension	extension	NOUN
ejpam-5118	9	18	,	,	PUNCT
ejpam-5118	9	19	isomorphism	isomorphism	NOUN
ejpam-5118	9	20	problem	problem	NOUN
ejpam-5118	9	21	,	,	PUNCT
ejpam-5118	9	22	lower	low	ADJ
ejpam-5118	9	23	isomorphic	isomorphic	ADJ
ejpam-5118	9	24	,	,	PUNCT
ejpam-5118	9	25	upper	upper	ADJ
ejpam-5118	9	26	isomorphic	isomorphic	NOUN
ejpam-5118	9	27	,	,	PUNCT
ejpam-5118	9	28	(	(	PUNCT
ejpam-5118	9	29	g)-isomorphic	g)-isomorphic	PROPN
ejpam-5118	9	30	1	1	NUM
ejpam-5118	9	31	.	.	X
ejpam-5118	9	32	introduction	introduction	NOUN
ejpam-5118	9	33	the	the	DET
ejpam-5118	9	34	classification	classification	NOUN
ejpam-5118	9	35	of	of	ADP
ejpam-5118	9	36	groups	group	NOUN
ejpam-5118	9	37	in	in	ADP
ejpam-5118	9	38	a	a	DET
ejpam-5118	9	39	certain	certain	ADJ
ejpam-5118	9	40	class	class	NOUN
ejpam-5118	9	41	is	be	AUX
ejpam-5118	9	42	one	one	NUM
ejpam-5118	9	43	of	of	ADP
ejpam-5118	9	44	the	the	DET
ejpam-5118	9	45	most	most	ADV
ejpam-5118	9	46	classical	classical	ADJ
ejpam-5118	9	47	problems	problem	NOUN
ejpam-5118	9	48	in	in	ADP
ejpam-5118	9	49	group	group	NOUN
ejpam-5118	9	50	theory	theory	NOUN
ejpam-5118	9	51	.	.	PUNCT
ejpam-5118	10	1	for	for	ADP
ejpam-5118	10	2	groups	group	NOUN
ejpam-5118	10	3	with	with	ADP
ejpam-5118	10	4	composition	composition	NOUN
ejpam-5118	10	5	series	series	NOUN
ejpam-5118	10	6	,	,	PUNCT
ejpam-5118	10	7	the	the	DET
ejpam-5118	10	8	jordan	jordan	PROPN
ejpam-5118	10	9	–	–	PUNCT
ejpam-5118	10	10	hölder	hölder	NOUN
ejpam-5118	10	11	theorem	theorem	VERB
ejpam-5118	10	12	states	state	NOUN
ejpam-5118	10	13	that	that	SCONJ
ejpam-5118	10	14	if	if	SCONJ
ejpam-5118	10	15	we	we	PRON
ejpam-5118	10	16	can	can	AUX
ejpam-5118	10	17	list	list	VERB
ejpam-5118	10	18	all	all	DET
ejpam-5118	10	19	simple	simple	ADJ
ejpam-5118	10	20	groups	group	NOUN
ejpam-5118	10	21	,	,	PUNCT
ejpam-5118	10	22	and	and	CCONJ
ejpam-5118	10	23	solve	solve	VERB
ejpam-5118	10	24	the	the	DET
ejpam-5118	10	25	extension	extension	NOUN
ejpam-5118	10	26	problem	problem	NOUN
ejpam-5118	10	27	then	then	ADV
ejpam-5118	10	28	we	we	PRON
ejpam-5118	10	29	can	can	AUX
ejpam-5118	10	30	construct	construct	VERB
ejpam-5118	10	31	and	and	CCONJ
ejpam-5118	10	32	classify	classify	VERB
ejpam-5118	10	33	all	all	DET
ejpam-5118	10	34	groups	group	NOUN
ejpam-5118	10	35	.	.	PUNCT
ejpam-5118	11	1	the	the	DET
ejpam-5118	11	2	classification	classification	NOUN
ejpam-5118	11	3	of	of	ADP
ejpam-5118	11	4	simple	simple	ADJ
ejpam-5118	11	5	groups	group	NOUN
ejpam-5118	11	6	has	have	AUX
ejpam-5118	11	7	been	be	AUX
ejpam-5118	11	8	achieved	achieve	VERB
ejpam-5118	11	9	in	in	ADP
ejpam-5118	11	10	the	the	DET
ejpam-5118	11	11	finite	finite	ADJ
ejpam-5118	11	12	case	case	NOUN
ejpam-5118	11	13	,	,	PUNCT
ejpam-5118	11	14	hence	hence	ADV
ejpam-5118	11	15	we	we	PRON
ejpam-5118	11	16	need	need	VERB
ejpam-5118	11	17	to	to	PART
ejpam-5118	11	18	solve	solve	VERB
ejpam-5118	11	19	the	the	DET
ejpam-5118	11	20	extension	extension	NOUN
ejpam-5118	11	21	problem	problem	NOUN
ejpam-5118	11	22	.	.	PUNCT
ejpam-5118	12	1	the	the	DET
ejpam-5118	12	2	extension	extension	NOUN
ejpam-5118	12	3	problem	problem	NOUN
ejpam-5118	12	4	for	for	ADP
ejpam-5118	12	5	two	two	NUM
ejpam-5118	12	6	groups	group	NOUN
ejpam-5118	12	7	g1	g1	VERB
ejpam-5118	12	8	and	and	CCONJ
ejpam-5118	12	9	g2	g2	PROPN
ejpam-5118	12	10	is	be	AUX
ejpam-5118	12	11	the	the	DET
ejpam-5118	12	12	problem	problem	NOUN
ejpam-5118	12	13	of	of	ADP
ejpam-5118	12	14	finding	find	VERB
ejpam-5118	12	15	all	all	DET
ejpam-5118	12	16	groups	group	NOUN
ejpam-5118	12	17	g	g	NOUN
ejpam-5118	12	18	with	with	ADP
ejpam-5118	12	19	g1	g1	NOUN
ejpam-5118	12	20	as	as	ADP
ejpam-5118	12	21	a	a	DET
ejpam-5118	12	22	normal	normal	ADJ
ejpam-5118	12	23	subgroup	subgroup	NOUN
ejpam-5118	12	24	of	of	ADP
ejpam-5118	12	25	g	g	PROPN
ejpam-5118	12	26	,	,	PUNCT
ejpam-5118	12	27	and	and	CCONJ
ejpam-5118	12	28	the	the	DET
ejpam-5118	12	29	quotient	quotient	NOUN
ejpam-5118	12	30	group	group	NOUN
ejpam-5118	12	31	g	g	PROPN
ejpam-5118	12	32	/	/	SYM
ejpam-5118	12	33	g1	g1	PROPN
ejpam-5118	12	34	isomorphic	isomorphic	ADJ
ejpam-5118	12	35	to	to	ADP
ejpam-5118	12	36	g2	g2	PROPN
ejpam-5118	12	37	.	.	PUNCT
ejpam-5118	13	1	such	such	DET
ejpam-5118	13	2	a	a	DET
ejpam-5118	13	3	group	group	NOUN
ejpam-5118	13	4	g	g	NOUN
ejpam-5118	13	5	is	be	AUX
ejpam-5118	13	6	called	call	VERB
ejpam-5118	13	7	an	an	DET
ejpam-5118	13	8	extension	extension	NOUN
ejpam-5118	13	9	of	of	ADP
ejpam-5118	13	10	g1	g1	NOUN
ejpam-5118	13	11	by	by	ADP
ejpam-5118	13	12	g2	g2	PROPN
ejpam-5118	14	1	[	[	X
ejpam-5118	14	2	6	6	NUM
ejpam-5118	14	3	]	]	PUNCT
ejpam-5118	14	4	.	.	PUNCT
ejpam-5118	15	1	the	the	DET
ejpam-5118	15	2	classification	classification	NOUN
ejpam-5118	15	3	of	of	ADP
ejpam-5118	15	4	extensions	extension	NOUN
ejpam-5118	15	5	with	with	ADP
ejpam-5118	15	6	non	non	ADJ
ejpam-5118	15	7	-	-	ADJ
ejpam-5118	15	8	abelian	abelian	ADJ
ejpam-5118	15	9	kernel	kernel	PROPN
ejpam-5118	15	10	group	group	NOUN
ejpam-5118	15	11	may	may	AUX
ejpam-5118	15	12	be	be	AUX
ejpam-5118	15	13	found	find	VERB
ejpam-5118	15	14	in	in	ADP
ejpam-5118	15	15	many	many	ADJ
ejpam-5118	15	16	texts	text	NOUN
ejpam-5118	15	17	,	,	PUNCT
ejpam-5118	15	18	but	but	CCONJ
ejpam-5118	15	19	the	the	DET
ejpam-5118	15	20	famous	famous	ADJ
ejpam-5118	15	21	references	reference	NOUN
ejpam-5118	15	22	for	for	ADP
ejpam-5118	15	23	these	these	DET
ejpam-5118	15	24	extensions	extension	NOUN
ejpam-5118	15	25	are	be	AUX
ejpam-5118	15	26	schreier	schreier	NOUN
ejpam-5118	15	27	’s	’s	PART
ejpam-5118	15	28	paper	paper	NOUN
ejpam-5118	16	1	[	[	X
ejpam-5118	16	2	7	7	X
ejpam-5118	16	3	]	]	PUNCT
ejpam-5118	16	4	and	and	CCONJ
ejpam-5118	16	5	eilenberg	eilenberg	PROPN
ejpam-5118	16	6	-	-	PUNCT
ejpam-5118	16	7	mac	mac	PROPN
ejpam-5118	16	8	lane	lane	NOUN
ejpam-5118	16	9	’s	’s	PART
ejpam-5118	16	10	paper	paper	NOUN
ejpam-5118	17	1	[	[	X
ejpam-5118	17	2	4	4	NUM
ejpam-5118	17	3	]	]	PUNCT
ejpam-5118	17	4	.	.	PUNCT
ejpam-5118	18	1	in	in	ADP
ejpam-5118	18	2	this	this	DET
ejpam-5118	18	3	work	work	NOUN
ejpam-5118	18	4	,	,	PUNCT
ejpam-5118	18	5	we	we	PRON
ejpam-5118	18	6	will	will	AUX
ejpam-5118	18	7	focus	focus	VERB
ejpam-5118	18	8	on	on	ADP
ejpam-5118	18	9	extensions	extension	NOUN
ejpam-5118	18	10	with	with	ADP
ejpam-5118	18	11	abelian	abelian	ADJ
ejpam-5118	18	12	kernel	kernel	PROPN
ejpam-5118	18	13	group	group	NOUN
ejpam-5118	18	14	.	.	PUNCT
ejpam-5118	19	1	in	in	ADP
ejpam-5118	19	2	particular	particular	ADJ
ejpam-5118	19	3	,	,	PUNCT
ejpam-5118	19	4	if	if	SCONJ
ejpam-5118	19	5	g1	g1	PROPN
ejpam-5118	19	6	is	be	AUX
ejpam-5118	19	7	a	a	DET
ejpam-5118	19	8	central	central	ADJ
ejpam-5118	19	9	subgroup	subgroup	NOUN
ejpam-5118	19	10	of	of	ADP
ejpam-5118	19	11	g	g	PROPN
ejpam-5118	19	12	,	,	PUNCT
ejpam-5118	19	13	then	then	ADV
ejpam-5118	19	14	we	we	PRON
ejpam-5118	19	15	say	say	VERB
ejpam-5118	19	16	that	that	SCONJ
ejpam-5118	19	17	g	g	PROPN
ejpam-5118	19	18	is	be	AUX
ejpam-5118	19	19	a	a	DET
ejpam-5118	19	20	central	central	ADJ
ejpam-5118	19	21	extension	extension	NOUN
ejpam-5118	19	22	of	of	ADP
ejpam-5118	19	23	g1	g1	NOUN
ejpam-5118	19	24	by	by	ADP
ejpam-5118	19	25	g2	g2	PROPN
ejpam-5118	19	26	.	.	PUNCT
ejpam-5118	20	1	for	for	ADP
ejpam-5118	20	2	central	central	ADJ
ejpam-5118	20	3	extensions	extension	NOUN
ejpam-5118	20	4	,	,	PUNCT
ejpam-5118	20	5	an	an	DET
ejpam-5118	20	6	answer	answer	NOUN
ejpam-5118	20	7	to	to	ADP
ejpam-5118	20	8	the	the	DET
ejpam-5118	20	9	extension	extension	NOUN
ejpam-5118	20	10	problem	problem	NOUN
ejpam-5118	20	11	has	have	AUX
ejpam-5118	20	12	been	be	AUX
ejpam-5118	20	13	given	give	VERB
ejpam-5118	20	14	by	by	ADP
ejpam-5118	20	15	hölder	hölder	NOUN
ejpam-5118	20	16	and	and	CCONJ
ejpam-5118	20	17	schreier	schreier	NOUN
ejpam-5118	20	18	by	by	ADP
ejpam-5118	20	19	using	use	VERB
ejpam-5118	20	20	the	the	DET
ejpam-5118	20	21	group	group	NOUN
ejpam-5118	20	22	cohomology	cohomology	NOUN
ejpam-5118	21	1	[	[	X
ejpam-5118	21	2	6	6	NUM
ejpam-5118	21	3	,	,	PUNCT
ejpam-5118	21	4	theorem	theorem	VERB
ejpam-5118	21	5	7.59	7.59	NUM
ejpam-5118	21	6	]	]	PUNCT
ejpam-5118	21	7	.	.	PUNCT
ejpam-5118	22	1	however	however	ADV
ejpam-5118	22	2	,	,	PUNCT
ejpam-5118	22	3	this	this	DET
ejpam-5118	22	4	answer	answer	NOUN
ejpam-5118	22	5	will	will	AUX
ejpam-5118	22	6	not	not	PART
ejpam-5118	22	7	enable	enable	VERB
ejpam-5118	22	8	us	we	PRON
ejpam-5118	22	9	to	to	PART
ejpam-5118	22	10	construct	construct	VERB
ejpam-5118	22	11	all	all	DET
ejpam-5118	22	12	possible	possible	ADJ
ejpam-5118	22	13	non	non	ADJ
ejpam-5118	22	14	-	-	ADJ
ejpam-5118	22	15	isomorphic	isomorphic	ADJ
ejpam-5118	22	16	central	central	ADJ
ejpam-5118	22	17	extensions	extension	NOUN
ejpam-5118	22	18	of	of	ADP
ejpam-5118	22	19	g1	g1	PROPN
ejpam-5118	22	20	by	by	ADP
ejpam-5118	22	21	g2	g2	PROPN
ejpam-5118	22	22	(	(	PUNCT
ejpam-5118	22	23	the	the	DET
ejpam-5118	22	24	isomorphism	isomorphism	NOUN
ejpam-5118	22	25	problem	problem	NOUN
ejpam-5118	22	26	)	)	PUNCT
ejpam-5118	22	27	.	.	PUNCT
ejpam-5118	23	1	in	in	ADP
ejpam-5118	23	2	fact	fact	NOUN
ejpam-5118	23	3	,	,	PUNCT
ejpam-5118	23	4	it	it	PRON
ejpam-5118	23	5	is	be	AUX
ejpam-5118	23	6	very	very	ADV
ejpam-5118	23	7	hard	hard	ADJ
ejpam-5118	23	8	to	to	PART
ejpam-5118	23	9	solve	solve	VERB
ejpam-5118	23	10	the	the	DET
ejpam-5118	23	11	isomorphism	isomorphism	NOUN
ejpam-5118	23	12	problem	problem	NOUN
ejpam-5118	23	13	,	,	PUNCT
ejpam-5118	23	14	but	but	CCONJ
ejpam-5118	23	15	it	it	PRON
ejpam-5118	23	16	has	have	AUX
ejpam-5118	23	17	been	be	AUX
ejpam-5118	23	18	discussed	discuss	VERB
ejpam-5118	23	19	for	for	ADP
ejpam-5118	23	20	some	some	DET
ejpam-5118	23	21	special	special	ADJ
ejpam-5118	23	22	cases	case	NOUN
ejpam-5118	23	23	in	in	ADP
ejpam-5118	23	24	[	[	X
ejpam-5118	23	25	8–10	8–10	NOUN
ejpam-5118	23	26	]	]	PUNCT
ejpam-5118	23	27	.	.	PUNCT
ejpam-5118	24	1	in	in	ADP
ejpam-5118	24	2	fact	fact	NOUN
ejpam-5118	24	3	,	,	PUNCT
ejpam-5118	24	4	doi	doi	PROPN
ejpam-5118	24	5	:	:	PUNCT
ejpam-5118	24	6	https://doi.org/10.29020/nybg.ejpam.v17i2.5118	https://doi.org/10.29020/nybg.ejpam.v17i2.5118	PRON
ejpam-5118	24	7	email	email	NOUN
ejpam-5118	24	8	address	address	NOUN
ejpam-5118	24	9	:	:	PUNCT
ejpam-5118	24	10	noureddine.snanou@usmba.ac.ma	noureddine.snanou@usmba.ac.ma	NUM
ejpam-5118	24	11	(	(	PUNCT
ejpam-5118	24	12	n.	n.	PROPN
ejpam-5118	24	13	snanou	snanou	PROPN
ejpam-5118	24	14	)	)	PUNCT
ejpam-5118	24	15	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5118	25	1	956	956	NUM
ejpam-5118	25	2	©	©	ADP
ejpam-5118	25	3	2024	2024	NUM
ejpam-5118	25	4	ejpam	ejpam	NOUN
ejpam-5118	25	5	all	all	DET
ejpam-5118	25	6	rights	right	NOUN
ejpam-5118	25	7	reserved	reserve	VERB
ejpam-5118	25	8	.	.	PUNCT
ejpam-5118	26	1	n.	n.	NOUN
ejpam-5118	26	2	snanou	snanou	PROPN
ejpam-5118	26	3	/	/	SYM
ejpam-5118	26	4	eur	eur	PROPN
ejpam-5118	26	5	.	.	PUNCT
ejpam-5118	27	1	j.	j.	PROPN
ejpam-5118	27	2	pure	pure	PROPN
ejpam-5118	27	3	appl	appl	PROPN
ejpam-5118	27	4	.	.	PROPN
ejpam-5118	27	5	math	math	PROPN
ejpam-5118	27	6	,	,	PUNCT
ejpam-5118	27	7	17	17	NUM
ejpam-5118	27	8	(	(	PUNCT
ejpam-5118	27	9	2	2	NUM
ejpam-5118	27	10	)	)	PUNCT
ejpam-5118	27	11	(	(	PUNCT
ejpam-5118	27	12	2024	2024	NUM
ejpam-5118	27	13	)	)	PUNCT
ejpam-5118	27	14	,	,	PUNCT
ejpam-5118	27	15	956	956	NUM
ejpam-5118	27	16	-	-	SYM
ejpam-5118	27	17	968	968	NUM
ejpam-5118	27	18	957	957	NUM
ejpam-5118	27	19	those	those	DET
ejpam-5118	27	20	results	result	NOUN
ejpam-5118	27	21	do	do	AUX
ejpam-5118	27	22	not	not	PART
ejpam-5118	27	23	concern	concern	VERB
ejpam-5118	27	24	general	general	ADJ
ejpam-5118	27	25	isomorphisms	isomorphism	NOUN
ejpam-5118	27	26	,	,	PUNCT
ejpam-5118	27	27	but	but	CCONJ
ejpam-5118	27	28	only	only	ADV
ejpam-5118	27	29	those	those	PRON
ejpam-5118	27	30	of	of	ADP
ejpam-5118	27	31	certain	certain	ADJ
ejpam-5118	27	32	type	type	NOUN
ejpam-5118	27	33	,	,	PUNCT
ejpam-5118	27	34	namely	namely	ADV
ejpam-5118	27	35	leaving	leave	VERB
ejpam-5118	27	36	the	the	DET
ejpam-5118	27	37	kernel	kernel	PROPN
ejpam-5118	27	38	group	group	NOUN
ejpam-5118	27	39	or	or	CCONJ
ejpam-5118	27	40	both	both	CCONJ
ejpam-5118	27	41	the	the	DET
ejpam-5118	27	42	two	two	NUM
ejpam-5118	27	43	factors	factor	NOUN
ejpam-5118	27	44	invariant	invariant	ADJ
ejpam-5118	27	45	,	,	PUNCT
ejpam-5118	27	46	inducing	induce	VERB
ejpam-5118	27	47	the	the	DET
ejpam-5118	27	48	identity	identity	NOUN
ejpam-5118	27	49	or	or	CCONJ
ejpam-5118	27	50	a	a	DET
ejpam-5118	27	51	commuting	commuting	NOUN
ejpam-5118	27	52	automorphism	automorphism	NOUN
ejpam-5118	27	53	on	on	ADP
ejpam-5118	27	54	the	the	DET
ejpam-5118	27	55	quotient	quotient	NOUN
ejpam-5118	27	56	group	group	NOUN
ejpam-5118	27	57	.	.	PUNCT
ejpam-5118	28	1	in	in	ADP
ejpam-5118	28	2	this	this	DET
ejpam-5118	28	3	work	work	NOUN
ejpam-5118	28	4	,	,	PUNCT
ejpam-5118	28	5	necessary	necessary	ADJ
ejpam-5118	28	6	and	and	CCONJ
ejpam-5118	28	7	sufficient	sufficient	ADJ
ejpam-5118	28	8	conditions	condition	NOUN
ejpam-5118	28	9	for	for	ADP
ejpam-5118	28	10	two	two	NUM
ejpam-5118	28	11	central	central	ADJ
ejpam-5118	28	12	extensions	extension	NOUN
ejpam-5118	28	13	of	of	ADP
ejpam-5118	28	14	g1	g1	NOUN
ejpam-5118	28	15	by	by	ADP
ejpam-5118	28	16	g2	g2	PROPN
ejpam-5118	28	17	to	to	PART
ejpam-5118	28	18	be	be	AUX
ejpam-5118	28	19	isomorphic	isomorphic	ADJ
ejpam-5118	28	20	are	be	AUX
ejpam-5118	28	21	given	give	VERB
ejpam-5118	28	22	in	in	ADP
ejpam-5118	28	23	some	some	DET
ejpam-5118	28	24	new	new	ADJ
ejpam-5118	28	25	situations	situation	NOUN
ejpam-5118	28	26	.	.	PUNCT
ejpam-5118	29	1	more	more	ADV
ejpam-5118	29	2	precisely	precisely	ADV
ejpam-5118	29	3	,	,	PUNCT
ejpam-5118	29	4	we	we	PRON
ejpam-5118	29	5	study	study	VERB
ejpam-5118	29	6	the	the	DET
ejpam-5118	29	7	case	case	NOUN
ejpam-5118	29	8	when	when	SCONJ
ejpam-5118	29	9	the	the	DET
ejpam-5118	29	10	quotient	quotient	NOUN
ejpam-5118	29	11	group	group	NOUN
ejpam-5118	29	12	is	be	AUX
ejpam-5118	29	13	simple	simple	ADJ
ejpam-5118	29	14	or	or	CCONJ
ejpam-5118	29	15	purely	purely	ADV
ejpam-5118	29	16	non	non	ADJ
ejpam-5118	29	17	-	-	ADJ
ejpam-5118	29	18	abelian	abelian	ADJ
ejpam-5118	29	19	.	.	PUNCT
ejpam-5118	30	1	furthermore	furthermore	ADV
ejpam-5118	30	2	,	,	PUNCT
ejpam-5118	30	3	we	we	PRON
ejpam-5118	30	4	characterize	characterize	VERB
ejpam-5118	30	5	isomorphisms	isomorphism	NOUN
ejpam-5118	30	6	leaving	leave	VERB
ejpam-5118	30	7	the	the	DET
ejpam-5118	30	8	quotient	quotient	NOUN
ejpam-5118	30	9	group	group	NOUN
ejpam-5118	30	10	invariant	invariant	PROPN
ejpam-5118	30	11	,	,	PUNCT
ejpam-5118	30	12	and	and	CCONJ
ejpam-5118	30	13	deal	deal	VERB
ejpam-5118	30	14	with	with	ADP
ejpam-5118	30	15	isomorphisms	isomorphism	NOUN
ejpam-5118	30	16	of	of	ADP
ejpam-5118	30	17	central	central	ADJ
ejpam-5118	30	18	extensions	extension	NOUN
ejpam-5118	30	19	where	where	SCONJ
ejpam-5118	30	20	the	the	DET
ejpam-5118	30	21	kernel	kernel	PROPN
ejpam-5118	30	22	group	group	PROPN
ejpam-5118	30	23	g1	g1	PROPN
ejpam-5118	30	24	and	and	CCONJ
ejpam-5118	30	25	the	the	DET
ejpam-5118	30	26	quotient	quotient	NOUN
ejpam-5118	30	27	group	group	PROPN
ejpam-5118	30	28	g2	g2	PROPN
ejpam-5118	30	29	are	be	AUX
ejpam-5118	30	30	isomorphic	isomorphic	ADJ
ejpam-5118	30	31	.	.	PUNCT
ejpam-5118	31	1	throughout	throughout	ADP
ejpam-5118	31	2	this	this	DET
ejpam-5118	31	3	paper	paper	NOUN
ejpam-5118	31	4	,	,	PUNCT
ejpam-5118	31	5	we	we	PRON
ejpam-5118	31	6	denote	denote	VERB
ejpam-5118	31	7	by	by	ADP
ejpam-5118	31	8	z(g	z(g	NOUN
ejpam-5118	31	9	)	)	PUNCT
ejpam-5118	31	10	,	,	PUNCT
ejpam-5118	31	11	g′	g′	NOUN
ejpam-5118	31	12	,	,	PUNCT
ejpam-5118	31	13	aut(g	aut(g	PROPN
ejpam-5118	31	14	)	)	PUNCT
ejpam-5118	31	15	and	and	CCONJ
ejpam-5118	31	16	end(g	end(g	NUM
ejpam-5118	31	17	)	)	PUNCT
ejpam-5118	31	18	,	,	PUNCT
ejpam-5118	31	19	respectively	respectively	ADV
ejpam-5118	31	20	,	,	PUNCT
ejpam-5118	31	21	the	the	DET
ejpam-5118	31	22	center	center	NOUN
ejpam-5118	31	23	,	,	PUNCT
ejpam-5118	31	24	the	the	DET
ejpam-5118	31	25	derived	derive	VERB
ejpam-5118	31	26	subgroup	subgroup	NOUN
ejpam-5118	31	27	,	,	PUNCT
ejpam-5118	31	28	the	the	DET
ejpam-5118	31	29	automorphism	automorphism	NOUN
ejpam-5118	31	30	group	group	NOUN
ejpam-5118	31	31	,	,	PUNCT
ejpam-5118	31	32	and	and	CCONJ
ejpam-5118	31	33	the	the	DET
ejpam-5118	31	34	monoid	monoid	NOUN
ejpam-5118	31	35	of	of	ADP
ejpam-5118	31	36	endomorphisms	endomorphism	NOUN
ejpam-5118	31	37	of	of	ADP
ejpam-5118	31	38	g.	g.	PROPN
ejpam-5118	31	39	for	for	ADP
ejpam-5118	31	40	any	any	DET
ejpam-5118	31	41	two	two	NUM
ejpam-5118	31	42	groups	group	NOUN
ejpam-5118	31	43	h	h	NOUN
ejpam-5118	31	44	and	and	CCONJ
ejpam-5118	31	45	k	k	NOUN
ejpam-5118	31	46	,	,	PUNCT
ejpam-5118	31	47	let	let	VERB
ejpam-5118	31	48	hom(h	hom(h	PROPN
ejpam-5118	31	49	,	,	PUNCT
ejpam-5118	31	50	k	k	NOUN
ejpam-5118	31	51	)	)	PUNCT
ejpam-5118	31	52	denote	denote	VERB
ejpam-5118	31	53	the	the	DET
ejpam-5118	31	54	set	set	NOUN
ejpam-5118	31	55	of	of	ADP
ejpam-5118	31	56	all	all	DET
ejpam-5118	31	57	homomorphisms	homomorphism	NOUN
ejpam-5118	31	58	from	from	ADP
ejpam-5118	31	59	h	h	NOUN
ejpam-5118	31	60	to	to	ADP
ejpam-5118	31	61	k.	k.	PROPN
ejpam-5118	31	62	2	2	X
ejpam-5118	31	63	.	.	PUNCT
ejpam-5118	31	64	central	central	ADJ
ejpam-5118	31	65	extension	extension	NOUN
ejpam-5118	31	66	in	in	ADP
ejpam-5118	31	67	this	this	DET
ejpam-5118	31	68	paper	paper	NOUN
ejpam-5118	31	69	,	,	PUNCT
ejpam-5118	31	70	aspects	aspect	NOUN
ejpam-5118	31	71	of	of	ADP
ejpam-5118	31	72	group	group	NOUN
ejpam-5118	31	73	cohomology	cohomology	NOUN
ejpam-5118	31	74	will	will	AUX
ejpam-5118	31	75	be	be	AUX
ejpam-5118	31	76	used	use	VERB
ejpam-5118	31	77	frequently	frequently	ADV
ejpam-5118	31	78	.	.	PUNCT
ejpam-5118	32	1	therefore	therefore	ADV
ejpam-5118	32	2	,	,	PUNCT
ejpam-5118	32	3	we	we	PRON
ejpam-5118	32	4	recall	recall	VERB
ejpam-5118	32	5	in	in	ADP
ejpam-5118	32	6	this	this	DET
ejpam-5118	32	7	section	section	NOUN
ejpam-5118	32	8	some	some	DET
ejpam-5118	32	9	basic	basic	ADJ
ejpam-5118	32	10	facts	fact	NOUN
ejpam-5118	32	11	of	of	ADP
ejpam-5118	32	12	this	this	DET
ejpam-5118	32	13	theory	theory	NOUN
ejpam-5118	32	14	and	and	CCONJ
ejpam-5118	32	15	fix	fix	VERB
ejpam-5118	32	16	additional	additional	ADJ
ejpam-5118	32	17	notations	notation	NOUN
ejpam-5118	32	18	and	and	CCONJ
ejpam-5118	32	19	terminology	terminology	NOUN
ejpam-5118	32	20	.	.	PUNCT
ejpam-5118	33	1	let	let	VERB
ejpam-5118	33	2	1	1	NUM
ejpam-5118	33	3	→	→	SYM
ejpam-5118	33	4	g1→g→g2	g1→g→g2	PROPN
ejpam-5118	33	5	→	→	SYM
ejpam-5118	33	6	1	1	NUM
ejpam-5118	33	7	be	be	AUX
ejpam-5118	33	8	a	a	DET
ejpam-5118	33	9	group	group	NOUN
ejpam-5118	33	10	extension	extension	NOUN
ejpam-5118	33	11	,	,	PUNCT
ejpam-5118	33	12	where	where	SCONJ
ejpam-5118	33	13	for	for	ADP
ejpam-5118	33	14	convenience	convenience	NOUN
ejpam-5118	33	15	we	we	PRON
ejpam-5118	33	16	regard	regard	VERB
ejpam-5118	33	17	the	the	DET
ejpam-5118	33	18	kernel	kernel	PROPN
ejpam-5118	33	19	group	group	PROPN
ejpam-5118	33	20	g1	g1	PROPN
ejpam-5118	33	21	as	as	ADP
ejpam-5118	33	22	a	a	DET
ejpam-5118	33	23	subgroup	subgroup	NOUN
ejpam-5118	33	24	of	of	ADP
ejpam-5118	33	25	g	g	PROPN
ejpam-5118	33	26	and	and	CCONJ
ejpam-5118	33	27	g2	g2	PROPN
ejpam-5118	33	28	is	be	AUX
ejpam-5118	33	29	identified	identify	VERB
ejpam-5118	33	30	with	with	ADP
ejpam-5118	33	31	the	the	DET
ejpam-5118	33	32	quotient	quotient	NOUN
ejpam-5118	33	33	group	group	NOUN
ejpam-5118	33	34	g	g	PROPN
ejpam-5118	33	35	/	/	SYM
ejpam-5118	33	36	g1	g1	PROPN
ejpam-5118	33	37	.	.	PUNCT
ejpam-5118	34	1	if	if	SCONJ
ejpam-5118	34	2	g1	g1	PROPN
ejpam-5118	34	3	is	be	AUX
ejpam-5118	34	4	a	a	DET
ejpam-5118	34	5	central	central	ADJ
ejpam-5118	34	6	subgroup	subgroup	NOUN
ejpam-5118	34	7	of	of	ADP
ejpam-5118	34	8	g	g	PROPN
ejpam-5118	34	9	,	,	PUNCT
ejpam-5118	34	10	then	then	ADV
ejpam-5118	34	11	we	we	PRON
ejpam-5118	34	12	say	say	VERB
ejpam-5118	34	13	that	that	SCONJ
ejpam-5118	34	14	g	g	PROPN
ejpam-5118	34	15	is	be	AUX
ejpam-5118	34	16	a	a	DET
ejpam-5118	34	17	central	central	ADJ
ejpam-5118	34	18	extension	extension	NOUN
ejpam-5118	34	19	of	of	ADP
ejpam-5118	34	20	g1	g1	NOUN
ejpam-5118	34	21	by	by	ADP
ejpam-5118	34	22	g2	g2	PROPN
ejpam-5118	34	23	.	.	PUNCT
ejpam-5118	35	1	two	two	NUM
ejpam-5118	35	2	central	central	ADJ
ejpam-5118	35	3	extensions	extension	NOUN
ejpam-5118	35	4	g	g	NOUN
ejpam-5118	35	5	and	and	CCONJ
ejpam-5118	35	6	g′	g′	NOUN
ejpam-5118	35	7	of	of	ADP
ejpam-5118	35	8	g1	g1	PROPN
ejpam-5118	35	9	by	by	ADP
ejpam-5118	35	10	g2	g2	PROPN
ejpam-5118	35	11	are	be	AUX
ejpam-5118	35	12	said	say	VERB
ejpam-5118	35	13	to	to	PART
ejpam-5118	35	14	be	be	AUX
ejpam-5118	35	15	equivalent	equivalent	ADJ
ejpam-5118	35	16	if	if	SCONJ
ejpam-5118	35	17	there	there	PRON
ejpam-5118	35	18	exists	exist	VERB
ejpam-5118	35	19	a	a	DET
ejpam-5118	35	20	homomorphism	homomorphism	NOUN
ejpam-5118	35	21	φ	φ	X
ejpam-5118	35	22	:	:	PUNCT
ejpam-5118	35	23	g→	g→	PROPN
ejpam-5118	35	24	g′	g′	NOUN
ejpam-5118	35	25	such	such	ADJ
ejpam-5118	35	26	that	that	SCONJ
ejpam-5118	35	27	the	the	DET
ejpam-5118	35	28	diagram	diagram	NOUN
ejpam-5118	35	29	1	1	NUM
ejpam-5118	35	30	→	→	SYM
ejpam-5118	35	31	g1	g1	PROPN
ejpam-5118	35	32	→	→	SYM
ejpam-5118	35	33	g	g	PROPN
ejpam-5118	35	34	→	→	SYM
ejpam-5118	35	35	g2	g2	PROPN
ejpam-5118	35	36	→	→	SYM
ejpam-5118	35	37	1	1	NUM
ejpam-5118	35	38	∥	∥	NUM
ejpam-5118	35	39	↓	↓	NOUN
ejpam-5118	35	40	φ	φ	PROPN
ejpam-5118	35	41	∥	∥	PROPN
ejpam-5118	35	42	1	1	NUM
ejpam-5118	35	43	→	→	SYM
ejpam-5118	35	44	g1	g1	PROPN
ejpam-5118	35	45	→	→	SYM
ejpam-5118	35	46	g′	g′	NOUN
ejpam-5118	35	47	→	→	SYM
ejpam-5118	35	48	g2	g2	PROPN
ejpam-5118	35	49	→	→	SYM
ejpam-5118	35	50	1	1	NUM
ejpam-5118	35	51	commutes	commute	NOUN
ejpam-5118	35	52	.	.	PUNCT
ejpam-5118	36	1	letg2	letg2	PROPN
ejpam-5118	36	2	be	be	AUX
ejpam-5118	36	3	a	a	DET
ejpam-5118	36	4	group	group	NOUN
ejpam-5118	36	5	which	which	PRON
ejpam-5118	36	6	acts	act	VERB
ejpam-5118	36	7	trivially	trivially	ADV
ejpam-5118	36	8	on	on	ADP
ejpam-5118	36	9	a	a	DET
ejpam-5118	36	10	groupg1	groupg1	NOUN
ejpam-5118	36	11	.	.	PUNCT
ejpam-5118	37	1	a	a	DET
ejpam-5118	37	2	2	2	NUM
ejpam-5118	37	3	-	-	PUNCT
ejpam-5118	37	4	cocycle	cocycle	NOUN
ejpam-5118	37	5	ofg2	ofg2	PROPN
ejpam-5118	37	6	with	with	ADP
ejpam-5118	37	7	coefficients	coefficient	NOUN
ejpam-5118	37	8	in	in	ADP
ejpam-5118	37	9	g1	g1	PROPN
ejpam-5118	37	10	is	be	AUX
ejpam-5118	37	11	a	a	DET
ejpam-5118	37	12	map	map	NOUN
ejpam-5118	37	13	ε	ε	PROPN
ejpam-5118	37	14	:	:	PUNCT
ejpam-5118	37	15	g2	g2	PROPN
ejpam-5118	37	16	×g2	×g2	PROPN
ejpam-5118	37	17	→	→	SYM
ejpam-5118	37	18	g1	g1	PROPN
ejpam-5118	37	19	satisfying	satisfy	VERB
ejpam-5118	37	20	the	the	DET
ejpam-5118	37	21	2	2	NUM
ejpam-5118	37	22	-	-	PUNCT
ejpam-5118	37	23	cocycle	cocycle	NOUN
ejpam-5118	37	24	condition	condition	NOUN
ejpam-5118	37	25	,	,	PUNCT
ejpam-5118	37	26	that	that	PRON
ejpam-5118	37	27	is	be	AUX
ejpam-5118	37	28	ε(h	ε(h	NOUN
ejpam-5118	37	29	,	,	PUNCT
ejpam-5118	37	30	g)ε(hg	g)ε(hg	NOUN
ejpam-5118	37	31	,	,	PUNCT
ejpam-5118	37	32	k	k	NOUN
ejpam-5118	37	33	)	)	PUNCT
ejpam-5118	37	34	=	=	SYM
ejpam-5118	37	35	ε(g	ε(g	PROPN
ejpam-5118	37	36	,	,	PUNCT
ejpam-5118	37	37	k)ε(h	k)ε(h	PROPN
ejpam-5118	37	38	,	,	PUNCT
ejpam-5118	37	39	gk	gk	PROPN
ejpam-5118	37	40	)	)	PUNCT
ejpam-5118	37	41	for	for	ADP
ejpam-5118	37	42	all	all	PRON
ejpam-5118	37	43	g	g	PROPN
ejpam-5118	37	44	,	,	PUNCT
ejpam-5118	37	45	h	h	NOUN
ejpam-5118	37	46	,	,	PUNCT
ejpam-5118	37	47	k	k	PROPN
ejpam-5118	37	48	∈	∈	PROPN
ejpam-5118	37	49	g2	g2	PROPN
ejpam-5118	37	50	.	.	PUNCT
ejpam-5118	38	1	we	we	PRON
ejpam-5118	38	2	always	always	ADV
ejpam-5118	38	3	assume	assume	VERB
ejpam-5118	38	4	that	that	SCONJ
ejpam-5118	38	5	ε	ε	PROPN
ejpam-5118	38	6	is	be	AUX
ejpam-5118	38	7	normalized	normalize	VERB
ejpam-5118	38	8	,	,	PUNCT
ejpam-5118	38	9	i.e.	i.e.	X
ejpam-5118	38	10	ε(g	ε(g	NOUN
ejpam-5118	38	11	,	,	PUNCT
ejpam-5118	38	12	1	1	NUM
ejpam-5118	38	13	)	)	PUNCT
ejpam-5118	38	14	=	=	SYM
ejpam-5118	39	1	ε(1	ε(1	PROPN
ejpam-5118	39	2	,	,	PUNCT
ejpam-5118	39	3	g	g	NOUN
ejpam-5118	39	4	)	)	PUNCT
ejpam-5118	39	5	=	=	SYM
ejpam-5118	39	6	1	1	NUM
ejpam-5118	39	7	for	for	ADP
ejpam-5118	39	8	all	all	DET
ejpam-5118	39	9	g	g	PROPN
ejpam-5118	39	10	∈	∈	PROPN
ejpam-5118	39	11	g2	g2	PROPN
ejpam-5118	39	12	.	.	PUNCT
ejpam-5118	40	1	note	note	VERB
ejpam-5118	40	2	that	that	SCONJ
ejpam-5118	40	3	2	2	NUM
ejpam-5118	40	4	-	-	PUNCT
ejpam-5118	40	5	cocycles	cocycle	NOUN
ejpam-5118	40	6	are	be	AUX
ejpam-5118	40	7	known	know	VERB
ejpam-5118	40	8	by	by	ADP
ejpam-5118	40	9	factor	factor	NOUN
ejpam-5118	40	10	sets	set	NOUN
ejpam-5118	40	11	in	in	ADP
ejpam-5118	40	12	many	many	ADJ
ejpam-5118	40	13	books	book	NOUN
ejpam-5118	40	14	(	(	PUNCT
ejpam-5118	40	15	see	see	VERB
ejpam-5118	40	16	for	for	ADP
ejpam-5118	40	17	example	example	NOUN
ejpam-5118	41	1	[	[	X
ejpam-5118	41	2	1–3	1–3	NOUN
ejpam-5118	41	3	,	,	PUNCT
ejpam-5118	41	4	5	5	NUM
ejpam-5118	41	5	,	,	PUNCT
ejpam-5118	41	6	6	6	NUM
ejpam-5118	41	7	,	,	PUNCT
ejpam-5118	41	8	12	12	NUM
ejpam-5118	41	9	]	]	PUNCT
ejpam-5118	41	10	)	)	PUNCT
ejpam-5118	41	11	.	.	PUNCT
ejpam-5118	42	1	the	the	DET
ejpam-5118	42	2	set	set	NOUN
ejpam-5118	42	3	of	of	ADP
ejpam-5118	42	4	normalized	normalize	VERB
ejpam-5118	42	5	2	2	NUM
ejpam-5118	42	6	-	-	PUNCT
ejpam-5118	42	7	cocycles	cocycle	NOUN
ejpam-5118	42	8	of	of	ADP
ejpam-5118	42	9	g2	g2	PROPN
ejpam-5118	42	10	with	with	ADP
ejpam-5118	42	11	coefficients	coefficient	NOUN
ejpam-5118	42	12	in	in	ADP
ejpam-5118	42	13	g1	g1	PROPN
ejpam-5118	42	14	is	be	AUX
ejpam-5118	42	15	denoted	denote	VERB
ejpam-5118	42	16	by	by	ADP
ejpam-5118	42	17	z2(g2	z2(g2	NOUN
ejpam-5118	42	18	,	,	PUNCT
ejpam-5118	42	19	g1	g1	NOUN
ejpam-5118	42	20	)	)	PUNCT
ejpam-5118	42	21	.	.	PUNCT
ejpam-5118	43	1	the	the	DET
ejpam-5118	43	2	trivial	trivial	ADJ
ejpam-5118	43	3	2	2	NUM
ejpam-5118	43	4	-	-	PUNCT
ejpam-5118	43	5	cocycle	cocycle	NOUN
ejpam-5118	43	6	is	be	AUX
ejpam-5118	43	7	the	the	DET
ejpam-5118	43	8	2	2	NUM
ejpam-5118	43	9	-	-	PUNCT
ejpam-5118	43	10	cocycle	cocycle	NOUN
ejpam-5118	43	11	c	c	NOUN
ejpam-5118	43	12	with	with	ADP
ejpam-5118	43	13	c(g	c(g	PROPN
ejpam-5118	43	14	,	,	PUNCT
ejpam-5118	43	15	h	h	NOUN
ejpam-5118	43	16	)	)	PUNCT
ejpam-5118	43	17	=	=	SYM
ejpam-5118	43	18	1	1	NUM
ejpam-5118	43	19	for	for	ADP
ejpam-5118	43	20	all	all	DET
ejpam-5118	43	21	g	g	NOUN
ejpam-5118	43	22	,	,	PUNCT
ejpam-5118	43	23	h	h	NOUN
ejpam-5118	43	24	∈	∈	PROPN
ejpam-5118	43	25	g2	g2	PROPN
ejpam-5118	43	26	.	.	PUNCT
ejpam-5118	44	1	let	let	VERB
ejpam-5118	44	2	ε1	ε1	VERB
ejpam-5118	44	3	,	,	PUNCT
ejpam-5118	44	4	ε2	ε2	PROPN
ejpam-5118	44	5	∈	∈	PROPN
ejpam-5118	44	6	z2(g2	z2(g2	NOUN
ejpam-5118	44	7	,	,	PUNCT
ejpam-5118	44	8	g1	g1	NOUN
ejpam-5118	44	9	)	)	PUNCT
ejpam-5118	44	10	.	.	PUNCT
ejpam-5118	45	1	we	we	PRON
ejpam-5118	45	2	write	write	VERB
ejpam-5118	45	3	ε1	ε1	VERB
ejpam-5118	45	4	∼	∼	NOUN
ejpam-5118	45	5	ε2	ε2	ADJ
ejpam-5118	45	6	and	and	CCONJ
ejpam-5118	45	7	say	say	VERB
ejpam-5118	45	8	that	that	PRON
ejpam-5118	45	9	ε1	ε1	PROPN
ejpam-5118	45	10	and	and	CCONJ
ejpam-5118	45	11	ε2	ε2	ADJ
ejpam-5118	45	12	are	be	AUX
ejpam-5118	45	13	cohomologous	cohomologous	ADJ
ejpam-5118	45	14	,	,	PUNCT
ejpam-5118	45	15	if	if	SCONJ
ejpam-5118	45	16	there	there	PRON
ejpam-5118	45	17	is	be	VERB
ejpam-5118	45	18	a	a	DET
ejpam-5118	45	19	map	map	NOUN
ejpam-5118	45	20	t	t	NOUN
ejpam-5118	45	21	:	:	PUNCT
ejpam-5118	45	22	g2	g2	PROPN
ejpam-5118	45	23	→	→	SYM
ejpam-5118	45	24	g1	g1	VERB
ejpam-5118	45	25	such	such	ADJ
