id	sid	tid	token	lemma	pos
ejpam-3118	1	1	european	european	PROPN
ejpam-3118	1	2	journal	journal	PROPN
ejpam-3118	1	3	of	of	ADP
ejpam-3118	1	4	pure	pure	ADJ
ejpam-3118	1	5	and	and	CCONJ
ejpam-3118	1	6	applied	apply	VERB
ejpam-3118	1	7	mathematics	mathematic	NOUN
ejpam-3118	1	8	vol	vol	NOUN
ejpam-3118	1	9	.	.	PROPN
ejpam-3118	2	1	10	10	NUM
ejpam-3118	2	2	,	,	PUNCT
ejpam-3118	2	3	no	no	INTJ
ejpam-3118	2	4	.	.	NOUN
ejpam-3118	2	5	5	5	NUM
ejpam-3118	2	6	,	,	PUNCT
ejpam-3118	2	7	2017	2017	NUM
ejpam-3118	3	1	,	,	PUNCT
ejpam-3118	3	2	955	955	NUM
ejpam-3118	3	3	-	-	SYM
ejpam-3118	3	4	966	966	NUM
ejpam-3118	3	5	issn	issn	PROPN
ejpam-3118	3	6	1307	1307	NUM
ejpam-3118	3	7	-	-	SYM
ejpam-3118	3	8	5543	5543	NUM
ejpam-3118	3	9	–	–	PUNCT
ejpam-3118	3	10	www.ejpam.com	www.ejpam.com	X
ejpam-3118	3	11	published	publish	VERB
ejpam-3118	3	12	by	by	ADP
ejpam-3118	3	13	new	new	PROPN
ejpam-3118	3	14	york	york	PROPN
ejpam-3118	3	15	business	business	PROPN
ejpam-3118	3	16	global	global	PROPN
ejpam-3118	3	17	the	the	DET
ejpam-3118	3	18	group	group	NOUN
ejpam-3118	3	19	of	of	ADP
ejpam-3118	3	20	units	unit	NOUN
ejpam-3118	3	21	of	of	ADP
ejpam-3118	3	22	integral	integral	ADJ
ejpam-3118	3	23	group	group	NOUN
ejpam-3118	3	24	rings	ring	NOUN
ejpam-3118	3	25	of	of	ADP
ejpam-3118	3	26	extra	extra	ADJ
ejpam-3118	3	27	-	-	ADJ
ejpam-3118	3	28	special	special	ADJ
ejpam-3118	3	29	2	2	NUM
ejpam-3118	3	30	-	-	PUNCT
ejpam-3118	3	31	groups	group	NOUN
ejpam-3118	3	32	cristiane	cristiane	PROPN
ejpam-3118	3	33	de	de	PROPN
ejpam-3118	3	34	mello	mello	PROPN
ejpam-3118	3	35	mathematics	mathematics	PROPN
ejpam-3118	3	36	institute	institute	PROPN
ejpam-3118	3	37	,	,	PUNCT
ejpam-3118	3	38	federal	federal	ADJ
ejpam-3118	3	39	university	university	NOUN
ejpam-3118	3	40	of	of	ADP
ejpam-3118	3	41	the	the	DET
ejpam-3118	3	42	state	state	NOUN
ejpam-3118	3	43	of	of	ADP
ejpam-3118	3	44	rio	rio	PROPN
ejpam-3118	3	45	de	de	PROPN
ejpam-3118	3	46	janeiro	janeiro	PROPN
ejpam-3118	3	47	,	,	PUNCT
ejpam-3118	3	48	rio	rio	PROPN
ejpam-3118	3	49	de	de	PROPN
ejpam-3118	3	50	janeiro	janeiro	PROPN
ejpam-3118	3	51	,	,	PUNCT
ejpam-3118	3	52	brazil	brazil	PROPN
ejpam-3118	3	53	abstract	abstract	NOUN
ejpam-3118	3	54	.	.	PUNCT
ejpam-3118	4	1	one	one	NUM
ejpam-3118	4	2	of	of	ADP
ejpam-3118	4	3	the	the	DET
ejpam-3118	4	4	main	main	ADJ
ejpam-3118	4	5	problems	problem	NOUN
ejpam-3118	4	6	on	on	ADP
ejpam-3118	4	7	group	group	NOUN
ejpam-3118	4	8	rings	ring	NOUN
ejpam-3118	4	9	is	be	AUX
ejpam-3118	4	10	to	to	PART
ejpam-3118	4	11	determine	determine	VERB
ejpam-3118	4	12	its	its	PRON
ejpam-3118	4	13	group	group	NOUN
ejpam-3118	4	14	of	of	ADP
ejpam-3118	4	15	units	unit	NOUN
ejpam-3118	4	16	.	.	PUNCT
ejpam-3118	5	1	in	in	ADP
ejpam-3118	5	2	this	this	DET
ejpam-3118	5	3	paper	paper	NOUN
ejpam-3118	5	4	,	,	PUNCT
ejpam-3118	5	5	we	we	PRON
ejpam-3118	5	6	describe	describe	VERB
ejpam-3118	5	7	the	the	DET
ejpam-3118	5	8	group	group	NOUN
ejpam-3118	5	9	of	of	ADP
ejpam-3118	5	10	units	unit	NOUN
ejpam-3118	5	11	of	of	ADP
ejpam-3118	5	12	integral	integral	ADJ
ejpam-3118	5	13	group	group	NOUN
ejpam-3118	5	14	rings	ring	NOUN
ejpam-3118	5	15	of	of	ADP
ejpam-3118	5	16	two	two	NUM
ejpam-3118	5	17	extra	extra	ADJ
ejpam-3118	5	18	-	-	ADJ
ejpam-3118	5	19	special	special	ADJ
ejpam-3118	5	20	2	2	NUM
ejpam-3118	5	21	-	-	PUNCT
ejpam-3118	5	22	groups	group	NOUN
ejpam-3118	5	23	:	:	PUNCT
ejpam-3118	5	24	one	one	NUM
ejpam-3118	5	25	of	of	ADP
ejpam-3118	5	26	order	order	NOUN
ejpam-3118	5	27	32	32	NUM
ejpam-3118	5	28	,	,	PUNCT
ejpam-3118	5	29	the	the	DET
ejpam-3118	5	30	central	central	ADJ
ejpam-3118	5	31	product	product	NOUN
ejpam-3118	5	32	of	of	ADP
ejpam-3118	5	33	two	two	NUM
ejpam-3118	5	34	copies	copy	NOUN
ejpam-3118	5	35	of	of	ADP
ejpam-3118	5	36	d4	d4	PROPN
ejpam-3118	5	37	,	,	PUNCT
ejpam-3118	5	38	and	and	CCONJ
ejpam-3118	5	39	another	another	PRON
ejpam-3118	5	40	of	of	ADP
ejpam-3118	5	41	order	order	NOUN
ejpam-3118	5	42	128	128	NUM
ejpam-3118	5	43	,	,	PUNCT
ejpam-3118	5	44	the	the	DET
ejpam-3118	5	45	central	central	ADJ
ejpam-3118	5	46	product	product	NOUN
ejpam-3118	5	47	of	of	ADP
ejpam-3118	5	48	three	three	NUM
ejpam-3118	5	49	copies	copy	NOUN
ejpam-3118	5	50	of	of	ADP
ejpam-3118	5	51	d4	d4	PROPN
ejpam-3118	5	52	.	.	PUNCT
ejpam-3118	6	1	2010	2010	NUM
ejpam-3118	6	2	mathematics	mathematic	NOUN
ejpam-3118	6	3	subject	subject	NOUN
ejpam-3118	6	4	classifications	classification	NOUN
ejpam-3118	6	5	:	:	PUNCT
ejpam-3118	6	6	16s34	16s34	NUM
ejpam-3118	6	7	,	,	PUNCT
ejpam-3118	6	8	16u60	16u60	NUM
ejpam-3118	6	9	,	,	PUNCT
ejpam-3118	6	10	20d15	20d15	NUM
ejpam-3118	6	11	key	key	ADJ
ejpam-3118	6	12	words	word	NOUN
ejpam-3118	6	13	and	and	CCONJ
ejpam-3118	6	14	phrases	phrase	NOUN
ejpam-3118	6	15	:	:	PUNCT
ejpam-3118	6	16	group	group	NOUN
ejpam-3118	6	17	rings	ring	NOUN
ejpam-3118	6	18	,	,	PUNCT
ejpam-3118	6	19	units	unit	NOUN
ejpam-3118	6	20	in	in	ADP
ejpam-3118	6	21	integral	integral	ADJ
ejpam-3118	6	22	group	group	NOUN
ejpam-3118	6	23	rings	ring	NOUN
ejpam-3118	6	24	,	,	PUNCT
ejpam-3118	6	25	the	the	DET
ejpam-3118	6	26	group	group	NOUN
ejpam-3118	6	27	of	of	ADP
ejpam-3118	6	28	units	unit	NOUN
ejpam-3118	6	29	of	of	ADP
ejpam-3118	6	30	zd4	zd4	NOUN
ejpam-3118	6	31	,	,	PUNCT
ejpam-3118	6	32	the	the	DET
ejpam-3118	6	33	group	group	NOUN
ejpam-3118	6	34	of	of	ADP
ejpam-3118	6	35	units	unit	NOUN
ejpam-3118	6	36	of	of	ADP
ejpam-3118	6	37	zg	zg	PROPN
ejpam-3118	6	38	,	,	PUNCT
ejpam-3118	6	39	g	g	ADP
ejpam-3118	6	40	extra	extra	ADJ
ejpam-3118	6	41	-	-	ADJ
ejpam-3118	6	42	special	special	ADJ
ejpam-3118	6	43	2	2	NUM
ejpam-3118	6	44	-	-	PUNCT
ejpam-3118	6	45	group	group	NOUN
ejpam-3118	6	46	.	.	PUNCT
ejpam-3118	7	1	1	1	X
ejpam-3118	7	2	.	.	X
ejpam-3118	7	3	introduction	introduction	NOUN
ejpam-3118	7	4	a	a	DET
ejpam-3118	7	5	important	important	ADJ
ejpam-3118	7	6	problem	problem	NOUN
ejpam-3118	7	7	on	on	ADP
ejpam-3118	7	8	group	group	NOUN
ejpam-3118	7	9	rings	ring	NOUN
ejpam-3118	7	10	is	be	AUX
ejpam-3118	7	11	to	to	PART
ejpam-3118	7	12	describe	describe	VERB
ejpam-3118	7	13	precisely	precisely	ADV
ejpam-3118	7	14	the	the	DET
ejpam-3118	7	15	group	group	NOUN
ejpam-3118	7	16	of	of	ADP
ejpam-3118	7	17	units	unit	NOUN
ejpam-3118	7	18	u(rg	u(rg	ADJ
ejpam-3118	7	19	)	)	PUNCT
ejpam-3118	7	20	of	of	ADP
ejpam-3118	7	21	a	a	DET
ejpam-3118	7	22	group	group	NOUN
ejpam-3118	7	23	ring	ring	NOUN
ejpam-3118	7	24	rg	rg	NOUN
ejpam-3118	7	25	,	,	PUNCT
ejpam-3118	7	26	where	where	SCONJ
ejpam-3118	7	27	r	r	NOUN
ejpam-3118	7	28	is	be	AUX
ejpam-3118	7	29	a	a	DET
ejpam-3118	7	30	commutative	commutative	ADJ
ejpam-3118	7	31	ring	ring	NOUN
ejpam-3118	7	32	with	with	ADP
ejpam-3118	7	33	identity	identity	NOUN
ejpam-3118	7	34	and	and	CCONJ
ejpam-3118	7	35	g	g	NOUN
ejpam-3118	7	36	is	be	AUX
ejpam-3118	7	37	a	a	DET
ejpam-3118	7	38	finite	finite	ADJ
ejpam-3118	7	39	group	group	NOUN
ejpam-3118	7	40	.	.	PUNCT
ejpam-3118	8	1	the	the	DET
ejpam-3118	8	2	high	high	ADJ
ejpam-3118	8	3	degree	degree	NOUN
ejpam-3118	8	4	of	of	ADP
ejpam-3118	8	5	complexity	complexity	NOUN
ejpam-3118	8	6	of	of	ADP
ejpam-3118	8	7	this	this	DET
ejpam-3118	8	8	problem	problem	NOUN
ejpam-3118	8	9	became	become	VERB
ejpam-3118	8	10	evident	evident	ADJ
ejpam-3118	8	11	in	in	ADP
ejpam-3118	8	12	the	the	DET
ejpam-3118	8	13	seventies	seventy	NOUN
ejpam-3118	8	14	,	,	PUNCT
ejpam-3118	8	15	when	when	SCONJ
ejpam-3118	8	16	it	it	PRON
ejpam-3118	8	17	was	be	AUX
ejpam-3118	8	18	proven	prove	VERB
ejpam-3118	8	19	that	that	SCONJ
ejpam-3118	8	20	,	,	PUNCT
ejpam-3118	8	21	in	in	ADP
ejpam-3118	8	22	general	general	ADJ
ejpam-3118	8	23	,	,	PUNCT
ejpam-3118	8	24	the	the	DET
ejpam-3118	8	25	group	group	NOUN
ejpam-3118	8	26	of	of	ADP
ejpam-3118	8	27	units	unit	NOUN
ejpam-3118	8	28	contains	contain	VERB
ejpam-3118	8	29	a	a	DET
ejpam-3118	8	30	non	non	X
ejpam-3118	8	31	abelian	abelian	PROPN
ejpam-3118	8	32	free	free	PROPN
ejpam-3118	8	33	subgroup	subgroup	PROPN
ejpam-3118	8	34	.	.	PUNCT
ejpam-3118	9	1	many	many	ADJ
ejpam-3118	9	2	researchers	researcher	NOUN
ejpam-3118	9	3	,	,	PUNCT
ejpam-3118	9	4	using	use	VERB
ejpam-3118	9	5	techniques	technique	NOUN
ejpam-3118	9	6	of	of	ADP
ejpam-3118	9	7	group	group	NOUN
ejpam-3118	9	8	representation	representation	NOUN
ejpam-3118	9	9	theory	theory	NOUN
ejpam-3118	9	10	and	and	CCONJ
ejpam-3118	9	11	algebraic	algebraic	ADJ
ejpam-3118	9	12	number	number	NOUN
ejpam-3118	9	13	theory	theory	NOUN
ejpam-3118	9	14	,	,	PUNCT
ejpam-3118	9	15	presented	present	VERB
ejpam-3118	9	16	an	an	DET
ejpam-3118	9	17	explicit	explicit	ADJ
ejpam-3118	9	18	description	description	NOUN
ejpam-3118	9	19	of	of	ADP
ejpam-3118	9	20	the	the	DET
ejpam-3118	9	21	group	group	NOUN
ejpam-3118	9	22	of	of	ADP
ejpam-3118	9	23	units	unit	NOUN
ejpam-3118	9	24	,	,	PUNCT
ejpam-3118	9	25	a	a	DET
ejpam-3118	9	26	description	description	NOUN
ejpam-3118	9	27	of	of	ADP
ejpam-3118	9	28	the	the	DET
ejpam-3118	9	29	general	general	ADJ
ejpam-3118	9	30	structure	structure	NOUN
ejpam-3118	9	31	of	of	ADP
ejpam-3118	9	32	u(rg	u(rg	PROPN
ejpam-3118	9	33	)	)	PUNCT
ejpam-3118	9	34	or	or	CCONJ
ejpam-3118	9	35	a	a	DET
ejpam-3118	9	36	set	set	NOUN
ejpam-3118	9	37	of	of	ADP
ejpam-3118	9	38	generators	generator	NOUN
ejpam-3118	9	39	of	of	ADP
ejpam-3118	9	40	a	a	DET
ejpam-3118	9	41	finite	finite	ADJ
ejpam-3118	9	42	index	index	NOUN