ejpam-5118	45	26	that	that	SCONJ
ejpam-5118	45	27	ε2(g	ε2(g	ADJ
ejpam-5118	45	28	,	,	PUNCT
ejpam-5118	45	29	h	h	NOUN
ejpam-5118	45	30	)	)	PUNCT
ejpam-5118	45	31	=	=	SYM
ejpam-5118	45	32	t(g)t(h)ε1(g	t(g)t(h)ε1(g	PROPN
ejpam-5118	45	33	,	,	PUNCT
ejpam-5118	45	34	h)t(gh	h)t(gh	PUNCT
ejpam-5118	45	35	)	)	PUNCT
ejpam-5118	45	36	−1	−1	NOUN
ejpam-5118	45	37	for	for	ADP
ejpam-5118	45	38	all	all	DET
ejpam-5118	45	39	g	g	NOUN
ejpam-5118	45	40	,	,	PUNCT
ejpam-5118	45	41	h	h	NOUN
ejpam-5118	45	42	∈	∈	PROPN
ejpam-5118	45	43	g2	g2	PROPN
ejpam-5118	45	44	.	.	PUNCT
ejpam-5118	46	1	then	then	ADV
ejpam-5118	46	2	(	(	PUNCT
ejpam-5118	46	3	∼	∼	NOUN
ejpam-5118	46	4	)	)	PUNCT
ejpam-5118	46	5	is	be	AUX
ejpam-5118	46	6	an	an	DET
ejpam-5118	46	7	equivalence	equivalence	NOUN
ejpam-5118	46	8	relation	relation	NOUN
ejpam-5118	46	9	on	on	ADP
ejpam-5118	46	10	z2(g2	z2(g2	NUM
ejpam-5118	46	11	,	,	PUNCT
ejpam-5118	46	12	g1	g1	NOUN
ejpam-5118	46	13	)	)	PUNCT
ejpam-5118	46	14	.	.	PUNCT
ejpam-5118	47	1	the	the	DET
ejpam-5118	47	2	cohomology	cohomology	NOUN
ejpam-5118	47	3	class	class	NOUN
ejpam-5118	47	4	of	of	ADP
ejpam-5118	47	5	ε	ε	PROPN
ejpam-5118	47	6	∈	∈	PROPN
ejpam-5118	47	7	z2(g2	z2(g2	PROPN
ejpam-5118	47	8	,	,	PUNCT
ejpam-5118	47	9	g1	g1	PROPN
ejpam-5118	47	10	)	)	PUNCT
ejpam-5118	47	11	is	be	AUX
ejpam-5118	47	12	denoted	denote	VERB
ejpam-5118	47	13	by	by	ADP
ejpam-5118	47	14	[	[	X
ejpam-5118	47	15	ε	ε	X
ejpam-5118	47	16	]	]	PUNCT
ejpam-5118	47	17	.	.	PUNCT
ejpam-5118	48	1	the	the	DET
ejpam-5118	48	2	set	set	NOUN
ejpam-5118	48	3	of	of	ADP
ejpam-5118	48	4	all	all	DET
ejpam-5118	48	5	cohomology	cohomology	NOUN
ejpam-5118	48	6	classes	class	NOUN
ejpam-5118	48	7	of	of	ADP
ejpam-5118	48	8	g2	g2	PROPN
ejpam-5118	48	9	with	with	ADP
ejpam-5118	48	10	coefficients	coefficient	NOUN
ejpam-5118	48	11	in	in	ADP
ejpam-5118	48	12	g1	g1	PROPN
ejpam-5118	48	13	is	be	AUX
ejpam-5118	48	14	denoted	denote	VERB
ejpam-5118	48	15	by	by	ADP
ejpam-5118	48	16	h2(g2	h2(g2	ADP
ejpam-5118	48	17	,	,	PUNCT
ejpam-5118	48	18	g1	g1	PROPN
ejpam-5118	48	19	)	)	PUNCT
ejpam-5118	48	20	and	and	CCONJ
ejpam-5118	48	21	called	call	VERB
ejpam-5118	48	22	the	the	DET
ejpam-5118	48	23	second	second	ADJ
ejpam-5118	48	24	cohomology	cohomology	NOUN
ejpam-5118	48	25	of	of	ADP
ejpam-5118	48	26	g2	g2	PROPN
ejpam-5118	48	27	with	with	ADP
ejpam-5118	48	28	coefficients	coefficient	NOUN
ejpam-5118	48	29	in	in	ADP
ejpam-5118	48	30	g1	g1	PROPN
ejpam-5118	48	31	.	.	PUNCT
ejpam-5118	49	1	from	from	ADP
ejpam-5118	49	2	now	now	ADV
ejpam-5118	49	3	,	,	PUNCT
ejpam-5118	49	4	g1	g1	PROPN
ejpam-5118	49	5	will	will	AUX
ejpam-5118	49	6	always	always	ADV
ejpam-5118	49	7	considered	consider	VERB
ejpam-5118	49	8	an	an	DET
ejpam-5118	49	9	abelian	abelian	ADJ
ejpam-5118	49	10	group	group	NOUN
ejpam-5118	49	11	.	.	PUNCT
ejpam-5118	50	1	then	then	ADV
ejpam-5118	50	2	z2(g2	z2(g2	NUM
ejpam-5118	50	3	,	,	PUNCT
ejpam-5118	50	4	g1	g1	PROPN
ejpam-5118	50	5	)	)	PUNCT
ejpam-5118	50	6	is	be	AUX
ejpam-5118	50	7	an	an	DET
ejpam-5118	50	8	abelian	abelian	ADJ
ejpam-5118	50	9	group	group	NOUN
ejpam-5118	50	10	and	and	CCONJ
ejpam-5118	50	11	we	we	PRON
ejpam-5118	50	12	have	have	VERB
ejpam-5118	50	13	h2(g2	h2(g2	NOUN
ejpam-5118	50	14	,	,	PUNCT
ejpam-5118	50	15	g1	g1	X
ejpam-5118	50	16	)	)	PUNCT
ejpam-5118	51	1	=	=	SYM
ejpam-5118	51	2	z2(g2	z2(g2	PROPN
ejpam-5118	51	3	,	,	PUNCT
ejpam-5118	51	4	g1)/b	g1)/b	NOUN
ejpam-5118	51	5	2(g2	2(g2	NUM
ejpam-5118	51	6	,	,	PUNCT
ejpam-5118	51	7	g1	g1	PROPN
ejpam-5118	51	8	)	)	PUNCT
ejpam-5118	51	9	where	where	SCONJ
ejpam-5118	51	10	b2(g2	b2(g2	X
ejpam-5118	51	11	,	,	PUNCT
ejpam-5118	51	12	g1	g1	PROPN
ejpam-5118	51	13	)	)	PUNCT
ejpam-5118	51	14	is	be	AUX
ejpam-5118	51	15	the	the	DET
ejpam-5118	51	16	subgroup	subgroup	NOUN
ejpam-5118	51	17	of	of	ADP
ejpam-5118	51	18	z2(g2	z2(g2	PROPN
ejpam-5118	51	19	,	,	PUNCT
ejpam-5118	51	20	g1	g1	PROPN
ejpam-5118	51	21	)	)	PUNCT
ejpam-5118	51	22	which	which	PRON
ejpam-5118	51	23	consists	consist	VERB
ejpam-5118	51	24	of	of	ADP
ejpam-5118	51	25	all	all	DET
ejpam-5118	51	26	functions	function	NOUN
ejpam-5118	51	27	ψ	ψ	NOUN
ejpam-5118	51	28	:	:	PUNCT
ejpam-5118	51	29	g2×g2	g2×g2	PROPN
ejpam-5118	51	30	→	→	SYM
ejpam-5118	51	31	g1	g1	PROPN
ejpam-5118	51	32	satisfying	satisfy	VERB
ejpam-5118	51	33	that	that	SCONJ
ejpam-5118	51	34	for	for	ADP
ejpam-5118	51	35	all	all	DET
ejpam-5118	51	36	n.	n.	PROPN
ejpam-5118	51	37	snanou	snanou	PROPN
ejpam-5118	51	38	/	/	SYM
ejpam-5118	51	39	eur	eur	PROPN
ejpam-5118	51	40	.	.	PUNCT
ejpam-5118	52	1	j.	j.	PROPN
ejpam-5118	52	2	pure	pure	PROPN
ejpam-5118	52	3	appl	appl	PROPN
ejpam-5118	52	4	.	.	PROPN
ejpam-5118	52	5	math	math	PROPN
ejpam-5118	52	6	,	,	PUNCT
ejpam-5118	52	7	17	17	NUM
ejpam-5118	52	8	(	(	PUNCT
ejpam-5118	52	9	2	2	NUM
ejpam-5118	52	10	)	)	PUNCT
ejpam-5118	52	11	(	(	PUNCT
ejpam-5118	52	12	2024	2024	NUM
ejpam-5118	52	13	)	)	PUNCT
ejpam-5118	52	14	,	,	PUNCT
ejpam-5118	52	15	956	956	NUM
ejpam-5118	52	16	-	-	SYM
ejpam-5118	52	17	968	968	NUM
ejpam-5118	52	18	958	958	NUM
ejpam-5118	52	19	g	g	NOUN
ejpam-5118	52	20	,	,	PUNCT
ejpam-5118	52	21	h	h	NOUN
ejpam-5118	52	22	∈	∈	PROPN
ejpam-5118	52	23	g2	g2	PROPN
ejpam-5118	52	24	:	:	PUNCT
ejpam-5118	53	1	ψ(h	ψ(h	NOUN
ejpam-5118	53	2	,	,	PUNCT
ejpam-5118	53	3	g	g	NOUN
ejpam-5118	53	4	)	)	PUNCT
ejpam-5118	53	5	=	=	SYM
ejpam-5118	53	6	δ(g)δ(hg)−1δ(h	δ(g)δ(hg)−1δ(h	NOUN
ejpam-5118	53	7	)	)	PUNCT
ejpam-5118	53	8	for	for	ADP
ejpam-5118	53	9	some	some	DET
ejpam-5118	53	10	δ	δ	NOUN
ejpam-5118	53	11	:	:	PUNCT
ejpam-5118	53	12	g2	g2	PROPN
ejpam-5118	53	13	→	→	SYM
ejpam-5118	53	14	g1	g1	PROPN
ejpam-5118	53	15	.	.	PUNCT
ejpam-5118	54	1	the	the	DET
ejpam-5118	54	2	elements	element	NOUN
ejpam-5118	54	3	of	of	ADP
ejpam-5118	54	4	b2(g2	b2(g2	PRON
ejpam-5118	54	5	,	,	PUNCT
ejpam-5118	54	6	g1	g1	PROPN
ejpam-5118	54	7	)	)	PUNCT
ejpam-5118	54	8	are	be	AUX
ejpam-5118	54	9	called	call	VERB
ejpam-5118	54	10	2	2	NUM
ejpam-5118	54	11	-	-	PUNCT
ejpam-5118	54	12	coboundaries	coboundarie	NOUN
ejpam-5118	54	13	.	.	PUNCT
ejpam-5118	55	1	the	the	DET
ejpam-5118	55	2	set	set	NOUN
ejpam-5118	55	3	of	of	ADP
ejpam-5118	55	4	all	all	PRON
ejpam-5118	55	5	normalized	normalize	VERB
ejpam-5118	55	6	2	2	NUM
ejpam-5118	55	7	-	-	PUNCT
ejpam-5118	55	8	cocycles	cocycle	NOUN
ejpam-5118	55	9	which	which	PRON
ejpam-5118	55	10	are	be	AUX
ejpam-5118	55	11	symmetric	symmetric	ADJ
ejpam-5118	55	12	forms	form	NOUN
ejpam-5118	55	13	a	a	DET
ejpam-5118	55	14	subgroup	subgroup	NOUN
ejpam-5118	55	15	of	of	ADP
ejpam-5118	55	16	z2(g2	z2(g2	PROPN
ejpam-5118	55	17	,	,	PUNCT
ejpam-5118	55	18	g1	g1	NOUN
ejpam-5118	55	19	)	)	PUNCT
ejpam-5118	55	20	and	and	CCONJ
ejpam-5118	55	21	denoted	denote	VERB
ejpam-5118	55	22	by	by	ADP
ejpam-5118	55	23	sz2(g2	sz2(g2	NOUN
ejpam-5118	55	24	,	,	PUNCT
ejpam-5118	55	25	g1	g1	NOUN
ejpam-5118	55	26	)	)	PUNCT
ejpam-5118	55	27	.	.	PUNCT
ejpam-5118	56	1	the	the	DET
ejpam-5118	56	2	famous	famous	ADJ
ejpam-5118	56	3	schreier	schreier	NOUN
ejpam-5118	56	4	theorem	theorem	NOUN
ejpam-5118	56	5	says	say	VERB
ejpam-5118	56	6	that	that	SCONJ
ejpam-5118	56	7	the	the	DET
ejpam-5118	56	8	central	central	ADJ
ejpam-5118	56	9	extensions	extension	NOUN
ejpam-5118	56	10	of	of	ADP
ejpam-5118	56	11	g1	g1	NOUN
ejpam-5118	56	12	by	by	ADP
ejpam-5118	56	13	g2	g2	PROPN
ejpam-5118	56	14	are	be	AUX
ejpam-5118	56	15	classified	classify	VERB
ejpam-5118	56	16	by	by	ADP
ejpam-5118	56	17	the	the	DET
ejpam-5118	56	18	non	non	ADJ
ejpam-5118	56	19	-	-	ADJ
ejpam-5118	56	20	trivial	trivial	ADJ
ejpam-5118	56	21	elements	element	NOUN
ejpam-5118	56	22	of	of	ADP
ejpam-5118	56	23	the	the	DET
ejpam-5118	56	24	second	second	ADJ
ejpam-5118	56	25	cohomology	cohomology	NOUN
ejpam-5118	56	26	group	group	NOUN
ejpam-5118	56	27	h2(g2	h2(g2	PROPN
ejpam-5118	56	28	,	,	PUNCT
ejpam-5118	56	29	g1	g1	PROPN
ejpam-5118	56	30	)	)	PUNCT
ejpam-5118	56	31	with	with	ADP
ejpam-5118	56	32	coefficients	coefficient	NOUN
ejpam-5118	56	33	in	in	ADP
ejpam-5118	56	34	g1	g1	PROPN
ejpam-5118	56	35	.	.	PUNCT
ejpam-5118	57	1	in	in	ADP
ejpam-5118	57	2	particular	particular	ADJ
ejpam-5118	57	3	,	,	PUNCT
ejpam-5118	57	4	a	a	DET
ejpam-5118	57	5	central	central	ADJ
ejpam-5118	57	6	extension	extension	NOUN
ejpam-5118	57	7	of	of	ADP
ejpam-5118	57	8	g1	g1	NOUN
ejpam-5118	57	9	by	by	ADP
ejpam-5118	57	10	g2	g2	PROPN
ejpam-5118	57	11	splits	split	VERB
ejpam-5118	57	12	if	if	SCONJ
ejpam-5118	57	13	and	and	CCONJ
ejpam-5118	57	14	only	only	ADV
ejpam-5118	57	15	if	if	SCONJ
ejpam-5118	57	16	the	the	DET
ejpam-5118	57	17	corresponding	correspond	VERB
ejpam-5118	57	18	2	2	NUM
ejpam-5118	57	19	-	-	PUNCT
ejpam-5118	57	20	cocycle	cocycle	NOUN
ejpam-5118	57	21	is	be	AUX
ejpam-5118	57	22	trivial	trivial	ADJ
ejpam-5118	57	23	in	in	ADP
ejpam-5118	57	24	h2(g2	h2(g2	ADP
ejpam-5118	57	25	,	,	PUNCT
ejpam-5118	57	26	g1	g1	NOUN
ejpam-5118	57	27	)	)	PUNCT
ejpam-5118	57	28	.	.	PUNCT
ejpam-5118	58	1	a	a	DET
ejpam-5118	58	2	2	2	NUM
ejpam-5118	58	3	-	-	PUNCT
ejpam-5118	58	4	cocycle	cocycle	NOUN
ejpam-5118	58	5	ε	ε	PROPN
ejpam-5118	58	6	∈	∈	PROPN
ejpam-5118	58	7	z2(g2	z2(g2	PROPN
ejpam-5118	58	8	,	,	PUNCT
ejpam-5118	58	9	g1	g1	PROPN
ejpam-5118	58	10	)	)	PUNCT
ejpam-5118	58	11	gives	give	VERB
ejpam-5118	58	12	rise	rise	NOUN
ejpam-5118	58	13	to	to	ADP
ejpam-5118	58	14	a	a	DET
ejpam-5118	58	15	central	central	ADJ
ejpam-5118	58	16	extension	extension	NOUN
ejpam-5118	58	17	g	g	NOUN
ejpam-5118	58	18	=	=	PROPN
ejpam-5118	58	19	g1	g1	PROPN
ejpam-5118	58	20	×	×	PROPN
ejpam-5118	58	21	ε	ε	PROPN
ejpam-5118	58	22	g2	g2	PROPN
ejpam-5118	58	23	of	of	ADP
ejpam-5118	58	24	g1	g1	PROPN
ejpam-5118	58	25	by	by	ADP
ejpam-5118	58	26	g2	g2	PROPN
ejpam-5118	58	27	induced	induce	VERB
ejpam-5118	58	28	by	by	ADP
ejpam-5118	58	29	ε	ε	PROPN
ejpam-5118	58	30	,	,	PUNCT
ejpam-5118	58	31	with	with	ADP
ejpam-5118	58	32	group	group	NOUN
ejpam-5118	58	33	operation	operation	NOUN
ejpam-5118	58	34	given	give	VERB
ejpam-5118	58	35	by	by	ADP
ejpam-5118	58	36	(	(	PUNCT
ejpam-5118	58	37	x	x	NOUN
ejpam-5118	58	38	,	,	PUNCT
ejpam-5118	58	39	y	y	PROPN
ejpam-5118	58	40	)	)	PUNCT
ejpam-5118	58	41	•	•	NUM
ejpam-5118	58	42	ε	ε	PROPN
ejpam-5118	58	43	(	(	PUNCT
ejpam-5118	58	44	x′	x′	PROPN
ejpam-5118	58	45	,	,	PUNCT
ejpam-5118	58	46	y′	y′	NUM
ejpam-5118	58	47	)	)	PUNCT
ejpam-5118	59	1	=	=	SYM
ejpam-5118	59	2	(	(	PUNCT
ejpam-5118	59	3	xx′ε(y	xx′ε(y	X
ejpam-5118	59	4	,	,	PUNCT
ejpam-5118	59	5	y′	y′	NUM
ejpam-5118	59	6	)	)	PUNCT
ejpam-5118	59	7	,	,	PUNCT
ejpam-5118	59	8	yy′	yy′	X
ejpam-5118	59	9	)	)	PUNCT
ejpam-5118	59	10	for	for	ADP
ejpam-5118	59	11	all	all	DET
ejpam-5118	59	12	x	x	NOUN
ejpam-5118	59	13	,	,	PUNCT
ejpam-5118	59	14	x′	x′	PROPN
ejpam-5118	59	15	∈	∈	PROPN
ejpam-5118	59	16	g1	g1	PROPN
ejpam-5118	59	17	and	and	CCONJ
ejpam-5118	59	18	y	y	NOUN
ejpam-5118	59	19	,	,	PUNCT
ejpam-5118	59	20	y′	y′	NOUN
ejpam-5118	59	21	∈	∈	PROPN
ejpam-5118	59	22	g2	g2	PROPN
ejpam-5118	59	23	.	.	PUNCT
ejpam-5118	60	1	conversely	conversely	ADV
ejpam-5118	60	2	,	,	PUNCT
ejpam-5118	60	3	given	give	VERB
ejpam-5118	60	4	a	a	DET
ejpam-5118	60	5	central	central	ADJ
ejpam-5118	60	6	extension	extension	NOUN
ejpam-5118	60	7	1	1	NUM
ejpam-5118	60	8	→	→	SYM
ejpam-5118	60	9	g1→g	g1→g	PROPN
ejpam-5118	60	10	j→	j→	PROPN
ejpam-5118	60	11	g2	g2	PROPN
ejpam-5118	60	12	→	→	SYM
ejpam-5118	60	13	1	1	NUM
ejpam-5118	60	14	and	and	CCONJ
ejpam-5118	60	15	choose	choose	VERB
ejpam-5118	60	16	a	a	DET
ejpam-5118	60	17	based	base	VERB
ejpam-5118	60	18	section	section	NOUN
ejpam-5118	60	19	λ	λ	PROPN
ejpam-5118	60	20	:	:	PUNCT
ejpam-5118	60	21	g2	g2	PROPN
ejpam-5118	60	22	→	→	SYM
ejpam-5118	60	23	g	g	PROPN
ejpam-5118	60	24	,	,	PUNCT
ejpam-5118	60	25	i.e.	i.e.	X
ejpam-5118	60	26	a	a	DET
ejpam-5118	60	27	set	set	NOUN
ejpam-5118	60	28	map	map	NOUN
ejpam-5118	60	29	with	with	ADP
ejpam-5118	60	30	λ(1	λ(1	PROPN
ejpam-5118	60	31	)	)	PUNCT
ejpam-5118	60	32	is	be	AUX
ejpam-5118	60	33	the	the	DET
ejpam-5118	60	34	identity	identity	NOUN
ejpam-5118	60	35	element	element	NOUN
ejpam-5118	60	36	of	of	ADP
ejpam-5118	60	37	g	g	PROPN
ejpam-5118	60	38	and	and	CCONJ
ejpam-5118	60	39	j	j	PROPN
ejpam-5118	60	40	◦	◦	NOUN
ejpam-5118	60	41	λ	λ	PROPN
ejpam-5118	60	42	=	=	SYM
ejpam-5118	60	43	idg2	idg2	PROPN
ejpam-5118	60	44	.	.	PUNCT
ejpam-5118	61	1	the	the	DET
ejpam-5118	61	2	based	base	VERB
ejpam-5118	61	3	section	section	NOUN
ejpam-5118	61	4	λ	λ	PROPN
ejpam-5118	61	5	induces	induce	VERB
ejpam-5118	61	6	a	a	DET
ejpam-5118	61	7	2	2	NUM
ejpam-5118	61	8	-	-	PUNCT
ejpam-5118	61	9	cocycle	cocycle	NOUN
ejpam-5118	61	10	ελ	ελ	NOUN
ejpam-5118	61	11	:	:	PUNCT
ejpam-5118	61	12	g2×g2	g2×g2	PROPN
ejpam-5118	61	13	−→	−→	NOUN
ejpam-5118	61	14	g1	g1	NOUN
ejpam-5118	61	15	given	give	VERB
ejpam-5118	61	16	by	by	ADP
ejpam-5118	61	17	ελ(h	ελ(h	ADP
ejpam-5118	61	18	,	,	PUNCT
ejpam-5118	61	19	g	g	NOUN
ejpam-5118	61	20	)	)	PUNCT
ejpam-5118	61	21	=	=	SYM
ejpam-5118	62	1	λ(h)λ(g)λ(hg)−1	λ(h)λ(g)λ(hg)−1	NOUN
ejpam-5118	62	2	and	and	CCONJ
ejpam-5118	62	3	therefore	therefore	ADV
ejpam-5118	62	4	,	,	PUNCT
ejpam-5118	62	5	the	the	DET
ejpam-5118	62	6	group	group	NOUN
ejpam-5118	62	7	g	g	PROPN
ejpam-5118	62	8	is	be	AUX
ejpam-5118	62	9	isomorphic	isomorphic	ADJ
ejpam-5118	62	10	to	to	ADP
ejpam-5118	62	11	the	the	DET
ejpam-5118	62	12	group	group	NOUN
ejpam-5118	62	13	g1	g1	VERB
ejpam-5118	62	14	×	×	PROPN
ejpam-5118	62	15	ελ	ελ	PROPN
ejpam-5118	62	16	g2	g2	PROPN
ejpam-5118	63	1	[	[	X
ejpam-5118	63	2	10	10	NUM
ejpam-5118	63	3	,	,	PUNCT
ejpam-5118	63	4	proposition	proposition	NOUN
ejpam-5118	63	5	2.3	2.3	NUM
ejpam-5118	63	6	]	]	PUNCT
ejpam-5118	63	7	.	.	PUNCT
ejpam-5118	64	1	we	we	PRON
ejpam-5118	64	2	can	can	AUX
ejpam-5118	64	3	easily	easily	ADV
ejpam-5118	64	4	see	see	VERB
ejpam-5118	64	5	that	that	SCONJ
ejpam-5118	64	6	the	the	DET
ejpam-5118	64	7	group	group	NOUN
ejpam-5118	64	8	g1	g1	VERB
ejpam-5118	64	9	×	×	PROPN
ejpam-5118	64	10	ε	ε	PROPN
ejpam-5118	64	11	g2	g2	PROPN
ejpam-5118	64	12	is	be	AUX
ejpam-5118	64	13	abelian	abelian	ADJ
ejpam-5118	64	14	if	if	SCONJ
ejpam-5118	64	15	and	and	CCONJ
ejpam-5118	64	16	only	only	ADV
ejpam-5118	64	17	if	if	SCONJ
ejpam-5118	64	18	g2	g2	PROPN
ejpam-5118	64	19	is	be	AUX
ejpam-5118	64	20	abelian	abelian	ADJ
ejpam-5118	64	21	and	and	CCONJ
ejpam-5118	64	22	ε	ε	PROPN
ejpam-5118	64	23	∈	∈	PROPN
ejpam-5118	64	24	sz2(g2	sz2(g2	X
ejpam-5118	64	25	,	,	PUNCT
ejpam-5118	64	26	g1	g1	NOUN
ejpam-5118	64	27	)	)	PUNCT
ejpam-5118	64	28	.	.	PUNCT
ejpam-5118	65	1	we	we	PRON
ejpam-5118	65	2	know	know	VERB
ejpam-5118	65	3	that	that	SCONJ
ejpam-5118	65	4	g1	g1	PROPN
ejpam-5118	65	5	×	×	PROPN
ejpam-5118	65	6	ε	ε	PROPN
ejpam-5118	65	7	g2	g2	PROPN
ejpam-5118	65	8	=	=	PUNCT
ejpam-5118	65	9	g1	g1	PROPN
ejpam-5118	65	10	×g2	×g2	PROPN
ejpam-5118	66	1	if	if	SCONJ
ejpam-5118	66	2	and	and	CCONJ
ejpam-5118	66	3	only	only	ADV
ejpam-5118	66	4	if	if	SCONJ
ejpam-5118	66	5	ε	ε	PROPN
ejpam-5118	66	6	=	=	SYM
ejpam-5118	66	7	1	1	NUM
ejpam-5118	66	8	.	.	PUNCT
ejpam-5118	67	1	but	but	CCONJ
ejpam-5118	67	2	,	,	PUNCT
ejpam-5118	67	3	it	it	PRON
ejpam-5118	67	4	is	be	AUX
ejpam-5118	67	5	possible	possible	ADJ
ejpam-5118	67	6	for	for	SCONJ
ejpam-5118	67	7	a	a	DET
ejpam-5118	67	8	central	central	ADJ
ejpam-5118	67	9	extension	extension	NOUN
ejpam-5118	67	10	of	of	ADP
ejpam-5118	67	11	g1	g1	NOUN
ejpam-5118	67	12	by	by	ADP
ejpam-5118	67	13	g2	g2	PROPN
ejpam-5118	67	14	induced	induce	VERB
ejpam-5118	67	15	by	by	ADP
ejpam-5118	67	16	a	a	DET
ejpam-5118	67	17	non	non	ADJ
ejpam-5118	67	18	-	-	ADJ
ejpam-5118	67	19	trivial	trivial	ADJ
ejpam-5118	67	20	2	2	NUM
ejpam-5118	67	21	-	-	PUNCT
ejpam-5118	67	22	cocycle	cocycle	NOUN
ejpam-5118	67	23	to	to	PART
ejpam-5118	67	24	be	be	AUX
ejpam-5118	67	25	isomorphic	isomorphic	ADJ
ejpam-5118	67	26	to	to	ADP
ejpam-5118	67	27	the	the	DET
ejpam-5118	67	28	direct	direct	ADJ
ejpam-5118	67	29	product	product	NOUN
ejpam-5118	67	30	g1	g1	VERB
ejpam-5118	67	31	×g2	×g2	PROPN
ejpam-5118	67	32	(	(	PUNCT
ejpam-5118	67	33	see	see	VERB
ejpam-5118	67	34	proposition	proposition	NOUN
ejpam-5118	67	35	3.2	3.2	NUM
ejpam-5118	67	36	)	)	PUNCT
ejpam-5118	67	37	.	.	PUNCT
ejpam-5118	68	1	3	3	X
ejpam-5118	68	2	.	.	X
ejpam-5118	68	3	preliminary	preliminary	ADJ
ejpam-5118	68	4	results	result	NOUN
ejpam-5118	68	5	let	let	VERB
ejpam-5118	68	6	pri	pri	NOUN
ejpam-5118	68	7	:	:	PUNCT
ejpam-5118	68	8	g1	g1	PROPN
ejpam-5118	68	9	×	×	PROPN
ejpam-5118	68	10	ε	ε	PROPN
ejpam-5118	68	11	g2	g2	PROPN
ejpam-5118	69	1	→	→	PUNCT
ejpam-5118	69	2	gi	gi	X
ejpam-5118	69	3	be	be	AUX
ejpam-5118	69	4	the	the	DET
ejpam-5118	69	5	ith	ith	PROPN
ejpam-5118	69	6	canonical	canonical	ADJ
ejpam-5118	69	7	projection	projection	NOUN
ejpam-5118	69	8	and	and	CCONJ
ejpam-5118	69	9	ti	ti	NOUN
ejpam-5118	69	10	:	:	PUNCT
ejpam-5118	69	11	gi	gi	PROPN
ejpam-5118	69	12	→	→	SYM
ejpam-5118	69	13	g1	g1	PROPN
ejpam-5118	69	14	×	×	PROPN
ejpam-5118	69	15	ε	ε	PROPN
ejpam-5118	69	16	g2	g2	PROPN
ejpam-5118	69	17	be	be	VERB
ejpam-5118	69	18	the	the	DET
ejpam-5118	69	19	ith	ith	ADJ
ejpam-5118	69	20	canonical	canonical	ADJ
ejpam-5118	69	21	injection	injection	NOUN
ejpam-5118	69	22	.	.	PUNCT
ejpam-5118	70	1	let	let	VERB
ejpam-5118	70	2	φ	φ	PROPN
ejpam-5118	70	3	be	be	AUX
ejpam-5118	70	4	a	a	DET
ejpam-5118	70	5	group	group	NOUN
ejpam-5118	70	6	homomorphism	homomorphism	NOUN
ejpam-5118	70	7	from	from	ADP
ejpam-5118	70	8	g1	g1	PROPN
ejpam-5118	70	9	×	×	PROPN
ejpam-5118	70	10	ε1	ε1	PROPN
ejpam-5118	70	11	g2	g2	PROPN
ejpam-5118	70	12	to	to	PART
ejpam-5118	70	13	g1	g1	VERB
ejpam-5118	70	14	×	×	PROPN
ejpam-5118	70	15	ε2	ε2	PROPN
ejpam-5118	70	16	g2	g2	PROPN
ejpam-5118	70	17	and	and	CCONJ
ejpam-5118	70	18	set	set	VERB
ejpam-5118	70	19	φij	φij	NOUN
ejpam-5118	70	20	=	=	PUNCT
ejpam-5118	70	21	pri	pri	PROPN
ejpam-5118	70	22	◦	◦	PROPN
ejpam-5118	70	23	φ	φ	NUM
ejpam-5118	70	24	◦	◦	NOUN
ejpam-5118	70	25	tj	tj	NOUN
ejpam-5118	70	26	,	,	PUNCT
ejpam-5118	70	27	where	where	SCONJ
ejpam-5118	70	28	1	1	NUM
ejpam-5118	70	29	≤	≤	PUNCT
ejpam-5118	70	30	i	i	PRON
ejpam-5118	70	31	,	,	PUNCT
ejpam-5118	70	32	j	j	PROPN
ejpam-5118	70	33	≤	≤	PROPN
ejpam-5118	70	34	2	2	NUM
ejpam-5118	70	35	.	.	PUNCT
ejpam-5118	71	1	so	so	ADV
ejpam-5118	71	2	we	we	PRON
ejpam-5118	71	3	can	can	AUX
ejpam-5118	71	4	write	write	VERB
ejpam-5118	71	5	φ	φ	PROPN
ejpam-5118	71	6	in	in	ADP
ejpam-5118	71	7	the	the	DET
ejpam-5118	71	8	matrix	matrix	NOUN
ejpam-5118	71	9	form	form	NOUN
ejpam-5118	71	10	:	:	PUNCT
ejpam-5118	71	11	φ	φ	PROPN
ejpam-5118	71	12	=	=	SYM
ejpam-5118	71	13	(	(	PUNCT
ejpam-5118	71	14	φ11	φ11	NUM
ejpam-5118	71	15	φ12	φ12	ADJ
ejpam-5118	71	16	φ21	φ21	NOUN
ejpam-5118	71	17	φ22	φ22	NOUN
ejpam-5118	71	18	)	)	PUNCT
ejpam-5118	71	19	.	.	PUNCT
ejpam-5118	72	1	obviously	obviously	ADV
ejpam-5118	72	2	,	,	PUNCT
ejpam-5118	72	3	we	we	PRON
ejpam-5118	72	4	see	see	VERB
ejpam-5118	72	5	that	that	SCONJ
ejpam-5118	72	6	pr2	pr2	PROPN
ejpam-5118	72	7	and	and	CCONJ
ejpam-5118	72	8	t1	t1	NOUN
ejpam-5118	72	9	are	be	AUX
ejpam-5118	72	10	group	group	NOUN
ejpam-5118	72	11	homomorphisms	homomorphism	NOUN
ejpam-5118	72	12	,	,	PUNCT
ejpam-5118	72	13	then	then	ADV
ejpam-5118	72	14	φ21	φ21	NOUN
ejpam-5118	72	15	is	be	AUX
ejpam-5118	72	16	a	a	DET
ejpam-5118	72	17	group	group	NOUN
ejpam-5118	72	18	homomorphism	homomorphism	NOUN
ejpam-5118	72	19	.	.	PUNCT
ejpam-5118	73	1	furthermore	furthermore	ADV
ejpam-5118	73	2	,	,	PUNCT
ejpam-5118	73	3	we	we	PRON
ejpam-5118	73	4	have	have	VERB
ejpam-5118	73	5	the	the	DET
ejpam-5118	73	6	following	follow	VERB
ejpam-5118	73	7	lemmas	lemma	NOUN
ejpam-5118	73	8	which	which	PRON
ejpam-5118	73	9	we	we	PRON
ejpam-5118	73	10	need	need	VERB
ejpam-5118	73	11	in	in	ADP
ejpam-5118	73	12	the	the	DET
ejpam-5118	73	13	sequel	sequel	NOUN
ejpam-5118	73	14	.	.	PUNCT
ejpam-5118	74	1	lemma	lemma	PROPN
ejpam-5118	74	2	3.1	3.1	NUM
ejpam-5118	74	3	.	.	PUNCT
ejpam-5118	75	1	[	[	X
ejpam-5118	75	2	10	10	NUM
ejpam-5118	75	3	,	,	PUNCT
ejpam-5118	75	4	lemma	lemma	PROPN
ejpam-5118	75	5	3.1	3.1	NUM
ejpam-5118	75	6	]	]	PUNCT
ejpam-5118	75	7	let	let	VERB
ejpam-5118	75	8	φ	φ	PROPN
ejpam-5118	75	9	=	=	SYM
ejpam-5118	75	10	(	(	PUNCT
ejpam-5118	75	11	φ11	φ11	NUM
ejpam-5118	75	12	φ12	φ12	ADJ
ejpam-5118	75	13	φ21	φ21	NOUN
ejpam-5118	75	14	φ22	φ22	NOUN
ejpam-5118	75	15	)	)	PUNCT
ejpam-5118	75	16	be	be	AUX
ejpam-5118	75	17	a	a	DET
ejpam-5118	75	18	group	group	NOUN
ejpam-5118	75	19	homomorphism	homomorphism	NOUN
ejpam-5118	75	20	from	from	ADP
ejpam-5118	75	21	g1	g1	PROPN
ejpam-5118	75	22	×	×	PROPN
ejpam-5118	75	23	ε1	ε1	PROPN
ejpam-5118	75	24	g2	g2	PROPN
ejpam-5118	75	25	to	to	PART
ejpam-5118	75	26	g1	g1	VERB
ejpam-5118	75	27	×	×	PROPN
ejpam-5118	75	28	ε2	ε2	PROPN
ejpam-5118	75	29	g2	g2	PROPN
ejpam-5118	75	30	.	.	PUNCT
ejpam-5118	76	1	then	then	ADV
ejpam-5118	76	2	φ(x	φ(x	PROPN
ejpam-5118	76	3	,	,	PUNCT
ejpam-5118	76	4	y	y	NOUN
ejpam-5118	76	5	)	)	PUNCT
ejpam-5118	76	6	=	=	PUNCT
ejpam-5118	76	7	(	(	PUNCT
ejpam-5118	76	8	φ11(x)φ12(y)ε2(φ21(x	φ11(x)φ12(y)ε2(φ21(x	PROPN
ejpam-5118	76	9	)	)	PUNCT
ejpam-5118	76	10	,	,	PUNCT
ejpam-5118	76	11	φ22(y	φ22(y	ADJ
ejpam-5118	76	12	)	)	PUNCT
ejpam-5118	76	13	)	)	PUNCT
ejpam-5118	76	14	,	,	PUNCT
ejpam-5118	76	15	φ21(x)φ22(y	φ21(x)φ22(y	ADJ
ejpam-5118	76	16	)	)	PUNCT
ejpam-5118	76	17	)	)	PUNCT
ejpam-5118	76	18	(	(	PUNCT
ejpam-5118	76	19	1	1	X
ejpam-5118	76	20	)	)	PUNCT
ejpam-5118	76	21	for	for	ADP
ejpam-5118	76	22	all	all	DET
ejpam-5118	76	23	x	x	PROPN
ejpam-5118	76	24	∈	∈	PROPN
ejpam-5118	76	25	g1	g1	NOUN
ejpam-5118	76	26	,	,	PUNCT
ejpam-5118	76	27	and	and	CCONJ
ejpam-5118	76	28	y	y	PROPN
ejpam-5118	76	29	∈	∈	PROPN
ejpam-5118	76	30	g2	g2	PROPN
ejpam-5118	76	31	.	.	PUNCT
ejpam-5118	77	1	lemma	lemma	PROPN
ejpam-5118	77	2	3.2	3.2	NUM
ejpam-5118	77	3	.	.	PUNCT
ejpam-5118	78	1	[	[	X
ejpam-5118	78	2	10	10	NUM
ejpam-5118	78	3	,	,	PUNCT
ejpam-5118	78	4	lemma	lemma	PROPN
ejpam-5118	78	5	3.2	3.2	NUM
ejpam-5118	78	6	]	]	PUNCT
ejpam-5118	78	7	let	let	VERB
ejpam-5118	78	8	φ	φ	PROPN
ejpam-5118	78	9	be	be	AUX
ejpam-5118	78	10	a	a	DET
ejpam-5118	78	11	set	set	NOUN
ejpam-5118	78	12	map	map	NOUN
ejpam-5118	78	13	from	from	ADP
ejpam-5118	78	14	g1	g1	PROPN
ejpam-5118	78	15	×	×	PROPN
ejpam-5118	78	16	ε1	ε1	PROPN
ejpam-5118	78	17	g2	g2	PROPN
ejpam-5118	78	18	to	to	PART
ejpam-5118	78	19	g1	g1	VERB
ejpam-5118	78	20	×	×	PROPN
ejpam-5118	78	21	ε2	ε2	PROPN
ejpam-5118	78	22	g2	g2	PROPN
ejpam-5118	78	23	.	.	PUNCT
ejpam-5118	79	1	then	then	ADV
ejpam-5118	79	2	φ	φ	PROPN
ejpam-5118	79	3	is	be	AUX
ejpam-5118	79	4	a	a	DET
ejpam-5118	79	5	group	group	NOUN
ejpam-5118	79	6	homomorphism	homomorphism	NOUN
ejpam-5118	79	7	if	if	SCONJ
ejpam-5118	79	8	and	and	CCONJ
ejpam-5118	79	9	only	only	ADV
ejpam-5118	79	10	if	if	SCONJ
ejpam-5118	79	11	n.	n.	PROPN
ejpam-5118	79	12	snanou	snanou	PROPN
ejpam-5118	79	13	/	/	SYM
ejpam-5118	79	14	eur	eur	PROPN
ejpam-5118	79	15	.	.	PUNCT
ejpam-5118	80	1	j.	j.	PROPN
ejpam-5118	80	2	pure	pure	PROPN
ejpam-5118	80	3	appl	appl	PROPN
ejpam-5118	80	4	.	.	PROPN
ejpam-5118	80	5	math	math	PROPN
ejpam-5118	80	6	,	,	PUNCT
ejpam-5118	80	7	17	17	NUM
ejpam-5118	80	8	(	(	PUNCT
ejpam-5118	80	9	2	2	NUM
ejpam-5118	80	10	)	)	PUNCT
ejpam-5118	80	11	(	(	PUNCT
ejpam-5118	80	12	2024	2024	NUM
ejpam-5118	80	13	)	)	PUNCT
ejpam-5118	80	14	,	,	PUNCT
ejpam-5118	80	15	956	956	NUM
ejpam-5118	80	16	-	-	SYM
ejpam-5118	80	17	968	968	NUM
ejpam-5118	80	18	959	959	NUM
ejpam-5118	80	19	φ(x	φ(x	NOUN
ejpam-5118	80	20	,	,	PUNCT
ejpam-5118	80	21	y	y	NOUN
ejpam-5118	80	22	)	)	PUNCT
ejpam-5118	80	23	•	•	NOUN
ejpam-5118	80	24	ε2	ε2	PROPN
ejpam-5118	80	25	φ(x′	φ(x′	NUM
ejpam-5118	80	26	,	,	PUNCT
ejpam-5118	80	27	1	1	NUM
ejpam-5118	80	28	)	)	PUNCT
ejpam-5118	80	29	=	=	VERB
ejpam-5118	81	1	φ(xx′	φ(xx′	NOUN
ejpam-5118	81	2	,	,	PUNCT
ejpam-5118	81	3	y	y	NOUN
ejpam-5118	81	4	)	)	PUNCT
ejpam-5118	81	5	,	,	PUNCT
ejpam-5118	81	6	(	(	PUNCT
ejpam-5118	81	7	2	2	X
ejpam-5118	81	8	)	)	PUNCT
ejpam-5118	81	9	and	and	CCONJ
ejpam-5118	81	10	φ(x	φ(x	PROPN
ejpam-5118	81	11	,	,	PUNCT
ejpam-5118	81	12	y	y	NOUN
ejpam-5118	81	13	)	)	PUNCT
ejpam-5118	81	14	•	•	NUM
ejpam-5118	81	15	ε2	ε2	PROPN
ejpam-5118	81	16	φ(1	φ(1	PROPN
ejpam-5118	81	17	,	,	PUNCT
ejpam-5118	81	18	y′	y′	NUM
ejpam-5118	81	19	)	)	PUNCT
ejpam-5118	82	1	=	=	SYM
ejpam-5118	82	2	φ(xε1(y	φ(xε1(y	PROPN
ejpam-5118	82	3	,	,	PUNCT
ejpam-5118	82	4	y	y	PROPN
ejpam-5118	82	5	′	′	NUM
ejpam-5118	82	6	)	)	PUNCT
ejpam-5118	82	7	,	,	PUNCT
ejpam-5118	82	8	yy′	yy′	X
ejpam-5118	82	9	)	)	PUNCT
ejpam-5118	82	10	(	(	PUNCT
ejpam-5118	82	11	3	3	X
ejpam-5118	82	12	)	)	PUNCT
ejpam-5118	82	13	for	for	ADP
ejpam-5118	82	14	all	all	DET
ejpam-5118	82	15	x	x	NOUN
ejpam-5118	82	16	,	,	PUNCT
ejpam-5118	82	17	x′	x′	PROPN
ejpam-5118	82	18	∈	∈	PROPN
ejpam-5118	82	19	g1	g1	PROPN
ejpam-5118	82	20	,	,	PUNCT
ejpam-5118	82	21	and	and	CCONJ
ejpam-5118	82	22	y	y	PROPN
ejpam-5118	82	23	,	,	PUNCT
ejpam-5118	82	24	y	y	PROPN
ejpam-5118	82	25	′	′	NOUN
ejpam-5118	82	26	∈	∈	PROPN
ejpam-5118	82	27	g2	g2	PROPN
ejpam-5118	82	28	.	.	PUNCT
ejpam-5118	83	1	definition	definition	NOUN
ejpam-5118	83	2	3.1	3.1	NUM
ejpam-5118	83	3	.	.	PUNCT
ejpam-5118	84	1	let	let	VERB
ejpam-5118	84	2	g2	g2	PROPN
ejpam-5118	84	3	be	be	AUX
ejpam-5118	84	4	a	a	DET
ejpam-5118	84	5	group	group	NOUN
ejpam-5118	84	6	which	which	PRON
ejpam-5118	84	7	acts	act	VERB
ejpam-5118	84	8	trivially	trivially	ADV
ejpam-5118	84	9	on	on	ADP
ejpam-5118	84	10	an	an	DET
ejpam-5118	84	11	abelian	abelian	ADJ
ejpam-5118	84	12	group	group	NOUN
ejpam-5118	84	13	g1	g1	PROPN
ejpam-5118	84	14	.	.	PUNCT
ejpam-5118	85	1	let	let	VERB
ejpam-5118	85	2	ε	ε	PROPN
ejpam-5118	85	3	∈	∈	PROPN
ejpam-5118	85	4	z2(g2	z2(g2	PROPN
ejpam-5118	85	5	,	,	PUNCT
ejpam-5118	85	6	g1	g1	NOUN
ejpam-5118	85	7	)	)	PUNCT
ejpam-5118	85	8	.	.	PUNCT
ejpam-5118	86	1	a	a	DET
ejpam-5118	86	2	map	map	NOUN
ejpam-5118	86	3	χ	χ	X
ejpam-5118	86	4	:	:	PUNCT
ejpam-5118	86	5	g1	g1	PROPN
ejpam-5118	86	6	→	→	SYM
ejpam-5118	86	7	g1	g1	PROPN
ejpam-5118	86	8	is	be	AUX
ejpam-5118	86	9	called	call	VERB
ejpam-5118	86	10	an	an	DET
ejpam-5118	86	11	ε	ε	PROPN
ejpam-5118	86	12	-	-	PUNCT
ejpam-5118	86	13	endomorphism	endomorphism	PROPN
ejpam-5118	86	14	of	of	ADP
ejpam-5118	86	15	g1	g1	NOUN
ejpam-5118	86	16	,	,	PUNCT
ejpam-5118	86	17	if	if	SCONJ
ejpam-5118	86	18	χ(xε(y	χ(xε(y	NOUN
ejpam-5118	86	19	,	,	PUNCT
ejpam-5118	86	20	y′	y′	NUM
ejpam-5118	86	21	)	)	PUNCT
ejpam-5118	86	22	)	)	PUNCT
ejpam-5118	87	1	=	=	PUNCT
ejpam-5118	87	2	χ(x)χ(ε(y	χ(x)χ(ε(y	PROPN
ejpam-5118	87	3	,	,	PUNCT
ejpam-5118	87	4	y′	y′	NUM
ejpam-5118	87	5	)	)	PUNCT
ejpam-5118	87	6	)	)	PUNCT
ejpam-5118	87	7	for	for	ADP
ejpam-5118	87	8	all	all	DET
ejpam-5118	87	9	x	x	PROPN
ejpam-5118	87	10	∈	∈	PROPN
ejpam-5118	87	11	g1	g1	NOUN
ejpam-5118	87	12	,	,	PUNCT
ejpam-5118	87	13	and	and	CCONJ
ejpam-5118	87	14	y	y	NOUN
ejpam-5118	87	15	,	,	PUNCT
ejpam-5118	87	16	y′	y′	NOUN
ejpam-5118	87	17	∈	∈	PROPN
ejpam-5118	87	18	g2	g2	PROPN
ejpam-5118	87	19	.	.	PUNCT
ejpam-5118	88	1	if	if	SCONJ
ejpam-5118	88	2	in	in	ADP
ejpam-5118	88	3	addition	addition	NOUN
ejpam-5118	88	4	χ	χ	NOUN
ejpam-5118	88	5	is	be	AUX
ejpam-5118	88	6	a	a	DET
ejpam-5118	88	7	bijection	bijection	NOUN
ejpam-5118	88	8	,	,	PUNCT
ejpam-5118	88	9	then	then	ADV
ejpam-5118	88	10	it	it	PRON
ejpam-5118	88	11	is	be	AUX
ejpam-5118	88	12	said	say	VERB
ejpam-5118	88	13	to	to	PART
ejpam-5118	88	14	be	be	AUX
ejpam-5118	88	15	ε	ε	NOUN
ejpam-5118	88	16	-	-	NOUN
ejpam-5118	88	17	automorphism	automorphism	NOUN
ejpam-5118	88	18	.	.	PUNCT
ejpam-5118	89	1	the	the	DET
ejpam-5118	89	2	following	follow	VERB
ejpam-5118	89	3	lemma	lemma	PROPN
ejpam-5118	89	4	follows	follow	VERB
ejpam-5118	89	5	directly	directly	ADV