ejpam-3118	9	43	subgroup	subgroup	NOUN
ejpam-3118	9	44	of	of	ADP
ejpam-3118	9	45	u(rg	u(rg	PROPN
ejpam-3118	9	46	)	)	PUNCT
ejpam-3118	9	47	.	.	PUNCT
ejpam-3118	10	1	on	on	ADP
ejpam-3118	10	2	these	these	DET
ejpam-3118	10	3	subjects	subject	NOUN
ejpam-3118	10	4	we	we	PRON
ejpam-3118	10	5	could	could	AUX
ejpam-3118	10	6	quote	quote	VERB
ejpam-3118	10	7	a.	a.	PROPN
ejpam-3118	10	8	k.	k.	PROPN
ejpam-3118	10	9	bhandari	bhandari	PROPN
ejpam-3118	10	10	and	and	CCONJ
ejpam-3118	10	11	i.	i.	PROPN
ejpam-3118	10	12	s.	s.	PROPN
ejpam-3118	10	13	luthar	luthar	PROPN
ejpam-3118	11	1	[	[	X
ejpam-3118	11	2	1	1	NUM
ejpam-3118	11	3	]	]	PUNCT
ejpam-3118	11	4	,	,	PUNCT
ejpam-3118	11	5	a.	a.	NOUN
ejpam-3118	11	6	bovdi	bovdi	NOUN
ejpam-3118	11	7	and	and	CCONJ
ejpam-3118	11	8	f.	f.	PROPN
ejpam-3118	11	9	c.	c.	PROPN
ejpam-3118	11	10	polcino	polcino	PROPN
ejpam-3118	11	11	milies	milie	NOUN
ejpam-3118	11	12	[	[	X
ejpam-3118	11	13	2	2	NUM
ejpam-3118	11	14	]	]	PUNCT
ejpam-3118	11	15	,	,	PUNCT
ejpam-3118	11	16	r.	r.	PROPN
ejpam-3118	11	17	a.	a.	PROPN
ejpam-3118	11	18	ferraz	ferraz	PROPN
ejpam-3118	12	1	[	[	X
ejpam-3118	12	2	3	3	NUM
ejpam-3118	12	3	]	]	PUNCT
ejpam-3118	12	4	,	,	PUNCT
ejpam-3118	12	5	a.	a.	PROPN
ejpam-3118	12	6	giambruno	giambruno	PROPN
ejpam-3118	12	7	and	and	CCONJ
ejpam-3118	12	8	s.	s.	PROPN
ejpam-3118	12	9	k.	k.	PROPN
ejpam-3118	12	10	seghal	seghal	PROPN
ejpam-3118	12	11	[	[	X
ejpam-3118	12	12	4	4	NUM
ejpam-3118	12	13	]	]	PUNCT
ejpam-3118	12	14	,	,	PUNCT
ejpam-3118	12	15	e.	e.	PROPN
ejpam-3118	12	16	g.	g.	PROPN
ejpam-3118	12	17	goodaire	goodaire	PROPN
ejpam-3118	12	18	and	and	CCONJ
ejpam-3118	12	19	e.	e.	PROPN
ejpam-3118	12	20	jespers	jespers	PROPN
ejpam-3118	13	1	[	[	X
ejpam-3118	13	2	5	5	NUM
ejpam-3118	13	3	]	]	PUNCT
ejpam-3118	13	4	,	,	PUNCT
ejpam-3118	13	5	e.	e.	PROPN
ejpam-3118	13	6	jespers	jespers	PROPN
ejpam-3118	13	7	and	and	CCONJ
ejpam-3118	13	8	g.	g.	PROPN
ejpam-3118	13	9	leal	leal	PROPN
ejpam-3118	14	1	[	[	X
ejpam-3118	14	2	8	8	NUM
ejpam-3118	14	3	]	]	PUNCT
ejpam-3118	14	4	,	,	PUNCT
ejpam-3118	15	1	[	[	X
ejpam-3118	15	2	9	9	NUM
ejpam-3118	15	3	]	]	PUNCT
ejpam-3118	15	4	,	,	PUNCT
ejpam-3118	15	5	e.	e.	PROPN
ejpam-3118	15	6	jespers	jespers	PROPN
ejpam-3118	15	7	and	and	CCONJ
ejpam-3118	15	8	g.	g.	PROPN
ejpam-3118	15	9	leal	leal	PROPN
ejpam-3118	15	10	and	and	CCONJ
ejpam-3118	15	11	f.	f.	PROPN
ejpam-3118	15	12	c.	c.	PROPN
ejpam-3118	15	13	polcino	polcino	PROPN
ejpam-3118	15	14	milies	milie	NOUN
ejpam-3118	15	15	[	[	X
ejpam-3118	15	16	10	10	NUM
ejpam-3118	15	17	]	]	PUNCT
ejpam-3118	15	18	,	,	PUNCT
ejpam-3118	15	19	e.	e.	PROPN
ejpam-3118	15	20	jespers	jespers	PROPN
ejpam-3118	15	21	and	and	CCONJ
ejpam-3118	15	22	m.	m.	NOUN
ejpam-3118	15	23	m.	m.	NOUN
ejpam-3118	15	24	parmenter	parmenter	NOUN
ejpam-3118	15	25	and	and	CCONJ
ejpam-3118	15	26	s.	s.	PROPN
ejpam-3118	15	27	k.	k.	PROPN
ejpam-3118	15	28	sehgal	sehgal	PROPN
ejpam-3118	16	1	[	[	X
ejpam-3118	16	2	11	11	NUM
ejpam-3118	16	3	]	]	PUNCT
ejpam-3118	16	4	,	,	PUNCT
ejpam-3118	16	5	f.	f.	PROPN
ejpam-3118	16	6	c.	c.	PROPN
ejpam-3118	16	7	polcino	polcino	PROPN
ejpam-3118	16	8	milies	milie	NOUN
ejpam-3118	16	9	[	[	X
ejpam-3118	16	10	12	12	NUM
ejpam-3118	16	11	]	]	PUNCT
ejpam-3118	16	12	,	,	PUNCT
ejpam-3118	16	13	j.	j.	PROPN
ejpam-3118	16	14	ritter	ritter	PROPN
ejpam-3118	16	15	and	and	CCONJ
ejpam-3118	16	16	s.	s.	PROPN
ejpam-3118	16	17	k.	k.	PROPN
ejpam-3118	16	18	sehgal	sehgal	PROPN
ejpam-3118	17	1	[	[	X
ejpam-3118	17	2	13	13	NUM
ejpam-3118	17	3	]	]	PUNCT
ejpam-3118	17	4	,	,	PUNCT
ejpam-3118	18	1	[	[	X
ejpam-3118	18	2	14	14	NUM
ejpam-3118	18	3	]	]	PUNCT
ejpam-3118	18	4	,	,	PUNCT
ejpam-3118	18	5	[	[	X
ejpam-3118	18	6	15	15	NUM
ejpam-3118	18	7	]	]	PUNCT
ejpam-3118	18	8	and	and	CCONJ
ejpam-3118	18	9	two	two	NUM
ejpam-3118	18	10	new	new	ADJ
ejpam-3118	18	11	books	book	NOUN
ejpam-3118	18	12	by	by	ADP
ejpam-3118	18	13	e.	e.	PROPN
ejpam-3118	18	14	jespers	jespers	PROPN
ejpam-3118	18	15	and	and	CCONJ
ejpam-3118	18	16	a.	a.	PROPN
ejpam-3118	18	17	del	del	PROPN
ejpam-3118	18	18	rio	rio	PROPN
ejpam-3118	19	1	[	[	X
ejpam-3118	19	2	6	6	NUM
ejpam-3118	19	3	]	]	PUNCT
ejpam-3118	19	4	,	,	PUNCT
ejpam-3118	19	5	[	[	X
ejpam-3118	19	6	7	7	NUM
ejpam-3118	19	7	]	]	PUNCT
ejpam-3118	19	8	,	,	PUNCT
ejpam-3118	19	9	and	and	CCONJ
ejpam-3118	19	10	many	many	ADJ
ejpam-3118	19	11	others	other	NOUN
ejpam-3118	19	12	.	.	PUNCT
ejpam-3118	20	1	in	in	ADP
ejpam-3118	20	2	[	[	X
ejpam-3118	20	3	6	6	NUM
ejpam-3118	20	4	,	,	PUNCT
ejpam-3118	20	5	7	7	NUM
ejpam-3118	20	6	]	]	PUNCT
ejpam-3118	20	7	,	,	PUNCT
ejpam-3118	20	8	for	for	ADP
ejpam-3118	20	9	many	many	ADJ
ejpam-3118	20	10	finite	finite	ADJ
ejpam-3118	20	11	groups	group	NOUN
ejpam-3118	20	12	g	g	ADP
ejpam-3118	20	13	,	,	PUNCT
ejpam-3118	20	14	methods	method	NOUN
ejpam-3118	20	15	are	be	AUX
ejpam-3118	20	16	given	give	VERB
ejpam-3118	20	17	to	to	PART
ejpam-3118	20	18	describe	describe	VERB
ejpam-3118	20	19	all	all	DET
ejpam-3118	20	20	the	the	DET
ejpam-3118	20	21	rational	rational	ADJ
ejpam-3118	20	22	representations	representation	NOUN
ejpam-3118	20	23	of	of	ADP
ejpam-3118	20	24	g.	g.	PROPN
ejpam-3118	20	25	in	in	ADP
ejpam-3118	20	26	particular	particular	ADJ
ejpam-3118	20	27	,	,	PUNCT
ejpam-3118	20	28	for	for	ADP
ejpam-3118	20	29	nilpotent	nilpotent	ADJ
ejpam-3118	20	30	nite	nite	ADJ
ejpam-3118	20	31	groups	group	NOUN
ejpam-3118	20	32	g	g	ADP
ejpam-3118	20	33	the	the	DET
ejpam-3118	20	34	wedderburn	wedderburn	NOUN
ejpam-3118	20	35	decomposition	decomposition	NOUN
ejpam-3118	20	36	of	of	ADP
ejpam-3118	20	37	the	the	DET
ejpam-3118	20	38	rational	rational	ADJ
ejpam-3118	20	39	group	group	NOUN
ejpam-3118	20	40	algebra	algebra	PROPN
ejpam-3118	20	41	qg	qg	PROPN
ejpam-3118	20	42	is	be	AUX
ejpam-3118	20	43	explicitly	explicitly	ADV
ejpam-3118	20	44	given	give	VERB
ejpam-3118	20	45	via	via	ADP
ejpam-3118	20	46	the	the	DET
ejpam-3118	20	47	construction	construction	NOUN
ejpam-3118	20	48	of	of	ADP
ejpam-3118	20	49	a	a	DET
ejpam-3118	20	50	complete	complete	ADJ
ejpam-3118	20	51	set	set	NOUN
ejpam-3118	20	52	of	of	ADP
ejpam-3118	20	53	matrix	matrix	NOUN
ejpam-3118	20	54	units	unit	NOUN
ejpam-3118	20	55	of	of	ADP
ejpam-3118	20	56	qg	qg	PROPN
ejpam-3118	20	57	.	.	PROPN
ejpam-3118	21	1	from	from	ADP
ejpam-3118	21	2	this	this	DET
ejpam-3118	21	3	one	one	NOUN
ejpam-3118	21	4	obtains	obtain	VERB
ejpam-3118	21	5	an	an	DET
ejpam-3118	21	6	explicit	explicit	ADJ
ejpam-3118	21	7	set	set	NOUN
ejpam-3118	21	8	of	of	ADP
ejpam-3118	21	9	nitely	nitely	ADV
ejpam-3118	21	10	many	many	ADJ
ejpam-3118	21	11	generators	generator	NOUN
ejpam-3118	21	12	for	for	ADP
ejpam-3118	21	13	a	a	DET
ejpam-3118	21	14	subgroup	subgroup	NOUN
ejpam-3118	21	15	of	of	ADP
ejpam-3118	21	16	nite	nite	ADJ
ejpam-3118	21	17	index	index	NOUN
ejpam-3118	21	18	of	of	ADP
ejpam-3118	21	19	the	the	DET
ejpam-3118	21	20	unit	unit	NOUN
ejpam-3118	21	21	group	group	NOUN
ejpam-3118	21	22	u(zg	u(zg	PROPN
ejpam-3118	21	23	)	)	PUNCT
ejpam-3118	21	24	;	;	PUNCT
ejpam-3118	21	25	these	these	DET
ejpam-3118	21	26	email	email	NOUN
ejpam-3118	21	27	addresses	address	NOUN
ejpam-3118	21	28	:	:	PUNCT
ejpam-3118	21	29	demello.cristiane@gmail.com	demello.cristiane@gmail.com	X
ejpam-3118	21	30	(	(	PUNCT
ejpam-3118	21	31	c.	c.	PROPN
ejpam-3118	21	32	mello	mello	PROPN
ejpam-3118	21	33	)	)	PUNCT
ejpam-3118	21	34	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3118	22	1	955	955	NUM
ejpam-3118	22	2	c	c	X
ejpam-3118	22	3	©	©	PROPN
ejpam-3118	22	4	2017	2017	NUM
ejpam-3118	22	5	ejpam	ejpam	NOUN
ejpam-3118	22	6	all	all	DET
ejpam-3118	22	7	rights	right	NOUN
ejpam-3118	22	8	reserved	reserve	VERB
ejpam-3118	22	9	.	.	PUNCT
ejpam-3118	23	1	c.	c.	PROPN
ejpam-3118	23	2	mello	mello	PROPN
ejpam-3118	23	3	/	/	SYM
ejpam-3118	23	4	eur	eur	PROPN
ejpam-3118	23	5	.	.	PUNCT
ejpam-3118	24	1	j.	j.	PROPN
ejpam-3118	24	2	pure	pure	PROPN
ejpam-3118	24	3	appl	appl	PROPN
ejpam-3118	24	4	.	.	PROPN
ejpam-3118	24	5	math	math	PROPN
ejpam-3118	24	6	,	,	PUNCT
ejpam-3118	24	7	10	10	NUM
ejpam-3118	24	8	(	(	PUNCT
ejpam-3118	24	9	5	5	NUM
ejpam-3118	24	10	)	)	PUNCT
ejpam-3118	24	11	(	(	PUNCT
ejpam-3118	24	12	2017	2017	NUM
ejpam-3118	24	13	)	)	PUNCT
ejpam-3118	24	14	,	,	PUNCT
ejpam-3118	24	15	955	955	NUM
ejpam-3118	24	16	-	-	SYM
ejpam-3118	24	17	966	966	NUM
ejpam-3118	24	18	956	956	NUM
ejpam-3118	24	19	generators	generator	NOUN
ejpam-3118	24	20	are	be	AUX
ejpam-3118	24	21	the	the	DET
ejpam-3118	24	22	so	so	ADV
ejpam-3118	24	23	called	call	VERB
ejpam-3118	24	24	bass	bass	NOUN
ejpam-3118	24	25	units	unit	NOUN
ejpam-3118	24	26	and	and	CCONJ
ejpam-3118	24	27	bicyclic	bicyclic	ADJ
ejpam-3118	24	28	units	unit	NOUN
ejpam-3118	24	29	.	.	PUNCT
ejpam-3118	25	1	actually	actually	ADV
ejpam-3118	25	2	,	,	PUNCT
ejpam-3118	25	3	it	it	PRON
ejpam-3118	25	4	known	know	VERB
ejpam-3118	25	5	that	that	SCONJ
ejpam-3118	25	6	for	for	ADP
ejpam-3118	25	7	many	many	ADJ
ejpam-3118	25	8	nite	nite	ADJ
ejpam-3118	25	9	groupsg	groupsg	NOUN
ejpam-3118	25	10	the	the	DET
ejpam-3118	25	11	bass	bass	NOUN
ejpam-3118	25	12	units	unit	NOUN
ejpam-3118	25	13	together	together	ADV
ejpam-3118	25	14	with	with	ADP
ejpam-3118	25	15	the	the	DET
ejpam-3118	25	16	bicyclic	bicyclic	ADJ
ejpam-3118	25	17	units	unit	NOUN
ejpam-3118	25	18	generate	generate	VERB
ejpam-3118	25	19	a	a	DET
ejpam-3118	25	20	subgroup	subgroup	NOUN