ejpam-5118	89	6	by	by	ADP
ejpam-5118	89	7	using	use	VERB
ejpam-5118	89	8	the	the	DET
ejpam-5118	89	9	2	2	NUM
ejpam-5118	89	10	-	-	PUNCT
ejpam-5118	89	11	cocycle	cocycle	NOUN
ejpam-5118	89	12	condition	condition	NOUN
ejpam-5118	89	13	.	.	PUNCT
ejpam-5118	90	1	lemma	lemma	PROPN
ejpam-5118	90	2	3.3	3.3	NUM
ejpam-5118	90	3	.	.	PUNCT
ejpam-5118	91	1	let	let	VERB
ejpam-5118	91	2	g2	g2	PROPN
ejpam-5118	91	3	be	be	AUX
ejpam-5118	91	4	a	a	DET
ejpam-5118	91	5	group	group	NOUN
ejpam-5118	91	6	which	which	PRON
ejpam-5118	91	7	acts	act	VERB
ejpam-5118	91	8	trivially	trivially	ADV
ejpam-5118	91	9	on	on	ADP
ejpam-5118	91	10	an	an	DET
ejpam-5118	91	11	abelian	abelian	ADJ
ejpam-5118	91	12	group	group	NOUN
ejpam-5118	91	13	g1	g1	PROPN
ejpam-5118	91	14	.	.	PUNCT
ejpam-5118	92	1	let	let	VERB
ejpam-5118	92	2	ε	ε	PROPN
ejpam-5118	92	3	∈	∈	PROPN
ejpam-5118	92	4	z2(g2	z2(g2	PROPN
ejpam-5118	92	5	,	,	PUNCT
ejpam-5118	92	6	g1	g1	PROPN
ejpam-5118	92	7	)	)	PUNCT
ejpam-5118	92	8	,	,	PUNCT
ejpam-5118	92	9	δ	δ	PROPN
ejpam-5118	92	10	∈	∈	PROPN
ejpam-5118	92	11	hom(g1	hom(g1	X
ejpam-5118	92	12	,	,	PUNCT
ejpam-5118	92	13	g2	g2	PROPN
ejpam-5118	92	14	)	)	PUNCT
ejpam-5118	92	15	and	and	CCONJ
ejpam-5118	92	16	σ	σ	NOUN
ejpam-5118	92	17	an	an	DET
ejpam-5118	92	18	ε	ε	PROPN
ejpam-5118	92	19	-	-	PUNCT
ejpam-5118	92	20	endomorphism	endomorphism	PROPN
ejpam-5118	92	21	of	of	ADP
ejpam-5118	92	22	g1	g1	PROPN
ejpam-5118	92	23	.	.	PUNCT
ejpam-5118	93	1	then	then	ADV
ejpam-5118	93	2	σ	σ	X
ejpam-5118	93	3	◦	◦	PROPN
ejpam-5118	93	4	ε	ε	PROPN
ejpam-5118	93	5	∈	∈	PROPN
ejpam-5118	93	6	z2(g2	z2(g2	NOUN
ejpam-5118	93	7	,	,	PUNCT
ejpam-5118	93	8	g1	g1	PROPN
ejpam-5118	93	9	)	)	PUNCT
ejpam-5118	93	10	,	,	PUNCT
ejpam-5118	93	11	δ	δ	PROPN
ejpam-5118	93	12	◦	◦	NOUN
ejpam-5118	93	13	ε	ε	PROPN
ejpam-5118	93	14	∈	∈	PROPN
ejpam-5118	93	15	z2(g2	z2(g2	PROPN
ejpam-5118	93	16	,	,	PUNCT
ejpam-5118	93	17	g2	g2	PROPN
ejpam-5118	93	18	)	)	PUNCT
ejpam-5118	93	19	and	and	CCONJ
ejpam-5118	93	20	ε	ε	PROPN
ejpam-5118	93	21	◦	◦	NOUN
ejpam-5118	93	22	(	(	PUNCT
ejpam-5118	93	23	δ	δ	PROPN
ejpam-5118	93	24	×	×	PROPN
ejpam-5118	93	25	δ	δ	PROPN
ejpam-5118	93	26	)	)	PUNCT
ejpam-5118	93	27	∈	∈	PROPN
ejpam-5118	93	28	z2(g1	z2(g1	NOUN
ejpam-5118	93	29	,	,	PUNCT
ejpam-5118	93	30	g1	g1	PROPN
ejpam-5118	93	31	)	)	PUNCT
ejpam-5118	93	32	.	.	PUNCT
ejpam-5118	94	1	from	from	ADP
ejpam-5118	94	2	now	now	ADV
ejpam-5118	94	3	,	,	PUNCT
ejpam-5118	94	4	if	if	SCONJ
ejpam-5118	94	5	φ	φ	PROPN
ejpam-5118	94	6	=	=	SYM
ejpam-5118	94	7	(	(	PUNCT
ejpam-5118	94	8	φ11	φ11	NUM
ejpam-5118	94	9	φ12	φ12	ADJ
ejpam-5118	94	10	φ21	φ21	NOUN
ejpam-5118	94	11	φ22	φ22	NOUN
ejpam-5118	94	12	)	)	PUNCT
ejpam-5118	94	13	is	be	AUX
ejpam-5118	94	14	a	a	DET
ejpam-5118	94	15	map	map	NOUN
ejpam-5118	94	16	from	from	ADP
ejpam-5118	94	17	g1	g1	PROPN
ejpam-5118	94	18	×	×	PROPN
ejpam-5118	94	19	ε1	ε1	PROPN
ejpam-5118	94	20	g2	g2	PROPN
ejpam-5118	94	21	to	to	PART
ejpam-5118	94	22	g1	g1	VERB
ejpam-5118	94	23	×	×	PROPN
ejpam-5118	94	24	ε2	ε2	PROPN
ejpam-5118	94	25	g2	g2	PROPN
ejpam-5118	94	26	,	,	PUNCT
ejpam-5118	94	27	then	then	ADV
ejpam-5118	94	28	φ	φ	PROPN
ejpam-5118	94	29	is	be	AUX
ejpam-5118	94	30	defined	define	VERB
ejpam-5118	94	31	by	by	ADP
ejpam-5118	94	32	the	the	DET
ejpam-5118	94	33	formula	formula	NOUN
ejpam-5118	94	34	(	(	PUNCT
ejpam-5118	94	35	1	1	NUM
ejpam-5118	94	36	)	)	PUNCT
ejpam-5118	94	37	.	.	PUNCT
ejpam-5118	95	1	from	from	ADP
ejpam-5118	95	2	the	the	DET
ejpam-5118	95	3	previous	previous	ADJ
ejpam-5118	95	4	lemmas	lemmas	NOUN
ejpam-5118	95	5	,	,	PUNCT
ejpam-5118	95	6	we	we	PRON
ejpam-5118	95	7	get	get	VERB
ejpam-5118	95	8	the	the	DET
ejpam-5118	95	9	following	follow	VERB
ejpam-5118	95	10	interesting	interesting	ADJ
ejpam-5118	95	11	result	result	NOUN
ejpam-5118	95	12	which	which	PRON
ejpam-5118	95	13	will	will	AUX
ejpam-5118	95	14	be	be	AUX
ejpam-5118	95	15	frequently	frequently	ADV
ejpam-5118	95	16	used	use	VERB
ejpam-5118	95	17	in	in	ADP
ejpam-5118	95	18	the	the	DET
ejpam-5118	95	19	sequel	sequel	NOUN
ejpam-5118	95	20	.	.	PUNCT
ejpam-5118	96	1	proposition	proposition	NOUN
ejpam-5118	96	2	3.1	3.1	NUM
ejpam-5118	96	3	.	.	PUNCT
ejpam-5118	97	1	let	let	VERB
ejpam-5118	97	2	g2	g2	PROPN
ejpam-5118	97	3	be	be	AUX
ejpam-5118	97	4	a	a	DET
ejpam-5118	97	5	group	group	NOUN
ejpam-5118	97	6	such	such	ADJ
ejpam-5118	97	7	that	that	SCONJ
ejpam-5118	97	8	the	the	DET
ejpam-5118	97	9	equivalence	equivalence	NOUN
ejpam-5118	97	10	relation	relation	NOUN
ejpam-5118	97	11	(	(	PUNCT
ejpam-5118	97	12	∼	∼	NOUN
ejpam-5118	97	13	)	)	PUNCT
ejpam-5118	97	14	is	be	AUX
ejpam-5118	97	15	trivial	trivial	ADJ
ejpam-5118	97	16	on	on	ADP
ejpam-5118	97	17	z2(g2	z2(g2	NUM
ejpam-5118	97	18	,	,	PUNCT
ejpam-5118	97	19	g2	g2	PROPN
ejpam-5118	97	20	)	)	PUNCT
ejpam-5118	97	21	.	.	PUNCT
ejpam-5118	98	1	let	let	VERB
ejpam-5118	98	2	φ	φ	PROPN
ejpam-5118	98	3	=	=	SYM
ejpam-5118	98	4	(	(	PUNCT
ejpam-5118	98	5	φ11	φ11	NUM
ejpam-5118	98	6	φ12	φ12	ADJ
ejpam-5118	98	7	φ21	φ21	NOUN
ejpam-5118	98	8	φ22	φ22	NOUN
ejpam-5118	98	9	)	)	PUNCT
ejpam-5118	98	10	be	be	AUX
ejpam-5118	98	11	a	a	DET
ejpam-5118	98	12	map	map	NOUN
ejpam-5118	98	13	from	from	ADP
ejpam-5118	98	14	g1	g1	PROPN
ejpam-5118	98	15	×	×	PROPN
ejpam-5118	98	16	ε1	ε1	PROPN
ejpam-5118	98	17	g2	g2	PROPN
ejpam-5118	98	18	to	to	PART
ejpam-5118	98	19	g1	g1	VERB
ejpam-5118	98	20	×	×	PROPN
ejpam-5118	98	21	ε2	ε2	PROPN
ejpam-5118	98	22	g2	g2	PROPN
ejpam-5118	98	23	.	.	PUNCT
ejpam-5118	99	1	then	then	ADV
ejpam-5118	99	2	,	,	PUNCT
ejpam-5118	99	3	φ	φ	PROPN
ejpam-5118	99	4	is	be	AUX
ejpam-5118	99	5	a	a	DET
ejpam-5118	99	6	group	group	NOUN
ejpam-5118	99	7	homomorphism	homomorphism	NOUN
ejpam-5118	99	8	if	if	SCONJ
ejpam-5118	99	9	and	and	CCONJ
ejpam-5118	99	10	only	only	ADV
ejpam-5118	99	11	if	if	SCONJ
ejpam-5118	99	12	(	(	PUNCT
ejpam-5118	99	13	i	i	NOUN
ejpam-5118	99	14	)	)	PUNCT
ejpam-5118	99	15	φ21	φ21	NOUN
ejpam-5118	99	16	∈	∈	PROPN
ejpam-5118	99	17	hom(g1	hom(g1	PRON
ejpam-5118	99	18	,	,	PUNCT
ejpam-5118	99	19	cg2(φ22(g2	cg2(φ22(g2	ADJ
ejpam-5118	99	20	)	)	PUNCT
ejpam-5118	99	21	)	)	PUNCT
ejpam-5118	99	22	)	)	PUNCT
ejpam-5118	99	23	,	,	PUNCT
ejpam-5118	99	24	φ22	φ22	NOUN
ejpam-5118	99	25	∈	∈	PROPN
ejpam-5118	99	26	end(g2	end(g2	X
ejpam-5118	99	27	)	)	PUNCT
ejpam-5118	99	28	and	and	CCONJ
ejpam-5118	99	29	φ11	φ11	NUM
ejpam-5118	99	30	is	be	AUX
ejpam-5118	99	31	an	an	DET
ejpam-5118	99	32	ε1	ε1	PROPN
ejpam-5118	99	33	-	-	PUNCT
ejpam-5118	99	34	endomorphism	endomorphism	NOUN
ejpam-5118	99	35	,	,	PUNCT
ejpam-5118	99	36	(	(	PUNCT
ejpam-5118	99	37	ii	ii	NOUN
ejpam-5118	99	38	)	)	PUNCT
ejpam-5118	100	1	[	[	X
ejpam-5118	100	2	{	{	PUNCT
ejpam-5118	100	3	1	1	NUM
ejpam-5118	100	4	}	}	PUNCT
ejpam-5118	100	5	×	×	NOUN
ejpam-5118	100	6	φ22(g2	φ22(g2	NUM
ejpam-5118	100	7	)	)	PUNCT
ejpam-5118	100	8	,	,	PUNCT
ejpam-5118	100	9	{	{	PUNCT
ejpam-5118	100	10	1	1	X
ejpam-5118	100	11	}	}	PUNCT
ejpam-5118	100	12	×	×	NOUN
ejpam-5118	100	13	φ21(g1	φ21(g1	NOUN
ejpam-5118	100	14	)	)	PUNCT
ejpam-5118	100	15	]	]	PUNCT
ejpam-5118	101	1	=	=	SYM
ejpam-5118	101	2	1	1	NUM
ejpam-5118	101	3	,	,	PUNCT
ejpam-5118	101	4	(	(	PUNCT
ejpam-5118	101	5	iii	iii	X
ejpam-5118	101	6	)	)	PUNCT
ejpam-5118	101	7	im(ε1	im(ε1	NOUN
ejpam-5118	101	8	)	)	PUNCT
ejpam-5118	101	9	≤	≤	NUM
ejpam-5118	101	10	ker(φ21	ker(φ21	NOUN
ejpam-5118	101	11	)	)	PUNCT
ejpam-5118	101	12	and	and	CCONJ
ejpam-5118	101	13	ε	ε	PROPN
ejpam-5118	101	14	−1	−1	NOUN
ejpam-5118	101	15	2	2	NUM
ejpam-5118	101	16	◦	◦	NOUN
ejpam-5118	101	17	(	(	PUNCT
ejpam-5118	101	18	φ21	φ21	NOUN
ejpam-5118	101	19	×	×	NOUN
ejpam-5118	101	20	φ21	φ21	NOUN
ejpam-5118	101	21	)	)	PUNCT
ejpam-5118	101	22	=	=	SYM
ejpam-5118	102	1	ψφ11	ψφ11	PROPN
ejpam-5118	102	2	∈	∈	PROPN
ejpam-5118	102	3	b2(g1	b2(g1	NOUN
ejpam-5118	102	4	,	,	PUNCT
ejpam-5118	102	5	g1	g1	PROPN
ejpam-5118	102	6	)	)	PUNCT
ejpam-5118	102	7	,	,	PUNCT
ejpam-5118	102	8	(	(	PUNCT
ejpam-5118	102	9	iv	iv	X
ejpam-5118	102	10	)	)	PUNCT
ejpam-5118	102	11	(	(	PUNCT
ejpam-5118	102	12	φ11	φ11	NUM
ejpam-5118	102	13	◦	◦	NOUN
ejpam-5118	102	14	ε1)(ε−1	ε1)(ε−1	ADJ
ejpam-5118	102	15	2	2	NUM
ejpam-5118	102	16	◦	◦	NOUN
ejpam-5118	102	17	(	(	PUNCT
ejpam-5118	102	18	φ22	φ22	NOUN
ejpam-5118	102	19	×	×	NOUN
ejpam-5118	102	20	φ22	φ22	NOUN
ejpam-5118	102	21	)	)	PUNCT
ejpam-5118	102	22	)	)	PUNCT
ejpam-5118	103	1	=	=	PUNCT
ejpam-5118	103	2	ψφ12	ψφ12	PROPN
ejpam-5118	103	3	∈	∈	PROPN
ejpam-5118	103	4	b2(g2	b2(g2	NOUN
ejpam-5118	103	5	,	,	PUNCT
ejpam-5118	103	6	g1	g1	PROPN
ejpam-5118	103	7	)	)	PUNCT
ejpam-5118	103	8	,	,	PUNCT
ejpam-5118	103	9	where	where	SCONJ
ejpam-5118	103	10	ψφij	ψφij	NOUN
ejpam-5118	103	11	(	(	PUNCT
ejpam-5118	103	12	y	y	PROPN
ejpam-5118	103	13	,	,	PUNCT
ejpam-5118	103	14	y	y	PROPN
ejpam-5118	103	15	′	′	NUM
ejpam-5118	103	16	)	)	PUNCT
ejpam-5118	103	17	=	=	VERB
ejpam-5118	104	1	φij(y)φij(y	φij(y)φij(y	ADJ
ejpam-5118	104	2	′)φij(yy	′)φij(yy	NOUN
ejpam-5118	104	3	′)−1	′)−1	NOUN
ejpam-5118	104	4	for	for	ADP
ejpam-5118	104	5	all	all	DET
ejpam-5118	104	6	1	1	NUM
ejpam-5118	104	7	≤	≤	NUM
ejpam-5118	104	8	i	i	PRON
ejpam-5118	104	9	,	,	PUNCT
ejpam-5118	104	10	j	j	PROPN
ejpam-5118	104	11	≤	≤	ADV
ejpam-5118	104	12	2	2	NUM
ejpam-5118	104	13	and	and	CCONJ
ejpam-5118	104	14	y	y	NOUN
ejpam-5118	104	15	,	,	PUNCT
ejpam-5118	104	16	y′	y′	NOUN
ejpam-5118	104	17	∈	∈	PROPN
ejpam-5118	104	18	gj	gj	NOUN
ejpam-5118	104	19	.	.	PUNCT
ejpam-5118	104	20	proof	proof	NOUN
ejpam-5118	104	21	.	.	PUNCT
ejpam-5118	105	1	indeed	indeed	ADV
ejpam-5118	105	2	,	,	PUNCT
ejpam-5118	105	3	evaluate	evaluate	VERB
ejpam-5118	105	4	the	the	DET
ejpam-5118	105	5	left	left	ADJ
ejpam-5118	105	6	hand	hand	NOUN
ejpam-5118	105	7	side	side	NOUN
ejpam-5118	105	8	and	and	CCONJ
ejpam-5118	105	9	right	right	ADJ
ejpam-5118	105	10	hand	hand	NOUN
ejpam-5118	105	11	side	side	NOUN
ejpam-5118	105	12	of	of	ADP
ejpam-5118	105	13	the	the	DET
ejpam-5118	105	14	formulas	formula	NOUN
ejpam-5118	105	15	(	(	PUNCT
ejpam-5118	105	16	2	2	NUM
ejpam-5118	105	17	)	)	PUNCT
ejpam-5118	105	18	and	and	CCONJ
ejpam-5118	105	19	(	(	PUNCT
ejpam-5118	105	20	3	3	NUM
ejpam-5118	105	21	)	)	PUNCT
ejpam-5118	105	22	,	,	PUNCT
ejpam-5118	105	23	we	we	PRON
ejpam-5118	105	24	obtain	obtain	VERB
ejpam-5118	105	25	φ(x	φ(x	PROPN
ejpam-5118	105	26	,	,	PUNCT
ejpam-5118	105	27	y	y	NOUN
ejpam-5118	105	28	)	)	PUNCT
ejpam-5118	105	29	·	·	PUNCT
ejpam-5118	106	1	ε2	ε2	PROPN
ejpam-5118	106	2	φ(x′	φ(x′	NUM
ejpam-5118	106	3	,	,	PUNCT
ejpam-5118	106	4	1	1	NUM
ejpam-5118	106	5	)	)	PUNCT
ejpam-5118	106	6	=	=	VERB
ejpam-5118	107	1	φ(xx′	φ(xx′	NOUN
ejpam-5118	107	2	,	,	PUNCT
ejpam-5118	107	3	y	y	NOUN
ejpam-5118	107	4	)	)	PUNCT
ejpam-5118	107	5	n.	n.	NOUN
ejpam-5118	107	6	snanou	snanou	PROPN
ejpam-5118	107	7	/	/	SYM
ejpam-5118	107	8	eur	eur	PROPN
ejpam-5118	107	9	.	.	PUNCT
ejpam-5118	108	1	j.	j.	PROPN
ejpam-5118	108	2	pure	pure	PROPN
ejpam-5118	108	3	appl	appl	PROPN
ejpam-5118	108	4	.	.	PROPN
ejpam-5118	108	5	math	math	PROPN
ejpam-5118	108	6	,	,	PUNCT
ejpam-5118	108	7	17	17	NUM
ejpam-5118	108	8	(	(	PUNCT
ejpam-5118	108	9	2	2	NUM
ejpam-5118	108	10	)	)	PUNCT
ejpam-5118	108	11	(	(	PUNCT
ejpam-5118	108	12	2024	2024	NUM
ejpam-5118	108	13	)	)	PUNCT
ejpam-5118	108	14	,	,	PUNCT
ejpam-5118	108	15	956	956	NUM
ejpam-5118	108	16	-	-	SYM
ejpam-5118	108	17	968	968	NUM
ejpam-5118	108	18	960	960	NUM
ejpam-5118	108	19	⇔	⇔	X
ejpam-5118	108	20	(	(	PUNCT
ejpam-5118	108	21	φ11(x)φ12(y)ε2(φ21(x	φ11(x)φ12(y)ε2(φ21(x	PROPN
ejpam-5118	108	22	)	)	PUNCT
ejpam-5118	108	23	,	,	PUNCT
ejpam-5118	108	24	φ22(y	φ22(y	ADJ
ejpam-5118	108	25	)	)	PUNCT
ejpam-5118	108	26	)	)	PUNCT
ejpam-5118	108	27	,	,	PUNCT
ejpam-5118	108	28	φ21(x)φ22(y	φ21(x)φ22(y	ADJ
ejpam-5118	108	29	)	)	PUNCT
ejpam-5118	108	30	)	)	PUNCT
ejpam-5118	108	31	·	·	PUNCT
ejpam-5118	109	1	ε2	ε2	ADJ
ejpam-5118	109	2	(	(	PUNCT
ejpam-5118	109	3	φ11(x	φ11(x	NOUN
ejpam-5118	109	4	′	′	NOUN
ejpam-5118	109	5	)	)	PUNCT
ejpam-5118	109	6	,	,	PUNCT
ejpam-5118	109	7	φ21(x	φ21(x	NOUN
ejpam-5118	109	8	′	′	NOUN
ejpam-5118	109	9	)	)	PUNCT
ejpam-5118	109	10	)	)	PUNCT
ejpam-5118	110	1	=	=	PUNCT
ejpam-5118	110	2	(	(	PUNCT
ejpam-5118	110	3	φ11(xx	φ11(xx	NOUN
ejpam-5118	110	4	′)φ12(y)ε2(φ21(xx	′)φ12(y)ε2(φ21(xx	PROPN
ejpam-5118	110	5	′	′	NUM
ejpam-5118	110	6	)	)	PUNCT
ejpam-5118	110	7	,	,	PUNCT
ejpam-5118	110	8	φ22(y	φ22(y	ADJ
ejpam-5118	110	9	)	)	PUNCT
ejpam-5118	110	10	)	)	PUNCT
ejpam-5118	110	11	,	,	PUNCT
ejpam-5118	110	12	φ21(xx	φ21(xx	NUM
ejpam-5118	110	13	′)φ22(y	′)φ22(y	NOUN
ejpam-5118	110	14	)	)	PUNCT
ejpam-5118	110	15	)	)	PUNCT
ejpam-5118	111	1	⇔	⇔	PROPN
ejpam-5118	111	2	φ21(x)φ22(y)φ21(x	φ21(x)φ22(y)φ21(x	PROPN
ejpam-5118	111	3	′	′	NOUN
ejpam-5118	111	4	)	)	PUNCT
ejpam-5118	111	5	=	=	SYM
ejpam-5118	112	1	φ21(xx	φ21(xx	NUM
ejpam-5118	112	2	′)φ22(y	′)φ22(y	NOUN
ejpam-5118	112	3	)	)	PUNCT
ejpam-5118	112	4	and	and	CCONJ
ejpam-5118	112	5	(	(	PUNCT
ejpam-5118	112	6	4	4	X
ejpam-5118	112	7	)	)	PUNCT
ejpam-5118	112	8	φ11(x)φ12(y)ε2(φ21(x	φ11(x)φ12(y)ε2(φ21(x	NOUN
ejpam-5118	112	9	)	)	PUNCT
ejpam-5118	112	10	,	,	PUNCT
ejpam-5118	112	11	φ22(y))φ11(x	φ22(y))φ11(x	PROPN
ejpam-5118	112	12	′)ε2(φ21(x)φ22(y	′)ε2(φ21(x)φ22(y	PROPN
ejpam-5118	112	13	)	)	PUNCT
ejpam-5118	112	14	,	,	PUNCT
ejpam-5118	112	15	φ21(x	φ21(x	NOUN
ejpam-5118	112	16	′	′	NOUN
ejpam-5118	112	17	)	)	PUNCT
ejpam-5118	112	18	)	)	PUNCT
ejpam-5118	112	19	(	(	PUNCT
ejpam-5118	112	20	5	5	X
ejpam-5118	112	21	)	)	PUNCT
ejpam-5118	112	22	=	=	PUNCT
ejpam-5118	112	23	φ11(xx	φ11(xx	NUM
ejpam-5118	112	24	′)φ12(y)ε2(φ21(xx	′)φ12(y)ε2(φ21(xx	PROPN
ejpam-5118	112	25	′	′	NUM
ejpam-5118	112	26	)	)	PUNCT
ejpam-5118	112	27	,	,	PUNCT
ejpam-5118	112	28	φ22(y	φ22(y	ADJ
ejpam-5118	112	29	)	)	PUNCT
ejpam-5118	112	30	)	)	PUNCT
ejpam-5118	112	31	.	.	PUNCT
ejpam-5118	113	1	setting	set	VERB
ejpam-5118	113	2	x	x	PUNCT
ejpam-5118	113	3	=	=	SYM
ejpam-5118	113	4	1	1	NUM
ejpam-5118	113	5	in	in	ADP
ejpam-5118	113	6	the	the	DET
ejpam-5118	113	7	equations	equation	NOUN
ejpam-5118	113	8	(	(	PUNCT
ejpam-5118	113	9	4	4	NUM
ejpam-5118	113	10	)	)	PUNCT
ejpam-5118	113	11	and	and	CCONJ
ejpam-5118	113	12	(	(	PUNCT
ejpam-5118	113	13	5	5	NUM
ejpam-5118	113	14	)	)	PUNCT
ejpam-5118	113	15	,	,	PUNCT
ejpam-5118	113	16	we	we	PRON
ejpam-5118	113	17	obtain	obtain	VERB
ejpam-5118	113	18	φ22(y)φ21(x	φ22(y)φ21(x	NOUN
ejpam-5118	113	19	′	′	NUM
ejpam-5118	113	20	)	)	PUNCT
ejpam-5118	114	1	=	=	SYM
ejpam-5118	114	2	φ21(x	φ21(x	NOUN
ejpam-5118	114	3	′)φ22(y	′)φ22(y	NOUN
ejpam-5118	114	4	)	)	PUNCT
ejpam-5118	114	5	(	(	PUNCT
ejpam-5118	114	6	6	6	NUM
ejpam-5118	114	7	)	)	PUNCT
ejpam-5118	114	8	and	and	CCONJ
ejpam-5118	114	9	ε2(φ22(y	ε2(φ22(y	PROPN
ejpam-5118	114	10	)	)	PUNCT
ejpam-5118	114	11	,	,	PUNCT
ejpam-5118	114	12	φ21(x	φ21(x	NOUN
ejpam-5118	114	13	′	′	NOUN
ejpam-5118	114	14	)	)	PUNCT
ejpam-5118	114	15	)	)	PUNCT
ejpam-5118	115	1	=	=	PUNCT
ejpam-5118	116	1	ε2(φ21(x	ε2(φ21(x	NUM
ejpam-5118	116	2	′	′	NUM
ejpam-5118	116	3	)	)	PUNCT
ejpam-5118	116	4	,	,	PUNCT
ejpam-5118	116	5	φ22(y	φ22(y	ADJ
ejpam-5118	116	6	)	)	PUNCT
ejpam-5118	116	7	)	)	PUNCT
ejpam-5118	116	8	.	.	PUNCT
ejpam-5118	117	1	(	(	PUNCT
ejpam-5118	117	2	7	7	X
ejpam-5118	117	3	)	)	PUNCT
ejpam-5118	117	4	that	that	PRON
ejpam-5118	117	5	is	be	AUX
ejpam-5118	117	6	,	,	PUNCT
ejpam-5118	117	7	[	[	X
ejpam-5118	117	8	{	{	PUNCT
ejpam-5118	117	9	1	1	NUM
ejpam-5118	117	10	}	}	PUNCT
ejpam-5118	117	11	×	×	NOUN
ejpam-5118	117	12	φ22(g2	φ22(g2	NUM
ejpam-5118	117	13	)	)	PUNCT
ejpam-5118	117	14	,	,	PUNCT
ejpam-5118	117	15	{	{	PUNCT
ejpam-5118	117	16	1	1	X
ejpam-5118	117	17	}	}	PUNCT
ejpam-5118	117	18	×	×	NOUN
ejpam-5118	117	19	φ21(g1	φ21(g1	NOUN
ejpam-5118	117	20	)	)	PUNCT
ejpam-5118	117	21	]	]	PUNCT
ejpam-5118	118	1	=	=	PUNCT
ejpam-5118	118	2	1	1	X
ejpam-5118	118	3	.	.	PUNCT
ejpam-5118	118	4	now	now	ADV
ejpam-5118	118	5	,	,	PUNCT
ejpam-5118	118	6	combining	combine	VERB
ejpam-5118	118	7	the	the	DET
ejpam-5118	118	8	equations	equation	NOUN
ejpam-5118	118	9	(	(	PUNCT
ejpam-5118	118	10	4	4	NUM
ejpam-5118	118	11	)	)	PUNCT
ejpam-5118	118	12	and	and	CCONJ
ejpam-5118	118	13	(	(	PUNCT
ejpam-5118	118	14	6	6	NUM
ejpam-5118	118	15	)	)	PUNCT
ejpam-5118	118	16	,	,	PUNCT
ejpam-5118	118	17	we	we	PRON
ejpam-5118	118	18	get	get	VERB
ejpam-5118	118	19	that	that	DET
ejpam-5118	118	20	φ21	φ21	NOUN
ejpam-5118	118	21	∈	∈	PROPN
ejpam-5118	118	22	hom(g1	hom(g1	PRON
ejpam-5118	118	23	,	,	PUNCT
ejpam-5118	118	24	cg2(φ22(g2	cg2(φ22(g2	ADJ
ejpam-5118	118	25	)	)	PUNCT
ejpam-5118	118	26	)	)	PUNCT
ejpam-5118	118	27	)	)	PUNCT
ejpam-5118	118	28	.	.	PUNCT
ejpam-5118	119	1	thus	thus	ADV
ejpam-5118	119	2	,	,	PUNCT
ejpam-5118	119	3	using	use	VERB
ejpam-5118	119	4	the	the	DET
ejpam-5118	119	5	2	2	NUM
ejpam-5118	119	6	-	-	PUNCT
ejpam-5118	119	7	cocycle	cocycle	NOUN
ejpam-5118	119	8	condition	condition	NOUN
ejpam-5118	119	9	together	together	ADV
ejpam-5118	119	10	with	with	ADP
ejpam-5118	119	11	the	the	DET
ejpam-5118	119	12	equations	equation	NOUN
ejpam-5118	119	13	(	(	PUNCT
ejpam-5118	119	14	6	6	NUM
ejpam-5118	119	15	)	)	PUNCT
ejpam-5118	119	16	and	and	CCONJ
ejpam-5118	119	17	(	(	PUNCT
ejpam-5118	119	18	7	7	NUM
ejpam-5118	119	19	)	)	PUNCT
ejpam-5118	119	20	,	,	PUNCT
ejpam-5118	119	21	the	the	DET
ejpam-5118	119	22	equation	equation	NOUN
ejpam-5118	119	23	(	(	PUNCT
ejpam-5118	119	24	5	5	X
ejpam-5118	119	25	)	)	PUNCT
ejpam-5118	119	26	yields	yield	NOUN
ejpam-5118	119	27	φ11(xx	φ11(xx	NOUN
ejpam-5118	119	28	′	′	NOUN
ejpam-5118	119	29	)	)	PUNCT
ejpam-5118	119	30	=	=	PUNCT
ejpam-5118	119	31	φ11(x)φ11(x	φ11(x)φ11(x	NOUN
ejpam-5118	119	32	′)ε2(φ21(x	′)ε2(φ21(x	NOUN
ejpam-5118	119	33	)	)	PUNCT
ejpam-5118	119	34	,	,	PUNCT
ejpam-5118	119	35	φ21(x	φ21(x	NOUN
ejpam-5118	119	36	′	′	NOUN
ejpam-5118	119	37	)	)	PUNCT
ejpam-5118	119	38	)	)	PUNCT
ejpam-5118	120	1	(	(	PUNCT
ejpam-5118	120	2	8)	8)	NUM
ejpam-5118	120	3	which	which	PRON
ejpam-5118	120	4	implies	imply	VERB
ejpam-5118	120	5	that	that	SCONJ
ejpam-5118	120	6	ε−1	ε−1	PROPN
ejpam-5118	120	7	2	2	NUM
ejpam-5118	120	8	◦	◦	NOUN
ejpam-5118	120	9	(	(	PUNCT
ejpam-5118	120	10	φ21	φ21	NOUN
ejpam-5118	120	11	×	×	NOUN
ejpam-5118	120	12	φ21	φ21	NOUN
ejpam-5118	120	13	)	)	PUNCT
ejpam-5118	120	14	∈	∈	PROPN
ejpam-5118	120	15	b2(g1	b2(g1	NOUN
ejpam-5118	120	16	,	,	PUNCT
ejpam-5118	120	17	g1	g1	NOUN
ejpam-5118	120	18	)	)	PUNCT
ejpam-5118	120	19	.	.	PUNCT
ejpam-5118	121	1	on	on	ADP
ejpam-5118	121	2	the	the	DET
ejpam-5118	121	3	other	other	ADJ
ejpam-5118	121	4	hand	hand	NOUN
ejpam-5118	121	5	,	,	PUNCT
ejpam-5118	121	6	we	we	PRON
ejpam-5118	121	7	have	have	VERB
ejpam-5118	121	8	that	that	PRON
ejpam-5118	121	9	φ(x	φ(x	PROPN
ejpam-5118	121	10	,	,	PUNCT
ejpam-5118	121	11	y	y	NOUN
ejpam-5118	121	12	)	)	PUNCT
ejpam-5118	121	13	·	·	PUNCT
ejpam-5118	121	14	ε2	ε2	PROPN
ejpam-5118	121	15	φ(1	φ(1	PROPN
ejpam-5118	121	16	,	,	PUNCT
ejpam-5118	121	17	y′	y′	NUM
ejpam-5118	121	18	)	)	PUNCT
ejpam-5118	122	1	=	=	SYM
ejpam-5118	122	2	φ(xε1(y	φ(xε1(y	PROPN
ejpam-5118	122	3	,	,	PUNCT
ejpam-5118	122	4	y	y	PROPN
ejpam-5118	122	5	′	′	NUM
ejpam-5118	122	6	)	)	PUNCT
ejpam-5118	122	7	,	,	PUNCT
ejpam-5118	122	8	yy′	yy′	X
ejpam-5118	122	9	)	)	PUNCT
ejpam-5118	122	10	⇔	⇔	NOUN
ejpam-5118	122	11	(	(	PUNCT
ejpam-5118	122	12	φ11(x)φ12(y)ε2(φ21(x	φ11(x)φ12(y)ε2(φ21(x	PROPN
ejpam-5118	122	13	)	)	PUNCT
ejpam-5118	122	14	,	,	PUNCT
ejpam-5118	122	15	φ22(y	φ22(y	ADJ
ejpam-5118	122	16	)	)	PUNCT
ejpam-5118	122	17	)	)	PUNCT
ejpam-5118	122	18	,	,	PUNCT
ejpam-5118	122	19	φ21(x)φ22(y	φ21(x)φ22(y	ADJ
ejpam-5118	122	20	)	)	PUNCT
ejpam-5118	122	21	)	)	PUNCT
ejpam-5118	122	22	·	·	PUNCT
ejpam-5118	123	1	ε2	ε2	ADJ
ejpam-5118	123	2	(	(	PUNCT
ejpam-5118	123	3	φ12(y	φ12(y	ADJ
ejpam-5118	123	4	′	′	NOUN
ejpam-5118	123	5	)	)	PUNCT
ejpam-5118	123	6	,	,	PUNCT
ejpam-5118	123	7	φ22(y	φ22(y	ADP
ejpam-5118	123	8	′	′	NOUN
ejpam-5118	123	9	)	)	PUNCT
ejpam-5118	123	10	)	)	PUNCT
ejpam-5118	124	1	=	=	SYM
ejpam-5118	124	2	(	(	PUNCT
ejpam-5118	124	3	φ11(xε1(y	φ11(xε1(y	PROPN
ejpam-5118	124	4	,	,	PUNCT
ejpam-5118	124	5	y	y	PROPN
ejpam-5118	124	6	′))φ12(yy	′))φ12(yy	PROPN
ejpam-5118	124	7	′)ε2(φ21(xε1(y	′)ε2(φ21(xε1(y	PROPN
ejpam-5118	124	8	,	,	PUNCT
ejpam-5118	124	9	y	y	PROPN
ejpam-5118	124	10	′	′	NUM
ejpam-5118	124	11	)	)	PUNCT
ejpam-5118	124	12	)	)	PUNCT
ejpam-5118	124	13	,	,	PUNCT
ejpam-5118	124	14	φ22(yy	φ22(yy	NUM
ejpam-5118	124	15	′	′	NUM
ejpam-5118	124	16	)	)	PUNCT
ejpam-5118	124	17	)	)	PUNCT
ejpam-5118	124	18	,	,	PUNCT
ejpam-5118	124	19	φ21(xε1(y	φ21(xε1(y	PROPN
ejpam-5118	124	20	,	,	PUNCT
ejpam-5118	124	21	y	y	PROPN
ejpam-5118	124	22	′))φ22(yy	′))φ22(yy	PROPN
ejpam-5118	124	23	′	′	NUM
ejpam-5118	124	24	)	)	PUNCT
ejpam-5118	124	25	)	)	PUNCT
ejpam-5118	125	1	⇔	⇔	NOUN
ejpam-5118	125	2	φ21(x)φ22(y)φ22(y	φ21(x)φ22(y)φ22(y	NOUN
ejpam-5118	125	3	′	′	NUM
ejpam-5118	125	4	)	)	PUNCT
ejpam-5118	126	1	=	=	SYM
ejpam-5118	126	2	φ21(xε1(y	φ21(xε1(y	PROPN
ejpam-5118	126	3	,	,	PUNCT
ejpam-5118	126	4	y	y	PROPN
ejpam-5118	126	5	′))φ22(yy	′))φ22(yy	PROPN
ejpam-5118	126	6	′	′	NUM
ejpam-5118	126	7	)	)	PUNCT
ejpam-5118	126	8	and	and	CCONJ
ejpam-5118	126	9	(	(	PUNCT
ejpam-5118	126	10	9	9	X
ejpam-5118	126	11	)	)	PUNCT
ejpam-5118	126	12	φ11(x)φ12(y)ε2(φ21(x	φ11(x)φ12(y)ε2(φ21(x	PROPN
ejpam-5118	126	13	)	)	PUNCT
ejpam-5118	126	14	,	,	PUNCT
ejpam-5118	126	15	φ22(y))φ12(y	φ22(y))φ12(y	PROPN
ejpam-5118	126	16	′)ε2(φ21(x)φ22(y	′)ε2(φ21(x)φ22(y	PROPN
ejpam-5118	126	17	)	)	PUNCT
ejpam-5118	126	18	,	,	PUNCT
ejpam-5118	126	19	φ22(y	φ22(y	ADP
ejpam-5118	126	20	′	′	NOUN
ejpam-5118	126	21	)	)	PUNCT
ejpam-5118	126	22	)	)	PUNCT
ejpam-5118	126	23	(	(	PUNCT
ejpam-5118	126	24	10	10	NUM
ejpam-5118	126	25	)	)	PUNCT
ejpam-5118	126	26	=	=	SYM
ejpam-5118	126	27	φ11(xε1(y	φ11(xε1(y	PROPN
ejpam-5118	126	28	,	,	PUNCT
ejpam-5118	126	29	y	y	PROPN
ejpam-5118	126	30	′))φ12(yy	′))φ12(yy	PROPN
ejpam-5118	126	31	′)ε2(φ21(xε1(y	′)ε2(φ21(xε1(y	PROPN
ejpam-5118	126	32	,	,	PUNCT
ejpam-5118	126	33	y	y	PROPN
ejpam-5118	126	34	′	′	NUM
ejpam-5118	126	35	)	)	PUNCT
ejpam-5118	126	36	)	)	PUNCT
ejpam-5118	126	37	,	,	PUNCT
ejpam-5118	126	38	φ22(yy	φ22(yy	NUM
ejpam-5118	126	39	′	′	NUM
ejpam-5118	126	40	)	)	PUNCT
ejpam-5118	126	41	)	)	PUNCT
ejpam-5118	126	42	.	.	PUNCT
ejpam-5118	127	1	since	since	SCONJ
ejpam-5118	127	2	φ21	φ21	NOUN
ejpam-5118	127	3	is	be	AUX
ejpam-5118	127	4	a	a	DET
ejpam-5118	127	5	group	group	NOUN
ejpam-5118	127	6	homomorphism	homomorphism	NOUN
ejpam-5118	127	7	,	,	PUNCT
ejpam-5118	127	8	the	the	DET
ejpam-5118	127	9	equation	equation	NOUN
ejpam-5118	127	10	(	(	PUNCT
ejpam-5118	127	11	9	9	NUM
ejpam-5118	127	12	)	)	PUNCT
ejpam-5118	127	13	implies	imply	VERB
ejpam-5118	127	14	that	that	SCONJ
ejpam-5118	127	15	φ21(ε1(y	φ21(ε1(y	PROPN
ejpam-5118	127	16	,	,	PUNCT
ejpam-5118	127	17	y	y	PROPN
ejpam-5118	127	18	′	′	NUM
ejpam-5118	127	19	)	)	PUNCT
ejpam-5118	127	20	)	)	PUNCT
ejpam-5118	128	1	=	=	SYM
ejpam-5118	128	2	φ22(y)φ22(y	φ22(y)φ22(y	PROPN
ejpam-5118	128	3	′)(φ22(yy	′)(φ22(yy	ADJ
ejpam-5118	128	4	′))−1	′))−1	NOUN
ejpam-5118	128	5	for	for	ADP
ejpam-5118	128	6	all	all	DET
ejpam-5118	128	7	y	y	PROPN
ejpam-5118	128	8	,	,	PUNCT
ejpam-5118	128	9	y′	y′	NOUN
ejpam-5118	128	10	∈	∈	PROPN
ejpam-5118	128	11	g2	g2	PROPN
ejpam-5118	128	12	.	.	PUNCT
ejpam-5118	129	1	so	so	ADV
ejpam-5118	129	2	,	,	PUNCT
ejpam-5118	129	3	φ21	φ21	PRON
ejpam-5118	129	4	◦	◦	NOUN
ejpam-5118	129	5	ε1	ε1	VERB
ejpam-5118	129	6	∼	∼	NOUN
ejpam-5118	129	7	1	1	NUM
ejpam-5118	129	8	.	.	PUNCT
ejpam-5118	130	1	but	but	CCONJ
ejpam-5118	130	2	,	,	PUNCT
ejpam-5118	130	3	by	by	ADP
ejpam-5118	130	4	the	the	DET
ejpam-5118	130	5	assumption	assumption	NOUN
ejpam-5118	130	6	,	,	PUNCT
ejpam-5118	130	7	there	there	PRON
ejpam-5118	130	8	is	be	VERB
ejpam-5118	130	9	no	no	DET
ejpam-5118	130	10	nontrivial	nontrivial	ADJ
ejpam-5118	130	11	2	2	NUM
ejpam-5118	130	12	-	-	PUNCT
ejpam-5118	130	13	cocycle	cocycle	NOUN
ejpam-5118	130	14	in	in	ADP
ejpam-5118	130	15	z2(g2	z2(g2	PROPN
ejpam-5118	130	16	,	,	PUNCT
ejpam-5118	130	17	g2	g2	PROPN
ejpam-5118	130	18	)	)	PUNCT
ejpam-5118	130	19	that	that	PRON
ejpam-5118	130	20	is	be	AUX
ejpam-5118	130	21	cohomologous	cohomologous	ADJ
ejpam-5118	130	22	to	to	ADP
ejpam-5118	130	23	the	the	DET
ejpam-5118	130	24	trivial	trivial	ADJ
ejpam-5118	130	25	2	2	NUM
ejpam-5118	130	26	-	-	PUNCT
ejpam-5118	130	27	cocycle	cocycle	NOUN
ejpam-5118	130	28	.	.	PUNCT
ejpam-5118	131	1	so	so	ADV
ejpam-5118	131	2	,	,	PUNCT
ejpam-5118	131	3	we	we	PRON
ejpam-5118	131	4	have	have	VERB
ejpam-5118	131	5	φ21	φ21	NOUN
ejpam-5118	131	6	◦	◦	NOUN
ejpam-5118	131	7	ε1	ε1	NOUN
ejpam-5118	131	8	=	=	SYM
ejpam-5118	131	9	1	1	NUM
ejpam-5118	131	10	and	and	CCONJ
ejpam-5118	131	11	then	then	ADV
ejpam-5118	131	12	φ22	φ22	PROPN
ejpam-5118	131	13	∈	∈	PROPN
ejpam-5118	131	14	end(g2	end(g2	X
ejpam-5118	131	15	)	)	PUNCT
ejpam-5118	131	16	.	.	PUNCT
ejpam-5118	132	1	furthermore	furthermore	ADV
ejpam-5118	132	2	,	,	PUNCT
ejpam-5118	132	3	by	by	ADP
ejpam-5118	132	4	using	use	VERB
ejpam-5118	132	5	the	the	DET
ejpam-5118	132	6	2	2	NUM
ejpam-5118	132	7	-	-	PUNCT
ejpam-5118	132	8	cocycle	cocycle	NOUN
ejpam-5118	132	9	condition	condition	NOUN
ejpam-5118	132	10	,	,	PUNCT
ejpam-5118	132	11	the	the	DET
ejpam-5118	132	12	equation	equation	NOUN
ejpam-5118	132	13	(	(	PUNCT
ejpam-5118	132	14	10	10	NUM
ejpam-5118	132	15	)	)	PUNCT
ejpam-5118	132	16	gives	give	VERB
ejpam-5118	132	17	us	we	PRON
ejpam-5118	132	18	φ11(xε1(y	φ11(xε1(y	NUM
ejpam-5118	132	19	,	,	PUNCT
ejpam-5118	132	20	y	y	PROPN
ejpam-5118	132	21	′))φ12(yy	′))φ12(yy	NOUN
ejpam-5118	132	22	′	′	NOUN
ejpam-5118	132	23	)	)	PUNCT
ejpam-5118	132	24	=	=	PUNCT
ejpam-5118	133	1	φ11(x)φ12(y)φ12(y	φ11(x)φ12(y)φ12(y	ADJ
ejpam-5118	133	2	′)ε2(φ22(y	′)ε2(φ22(y	NUM
ejpam-5118	133	3	)	)	PUNCT
ejpam-5118	133	4	,	,	PUNCT
ejpam-5118	133	5	φ22(y	φ22(y	ADP
ejpam-5118	133	6	′	′	NOUN
ejpam-5118	133	7	)	)	PUNCT
ejpam-5118	133	8	)	)	PUNCT
ejpam-5118	133	9	.	.	PUNCT
ejpam-5118	134	1	(	(	PUNCT
ejpam-5118	134	2	11	11	NUM
ejpam-5118	134	3	)	)	PUNCT
ejpam-5118	134	4	but	but	CCONJ
ejpam-5118	134	5	,	,	PUNCT
ejpam-5118	134	6	the	the	DET
ejpam-5118	134	7	equation	equation	NOUN
ejpam-5118	134	8	(	(	PUNCT
ejpam-5118	134	9	8)	8)	NUM
ejpam-5118	134	10	yields	yield	NOUN
ejpam-5118	134	11	φ11(xε1(y	φ11(xε1(y	PROPN
ejpam-5118	134	12	,	,	PUNCT
ejpam-5118	134	13	y	y	PROPN
ejpam-5118	134	14	′	′	NUM
ejpam-5118	134	15	)	)	PUNCT
ejpam-5118	134	16	)	)	PUNCT
ejpam-5118	135	1	=	=	SYM
ejpam-5118	135	2	φ11(x)φ11(ε1(y	φ11(x)φ11(ε1(y	PROPN
ejpam-5118	135	3	,	,	PUNCT
ejpam-5118	135	4	y	y	PROPN
ejpam-5118	135	5	′	′	NUM
ejpam-5118	135	6	)	)	PUNCT
ejpam-5118	135	7	)	)	PUNCT
ejpam-5118	135	8	.	.	PUNCT
ejpam-5118	136	1	thus	thus	ADV
ejpam-5118	136	2	,	,	PUNCT
ejpam-5118	136	3	the	the	DET
ejpam-5118	136	4	equation	equation	NOUN
ejpam-5118	136	5	(	(	PUNCT
ejpam-5118	136	6	11	11	NUM
ejpam-5118	136	7	)	)	PUNCT
ejpam-5118	136	8	is	be	AUX
ejpam-5118	136	9	equivalent	equivalent	ADJ
ejpam-5118	136	10	to	to	ADP
ejpam-5118	136	11	φ11(ε1(y	φ11(ε1(y	ADV
ejpam-5118	136	12	,	,	PUNCT
ejpam-5118	136	13	y	y	PROPN
ejpam-5118	136	14	′))φ12(yy	′))φ12(yy	PROPN
ejpam-5118	136	15	′	′	NOUN
ejpam-5118	136	16	)	)	PUNCT
ejpam-5118	136	17	=	=	PUNCT
ejpam-5118	136	18	φ12(y)φ12(y	φ12(y)φ12(y	NOUN
ejpam-5118	136	19	′)ε2(φ22(y	′)ε2(φ22(y	NUM
ejpam-5118	136	20	)	)	PUNCT
ejpam-5118	136	21	,	,	PUNCT
ejpam-5118	136	22	φ22(y	φ22(y	ADP
ejpam-5118	136	23	′	′	NOUN
ejpam-5118	136	24	)	)	PUNCT
ejpam-5118	136	25	)	)	PUNCT
ejpam-5118	136	26	,	,	PUNCT
ejpam-5118	136	27	n.	n.	PROPN
ejpam-5118	136	28	snanou	snanou	PROPN
ejpam-5118	136	29	/	/	SYM
ejpam-5118	136	30	eur	eur	PROPN
ejpam-5118	136	31	.	.	PUNCT
ejpam-5118	137	1	j.	j.	PROPN
ejpam-5118	137	2	pure	pure	PROPN