ejpam-3118	25	21	of	of	ADP
ejpam-3118	25	22	nite	nite	PROPN
ejpam-3118	25	23	index	index	NOUN
ejpam-3118	25	24	,	,	PUNCT
ejpam-3118	25	25	the	the	DET
ejpam-3118	25	26	groups	group	NOUN
ejpam-3118	25	27	excluded	exclude	VERB
ejpam-3118	25	28	are	be	AUX
ejpam-3118	25	29	determined	determine	VERB
ejpam-3118	25	30	by	by	ADP
ejpam-3118	25	31	the	the	DET
ejpam-3118	25	32	existence	existence	NOUN
ejpam-3118	25	33	of	of	ADP
ejpam-3118	25	34	exceptional	exceptional	ADJ
ejpam-3118	25	35	simple	simple	ADJ
ejpam-3118	25	36	components	component	NOUN
ejpam-3118	25	37	of	of	ADP
ejpam-3118	25	38	qg	qg	PROPN
ejpam-3118	25	39	(	(	PUNCT
ejpam-3118	25	40	such	such	ADJ
ejpam-3118	25	41	as	as	ADP
ejpam-3118	25	42	non	non	ADJ
ejpam-3118	25	43	-	-	ADJ
ejpam-3118	25	44	commutative	commutative	ADJ
ejpam-3118	25	45	division	division	NOUN
ejpam-3118	25	46	algebras	algebra	NOUN
ejpam-3118	25	47	and	and	CCONJ
ejpam-3118	25	48	m2(q	m2(q	NOUN
ejpam-3118	25	49	)	)	PUNCT
ejpam-3118	25	50	)	)	PUNCT
ejpam-3118	25	51	.	.	PUNCT
ejpam-3118	26	1	in	in	ADP
ejpam-3118	26	2	general	general	ADJ
ejpam-3118	26	3	it	it	PRON
ejpam-3118	26	4	remains	remain	VERB
ejpam-3118	26	5	a	a	DET
ejpam-3118	26	6	problem	problem	NOUN
ejpam-3118	26	7	to	to	PART
ejpam-3118	26	8	describe	describe	VERB
ejpam-3118	26	9	the	the	DET
ejpam-3118	26	10	full	full	ADJ
ejpam-3118	26	11	unit	unit	NOUN
ejpam-3118	26	12	group	group	NOUN
ejpam-3118	26	13	u(zg	u(zg	NUM
ejpam-3118	26	14	)	)	PUNCT
ejpam-3118	26	15	.	.	PUNCT
ejpam-3118	27	1	in	in	ADP
ejpam-3118	27	2	[	[	X
ejpam-3118	27	3	6	6	NUM
ejpam-3118	27	4	]	]	PUNCT
ejpam-3118	27	5	this	this	PRON
ejpam-3118	27	6	has	have	AUX
ejpam-3118	27	7	been	be	AUX
ejpam-3118	27	8	done	do	VERB
ejpam-3118	27	9	for	for	ADP
ejpam-3118	27	10	several	several	ADJ
ejpam-3118	27	11	examples	example	NOUN
ejpam-3118	27	12	of	of	ADP
ejpam-3118	27	13	nite	nite	ADJ
ejpam-3118	27	14	groups	group	NOUN
ejpam-3118	27	15	.	.	PUNCT
ejpam-3118	28	1	f.	f.	PROPN
ejpam-3118	28	2	c.	c.	PROPN
ejpam-3118	28	3	polcino	polcino	PROPN
ejpam-3118	28	4	milies	milie	NOUN
ejpam-3118	28	5	[	[	X
ejpam-3118	28	6	10	10	NUM
ejpam-3118	28	7	]	]	PUNCT
ejpam-3118	28	8	was	be	AUX
ejpam-3118	28	9	the	the	DET
ejpam-3118	28	10	first	first	ADJ
ejpam-3118	28	11	to	to	PART
ejpam-3118	28	12	describe	describe	VERB
ejpam-3118	28	13	the	the	DET
ejpam-3118	28	14	unit	unit	NOUN
ejpam-3118	28	15	group	group	NOUN
ejpam-3118	28	16	u(zd4	u(zd4	NOUN
ejpam-3118	28	17	)	)	PUNCT
ejpam-3118	28	18	,	,	PUNCT
ejpam-3118	28	19	where	where	SCONJ
ejpam-3118	28	20	d4	d4	PROPN
ejpam-3118	28	21	denotes	denote	VERB
ejpam-3118	28	22	the	the	DET
ejpam-3118	28	23	dihedral	dihedral	ADJ
ejpam-3118	28	24	group	group	NOUN
ejpam-3118	28	25	of	of	ADP
ejpam-3118	28	26	order	order	NOUN
ejpam-3118	28	27	8	8	NUM
ejpam-3118	28	28	.	.	PUNCT
ejpam-3118	29	1	later	later	ADV
ejpam-3118	29	2	,	,	PUNCT
ejpam-3118	29	3	e.	e.	PROPN
ejpam-3118	29	4	jespers	jespers	PROPN
ejpam-3118	29	5	and	and	CCONJ
ejpam-3118	29	6	g.	g.	PROPN
ejpam-3118	29	7	leal	leal	PROPN
ejpam-3118	30	1	[	[	X
ejpam-3118	30	2	6	6	NUM
ejpam-3118	30	3	]	]	PUNCT
ejpam-3118	30	4	described	describe	VERB
ejpam-3118	30	5	the	the	DET
ejpam-3118	30	6	same	same	ADJ
ejpam-3118	30	7	group	group	NOUN
ejpam-3118	30	8	using	use	VERB
ejpam-3118	30	9	a	a	DET
ejpam-3118	30	10	different	different	ADJ
ejpam-3118	30	11	method	method	NOUN
ejpam-3118	30	12	that	that	PRON
ejpam-3118	30	13	also	also	ADV
ejpam-3118	30	14	was	be	AUX
ejpam-3118	30	15	applied	apply	VERB
ejpam-3118	30	16	to	to	ADP
ejpam-3118	30	17	other	other	ADJ
ejpam-3118	30	18	2	2	NUM
ejpam-3118	30	19	-	-	PUNCT
ejpam-3118	30	20	groups	group	NOUN
ejpam-3118	30	21	.	.	PUNCT
ejpam-3118	31	1	in	in	ADP
ejpam-3118	31	2	this	this	DET
ejpam-3118	31	3	paper	paper	NOUN
ejpam-3118	31	4	we	we	PRON
ejpam-3118	31	5	describe∗	describe∗	VERB
ejpam-3118	31	6	the	the	DET
ejpam-3118	31	7	group	group	NOUN
ejpam-3118	31	8	of	of	ADP
ejpam-3118	31	9	units	unit	NOUN
ejpam-3118	31	10	of	of	ADP
ejpam-3118	31	11	the	the	DET
ejpam-3118	31	12	integral	integral	ADJ
ejpam-3118	31	13	group	group	NOUN
ejpam-3118	31	14	rings	ring	NOUN
ejpam-3118	31	15	of	of	ADP
ejpam-3118	31	16	two	two	NUM
ejpam-3118	31	17	extra	extra	ADJ
ejpam-3118	31	18	-	-	ADJ
ejpam-3118	31	19	special	special	ADJ
ejpam-3118	31	20	2	2	NUM
ejpam-3118	31	21	-	-	PUNCT
ejpam-3118	31	22	groups	group	NOUN
ejpam-3118	31	23	:	:	PUNCT
ejpam-3118	31	24	g1	g1	NOUN
ejpam-3118	31	25	of	of	ADP
ejpam-3118	31	26	order	order	NOUN
ejpam-3118	31	27	32	32	NUM
ejpam-3118	31	28	,	,	PUNCT
ejpam-3118	31	29	the	the	DET
ejpam-3118	31	30	central	central	ADJ
ejpam-3118	31	31	product	product	NOUN