ejpam-5118	137	3	appl	appl	PROPN
ejpam-5118	137	4	.	.	PROPN
ejpam-5118	137	5	math	math	PROPN
ejpam-5118	137	6	,	,	PUNCT
ejpam-5118	137	7	17	17	NUM
ejpam-5118	137	8	(	(	PUNCT
ejpam-5118	137	9	2	2	NUM
ejpam-5118	137	10	)	)	PUNCT
ejpam-5118	137	11	(	(	PUNCT
ejpam-5118	137	12	2024	2024	NUM
ejpam-5118	137	13	)	)	PUNCT
ejpam-5118	137	14	,	,	PUNCT
ejpam-5118	137	15	956	956	NUM
ejpam-5118	137	16	-	-	SYM
ejpam-5118	137	17	968	968	NUM
ejpam-5118	137	18	961	961	NUM
ejpam-5118	137	19	which	which	PRON
ejpam-5118	137	20	implies	imply	VERB
ejpam-5118	137	21	that	that	SCONJ
ejpam-5118	137	22	φ11(ε1(y	φ11(ε1(y	ADV
ejpam-5118	137	23	,	,	PUNCT
ejpam-5118	137	24	y	y	PROPN
ejpam-5118	137	25	′))(ε2(φ22(y	′))(ε2(φ22(y	PROPN
ejpam-5118	137	26	)	)	PUNCT
ejpam-5118	137	27	,	,	PUNCT
ejpam-5118	137	28	φ22(y	φ22(y	ADJ
ejpam-5118	137	29	′)))−1	′)))−1	NOUN
ejpam-5118	137	30	=	=	SYM
ejpam-5118	137	31	φ12(y)φ12(y	φ12(y)φ12(y	ADJ
ejpam-5118	137	32	′)(φ12(yy	′)(φ12(yy	NOUN
ejpam-5118	137	33	′))−1	′))−1	NOUN
ejpam-5118	137	34	.	.	PUNCT
ejpam-5118	138	1	thus	thus	ADV
ejpam-5118	138	2	,	,	PUNCT
ejpam-5118	138	3	the	the	DET
ejpam-5118	138	4	proof	proof	NOUN
ejpam-5118	138	5	is	be	AUX
ejpam-5118	138	6	completed	complete	VERB
ejpam-5118	138	7	.	.	PUNCT
ejpam-5118	139	1	remark	remark	PROPN
ejpam-5118	139	2	3.1	3.1	NUM
ejpam-5118	139	3	.	.	PUNCT
ejpam-5118	140	1	(	(	PUNCT
ejpam-5118	140	2	i	i	NOUN
ejpam-5118	140	3	)	)	PUNCT
ejpam-5118	140	4	note	note	VERB
ejpam-5118	140	5	that	that	SCONJ
ejpam-5118	140	6	if	if	SCONJ
ejpam-5118	140	7	g2	g2	PROPN
ejpam-5118	140	8	is	be	AUX
ejpam-5118	140	9	abelian	abelian	ADJ
ejpam-5118	140	10	then	then	ADV
ejpam-5118	140	11	the	the	DET
ejpam-5118	140	12	assumption	assumption	NOUN
ejpam-5118	140	13	of	of	ADP
ejpam-5118	140	14	the	the	DET
ejpam-5118	140	15	previous	previous	ADJ
ejpam-5118	140	16	proposition	proposition	NOUN
ejpam-5118	140	17	and	and	CCONJ
ejpam-5118	140	18	the	the	DET
ejpam-5118	140	19	condition	condition	NOUN
ejpam-5118	140	20	b2(g2	b2(g2	AUX
ejpam-5118	140	21	,	,	PUNCT
ejpam-5118	140	22	g2	g2	PROPN
ejpam-5118	140	23	)	)	PUNCT
ejpam-5118	141	1	=	=	SYM
ejpam-5118	141	2	1	1	NUM
ejpam-5118	141	3	are	be	AUX
ejpam-5118	141	4	equivalent	equivalent	ADJ
ejpam-5118	141	5	.	.	PUNCT
ejpam-5118	142	1	(	(	PUNCT
ejpam-5118	142	2	ii	ii	NOUN
ejpam-5118	142	3	)	)	PUNCT
ejpam-5118	142	4	if	if	SCONJ
ejpam-5118	142	5	ε2	ε2	PROPN
ejpam-5118	142	6	∈	∈	PROPN
ejpam-5118	142	7	sz2(g2	sz2(g2	X
ejpam-5118	142	8	,	,	PUNCT
ejpam-5118	142	9	g1	g1	PROPN
ejpam-5118	142	10	)	)	PUNCT
ejpam-5118	142	11	then	then	ADV
ejpam-5118	142	12	the	the	DET
ejpam-5118	142	13	second	second	ADJ
ejpam-5118	142	14	condition	condition	NOUN
ejpam-5118	142	15	of	of	ADP
ejpam-5118	142	16	the	the	DET
ejpam-5118	142	17	previous	previous	ADJ
ejpam-5118	142	18	proposition	proposition	NOUN
ejpam-5118	142	19	is	be	AUX
ejpam-5118	142	20	not	not	PART
ejpam-5118	142	21	required	require	VERB
ejpam-5118	142	22	.	.	PUNCT
ejpam-5118	143	1	definition	definition	NOUN
ejpam-5118	143	2	3.2	3.2	NUM
ejpam-5118	143	3	.	.	PUNCT
ejpam-5118	144	1	the	the	DET
ejpam-5118	144	2	groups	group	NOUN
ejpam-5118	144	3	g1	g1	VERB
ejpam-5118	144	4	×	×	PROPN
ejpam-5118	144	5	ε1	ε1	PROPN
ejpam-5118	144	6	g2	g2	PROPN
ejpam-5118	144	7	and	and	CCONJ
ejpam-5118	144	8	g1	g1	PROPN
ejpam-5118	144	9	×	×	PROPN
ejpam-5118	144	10	ε2	ε2	PROPN
ejpam-5118	144	11	g2	g2	PROPN
ejpam-5118	144	12	are	be	AUX
ejpam-5118	144	13	called	call	VERB
ejpam-5118	144	14	upper	upper	ADJ
ejpam-5118	144	15	isomorphic	isomorphic	NOUN
ejpam-5118	144	16	,	,	PUNCT
ejpam-5118	144	17	if	if	SCONJ
ejpam-5118	144	18	there	there	PRON
ejpam-5118	144	19	exists	exist	VERB
ejpam-5118	144	20	an	an	DET
ejpam-5118	144	21	isomorphism	isomorphism	NOUN
ejpam-5118	144	22	φ	φ	NOUN
ejpam-5118	144	23	:	:	PUNCT
ejpam-5118	144	24	g1	g1	PROPN
ejpam-5118	144	25	×	×	PROPN
ejpam-5118	144	26	ε1	ε1	PROPN
ejpam-5118	144	27	g2	g2	PROPN
ejpam-5118	144	28	−→	−→	NOUN
ejpam-5118	144	29	g1	g1	PROPN
ejpam-5118	144	30	×	×	PROPN
ejpam-5118	144	31	ε2	ε2	PROPN
ejpam-5118	144	32	g2	g2	PROPN
ejpam-5118	144	33	leaving	leave	VERB
ejpam-5118	144	34	g1	g1	PROPN
ejpam-5118	144	35	invariant	invariant	PROPN
ejpam-5118	144	36	.	.	PUNCT
ejpam-5118	144	37	remark	remark	PROPN
ejpam-5118	144	38	3.2	3.2	NUM
ejpam-5118	144	39	.	.	PUNCT
ejpam-5118	145	1	it	it	PRON
ejpam-5118	145	2	is	be	AUX
ejpam-5118	145	3	possible	possible	ADJ
ejpam-5118	145	4	for	for	SCONJ
ejpam-5118	145	5	two	two	NUM
ejpam-5118	145	6	central	central	ADJ
ejpam-5118	145	7	extensions	extension	NOUN
ejpam-5118	145	8	to	to	PART
ejpam-5118	145	9	be	be	AUX
ejpam-5118	145	10	isomorphic	isomorphic	ADJ
ejpam-5118	145	11	without	without	ADP
ejpam-5118	145	12	being	be	AUX
ejpam-5118	145	13	upper	upper	ADJ
ejpam-5118	145	14	isomorphic	isomorphic	NOUN
ejpam-5118	145	15	.	.	PUNCT
ejpam-5118	146	1	for	for	ADP
ejpam-5118	146	2	example	example	NOUN
ejpam-5118	146	3	,	,	PUNCT
ejpam-5118	146	4	consider	consider	VERB
ejpam-5118	146	5	the	the	DET
ejpam-5118	146	6	central	central	ADJ
ejpam-5118	146	7	extensions	extension	NOUN
ejpam-5118	146	8	1	1	NUM
ejpam-5118	146	9	→	→	SYM
ejpam-5118	146	10	zn	zn	X
ejpam-5118	146	11	p	p	X
ejpam-5118	146	12	i1→	i1→	X
ejpam-5118	146	13	g→zn	g→zn	PROPN
ejpam-5118	146	14	p	p	X
ejpam-5118	146	15	→	→	SYM
ejpam-5118	146	16	1	1	NUM
ejpam-5118	146	17	and	and	CCONJ
ejpam-5118	146	18	1	1	NUM
ejpam-5118	146	19	→	→	SYM
ejpam-5118	146	20	zn	zn	NUM
ejpam-5118	146	21	p	p	NOUN
ejpam-5118	146	22	i2→	i2→	PRON
ejpam-5118	146	23	g→zn	g→zn	PUNCT
ejpam-5118	146	24	p	p	X
ejpam-5118	146	25	→	→	SYM
ejpam-5118	146	26	1	1	NUM
ejpam-5118	146	27	such	such	ADJ
ejpam-5118	146	28	that	that	SCONJ
ejpam-5118	146	29	g	g	NOUN
ejpam-5118	146	30	=	=	PUNCT
ejpam-5118	146	31	zp	zp	PROPN
ejpam-5118	146	32	×	×	NOUN
ejpam-5118	146	33	(	(	PUNCT
ejpam-5118	146	34	zp2	zp2	PROPN
ejpam-5118	146	35	)	)	PUNCT
ejpam-5118	146	36	n	n	CCONJ
ejpam-5118	146	37	,	,	PUNCT
ejpam-5118	146	38	i1(zn	i1(zn	PROPN
ejpam-5118	146	39	p	p	NOUN
ejpam-5118	146	40	)	)	PUNCT
ejpam-5118	146	41	=	=	PUNCT
ejpam-5118	146	42	{	{	PUNCT
ejpam-5118	146	43	1	1	NUM
ejpam-5118	146	44	}	}	PUNCT
ejpam-5118	146	45	×	×	NOUN
ejpam-5118	146	46	(	(	PUNCT
ejpam-5118	146	47	pzp2	pzp2	PROPN
ejpam-5118	146	48	)	)	PUNCT
ejpam-5118	146	49	n	n	PROPN
ejpam-5118	146	50	and	and	CCONJ
ejpam-5118	146	51	i2(zn	i2(zn	PROPN
ejpam-5118	146	52	p	p	NOUN
ejpam-5118	146	53	)	)	PUNCT
ejpam-5118	147	1	=	=	PUNCT
ejpam-5118	147	2	zp	zp	NUM
ejpam-5118	147	3	×	×	NOUN
ejpam-5118	147	4	(	(	PUNCT
ejpam-5118	147	5	pzp2	pzp2	PROPN
ejpam-5118	147	6	)	)	PUNCT
ejpam-5118	147	7	n.	n.	NOUN
ejpam-5118	148	1	we	we	PRON
ejpam-5118	148	2	have	have	VERB
ejpam-5118	148	3	i1(zn	i1(zn	PROPN
ejpam-5118	148	4	p	p	NOUN
ejpam-5118	148	5	)	)	PUNCT
ejpam-5118	148	6	∼=	∼=	PROPN
ejpam-5118	148	7	i2(zn	i2(zn	PROPN
ejpam-5118	148	8	p	p	NOUN
ejpam-5118	148	9	)	)	PUNCT
ejpam-5118	148	10	∼=	∼=	PROPN
ejpam-5118	148	11	zn	zn	NOUN
ejpam-5118	148	12	p	p	NOUN
ejpam-5118	149	1	and	and	CCONJ
ejpam-5118	149	2	g	g	NOUN
ejpam-5118	149	3	/	/	SYM
ejpam-5118	149	4	i1(zn	i1(zn	PROPN
ejpam-5118	149	5	p	p	NOUN
ejpam-5118	149	6	)	)	PUNCT
ejpam-5118	149	7	∼=	∼=	PROPN
ejpam-5118	149	8	g	g	NOUN
ejpam-5118	149	9	/	/	SYM
ejpam-5118	149	10	i2(zn	i2(zn	PROPN
ejpam-5118	149	11	p	p	NOUN
ejpam-5118	149	12	)	)	PUNCT
ejpam-5118	149	13	∼=	∼=	PROPN
ejpam-5118	149	14	zn	zn	NOUN
ejpam-5118	149	15	p	p	NOUN
ejpam-5118	149	16	.	.	PUNCT
ejpam-5118	150	1	since	since	SCONJ
ejpam-5118	150	2	i1(zn	i1(zn	PROPN
ejpam-5118	150	3	p	p	NOUN
ejpam-5118	150	4	)	)	PUNCT
ejpam-5118	150	5	=	=	PRON
ejpam-5118	150	6	pg	pg	NOUN
ejpam-5118	150	7	is	be	AUX
ejpam-5118	150	8	a	a	DET
ejpam-5118	150	9	characteristic	characteristic	ADJ
ejpam-5118	150	10	subgroup	subgroup	NOUN
ejpam-5118	150	11	of	of	ADP
ejpam-5118	150	12	g	g	PROPN
ejpam-5118	150	13	and	and	CCONJ
ejpam-5118	150	14	i2(zn	i2(zn	PROPN
ejpam-5118	150	15	p	p	NOUN
ejpam-5118	150	16	)	)	PUNCT
ejpam-5118	150	17	̸=	̸=	PROPN
ejpam-5118	150	18	pg	pg	NOUN
ejpam-5118	150	19	,	,	PUNCT
ejpam-5118	150	20	it	it	PRON
ejpam-5118	150	21	follows	follow	VERB
ejpam-5118	150	22	that	that	SCONJ
ejpam-5118	150	23	there	there	PRON
ejpam-5118	150	24	is	be	VERB
ejpam-5118	150	25	no	no	DET
ejpam-5118	150	26	automorphism	automorphism	NOUN
ejpam-5118	150	27	of	of	ADP
ejpam-5118	150	28	g	g	NOUN
ejpam-5118	150	29	sending	send	VERB
ejpam-5118	150	30	i1(zn	i1(zn	PROPN
ejpam-5118	150	31	p	p	NOUN
ejpam-5118	150	32	)	)	PUNCT
ejpam-5118	150	33	to	to	ADP
ejpam-5118	150	34	i2(zn	i2(zn	PROPN
ejpam-5118	150	35	p	p	NOUN
ejpam-5118	150	36	)	)	PUNCT
ejpam-5118	150	37	.	.	PUNCT
ejpam-5118	151	1	in	in	ADP
ejpam-5118	151	2	particular	particular	ADJ
ejpam-5118	151	3	,	,	PUNCT
ejpam-5118	151	4	suppose	suppose	VERB
ejpam-5118	151	5	that	that	SCONJ
ejpam-5118	151	6	z(g1×	z(g1×	PROPN
ejpam-5118	151	7	ε1	ε1	PROPN
ejpam-5118	151	8	g2	g2	PROPN
ejpam-5118	151	9	)	)	PUNCT
ejpam-5118	151	10	=	=	SYM
ejpam-5118	151	11	z(g1×	z(g1×	PROPN
ejpam-5118	151	12	ε2	ε2	PROPN
ejpam-5118	151	13	g2	g2	PROPN
ejpam-5118	151	14	)	)	PUNCT
ejpam-5118	151	15	=	=	SYM
ejpam-5118	151	16	g1	g1	PROPN
ejpam-5118	151	17	or	or	CCONJ
ejpam-5118	151	18	(	(	PUNCT
ejpam-5118	151	19	g1×	g1×	NOUN
ejpam-5118	151	20	ε1	ε1	PROPN
ejpam-5118	151	21	g2	g2	PROPN
ejpam-5118	151	22	)	)	PUNCT
ejpam-5118	151	23	′	′	NUM
ejpam-5118	152	1	=	=	PUNCT
ejpam-5118	152	2	(	(	PUNCT
ejpam-5118	152	3	g1×	g1×	NOUN
ejpam-5118	152	4	ε2	ε2	PROPN
ejpam-5118	152	5	g2	g2	PROPN
ejpam-5118	152	6	)	)	PUNCT
ejpam-5118	152	7	′	′	NUM
ejpam-5118	153	1	=	=	PUNCT
ejpam-5118	153	2	g1	g1	PROPN
ejpam-5118	153	3	.	.	PUNCT
ejpam-5118	154	1	so	so	ADV
ejpam-5118	154	2	each	each	DET
ejpam-5118	154	3	isomorphism	isomorphism	NOUN
ejpam-5118	154	4	φ	φ	PROPN
ejpam-5118	154	5	=	=	SYM
ejpam-5118	154	6	(	(	PUNCT
ejpam-5118	154	7	φ11	φ11	NUM
ejpam-5118	154	8	φ12	φ12	ADJ
ejpam-5118	154	9	φ21	φ21	NOUN
ejpam-5118	154	10	φ22	φ22	NOUN
ejpam-5118	154	11	)	)	PUNCT
ejpam-5118	154	12	between	between	ADP
ejpam-5118	154	13	g1	g1	PROPN
ejpam-5118	154	14	×	×	PROPN
ejpam-5118	154	15	ε1	ε1	PROPN
ejpam-5118	154	16	g2	g2	PROPN
ejpam-5118	154	17	and	and	CCONJ
ejpam-5118	154	18	g1	g1	PROPN
ejpam-5118	154	19	×	×	PROPN
ejpam-5118	154	20	ε2	ε2	PROPN
ejpam-5118	154	21	g2	g2	PROPN
ejpam-5118	154	22	leaves	leave	VERB
ejpam-5118	154	23	g1	g1	NOUN
ejpam-5118	154	24	invariant	invariant	ADJ
ejpam-5118	154	25	and	and	CCONJ
ejpam-5118	154	26	then	then	ADV
ejpam-5118	154	27	φ21	φ21	VERB
ejpam-5118	154	28	=	=	SYM
ejpam-5118	154	29	1	1	X
ejpam-5118	154	30	.	.	PUNCT
ejpam-5118	155	1	so	so	ADV
ejpam-5118	155	2	,	,	PUNCT
ejpam-5118	155	3	the	the	DET
ejpam-5118	155	4	equation	equation	NOUN
ejpam-5118	155	5	(	(	PUNCT
ejpam-5118	155	6	9	9	NUM
ejpam-5118	155	7	)	)	PUNCT
ejpam-5118	155	8	implies	imply	VERB
ejpam-5118	155	9	that	that	SCONJ
ejpam-5118	155	10	φ22	φ22	PROPN
ejpam-5118	155	11	∈	∈	PROPN
ejpam-5118	155	12	end(g2	end(g2	X
ejpam-5118	155	13	)	)	PUNCT
ejpam-5118	155	14	and	and	CCONJ
ejpam-5118	155	15	then	then	ADV
ejpam-5118	155	16	the	the	DET
ejpam-5118	155	17	assumption	assumption	NOUN
ejpam-5118	155	18	of	of	ADP
ejpam-5118	155	19	the	the	DET
ejpam-5118	155	20	previous	previous	ADJ
ejpam-5118	155	21	proposition	proposition	NOUN
ejpam-5118	155	22	is	be	AUX
ejpam-5118	155	23	not	not	PART
ejpam-5118	155	24	required	require	VERB
ejpam-5118	155	25	.	.	PUNCT
ejpam-5118	156	1	this	this	DET
ejpam-5118	156	2	case	case	NOUN
ejpam-5118	156	3	is	be	AUX
ejpam-5118	156	4	covered	cover	VERB
ejpam-5118	156	5	by	by	ADP
ejpam-5118	156	6	the	the	DET
ejpam-5118	156	7	following	following	ADJ
ejpam-5118	156	8	result	result	NOUN
ejpam-5118	156	9	which	which	PRON
ejpam-5118	156	10	can	can	AUX
ejpam-5118	156	11	be	be	AUX
ejpam-5118	156	12	viewed	view	VERB
ejpam-5118	156	13	as	as	ADP
ejpam-5118	156	14	a	a	DET
ejpam-5118	156	15	consequence	consequence	NOUN
ejpam-5118	156	16	of	of	ADP
ejpam-5118	156	17	[	[	X
ejpam-5118	156	18	8	8	NUM
ejpam-5118	156	19	,	,	PUNCT
ejpam-5118	156	20	theorem	theorem	VERB
ejpam-5118	156	21	3.7	3.7	NUM
ejpam-5118	156	22	]	]	PUNCT
ejpam-5118	156	23	.	.	PUNCT
ejpam-5118	157	1	proposition	proposition	NOUN
ejpam-5118	157	2	3.2	3.2	NUM
ejpam-5118	157	3	.	.	PUNCT
ejpam-5118	158	1	the	the	DET
ejpam-5118	158	2	groups	group	NOUN
ejpam-5118	158	3	g1	g1	VERB
ejpam-5118	158	4	×	×	PROPN
ejpam-5118	158	5	ε1	ε1	PROPN
ejpam-5118	158	6	g2	g2	PROPN
ejpam-5118	158	7	and	and	CCONJ
ejpam-5118	158	8	g1	g1	PROPN
ejpam-5118	158	9	×	×	PROPN
ejpam-5118	158	10	ε2	ε2	PROPN
ejpam-5118	158	11	g2	g2	PROPN
ejpam-5118	158	12	are	be	AUX
ejpam-5118	158	13	upper	upper	ADJ
ejpam-5118	158	14	isomorphic	isomorphic	ADJ
ejpam-5118	158	15	if	if	SCONJ
ejpam-5118	158	16	and	and	CCONJ
ejpam-5118	158	17	only	only	ADV
ejpam-5118	158	18	if	if	SCONJ
ejpam-5118	158	19	there	there	PRON
ejpam-5118	158	20	exist	exist	VERB
ejpam-5118	158	21	σ	σ	NOUN
ejpam-5118	158	22	∈	∈	PROPN
ejpam-5118	158	23	aut(g1	aut(g1	NOUN
ejpam-5118	158	24	)	)	PUNCT
ejpam-5118	158	25	and	and	CCONJ
ejpam-5118	158	26	ρ	ρ	PROPN
ejpam-5118	158	27	∈	∈	PROPN
ejpam-5118	158	28	aut(g2	aut(g2	ADP
ejpam-5118	158	29	)	)	PUNCT
ejpam-5118	158	30	such	such	ADJ
ejpam-5118	158	31	that	that	SCONJ
ejpam-5118	158	32	(	(	PUNCT
ejpam-5118	158	33	σ	σ	NUM
ejpam-5118	158	34	◦	◦	NOUN
ejpam-5118	158	35	ε1)(ε−1	ε1)(ε−1	ADJ
ejpam-5118	158	36	2	2	NUM
ejpam-5118	158	37	◦	◦	NOUN
ejpam-5118	158	38	(	(	PUNCT
ejpam-5118	158	39	ρ×	ρ×	NOUN
ejpam-5118	158	40	ρ	ρ	NOUN
ejpam-5118	158	41	)	)	PUNCT
ejpam-5118	158	42	)	)	PUNCT
ejpam-5118	158	43	∈	∈	PROPN
ejpam-5118	158	44	b2(g2	b2(g2	NOUN
ejpam-5118	158	45	,	,	PUNCT
ejpam-5118	158	46	g1	g1	PROPN
ejpam-5118	158	47	)	)	PUNCT
ejpam-5118	158	48	.	.	PUNCT
ejpam-5118	159	1	example	example	NOUN
ejpam-5118	159	2	3.1	3.1	NUM
ejpam-5118	159	3	.	.	PUNCT
ejpam-5118	160	1	define	define	VERB
ejpam-5118	160	2	a	a	DET
ejpam-5118	160	3	function	function	NOUN
ejpam-5118	160	4	ε0	ε0	NOUN
ejpam-5118	160	5	:	:	PUNCT
ejpam-5118	160	6	z2	z2	PROPN
ejpam-5118	160	7	p	p	PROPN
ejpam-5118	160	8	→	→	SYM
ejpam-5118	160	9	zp	zp	PROPN
ejpam-5118	160	10	by	by	ADP
ejpam-5118	160	11	ε0(i	ε0(i	PROPN
ejpam-5118	160	12	,	,	PUNCT
ejpam-5118	160	13	j	j	NOUN
ejpam-5118	160	14	)	)	PUNCT
ejpam-5118	160	15	=	=	SYM
ejpam-5118	160	16	0	0	PUNCT
ejpam-5118	161	1	if	if	SCONJ
ejpam-5118	161	2	i+	i+	NUM
ejpam-5118	161	3	j	j	X
ejpam-5118	161	4	<	<	X
ejpam-5118	161	5	p	p	X
ejpam-5118	161	6	,	,	PUNCT
ejpam-5118	161	7	and	and	CCONJ
ejpam-5118	161	8	ε0(i	ε0(i	PROPN
ejpam-5118	161	9	,	,	PUNCT
ejpam-5118	161	10	j	j	NOUN
ejpam-5118	161	11	)	)	PUNCT
ejpam-5118	161	12	=	=	SYM
ejpam-5118	161	13	1	1	NUM
ejpam-5118	161	14	if	if	SCONJ
ejpam-5118	161	15	i+	i+	PRON
ejpam-5118	161	16	j	j	NOUN
ejpam-5118	162	1	⩾	⩾	PROPN
ejpam-5118	162	2	p	p	PROPN
ejpam-5118	162	3	for	for	ADP
ejpam-5118	162	4	all	all	DET
ejpam-5118	162	5	0	0	NUM
ejpam-5118	162	6	⩽	⩽	PROPN
ejpam-5118	162	7	i	i	PROPN
ejpam-5118	162	8	,	,	PUNCT
ejpam-5118	163	1	j	j	PROPN
ejpam-5118	163	2	<	<	X
ejpam-5118	163	3	p.	p.	NOUN
ejpam-5118	163	4	this	this	DET
ejpam-5118	163	5	function	function	NOUN
ejpam-5118	163	6	is	be	AUX
ejpam-5118	163	7	the	the	DET
ejpam-5118	163	8	2	2	NUM
ejpam-5118	163	9	-	-	PUNCT
ejpam-5118	163	10	cocycle	cocycle	NOUN
ejpam-5118	163	11	corresponding	corresponding	NOUN
ejpam-5118	163	12	to	to	ADP
ejpam-5118	163	13	the	the	DET
ejpam-5118	163	14	central	central	ADJ
ejpam-5118	163	15	extension	extension	NOUN
ejpam-5118	163	16	0	0	NUM
ejpam-5118	164	1	→	→	SYM
ejpam-5118	164	2	zp	zp	PROPN
ejpam-5118	164	3	→	→	SYM
ejpam-5118	164	4	zp2	zp2	PROPN
ejpam-5118	164	5	→	→	SYM
ejpam-5118	164	6	zp	zp	PROPN
ejpam-5118	164	7	→	→	SYM
ejpam-5118	164	8	0	0	NUM
ejpam-5118	164	9	induced	induce	VERB
ejpam-5118	164	10	by	by	ADP
ejpam-5118	164	11	the	the	DET
ejpam-5118	164	12	based	base	VERB
ejpam-5118	164	13	section	section	NOUN
ejpam-5118	164	14	λ	λ	PROPN
ejpam-5118	164	15	:	:	PUNCT
ejpam-5118	164	16	zp	zp	PROPN
ejpam-5118	164	17	→	→	SYM
ejpam-5118	164	18	zp2	zp2	PROPN
ejpam-5118	164	19	defined	define	VERB
ejpam-5118	164	20	by	by	ADP
ejpam-5118	164	21	λ(i	λ(i	PROPN
ejpam-5118	165	1	mod	mod	PROPN
ejpam-5118	165	2	p	p	X
ejpam-5118	165	3	)	)	PUNCT
ejpam-5118	166	1	=	=	VERB
ejpam-5118	166	2	i	i	PRON
ejpam-5118	166	3	mod	mod	PROPN
ejpam-5118	166	4	p2	p2	PROPN
ejpam-5118	166	5	for	for	ADP
ejpam-5118	166	6	all	all	PRON
ejpam-5118	166	7	0	0	NUM
ejpam-5118	166	8	⩽	⩽	ADJ
ejpam-5118	167	1	i	i	PRON
ejpam-5118	167	2	<	<	X
ejpam-5118	167	3	p.	p.	NOUN
ejpam-5118	167	4	now	now	ADV
ejpam-5118	167	5	,	,	PUNCT
ejpam-5118	167	6	let	let	VERB
ejpam-5118	167	7	ε	ε	PROPN
ejpam-5118	167	8	∈	∈	PROPN
ejpam-5118	167	9	z2(zp	z2(zp	PROPN
ejpam-5118	167	10	,	,	PUNCT
ejpam-5118	167	11	zp	zp	PROPN
ejpam-5118	167	12	)	)	PUNCT
ejpam-5118	167	13	and	and	CCONJ
ejpam-5118	167	14	mε	mε	NOUN
ejpam-5118	167	15	=	=	PUNCT
ejpam-5118	167	16	∑p−1	∑p−1	NOUN
ejpam-5118	167	17	k=0	k=0	PUNCT
ejpam-5118	167	18	ε(k	ε(k	PROPN
ejpam-5118	167	19	,	,	PUNCT
ejpam-5118	167	20	1	1	NUM
ejpam-5118	167	21	)	)	PUNCT
ejpam-5118	167	22	.	.	PUNCT
ejpam-5118	168	1	by	by	ADP
ejpam-5118	168	2	using	use	VERB
ejpam-5118	168	3	the	the	DET
ejpam-5118	168	4	2	2	NUM
ejpam-5118	168	5	-	-	PUNCT
ejpam-5118	168	6	cocycle	cocycle	NOUN
ejpam-5118	168	7	condition	condition	NOUN
ejpam-5118	168	8	,	,	PUNCT
ejpam-5118	168	9	we	we	PRON
ejpam-5118	168	10	can	can	AUX
ejpam-5118	168	11	check	check	VERB
ejpam-5118	168	12	that	that	PRON
ejpam-5118	168	13	ε	ε	PROPN
ejpam-5118	168	14	−mεε0	−mεε0	PROPN
ejpam-5118	168	15	∈	∈	PROPN
ejpam-5118	169	1	b2(zp	b2(zp	PROPN
ejpam-5118	169	2	,	,	PUNCT
ejpam-5118	169	3	zp	zp	NOUN
ejpam-5118	169	4	)	)	PUNCT
ejpam-5118	169	5	.	.	PUNCT
ejpam-5118	170	1	so	so	ADV
ejpam-5118	170	2	,	,	PUNCT
ejpam-5118	170	3	putting	put	VERB
ejpam-5118	170	4	g1	g1	NOUN
ejpam-5118	170	5	=	=	SYM
ejpam-5118	170	6	g2	g2	PROPN
ejpam-5118	170	7	=	=	SYM
ejpam-5118	170	8	zp	zp	PROPN
ejpam-5118	170	9	,	,	PUNCT
ejpam-5118	170	10	σ	σ	PROPN
ejpam-5118	170	11	=	=	PUNCT
ejpam-5118	170	12	idg1	idg1	PROPN
ejpam-5118	170	13	and	and	CCONJ
ejpam-5118	170	14	ρ	ρ	PROPN
ejpam-5118	170	15	=	=	PROPN
ejpam-5118	170	16	idg2	idg2	PROPN
ejpam-5118	170	17	in	in	ADP
ejpam-5118	170	18	the	the	DET
ejpam-5118	170	19	preceding	precede	VERB
ejpam-5118	170	20	proposition	proposition	NOUN
ejpam-5118	170	21	,	,	PUNCT
ejpam-5118	170	22	the	the	DET
ejpam-5118	170	23	groups	group	NOUN
ejpam-5118	170	24	zp	zp	VERB
ejpam-5118	170	25	×	×	PROPN
ejpam-5118	170	26	ε	ε	PROPN
ejpam-5118	170	27	zp	zp	PROPN
ejpam-5118	170	28	and	and	CCONJ
ejpam-5118	170	29	zp	zp	PROPN
ejpam-5118	170	30	×	×	PROPN
ejpam-5118	170	31	mεε0	mεε0	PROPN
ejpam-5118	170	32	zp	zp	PROPN
ejpam-5118	170	33	are	be	AUX
ejpam-5118	170	34	upper	upper	ADJ
ejpam-5118	170	35	isomorphic	isomorphic	NOUN
ejpam-5118	170	36	.	.	PUNCT
ejpam-5118	171	1	n.	n.	PROPN
ejpam-5118	171	2	snanou	snanou	PROPN
ejpam-5118	171	3	/	/	SYM
ejpam-5118	171	4	eur	eur	PROPN
ejpam-5118	171	5	.	.	PUNCT
ejpam-5118	172	1	j.	j.	PROPN
ejpam-5118	172	2	pure	pure	PROPN
ejpam-5118	172	3	appl	appl	PROPN
ejpam-5118	172	4	.	.	PROPN
ejpam-5118	172	5	math	math	PROPN
ejpam-5118	172	6	,	,	PUNCT
ejpam-5118	172	7	17	17	NUM
ejpam-5118	172	8	(	(	PUNCT
ejpam-5118	172	9	2	2	NUM
ejpam-5118	172	10	)	)	PUNCT
ejpam-5118	172	11	(	(	PUNCT
ejpam-5118	172	12	2024	2024	NUM
ejpam-5118	172	13	)	)	PUNCT
ejpam-5118	172	14	,	,	PUNCT
ejpam-5118	172	15	956	956	NUM
ejpam-5118	172	16	-	-	SYM
ejpam-5118	172	17	968	968	NUM
ejpam-5118	172	18	962	962	NUM
ejpam-5118	172	19	in	in	ADP
ejpam-5118	172	20	view	view	NOUN
ejpam-5118	172	21	of	of	ADP
ejpam-5118	172	22	the	the	DET
ejpam-5118	172	23	preceding	precede	VERB
ejpam-5118	172	24	proposition	proposition	NOUN
ejpam-5118	172	25	,	,	PUNCT
ejpam-5118	172	26	it	it	PRON
ejpam-5118	172	27	is	be	AUX
ejpam-5118	172	28	possible	possible	ADJ
ejpam-5118	172	29	for	for	SCONJ
ejpam-5118	172	30	a	a	DET
ejpam-5118	172	31	central	central	ADJ
ejpam-5118	172	32	extension	extension	NOUN
ejpam-5118	172	33	induced	induce	VERB
ejpam-5118	172	34	by	by	ADP
ejpam-5118	172	35	a	a	DET
ejpam-5118	172	36	non	non	ADJ
ejpam-5118	172	37	-	-	ADJ
ejpam-5118	172	38	trivial	trivial	ADJ
ejpam-5118	172	39	2	2	NUM
ejpam-5118	172	40	-	-	PUNCT
ejpam-5118	172	41	cocycle	cocycle	NOUN
ejpam-5118	172	42	to	to	PART
ejpam-5118	172	43	be	be	AUX
ejpam-5118	172	44	isomorphic	isomorphic	ADJ
ejpam-5118	172	45	to	to	ADP
ejpam-5118	172	46	the	the	DET
ejpam-5118	172	47	direct	direct	ADJ
ejpam-5118	172	48	product	product	NOUN
ejpam-5118	172	49	of	of	ADP
ejpam-5118	172	50	the	the	DET
ejpam-5118	172	51	two	two	NUM
ejpam-5118	172	52	factors	factor	NOUN
ejpam-5118	172	53	group	group	NOUN
ejpam-5118	172	54	.	.	PUNCT
ejpam-5118	173	1	more	more	ADV
ejpam-5118	173	2	precisely	precisely	ADV
ejpam-5118	173	3	,	,	PUNCT
ejpam-5118	173	4	for	for	ADP
ejpam-5118	173	5	a	a	DET
ejpam-5118	173	6	non	non	ADJ
ejpam-5118	173	7	-	-	ADJ
ejpam-5118	173	8	trivial	trivial	ADJ
ejpam-5118	173	9	2	2	NUM
ejpam-5118	173	10	-	-	PUNCT
ejpam-5118	173	11	cocycle	cocycle	NOUN
ejpam-5118	173	12	ε	ε	PROPN
ejpam-5118	173	13	∈	∈	PROPN
ejpam-5118	173	14	z2(g2	z2(g2	PROPN
ejpam-5118	173	15	,	,	PUNCT
ejpam-5118	173	16	g1	g1	PROPN
ejpam-5118	173	17	)	)	PUNCT
ejpam-5118	173	18	,	,	PUNCT
ejpam-5118	173	19	it	it	PRON
ejpam-5118	173	20	is	be	AUX
ejpam-5118	173	21	easy	easy	ADJ
ejpam-5118	173	22	to	to	PART
ejpam-5118	173	23	deduce	deduce	VERB
ejpam-5118	173	24	that	that	SCONJ
ejpam-5118	173	25	the	the	DET
ejpam-5118	173	26	groups	group	NOUN
ejpam-5118	173	27	g1×	g1×	VERB
ejpam-5118	173	28	ε	ε	PROPN
ejpam-5118	173	29	g2	g2	PROPN
ejpam-5118	173	30	and	and	CCONJ
ejpam-5118	173	31	g1×g2	g1×g2	PROPN
ejpam-5118	173	32	are	be	AUX
ejpam-5118	173	33	upper	upper	ADJ
ejpam-5118	173	34	isomorphic	isomorphic	ADJ
ejpam-5118	173	35	if	if	SCONJ
ejpam-5118	173	36	and	and	CCONJ
ejpam-5118	173	37	only	only	ADV
ejpam-5118	173	38	if	if	SCONJ
ejpam-5118	173	39	there	there	PRON
ejpam-5118	173	40	exists	exist	VERB
ejpam-5118	173	41	σ	σ	PROPN
ejpam-5118	173	42	∈	∈	PROPN
ejpam-5118	173	43	aut(g1	aut(g1	NOUN
ejpam-5118	173	44	)	)	PUNCT
ejpam-5118	173	45	such	such	ADJ
ejpam-5118	173	46	that	that	SCONJ
ejpam-5118	173	47	σ	σ	NUM
ejpam-5118	173	48	◦	◦	NOUN
ejpam-5118	173	49	ε	ε	PROPN
ejpam-5118	173	50	∈	∈	PROPN
ejpam-5118	173	51	b2(g2	b2(g2	NOUN
ejpam-5118	173	52	,	,	PUNCT
ejpam-5118	173	53	g1	g1	PROPN
ejpam-5118	173	54	)	)	PUNCT
ejpam-5118	173	55	.	.	PUNCT
ejpam-5118	174	1	4	4	X
ejpam-5118	174	2	.	.	X
ejpam-5118	174	3	central	central	ADJ
ejpam-5118	174	4	extensions	extension	NOUN
ejpam-5118	174	5	with	with	ADP
ejpam-5118	174	6	simple	simple	ADJ
ejpam-5118	174	7	or	or	CCONJ
ejpam-5118	174	8	purely	purely	ADV
ejpam-5118	174	9	non	non	ADJ
ejpam-5118	174	10	-	-	ADJ
ejpam-5118	174	11	abelian	abelian	ADJ
ejpam-5118	174	12	quotient	quotient	NOUN
ejpam-5118	174	13	group	group	NOUN
ejpam-5118	174	14	proposition	proposition	NOUN
ejpam-5118	174	15	4.1	4.1	NUM
ejpam-5118	174	16	.	.	PUNCT
ejpam-5118	175	1	let	let	VERB
ejpam-5118	175	2	g2	g2	PROPN
ejpam-5118	175	3	be	be	AUX
ejpam-5118	175	4	a	a	DET
ejpam-5118	175	5	simple	simple	ADJ
ejpam-5118	175	6	non	non	ADJ
ejpam-5118	175	7	-	-	ADJ
ejpam-5118	175	8	abelian	abelian	ADJ
ejpam-5118	175	9	group	group	NOUN
ejpam-5118	175	10	which	which	PRON
ejpam-5118	175	11	acts	act	VERB
ejpam-5118	175	12	trivially	trivially	ADV
ejpam-5118	175	13	on	on	ADP
ejpam-5118	175	14	an	an	DET
ejpam-5118	175	15	abelian	abelian	ADJ
ejpam-5118	175	16	group	group	NOUN
ejpam-5118	175	17	g1	g1	PROPN
ejpam-5118	175	18	.	.	PUNCT
ejpam-5118	176	1	the	the	DET
ejpam-5118	176	2	groups	group	NOUN
ejpam-5118	176	3	g1	g1	VERB
ejpam-5118	176	4	×	×	PROPN
ejpam-5118	176	5	ε1	ε1	PROPN
ejpam-5118	176	6	g2	g2	PROPN
ejpam-5118	176	7	and	and	CCONJ
ejpam-5118	176	8	g1	g1	PROPN
ejpam-5118	176	9	×	×	PROPN
ejpam-5118	176	10	ε2	ε2	PROPN
ejpam-5118	176	11	g2	g2	PROPN
ejpam-5118	176	12	are	be	AUX
ejpam-5118	176	13	isomorphic	isomorphic	ADJ
ejpam-5118	176	14	if	if	SCONJ
ejpam-5118	176	15	and	and	CCONJ
ejpam-5118	176	16	only	only	ADV
ejpam-5118	176	17	if	if	SCONJ
ejpam-5118	176	18	they	they	PRON
ejpam-5118	176	19	are	be	AUX
ejpam-5118	176	20	upper	upper	ADJ
ejpam-5118	176	21	isomorphic	isomorphic	NOUN
ejpam-5118	176	22	.	.	PUNCT
ejpam-5118	177	1	proof	proof	NOUN
ejpam-5118	177	2	.	.	PUNCT
ejpam-5118	178	1	the	the	DET
ejpam-5118	178	2	if	if	SCONJ
ejpam-5118	178	3	direction	direction	NOUN
ejpam-5118	178	4	is	be	AUX
ejpam-5118	178	5	clear	clear	ADJ
ejpam-5118	178	6	.	.	PUNCT
ejpam-5118	179	1	for	for	ADP
ejpam-5118	179	2	the	the	DET
ejpam-5118	179	3	converse	converse	NOUN
ejpam-5118	179	4	,	,	PUNCT
ejpam-5118	179	5	assume	assume	VERB
ejpam-5118	179	6	that	that	SCONJ
ejpam-5118	179	7	g1	g1	PROPN
ejpam-5118	179	8	×	×	PROPN
ejpam-5118	179	9	ε1	ε1	PROPN
ejpam-5118	179	10	g2	g2	PROPN
ejpam-5118	179	11	and	and	CCONJ
ejpam-5118	179	12	g1	g1	PROPN
ejpam-5118	179	13	×	×	PROPN
ejpam-5118	179	14	ε2	ε2	PROPN
ejpam-5118	179	15	g2	g2	PROPN
ejpam-5118	179	16	are	be	AUX
ejpam-5118	179	17	isomorphic	isomorphic	ADJ
ejpam-5118	179	18	by	by	ADP
ejpam-5118	179	19	an	an	DET
ejpam-5118	179	20	isomorphism	isomorphism	NOUN
ejpam-5118	179	21	φ	φ	NOUN
ejpam-5118	179	22	=	=	SYM
ejpam-5118	179	23	(	(	PUNCT
ejpam-5118	179	24	φ11	φ11	NUM
ejpam-5118	179	25	φ12	φ12	ADJ
ejpam-5118	179	26	φ21	φ21	NOUN
ejpam-5118	179	27	φ22	φ22	NOUN
ejpam-5118	179	28	)	)	PUNCT
ejpam-5118	179	29	.	.	PUNCT
ejpam-5118	180	1	it	it	PRON
ejpam-5118	180	2	follows	follow	VERB
ejpam-5118	180	3	from	from	ADP
ejpam-5118	180	4	the	the	DET
ejpam-5118	180	5	equation	equation	NOUN
ejpam-5118	180	6	φ(x	φ(x	NOUN
ejpam-5118	180	7	,	,	PUNCT
ejpam-5118	180	8	1	1	NUM
ejpam-5118	180	9	)	)	PUNCT
ejpam-5118	180	10	•	•	NUM
ejpam-5118	180	11	ε2	ε2	PROPN
ejpam-5118	180	12	φ(1	φ(1	PROPN
ejpam-5118	180	13	,	,	PUNCT
ejpam-5118	180	14	y	y	NOUN
ejpam-5118	180	15	)	)	PUNCT
ejpam-5118	181	1	=	=	SYM
ejpam-5118	181	2	φ(1	φ(1	PROPN
ejpam-5118	181	3	,	,	PUNCT
ejpam-5118	181	4	y	y	NOUN
ejpam-5118	181	5	)	)	PUNCT
ejpam-5118	181	6	•	•	NOUN
ejpam-5118	181	7	ε2	ε2	PROPN
ejpam-5118	181	8	φ(x	φ(x	NOUN
ejpam-5118	181	9	,	,	PUNCT
ejpam-5118	181	10	1	1	NUM
ejpam-5118	181	11	)	)	PUNCT
ejpam-5118	181	12	that	that	SCONJ
ejpam-5118	182	1	[	[	X
ejpam-5118	182	2	φ21(x	φ21(x	NOUN
ejpam-5118	182	3	)	)	PUNCT
ejpam-5118	182	4	,	,	PUNCT
ejpam-5118	182	5	φ22(y	φ22(y	ADP
ejpam-5118	182	6	)	)	PUNCT
ejpam-5118	182	7	]	]	PUNCT
ejpam-5118	182	8	=	=	PUNCT
ejpam-5118	182	9	1	1	NUM
ejpam-5118	182	10	for	for	ADP
ejpam-5118	182	11	all	all	DET
ejpam-5118	182	12	x	x	SYM
ejpam-5118	182	13	∈	∈	PROPN
ejpam-5118	182	14	g1	g1	NOUN
ejpam-5118	182	15	,	,	PUNCT
ejpam-5118	182	16	and	and	CCONJ
ejpam-5118	182	17	y	y	PROPN
ejpam-5118	182	18	∈	∈	PROPN
ejpam-5118	182	19	g2	g2	PROPN
ejpam-5118	182	20	.	.	PUNCT
ejpam-5118	183	1	now	now	ADV
ejpam-5118	183	2	let	let	VERB
ejpam-5118	183	3	g	g	PROPN
ejpam-5118	183	4	∈	∈	PROPN
ejpam-5118	183	5	g2	g2	PROPN
ejpam-5118	183	6	,	,	PUNCT
ejpam-5118	183	7	there	there	PRON
ejpam-5118	183	8	exists	exist	VERB
ejpam-5118	183	9	an	an	DET
ejpam-5118	183	10	element	element	NOUN
ejpam-5118	183	11	(	(	PUNCT
ejpam-5118	183	12	x	x	NOUN
ejpam-5118	183	13	,	,	PUNCT
ejpam-5118	183	14	y	y	NOUN
ejpam-5118	183	15	)	)	PUNCT
ejpam-5118	183	16	∈	∈	PROPN
ejpam-5118	183	17	g1	g1	PROPN
ejpam-5118	183	18	×	×	PROPN
ejpam-5118	183	19	ε1	ε1	PROPN
ejpam-5118	183	20	g2	g2	PROPN
ejpam-5118	183	21	such	such	ADJ
ejpam-5118	183	22	that	that	SCONJ
ejpam-5118	183	23	φ(x	φ(x	PROPN
ejpam-5118	183	24	,	,	PUNCT
ejpam-5118	183	25	y	y	NOUN
ejpam-5118	183	26	)	)	PUNCT
ejpam-5118	183	27	=	=	PUNCT
ejpam-5118	184	1	(	(	PUNCT