ejpam-3118	31	32	of	of	ADP
ejpam-3118	31	33	two	two	NUM
ejpam-3118	31	34	copies	copy	NOUN
ejpam-3118	31	35	of	of	ADP
ejpam-3118	31	36	d4	d4	PROPN
ejpam-3118	31	37	,	,	PUNCT
ejpam-3118	31	38	and	and	CCONJ
ejpam-3118	31	39	g2	g2	PROPN
ejpam-3118	31	40	of	of	ADP
ejpam-3118	31	41	order	order	NOUN
ejpam-3118	31	42	128	128	NUM
ejpam-3118	31	43	,	,	PUNCT
ejpam-3118	31	44	the	the	DET
ejpam-3118	31	45	central	central	ADJ
ejpam-3118	31	46	product	product	NOUN
ejpam-3118	31	47	of	of	ADP
ejpam-3118	31	48	three	three	NUM
ejpam-3118	31	49	copies	copy	NOUN
ejpam-3118	31	50	of	of	ADP
ejpam-3118	31	51	d4	d4	PROPN
ejpam-3118	31	52	.	.	PUNCT
ejpam-3118	32	1	2	2	X
ejpam-3118	32	2	.	.	X
ejpam-3118	32	3	notation	notation	NOUN
ejpam-3118	32	4	and	and	CCONJ
ejpam-3118	32	5	terminology	terminology	NOUN
ejpam-3118	32	6	before	before	SCONJ
ejpam-3118	32	7	we	we	PRON
ejpam-3118	32	8	begin	begin	VERB
ejpam-3118	32	9	,	,	PUNCT
ejpam-3118	32	10	we	we	PRON
ejpam-3118	32	11	will	will	AUX
ejpam-3118	32	12	recall	recall	VERB
ejpam-3118	32	13	the	the	DET
ejpam-3118	32	14	definition	definition	NOUN
ejpam-3118	32	15	of	of	ADP
ejpam-3118	32	16	extra	extra	ADJ
ejpam-3118	32	17	-	-	ADJ
ejpam-3118	32	18	special	special	ADJ
ejpam-3118	32	19	p	p	NOUN
ejpam-3118	32	20	-	-	PUNCT
ejpam-3118	32	21	group	group	NOUN
ejpam-3118	32	22	,	,	PUNCT
ejpam-3118	32	23	where	where	SCONJ
ejpam-3118	32	24	p	p	NOUN
ejpam-3118	32	25	is	be	AUX
ejpam-3118	32	26	a	a	DET
ejpam-3118	32	27	prime	prime	ADJ
ejpam-3118	32	28	number	number	NOUN
ejpam-3118	32	29	:	:	PUNCT
ejpam-3118	32	30	definition	definition	NOUN
ejpam-3118	32	31	1	1	NUM
ejpam-3118	32	32	.	.	PUNCT
ejpam-3118	33	1	a	a	DET
ejpam-3118	33	2	p	p	NOUN
ejpam-3118	33	3	-	-	PUNCT
ejpam-3118	33	4	group	group	NOUN
ejpam-3118	33	5	g	g	PROPN
ejpam-3118	33	6	is	be	AUX
ejpam-3118	33	7	called	call	VERB
ejpam-3118	33	8	extra	extra	ADJ
ejpam-3118	33	9	-	-	ADJ
ejpam-3118	33	10	special	special	ADJ
ejpam-3118	33	11	if	if	SCONJ
ejpam-3118	33	12	it	it	PRON
ejpam-3118	33	13	is	be	AUX
ejpam-3118	33	14	not	not	PART
ejpam-3118	33	15	abelian	abelian	ADJ
ejpam-3118	33	16	and	and	CCONJ
ejpam-3118	33	17	its	its	PRON
ejpam-3118	33	18	commutator	commutator	NOUN
ejpam-3118	33	19	subgroup	subgroup	PROPN
ejpam-3118	33	20	g′	g′	PROPN
ejpam-3118	33	21	coincides	coincide	VERB
ejpam-3118	33	22	with	with	ADP
ejpam-3118	33	23	its	its	PRON
ejpam-3118	33	24	center	center	NOUN
ejpam-3118	33	25	z(g	z(g	NOUN
ejpam-3118	33	26	)	)	PUNCT
ejpam-3118	33	27	and	and	CCONJ
ejpam-3118	33	28	is	be	AUX
ejpam-3118	33	29	of	of	ADP
ejpam-3118	33	30	order	order	NOUN
ejpam-3118	33	31	p.	p.	NOUN
ejpam-3118	33	32	in	in	ADP
ejpam-3118	33	33	particular	particular	ADJ
ejpam-3118	33	34	,	,	PUNCT
ejpam-3118	33	35	every	every	DET
ejpam-3118	33	36	extraspecial	extraspecial	ADJ
ejpam-3118	33	37	p	p	NOUN
ejpam-3118	33	38	-	-	PUNCT
ejpam-3118	33	39	group	group	NOUN
ejpam-3118	33	40	is	be	AUX
ejpam-3118	33	41	the	the	DET
ejpam-3118	33	42	central	central	ADJ
ejpam-3118	33	43	product	product	NOUN
ejpam-3118	33	44	of	of	ADP
ejpam-3118	33	45	non	non	ADJ
ejpam-3118	33	46	-	-	ADJ
ejpam-3118	33	47	abelian	abelian	ADJ
ejpam-3118	33	48	subgroups	subgroup	NOUN
ejpam-3118	33	49	of	of	ADP
ejpam-3118	33	50	order	order	NOUN
ejpam-3118	33	51	p3	p3	PROPN
ejpam-3118	33	52	.	.	PUNCT
ejpam-3118	34	1	let	let	VERB
ejpam-3118	34	2	d4	d4	PROPN
ejpam-3118	34	3	=	=	SYM
ejpam-3118	34	4	〈	〈	PROPN
ejpam-3118	34	5	b	b	PROPN
ejpam-3118	34	6	,	,	PUNCT
ejpam-3118	34	7	v|	v|	NOUN
ejpam-3118	34	8	b2	b2	NOUN
ejpam-3118	34	9	=	=	SYM
ejpam-3118	34	10	v4	v4	NOUN
ejpam-3118	34	11	=	=	SYM
ejpam-3118	34	12	1	1	NUM
ejpam-3118	34	13	and	and	CCONJ
ejpam-3118	34	14	bvbv	bvbv	NOUN
ejpam-3118	34	15	=	=	SYM
ejpam-3118	34	16	1	1	NUM
ejpam-3118	34	17	〉	〉	NOUN
ejpam-3118	34	18	be	be	VERB
ejpam-3118	34	19	the	the	DET
ejpam-3118	34	20	dihedral	dihedral	ADJ
ejpam-3118	34	21	group	group	NOUN
ejpam-3118	34	22	of	of	ADP
ejpam-3118	34	23	order	order	NOUN
ejpam-3118	34	24	8	8	NUM
ejpam-3118	34	25	.	.	PUNCT
ejpam-3118	35	1	we	we	PRON
ejpam-3118	35	2	also	also	ADV
ejpam-3118	35	3	adopt	adopt	VERB
ejpam-3118	35	4	the	the	DET
ejpam-3118	35	5	following	following	ADJ
ejpam-3118	35	6	notation	notation	NOUN
ejpam-3118	35	7	for	for	ADP
ejpam-3118	35	8	elements	element	NOUN
ejpam-3118	35	9	of	of	ADP
ejpam-3118	35	10	d4	d4	PROPN
ejpam-3118	35	11	:	:	PUNCT
ejpam-3118	35	12	a	a	DET
ejpam-3118	35	13	=	=	ADJ
ejpam-3118	35	14	bv2	bv2	PROPN
ejpam-3118	35	15	,	,	PUNCT
ejpam-3118	35	16	s	s	PART
ejpam-3118	35	17	=	=	SYM
ejpam-3118	35	18	v2	v2	PROPN
ejpam-3118	35	19	,	,	PUNCT
ejpam-3118	35	20	t	t	NOUN
ejpam-3118	35	21	=	=	SYM
ejpam-3118	35	22	bv	bv	PROPN
ejpam-3118	35	23	,	,	PUNCT
ejpam-3118	35	24	u	u	NOUN
ejpam-3118	35	25	=	=	SYM
ejpam-3118	35	26	vb	vb	PROPN
ejpam-3118	35	27	,	,	PUNCT
ejpam-3118	35	28	w	w	PROPN
ejpam-3118	35	29	=	=	SYM
ejpam-3118	35	30	v3	v3	PROPN
ejpam-3118	35	31	.	.	PUNCT
ejpam-3118	36	1	let	let	VERB
ejpam-3118	36	2	d	d	NOUN
ejpam-3118	36	3	,	,	PUNCT
ejpam-3118	36	4	d1	d1	PROPN
ejpam-3118	36	5	and	and	CCONJ
ejpam-3118	36	6	d2	d2	PROPN
ejpam-3118	36	7	be	be	NOUN
ejpam-3118	36	8	groups	group	NOUN
ejpam-3118	36	9	isomorphic	isomorphic	ADJ
ejpam-3118	36	10	d4	d4	PROPN
ejpam-3118	36	11	,	,	PUNCT
ejpam-3118	36	12	where	where	SCONJ
ejpam-3118	36	13	the	the	DET
ejpam-3118	36	14	indices	index	NOUN
ejpam-3118	36	15	used	use	VERB
ejpam-3118	36	16	are	be	AUX
ejpam-3118	36	17	necessary	necessary	ADJ
ejpam-3118	36	18	to	to	PART
ejpam-3118	36	19	differentiate	differentiate	VERB
ejpam-3118	36	20	the	the	DET
ejpam-3118	36	21	elements	element	NOUN
ejpam-3118	36	22	.	.	PUNCT
ejpam-3118	37	1	for	for	ADP
ejpam-3118	37	2	example	example	NOUN
ejpam-3118	37	3	,	,	PUNCT
ejpam-3118	37	4	we	we	PRON
ejpam-3118	37	5	denote	denote	VERB
ejpam-3118	37	6	by	by	ADP
ejpam-3118	37	7	bi	bi	NOUN
ejpam-3118	37	8	and	and	CCONJ
ejpam-3118	37	9	vi	vi	PROPN
ejpam-3118	37	10	,	,	PUNCT
ejpam-3118	37	11	1	1	NUM
ejpam-3118	37	12	≤	≤	NUM
ejpam-3118	37	13	i	i	X
ejpam-3118	37	14	≤	≤	ADV
ejpam-3118	37	15	2	2	NUM
ejpam-3118	37	16	,	,	PUNCT
ejpam-3118	37	17	the	the	DET
ejpam-3118	37	18	elements	element	NOUN
ejpam-3118	37	19	of	of	ADP
ejpam-3118	37	20	d	d	X
ejpam-3118	37	21	i	i	PRON
ejpam-3118	37	22	wich	wich	ADV
ejpam-3118	37	23	correspond	correspond	VERB
ejpam-3118	37	24	respectively	respectively	ADV
ejpam-3118	37	25	to	to	ADP
ejpam-3118	37	26	b	b	NOUN
ejpam-3118	37	27	and	and	CCONJ
ejpam-3118	37	28	v	v	NOUN
ejpam-3118	37	29	in	in	ADP
ejpam-3118	37	30	d	d	PROPN
ejpam-3118	37	31	.	.	PUNCT
ejpam-3118	38	1	the	the	DET
ejpam-3118	38	2	distinction	distinction	NOUN
ejpam-3118	38	3	of	of	ADP
ejpam-3118	38	4	the	the	DET
ejpam-3118	38	5	elements	element	NOUN
ejpam-3118	38	6	is	be	AUX
ejpam-3118	38	7	essential	essential	ADJ
ejpam-3118	38	8	for	for	ADP
ejpam-3118	38	9	the	the	DET
ejpam-3118	38	10	proofs	proof	NOUN
ejpam-3118	38	11	we	we	PRON
ejpam-3118	38	12	make	make	VERB
ejpam-3118	38	13	in	in	ADP
ejpam-3118	38	14	this	this	DET
ejpam-3118	38	15	work	work	NOUN
ejpam-3118	38	16	.	.	PUNCT
ejpam-3118	39	1	with	with	ADP
ejpam-3118	39	2	this	this	DET
ejpam-3118	39	3	notation	notation	NOUN
ejpam-3118	39	4	,	,	PUNCT
ejpam-3118	39	5	si	si	NOUN
ejpam-3118	39	6	=	=	SYM
ejpam-3118	39	7	v2i	v2i	PROPN
ejpam-3118	39	8	,	,	PUNCT
ejpam-3118	39	9	1	1	NUM
ejpam-3118	39	10	≤	≤	NUM
ejpam-3118	39	11	i	i	X
ejpam-3118	39	12	≤	≤	ADV
ejpam-3118	39	13	2	2	NUM
ejpam-3118	39	14	,	,	PUNCT
ejpam-3118	39	15	and	and	CCONJ
ejpam-3118	39	16	the	the	DET
ejpam-3118	39	17	correspondence	correspondence	NOUN
ejpam-3118	39	18	of	of	ADP
ejpam-3118	39	19	the	the	DET
ejpam-3118	39	20	other	other	ADJ
ejpam-3118	39	21	elements	element	NOUN
ejpam-3118	39	22	is	be	AUX
ejpam-3118	39	23	obvious	obvious	ADJ
ejpam-3118	39	24	.	.	PUNCT
ejpam-3118	40	1	thus	thus	ADV
ejpam-3118	40	2	we	we	PRON
ejpam-3118	40	3	have	have	VERB
ejpam-3118	40	4	the	the	DET
ejpam-3118	40	5	extra	extra	ADJ
ejpam-3118	40	6	-	-	ADJ
ejpam-3118	40	7	special	special	ADJ
ejpam-3118	40	8	2	2	NUM
ejpam-3118	40	9	-	-	PUNCT
ejpam-3118	40	10	group	group	NOUN
ejpam-3118	40	11	g1	g1	NOUN
ejpam-3118	40	12	of	of	ADP
ejpam-3118	40	13	order	order	NOUN
ejpam-3118	40	14	32	32	NUM
ejpam-3118	40	15	,	,	PUNCT
ejpam-3118	40	16	the	the	DET
ejpam-3118	40	17	central	central	ADJ
ejpam-3118	40	18	product	product	NOUN
ejpam-3118	40	19	of	of	ADP
ejpam-3118	40	20	two	two	NUM
ejpam-3118	40	21	copies	copy	NOUN
ejpam-3118	40	22	of	of	ADP
ejpam-3118	40	23	d4	d4	PROPN
ejpam-3118	40	24	,	,	PUNCT
ejpam-3118	40	25	and	and	CCONJ
ejpam-3118	40	26	the	the	DET
ejpam-3118	40	27	2	2	NUM
ejpam-3118	40	28	-	-	PUNCT
ejpam-3118	40	29	group	group	NOUN
ejpam-3118	40	30	extra	extra	ADJ
ejpam-3118	40	31	-	-	ADJ
ejpam-3118	40	32	special	special	ADJ
ejpam-3118	40	33	g2	g2	NOUN
ejpam-3118	40	34	of	of	ADP
ejpam-3118	40	35	order	order	NOUN
ejpam-3118	40	36	128	128	NUM
ejpam-3118	40	37	,	,	PUNCT
ejpam-3118	40	38	the	the	DET
ejpam-3118	40	39	central	central	ADJ
ejpam-3118	40	40	product	product	NOUN
ejpam-3118	40	41	of	of	ADP
ejpam-3118	40	42	three	three	NUM
ejpam-3118	40	43	copies	copy	NOUN
ejpam-3118	40	44	of	of	ADP
ejpam-3118	40	45	d4	d4	PROPN
ejpam-3118	40	46	:	:	PUNCT
ejpam-3118	40	47	g1	g1	PROPN
ejpam-3118	40	48	=	=	PUNCT
ejpam-3118	41	1	d	d	X
ejpam-3118	41	2	×d1	×d1	PROPN
ejpam-3118	41	3	/	/	SYM
ejpam-3118	41	4	{	{	PUNCT