ejpam-5118	184	2	1	1	NUM
ejpam-5118	184	3	,	,	PUNCT
ejpam-5118	184	4	g	g	NOUN
ejpam-5118	184	5	)	)	PUNCT
ejpam-5118	184	6	,	,	PUNCT
ejpam-5118	184	7	that	that	PRON
ejpam-5118	184	8	is	be	AUX
ejpam-5118	184	9	g	g	PROPN
ejpam-5118	184	10	=	=	SYM
ejpam-5118	184	11	φ21(x)φ22(y	φ21(x)φ22(y	ADJ
ejpam-5118	184	12	)	)	PUNCT
ejpam-5118	184	13	.	.	PUNCT
ejpam-5118	185	1	so	so	ADV
ejpam-5118	185	2	,	,	PUNCT
ejpam-5118	185	3	for	for	ADP
ejpam-5118	185	4	all	all	DET
ejpam-5118	185	5	h	h	NOUN
ejpam-5118	185	6	∈	∈	PROPN
ejpam-5118	185	7	g1	g1	NOUN
ejpam-5118	185	8	,	,	PUNCT
ejpam-5118	185	9	we	we	PRON
ejpam-5118	185	10	have	have	VERB
ejpam-5118	185	11	gφ21(h)g	gφ21(h)g	ADJ
ejpam-5118	185	12	−1	−1	NOUN
ejpam-5118	185	13	=	=	SYM
ejpam-5118	185	14	φ21(x)φ22(y)φ21(h)φ22(y	φ21(x)φ22(y)φ21(h)φ22(y	PROPN
ejpam-5118	185	15	)	)	PUNCT
ejpam-5118	185	16	−1φ21(x	−1φ21(x	NOUN
ejpam-5118	185	17	)	)	PUNCT
ejpam-5118	185	18	−1	−1	NOUN
ejpam-5118	185	19	=	=	SYM
ejpam-5118	185	20	φ21(x)φ21(h)φ21(x	φ21(x)φ21(h)φ21(x	NOUN
ejpam-5118	185	21	)	)	PUNCT
ejpam-5118	185	22	−1	−1	NOUN
ejpam-5118	185	23	∈	∈	NOUN
ejpam-5118	185	24	φ21(g1	φ21(g1	NOUN
ejpam-5118	185	25	)	)	PUNCT
ejpam-5118	185	26	.	.	PUNCT
ejpam-5118	186	1	thus	thus	ADV
ejpam-5118	186	2	,	,	PUNCT
ejpam-5118	186	3	φ21(g1	φ21(g1	NOUN
ejpam-5118	186	4	)	)	PUNCT
ejpam-5118	186	5	is	be	AUX
ejpam-5118	186	6	a	a	DET
ejpam-5118	186	7	normal	normal	ADJ
ejpam-5118	186	8	subgroup	subgroup	NOUN
ejpam-5118	186	9	of	of	ADP
ejpam-5118	186	10	g2	g2	PROPN
ejpam-5118	186	11	.	.	PUNCT
ejpam-5118	187	1	as	as	SCONJ
ejpam-5118	187	2	g2	g2	PROPN
ejpam-5118	187	3	is	be	AUX
ejpam-5118	187	4	simple	simple	ADJ
ejpam-5118	187	5	non	non	ADJ
ejpam-5118	187	6	-	-	ADJ
ejpam-5118	187	7	abelian	abelian	ADJ
ejpam-5118	187	8	,	,	PUNCT
ejpam-5118	187	9	then	then	ADV
ejpam-5118	187	10	φ21(g1	φ21(g1	NUM
ejpam-5118	187	11	)	)	PUNCT
ejpam-5118	187	12	is	be	AUX
ejpam-5118	187	13	either	either	CCONJ
ejpam-5118	187	14	trivial	trivial	ADJ
ejpam-5118	187	15	or	or	CCONJ
ejpam-5118	187	16	g2	g2	PROPN
ejpam-5118	187	17	.	.	PUNCT
ejpam-5118	188	1	if	if	SCONJ
ejpam-5118	188	2	φ21(g1	φ21(g1	NUM
ejpam-5118	188	3	)	)	PUNCT
ejpam-5118	188	4	=	=	SYM
ejpam-5118	188	5	g2	g2	PROPN
ejpam-5118	188	6	,	,	PUNCT
ejpam-5118	188	7	then	then	ADV
ejpam-5118	188	8	φ21	φ21	NOUN
ejpam-5118	188	9	is	be	AUX
ejpam-5118	188	10	an	an	DET
ejpam-5118	188	11	epimorphism	epimorphism	NOUN
ejpam-5118	188	12	and	and	CCONJ
ejpam-5118	188	13	therefore	therefore	ADV
ejpam-5118	188	14	g2	g2	PROPN
ejpam-5118	188	15	is	be	AUX
ejpam-5118	188	16	abelian	abelian	ADJ
ejpam-5118	188	17	,	,	PUNCT
ejpam-5118	188	18	a	a	DET
ejpam-5118	188	19	contradiction	contradiction	NOUN
ejpam-5118	188	20	.	.	PUNCT
ejpam-5118	189	1	hence	hence	ADV
ejpam-5118	189	2	,	,	PUNCT
ejpam-5118	189	3	φ21	φ21	X
ejpam-5118	189	4	=	=	SYM
ejpam-5118	189	5	1	1	NUM
ejpam-5118	189	6	and	and	CCONJ
ejpam-5118	189	7	then	then	ADV
ejpam-5118	189	8	φ	φ	PROPN
ejpam-5118	189	9	maps	maps	PROPN
ejpam-5118	189	10	g1	g1	PROPN
ejpam-5118	189	11	to	to	ADP
ejpam-5118	189	12	itself	itself	PRON
ejpam-5118	189	13	,	,	PUNCT
ejpam-5118	189	14	as	as	SCONJ
ejpam-5118	189	15	required	require	VERB
ejpam-5118	189	16	.	.	PUNCT
ejpam-5118	190	1	recall	recall	VERB
ejpam-5118	190	2	that	that	SCONJ
ejpam-5118	190	3	a	a	DET
ejpam-5118	190	4	non	non	ADJ
ejpam-5118	190	5	-	-	ADJ
ejpam-5118	190	6	abelian	abelian	ADJ
ejpam-5118	190	7	group	group	NOUN
ejpam-5118	190	8	which	which	PRON
ejpam-5118	190	9	has	have	VERB
ejpam-5118	190	10	no	no	DET
ejpam-5118	190	11	non	non	ADJ
ejpam-5118	190	12	-	-	ADJ
ejpam-5118	190	13	trivial	trivial	ADJ
ejpam-5118	190	14	abelian	abelian	ADJ
ejpam-5118	190	15	direct	direct	ADJ
ejpam-5118	190	16	factor	factor	NOUN
ejpam-5118	190	17	is	be	AUX
ejpam-5118	190	18	said	say	VERB
ejpam-5118	190	19	to	to	PART
ejpam-5118	190	20	be	be	AUX
ejpam-5118	190	21	purely	purely	ADV
ejpam-5118	190	22	non	non	ADJ
ejpam-5118	190	23	-	-	ADJ
ejpam-5118	190	24	abelian	abelian	ADJ
ejpam-5118	190	25	.	.	PUNCT
ejpam-5118	191	1	theorem	theorem	VERB
ejpam-5118	191	2	4.1	4.1	NUM
ejpam-5118	191	3	.	.	PUNCT
ejpam-5118	192	1	let	let	VERB
ejpam-5118	192	2	g2	g2	PROPN
ejpam-5118	192	3	be	be	AUX
ejpam-5118	192	4	a	a	DET
ejpam-5118	192	5	finite	finite	NOUN
ejpam-5118	192	6	purely	purely	ADV
ejpam-5118	192	7	non	non	ADJ
ejpam-5118	192	8	-	-	ADJ
ejpam-5118	192	9	abelian	abelian	ADJ
ejpam-5118	192	10	group	group	NOUN
ejpam-5118	192	11	which	which	PRON
ejpam-5118	192	12	acts	act	VERB
ejpam-5118	192	13	trivially	trivially	ADV
ejpam-5118	192	14	on	on	ADP
ejpam-5118	192	15	a	a	DET
ejpam-5118	192	16	finite	finite	ADJ
ejpam-5118	192	17	abelian	abelian	PROPN
ejpam-5118	192	18	group	group	NOUN
ejpam-5118	192	19	g1	g1	PROPN
ejpam-5118	192	20	.	.	PUNCT
ejpam-5118	193	1	let	let	VERB
ejpam-5118	193	2	φ	φ	PROPN
ejpam-5118	193	3	∈	∈	PROPN
ejpam-5118	193	4	{	{	PUNCT
ejpam-5118	193	5	(	(	PUNCT
ejpam-5118	193	6	σ	σ	PROPN
ejpam-5118	193	7	η	η	PROPN
ejpam-5118	193	8	δ	δ	PROPN
ejpam-5118	193	9	ρ	ρ	PROPN
ejpam-5118	193	10	)	)	PUNCT
ejpam-5118	193	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5118	193	12	σ	σ	PROPN
ejpam-5118	193	13	∈	∈	PROPN
ejpam-5118	193	14	aut(g1	aut(g1	NOUN
ejpam-5118	193	15	)	)	PUNCT
ejpam-5118	193	16	,	,	PUNCT
ejpam-5118	193	17	η	η	PROPN
ejpam-5118	193	18	∈	∈	PROPN
ejpam-5118	193	19	hom(g2	hom(g2	PROPN
ejpam-5118	193	20	,	,	PUNCT
ejpam-5118	193	21	g1	g1	NOUN
ejpam-5118	193	22	)	)	PUNCT
ejpam-5118	193	23	δ	δ	PROPN
ejpam-5118	193	24	∈	∈	PROPN
ejpam-5118	193	25	hom(g1	hom(g1	X
ejpam-5118	193	26	,	,	PUNCT
ejpam-5118	193	27	g2	g2	PROPN
ejpam-5118	193	28	)	)	PUNCT
ejpam-5118	193	29	,	,	PUNCT
ejpam-5118	193	30	ρ	ρ	PROPN
ejpam-5118	193	31	∈	∈	PROPN
ejpam-5118	193	32	aut(g2	aut(g2	ADP
ejpam-5118	193	33	)	)	PUNCT
ejpam-5118	193	34	}	}	PUNCT
ejpam-5118	193	35	where	where	SCONJ
ejpam-5118	193	36	σ	σ	PROPN
ejpam-5118	193	37	,	,	PUNCT
ejpam-5118	193	38	δ	δ	PROPN
ejpam-5118	193	39	and	and	CCONJ
ejpam-5118	193	40	ρ	ρ	PROPN
ejpam-5118	193	41	satisfy	satisfy	VERB
ejpam-5118	193	42	the	the	DET
ejpam-5118	193	43	conditions	condition	NOUN
ejpam-5118	193	44	:	:	PUNCT
ejpam-5118	193	45	(	(	PUNCT
ejpam-5118	193	46	i	i	NOUN
ejpam-5118	193	47	)	)	PUNCT
ejpam-5118	194	1	[	[	X
ejpam-5118	194	2	{	{	PUNCT
ejpam-5118	194	3	1	1	NUM
ejpam-5118	194	4	}	}	PUNCT
ejpam-5118	194	5	×g2	×g2	PROPN
ejpam-5118	194	6	,	,	PUNCT
ejpam-5118	194	7	{	{	PUNCT
ejpam-5118	194	8	1	1	NUM
ejpam-5118	194	9	}	}	PUNCT
ejpam-5118	194	10	×	×	NOUN
ejpam-5118	194	11	δ(g1	δ(g1	NOUN
ejpam-5118	194	12	)	)	PUNCT
ejpam-5118	194	13	]	]	PUNCT
ejpam-5118	194	14	=	=	PUNCT
ejpam-5118	194	15	1	1	NUM
ejpam-5118	194	16	,	,	PUNCT
ejpam-5118	194	17	(	(	PUNCT
ejpam-5118	194	18	ii	ii	NOUN
ejpam-5118	194	19	)	)	PUNCT
ejpam-5118	194	20	ε2	ε2	ADJ
ejpam-5118	194	21	◦	◦	NOUN
ejpam-5118	194	22	(	(	PUNCT
ejpam-5118	194	23	δ	δ	PROPN
ejpam-5118	194	24	×	×	PROPN
ejpam-5118	194	25	δ	δ	PROPN
ejpam-5118	194	26	)	)	PUNCT
ejpam-5118	194	27	=	=	SYM
ejpam-5118	194	28	1	1	NUM
ejpam-5118	194	29	and	and	CCONJ
ejpam-5118	194	30	δ	δ	PROPN
ejpam-5118	194	31	◦	◦	NOUN
ejpam-5118	194	32	ε1	ε1	VERB
ejpam-5118	194	33	=	=	SYM
ejpam-5118	194	34	1	1	NUM
ejpam-5118	194	35	,	,	PUNCT
ejpam-5118	194	36	(	(	PUNCT
ejpam-5118	194	37	iii	iii	NOUN
ejpam-5118	194	38	)	)	PUNCT
ejpam-5118	194	39	σ	σ	NOUN
ejpam-5118	194	40	◦	◦	NOUN
ejpam-5118	194	41	ε1	ε1	PROPN
ejpam-5118	194	42	=	=	SYM
ejpam-5118	194	43	ε2	ε2	ADJ
ejpam-5118	194	44	◦	◦	NOUN
ejpam-5118	194	45	(	(	PUNCT
ejpam-5118	194	46	ρ×	ρ×	NOUN
ejpam-5118	194	47	ρ	ρ	NOUN
ejpam-5118	194	48	)	)	PUNCT
ejpam-5118	194	49	.	.	PUNCT
ejpam-5118	195	1	then	then	ADV
ejpam-5118	195	2	,	,	PUNCT
ejpam-5118	195	3	φ	φ	PROPN
ejpam-5118	195	4	is	be	AUX
ejpam-5118	195	5	an	an	DET
ejpam-5118	195	6	isomorphism	isomorphism	NOUN
ejpam-5118	195	7	from	from	ADP
ejpam-5118	195	8	g1	g1	PROPN
ejpam-5118	195	9	×	×	PROPN
ejpam-5118	195	10	ε1	ε1	PROPN
ejpam-5118	195	11	g2	g2	PROPN
ejpam-5118	195	12	to	to	PART
ejpam-5118	195	13	g1	g1	VERB
ejpam-5118	195	14	×	×	PROPN
ejpam-5118	195	15	ε2	ε2	PROPN
ejpam-5118	195	16	g2	g2	PROPN
ejpam-5118	195	17	.	.	PUNCT
ejpam-5118	196	1	proof	proof	NOUN
ejpam-5118	196	2	.	.	PUNCT
ejpam-5118	197	1	indeed	indeed	ADV
ejpam-5118	197	2	,	,	PUNCT
ejpam-5118	197	3	the	the	DET
ejpam-5118	197	4	map	map	NOUN
ejpam-5118	197	5	φ	φ	PROPN
ejpam-5118	197	6	is	be	AUX
ejpam-5118	197	7	defined	define	VERB
ejpam-5118	197	8	by	by	ADP
ejpam-5118	197	9	the	the	DET
ejpam-5118	197	10	formula	formula	NOUN
ejpam-5118	197	11	(	(	PUNCT
ejpam-5118	197	12	1	1	NUM
ejpam-5118	197	13	)	)	PUNCT
ejpam-5118	197	14	.	.	PUNCT
ejpam-5118	198	1	by	by	ADP
ejpam-5118	198	2	proposition	proposition	NOUN
ejpam-5118	198	3	3.1	3.1	NUM
ejpam-5118	198	4	,	,	PUNCT
ejpam-5118	198	5	the	the	DET
ejpam-5118	198	6	map	map	NOUN
ejpam-5118	198	7	φ	φ	NOUN
ejpam-5118	198	8	is	be	AUX
ejpam-5118	198	9	clearly	clearly	ADV
ejpam-5118	198	10	a	a	DET
ejpam-5118	198	11	group	group	NOUN
ejpam-5118	198	12	homomorphism	homomorphism	NOUN
ejpam-5118	198	13	.	.	PUNCT
ejpam-5118	199	1	now	now	ADV
ejpam-5118	199	2	,	,	PUNCT
ejpam-5118	199	3	assume	assume	VERB
ejpam-5118	199	4	that	that	SCONJ
ejpam-5118	199	5	φ(x	φ(x	PROPN
ejpam-5118	199	6	,	,	PUNCT
ejpam-5118	199	7	y	y	NOUN
ejpam-5118	199	8	)	)	PUNCT
ejpam-5118	199	9	=	=	SYM
ejpam-5118	200	1	1	1	X
ejpam-5118	200	2	.	.	PUNCT
ejpam-5118	201	1	so	so	ADV
ejpam-5118	201	2	δ(x)ρ(y	δ(x)ρ(y	NOUN
ejpam-5118	201	3	)	)	PUNCT
ejpam-5118	201	4	=	=	SYM
ejpam-5118	202	1	1	1	NUM
ejpam-5118	202	2	n.	n.	NOUN
ejpam-5118	202	3	snanou	snanou	PROPN
ejpam-5118	202	4	/	/	SYM
ejpam-5118	202	5	eur	eur	PROPN
ejpam-5118	202	6	.	.	PUNCT
ejpam-5118	203	1	j.	j.	PROPN
ejpam-5118	203	2	pure	pure	PROPN
ejpam-5118	203	3	appl	appl	PROPN
ejpam-5118	203	4	.	.	PROPN
ejpam-5118	203	5	math	math	PROPN
ejpam-5118	203	6	,	,	PUNCT
ejpam-5118	203	7	17	17	NUM
ejpam-5118	203	8	(	(	PUNCT
ejpam-5118	203	9	2	2	NUM
ejpam-5118	203	10	)	)	PUNCT
ejpam-5118	203	11	(	(	PUNCT
ejpam-5118	203	12	2024	2024	NUM
ejpam-5118	203	13	)	)	PUNCT
ejpam-5118	203	14	,	,	PUNCT
ejpam-5118	203	15	956	956	NUM
ejpam-5118	203	16	-	-	SYM
ejpam-5118	203	17	968	968	NUM
ejpam-5118	203	18	963	963	NUM
ejpam-5118	203	19	and	and	CCONJ
ejpam-5118	203	20	then	then	ADV
ejpam-5118	203	21	ρ(y	ρ(y	NOUN
ejpam-5118	203	22	)	)	PUNCT
ejpam-5118	203	23	=	=	SYM
ejpam-5118	204	1	δ(x−1	δ(x−1	NOUN
ejpam-5118	204	2	)	)	PUNCT
ejpam-5118	204	3	,	,	PUNCT
ejpam-5118	204	4	which	which	PRON
ejpam-5118	204	5	implies	imply	VERB
ejpam-5118	204	6	that	that	SCONJ
ejpam-5118	204	7	σ(x)η(y)ε2(δ(x	σ(x)η(y)ε2(δ(x	NUM
ejpam-5118	204	8	)	)	PUNCT
ejpam-5118	204	9	,	,	PUNCT
ejpam-5118	204	10	δ(x	δ(x	PROPN
ejpam-5118	204	11	−1	−1	NOUN
ejpam-5118	204	12	)	)	PUNCT
ejpam-5118	204	13	)	)	PUNCT
ejpam-5118	205	1	=	=	PUNCT
ejpam-5118	205	2	1	1	X
ejpam-5118	205	3	.	.	PUNCT
ejpam-5118	206	1	so	so	ADV
ejpam-5118	206	2	,	,	PUNCT
ejpam-5118	206	3	the	the	DET
ejpam-5118	206	4	first	first	ADJ
ejpam-5118	206	5	equation	equation	NOUN
ejpam-5118	206	6	of	of	ADP
ejpam-5118	206	7	the	the	DET
ejpam-5118	206	8	condition	condition	NOUN
ejpam-5118	206	9	(	(	PUNCT
ejpam-5118	206	10	ii	ii	NOUN
ejpam-5118	206	11	)	)	PUNCT
ejpam-5118	206	12	ensures	ensure	VERB
ejpam-5118	206	13	that	that	SCONJ
ejpam-5118	206	14	σ(x)η(y	σ(x)η(y	NOUN
ejpam-5118	206	15	)	)	PUNCT
ejpam-5118	206	16	=	=	SYM
ejpam-5118	206	17	1	1	NUM
ejpam-5118	206	18	,	,	PUNCT
ejpam-5118	206	19	and	and	CCONJ
ejpam-5118	206	20	then	then	ADV
ejpam-5118	206	21	x	x	X
ejpam-5118	206	22	=	=	SYM
ejpam-5118	206	23	σ−1(η(y−1	σ−1(η(y−1	PROPN
ejpam-5118	206	24	)	)	PUNCT
ejpam-5118	206	25	)	)	PUNCT
ejpam-5118	206	26	.	.	PUNCT
ejpam-5118	207	1	hence	hence	ADV
ejpam-5118	207	2	,	,	PUNCT
ejpam-5118	207	3	ρ−1(δ(σ−1(η(y	ρ−1(δ(σ−1(η(y	PROPN
ejpam-5118	207	4	)	)	PUNCT
ejpam-5118	207	5	)	)	PUNCT
ejpam-5118	207	6	)	)	PUNCT
ejpam-5118	207	7	)	)	PUNCT
ejpam-5118	208	1	=	=	PUNCT
ejpam-5118	208	2	y.	y.	NOUN
ejpam-5118	208	3	from	from	ADP
ejpam-5118	208	4	the	the	DET
ejpam-5118	208	5	condition	condition	NOUN
ejpam-5118	208	6	(	(	PUNCT
ejpam-5118	208	7	i	i	NOUN
ejpam-5118	208	8	)	)	PUNCT
ejpam-5118	208	9	,	,	PUNCT
ejpam-5118	208	10	we	we	PRON
ejpam-5118	208	11	have	have	VERB
ejpam-5118	208	12	[	[	X
ejpam-5118	208	13	g2	g2	PROPN
ejpam-5118	208	14	,	,	PUNCT
ejpam-5118	208	15	δ(g1	δ(g1	NOUN
ejpam-5118	208	16	)	)	PUNCT
ejpam-5118	208	17	]	]	PUNCT
ejpam-5118	209	1	=	=	PUNCT
ejpam-5118	209	2	1	1	NUM
ejpam-5118	209	3	,	,	PUNCT
ejpam-5118	209	4	that	that	PRON
ejpam-5118	209	5	is	be	AUX
ejpam-5118	209	6	δ(g1	δ(g1	NOUN
ejpam-5118	209	7	)	)	PUNCT
ejpam-5118	209	8	≤	≤	NOUN
ejpam-5118	209	9	z(g2	z(g2	NUM
ejpam-5118	209	10	)	)	PUNCT
ejpam-5118	209	11	.	.	PUNCT
ejpam-5118	210	1	hence	hence	ADV
ejpam-5118	210	2	,	,	PUNCT
ejpam-5118	210	3	we	we	PRON
ejpam-5118	210	4	have	have	VERB
ejpam-5118	210	5	ψ	ψ	X
ejpam-5118	210	6	=	=	PUNCT
ejpam-5118	210	7	ρ−1	ρ−1	PROPN
ejpam-5118	210	8	◦	◦	NOUN
ejpam-5118	210	9	δ	δ	PROPN
ejpam-5118	211	1	◦	◦	NOUN
ejpam-5118	212	1	σ−1	σ−1	PRON
ejpam-5118	212	2	◦	◦	NOUN
ejpam-5118	212	3	η	η	PROPN
ejpam-5118	212	4	∈	∈	PROPN
ejpam-5118	212	5	hom(g2	hom(g2	PROPN
ejpam-5118	212	6	,	,	PUNCT
ejpam-5118	212	7	z(g2	z(g2	ADV
ejpam-5118	212	8	)	)	PUNCT
ejpam-5118	212	9	)	)	PUNCT
ejpam-5118	212	10	,	,	PUNCT
ejpam-5118	212	11	and	and	CCONJ
ejpam-5118	212	12	then	then	ADV
ejpam-5118	212	13	imψ	imψ	NOUN
ejpam-5118	212	14	⊴	⊴	ADP
ejpam-5118	212	15	g2	g2	PROPN
ejpam-5118	212	16	.	.	PUNCT
ejpam-5118	213	1	so	so	ADV
ejpam-5118	213	2	,	,	PUNCT
ejpam-5118	213	3	by	by	ADP
ejpam-5118	213	4	fitting	fitting	PROPN
ejpam-5118	213	5	’s	’s	PART
ejpam-5118	213	6	lemma	lemma	PROPN
ejpam-5118	213	7	,	,	PUNCT
ejpam-5118	213	8	we	we	PRON
ejpam-5118	213	9	have	have	VERB
ejpam-5118	213	10	g2	g2	PROPN
ejpam-5118	213	11	∼=	∼=	PART
ejpam-5118	213	12	kerψ	kerψ	ADJ
ejpam-5118	213	13	×	×	NOUN
ejpam-5118	213	14	imψ	imψ	NOUN
ejpam-5118	213	15	which	which	PRON
ejpam-5118	213	16	contradicts	contradict	VERB
ejpam-5118	213	17	to	to	ADP
ejpam-5118	213	18	the	the	DET
ejpam-5118	213	19	fact	fact	NOUN
ejpam-5118	213	20	that	that	SCONJ
ejpam-5118	213	21	g2	g2	PROPN
ejpam-5118	213	22	is	be	AUX
ejpam-5118	213	23	purely	purely	ADV
ejpam-5118	213	24	non	non	ADJ
ejpam-5118	213	25	-	-	ADJ
ejpam-5118	213	26	abelian	abelian	ADJ
ejpam-5118	213	27	.	.	PUNCT
ejpam-5118	214	1	thus	thus	ADV
ejpam-5118	214	2	y	y	PROPN
ejpam-5118	214	3	=	=	SYM
ejpam-5118	214	4	1	1	NUM
ejpam-5118	214	5	and	and	CCONJ
ejpam-5118	214	6	then	then	ADV
ejpam-5118	214	7	x	x	X
ejpam-5118	215	1	=	=	SYM
ejpam-5118	215	2	1	1	X
ejpam-5118	215	3	.	.	PUNCT
ejpam-5118	216	1	therefore	therefore	ADV
ejpam-5118	216	2	,	,	PUNCT
ejpam-5118	216	3	the	the	DET
ejpam-5118	216	4	map	map	NOUN
ejpam-5118	216	5	φ	φ	PROPN
ejpam-5118	216	6	is	be	AUX
ejpam-5118	216	7	injective	injective	ADJ
ejpam-5118	216	8	,	,	PUNCT
ejpam-5118	216	9	and	and	CCONJ
ejpam-5118	216	10	then	then	ADV
ejpam-5118	216	11	it	it	PRON
ejpam-5118	216	12	is	be	AUX
ejpam-5118	216	13	an	an	DET
ejpam-5118	216	14	isomorphism	isomorphism	NOUN
ejpam-5118	216	15	.	.	PUNCT
ejpam-5118	217	1	remark	remark	PROPN
ejpam-5118	217	2	4.1	4.1	NUM
ejpam-5118	217	3	.	.	PUNCT
ejpam-5118	218	1	the	the	DET
ejpam-5118	218	2	previous	previous	ADJ
ejpam-5118	218	3	proposition	proposition	NOUN
ejpam-5118	218	4	will	will	AUX
ejpam-5118	218	5	not	not	PART
ejpam-5118	218	6	be	be	AUX
ejpam-5118	218	7	true	true	ADJ
ejpam-5118	218	8	if	if	SCONJ
ejpam-5118	218	9	g2	g2	PROPN
ejpam-5118	218	10	is	be	AUX
ejpam-5118	218	11	not	not	PART
ejpam-5118	218	12	purely	purely	ADV
ejpam-5118	218	13	non	non	ADJ
ejpam-5118	218	14	-	-	ADJ
ejpam-5118	218	15	abelian	abelian	ADJ
ejpam-5118	218	16	.	.	PUNCT
ejpam-5118	219	1	indeed	indeed	ADV
ejpam-5118	219	2	,	,	PUNCT
ejpam-5118	219	3	assume	assume	VERB
ejpam-5118	219	4	that	that	SCONJ
ejpam-5118	219	5	g1	g1	PROPN
ejpam-5118	219	6	is	be	AUX
ejpam-5118	219	7	a	a	DET
ejpam-5118	219	8	direct	direct	ADJ
ejpam-5118	219	9	factor	factor	NOUN
ejpam-5118	219	10	of	of	ADP
ejpam-5118	219	11	g2	g2	PROPN
ejpam-5118	219	12	and	and	CCONJ
ejpam-5118	219	13	let	let	VERB
ejpam-5118	219	14	φ	φ	PROPN
ejpam-5118	219	15	=	=	SYM
ejpam-5118	219	16	(	(	PUNCT
ejpam-5118	219	17	idg1	idg1	PROPN
ejpam-5118	219	18	φ12	φ12	NOUN
ejpam-5118	219	19	φ21	φ21	NOUN
ejpam-5118	219	20	idg2	idg2	NOUN
ejpam-5118	219	21	)	)	PUNCT
ejpam-5118	219	22	be	be	AUX
ejpam-5118	219	23	a	a	DET
ejpam-5118	219	24	map	map	NOUN
ejpam-5118	219	25	from	from	ADP
ejpam-5118	219	26	g1	g1	PROPN
ejpam-5118	219	27	×	×	PROPN
ejpam-5118	219	28	ε1	ε1	PROPN
ejpam-5118	219	29	g2	g2	PROPN
ejpam-5118	219	30	to	to	PART
ejpam-5118	219	31	g1	g1	VERB
ejpam-5118	219	32	×	×	PROPN
ejpam-5118	219	33	ε2	ε2	PROPN
ejpam-5118	219	34	g2	g2	PROPN
ejpam-5118	219	35	where	where	SCONJ
ejpam-5118	219	36	φ12(x	φ12(x	NOUN
ejpam-5118	219	37	)	)	PUNCT
ejpam-5118	219	38	=	=	SYM
ejpam-5118	219	39	φ21(x	φ21(x	NOUN
ejpam-5118	219	40	)	)	PUNCT
ejpam-5118	219	41	=	=	PUNCT
ejpam-5118	220	1	x−1	x−1	PROPN
ejpam-5118	220	2	for	for	ADP
ejpam-5118	220	3	all	all	DET
ejpam-5118	220	4	x	x	SYM
ejpam-5118	220	5	∈	∈	PROPN
ejpam-5118	220	6	g1	g1	NOUN
ejpam-5118	220	7	.	.	PUNCT
ejpam-5118	221	1	so	so	ADV
ejpam-5118	221	2	,	,	PUNCT
ejpam-5118	221	3	using	use	VERB
ejpam-5118	221	4	the	the	DET
ejpam-5118	221	5	formula	formula	NOUN
ejpam-5118	221	6	(	(	PUNCT
ejpam-5118	221	7	1	1	NUM
ejpam-5118	221	8	)	)	PUNCT
ejpam-5118	221	9	,	,	PUNCT
ejpam-5118	221	10	we	we	PRON
ejpam-5118	221	11	obtain	obtain	VERB
ejpam-5118	221	12	φ(x	φ(x	NOUN
ejpam-5118	221	13	,	,	PUNCT
ejpam-5118	221	14	x	x	NOUN
ejpam-5118	221	15	)	)	PUNCT
ejpam-5118	221	16	=	=	SYM
ejpam-5118	221	17	(	(	PUNCT
ejpam-5118	221	18	ε2(φ21(x	ε2(φ21(x	NOUN
ejpam-5118	221	19	)	)	PUNCT
ejpam-5118	221	20	,	,	PUNCT
ejpam-5118	221	21	φ21(x	φ21(x	NOUN
ejpam-5118	221	22	−1	−1	NOUN
ejpam-5118	221	23	)	)	PUNCT
ejpam-5118	221	24	)	)	PUNCT
ejpam-5118	221	25	,	,	PUNCT
ejpam-5118	221	26	1	1	NUM
ejpam-5118	221	27	)	)	PUNCT
ejpam-5118	221	28	.	.	PUNCT
ejpam-5118	222	1	hence	hence	ADV
ejpam-5118	222	2	,	,	PUNCT
ejpam-5118	222	3	by	by	ADP
ejpam-5118	222	4	using	use	VERB
ejpam-5118	222	5	the	the	DET
ejpam-5118	222	6	first	first	ADJ
ejpam-5118	222	7	equation	equation	NOUN
ejpam-5118	222	8	of	of	ADP
ejpam-5118	222	9	the	the	DET
ejpam-5118	222	10	condition	condition	NOUN
ejpam-5118	222	11	(	(	PUNCT
ejpam-5118	222	12	ii	ii	NOUN
ejpam-5118	222	13	)	)	PUNCT
ejpam-5118	222	14	,	,	PUNCT
ejpam-5118	222	15	we	we	PRON
ejpam-5118	222	16	get	get	VERB
ejpam-5118	222	17	φ(x	φ(x	NOUN
ejpam-5118	222	18	,	,	PUNCT
ejpam-5118	222	19	x	x	NOUN
ejpam-5118	222	20	)	)	PUNCT
ejpam-5118	222	21	=	=	SYM
ejpam-5118	222	22	(	(	PUNCT
ejpam-5118	222	23	1	1	NUM
ejpam-5118	222	24	,	,	PUNCT
ejpam-5118	222	25	1	1	NUM
ejpam-5118	222	26	)	)	PUNCT
ejpam-5118	222	27	.	.	PUNCT
ejpam-5118	223	1	therefore	therefore	ADV
ejpam-5118	223	2	,	,	PUNCT
ejpam-5118	223	3	φ	φ	PROPN
ejpam-5118	223	4	is	be	AUX
ejpam-5118	223	5	not	not	PART
ejpam-5118	223	6	an	an	DET
ejpam-5118	223	7	isomorphism	isomorphism	NOUN
ejpam-5118	223	8	.	.	PUNCT
ejpam-5118	224	1	5	5	X
ejpam-5118	224	2	.	.	X
ejpam-5118	224	3	lower	low	ADJ
ejpam-5118	224	4	isomorphism	isomorphism	NOUN
ejpam-5118	224	5	problem	problem	NOUN
ejpam-5118	224	6	for	for	ADP
ejpam-5118	224	7	central	central	ADJ
ejpam-5118	224	8	extensions	extension	NOUN
ejpam-5118	224	9	definition	definition	NOUN
ejpam-5118	224	10	5.1	5.1	NUM
ejpam-5118	224	11	.	.	PUNCT
ejpam-5118	225	1	let	let	VERB
ejpam-5118	225	2	g2	g2	PROPN
ejpam-5118	225	3	be	be	AUX
ejpam-5118	225	4	a	a	DET
ejpam-5118	225	5	group	group	NOUN
ejpam-5118	225	6	which	which	PRON
ejpam-5118	225	7	acts	act	VERB
ejpam-5118	225	8	trivially	trivially	ADV
ejpam-5118	225	9	on	on	ADP
ejpam-5118	225	10	an	an	DET
ejpam-5118	225	11	abelian	abelian	ADJ
ejpam-5118	225	12	group	group	NOUN
ejpam-5118	225	13	g1	g1	PROPN
ejpam-5118	225	14	.	.	PUNCT
ejpam-5118	226	1	the	the	DET
ejpam-5118	226	2	groups	group	NOUN
ejpam-5118	226	3	g1	g1	VERB
ejpam-5118	226	4	×	×	PROPN
ejpam-5118	226	5	ε1	ε1	PROPN
ejpam-5118	226	6	g2	g2	PROPN
ejpam-5118	226	7	and	and	CCONJ
ejpam-5118	226	8	g1	g1	PROPN
ejpam-5118	226	9	×	×	PROPN
ejpam-5118	226	10	ε2	ε2	PROPN
ejpam-5118	226	11	g2	g2	PROPN
ejpam-5118	226	12	are	be	AUX
ejpam-5118	226	13	called	call	VERB
ejpam-5118	226	14	lower	lower	ADV
ejpam-5118	226	15	isomorphic	isomorphic	ADJ
ejpam-5118	226	16	if	if	SCONJ
ejpam-5118	226	17	there	there	PRON
ejpam-5118	226	18	exists	exist	VERB
ejpam-5118	226	19	an	an	DET
ejpam-5118	226	20	isomorphism	isomorphism	NOUN
ejpam-5118	226	21	φ	φ	NOUN
ejpam-5118	226	22	:	:	PUNCT
ejpam-5118	226	23	g1	g1	PROPN
ejpam-5118	226	24	×	×	PROPN
ejpam-5118	226	25	ε1	ε1	PROPN
ejpam-5118	226	26	g2	g2	PROPN
ejpam-5118	226	27	−→	−→	NOUN
ejpam-5118	226	28	g1	g1	PROPN
ejpam-5118	226	29	×	×	PROPN
ejpam-5118	226	30	ε2	ε2	PROPN
ejpam-5118	226	31	g2	g2	PROPN
ejpam-5118	226	32	leaving	leave	VERB
ejpam-5118	226	33	g2	g2	PROPN
ejpam-5118	226	34	invariant	invariant	PROPN
ejpam-5118	226	35	.	.	PUNCT
ejpam-5118	227	1	note	note	NOUN
ejpam-5118	227	2	that	that	DET
ejpam-5118	227	3	remark	remark	NOUN
ejpam-5118	227	4	3.2	3.2	NUM
ejpam-5118	227	5	also	also	ADV
ejpam-5118	227	6	shows	show	VERB
ejpam-5118	227	7	that	that	SCONJ
ejpam-5118	227	8	two	two	NUM
ejpam-5118	227	9	central	central	ADJ
ejpam-5118	227	10	extensions	extension	NOUN
ejpam-5118	227	11	can	can	AUX
ejpam-5118	227	12	be	be	AUX
ejpam-5118	227	13	isomorphic	isomorphic	ADJ
ejpam-5118	227	14	without	without	ADP
ejpam-5118	227	15	being	be	AUX
ejpam-5118	227	16	lower	low	ADJ
ejpam-5118	227	17	isomorphic	isomorphic	ADJ
ejpam-5118	227	18	.	.	PUNCT
ejpam-5118	228	1	we	we	PRON
ejpam-5118	228	2	now	now	ADV
ejpam-5118	228	3	present	present	VERB
ejpam-5118	228	4	the	the	DET
ejpam-5118	228	5	following	follow	VERB
ejpam-5118	228	6	main	main	ADJ
ejpam-5118	228	7	result	result	NOUN
ejpam-5118	228	8	of	of	ADP
ejpam-5118	228	9	this	this	DET
ejpam-5118	228	10	section	section	NOUN
ejpam-5118	228	11	.	.	PUNCT
ejpam-5118	229	1	theorem	theorem	VERB
ejpam-5118	229	2	5.1	5.1	NUM
ejpam-5118	229	3	.	.	PUNCT
ejpam-5118	230	1	let	let	VERB
ejpam-5118	230	2	g2	g2	PROPN
ejpam-5118	230	3	be	be	AUX
ejpam-5118	230	4	a	a	DET
ejpam-5118	230	5	group	group	NOUN
ejpam-5118	230	6	such	such	ADJ
ejpam-5118	230	7	that	that	SCONJ
ejpam-5118	230	8	the	the	DET
ejpam-5118	230	9	equivalence	equivalence	NOUN
ejpam-5118	230	10	relation	relation	NOUN
ejpam-5118	230	11	(	(	PUNCT
ejpam-5118	230	12	∼	∼	NOUN
ejpam-5118	230	13	)	)	PUNCT
ejpam-5118	230	14	is	be	AUX
ejpam-5118	230	15	trivial	trivial	ADJ
ejpam-5118	230	16	on	on	ADP
ejpam-5118	230	17	z2(g2	z2(g2	NUM
ejpam-5118	230	18	,	,	PUNCT
ejpam-5118	230	19	g2	g2	PROPN
ejpam-5118	230	20	)	)	PUNCT
ejpam-5118	230	21	.	.	PUNCT
ejpam-5118	231	1	if	if	SCONJ
ejpam-5118	231	2	the	the	DET
ejpam-5118	231	3	groups	group	NOUN
ejpam-5118	231	4	g1	g1	VERB
ejpam-5118	231	5	×	×	PROPN
ejpam-5118	231	6	ε1	ε1	PROPN
ejpam-5118	231	7	g2	g2	PROPN
ejpam-5118	231	8	and	and	CCONJ
ejpam-5118	231	9	g1	g1	PROPN
ejpam-5118	231	10	×	×	PROPN
ejpam-5118	231	11	ε2	ε2	PROPN
ejpam-5118	231	12	g2	g2	PROPN
ejpam-5118	231	13	are	be	AUX
ejpam-5118	231	14	lower	low	ADJ
ejpam-5118	231	15	isomorphic	isomorphic	ADJ
ejpam-5118	231	16	then	then	ADV
ejpam-5118	231	17	there	there	PRON
ejpam-5118	231	18	exist	exist	VERB
ejpam-5118	231	19	ρ	ρ	PROPN
ejpam-5118	231	20	∈	∈	PROPN
ejpam-5118	231	21	aut(g2	aut(g2	PROPN
ejpam-5118	231	22	)	)	PUNCT
ejpam-5118	231	23	,	,	PUNCT
ejpam-5118	231	24	δ	δ	PROPN
ejpam-5118	231	25	∈	∈	PROPN
ejpam-5118	231	26	hom(g1	hom(g1	NOUN
ejpam-5118	231	27	,	,	PUNCT
ejpam-5118	231	28	z(g2	z(g2	NUM
ejpam-5118	231	29	)	)	PUNCT
ejpam-5118	231	30	)	)	PUNCT
ejpam-5118	231	31	and	and	CCONJ
ejpam-5118	231	32	an	an	DET
ejpam-5118	231	33	ε1	ε1	NOUN
ejpam-5118	231	34	-	-	PUNCT
ejpam-5118	231	35	automorphism	automorphism	NOUN
ejpam-5118	231	36	σ	σ	NOUN
ejpam-5118	231	37	such	such	ADJ
ejpam-5118	231	38	that	that	SCONJ
ejpam-5118	231	39	(	(	PUNCT
ejpam-5118	231	40	i	i	NOUN
ejpam-5118	231	41	)	)	PUNCT
ejpam-5118	232	1	[	[	X
ejpam-5118	232	2	{	{	PUNCT
ejpam-5118	232	3	1	1	NUM
ejpam-5118	232	4	}	}	PUNCT
ejpam-5118	232	5	×g2	×g2	PROPN
ejpam-5118	232	6	,	,	PUNCT
ejpam-5118	232	7	{	{	PUNCT
ejpam-5118	232	8	1	1	NUM
ejpam-5118	232	9	}	}	PUNCT
ejpam-5118	232	10	×	×	NOUN
ejpam-5118	232	11	δ(g1	δ(g1	NOUN
ejpam-5118	232	12	)	)	PUNCT
ejpam-5118	232	13	]	]	PUNCT
ejpam-5118	232	14	=	=	SYM
ejpam-5118	232	15	1	1	NUM
ejpam-5118	232	16	,	,	PUNCT
ejpam-5118	232	17	im(ε1	im(ε1	NOUN
ejpam-5118	232	18	)	)	PUNCT
ejpam-5118	232	19	≤	≤	PROPN
ejpam-5118	232	20	ker(δ	ker(δ	PROPN
ejpam-5118	232	21	)	)	PUNCT
ejpam-5118	232	22	,	,	PUNCT
ejpam-5118	232	23	(	(	PUNCT
ejpam-5118	232	24	ii	ii	NOUN
ejpam-5118	232	25	)	)	PUNCT
ejpam-5118	232	26	ε−1	ε−1	PROPN
ejpam-5118	232	27	2	2	NUM
ejpam-5118	232	28	◦	◦	NOUN
ejpam-5118	232	29	(	(	PUNCT
ejpam-5118	232	30	δ	δ	PROPN
ejpam-5118	232	31	×	×	PROPN
ejpam-5118	232	32	δ	δ	PROPN
ejpam-5118	232	33	)	)	PUNCT
ejpam-5118	232	34	=	=	PUNCT
ejpam-5118	232	35	ψσ	ψσ	ADP
ejpam-5118	232	36	∈	∈	PROPN
ejpam-5118	232	37	b2(g1	b2(g1	NOUN
ejpam-5118	232	38	,	,	PUNCT
ejpam-5118	232	39	g1	g1	NOUN
ejpam-5118	232	40	)	)	PUNCT
ejpam-5118	232	41	where	where	SCONJ
ejpam-5118	232	42	ψσ(x	ψσ(x	NOUN
ejpam-5118	232	43	,	,	PUNCT
ejpam-5118	232	44	x	x	NOUN
ejpam-5118	232	45	′	′	NUM
ejpam-5118	232	46	)	)	PUNCT
ejpam-5118	232	47	=	=	NOUN
ejpam-5118	232	48	σ(x)σ(x′)σ(xx′)−1	σ(x)σ(x′)σ(xx′)−1	PROPN
ejpam-5118	232	49	for	for	ADP
ejpam-5118	232	50	all	all	DET
ejpam-5118	232	51	x	x	NOUN
ejpam-5118	232	52	,	,	PUNCT
ejpam-5118	232	53	x′	x′	PROPN
ejpam-5118	232	54	∈	∈	PROPN
ejpam-5118	232	55	g1	g1	PROPN
ejpam-5118	232	56	,	,	PUNCT
ejpam-5118	232	57	(	(	PUNCT
ejpam-5118	232	58	iii	iii	NOUN
ejpam-5118	232	59	)	)	PUNCT
ejpam-5118	232	60	ε2	ε2	ADJ
ejpam-5118	232	61	◦	◦	NOUN
ejpam-5118	232	62	(	(	PUNCT
ejpam-5118	232	63	ρ×	ρ×	NOUN
ejpam-5118	232	64	ρ	ρ	NOUN
ejpam-5118	232	65	)	)	PUNCT
ejpam-5118	232	66	=	=	SYM
ejpam-5118	232	67	σ	σ	PROPN
ejpam-5118	232	68	◦	◦	PROPN
ejpam-5118	232	69	ε1	ε1	PROPN
ejpam-5118	232	70	.	.	PUNCT
ejpam-5118	233	1	proof	proof	NOUN
ejpam-5118	233	2	.	.	PUNCT
ejpam-5118	234	1	suppose	suppose	VERB
ejpam-5118	234	2	that	that	SCONJ
ejpam-5118	234	3	g1	g1	PROPN
ejpam-5118	234	4	×	×	PROPN
ejpam-5118	234	5	ε1	ε1	PROPN
ejpam-5118	234	6	g2	g2	PROPN
ejpam-5118	234	7	and	and	CCONJ
ejpam-5118	234	8	g1	g1	PROPN
ejpam-5118	234	9	×	×	PROPN
ejpam-5118	234	10	ε2	ε2	PROPN
ejpam-5118	234	11	g2	g2	PROPN
ejpam-5118	234	12	are	be	AUX
ejpam-5118	234	13	isomorphic	isomorphic	ADJ
ejpam-5118	234	14	by	by	ADP
ejpam-5118	234	15	an	an	DET
ejpam-5118	234	16	isomorphism	isomorphism	NOUN
ejpam-5118	234	17	φ	φ	PROPN
ejpam-5118	234	18	=(	=(	PROPN
ejpam-5118	234	19	φ11	φ11	PROPN
ejpam-5118	234	20	1	1	NUM
ejpam-5118	234	21	φ21	φ21	NOUN
ejpam-5118	234	22	φ22	φ22	NOUN
ejpam-5118	234	23	)	)	PUNCT
ejpam-5118	234	24	.	.	PUNCT
ejpam-5118	235	1	from	from	ADP
ejpam-5118	235	2	lemma	lemma	PROPN
ejpam-5118	235	3	3.1	3.1	NUM
ejpam-5118	235	4	,	,	PUNCT
ejpam-5118	235	5	we	we	PRON
ejpam-5118	235	6	have	have	VERB
ejpam-5118	235	7	that	that	DET
ejpam-5118	235	8	φ(x	φ(x	PROPN
ejpam-5118	235	9	,	,	PUNCT
ejpam-5118	235	10	y	y	NOUN
ejpam-5118	235	11	)	)	PUNCT
ejpam-5118	235	12	=	=	NOUN
ejpam-5118	235	13	(	(	PUNCT
ejpam-5118	235	14	φ11(x)ε2(φ21(x	φ11(x)ε2(φ21(x	NOUN
ejpam-5118	235	15	)	)	PUNCT
ejpam-5118	235	16	,	,	PUNCT
ejpam-5118	236	1	φ22(y	φ22(y	NOUN
ejpam-5118	236	2	)	)	PUNCT
ejpam-5118	236	3	)	)	PUNCT
ejpam-5118	236	4	,	,	PUNCT
ejpam-5118	236	5	φ21(x)φ22(y	φ21(x)φ22(y	ADJ
ejpam-5118	236	6	)	)	PUNCT
ejpam-5118	236	7	)	)	PUNCT
ejpam-5118	237	1	for	for	ADP
ejpam-5118	237	2	all	all	DET
ejpam-5118	237	3	x	x	PROPN
ejpam-5118	237	4	∈	∈	PROPN
ejpam-5118	237	5	g1	g1	NOUN
ejpam-5118	237	6	,	,	PUNCT
ejpam-5118	237	7	y	y	PROPN
ejpam-5118	237	8	∈	∈	PROPN
ejpam-5118	237	9	g2	g2	PROPN
ejpam-5118	237	10	.	.	PUNCT
ejpam-5118	238	1	since	since	SCONJ
ejpam-5118	238	2	φ	φ	PROPN
ejpam-5118	238	3	is	be	AUX
ejpam-5118	238	4	bijective	bijective	ADJ
ejpam-5118	238	5	,	,	PUNCT
ejpam-5118	238	6	so	so	ADV
ejpam-5118	238	7	is	be	AUX
ejpam-5118	238	8	φ22	φ22	NOUN
ejpam-5118	238	9	.	.	PUNCT
ejpam-5118	239	1	by	by	ADP
ejpam-5118	239	2	proposition	proposition	NOUN
ejpam-5118	239	3	3.1	3.1	NUM
ejpam-5118	239	4	,	,	PUNCT
ejpam-5118	239	5	the	the	DET
ejpam-5118	239	6	maps	map	NOUN
ejpam-5118	239	7	φ21	φ21	NOUN
ejpam-5118	239	8	∈	∈	PROPN
ejpam-5118	239	9	hom(g1	hom(g1	NOUN
ejpam-5118	239	10	,	,	PUNCT
ejpam-5118	239	11	z(g2	z(g2	NUM
ejpam-5118	239	12	)	)	PUNCT
ejpam-5118	239	13	)	)	PUNCT
ejpam-5118	239	14	,	,	PUNCT
ejpam-5118	239	15	φ22	φ22	NOUN
ejpam-5118	239	16	∈	∈	PROPN
ejpam-5118	239	17	aut(g2	aut(g2	ADP
ejpam-5118	239	18	)	)	PUNCT
ejpam-5118	239	19	and	and	CCONJ
ejpam-5118	239	20	the	the	DET
ejpam-5118	239	21	ε1	ε1	PROPN
ejpam-5118	239	22	-	-	PUNCT
ejpam-5118	239	23	endomorphism	endomorphism	NOUN
ejpam-5118	239	24	φ11	φ11	NOUN
ejpam-5118	239	25	satisfy	satisfy	VERB
ejpam-5118	239	26	the	the	DET
ejpam-5118	239	27	conditions	condition	NOUN
ejpam-5118	239	28	(	(	PUNCT
ejpam-5118	239	29	i)-(iii	i)-(iii	NOUN
ejpam-5118	239	30	)	)	PUNCT
ejpam-5118	239	31	.	.	PUNCT
ejpam-5118	240	1	so	so	ADV
ejpam-5118	240	2	,	,	PUNCT
ejpam-5118	240	3	it	it	PRON
ejpam-5118	240	4	remains	remain	VERB
ejpam-5118	240	5	to	to	PART
ejpam-5118	240	6	show	show	VERB
ejpam-5118	240	7	that	that	SCONJ
ejpam-5118	240	8	φ11	φ11	NOUN
ejpam-5118	240	9	is	be	AUX
ejpam-5118	240	10	bijective	bijective	ADJ
ejpam-5118	240	11	.	.	PUNCT
ejpam-5118	241	1	let	let	VERB
ejpam-5118	241	2	g	g	PROPN
ejpam-5118	241	3	∈	∈	PROPN
ejpam-5118	241	4	g1	g1	NOUN
ejpam-5118	241	5	,	,	PUNCT
ejpam-5118	241	6	since	since	SCONJ
ejpam-5118	241	7	φ	φ	PROPN
ejpam-5118	241	8	is	be	AUX
ejpam-5118	241	9	n.	n.	PROPN
ejpam-5118	241	10	snanou	snanou	PROPN
ejpam-5118	241	11	/	/	SYM
ejpam-5118	241	12	eur	eur	PROPN
ejpam-5118	241	13	.	.	PUNCT
ejpam-5118	242	1	j.	j.	PROPN
ejpam-5118	242	2	pure	pure	PROPN
ejpam-5118	242	3	appl	appl	PROPN
ejpam-5118	242	4	.	.	PROPN
ejpam-5118	242	5	math	math	PROPN
ejpam-5118	242	6	,	,	PUNCT
ejpam-5118	242	7	17	17	NUM
ejpam-5118	242	8	(	(	PUNCT
ejpam-5118	242	9	2	2	NUM
ejpam-5118	242	10	)	)	PUNCT
ejpam-5118	242	11	(	(	PUNCT
ejpam-5118	242	12	2024	2024	NUM
ejpam-5118	242	13	)	)	PUNCT
ejpam-5118	242	14	,	,	PUNCT
ejpam-5118	242	15	956	956	NUM
ejpam-5118	242	16	-	-	SYM
ejpam-5118	242	17	968	968	NUM
ejpam-5118	242	18	964	964	NUM
ejpam-5118	242	19	surjective	surjective	ADJ
ejpam-5118	242	20	,	,	PUNCT
ejpam-5118	242	21	there	there	PRON
ejpam-5118	242	22	exists	exist	VERB
ejpam-5118	242	23	an	an	DET
ejpam-5118	242	24	element	element	NOUN
ejpam-5118	242	25	(	(	PUNCT
ejpam-5118	242	26	x	x	NOUN
ejpam-5118	242	27	,	,	PUNCT
ejpam-5118	242	28	y	y	NOUN
ejpam-5118	242	29	)	)	PUNCT
ejpam-5118	242	30	∈	∈	PROPN
ejpam-5118	242	31	g1	g1	PROPN
ejpam-5118	242	32	×	×	PROPN
ejpam-5118	242	33	ε1	ε1	PROPN
ejpam-5118	242	34	g2	g2	PROPN
ejpam-5118	242	35	such	such	ADJ
ejpam-5118	242	36	that	that	SCONJ
ejpam-5118	242	37	φ(x	φ(x	PROPN
ejpam-5118	242	38	,	,	PUNCT
ejpam-5118	242	39	y	y	NOUN
ejpam-5118	242	40	)	)	PUNCT
ejpam-5118	242	41	=	=	SYM
ejpam-5118	243	1	(	(	PUNCT
ejpam-5118	243	2	g	g	NOUN
ejpam-5118	243	3	,	,	PUNCT
ejpam-5118	243	4	1	1	NUM
ejpam-5118	243	5	)	)	PUNCT
ejpam-5118	243	6	,	,	PUNCT
ejpam-5118	243	7	that	that	PRON
ejpam-5118	243	8	is	be	AUX
ejpam-5118	243	9	φ11(x)ε2(φ21(x	φ11(x)ε2(φ21(x	ADV
ejpam-5118	243	10	)	)	PUNCT
ejpam-5118	243	11	,	,	PUNCT
ejpam-5118	243	12	φ22(y	φ22(y	ADJ
ejpam-5118	243	13	)	)	PUNCT
ejpam-5118	243	14	)	)	PUNCT
ejpam-5118	244	1	=	=	SYM
ejpam-5118	244	2	g	g	PROPN
ejpam-5118	244	3	and	and	CCONJ
ejpam-5118	244	4	φ21(x)φ22(y	φ21(x)φ22(y	NUM
ejpam-5118	244	5	)	)	PUNCT
ejpam-5118	244	6	=	=	SYM
ejpam-5118	245	1	1	1	X
ejpam-5118	245	2	.	.	PUNCT
ejpam-5118	246	1	so	so	ADV
ejpam-5118	246	2	,	,	PUNCT
ejpam-5118	246	3	φ11(x)ε2(φ21(x	φ11(x)ε2(φ21(x	NOUN
ejpam-5118	246	4	)	)	PUNCT
ejpam-5118	246	5	,	,	PUNCT
ejpam-5118	246	6	φ21(x	φ21(x	NOUN
ejpam-5118	246	7	−1	−1	NOUN
ejpam-5118	246	8	)	)	PUNCT
ejpam-5118	246	9	)	)	PUNCT
ejpam-5118	247	1	=	=	SYM
ejpam-5118	247	2	g	g	NOUN
ejpam-5118	247	3	and	and	CCONJ
ejpam-5118	247	4	then	then	ADV
ejpam-5118	247	5	,	,	PUNCT
ejpam-5118	247	6	using	use	VERB
ejpam-5118	247	7	the	the	DET
ejpam-5118	247	8	condition	condition	NOUN
ejpam-5118	247	9	(	(	PUNCT
ejpam-5118	247	10	ii	ii	NOUN
ejpam-5118	247	11	)	)	PUNCT
ejpam-5118	247	12	,	,	PUNCT
ejpam-5118	247	13	we	we	PRON
ejpam-5118	247	14	have	have	VERB
ejpam-5118	247	15	φ11(x	φ11(x	NOUN
ejpam-5118	247	16	)	)	PUNCT
ejpam-5118	248	1	=	=	SYM
ejpam-5118	248	2	g.	g.	PROPN
ejpam-5118	248	3	therefore	therefore	ADV
ejpam-5118	248	4	,	,	PUNCT
ejpam-5118	248	5	φ11	φ11	PROPN
ejpam-5118	248	6	is	be	AUX
ejpam-5118	248	7	surjective	surjective	ADJ
ejpam-5118	248	8	.	.	PUNCT
ejpam-5118	249	1	on	on	ADP
ejpam-5118	249	2	the	the	DET
ejpam-5118	249	3	other	other	ADJ
ejpam-5118	249	4	hand	hand	NOUN
ejpam-5118	249	5	,	,	PUNCT
ejpam-5118	249	6	the	the	DET
ejpam-5118	249	7	map	map	NOUN
ejpam-5118	249	8	ψ	ψ	PRON
ejpam-5118	249	9	defined	define	VERB
ejpam-5118	249	10	by	by	ADP
ejpam-5118	249	11	ψ(x	ψ(x	PROPN
ejpam-5118	249	12	,	,	PUNCT
ejpam-5118	249	13	y	y	NOUN
ejpam-5118	249	14	)	)	PUNCT
ejpam-5118	249	15	=	=	SYM
ejpam-5118	249	16	(	(	PUNCT
ejpam-5118	249	17	x	x	X
ejpam-5118	249	18	,	,	PUNCT
ejpam-5118	249	19	yφ−1	yφ−1	ADV
ejpam-5118	249	20	22	22	NUM
ejpam-5118	249	21	(	(	PUNCT
ejpam-5118	249	22	φ21(x	φ21(x	NOUN
ejpam-5118	249	23	)	)	PUNCT
ejpam-5118	249	24	−1	−1	NOUN
ejpam-5118	249	25	)	)	PUNCT
ejpam-5118	249	26	)	)	PUNCT
ejpam-5118	249	27	is	be	AUX
ejpam-5118	249	28	a	a	DET
ejpam-5118	249	29	bijection	bijection	NOUN
ejpam-5118	249	30	and	and	CCONJ
ejpam-5118	249	31	we	we	PRON
ejpam-5118	249	32	have	have	VERB
ejpam-5118	249	33	φ	φ	VERB
ejpam-5118	249	34	◦	◦	NOUN
ejpam-5118	249	35	ψ(x−1	ψ(x−1	NOUN
ejpam-5118	249	36	,	,	PUNCT
ejpam-5118	249	37	1	1	NUM
ejpam-5118	249	38	)	)	PUNCT
ejpam-5118	249	39	=	=	SYM
ejpam-5118	249	40	(	(	PUNCT
ejpam-5118	249	41	φ11(x	φ11(x	NOUN
ejpam-5118	249	42	−1)ε2(φ21(x	−1)ε2(φ21(x	NOUN
ejpam-5118	249	43	−1	−1	NOUN
ejpam-5118	249	44	)	)	PUNCT
ejpam-5118	249	45	,	,	PUNCT
ejpam-5118	249	46	φ21(x	φ21(x	NOUN
ejpam-5118	249	47	)	)	PUNCT
ejpam-5118	249	48	)	)	PUNCT
ejpam-5118	249	49	,	,	PUNCT
ejpam-5118	249	50	1	1	X
ejpam-5118	249	51	)	)	PUNCT
ejpam-5118	249	52	for	for	ADP
ejpam-5118	249	53	all	all	DET
ejpam-5118	249	54	x	x	PROPN
ejpam-5118	249	55	∈	∈	PROPN
ejpam-5118	249	56	g1	g1	NOUN
ejpam-5118	249	57	.	.	PUNCT
ejpam-5118	250	1	thus	thus	ADV
ejpam-5118	250	2	,	,	PUNCT
ejpam-5118	250	3	the	the	DET
ejpam-5118	250	4	condition	condition	NOUN
ejpam-5118	250	5	(	(	PUNCT
ejpam-5118	250	6	ii	ii	NOUN
ejpam-5118	250	7	)	)	PUNCT
ejpam-5118	250	8	ensures	ensure	VERB
ejpam-5118	250	9	that	that	SCONJ
ejpam-5118	250	10	φ	φ	PROPN
ejpam-5118	250	11	◦	◦	PROPN
ejpam-5118	250	12	ψ(x−1	ψ(x−1	NOUN
ejpam-5118	250	13	,	,	PUNCT
ejpam-5118	250	14	1	1	NUM
ejpam-5118	250	15	)	)	PUNCT
ejpam-5118	250	16	=	=	SYM
ejpam-5118	250	17	(	(	PUNCT
ejpam-5118	250	18	φ11(x	φ11(x	NOUN
ejpam-5118	250	19	)	)	PUNCT
ejpam-5118	250	20	−1	−1	NOUN
ejpam-5118	250	21	,	,	PUNCT
ejpam-5118	250	22	1	1	NUM
ejpam-5118	250	23	)	)	PUNCT
ejpam-5118	250	24	for	for	ADP
ejpam-5118	250	25	all	all	DET
ejpam-5118	250	26	x	x	PROPN
ejpam-5118	250	27	∈	∈	PROPN
ejpam-5118	250	28	g1	g1	NOUN
ejpam-5118	250	29	.	.	PUNCT
ejpam-5118	251	1	since	since	SCONJ
ejpam-5118	251	2	φ	φ	PROPN
ejpam-5118	251	3	◦	◦	PROPN
ejpam-5118	251	4	ψ	ψ	NOUN
ejpam-5118	251	5	is	be	AUX
ejpam-5118	251	6	injective	injective	ADJ
ejpam-5118	251	7	,	,	PUNCT
ejpam-5118	251	8	so	so	ADV
ejpam-5118	251	9	is	be	AUX
ejpam-5118	251	10	φ11	φ11	ADJ
ejpam-5118	251	11	.	.	PUNCT
ejpam-5118	252	1	thus	thus	ADV
ejpam-5118	252	2	,	,	PUNCT
ejpam-5118	252	3	the	the	DET
ejpam-5118	252	4	desired	desire	VERB
ejpam-5118	252	5	result	result	NOUN
ejpam-5118	252	6	follows	follow	VERB
ejpam-5118	252	7	directly	directly	ADV
ejpam-5118	252	8	by	by	ADP
ejpam-5118	252	9	taking	take	VERB
ejpam-5118	252	10	ρ	ρ	NOUN
ejpam-5118	252	11	=	=	SYM
ejpam-5118	252	12	φ22	φ22	PROPN
ejpam-5118	252	13	,	,	PUNCT
ejpam-5118	252	14	σ	σ	NOUN
ejpam-5118	252	15	=	=	SYM
ejpam-5118	252	16	φ11	φ11	X
ejpam-5118	252	17	and	and	CCONJ
ejpam-5118	252	18	δ	δ	NOUN
ejpam-5118	252	19	=	=	NOUN
ejpam-5118	252	20	φ21	φ21	PROPN
ejpam-5118	252	21	.	.	PUNCT
ejpam-5118	252	22	remark	remark	VERB
ejpam-5118	252	23	5.1	5.1	NUM
ejpam-5118	252	24	.	.	PUNCT
ejpam-5118	253	1	the	the	DET
ejpam-5118	253	2	converse	converse	NOUN
ejpam-5118	253	3	of	of	ADP
ejpam-5118	253	4	the	the	DET
ejpam-5118	253	5	previous	previous	ADJ
ejpam-5118	253	6	result	result	NOUN
ejpam-5118	253	7	holds	hold	VERB
ejpam-5118	253	8	if	if	SCONJ
ejpam-5118	253	9	g1	g1	PROPN
ejpam-5118	253	10	and	and	CCONJ
ejpam-5118	253	11	g2	g2	PROPN
ejpam-5118	253	12	are	be	AUX
ejpam-5118	253	13	finite	finite	ADJ
ejpam-5118	253	14	.	.	PUNCT
ejpam-5118	254	1	indeed	indeed	ADV
ejpam-5118	254	2	,	,	PUNCT
ejpam-5118	254	3	it	it	PRON
ejpam-5118	254	4	suffices	suffice	VERB
ejpam-5118	254	5	to	to	PART
ejpam-5118	254	6	show	show	VERB
ejpam-5118	254	7	that	that	SCONJ
ejpam-5118	254	8	φ	φ	PROPN
ejpam-5118	254	9	is	be	AUX
ejpam-5118	254	10	injective	injective	ADJ
ejpam-5118	254	11	.	.	PUNCT
ejpam-5118	255	1	let	let	VERB
ejpam-5118	255	2	(	(	PUNCT
ejpam-5118	255	3	x	x	NOUN
ejpam-5118	255	4	,	,	PUNCT
ejpam-5118	255	5	y	y	NOUN
ejpam-5118	255	6	)	)	PUNCT
ejpam-5118	255	7	∈	∈	PROPN
ejpam-5118	255	8	g1	g1	PROPN
ejpam-5118	255	9	×ε	×ε	ADP
ejpam-5118	255	10	g2	g2	PROPN
ejpam-5118	255	11	such	such	ADJ
ejpam-5118	255	12	that	that	SCONJ
ejpam-5118	255	13	φ(x	φ(x	PROPN
ejpam-5118	255	14	,	,	PUNCT
ejpam-5118	255	15	y	y	NOUN
ejpam-5118	255	16	)	)	PUNCT
ejpam-5118	255	17	=	=	PUNCT
ejpam-5118	256	1	(	(	PUNCT
ejpam-5118	256	2	1	1	NUM
ejpam-5118	256	3	,	,	PUNCT
ejpam-5118	256	4	1	1	NUM
ejpam-5118	256	5	)	)	PUNCT
ejpam-5118	256	6	.	.	PUNCT
ejpam-5118	257	1	then	then	ADV
ejpam-5118	257	2	,	,	PUNCT
ejpam-5118	257	3	the	the	DET
ejpam-5118	257	4	equality	equality	NOUN
ejpam-5118	257	5	φ21(x)φ22(y	φ21(x)φ22(y	ADV
ejpam-5118	257	6	)	)	PUNCT
ejpam-5118	257	7	=	=	SYM
ejpam-5118	257	8	1	1	NUM
ejpam-5118	257	9	implies	imply	VERB
ejpam-5118	257	10	that	that	SCONJ
ejpam-5118	257	11	φ22(y	φ22(y	VERB
ejpam-5118	257	12	)	)	PUNCT
ejpam-5118	257	13	=	=	SYM
ejpam-5118	257	14	φ21(x	φ21(x	NOUN
ejpam-5118	257	15	−1	−1	NOUN
ejpam-5118	257	16	)	)	PUNCT
ejpam-5118	257	17	.	.	PUNCT
ejpam-5118	258	1	so	so	ADV
ejpam-5118	258	2	φ11(x)ε2(φ21(x	φ11(x)ε2(φ21(x	NOUN
ejpam-5118	258	3	)	)	PUNCT
ejpam-5118	258	4	,	,	PUNCT
ejpam-5118	258	5	φ21(x	φ21(x	NOUN
ejpam-5118	258	6	−1	−1	NOUN
ejpam-5118	258	7	)	)	PUNCT
ejpam-5118	258	8	)	)	PUNCT
ejpam-5118	259	1	=	=	PUNCT
ejpam-5118	259	2	1	1	X
ejpam-5118	259	3	.	.	PUNCT
ejpam-5118	259	4	using	use	VERB
ejpam-5118	259	5	the	the	DET
ejpam-5118	259	6	condition	condition	NOUN
ejpam-5118	259	7	(	(	PUNCT
ejpam-5118	259	8	ii	ii	NOUN
ejpam-5118	259	9	)	)	PUNCT
ejpam-5118	259	10	,	,	PUNCT
ejpam-5118	259	11	we	we	PRON
ejpam-5118	259	12	get	get	VERB
ejpam-5118	259	13	φ11(x	φ11(x	NOUN
ejpam-5118	259	14	−1)−1	−1)−1	NOUN
ejpam-5118	259	15	=	=	NOUN
ejpam-5118	259	16	1	1	NUM
ejpam-5118	259	17	and	and	CCONJ
ejpam-5118	259	18	then	then	ADV
ejpam-5118	259	19	x	x	X
ejpam-5118	259	20	=	=	SYM
ejpam-5118	259	21	1	1	NUM
ejpam-5118	259	22	since	since	SCONJ
ejpam-5118	259	23	φ11	φ11	NUM
ejpam-5118	259	24	is	be	AUX
ejpam-5118	259	25	injective	injective	ADJ
ejpam-5118	259	26	.	.	PUNCT
ejpam-5118	260	1	since	since	SCONJ
ejpam-5118	260	2	φ21(1	φ21(1	NOUN
ejpam-5118	260	3	)	)	PUNCT
ejpam-5118	260	4	=	=	SYM
ejpam-5118	260	5	1	1	NUM
ejpam-5118	260	6	,	,	PUNCT
ejpam-5118	260	7	it	it	PRON
ejpam-5118	260	8	follows	follow	VERB
ejpam-5118	260	9	that	that	SCONJ
ejpam-5118	260	10	φ22(y	φ22(y	VERB
ejpam-5118	260	11	)	)	PUNCT
ejpam-5118	260	12	=	=	SYM
ejpam-5118	260	13	1	1	NUM
ejpam-5118	260	14	and	and	CCONJ
ejpam-5118	260	15	then	then	ADV
ejpam-5118	260	16	y	y	PROPN
ejpam-5118	260	17	=	=	PUNCT
ejpam-5118	260	18	1	1	NUM
ejpam-5118	260	19	since	since	SCONJ
ejpam-5118	260	20	φ22	φ22	NOUN
ejpam-5118	260	21	is	be	AUX
ejpam-5118	260	22	injective	injective	ADJ
ejpam-5118	260	23	.	.	PUNCT
ejpam-5118	261	1	therefore	therefore	ADV
ejpam-5118	261	2	,	,	PUNCT
ejpam-5118	261	3	φ	φ	PROPN
ejpam-5118	261	4	is	be	AUX
ejpam-5118	261	5	bijective	bijective	ADJ
ejpam-5118	261	6	and	and	CCONJ
ejpam-5118	261	7	so	so	ADV
ejpam-5118	261	8	it	it	PRON
ejpam-5118	261	9	is	be	AUX
ejpam-5118	261	10	a	a	DET
ejpam-5118	261	11	lower	low	ADJ
ejpam-5118	261	12	isomorphism	isomorphism	NOUN
ejpam-5118	261	13	by	by	ADP
ejpam-5118	261	14	proposition	proposition	NOUN
ejpam-5118	261	15	3.1	3.1	NUM
ejpam-5118	261	16	.	.	PUNCT
ejpam-5118	262	1	as	as	SCONJ
ejpam-5118	262	2	required	require	VERB
ejpam-5118	262	3	.	.	PUNCT
ejpam-5118	263	1	let	let	AUX
ejpam-5118	263	2	ε	ε	PROPN
ejpam-5118	263	3	∈	∈	PROPN
ejpam-5118	263	4	z2(g2	z2(g2	PROPN
ejpam-5118	263	5	,	,	PUNCT
ejpam-5118	263	6	g1	g1	PROPN
ejpam-5118	263	7	)	)	PUNCT
ejpam-5118	263	8	be	be	AUX
ejpam-5118	263	9	a	a	DET
ejpam-5118	263	10	non	non	ADJ
ejpam-5118	263	11	-	-	ADJ
ejpam-5118	263	12	trivial	trivial	ADJ
ejpam-5118	263	13	2	2	NUM
ejpam-5118	263	14	-	-	PUNCT
ejpam-5118	263	15	cocycle	cocycle	NOUN
ejpam-5118	263	16	.	.	PUNCT
ejpam-5118	264	1	in	in	ADP
ejpam-5118	264	2	view	view	NOUN
ejpam-5118	264	3	of	of	ADP
ejpam-5118	264	4	the	the	DET
ejpam-5118	264	5	preceding	precede	VERB
ejpam-5118	264	6	theorem	theorem	NOUN
ejpam-5118	264	7	,	,	PUNCT
ejpam-5118	264	8	the	the	DET
ejpam-5118	264	9	group	group	NOUN
ejpam-5118	264	10	g1	g1	VERB
ejpam-5118	264	11	×	×	PROPN
ejpam-5118	264	12	ε	ε	PROPN
ejpam-5118	264	13	g2	g2	PROPN
ejpam-5118	264	14	can	can	AUX
ejpam-5118	264	15	not	not	PART
ejpam-5118	264	16	be	be	AUX
ejpam-5118	264	17	lower	low	ADJ
ejpam-5118	264	18	isomorphic	isomorphic	ADJ
ejpam-5118	264	19	to	to	ADP
ejpam-5118	264	20	the	the	DET
ejpam-5118	264	21	direct	direct	ADJ
ejpam-5118	264	22	product	product	NOUN
ejpam-5118	264	23	g1	g1	VERB
ejpam-5118	264	24	×g2	×g2	PROPN
ejpam-5118	264	25	.	.	PUNCT
ejpam-5118	265	1	corollary	corollary	ADJ
ejpam-5118	265	2	5.1	5.1	NUM
ejpam-5118	265	3	.	.	PUNCT
ejpam-5118	266	1	further	far	ADV
ejpam-5118	266	2	to	to	ADP
ejpam-5118	266	3	the	the	DET
ejpam-5118	266	4	assumption	assumption	NOUN
ejpam-5118	266	5	of	of	ADP
ejpam-5118	266	6	the	the	DET
ejpam-5118	266	7	previous	previous	ADJ
ejpam-5118	266	8	theorem	theorem	NOUN
ejpam-5118	266	9	,	,	PUNCT
ejpam-5118	266	10	suppose	suppose	VERB
ejpam-5118	266	11	that	that	SCONJ
ejpam-5118	266	12	b2(g1	b2(g1	NOUN
ejpam-5118	266	13	,	,	PUNCT
ejpam-5118	266	14	g1	g1	X
ejpam-5118	266	15	)	)	PUNCT
ejpam-5118	266	16	=	=	SYM
ejpam-5118	267	1	1	1	X
ejpam-5118	267	2	.	.	PUNCT
ejpam-5118	268	1	the	the	DET
ejpam-5118	268	2	groups	group	NOUN
ejpam-5118	268	3	g1	g1	VERB
ejpam-5118	268	4	×	×	PROPN
ejpam-5118	268	5	ε1	ε1	PROPN
ejpam-5118	268	6	g2	g2	PROPN
ejpam-5118	268	7	and	and	CCONJ
ejpam-5118	268	8	g1	g1	PROPN
ejpam-5118	268	9	×	×	PROPN
ejpam-5118	268	10	ε2	ε2	PROPN
ejpam-5118	268	11	g2	g2	PROPN
ejpam-5118	268	12	are	be	AUX
ejpam-5118	268	13	lower	low	ADJ
ejpam-5118	268	14	isomorphic	isomorphic	ADJ
ejpam-5118	268	15	if	if	SCONJ
ejpam-5118	268	16	and	and	CCONJ
ejpam-5118	268	17	only	only	ADV
ejpam-5118	268	18	if	if	SCONJ
ejpam-5118	268	19	there	there	PRON
ejpam-5118	268	20	exist	exist	VERB
ejpam-5118	268	21	ρ	ρ	PROPN
ejpam-5118	268	22	∈	∈	PROPN
ejpam-5118	268	23	aut(g2	aut(g2	ADP
ejpam-5118	268	24	)	)	PUNCT
ejpam-5118	268	25	and	and	CCONJ
ejpam-5118	268	26	σ	σ	NUM
ejpam-5118	268	27	∈	∈	PROPN
ejpam-5118	268	28	aut(g1	aut(g1	NOUN
ejpam-5118	268	29	)	)	PUNCT
ejpam-5118	268	30	such	such	ADJ
ejpam-5118	268	31	that	that	DET
ejpam-5118	268	32	ε2	ε2	ADJ
ejpam-5118	268	33	◦	◦	NOUN
ejpam-5118	268	34	(	(	PUNCT
ejpam-5118	268	35	ρ×	ρ×	NOUN
ejpam-5118	268	36	ρ	ρ	NOUN
ejpam-5118	268	37	)	)	PUNCT
ejpam-5118	268	38	=	=	SYM
ejpam-5118	268	39	σ	σ	PROPN
ejpam-5118	268	40	◦	◦	PROPN
ejpam-5118	268	41	ε1	ε1	PROPN
ejpam-5118	268	42	.	.	PUNCT
ejpam-5118	269	1	proof	proof	NOUN
ejpam-5118	269	2	.	.	PUNCT
ejpam-5118	270	1	indeed	indeed	ADV
ejpam-5118	270	2	,	,	PUNCT
ejpam-5118	270	3	suppose	suppose	VERB
ejpam-5118	270	4	that	that	SCONJ
ejpam-5118	270	5	the	the	DET
ejpam-5118	270	6	groups	group	NOUN
ejpam-5118	270	7	g1×	g1×	NOUN
ejpam-5118	270	8	ε1	ε1	VERB
ejpam-5118	270	9	g2	g2	PROPN
ejpam-5118	270	10	and	and	CCONJ
ejpam-5118	270	11	g1×	g1×	NOUN
ejpam-5118	270	12	ε2	ε2	PROPN
ejpam-5118	270	13	g2	g2	PROPN
ejpam-5118	270	14	are	be	AUX
ejpam-5118	270	15	lower	low	ADJ
ejpam-5118	270	16	isomorphic	isomorphic	ADJ
ejpam-5118	270	17	.	.	PUNCT
ejpam-5118	271	1	by	by	ADP
ejpam-5118	271	2	theorem	theorem	NOUN
ejpam-5118	271	3	5.1	5.1	NUM
ejpam-5118	271	4	,	,	PUNCT
ejpam-5118	271	5	there	there	PRON
ejpam-5118	271	6	exist	exist	VERB
ejpam-5118	271	7	ρ	ρ	PROPN
ejpam-5118	271	8	∈	∈	PROPN
ejpam-5118	271	9	aut(g2	aut(g2	PROPN
ejpam-5118	271	10	)	)	PUNCT
ejpam-5118	271	11	,	,	PUNCT
ejpam-5118	271	12	δ	δ	PROPN
ejpam-5118	271	13	∈	∈	PROPN
ejpam-5118	271	14	hom(g1	hom(g1	NOUN
ejpam-5118	271	15	,	,	PUNCT
ejpam-5118	271	16	z(g2	z(g2	NUM
ejpam-5118	271	17	)	)	PUNCT
ejpam-5118	271	18	)	)	PUNCT
ejpam-5118	271	19	and	and	CCONJ
ejpam-5118	271	20	an	an	DET
ejpam-5118	271	21	ε1	ε1	NOUN
ejpam-5118	271	22	-	-	PUNCT
ejpam-5118	271	23	automorphism	automorphism	NOUN
ejpam-5118	271	24	σ	σ	NOUN
ejpam-5118	271	25	satisfying	satisfy	VERB
ejpam-5118	271	26	the	the	DET
ejpam-5118	271	27	conditions	condition	NOUN
ejpam-5118	271	28	(	(	PUNCT
ejpam-5118	271	29	ii	ii	NOUN
ejpam-5118	271	30	)	)	PUNCT
ejpam-5118	271	31	and	and	CCONJ
ejpam-5118	271	32	(	(	PUNCT
ejpam-5118	271	33	iii	iii	NOUN
ejpam-5118	271	34	)	)	PUNCT
ejpam-5118	271	35	.	.	PUNCT
ejpam-5118	272	1	since	since	SCONJ
ejpam-5118	272	2	b2(g1	b2(g1	NUM
ejpam-5118	272	3	,	,	PUNCT
ejpam-5118	272	4	g1	g1	NOUN
ejpam-5118	272	5	)	)	PUNCT
ejpam-5118	272	6	=	=	SYM
ejpam-5118	272	7	1	1	NUM
ejpam-5118	272	8	,	,	PUNCT
ejpam-5118	272	9	the	the	DET
ejpam-5118	272	10	condition	condition	NOUN
ejpam-5118	272	11	(	(	PUNCT
ejpam-5118	272	12	ii	ii	NOUN
ejpam-5118	272	13	)	)	PUNCT
ejpam-5118	272	14	implies	imply	VERB
ejpam-5118	272	15	that	that	SCONJ
ejpam-5118	272	16	σ	σ	PROPN
ejpam-5118	272	17	∈	∈	PROPN
ejpam-5118	272	18	aut(g1	aut(g1	PROPN
ejpam-5118	272	19	)	)	PUNCT
ejpam-5118	272	20	.	.	PUNCT
ejpam-5118	273	1	therefore	therefore	ADV
ejpam-5118	273	2	,	,	PUNCT
ejpam-5118	273	3	we	we	PRON
ejpam-5118	273	4	conclude	conclude	VERB
ejpam-5118	273	5	by	by	ADP
ejpam-5118	273	6	using	use	VERB
ejpam-5118	273	7	the	the	DET
ejpam-5118	273	8	condition	condition	NOUN
ejpam-5118	273	9	(	(	PUNCT
ejpam-5118	273	10	iii	iii	NOUN
ejpam-5118	273	11	)	)	PUNCT
ejpam-5118	273	12	.	.	PUNCT
ejpam-5118	274	1	for	for	ADP
ejpam-5118	274	2	the	the	DET
ejpam-5118	274	3	converse	converse	NOUN
ejpam-5118	274	4	,	,	PUNCT
ejpam-5118	274	5	we	we	PRON
ejpam-5118	274	6	can	can	AUX
ejpam-5118	274	7	easily	easily	ADV
ejpam-5118	274	8	prove	prove	VERB
ejpam-5118	274	9	that	that	SCONJ
ejpam-5118	274	10	the	the	DET
ejpam-5118	274	11	bijection	bijection	PROPN
ejpam-5118	274	12	φ	φ	NOUN
ejpam-5118	274	13	defined	define	VERB
ejpam-5118	274	14	by	by	ADP
ejpam-5118	274	15	φ(x	φ(x	PROPN
ejpam-5118	274	16	,	,	PUNCT
ejpam-5118	274	17	y	y	NOUN
ejpam-5118	274	18	)	)	PUNCT
ejpam-5118	274	19	=	=	SYM
ejpam-5118	274	20	(	(	PUNCT
ejpam-5118	274	21	σ(x	σ(x	PROPN
ejpam-5118	274	22	)	)	PUNCT
ejpam-5118	274	23	,	,	PUNCT
ejpam-5118	274	24	ρ(y	ρ(y	NOUN
ejpam-5118	274	25	)	)	PUNCT
ejpam-5118	274	26	)	)	PUNCT
ejpam-5118	274	27	is	be	AUX
ejpam-5118	274	28	an	an	DET
ejpam-5118	274	29	isomorphism	isomorphism	NOUN
ejpam-5118	274	30	.	.	PUNCT
ejpam-5118	275	1	hence	hence	ADV
ejpam-5118	275	2	the	the	DET
ejpam-5118	275	3	corollary	corollary	NOUN
ejpam-5118	275	4	follows	follow	VERB
ejpam-5118	275	5	.	.	PUNCT
ejpam-5118	276	1	example	example	NOUN
ejpam-5118	276	2	5.1	5.1	NUM
ejpam-5118	276	3	.	.	PUNCT
ejpam-5118	277	1	define	define	NOUN
ejpam-5118	277	2	functions	function	NOUN
ejpam-5118	277	3	ε1	ε1	PROPN
ejpam-5118	277	4	,	,	PUNCT
ejpam-5118	277	5	ε2	ε2	ADJ
ejpam-5118	277	6	:	:	PUNCT
ejpam-5118	277	7	(	(	PUNCT
ejpam-5118	277	8	z2	z2	PROPN
ejpam-5118	277	9	×	×	PROPN
ejpam-5118	277	10	z2	z2	PROPN
ejpam-5118	277	11	)	)	PUNCT
ejpam-5118	277	12	2	2	NUM
ejpam-5118	277	13	→	→	SYM
ejpam-5118	277	14	z2	z2	PROPN
ejpam-5118	277	15	by	by	ADP
ejpam-5118	277	16	ε1((h1	ε1((h1	PROPN
ejpam-5118	277	17	,	,	PUNCT
ejpam-5118	277	18	h2	h2	PROPN
ejpam-5118	277	19	)	)	PUNCT
ejpam-5118	277	20	,	,	PUNCT
ejpam-5118	277	21	(	(	PUNCT
ejpam-5118	277	22	g1	g1	PROPN
ejpam-5118	277	23	,	,	PUNCT
ejpam-5118	277	24	g2	g2	PROPN
ejpam-5118	277	25	)	)	PUNCT
ejpam-5118	277	26	)	)	PUNCT
ejpam-5118	278	1	=	=	SYM
ejpam-5118	278	2	h1g1	h1g1	PROPN
ejpam-5118	278	3	and	and	CCONJ
ejpam-5118	278	4	ε2((h1	ε2((h1	PROPN
ejpam-5118	278	5	,	,	PUNCT
ejpam-5118	278	6	h2	h2	PROPN
ejpam-5118	278	7	)	)	PUNCT
ejpam-5118	278	8	,	,	PUNCT
ejpam-5118	278	9	(	(	PUNCT
ejpam-5118	278	10	g1	g1	PROPN
ejpam-5118	278	11	,	,	PUNCT
ejpam-5118	278	12	g2	g2	PROPN
ejpam-5118	278	13	)	)	PUNCT
ejpam-5118	278	14	)	)	PUNCT
ejpam-5118	279	1	=	=	SYM
ejpam-5118	279	2	h2g2	h2g2	PROPN
ejpam-5118	279	3	.	.	PUNCT
ejpam-5118	280	1	these	these	DET
ejpam-5118	280	2	functions	function	NOUN
ejpam-5118	280	3	are	be	AUX
ejpam-5118	280	4	2	2	NUM
ejpam-5118	280	5	-	-	PUNCT
ejpam-5118	280	6	cocycles	cocycle	NOUN
ejpam-5118	280	7	corresponding	correspond	VERB
ejpam-5118	280	8	to	to	ADP
ejpam-5118	280	9	two	two	NUM
ejpam-5118	280	10	inequivalent	inequivalent	ADJ
ejpam-5118	280	11	central	central	ADJ
ejpam-5118	280	12	extensions	extension	NOUN
ejpam-5118	280	13	of	of	ADP
ejpam-5118	280	14	⟨(2	⟨(2	NUM
ejpam-5118	280	15	,	,	PUNCT
ejpam-5118	280	16	0)⟩	0)⟩	X
ejpam-5118	280	17	∼=	∼=	PROPN
ejpam-5118	280	18	z2	z2	NOUN
ejpam-5118	280	19	by	by	ADP
ejpam-5118	280	20	z2×z2	z2×z2	PROPN
ejpam-5118	280	21	whose	whose	DET
ejpam-5118	280	22	the	the	DET
ejpam-5118	280	23	middle	middle	ADJ
ejpam-5118	280	24	group	group	NOUN
ejpam-5118	280	25	is	be	AUX
ejpam-5118	280	26	z4×z2	z4×z2	PROPN
ejpam-5118	280	27	.	.	PUNCT
ejpam-5118	281	1	note	note	VERB
ejpam-5118	281	2	that	that	SCONJ
ejpam-5118	281	3	ε1	ε1	PROPN
ejpam-5118	281	4	and	and	CCONJ
ejpam-5118	281	5	ε2	ε2	ADJ
ejpam-5118	281	6	are	be	AUX
ejpam-5118	281	7	the	the	DET
ejpam-5118	281	8	2	2	NUM
ejpam-5118	281	9	-	-	PUNCT
ejpam-5118	281	10	cocycles	cocycle	NOUN
ejpam-5118	281	11	induced	induce	VERB
ejpam-5118	281	12	by	by	ADP
ejpam-5118	281	13	the	the	DET
ejpam-5118	281	14	based	base	VERB
ejpam-5118	281	15	sections	section	NOUN
ejpam-5118	281	16	λ1	λ1	ADJ
ejpam-5118	281	17	,	,	PUNCT
ejpam-5118	281	18	λ2	λ2	PRON
ejpam-5118	281	19	:	:	PUNCT
ejpam-5118	281	20	z2×z2	z2×z2	PROPN
ejpam-5118	281	21	→	→	SYM
ejpam-5118	281	22	z4×	z4×	NOUN
ejpam-5118	281	23	z2	z2	NOUN
ejpam-5118	281	24	defined	define	VERB
ejpam-5118	281	25	by	by	ADP
ejpam-5118	281	26	λ1(h	λ1(h	X
ejpam-5118	281	27	mod	mod	PROPN
ejpam-5118	281	28	2	2	NUM
ejpam-5118	281	29	,	,	PUNCT
ejpam-5118	281	30	g	g	NOUN
ejpam-5118	281	31	mod	mod	NOUN
ejpam-5118	281	32	2	2	NUM
ejpam-5118	281	33	)	)	PUNCT
ejpam-5118	281	34	=	=	SYM
ejpam-5118	281	35	(	(	PUNCT
ejpam-5118	281	36	h	h	NOUN
ejpam-5118	281	37	mod	mod	NOUN
ejpam-5118	281	38	4	4	NUM
ejpam-5118	281	39	,	,	PUNCT
ejpam-5118	281	40	g	g	PROPN
ejpam-5118	281	41	mod	mod	NOUN
ejpam-5118	281	42	2	2	NUM
ejpam-5118	281	43	)	)	PUNCT
ejpam-5118	281	44	and	and	CCONJ
ejpam-5118	281	45	λ2(h	λ2(h	X
ejpam-5118	281	46	mod	mod	ADJ
ejpam-5118	281	47	2	2	NUM
ejpam-5118	281	48	,	,	PUNCT
ejpam-5118	281	49	g	g	NOUN
ejpam-5118	281	50	mod	mod	NOUN
ejpam-5118	281	51	2	2	NUM
ejpam-5118	281	52	)	)	PUNCT
ejpam-5118	281	53	=	=	NOUN
ejpam-5118	281	54	(	(	PUNCT
ejpam-5118	281	55	g	g	NOUN
ejpam-5118	281	56	mod	mod	PROPN
ejpam-5118	281	57	4	4	NUM
ejpam-5118	281	58	,	,	PUNCT
ejpam-5118	281	59	h	h	NOUN
ejpam-5118	281	60	mod	mod	NOUN
ejpam-5118	282	1	2	2	NUM
ejpam-5118	282	2	)	)	PUNCT
ejpam-5118	282	3	.	.	PUNCT
ejpam-5118	283	1	let	let	VERB
ejpam-5118	283	2	ρ	ρ	PROPN
ejpam-5118	283	3	∈	∈	PROPN
ejpam-5118	283	4	aut(z2×z2	aut(z2×z2	PROPN
ejpam-5118	283	5	)	)	PUNCT
ejpam-5118	283	6	defined	define	VERB
ejpam-5118	283	7	by	by	ADP
ejpam-5118	283	8	ρ(g1	ρ(g1	NOUN
ejpam-5118	283	9	,	,	PUNCT
ejpam-5118	283	10	g2	g2	PROPN
ejpam-5118	283	11	)	)	PUNCT
ejpam-5118	284	1	=	=	PRON
ejpam-5118	284	2	(	(	PUNCT
ejpam-5118	284	3	g2	g2	PROPN
ejpam-5118	284	4	,	,	PUNCT
ejpam-5118	284	5	g1	g1	PROPN
ejpam-5118	284	6	)	)	PUNCT
ejpam-5118	284	7	and	and	CCONJ
ejpam-5118	284	8	take	take	VERB
ejpam-5118	284	9	σ	σ	NOUN
ejpam-5118	284	10	=	=	SYM
ejpam-5118	284	11	idz2	idz2	NOUN
ejpam-5118	284	12	,	,	PUNCT
ejpam-5118	284	13	we	we	PRON
ejpam-5118	284	14	can	can	AUX
ejpam-5118	284	15	check	check	VERB
ejpam-5118	284	16	easily	easily	ADV
ejpam-5118	284	17	that	that	SCONJ
ejpam-5118	284	18	ε2	ε2	ADJ
ejpam-5118	284	19	◦	◦	NOUN
ejpam-5118	284	20	(	(	PUNCT
ejpam-5118	284	21	ρ	ρ	PROPN
ejpam-5118	284	22	×	×	PROPN
ejpam-5118	284	23	ρ	ρ	NOUN
ejpam-5118	284	24	)	)	PUNCT
ejpam-5118	284	25	=	=	SYM
ejpam-5118	284	26	σ	σ	PROPN
ejpam-5118	284	27	◦	◦	PROPN
ejpam-5118	284	28	ε1	ε1	PROPN
ejpam-5118	284	29	.	.	PUNCT
ejpam-5118	285	1	therefore	therefore	ADV
ejpam-5118	285	2	,	,	PUNCT
ejpam-5118	285	3	the	the	DET
ejpam-5118	285	4	groups	group	NOUN
ejpam-5118	285	5	z2	z2	PROPN
ejpam-5118	285	6	×	×	PROPN
ejpam-5118	285	7	ε1	ε1	PROPN
ejpam-5118	285	8	(	(	PUNCT
ejpam-5118	285	9	z2	z2	PROPN
ejpam-5118	285	10	×	×	PROPN
ejpam-5118	285	11	z2	z2	PROPN
ejpam-5118	285	12	)	)	PUNCT
ejpam-5118	285	13	and	and	CCONJ
ejpam-5118	285	14	z2	z2	PROPN
ejpam-5118	285	15	×	×	PROPN
ejpam-5118	285	16	ε2	ε2	NOUN
ejpam-5118	285	17	(	(	PUNCT
ejpam-5118	285	18	z2	z2	PROPN
ejpam-5118	285	19	×	×	PROPN
ejpam-5118	285	20	z2	z2	PROPN
ejpam-5118	285	21	)	)	PUNCT
ejpam-5118	285	22	are	be	AUX
ejpam-5118	285	23	lower	low	ADJ
ejpam-5118	285	24	isomorphic	isomorphic	ADJ
ejpam-5118	285	25	.	.	PUNCT
ejpam-5118	286	1	n.	n.	PROPN
ejpam-5118	286	2	snanou	snanou	PROPN
ejpam-5118	286	3	/	/	SYM
ejpam-5118	286	4	eur	eur	PROPN
ejpam-5118	286	5	.	.	PUNCT
ejpam-5118	287	1	j.	j.	PROPN
ejpam-5118	287	2	pure	pure	PROPN
ejpam-5118	287	3	appl	appl	PROPN
ejpam-5118	287	4	.	.	PROPN
ejpam-5118	287	5	math	math	PROPN
ejpam-5118	287	6	,	,	PUNCT
ejpam-5118	287	7	17	17	NUM
ejpam-5118	287	8	(	(	PUNCT
ejpam-5118	287	9	2	2	NUM
ejpam-5118	287	10	)	)	PUNCT
ejpam-5118	287	11	(	(	PUNCT
ejpam-5118	287	12	2024	2024	NUM
ejpam-5118	287	13	)	)	PUNCT
ejpam-5118	287	14	,	,	PUNCT
ejpam-5118	287	15	956	956	NUM
ejpam-5118	287	16	-	-	SYM
ejpam-5118	287	17	968	968	NUM
ejpam-5118	287	18	965	965	NUM
ejpam-5118	287	19	6	6	NUM
ejpam-5118	287	20	.	.	PUNCT
ejpam-5118	288	1	isomorphisms	isomorphism	NOUN
ejpam-5118	288	2	of	of	ADP
ejpam-5118	288	3	central	central	ADJ
ejpam-5118	288	4	extensions	extension	NOUN
ejpam-5118	288	5	with	with	ADP
ejpam-5118	288	6	isomorphic	isomorphic	ADJ
ejpam-5118	288	7	factors	factor	NOUN
ejpam-5118	288	8	group	group	NOUN
ejpam-5118	288	9	definition	definition	NOUN
ejpam-5118	288	10	6.1	6.1	NUM
ejpam-5118	288	11	.	.	PUNCT
ejpam-5118	289	1	let	let	VERB
ejpam-5118	289	2	g2	g2	PROPN
ejpam-5118	289	3	be	be	AUX
ejpam-5118	289	4	a	a	DET
ejpam-5118	289	5	group	group	NOUN
ejpam-5118	289	6	which	which	PRON
ejpam-5118	289	7	acts	act	VERB
ejpam-5118	289	8	trivially	trivially	ADV
ejpam-5118	289	9	on	on	ADP
ejpam-5118	289	10	an	an	DET
ejpam-5118	289	11	abelian	abelian	ADJ
ejpam-5118	289	12	group	group	NOUN
ejpam-5118	289	13	g1	g1	PROPN
ejpam-5118	289	14	.	.	PUNCT
ejpam-5118	290	1	let	let	VERB
ejpam-5118	290	2	1	1	NUM
ejpam-5118	290	3	≤	≤	NUM
ejpam-5118	290	4	i	i	PRON
ejpam-5118	290	5	≤	≤	ADV
ejpam-5118	290	6	2	2	NUM
ejpam-5118	290	7	,	,	PUNCT
ejpam-5118	290	8	the	the	DET
ejpam-5118	290	9	groups	group	NOUN
ejpam-5118	290	10	g1	g1	VERB
ejpam-5118	290	11	×	×	PROPN
ejpam-5118	290	12	ε1	ε1	PROPN
ejpam-5118	290	13	g2	g2	PROPN
ejpam-5118	290	14	and	and	CCONJ
ejpam-5118	290	15	g1	g1	PROPN
ejpam-5118	290	16	×	×	PROPN
ejpam-5118	290	17	ε2	ε2	PROPN
ejpam-5118	290	18	g2	g2	PROPN
ejpam-5118	290	19	are	be	AUX
ejpam-5118	290	20	called	call	VERB
ejpam-5118	290	21	(	(	PUNCT
ejpam-5118	290	22	gi)-isomorphic	gi)-isomorphic	ADJ
ejpam-5118	290	23	if	if	SCONJ
ejpam-5118	290	24	there	there	PRON
ejpam-5118	290	25	exists	exist	VERB
ejpam-5118	290	26	an	an	DET
ejpam-5118	290	27	isomorphism	isomorphism	NOUN
ejpam-5118	290	28	φ	φ	NOUN
ejpam-5118	290	29	=	=	SYM
ejpam-5118	290	30	(	(	PUNCT
ejpam-5118	290	31	φ11	φ11	NUM
ejpam-5118	290	32	φ12	φ12	ADJ
ejpam-5118	290	33	φ21	φ21	NOUN
ejpam-5118	290	34	φ22	φ22	NOUN
ejpam-5118	290	35	)	)	PUNCT
ejpam-5118	290	36	between	between	ADP
ejpam-5118	290	37	them	they	PRON
ejpam-5118	290	38	such	such	ADJ
ejpam-5118	290	39	that	that	DET
ejpam-5118	290	40	φii	φii	NOUN
ejpam-5118	291	1	=	=	SYM
ejpam-5118	291	2	1	1	X
ejpam-5118	291	3	.	.	PUNCT
ejpam-5118	291	4	proposition	proposition	NOUN
ejpam-5118	291	5	6.1	6.1	NUM
ejpam-5118	291	6	.	.	PUNCT
ejpam-5118	292	1	let	let	VERB
ejpam-5118	292	2	g2	g2	PROPN
ejpam-5118	292	3	be	be	AUX
ejpam-5118	292	4	an	an	DET
ejpam-5118	292	5	abelian	abelian	ADJ
ejpam-5118	292	6	group	group	NOUN
ejpam-5118	292	7	and	and	CCONJ
ejpam-5118	292	8	suppose	suppose	VERB
ejpam-5118	292	9	that	that	SCONJ
ejpam-5118	292	10	the	the	DET
ejpam-5118	292	11	groups	group	NOUN
ejpam-5118	292	12	g1	g1	VERB
ejpam-5118	292	13	×	×	PROPN
ejpam-5118	292	14	ε1	ε1	PROPN
ejpam-5118	292	15	g2	g2	PROPN
ejpam-5118	292	16	and	and	CCONJ
ejpam-5118	292	17	g1×	g1×	NOUN
ejpam-5118	292	18	ε2	ε2	PROPN
ejpam-5118	292	19	g2	g2	PROPN
ejpam-5118	292	20	are	be	AUX
ejpam-5118	292	21	(	(	PUNCT
ejpam-5118	292	22	g2)-isomorphic	g2)-isomorphic	PROPN
ejpam-5118	292	23	.	.	PUNCT
ejpam-5118	293	1	then	then	ADV
ejpam-5118	293	2	,	,	PUNCT
ejpam-5118	293	3	there	there	PRON
ejpam-5118	293	4	exist	exist	VERB
ejpam-5118	293	5	an	an	DET
ejpam-5118	293	6	ε1	ε1	PROPN
ejpam-5118	293	7	-	-	PUNCT
ejpam-5118	293	8	endomorphism	endomorphism	PROPN
ejpam-5118	293	9	σ	σ	NOUN
ejpam-5118	293	10	of	of	ADP
ejpam-5118	293	11	g1	g1	PROPN
ejpam-5118	293	12	,	,	PUNCT
ejpam-5118	293	13	an	an	DET
ejpam-5118	293	14	injective	injective	ADJ
ejpam-5118	293	15	map	map	NOUN
ejpam-5118	293	16	η	η	PROPN
ejpam-5118	293	17	:	:	PUNCT
ejpam-5118	293	18	g2	g2	PROPN
ejpam-5118	293	19	→	→	SYM
ejpam-5118	293	20	g1	g1	PROPN
ejpam-5118	293	21	and	and	CCONJ
ejpam-5118	293	22	an	an	DET
ejpam-5118	293	23	epimorphism	epimorphism	NOUN
ejpam-5118	293	24	δ	δ	NOUN
ejpam-5118	293	25	:	:	PUNCT
ejpam-5118	293	26	g1	g1	PROPN
ejpam-5118	293	27	→	→	PUNCT
ejpam-5118	293	28	g2	g2	PROPN
ejpam-5118	293	29	such	such	ADJ
ejpam-5118	293	30	that	that	PRON
ejpam-5118	293	31	:	:	PUNCT
ejpam-5118	293	32	(	(	PUNCT
ejpam-5118	293	33	i	i	NOUN
ejpam-5118	293	34	)	)	PUNCT
ejpam-5118	294	1	ε−1	ε−1	PROPN
ejpam-5118	294	2	2	2	NUM
ejpam-5118	294	3	◦	◦	NOUN
ejpam-5118	294	4	(	(	PUNCT
ejpam-5118	294	5	δ	δ	PROPN
ejpam-5118	294	6	×	×	PROPN
ejpam-5118	294	7	δ	δ	PROPN
ejpam-5118	294	8	)	)	PUNCT
ejpam-5118	295	1	=	=	PUNCT
ejpam-5118	295	2	ψσ	ψσ	ADP
ejpam-5118	295	3	∈	∈	PROPN
ejpam-5118	295	4	b2(g1	b2(g1	NOUN
ejpam-5118	295	5	,	,	PUNCT
ejpam-5118	295	6	g1	g1	PROPN
ejpam-5118	295	7	)	)	PUNCT
ejpam-5118	295	8	,	,	PUNCT
ejpam-5118	295	9	im(ε1	im(ε1	PROPN
ejpam-5118	295	10	)	)	PUNCT
ejpam-5118	295	11	≤	≤	PROPN
ejpam-5118	295	12	ker(δ	ker(δ	PROPN
ejpam-5118	295	13	)	)	PUNCT
ejpam-5118	295	14	,	,	PUNCT
ejpam-5118	295	15	(	(	PUNCT
ejpam-5118	295	16	ii	ii	NOUN
ejpam-5118	295	17	)	)	PUNCT
ejpam-5118	295	18	σ	σ	PROPN
ejpam-5118	295	19	◦	◦	NOUN
ejpam-5118	295	20	ε1	ε1	NOUN
ejpam-5118	295	21	=	=	PUNCT
ejpam-5118	295	22	ψη	ψη	PART
ejpam-5118	295	23	∈	∈	PROPN
ejpam-5118	295	24	b2(g2	b2(g2	ADV
ejpam-5118	295	25	,	,	PUNCT
ejpam-5118	295	26	g1	g1	PROPN
ejpam-5118	295	27	)	)	PUNCT
ejpam-5118	295	28	.	.	PUNCT
ejpam-5118	296	1	proof	proof	NOUN
ejpam-5118	296	2	.	.	PUNCT
ejpam-5118	297	1	let	let	VERB
ejpam-5118	297	2	φ	φ	PROPN
ejpam-5118	297	3	=	=	SYM
ejpam-5118	297	4	(	(	PUNCT
ejpam-5118	297	5	φ11	φ11	NUM
ejpam-5118	297	6	φ12	φ12	ADJ
ejpam-5118	297	7	φ21	φ21	NOUN
ejpam-5118	297	8	φ22	φ22	NOUN
ejpam-5118	297	9	)	)	PUNCT
ejpam-5118	297	10	be	be	AUX
ejpam-5118	297	11	a	a	DET
ejpam-5118	297	12	(	(	PUNCT
ejpam-5118	297	13	g2)-isomorphism	g2)-isomorphism	NOUN
ejpam-5118	297	14	from	from	ADP
ejpam-5118	297	15	g1	g1	PROPN
ejpam-5118	297	16	×	×	PROPN
ejpam-5118	297	17	ε1	ε1	PROPN
ejpam-5118	297	18	g2	g2	PROPN
ejpam-5118	297	19	to	to	PART
ejpam-5118	297	20	g1	g1	VERB
ejpam-5118	297	21	×	×	PROPN
ejpam-5118	297	22	ε2	ε2	PROPN
ejpam-5118	297	23	g2	g2	PROPN
ejpam-5118	297	24	.	.	PUNCT
ejpam-5118	298	1	so	so	ADV
ejpam-5118	298	2	φ22	φ22	NOUN
ejpam-5118	298	3	=	=	SYM
ejpam-5118	298	4	1	1	NUM
ejpam-5118	298	5	,	,	PUNCT
ejpam-5118	298	6	and	and	CCONJ
ejpam-5118	298	7	therefore	therefore	ADV
ejpam-5118	298	8	we	we	PRON
ejpam-5118	298	9	can	can	AUX
ejpam-5118	298	10	show	show	VERB
ejpam-5118	298	11	easily	easily	ADV
ejpam-5118	298	12	that	that	SCONJ
ejpam-5118	298	13	φ21	φ21	NOUN
ejpam-5118	298	14	is	be	AUX
ejpam-5118	298	15	surjective	surjective	ADJ
ejpam-5118	298	16	and	and	CCONJ
ejpam-5118	298	17	φ12	φ12	NOUN
ejpam-5118	298	18	is	be	AUX
ejpam-5118	298	19	injective	injective	ADJ
ejpam-5118	298	20	.	.	PUNCT
ejpam-5118	299	1	hence	hence	ADV
ejpam-5118	299	2	,	,	PUNCT
ejpam-5118	299	3	by	by	ADP
ejpam-5118	299	4	proposition	proposition	NOUN
ejpam-5118	299	5	3.1	3.1	NUM
ejpam-5118	299	6	,	,	PUNCT
ejpam-5118	299	7	the	the	DET
ejpam-5118	299	8	desired	desire	VERB
ejpam-5118	299	9	conditions	condition	NOUN
ejpam-5118	299	10	follows	follow	VERB
ejpam-5118	299	11	directly	directly	ADV
ejpam-5118	299	12	by	by	ADP
ejpam-5118	299	13	taking	take	VERB
ejpam-5118	299	14	σ	σ	NOUN
ejpam-5118	299	15	=	=	SYM
ejpam-5118	299	16	φ11	φ11	NOUN
ejpam-5118	299	17	,	,	PUNCT
ejpam-5118	299	18	δ	δ	NOUN
ejpam-5118	299	19	=	=	SYM
ejpam-5118	299	20	φ21	φ21	NOUN
ejpam-5118	299	21	and	and	CCONJ
ejpam-5118	299	22	η	η	PROPN
ejpam-5118	299	23	=	=	PROPN
ejpam-5118	299	24	φ12	φ12	PROPN
ejpam-5118	299	25	.	.	PUNCT
ejpam-5118	300	1	note	note	VERB
ejpam-5118	300	2	that	that	SCONJ
ejpam-5118	300	3	if	if	SCONJ
ejpam-5118	300	4	g2	g2	PROPN
ejpam-5118	300	5	is	be	AUX
ejpam-5118	300	6	non	non	ADJ
ejpam-5118	300	7	-	-	ADJ
ejpam-5118	300	8	abelian	abelian	ADJ
ejpam-5118	300	9	,	,	PUNCT
ejpam-5118	300	10	then	then	ADV
ejpam-5118	300	11	the	the	DET
ejpam-5118	300	12	condition	condition	NOUN
ejpam-5118	300	13	δ	δ	PROPN
ejpam-5118	300	14	∈	∈	PROPN
ejpam-5118	300	15	epi(g1	epi(g1	PROPN
ejpam-5118	300	16	,	,	PUNCT
ejpam-5118	300	17	g2	g2	PROPN
ejpam-5118	300	18	)	)	PUNCT
ejpam-5118	300	19	implies	imply	VERB
ejpam-5118	300	20	that	that	SCONJ
ejpam-5118	300	21	δ	δ	PROPN
ejpam-5118	300	22	=	=	SYM
ejpam-5118	300	23	1	1	X
ejpam-5118	300	24	.	.	PUNCT
ejpam-5118	300	25	therefore	therefore	ADV
ejpam-5118	300	26	,	,	PUNCT
ejpam-5118	300	27	the	the	DET
ejpam-5118	300	28	previous	previous	ADJ
ejpam-5118	300	29	result	result	NOUN
ejpam-5118	300	30	becomes	become	VERB
ejpam-5118	300	31	a	a	DET
ejpam-5118	300	32	direct	direct	ADJ
ejpam-5118	300	33	consequence	consequence	NOUN
ejpam-5118	300	34	of	of	ADP
ejpam-5118	300	35	proposition	proposition	NOUN
ejpam-5118	300	36	3.2	3.2	NUM
ejpam-5118	300	37	.	.	PUNCT
ejpam-5118	301	1	corollary	corollary	ADJ
ejpam-5118	301	2	6.1	6.1	NUM
ejpam-5118	301	3	.	.	PUNCT
ejpam-5118	301	4	suppose	suppose	VERB
ejpam-5118	301	5	that	that	SCONJ
ejpam-5118	301	6	g1	g1	PROPN
ejpam-5118	301	7	and	and	CCONJ
ejpam-5118	301	8	g2	g2	PROPN
ejpam-5118	301	9	are	be	AUX
ejpam-5118	301	10	two	two	NUM
ejpam-5118	301	11	finite	finite	ADJ
ejpam-5118	301	12	abelian	abelian	ADJ
ejpam-5118	301	13	groups	group	NOUN
ejpam-5118	301	14	with	with	ADP
ejpam-5118	301	15	the	the	DET
ejpam-5118	301	16	same	same	ADJ
ejpam-5118	301	17	order	order	NOUN
ejpam-5118	301	18	.	.	PUNCT
ejpam-5118	302	1	the	the	DET
ejpam-5118	302	2	groups	group	NOUN
ejpam-5118	302	3	g1	g1	VERB
ejpam-5118	302	4	×	×	PROPN
ejpam-5118	302	5	ε1	ε1	PROPN
ejpam-5118	302	6	g2	g2	PROPN
ejpam-5118	302	7	and	and	CCONJ
ejpam-5118	302	8	g1	g1	PROPN
ejpam-5118	302	9	×	×	PROPN
ejpam-5118	302	10	ε2	ε2	PROPN
ejpam-5118	302	11	g2	g2	PROPN
ejpam-5118	302	12	are	be	AUX
ejpam-5118	302	13	(	(	PUNCT
ejpam-5118	302	14	g2)-isomorphic	g2)-isomorphic	ADJ
ejpam-5118	302	15	if	if	SCONJ
ejpam-5118	302	16	and	and	CCONJ
ejpam-5118	302	17	only	only	ADV
ejpam-5118	302	18	if	if	SCONJ
ejpam-5118	302	19	ε1	ε1	PROPN
ejpam-5118	302	20	=	=	SYM
ejpam-5118	302	21	1	1	NUM
ejpam-5118	302	22	and	and	CCONJ
ejpam-5118	302	23	there	there	PRON
ejpam-5118	302	24	exists	exist	VERB
ejpam-5118	302	25	an	an	DET
ejpam-5118	302	26	isomorphism	isomorphism	NOUN
ejpam-5118	302	27	δ	δ	NOUN
ejpam-5118	302	28	:	:	PUNCT
ejpam-5118	302	29	g1	g1	PROPN
ejpam-5118	302	30	→	→	PUNCT
ejpam-5118	302	31	g2	g2	PROPN
ejpam-5118	302	32	such	such	ADJ
ejpam-5118	302	33	that	that	SCONJ
ejpam-5118	302	34	ε−1	ε−1	PROPN
ejpam-5118	302	35	2	2	NUM
ejpam-5118	302	36	◦	◦	NOUN
ejpam-5118	302	37	(	(	PUNCT
ejpam-5118	302	38	δ	δ	PROPN
ejpam-5118	302	39	×	×	PROPN
ejpam-5118	302	40	δ	δ	PROPN
ejpam-5118	302	41	)	)	PUNCT
ejpam-5118	302	42	∈	∈	PROPN
ejpam-5118	302	43	b2(g1	b2(g1	NOUN
ejpam-5118	302	44	,	,	PUNCT
ejpam-5118	302	45	g1	g1	NOUN
ejpam-5118	302	46	)	)	PUNCT
ejpam-5118	302	47	.	.	PUNCT
ejpam-5118	303	1	proof	proof	NOUN
ejpam-5118	303	2	.	.	PUNCT
ejpam-5118	304	1	indeed	indeed	ADV
ejpam-5118	304	2	,	,	PUNCT
ejpam-5118	304	3	suppose	suppose	VERB
ejpam-5118	304	4	that	that	SCONJ
ejpam-5118	304	5	the	the	DET
ejpam-5118	304	6	groups	group	NOUN
ejpam-5118	304	7	g1×	g1×	NOUN
ejpam-5118	304	8	ε1	ε1	VERB
ejpam-5118	304	9	g2	g2	PROPN
ejpam-5118	304	10	and	and	CCONJ
ejpam-5118	304	11	g1×	g1×	NOUN
ejpam-5118	304	12	ε2	ε2	PROPN
ejpam-5118	304	13	g2	g2	PROPN
ejpam-5118	304	14	are	be	AUX
ejpam-5118	304	15	(	(	PUNCT
ejpam-5118	304	16	g2)-isomorphic	g2)-isomorphic	PROPN
ejpam-5118	304	17	.	.	PUNCT
ejpam-5118	304	18	by	by	ADP
ejpam-5118	304	19	the	the	DET
ejpam-5118	304	20	previous	previous	ADJ
ejpam-5118	304	21	proposition	proposition	NOUN
ejpam-5118	304	22	,	,	PUNCT
ejpam-5118	304	23	there	there	PRON
ejpam-5118	304	24	exists	exist	VERB
ejpam-5118	304	25	an	an	DET
ejpam-5118	304	26	epimorphism	epimorphism	NOUN
ejpam-5118	304	27	δ	δ	NOUN
ejpam-5118	304	28	:	:	PUNCT
ejpam-5118	304	29	g1	g1	PROPN
ejpam-5118	304	30	→	→	PUNCT
ejpam-5118	304	31	g2	g2	PROPN
ejpam-5118	304	32	such	such	ADJ
ejpam-5118	304	33	that	that	SCONJ
ejpam-5118	304	34	im(ε1	im(ε1	NOUN
ejpam-5118	304	35	)	)	PUNCT
ejpam-5118	304	36	≤	≤	PROPN
ejpam-5118	304	37	ker(δ	ker(δ	PROPN
ejpam-5118	304	38	)	)	PUNCT
ejpam-5118	304	39	and	and	CCONJ
ejpam-5118	304	40	ε−1	ε−1	PROPN
ejpam-5118	304	41	2	2	NUM
ejpam-5118	304	42	◦	◦	NOUN
ejpam-5118	304	43	(	(	PUNCT
ejpam-5118	304	44	δ×δ	δ×δ	ADJ
ejpam-5118	304	45	)	)	PUNCT
ejpam-5118	304	46	∈	∈	PROPN
ejpam-5118	304	47	b2(g1	b2(g1	NOUN
ejpam-5118	304	48	,	,	PUNCT
ejpam-5118	304	49	g1	g1	NOUN
ejpam-5118	304	50	)	)	PUNCT
ejpam-5118	304	51	.	.	PUNCT
ejpam-5118	305	1	but	but	CCONJ
ejpam-5118	305	2	δ	δ	PROPN
ejpam-5118	305	3	is	be	AUX
ejpam-5118	305	4	in	in	ADP
ejpam-5118	305	5	fact	fact	NOUN
ejpam-5118	305	6	an	an	DET
ejpam-5118	305	7	isomorphism	isomorphism	NOUN
ejpam-5118	305	8	by	by	ADP
ejpam-5118	305	9	the	the	DET
ejpam-5118	305	10	assumption	assumption	NOUN
ejpam-5118	305	11	,	,	PUNCT
ejpam-5118	305	12	so	so	CCONJ
ejpam-5118	305	13	we	we	PRON
ejpam-5118	305	14	must	must	AUX
ejpam-5118	305	15	have	have	AUX
ejpam-5118	305	16	ε1	ε1	VERB
ejpam-5118	305	17	=	=	SYM
ejpam-5118	305	18	1	1	X
ejpam-5118	305	19	.	.	PUNCT
ejpam-5118	306	1	conversely	conversely	ADV
ejpam-5118	306	2	,	,	PUNCT
ejpam-5118	306	3	since	since	SCONJ
ejpam-5118	306	4	ε−1	ε−1	PROPN
ejpam-5118	306	5	2	2	NUM
ejpam-5118	306	6	◦	◦	NOUN
ejpam-5118	306	7	(	(	PUNCT
ejpam-5118	306	8	δ×	δ×	PROPN
ejpam-5118	306	9	δ	δ	PROPN
ejpam-5118	306	10	)	)	PUNCT
ejpam-5118	306	11	∈	∈	PROPN
ejpam-5118	306	12	b2(g1	b2(g1	NOUN
ejpam-5118	306	13	,	,	PUNCT
ejpam-5118	306	14	g1	g1	PROPN
ejpam-5118	306	15	)	)	PUNCT
ejpam-5118	306	16	,	,	PUNCT
ejpam-5118	306	17	it	it	PRON
ejpam-5118	306	18	follows	follow	VERB
ejpam-5118	306	19	that	that	SCONJ
ejpam-5118	306	20	there	there	PRON
ejpam-5118	306	21	exists	exist	VERB
ejpam-5118	306	22	a	a	DET
ejpam-5118	306	23	map	map	NOUN
ejpam-5118	306	24	σ	σ	NOUN
ejpam-5118	306	25	:	:	PUNCT
ejpam-5118	306	26	g1	g1	PROPN
ejpam-5118	306	27	→	→	SYM
ejpam-5118	306	28	g1	g1	VERB
ejpam-5118	306	29	such	such	ADJ
ejpam-5118	306	30	that	that	PRON
ejpam-5118	306	31	ε−1	ε−1	PROPN
ejpam-5118	306	32	2	2	NUM
ejpam-5118	306	33	(	(	PUNCT
ejpam-5118	306	34	δ(x	δ(x	NOUN
ejpam-5118	306	35	)	)	PUNCT
ejpam-5118	306	36	,	,	PUNCT
ejpam-5118	306	37	δ(x′	δ(x′	NUM
ejpam-5118	306	38	)	)	PUNCT
ejpam-5118	306	39	)	)	PUNCT
ejpam-5118	307	1	=	=	SYM
ejpam-5118	307	2	σ(x)σ(x′)σ(xx′)−1	σ(x)σ(x′)σ(xx′)−1	PROPN
ejpam-5118	307	3	for	for	ADP
ejpam-5118	307	4	all	all	DET
ejpam-5118	307	5	x	x	NOUN
ejpam-5118	307	6	,	,	PUNCT
ejpam-5118	307	7	x′	x′	PROPN
ejpam-5118	307	8	∈	∈	PROPN
ejpam-5118	307	9	g1	g1	PROPN
ejpam-5118	307	10	.	.	PUNCT
ejpam-5118	308	1	let	let	VERB
ejpam-5118	308	2	δ′	δ′	NOUN
ejpam-5118	308	3	be	be	AUX
ejpam-5118	308	4	the	the	DET
ejpam-5118	308	5	inverse	inverse	NOUN
ejpam-5118	308	6	of	of	ADP
ejpam-5118	308	7	δ	δ	PROPN
ejpam-5118	308	8	.	.	PUNCT
ejpam-5118	309	1	by	by	ADP
ejpam-5118	309	2	the	the	DET
ejpam-5118	309	3	normalization	normalization	NOUN
ejpam-5118	309	4	condition	condition	NOUN
ejpam-5118	309	5	,	,	PUNCT
ejpam-5118	309	6	we	we	PRON
ejpam-5118	309	7	have	have	VERB
ejpam-5118	309	8	σ(1	σ(1	NOUN
ejpam-5118	309	9	)	)	PUNCT
ejpam-5118	310	1	=	=	SYM
ejpam-5118	310	2	1	1	X
ejpam-5118	310	3	.	.	PUNCT
ejpam-5118	311	1	so	so	ADV
ejpam-5118	311	2	,	,	PUNCT
ejpam-5118	311	3	the	the	DET
ejpam-5118	311	4	bijection	bijection	PROPN
ejpam-5118	311	5	φ	φ	NOUN
ejpam-5118	311	6	defined	define	VERB
ejpam-5118	311	7	by	by	ADP
ejpam-5118	311	8	φ(x	φ(x	PROPN
ejpam-5118	311	9	,	,	PUNCT
ejpam-5118	311	10	y	y	NOUN
ejpam-5118	311	11	)	)	PUNCT
ejpam-5118	311	12	=	=	SYM
ejpam-5118	311	13	(	(	PUNCT
ejpam-5118	311	14	σ(x)δ′(y	σ(x)δ′(y	PROPN
ejpam-5118	311	15	)	)	PUNCT
ejpam-5118	311	16	,	,	PUNCT
ejpam-5118	311	17	δ(x	δ(x	NOUN
ejpam-5118	311	18	)	)	PUNCT
ejpam-5118	311	19	)	)	PUNCT
ejpam-5118	311	20	is	be	AUX
ejpam-5118	311	21	clearly	clearly	ADV
ejpam-5118	311	22	an	an	DET
ejpam-5118	311	23	isomorphism	isomorphism	NOUN
ejpam-5118	311	24	.	.	PUNCT
ejpam-5118	312	1	as	as	SCONJ
ejpam-5118	312	2	required	require	VERB
ejpam-5118	312	3	.	.	PUNCT
ejpam-5118	313	1	proposition	proposition	NOUN
ejpam-5118	313	2	6.2	6.2	NUM
ejpam-5118	313	3	.	.	PUNCT
ejpam-5118	314	1	let	let	VERB
ejpam-5118	314	2	g2	g2	PROPN
ejpam-5118	314	3	be	be	AUX
ejpam-5118	314	4	a	a	DET
ejpam-5118	314	5	group	group	NOUN
ejpam-5118	314	6	such	such	ADJ
ejpam-5118	314	7	that	that	SCONJ
ejpam-5118	314	8	the	the	DET
ejpam-5118	314	9	equivalence	equivalence	NOUN
ejpam-5118	314	10	relation	relation	NOUN
ejpam-5118	314	11	(	(	PUNCT
ejpam-5118	314	12	∼	∼	NOUN
ejpam-5118	314	13	)	)	PUNCT
ejpam-5118	314	14	is	be	AUX
ejpam-5118	314	15	trivial	trivial	ADJ
ejpam-5118	314	16	on	on	ADP
ejpam-5118	314	17	z2(g2	z2(g2	NUM
ejpam-5118	314	18	,	,	PUNCT
ejpam-5118	314	19	g2	g2	PROPN
ejpam-5118	314	20	)	)	PUNCT
ejpam-5118	314	21	.	.	PUNCT
ejpam-5118	315	1	suppose	suppose	VERB
ejpam-5118	315	2	that	that	SCONJ
ejpam-5118	315	3	the	the	DET
ejpam-5118	315	4	groups	group	NOUN
ejpam-5118	315	5	g1	g1	VERB
ejpam-5118	315	6	×	×	PROPN
ejpam-5118	315	7	ε1	ε1	PROPN
ejpam-5118	315	8	g2	g2	PROPN
ejpam-5118	315	9	and	and	CCONJ
ejpam-5118	315	10	g1	g1	PROPN
ejpam-5118	315	11	×	×	PROPN
ejpam-5118	315	12	ε2	ε2	PROPN
ejpam-5118	315	13	g2	g2	PROPN
ejpam-5118	315	14	are	be	AUX
ejpam-5118	315	15	(	(	PUNCT
ejpam-5118	315	16	g1)-isomorphic	g1)-isomorphic	ADJ
ejpam-5118	315	17	.	.	PUNCT
ejpam-5118	316	1	then	then	ADV
ejpam-5118	316	2	,	,	PUNCT
ejpam-5118	316	3	there	there	PRON
ejpam-5118	316	4	exist	exist	VERB
ejpam-5118	316	5	ρ	ρ	PROPN
ejpam-5118	316	6	∈	∈	PROPN
ejpam-5118	316	7	end(g2	end(g2	X
ejpam-5118	316	8	)	)	PUNCT
ejpam-5118	316	9	,	,	PUNCT
ejpam-5118	316	10	a	a	DET
ejpam-5118	316	11	surjective	surjective	ADJ
ejpam-5118	316	12	map	map	NOUN
ejpam-5118	316	13	η	η	PROPN
ejpam-5118	316	14	:	:	PUNCT
ejpam-5118	316	15	g2	g2	PROPN
ejpam-5118	316	16	→	→	SYM
ejpam-5118	316	17	g1	g1	PROPN
ejpam-5118	316	18	and	and	CCONJ
ejpam-5118	316	19	a	a	DET
ejpam-5118	316	20	monomorphism	monomorphism	NOUN
ejpam-5118	316	21	δ	δ	NOUN
ejpam-5118	316	22	:	:	PUNCT
ejpam-5118	316	23	g1	g1	PROPN
ejpam-5118	316	24	→	→	PUNCT
ejpam-5118	316	25	g2	g2	PROPN
ejpam-5118	316	26	such	such	ADJ
ejpam-5118	316	27	that	that	SCONJ
ejpam-5118	316	28	(	(	PUNCT
ejpam-5118	316	29	i	i	NOUN
ejpam-5118	316	30	)	)	PUNCT
ejpam-5118	316	31	ε1	ε1	PROPN
ejpam-5118	316	32	=	=	SYM
ejpam-5118	316	33	1	1	NUM
ejpam-5118	316	34	,	,	PUNCT
ejpam-5118	316	35	(	(	PUNCT
ejpam-5118	316	36	ii	ii	NOUN
ejpam-5118	316	37	)	)	PUNCT
ejpam-5118	316	38	ε2	ε2	ADJ
ejpam-5118	316	39	◦	◦	NOUN
ejpam-5118	316	40	(	(	PUNCT
ejpam-5118	316	41	δ	δ	PROPN
ejpam-5118	316	42	×	×	PROPN
ejpam-5118	316	43	δ	δ	PROPN
ejpam-5118	316	44	)	)	PUNCT
ejpam-5118	316	45	=	=	SYM
ejpam-5118	316	46	1	1	NUM
ejpam-5118	316	47	and	and	CCONJ
ejpam-5118	316	48	n.	n.	PROPN
ejpam-5118	316	49	snanou	snanou	PROPN
ejpam-5118	316	50	/	/	SYM
ejpam-5118	316	51	eur	eur	PROPN
ejpam-5118	316	52	.	.	PUNCT
ejpam-5118	317	1	j.	j.	PROPN
ejpam-5118	317	2	pure	pure	PROPN
ejpam-5118	317	3	appl	appl	PROPN
ejpam-5118	317	4	.	.	PROPN
ejpam-5118	317	5	math	math	PROPN
ejpam-5118	317	6	,	,	PUNCT
ejpam-5118	317	7	17	17	NUM
ejpam-5118	317	8	(	(	PUNCT
ejpam-5118	317	9	2	2	NUM
ejpam-5118	317	10	)	)	PUNCT
ejpam-5118	317	11	(	(	PUNCT
ejpam-5118	317	12	2024	2024	NUM
ejpam-5118	317	13	)	)	PUNCT
ejpam-5118	317	14	,	,	PUNCT
ejpam-5118	317	15	956	956	NUM
ejpam-5118	317	16	-	-	SYM
ejpam-5118	317	17	968	968	NUM
ejpam-5118	317	18	966	966	NUM
ejpam-5118	317	19	(	(	PUNCT
ejpam-5118	317	20	iii	iii	NOUN
ejpam-5118	317	21	)	)	PUNCT
ejpam-5118	317	22	ε−1	ε−1	PROPN
ejpam-5118	317	23	2	2	NUM
ejpam-5118	317	24	◦	◦	NOUN
ejpam-5118	317	25	(	(	PUNCT
ejpam-5118	317	26	ρ×	ρ×	NOUN
ejpam-5118	317	27	ρ	ρ	NOUN
ejpam-5118	317	28	)	)	PUNCT
ejpam-5118	317	29	=	=	PRON
ejpam-5118	317	30	ψη	ψη	PART
ejpam-5118	317	31	∈	∈	PROPN
ejpam-5118	317	32	b2(g2	b2(g2	ADV
ejpam-5118	317	33	,	,	PUNCT
ejpam-5118	317	34	g1	g1	PROPN
ejpam-5118	317	35	)	)	PUNCT
ejpam-5118	317	36	.	.	PUNCT
ejpam-5118	318	1	proof	proof	NOUN
ejpam-5118	318	2	.	.	PUNCT
ejpam-5118	319	1	let	let	VERB
ejpam-5118	319	2	φ	φ	PROPN
ejpam-5118	319	3	=	=	SYM
ejpam-5118	319	4	(	(	PUNCT
ejpam-5118	319	5	1	1	NUM
ejpam-5118	319	6	φ12	φ12	NOUN
ejpam-5118	319	7	φ21	φ21	NOUN
ejpam-5118	319	8	φ22	φ22	NOUN
ejpam-5118	319	9	)	)	PUNCT
ejpam-5118	319	10	be	be	AUX
ejpam-5118	319	11	an	an	DET
ejpam-5118	319	12	isomorphism	isomorphism	NOUN
ejpam-5118	319	13	from	from	ADP
ejpam-5118	319	14	g1	g1	PROPN
ejpam-5118	319	15	×	×	PROPN
ejpam-5118	319	16	ε1	ε1	PROPN
ejpam-5118	319	17	g2	g2	PROPN
ejpam-5118	319	18	to	to	PART
ejpam-5118	319	19	g1	g1	VERB
ejpam-5118	319	20	×	×	PROPN
ejpam-5118	319	21	ε2	ε2	PROPN
ejpam-5118	319	22	g2	g2	PROPN
ejpam-5118	319	23	.	.	PUNCT
ejpam-5118	320	1	hence	hence	ADV
ejpam-5118	320	2	,	,	PUNCT
ejpam-5118	320	3	by	by	ADP
ejpam-5118	320	4	taking	take	VERB
ejpam-5118	320	5	ρ	ρ	NOUN
ejpam-5118	320	6	=	=	SYM
ejpam-5118	320	7	φ22	φ22	PROPN
ejpam-5118	320	8	,	,	PUNCT
ejpam-5118	320	9	η	η	PROPN
ejpam-5118	320	10	=	=	SYM
ejpam-5118	320	11	φ12	φ12	PROPN
ejpam-5118	320	12	and	and	CCONJ
ejpam-5118	320	13	δ	δ	NOUN
ejpam-5118	320	14	=	=	NOUN
ejpam-5118	320	15	φ21	φ21	PROPN
ejpam-5118	320	16	,	,	PUNCT
ejpam-5118	320	17	the	the	DET
ejpam-5118	320	18	conditions	condition	NOUN
ejpam-5118	320	19	(	(	PUNCT
ejpam-5118	320	20	ii	ii	NOUN
ejpam-5118	320	21	)	)	PUNCT
ejpam-5118	320	22	and	and	CCONJ
ejpam-5118	320	23	(	(	PUNCT
ejpam-5118	320	24	iii	iii	X
ejpam-5118	320	25	)	)	PUNCT
ejpam-5118	320	26	follow	follow	VERB
ejpam-5118	320	27	directly	directly	ADV
ejpam-5118	320	28	from	from	ADP
ejpam-5118	320	29	proposition	proposition	NOUN
ejpam-5118	320	30	3.1	3.1	NUM
ejpam-5118	320	31	.	.	PUNCT
ejpam-5118	320	32	notice	notice	VERB
ejpam-5118	320	33	that	that	SCONJ
ejpam-5118	320	34	φ(x	φ(x	PROPN
ejpam-5118	320	35	,	,	PUNCT
ejpam-5118	320	36	y	y	NOUN
ejpam-5118	320	37	)	)	PUNCT
ejpam-5118	320	38	=	=	SYM
ejpam-5118	320	39	(	(	PUNCT
ejpam-5118	320	40	φ12(y)ε2(φ21(x	φ12(y)ε2(φ21(x	NOUN
ejpam-5118	320	41	)	)	PUNCT
ejpam-5118	320	42	,	,	PUNCT
ejpam-5118	320	43	φ22(y	φ22(y	NOUN
ejpam-5118	320	44	)	)	PUNCT
ejpam-5118	320	45	)	)	PUNCT
ejpam-5118	320	46	,	,	PUNCT
ejpam-5118	320	47	φ21(x)φ22(y	φ21(x)φ22(y	ADJ
ejpam-5118	320	48	)	)	PUNCT
ejpam-5118	320	49	)	)	PUNCT
ejpam-5118	320	50	for	for	ADP
ejpam-5118	320	51	all	all	DET
ejpam-5118	320	52	x	x	PROPN
ejpam-5118	320	53	∈	∈	PROPN
ejpam-5118	320	54	g1	g1	NOUN
ejpam-5118	320	55	,	,	PUNCT
ejpam-5118	320	56	y	y	PROPN
ejpam-5118	320	57	∈	∈	PROPN
ejpam-5118	320	58	g2	g2	PROPN
ejpam-5118	320	59	.	.	PUNCT
ejpam-5118	321	1	so	so	ADV
ejpam-5118	321	2	,	,	PUNCT
ejpam-5118	321	3	φ(x	φ(x	PROPN
ejpam-5118	321	4	,	,	PUNCT
ejpam-5118	321	5	1	1	NUM
ejpam-5118	321	6	)	)	PUNCT
ejpam-5118	321	7	=	=	SYM
ejpam-5118	321	8	(	(	PUNCT
ejpam-5118	321	9	1	1	NUM
ejpam-5118	321	10	,	,	PUNCT
ejpam-5118	321	11	φ21(x	φ21(x	NOUN
ejpam-5118	321	12	)	)	PUNCT
ejpam-5118	321	13	)	)	PUNCT
ejpam-5118	321	14	and	and	CCONJ
ejpam-5118	321	15	then	then	ADV
ejpam-5118	321	16	φ21	φ21	NOUN
ejpam-5118	321	17	is	be	AUX
ejpam-5118	321	18	injective	injective	ADJ
ejpam-5118	321	19	.	.	PUNCT
ejpam-5118	322	1	but	but	CCONJ
ejpam-5118	322	2	,	,	PUNCT
ejpam-5118	322	3	by	by	ADP
ejpam-5118	322	4	the	the	DET
ejpam-5118	322	5	condition	condition	NOUN
ejpam-5118	322	6	(	(	PUNCT
ejpam-5118	322	7	iii	iii	NOUN
ejpam-5118	322	8	)	)	PUNCT
ejpam-5118	322	9	of	of	ADP
ejpam-5118	322	10	proposition	proposition	NOUN
ejpam-5118	322	11	3.1	3.1	NUM
ejpam-5118	322	12	,	,	PUNCT
ejpam-5118	322	13	we	we	PRON
ejpam-5118	322	14	have	have	VERB
ejpam-5118	322	15	im(ε1	im(ε1	NOUN
ejpam-5118	322	16	)	)	PUNCT
ejpam-5118	322	17	≤	≤	NUM
ejpam-5118	322	18	ker(φ21	ker(φ21	NOUN
ejpam-5118	322	19	)	)	PUNCT
ejpam-5118	322	20	,	,	PUNCT
ejpam-5118	322	21	which	which	PRON
ejpam-5118	322	22	implies	imply	VERB
ejpam-5118	322	23	that	that	SCONJ
ejpam-5118	322	24	ε1	ε1	PROPN
ejpam-5118	322	25	=	=	SYM
ejpam-5118	322	26	1	1	X
ejpam-5118	322	27	.	.	PUNCT
ejpam-5118	323	1	on	on	ADP
ejpam-5118	323	2	the	the	DET
ejpam-5118	323	3	other	other	ADJ
ejpam-5118	323	4	hand	hand	NOUN
ejpam-5118	323	5	,	,	PUNCT
ejpam-5118	323	6	let	let	VERB
ejpam-5118	323	7	g	g	PROPN
ejpam-5118	323	8	∈	∈	PROPN
ejpam-5118	323	9	g1	g1	NOUN
ejpam-5118	323	10	,	,	PUNCT
ejpam-5118	323	11	then	then	ADV
ejpam-5118	323	12	there	there	PRON
ejpam-5118	323	13	exists	exist	VERB
ejpam-5118	323	14	(	(	PUNCT
ejpam-5118	323	15	x	x	X
ejpam-5118	323	16	,	,	PUNCT
ejpam-5118	323	17	y	y	NOUN
ejpam-5118	323	18	)	)	PUNCT
ejpam-5118	323	19	∈	∈	PROPN
ejpam-5118	323	20	g1	g1	PROPN
ejpam-5118	323	21	×	×	PROPN
ejpam-5118	323	22	ε1	ε1	PROPN
ejpam-5118	323	23	g2	g2	PROPN
ejpam-5118	323	24	such	such	ADJ
ejpam-5118	323	25	that	that	SCONJ
ejpam-5118	323	26	φ(x	φ(x	PROPN
ejpam-5118	323	27	,	,	PUNCT
ejpam-5118	323	28	y	y	NOUN
ejpam-5118	323	29	)	)	PUNCT
ejpam-5118	323	30	=	=	SYM
ejpam-5118	324	1	(	(	PUNCT
ejpam-5118	324	2	g	g	NOUN
ejpam-5118	324	3	,	,	PUNCT
ejpam-5118	324	4	1	1	NUM
ejpam-5118	324	5	)	)	PUNCT
ejpam-5118	324	6	.	.	PUNCT
ejpam-5118	325	1	this	this	PRON
ejpam-5118	325	2	gives	give	VERB
ejpam-5118	325	3	us	we	PRON
ejpam-5118	325	4	φ12(y)ε2(φ21(x	φ12(y)ε2(φ21(x	NOUN
ejpam-5118	325	5	)	)	PUNCT
ejpam-5118	325	6	,	,	PUNCT
ejpam-5118	325	7	φ21(x	φ21(x	NOUN
ejpam-5118	325	8	−1	−1	NOUN
ejpam-5118	325	9	)	)	PUNCT
ejpam-5118	325	10	)	)	PUNCT
ejpam-5118	326	1	=	=	PUNCT
ejpam-5118	326	2	g.	g.	PROPN
ejpam-5118	327	1	so	so	ADV
ejpam-5118	327	2	the	the	DET
ejpam-5118	327	3	condition	condition	NOUN
ejpam-5118	327	4	(	(	PUNCT
ejpam-5118	327	5	ii	ii	NOUN
ejpam-5118	327	6	)	)	PUNCT
ejpam-5118	327	7	ensures	ensure	VERB
ejpam-5118	327	8	that	that	SCONJ
ejpam-5118	327	9	φ12(y	φ12(y	ADJ
ejpam-5118	327	10	)	)	PUNCT
ejpam-5118	327	11	=	=	SYM
ejpam-5118	327	12	g	g	PROPN
ejpam-5118	327	13	and	and	CCONJ
ejpam-5118	327	14	then	then	ADV
ejpam-5118	327	15	φ12	φ12	PROPN
ejpam-5118	327	16	is	be	AUX
ejpam-5118	327	17	surjective	surjective	ADJ
ejpam-5118	327	18	.	.	PUNCT
ejpam-5118	328	1	as	as	SCONJ
ejpam-5118	328	2	required	require	VERB
ejpam-5118	328	3	.	.	PUNCT
ejpam-5118	329	1	now	now	ADV
ejpam-5118	329	2	,	,	PUNCT
ejpam-5118	329	3	we	we	PRON
ejpam-5118	329	4	derive	derive	VERB
ejpam-5118	329	5	the	the	DET
ejpam-5118	329	6	following	follow	VERB
ejpam-5118	329	7	consequence	consequence	NOUN
ejpam-5118	329	8	.	.	PUNCT
ejpam-5118	330	1	corollary	corollary	ADJ
ejpam-5118	330	2	6.2	6.2	NUM
ejpam-5118	330	3	.	.	PUNCT
ejpam-5118	331	1	further	far	ADV
ejpam-5118	331	2	to	to	ADP
ejpam-5118	331	3	the	the	DET
ejpam-5118	331	4	assumption	assumption	NOUN
ejpam-5118	331	5	of	of	ADP
ejpam-5118	331	6	the	the	DET
ejpam-5118	331	7	previous	previous	ADJ
ejpam-5118	331	8	proposition	proposition	NOUN
ejpam-5118	331	9	,	,	PUNCT
ejpam-5118	331	10	suppose	suppose	VERB
ejpam-5118	331	11	that	that	SCONJ
ejpam-5118	331	12	g1	g1	PROPN
ejpam-5118	331	13	and	and	CCONJ
ejpam-5118	331	14	g2	g2	PROPN
ejpam-5118	331	15	are	be	AUX
ejpam-5118	331	16	two	two	NUM
ejpam-5118	331	17	finite	finite	ADJ
ejpam-5118	331	18	abelian	abelian	ADJ
ejpam-5118	331	19	groups	group	NOUN
ejpam-5118	331	20	with	with	ADP
ejpam-5118	331	21	the	the	DET
ejpam-5118	331	22	same	same	ADJ
ejpam-5118	331	23	order	order	NOUN
ejpam-5118	331	24	.	.	PUNCT
ejpam-5118	332	1	the	the	DET
ejpam-5118	332	2	groups	group	NOUN
ejpam-5118	332	3	g1×	g1×	NOUN
ejpam-5118	332	4	ε1	ε1	VERB
ejpam-5118	332	5	g2	g2	PROPN
ejpam-5118	332	6	and	and	CCONJ
ejpam-5118	332	7	g1×	g1×	NOUN
ejpam-5118	332	8	ε2	ε2	PROPN
ejpam-5118	332	9	g2	g2	PROPN
ejpam-5118	332	10	are	be	AUX
ejpam-5118	332	11	(	(	PUNCT
ejpam-5118	332	12	g1)-isomorphic	g1)-isomorphic	ADJ
ejpam-5118	332	13	if	if	SCONJ
ejpam-5118	332	14	and	and	CCONJ
ejpam-5118	332	15	only	only	ADV
ejpam-5118	332	16	if	if	SCONJ
ejpam-5118	332	17	ε1	ε1	PROPN
ejpam-5118	332	18	=	=	SYM
ejpam-5118	332	19	1	1	NUM
ejpam-5118	332	20	and	and	CCONJ
ejpam-5118	332	21	there	there	PRON
ejpam-5118	332	22	exists	exist	VERB
ejpam-5118	332	23	an	an	DET
ejpam-5118	332	24	isomorphism	isomorphism	NOUN
ejpam-5118	332	25	δ	δ	NOUN
ejpam-5118	332	26	:	:	PUNCT
ejpam-5118	332	27	g1	g1	PROPN
ejpam-5118	332	28	→	→	PUNCT
ejpam-5118	332	29	g2	g2	PROPN
ejpam-5118	332	30	such	such	ADJ
ejpam-5118	332	31	that	that	SCONJ
ejpam-5118	332	32	ε2	ε2	ADJ
ejpam-5118	332	33	◦	◦	NOUN
ejpam-5118	332	34	(	(	PUNCT
ejpam-5118	332	35	δ	δ	PROPN
ejpam-5118	332	36	×	×	PROPN
ejpam-5118	332	37	δ	δ	PROPN
ejpam-5118	332	38	)	)	PUNCT
ejpam-5118	332	39	=	=	SYM
ejpam-5118	333	1	1	1	X
ejpam-5118	333	2	.	.	PUNCT
ejpam-5118	333	3	proof	proof	NOUN
ejpam-5118	333	4	.	.	PUNCT
ejpam-5118	334	1	indeed	indeed	ADV
ejpam-5118	334	2	,	,	PUNCT
ejpam-5118	334	3	using	use	VERB
ejpam-5118	334	4	the	the	DET
ejpam-5118	334	5	assumptions	assumption	NOUN
ejpam-5118	334	6	,	,	PUNCT
ejpam-5118	334	7	the	the	PRON
ejpam-5118	334	8	only	only	ADJ
ejpam-5118	334	9	if	if	SCONJ
ejpam-5118	334	10	direction	direction	NOUN
ejpam-5118	334	11	comes	come	VERB
ejpam-5118	334	12	immediately	immediately	ADV
ejpam-5118	334	13	from	from	ADP
ejpam-5118	334	14	the	the	DET
ejpam-5118	334	15	previous	previous	ADJ
ejpam-5118	334	16	result	result	NOUN
ejpam-5118	334	17	.	.	PUNCT
ejpam-5118	335	1	conversely	conversely	ADV
ejpam-5118	335	2	,	,	PUNCT
ejpam-5118	335	3	let	let	VERB
ejpam-5118	335	4	δ′	δ′	NOUN
ejpam-5118	335	5	be	be	AUX
ejpam-5118	335	6	the	the	DET
ejpam-5118	335	7	inverse	inverse	NOUN
ejpam-5118	335	8	of	of	ADP
ejpam-5118	335	9	δ	δ	PROPN
ejpam-5118	335	10	.	.	PUNCT
ejpam-5118	335	11	define	define	VERB
ejpam-5118	335	12	a	a	DET
ejpam-5118	335	13	bijective	bijective	ADJ
ejpam-5118	335	14	map	map	NOUN
ejpam-5118	335	15	φ	φ	X
ejpam-5118	335	16	between	between	ADP
ejpam-5118	335	17	g1	g1	PROPN
ejpam-5118	335	18	×	×	PROPN
ejpam-5118	335	19	g2	g2	PROPN
ejpam-5118	335	20	and	and	CCONJ
ejpam-5118	335	21	g1	g1	PROPN
ejpam-5118	335	22	×	×	PROPN
ejpam-5118	335	23	ε2	ε2	PROPN
ejpam-5118	335	24	g2	g2	PROPN
ejpam-5118	335	25	given	give	VERB
ejpam-5118	335	26	by	by	ADP
ejpam-5118	335	27	φ(x	φ(x	PROPN
ejpam-5118	335	28	,	,	PUNCT
ejpam-5118	335	29	y	y	NOUN
ejpam-5118	335	30	)	)	PUNCT
ejpam-5118	336	1	=	=	SYM
ejpam-5118	336	2	(	(	PUNCT
ejpam-5118	336	3	δ′(y	δ′(y	PROPN
ejpam-5118	336	4	)	)	PUNCT
ejpam-5118	336	5	,	,	PUNCT
ejpam-5118	336	6	δ(x	δ(x	NOUN
ejpam-5118	336	7	)	)	PUNCT
ejpam-5118	336	8	)	)	PUNCT
ejpam-5118	336	9	,	,	PUNCT
ejpam-5118	336	10	for	for	ADP
ejpam-5118	336	11	all	all	DET
ejpam-5118	336	12	x	x	SYM
ejpam-5118	336	13	∈	∈	PROPN
ejpam-5118	336	14	g1	g1	NOUN
ejpam-5118	336	15	,	,	PUNCT
ejpam-5118	336	16	y	y	PROPN
ejpam-5118	336	17	∈	∈	PROPN
ejpam-5118	336	18	g2	g2	PROPN
ejpam-5118	336	19	.	.	PUNCT
ejpam-5118	337	1	since	since	SCONJ
ejpam-5118	337	2	ε2	ε2	PROPN
ejpam-5118	337	3	◦	◦	NOUN
ejpam-5118	337	4	(	(	PUNCT
ejpam-5118	337	5	δ	δ	PROPN
ejpam-5118	337	6	×	×	PROPN
ejpam-5118	337	7	δ	δ	PROPN
ejpam-5118	337	8	)	)	PUNCT
ejpam-5118	337	9	=	=	SYM
ejpam-5118	337	10	1	1	NUM
ejpam-5118	337	11	,	,	PUNCT
ejpam-5118	337	12	it	it	PRON
ejpam-5118	337	13	is	be	AUX
ejpam-5118	337	14	easy	easy	ADJ
ejpam-5118	337	15	to	to	PART
ejpam-5118	337	16	check	check	VERB
ejpam-5118	337	17	that	that	SCONJ
ejpam-5118	337	18	φ	φ	PROPN
ejpam-5118	337	19	is	be	AUX
ejpam-5118	337	20	a	a	DET
ejpam-5118	337	21	group	group	NOUN
ejpam-5118	337	22	homomorphism	homomorphism	NOUN
ejpam-5118	337	23	,	,	PUNCT
ejpam-5118	337	24	and	and	CCONJ
ejpam-5118	337	25	therefore	therefore	ADV
ejpam-5118	337	26	it	it	PRON
ejpam-5118	337	27	is	be	AUX
ejpam-5118	337	28	a	a	DET
ejpam-5118	337	29	group	group	NOUN
ejpam-5118	337	30	isomorphism	isomorphism	NOUN
ejpam-5118	337	31	.	.	PUNCT
ejpam-5118	338	1	7	7	X
ejpam-5118	338	2	.	.	NUM
ejpam-5118	338	3	conclusions	conclusion	NOUN
ejpam-5118	338	4	and	and	CCONJ
ejpam-5118	338	5	future	future	ADJ
ejpam-5118	338	6	problems	problem	NOUN
ejpam-5118	338	7	as	as	SCONJ
ejpam-5118	338	8	mentioned	mention	VERB
ejpam-5118	338	9	in	in	ADP
ejpam-5118	338	10	the	the	DET
ejpam-5118	338	11	introduction	introduction	NOUN
ejpam-5118	338	12	,	,	PUNCT
ejpam-5118	338	13	our	our	PRON
ejpam-5118	338	14	choice	choice	NOUN
ejpam-5118	338	15	to	to	PART
ejpam-5118	338	16	focus	focus	VERB
ejpam-5118	338	17	on	on	ADP
ejpam-5118	338	18	the	the	DET
ejpam-5118	338	19	isomorphism	isomorphism	NOUN
ejpam-5118	338	20	problem	problem	NOUN
ejpam-5118	338	21	for	for	ADP
ejpam-5118	338	22	extensions	extension	NOUN
ejpam-5118	338	23	with	with	ADP
ejpam-5118	338	24	abelian	abelian	ADJ
ejpam-5118	338	25	kernel	kernel	PROPN
ejpam-5118	338	26	group	group	PROPN
ejpam-5118	338	27	is	be	AUX
ejpam-5118	338	28	partially	partially	ADV
ejpam-5118	338	29	motivated	motivate	VERB
ejpam-5118	338	30	by	by	ADP
ejpam-5118	338	31	the	the	DET
ejpam-5118	338	32	jordan	jordan	PROPN
ejpam-5118	338	33	–	–	PUNCT
ejpam-5118	338	34	hölder	hölder	NOUN
ejpam-5118	338	35	theorem	theorem	VERB
ejpam-5118	338	36	.	.	PUNCT
ejpam-5118	339	1	our	our	PRON
ejpam-5118	339	2	other	other	ADJ
ejpam-5118	339	3	works	work	NOUN
ejpam-5118	339	4	of	of	ADP
ejpam-5118	339	5	particular	particular	ADJ
ejpam-5118	339	6	relevance	relevance	NOUN
ejpam-5118	339	7	are	be	AUX
ejpam-5118	339	8	[	[	X
ejpam-5118	339	9	8–11	8–11	NOUN
ejpam-5118	339	10	]	]	PUNCT
ejpam-5118	339	11	.	.	PUNCT
ejpam-5118	340	1	we	we	PRON
ejpam-5118	340	2	study	study	VERB
ejpam-5118	340	3	in	in	ADP
ejpam-5118	340	4	[	[	X
ejpam-5118	340	5	11	11	NUM
ejpam-5118	340	6	]	]	PUNCT
ejpam-5118	340	7	the	the	DET
ejpam-5118	340	8	isomorphism	isomorphism	NOUN
ejpam-5118	340	9	problem	problem	NOUN
ejpam-5118	340	10	for	for	ADP
ejpam-5118	340	11	split	split	ADJ
ejpam-5118	340	12	extensions	extension	NOUN
ejpam-5118	340	13	,	,	PUNCT
ejpam-5118	340	14	and	and	CCONJ
ejpam-5118	340	15	as	as	ADP
ejpam-5118	340	16	an	an	DET
ejpam-5118	340	17	application	application	NOUN
ejpam-5118	340	18	,	,	PUNCT
ejpam-5118	340	19	we	we	PRON
ejpam-5118	340	20	determine	determine	VERB
ejpam-5118	340	21	how	how	SCONJ
ejpam-5118	340	22	isomorphism	isomorphism	NOUN
ejpam-5118	340	23	of	of	ADP
ejpam-5118	340	24	split	split	ADJ
ejpam-5118	340	25	extensions	extension	NOUN
ejpam-5118	340	26	and	and	CCONJ
ejpam-5118	340	27	conjugacy	conjugacy	NOUN
ejpam-5118	340	28	of	of	ADP
ejpam-5118	340	29	the	the	DET
ejpam-5118	340	30	images	image	NOUN
ejpam-5118	340	31	of	of	ADP
ejpam-5118	340	32	the	the	DET
ejpam-5118	340	33	corresponding	corresponding	ADJ
ejpam-5118	340	34	actions	action	NOUN
ejpam-5118	340	35	are	be	AUX
ejpam-5118	340	36	related	relate	VERB
ejpam-5118	340	37	.	.	PUNCT
ejpam-5118	341	1	as	as	SCONJ
ejpam-5118	341	2	is	be	AUX
ejpam-5118	341	3	well	well	ADV
ejpam-5118	341	4	known	know	VERB
ejpam-5118	341	5	,	,	PUNCT
ejpam-5118	341	6	the	the	DET
ejpam-5118	341	7	identity	identity	NOUN
ejpam-5118	341	8	element	element	NOUN
ejpam-5118	341	9	of	of	ADP
ejpam-5118	341	10	the	the	DET
ejpam-5118	341	11	second	second	ADJ
ejpam-5118	341	12	cohomology	cohomology	NOUN
ejpam-5118	341	13	group	group	NOUN
ejpam-5118	341	14	corresponds	correspond	VERB
ejpam-5118	341	15	to	to	ADP
ejpam-5118	341	16	the	the	DET
ejpam-5118	341	17	split	split	NOUN
ejpam-5118	341	18	extensions	extension	NOUN
ejpam-5118	341	19	.	.	PUNCT
ejpam-5118	342	1	this	this	PRON
ejpam-5118	342	2	motivates	motivate	VERB
ejpam-5118	342	3	us	we	PRON
ejpam-5118	342	4	to	to	PART
ejpam-5118	342	5	consider	consider	VERB
ejpam-5118	342	6	also	also	ADV
ejpam-5118	342	7	the	the	DET
ejpam-5118	342	8	non	non	ADJ
ejpam-5118	342	9	-	-	ADJ
ejpam-5118	342	10	identity	identity	ADJ
ejpam-5118	342	11	different	different	ADJ
ejpam-5118	342	12	elements	element	NOUN
ejpam-5118	342	13	,	,	PUNCT
ejpam-5118	342	14	which	which	PRON
ejpam-5118	342	15	give	give	VERB
ejpam-5118	342	16	rise	rise	NOUN
ejpam-5118	342	17	to	to	ADP
ejpam-5118	342	18	the	the	DET
ejpam-5118	342	19	construction	construction	NOUN
ejpam-5118	342	20	of	of	ADP
ejpam-5118	342	21	non	non	ADJ
ejpam-5118	342	22	-	-	ADJ
ejpam-5118	342	23	split	split	ADJ
ejpam-5118	342	24	extensions	extension	NOUN
ejpam-5118	342	25	.	.	PUNCT
ejpam-5118	343	1	so	so	ADV
ejpam-5118	343	2	,	,	PUNCT
ejpam-5118	343	3	in	in	ADP
ejpam-5118	343	4	[	[	X
ejpam-5118	343	5	8–10	8–10	NOUN
ejpam-5118	343	6	]	]	PUNCT
ejpam-5118	343	7	,	,	PUNCT
ejpam-5118	343	8	we	we	PRON
ejpam-5118	343	9	study	study	VERB
ejpam-5118	343	10	the	the	DET
ejpam-5118	343	11	isomorphism	isomorphism	NOUN
ejpam-5118	343	12	problem	problem	NOUN
ejpam-5118	343	13	for	for	ADP
ejpam-5118	343	14	non	non	ADJ
ejpam-5118	343	15	-	-	ADJ
ejpam-5118	343	16	split	split	ADJ
ejpam-5118	343	17	abelian	abelian	ADJ
ejpam-5118	343	18	extensions	extension	NOUN
ejpam-5118	343	19	in	in	ADP
ejpam-5118	343	20	some	some	DET
ejpam-5118	343	21	special	special	ADJ
ejpam-5118	343	22	cases	case	NOUN
ejpam-5118	343	23	.	.	PUNCT
ejpam-5118	344	1	we	we	PRON
ejpam-5118	344	2	mainly	mainly	ADV
ejpam-5118	344	3	deal	deal	VERB
ejpam-5118	344	4	with	with	ADP
ejpam-5118	344	5	isomorphisms	isomorphism	NOUN
ejpam-5118	344	6	leaving	leave	VERB
ejpam-5118	344	7	one	one	NUM
ejpam-5118	344	8	of	of	ADP
ejpam-5118	344	9	the	the	DET
ejpam-5118	344	10	two	two	NUM
ejpam-5118	344	11	factors	factor	NOUN
ejpam-5118	344	12	or	or	CCONJ
ejpam-5118	344	13	even	even	ADV
ejpam-5118	344	14	both	both	PRON
ejpam-5118	344	15	invariant	invariant	ADJ
ejpam-5118	344	16	.	.	PUNCT
ejpam-5118	345	1	we	we	PRON
ejpam-5118	345	2	characterize	characterize	VERB
ejpam-5118	345	3	such	such	ADJ
ejpam-5118	345	4	isomorphisms	isomorphism	NOUN
ejpam-5118	345	5	in	in	ADP
ejpam-5118	345	6	various	various	ADJ
ejpam-5118	345	7	situations	situation	NOUN
ejpam-5118	345	8	with	with	ADP
ejpam-5118	345	9	some	some	DET
ejpam-5118	345	10	assumptions	assumption	NOUN
ejpam-5118	345	11	on	on	ADP
ejpam-5118	345	12	the	the	DET
ejpam-5118	345	13	quotient	quotient	NOUN
ejpam-5118	345	14	and	and	CCONJ
ejpam-5118	345	15	the	the	DET
ejpam-5118	345	16	kernel	kernel	PROPN
ejpam-5118	345	17	group	group	NOUN
ejpam-5118	345	18	.	.	PUNCT
ejpam-5118	346	1	in	in	ADP
ejpam-5118	346	2	this	this	DET
ejpam-5118	346	3	paper	paper	NOUN
ejpam-5118	346	4	,	,	PUNCT
ejpam-5118	346	5	by	by	ADP
ejpam-5118	346	6	using	use	VERB
ejpam-5118	346	7	a	a	DET
ejpam-5118	346	8	similar	similar	ADJ
ejpam-5118	346	9	approach	approach	NOUN
ejpam-5118	346	10	,	,	PUNCT
ejpam-5118	346	11	we	we	PRON
ejpam-5118	346	12	give	give	VERB
ejpam-5118	346	13	a	a	DET
ejpam-5118	346	14	further	further	ADJ
ejpam-5118	346	15	contribution	contribution	NOUN
ejpam-5118	346	16	to	to	ADP
ejpam-5118	346	17	this	this	DET
ejpam-5118	346	18	topic	topic	NOUN
ejpam-5118	346	19	.	.	PUNCT
ejpam-5118	347	1	more	more	ADV
ejpam-5118	347	2	precisely	precisely	ADV
ejpam-5118	347	3	,	,	PUNCT
ejpam-5118	347	4	we	we	PRON
ejpam-5118	347	5	complete	complete	VERB
ejpam-5118	347	6	the	the	DET
ejpam-5118	347	7	work	work	NOUN
ejpam-5118	347	8	with	with	ADP
ejpam-5118	347	9	the	the	DET
ejpam-5118	347	10	isomorphism	isomorphism	NOUN
ejpam-5118	347	11	problem	problem	NOUN
ejpam-5118	347	12	for	for	ADP
ejpam-5118	347	13	central	central	ADJ
ejpam-5118	347	14	extensions	extension	NOUN
ejpam-5118	347	15	in	in	ADP
ejpam-5118	347	16	different	different	ADJ
ejpam-5118	347	17	special	special	ADJ
ejpam-5118	347	18	cases	case	NOUN
ejpam-5118	347	19	.	.	PUNCT
ejpam-5118	348	1	so	so	ADV
ejpam-5118	348	2	most	most	ADJ
ejpam-5118	348	3	of	of	ADP
ejpam-5118	348	4	the	the	DET
ejpam-5118	348	5	results	result	NOUN
ejpam-5118	348	6	obtained	obtain	VERB
ejpam-5118	348	7	here	here	ADV
ejpam-5118	348	8	considered	consider	VERB
ejpam-5118	348	9	as	as	ADP
ejpam-5118	348	10	a	a	DET
ejpam-5118	348	11	generalization	generalization	NOUN
ejpam-5118	348	12	of	of	ADP
ejpam-5118	348	13	those	those	PRON
ejpam-5118	348	14	in	in	ADP
ejpam-5118	348	15	[	[	X
ejpam-5118	348	16	9	9	NUM
ejpam-5118	348	17	,	,	PUNCT
ejpam-5118	348	18	10	10	NUM
ejpam-5118	348	19	]	]	PUNCT
ejpam-5118	348	20	.	.	PUNCT
ejpam-5118	349	1	references	reference	NOUN
ejpam-5118	349	2	967	967	NUM
ejpam-5118	349	3	after	after	ADP
ejpam-5118	349	4	the	the	DET
ejpam-5118	349	5	outcomes	outcome	NOUN
ejpam-5118	349	6	obtained	obtain	VERB
ejpam-5118	349	7	in	in	ADP
ejpam-5118	349	8	this	this	DET
ejpam-5118	349	9	work	work	NOUN
ejpam-5118	349	10	,	,	PUNCT
ejpam-5118	349	11	one	one	PRON
ejpam-5118	349	12	may	may	AUX
ejpam-5118	349	13	naturally	naturally	ADV
ejpam-5118	349	14	try	try	VERB
ejpam-5118	349	15	to	to	PART
ejpam-5118	349	16	obtain	obtain	VERB
ejpam-5118	349	17	similar	similar	ADJ
ejpam-5118	349	18	results	result	NOUN
ejpam-5118	349	19	with	with	ADP
ejpam-5118	349	20	suitable	suitable	ADJ
ejpam-5118	349	21	properties	property	NOUN
ejpam-5118	349	22	for	for	ADP
ejpam-5118	349	23	g1	g1	NOUN
ejpam-5118	349	24	and	and	CCONJ
ejpam-5118	349	25	g2	g2	PROPN
ejpam-5118	349	26	other	other	ADJ
ejpam-5118	349	27	than	than	SCONJ
ejpam-5118	349	28	previously	previously	ADV
ejpam-5118	349	29	studied	study	VERB
ejpam-5118	349	30	.	.	PUNCT
ejpam-5118	350	1	one	one	PRON
ejpam-5118	350	2	may	may	AUX
ejpam-5118	350	3	also	also	ADV
ejpam-5118	350	4	would	would	AUX
ejpam-5118	350	5	like	like	VERB
ejpam-5118	350	6	to	to	PART
ejpam-5118	350	7	study	study	VERB
ejpam-5118	350	8	the	the	DET
ejpam-5118	350	9	isomorphism	isomorphism	NOUN
ejpam-5118	350	10	problem	problem	NOUN
ejpam-5118	350	11	for	for	ADP
ejpam-5118	350	12	non	non	ADJ
ejpam-5118	350	13	-	-	ADJ
ejpam-5118	350	14	split	split	ADJ
ejpam-5118	350	15	extensions	extension	NOUN
ejpam-5118	350	16	with	with	ADP
ejpam-5118	350	17	non	non	ADJ
ejpam-5118	350	18	-	-	ADJ
ejpam-5118	350	19	abelian	abelian	ADJ
ejpam-5118	350	20	kernel	kernel	NOUN
ejpam-5118	350	21	.	.	PUNCT
ejpam-5118	351	1	this	this	PRON
ejpam-5118	351	2	is	be	AUX
ejpam-5118	351	3	of	of	ADP
ejpam-5118	351	4	course	course	NOUN
ejpam-5118	351	5	the	the	DET
ejpam-5118	351	6	most	most	ADV
ejpam-5118	351	7	important	important	ADJ
ejpam-5118	351	8	future	future	ADJ
ejpam-5118	351	9	problem	problem	NOUN
ejpam-5118	351	10	on	on	ADP
ejpam-5118	351	11	this	this	DET
ejpam-5118	351	12	topic	topic	NOUN
ejpam-5118	351	13	.	.	PUNCT
ejpam-5118	352	1	in	in	ADP
ejpam-5118	352	2	our	our	PRON
ejpam-5118	352	3	future	future	ADJ
ejpam-5118	352	4	works	work	NOUN
ejpam-5118	352	5	,	,	PUNCT
ejpam-5118	352	6	we	we	PRON
ejpam-5118	352	7	will	will	AUX
ejpam-5118	352	8	continue	continue	VERB
ejpam-5118	352	9	with	with	ADP
ejpam-5118	352	10	the	the	DET
ejpam-5118	352	11	isomorphism	isomorphism	NOUN
ejpam-5118	352	12	problem	problem	NOUN
ejpam-5118	352	13	for	for	ADP
ejpam-5118	352	14	extensions	extension	NOUN
ejpam-5118	352	15	with	with	ADP
ejpam-5118	352	16	abelian	abelian	ADJ
ejpam-5118	352	17	kernel	kernel	PROPN
ejpam-5118	352	18	group	group	NOUN
ejpam-5118	352	19	and	and	CCONJ
ejpam-5118	352	20	try	try	VERB
ejpam-5118	352	21	to	to	PART
ejpam-5118	352	22	generalize	generalize	VERB
ejpam-5118	352	23	the	the	DET
ejpam-5118	352	24	results	result	NOUN
ejpam-5118	352	25	into	into	ADP
ejpam-5118	352	26	any	any	DET
ejpam-5118	352	27	groups	group	NOUN
ejpam-5118	352	28	g1	g1	NOUN
ejpam-5118	352	29	and	and	CCONJ
ejpam-5118	352	30	g2	g2	PROPN
ejpam-5118	352	31	.	.	PUNCT
ejpam-5118	353	1	we	we	PRON
ejpam-5118	353	2	also	also	ADV
ejpam-5118	353	3	would	would	AUX
ejpam-5118	353	4	like	like	VERB
ejpam-5118	353	5	to	to	PART
ejpam-5118	353	6	choose	choose	VERB
ejpam-5118	353	7	another	another	DET
ejpam-5118	353	8	groups	group	NOUN
ejpam-5118	353	9	extension	extension	NOUN
ejpam-5118	353	10	such	such	ADJ
ejpam-5118	353	11	as	as	ADP
ejpam-5118	353	12	zappa	zappa	PROPN
ejpam-5118	353	13	-	-	PUNCT
ejpam-5118	353	14	szep	szep	PROPN
ejpam-5118	353	15	product	product	NOUN
ejpam-5118	353	16	to	to	PART
ejpam-5118	353	17	apply	apply	VERB
ejpam-5118	353	18	similar	similar	ADJ
ejpam-5118	353	19	results	result	NOUN
ejpam-5118	353	20	.	.	PUNCT
ejpam-5118	354	1	acknowledgements	acknowledgement	VERB
ejpam-5118	354	2	the	the	DET
ejpam-5118	354	3	author	author	NOUN
ejpam-5118	354	4	thanks	thank	NOUN
ejpam-5118	354	5	the	the	DET
ejpam-5118	354	6	reviewers	reviewer	NOUN
ejpam-5118	354	7	and	and	CCONJ
ejpam-5118	354	8	the	the	DET
ejpam-5118	354	9	editor	editor	NOUN
ejpam-5118	354	10	for	for	ADP
ejpam-5118	354	11	their	their	PRON
ejpam-5118	354	12	helpful	helpful	ADJ
ejpam-5118	354	13	comments	comment	NOUN
ejpam-5118	354	14	and	and	CCONJ
ejpam-5118	354	15	corrections	correction	NOUN
ejpam-5118	354	16	,	,	PUNCT
ejpam-5118	354	17	which	which	PRON
ejpam-5118	354	18	have	have	AUX
ejpam-5118	354	19	greatly	greatly	ADV
ejpam-5118	354	20	improved	improve	VERB
ejpam-5118	354	21	the	the	DET
ejpam-5118	354	22	presentation	presentation	NOUN
ejpam-5118	354	23	of	of	ADP
ejpam-5118	354	24	the	the	DET
ejpam-5118	354	25	paper	paper	NOUN
ejpam-5118	354	26	.	.	PUNCT
ejpam-5118	355	1	references	reference	NOUN
ejpam-5118	355	2	[	[	X
ejpam-5118	355	3	1	1	NUM
ejpam-5118	355	4	]	]	PUNCT
ejpam-5118	355	5	k.	k.	PROPN
ejpam-5118	355	6	s.	s.	PROPN
ejpam-5118	355	7	brown	brown	PROPN
ejpam-5118	355	8	.	.	PUNCT
ejpam-5118	356	1	cohomology	cohomology	NOUN
ejpam-5118	356	2	of	of	ADP
ejpam-5118	356	3	groups	group	NOUN
ejpam-5118	356	4	.	.	PUNCT
ejpam-5118	357	1	in	in	ADP
ejpam-5118	357	2	graduate	graduate	NOUN
ejpam-5118	357	3	texts	text	NOUN
ejpam-5118	357	4	in	in	ADP
ejpam-5118	357	5	mathematics	mathematic	NOUN
ejpam-5118	357	6	.	.	PUNCT
ejpam-5118	357	7	,	,	PUNCT
ejpam-5118	357	8	volume	volume	NOUN
ejpam-5118	357	9	87	87	NUM
ejpam-5118	357	10	.	.	PUNCT
ejpam-5118	358	1	springer	springer	NOUN
ejpam-5118	358	2	-	-	PUNCT
ejpam-5118	358	3	verlag	verlag	PROPN
ejpam-5118	358	4	,	,	PUNCT
ejpam-5118	358	5	new	new	PROPN
ejpam-5118	358	6	york	york	PROPN
ejpam-5118	358	7	,	,	PUNCT
ejpam-5118	358	8	heidelberg	heidelberg	PROPN
ejpam-5118	358	9	,	,	PUNCT
ejpam-5118	358	10	berlin	berlin	PROPN
ejpam-5118	358	11	,	,	PUNCT
ejpam-5118	358	12	1982	1982	NUM
ejpam-5118	358	13	.	.	PUNCT
ejpam-5118	359	1	[	[	X
ejpam-5118	359	2	2	2	X
ejpam-5118	359	3	]	]	PUNCT
ejpam-5118	359	4	d.	d.	PROPN
ejpam-5118	359	5	s.	s.	PROPN
ejpam-5118	359	6	dummit	dummit	PROPN
ejpam-5118	359	7	and	and	CCONJ
ejpam-5118	359	8	r.	r.	PROPN
ejpam-5118	359	9	m.	m.	PROPN
ejpam-5118	359	10	foote	foote	PROPN
ejpam-5118	359	11	.	.	PUNCT
ejpam-5118	360	1	abstract	abstract	ADJ
ejpam-5118	360	2	algebra	algebra	PROPN
ejpam-5118	360	3	.	.	PUNCT
ejpam-5118	361	1	john	john	PROPN
ejpam-5118	361	2	wiley	wiley	PROPN
ejpam-5118	361	3	and	and	CCONJ
ejpam-5118	361	4	sons	son	NOUN
ejpam-5118	361	5	,	,	PUNCT
ejpam-5118	361	6	inc	inc	PROPN
ejpam-5118	361	7	,	,	PUNCT
ejpam-5118	361	8	new	new	PROPN
ejpam-5118	361	9	york	york	PROPN
ejpam-5118	361	10	,	,	PUNCT
ejpam-5118	361	11	3rd	3rd	ADJ
ejpam-5118	361	12	edition	edition	NOUN
ejpam-5118	361	13	,	,	PUNCT
ejpam-5118	361	14	2004	2004	NUM
ejpam-5118	361	15	.	.	PUNCT
ejpam-5118	362	1	[	[	X
ejpam-5118	362	2	3	3	X
ejpam-5118	362	3	]	]	PUNCT
ejpam-5118	362	4	s.	s.	PROPN
ejpam-5118	362	5	eilenberg	eilenberg	PROPN
ejpam-5118	362	6	and	and	CCONJ
ejpam-5118	362	7	s.	s.	PROPN
ejpam-5118	362	8	maclane	maclane	PROPN
ejpam-5118	362	9	.	.	PUNCT
ejpam-5118	363	1	group	group	NOUN
ejpam-5118	363	2	extensions	extension	NOUN
ejpam-5118	363	3	and	and	CCONJ
ejpam-5118	363	4	homology	homology	NOUN
ejpam-5118	363	5	.	.	PUNCT
ejpam-5118	364	1	ann	ann	PROPN
ejpam-5118	364	2	.	.	PROPN
ejpam-5118	364	3	of	of	ADP
ejpam-5118	364	4	math	math	NOUN
ejpam-5118	364	5	.	.	PUNCT
ejpam-5118	364	6	,	,	PUNCT
ejpam-5118	364	7	second	second	ADJ
ejpam-5118	364	8	series	series	NOUN
ejpam-5118	364	9	,	,	PUNCT
ejpam-5118	364	10	43(4):757–831	43(4):757–831	PROPN
ejpam-5118	364	11	,	,	PUNCT
ejpam-5118	364	12	1942	1942	NUM
ejpam-5118	364	13	.	.	PUNCT
ejpam-5118	365	1	[	[	X
ejpam-5118	365	2	4	4	X
ejpam-5118	365	3	]	]	PUNCT
ejpam-5118	365	4	s.	s.	PROPN
ejpam-5118	365	5	eilenberg	eilenberg	PROPN
ejpam-5118	365	6	and	and	CCONJ
ejpam-5118	365	7	s.	s.	PROPN
ejpam-5118	365	8	maclane	maclane	PROPN
ejpam-5118	365	9	.	.	PUNCT
ejpam-5118	366	1	cohomology	cohomology	NOUN
ejpam-5118	366	2	theory	theory	NOUN
ejpam-5118	366	3	in	in	ADP
ejpam-5118	366	4	abstract	abstract	ADJ
ejpam-5118	366	5	groups	groups	PROPN
ejpam-5118	366	6	ii	ii	PROPN
ejpam-5118	366	7	.	.	PUNCT
ejpam-5118	367	1	ann	ann	PROPN
ejpam-5118	367	2	.	.	PROPN
ejpam-5118	367	3	of	of	ADP
ejpam-5118	367	4	math	math	NOUN
ejpam-5118	367	5	.	.	PUNCT
ejpam-5118	367	6	,	,	PUNCT
ejpam-5118	367	7	second	second	ADJ
ejpam-5118	367	8	series	series	NOUN
ejpam-5118	367	9	,	,	PUNCT
ejpam-5118	367	10	48(1):326–341	48(1):326–341	PROPN
ejpam-5118	367	11	,	,	PUNCT
ejpam-5118	367	12	1947	1947	NUM
ejpam-5118	367	13	.	.	PUNCT
ejpam-5118	368	1	[	[	X
ejpam-5118	368	2	5	5	X
ejpam-5118	368	3	]	]	PUNCT
ejpam-5118	368	4	s.	s.	PROPN
ejpam-5118	368	5	maclane	maclane	PROPN
ejpam-5118	368	6	.	.	PUNCT
ejpam-5118	369	1	homology	homology	PROPN
ejpam-5118	369	2	.	.	PUNCT
ejpam-5118	370	1	springer	springer	NOUN
ejpam-5118	370	2	-	-	PUNCT
ejpam-5118	370	3	verlag	verlag	PROPN
ejpam-5118	370	4	,	,	PUNCT
ejpam-5118	370	5	berlin	berlin	PROPN
ejpam-5118	370	6	,	,	PUNCT
ejpam-5118	370	7	gottingen	gottingen	NOUN
ejpam-5118	370	8	,	,	PUNCT
ejpam-5118	370	9	heidelberg	heidelberg	PROPN
ejpam-5118	370	10	,	,	PUNCT
ejpam-5118	370	11	1963	1963	NUM
ejpam-5118	370	12	.	.	PUNCT
ejpam-5118	371	1	[	[	X
ejpam-5118	371	2	6	6	X
ejpam-5118	371	3	]	]	PUNCT
ejpam-5118	371	4	j.	j.	PROPN
ejpam-5118	371	5	j.	j.	PROPN
ejpam-5118	371	6	rotman	rotman	PROPN
ejpam-5118	371	7	.	.	PUNCT
ejpam-5118	372	1	an	an	DET
ejpam-5118	372	2	introduction	introduction	NOUN
ejpam-5118	372	3	to	to	ADP
ejpam-5118	372	4	the	the	DET
ejpam-5118	372	5	theory	theory	NOUN
ejpam-5118	372	6	of	of	ADP
ejpam-5118	372	7	groups	group	NOUN
ejpam-5118	372	8	.	.	PUNCT
ejpam-5118	373	1	in	in	ADP
ejpam-5118	373	2	graduate	graduate	NOUN
ejpam-5118	373	3	texts	text	NOUN
ejpam-5118	373	4	in	in	ADP
ejpam-5118	373	5	mathematics	mathematic	NOUN
ejpam-5118	373	6	.	.	PUNCT
ejpam-5118	373	7	,	,	PUNCT
ejpam-5118	373	8	volume	volume	NOUN
ejpam-5118	373	9	148	148	NUM
ejpam-5118	373	10	.	.	PUNCT
ejpam-5118	373	11	springer	springer	NOUN
ejpam-5118	373	12	-	-	PUNCT
ejpam-5118	373	13	verlag	verlag	PROPN
ejpam-5118	373	14	,	,	PUNCT
ejpam-5118	373	15	new	new	PROPN
ejpam-5118	373	16	york	york	PROPN
ejpam-5118	373	17	,	,	PUNCT
ejpam-5118	373	18	inc	inc	PROPN
ejpam-5118	373	19	.	.	PROPN
ejpam-5118	373	20	,	,	PUNCT
ejpam-5118	373	21	4th	4th	PROPN
ejpam-5118	373	22	edition	edition	NOUN
ejpam-5118	373	23	,	,	PUNCT
ejpam-5118	373	24	1995	1995	NUM
ejpam-5118	373	25	.	.	PUNCT
ejpam-5118	374	1	[	[	X
ejpam-5118	374	2	7	7	X
ejpam-5118	374	3	]	]	X
ejpam-5118	374	4	o.	o.	NOUN
ejpam-5118	374	5	schreier	schreier	NOUN
ejpam-5118	374	6	.	.	PUNCT
ejpam-5118	375	1	über	über	PROPN
ejpam-5118	375	2	die	die	VERB
ejpam-5118	375	3	erweiterung	erweiterung	PROPN
ejpam-5118	375	4	von	von	PROPN
ejpam-5118	375	5	gruppen	gruppen	PROPN
ejpam-5118	375	6	i.	i.	PROPN
ejpam-5118	375	7	monatsh	monatsh	PROPN
ejpam-5118	375	8	.	.	PUNCT
ejpam-5118	376	1	math	math	NOUN
ejpam-5118	376	2	.	.	PUNCT
ejpam-5118	377	1	phys	phy	NOUN
ejpam-5118	377	2	.	.	PUNCT
ejpam-5118	377	3	,	,	PUNCT
ejpam-5118	377	4	34:165–180	34:165–180	NUM
ejpam-5118	377	5	,	,	PUNCT
ejpam-5118	377	6	1926	1926	NUM
ejpam-5118	377	7	.	.	PUNCT
ejpam-5118	378	1	[	[	X
ejpam-5118	378	2	8	8	NUM
ejpam-5118	378	3	]	]	X
ejpam-5118	378	4	n.	n.	PROPN
ejpam-5118	378	5	snanou	snanou	PROPN
ejpam-5118	378	6	.	.	PUNCT
ejpam-5118	379	1	on	on	ADP
ejpam-5118	379	2	non	non	ADJ
ejpam-5118	379	3	-	-	ADJ
ejpam-5118	379	4	split	split	ADJ
ejpam-5118	379	5	abelian	abelian	PROPN
ejpam-5118	379	6	extensions	extensions	PROPN
ejpam-5118	379	7	ii	ii	PROPN
ejpam-5118	379	8	.	.	PUNCT
ejpam-5118	379	9	asian	asian	PROPN
ejpam-5118	379	10	-	-	PUNCT
ejpam-5118	379	11	eur	eur	NOUN
ejpam-5118	379	12	.	.	PUNCT
ejpam-5118	380	1	j.	j.	PROPN
ejpam-5118	380	2	math	math	PROPN
ejpam-5118	380	3	.	.	PROPN
ejpam-5118	380	4	,	,	PUNCT
ejpam-5118	380	5	14(9):2150164	14(9):2150164	NUM
ejpam-5118	380	6	,	,	PUNCT
ejpam-5118	380	7	2021	2021	NUM
ejpam-5118	380	8	.	.	PUNCT
ejpam-5118	381	1	[	[	X
ejpam-5118	381	2	9	9	NUM
ejpam-5118	381	3	]	]	X
ejpam-5118	381	4	n.	n.	PROPN
ejpam-5118	381	5	snanou	snanou	PROPN
ejpam-5118	381	6	.	.	PUNCT
ejpam-5118	382	1	on	on	ADP
ejpam-5118	382	2	the	the	DET
ejpam-5118	382	3	isomorphism	isomorphism	NOUN
ejpam-5118	382	4	problem	problem	NOUN
ejpam-5118	382	5	for	for	ADP
ejpam-5118	382	6	central	central	ADJ
ejpam-5118	382	7	extensions	extension	NOUN
ejpam-5118	382	8	i.	i.	NOUN
ejpam-5118	382	9	proc	proc	PROPN
ejpam-5118	382	10	.	.	PUNCT
ejpam-5118	383	1	jangjeon	jangjeon	PROPN
ejpam-5118	383	2	math	math	PROPN
ejpam-5118	383	3	.	.	PUNCT
ejpam-5118	384	1	soc	soc	PROPN
ejpam-5118	384	2	.	.	PUNCT
ejpam-5118	384	3	,	,	PUNCT
ejpam-5118	384	4	27(2):101–109	27(2):101–109	NUM
ejpam-5118	384	5	,	,	PUNCT
ejpam-5118	384	6	2024	2024	NUM
ejpam-5118	384	7	.	.	PUNCT
ejpam-5118	385	1	[	[	X
ejpam-5118	385	2	10	10	NUM
ejpam-5118	385	3	]	]	X
ejpam-5118	385	4	n.	n.	NOUN
ejpam-5118	385	5	snanou	snanou	PROPN
ejpam-5118	385	6	and	and	CCONJ
ejpam-5118	385	7	m.	m.	PROPN
ejpam-5118	385	8	e.	e.	PROPN
ejpam-5118	385	9	charkani	charkani	PROPN
ejpam-5118	385	10	.	.	PUNCT
ejpam-5118	386	1	on	on	ADP
ejpam-5118	386	2	non	non	ADJ
ejpam-5118	386	3	-	-	ADJ
ejpam-5118	386	4	split	split	ADJ
ejpam-5118	386	5	abelian	abelian	ADJ
ejpam-5118	386	6	extensions	extension	NOUN
ejpam-5118	386	7	.	.	PUNCT
ejpam-5118	387	1	bull	bull	NOUN
ejpam-5118	387	2	.	.	PUNCT
ejpam-5118	388	1	iran	iran	PROPN
ejpam-5118	388	2	.	.	PUNCT
ejpam-5118	389	1	math	math	NOUN
ejpam-5118	389	2	.	.	PUNCT
ejpam-5118	390	1	soc	soc	PROPN
ejpam-5118	390	2	.	.	PUNCT
ejpam-5118	390	3	,	,	PUNCT
ejpam-5118	390	4	47(3):743–753	47(3):743–753	PROPN
ejpam-5118	390	5	,	,	PUNCT
ejpam-5118	390	6	2021	2021	NUM
ejpam-5118	390	7	.	.	PUNCT
ejpam-5118	391	1	[	[	X
ejpam-5118	391	2	11	11	NUM
ejpam-5118	391	3	]	]	X
ejpam-5118	391	4	n.	n.	PROPN
ejpam-5118	391	5	snanou	snanou	PROPN
ejpam-5118	391	6	and	and	CCONJ
ejpam-5118	391	7	m.	m.	PROPN
ejpam-5118	391	8	e.	e.	PROPN
ejpam-5118	391	9	charkani	charkani	PROPN
ejpam-5118	391	10	.	.	PUNCT
ejpam-5118	392	1	on	on	ADP
ejpam-5118	392	2	the	the	DET
ejpam-5118	392	3	isomorphism	isomorphism	NOUN
ejpam-5118	392	4	problem	problem	NOUN
ejpam-5118	392	5	for	for	ADP
ejpam-5118	392	6	split	split	ADJ
ejpam-5118	392	7	extensions	extension	NOUN
ejpam-5118	392	8	.	.	PUNCT
ejpam-5118	393	1	j.	j.	PROPN
ejpam-5118	393	2	algebra	algebra	PROPN
ejpam-5118	393	3	appl	appl	PROPN
ejpam-5118	393	4	.	.	PROPN
ejpam-5118	393	5	,	,	PUNCT
ejpam-5118	393	6	23(2):2430002	23(2):2430002	NUM
ejpam-5118	393	7	,	,	PUNCT
ejpam-5118	393	8	2024	2024	NUM
ejpam-5118	393	9	.	.	PUNCT
ejpam-5118	394	1	references	reference	NOUN
ejpam-5118	394	2	968	968	NUM
ejpam-5118	395	1	[	[	X
ejpam-5118	395	2	12	12	NUM
ejpam-5118	395	3	]	]	X
ejpam-5118	395	4	c.	c.	PROPN
ejpam-5118	395	5	weibel	weibel	PROPN
ejpam-5118	395	6	.	.	PUNCT
ejpam-5118	396	1	an	an	DET
ejpam-5118	396	2	introduction	introduction	NOUN
ejpam-5118	396	3	to	to	ADP
ejpam-5118	396	4	homological	homological	ADJ
ejpam-5118	396	5	algebra	algebra	NOUN
ejpam-5118	396	6	.	.	PUNCT
ejpam-5118	397	1	in	in	ADP
ejpam-5118	397	2	cambridge	cambridge	PROPN
ejpam-5118	397	3	studies	study	NOUN
ejpam-5118	397	4	in	in	ADP
ejpam-5118	397	5	advanced	advanced	ADJ
ejpam-5118	397	6	mathematics	mathematic	NOUN
ejpam-5118	397	7	.	.	PUNCT
ejpam-5118	397	8	,	,	PUNCT
ejpam-5118	397	9	volume	volume	NOUN
ejpam-5118	397	10	38	38	NUM
ejpam-5118	397	11	.	.	PUNCT
ejpam-5118	398	1	cambridge	cambridge	PROPN
ejpam-5118	398	2	university	university	PROPN
ejpam-5118	398	3	press	press	PROPN
ejpam-5118	398	4	,	,	PUNCT
ejpam-5118	398	5	cambridge	cambridge	PROPN
ejpam-5118	398	6	,	,	PUNCT
ejpam-5118	398	7	1994	1994	NUM
ejpam-5118	398	8	.	.	PUNCT