ejpam-3118	41	5	1	1	NUM
ejpam-3118	41	6	,	,	PUNCT
ejpam-3118	41	7	ss1	ss1	PROPN
ejpam-3118	41	8	}	}	PUNCT
ejpam-3118	41	9	,	,	PUNCT
ejpam-3118	41	10	g2	g2	PROPN
ejpam-3118	41	11	=	=	PUNCT
ejpam-3118	42	1	d	d	PROPN
ejpam-3118	42	2	×d1	×d1	PROPN
ejpam-3118	42	3	×d2	×d2	NOUN
ejpam-3118	42	4	/	/	SYM
ejpam-3118	42	5	{	{	PUNCT
ejpam-3118	42	6	1	1	PROPN
ejpam-3118	42	7	,	,	PUNCT
ejpam-3118	42	8	ss1	ss1	PROPN
ejpam-3118	42	9	,	,	PUNCT
ejpam-3118	42	10	ss2	ss2	PROPN
ejpam-3118	42	11	,	,	PUNCT
ejpam-3118	42	12	s1s2	s1s2	PROPN
ejpam-3118	42	13	}	}	PUNCT
ejpam-3118	42	14	.	.	PUNCT
ejpam-3118	43	1	the	the	DET
ejpam-3118	43	2	elements	element	NOUN
ejpam-3118	43	3	of	of	ADP
ejpam-3118	43	4	g1	g1	PROPN
ejpam-3118	43	5	/	/	SYM
ejpam-3118	43	6	g	g	NOUN
ejpam-3118	43	7	′	′	NUM
ejpam-3118	43	8	1	1	NUM
ejpam-3118	43	9	,	,	PUNCT
ejpam-3118	43	10	where	where	SCONJ
ejpam-3118	43	11	g′1	g′1	ADJ
ejpam-3118	43	12	=	=	SYM
ejpam-3118	43	13	{	{	PUNCT
ejpam-3118	43	14	1	1	NUM
ejpam-3118	43	15	,	,	PUNCT
ejpam-3118	43	16	s	s	AUX
ejpam-3118	43	17	}	}	PUNCT
ejpam-3118	43	18	is	be	AUX
ejpam-3118	43	19	the	the	DET
ejpam-3118	43	20	commutator	commutator	NOUN
ejpam-3118	43	21	subgroup	subgroup	NOUN
ejpam-3118	43	22	of	of	ADP
ejpam-3118	43	23	g1	g1	PROPN
ejpam-3118	43	24	,	,	PUNCT
ejpam-3118	43	25	and	and	CCONJ
ejpam-3118	43	26	the	the	DET
ejpam-3118	43	27	elements	element	NOUN
ejpam-3118	43	28	of	of	ADP
ejpam-3118	43	29	g2	g2	PROPN
ejpam-3118	43	30	/	/	SYM
ejpam-3118	43	31	g	g	PROPN
ejpam-3118	43	32	′	′	NUM
ejpam-3118	43	33	2	2	NUM
ejpam-3118	43	34	,	,	PUNCT
ejpam-3118	43	35	where	where	SCONJ
ejpam-3118	43	36	g′2	g′2	NOUN
ejpam-3118	43	37	=	=	SYM
ejpam-3118	43	38	{	{	PUNCT
ejpam-3118	43	39	1	1	NUM
ejpam-3118	43	40	,	,	PUNCT
ejpam-3118	43	41	s	s	AUX
ejpam-3118	43	42	}	}	PUNCT
ejpam-3118	43	43	is	be	AUX
ejpam-3118	43	44	the	the	DET
ejpam-3118	43	45	commutator	commutator	NOUN
ejpam-3118	43	46	subgroup	subgroup	NOUN
ejpam-3118	43	47	of	of	ADP
ejpam-3118	43	48	g2	g2	PROPN
ejpam-3118	43	49	,	,	PUNCT
ejpam-3118	43	50	are	be	AUX
ejpam-3118	43	51	denoted	denote	VERB
ejpam-3118	43	52	as	as	SCONJ
ejpam-3118	43	53	follows	follow	VERB
ejpam-3118	43	54	:	:	PUNCT
ejpam-3118	43	55	g1	g1	VERB
ejpam-3118	43	56	/	/	SYM
ejpam-3118	43	57	g	g	NOUN
ejpam-3118	43	58	′	′	NOUN
ejpam-3118	43	59	1	1	NUM
ejpam-3118	43	60	=	=	SYM
ejpam-3118	43	61	{	{	PUNCT
ejpam-3118	43	62	1	1	NUM
ejpam-3118	43	63	,	,	PUNCT
ejpam-3118	43	64	b	b	PROPN
ejpam-3118	43	65	,	,	PUNCT
ejpam-3118	43	66	u	u	NOUN
ejpam-3118	43	67	,	,	PUNCT
ejpam-3118	43	68	v	v	NOUN
ejpam-3118	43	69	,	,	PUNCT
ejpam-3118	43	70	b1	b1	NOUN
ejpam-3118	43	71	,	,	PUNCT
ejpam-3118	43	72	u1	u1	NOUN
ejpam-3118	43	73	,	,	PUNCT
ejpam-3118	43	74	v1	v1	NOUN
ejpam-3118	43	75	,	,	PUNCT
ejpam-3118	43	76	bb1	bb1	NOUN
ejpam-3118	43	77	,	,	PUNCT
ejpam-3118	43	78	bu1	bu1	NOUN
ejpam-3118	43	79	,	,	PUNCT
ejpam-3118	43	80	bv1	bv1	PROPN
ejpam-3118	43	81	,	,	PUNCT
ejpam-3118	43	82	ub1	ub1	PROPN
ejpam-3118	43	83	,	,	PUNCT
ejpam-3118	43	84	uu1	uu1	PROPN
ejpam-3118	43	85	,	,	PUNCT
ejpam-3118	43	86	uv1	uv1	PROPN
ejpam-3118	43	87	,	,	PUNCT
ejpam-3118	43	88	vb1	vb1	NOUN
ejpam-3118	43	89	,	,	PUNCT
ejpam-3118	43	90	vu1	vu1	X
ejpam-3118	43	91	,	,	PUNCT
ejpam-3118	43	92	vv1	vv1	NOUN
ejpam-3118	43	93	}	}	PUNCT
ejpam-3118	43	94	;	;	PUNCT
ejpam-3118	43	95	∗the	∗the	DET
ejpam-3118	43	96	calculations	calculation	NOUN
ejpam-3118	43	97	given	give	VERB
ejpam-3118	43	98	are	be	AUX
ejpam-3118	43	99	complete	complete	ADJ
ejpam-3118	43	100	and	and	CCONJ
ejpam-3118	43	101	are	be	AUX
ejpam-3118	43	102	independent	independent	ADJ
ejpam-3118	43	103	of	of	ADP
ejpam-3118	43	104	the	the	DET
ejpam-3118	43	105	general	general	ADJ
ejpam-3118	43	106	frame	frame	NOUN
ejpam-3118	43	107	work	work	NOUN
ejpam-3118	43	108	given	give	VERB
ejpam-3118	43	109	in	in	ADP
ejpam-3118	43	110	[	[	X
ejpam-3118	43	111	1	1	NUM
ejpam-3118	43	112	,	,	PUNCT
ejpam-3118	43	113	2	2	NUM
ejpam-3118	43	114	]	]	PUNCT
ejpam-3118	43	115	.	.	PUNCT
ejpam-3118	44	1	c.	c.	PROPN
ejpam-3118	44	2	mello	mello	PROPN
ejpam-3118	44	3	/	/	SYM
ejpam-3118	44	4	eur	eur	PROPN
ejpam-3118	44	5	.	.	PUNCT
ejpam-3118	45	1	j.	j.	PROPN
ejpam-3118	45	2	pure	pure	PROPN
ejpam-3118	45	3	appl	appl	PROPN
ejpam-3118	45	4	.	.	PROPN
ejpam-3118	45	5	math	math	PROPN
ejpam-3118	45	6	,	,	PUNCT
ejpam-3118	45	7	10	10	NUM
ejpam-3118	45	8	(	(	PUNCT
ejpam-3118	45	9	5	5	NUM
ejpam-3118	45	10	)	)	PUNCT
ejpam-3118	45	11	(	(	PUNCT
ejpam-3118	45	12	2017	2017	NUM
ejpam-3118	45	13	)	)	PUNCT
ejpam-3118	45	14	,	,	PUNCT
ejpam-3118	45	15	955	955	NUM
ejpam-3118	45	16	-	-	SYM
ejpam-3118	45	17	966	966	NUM
ejpam-3118	45	18	957	957	NUM
ejpam-3118	45	19	g2	g2	NOUN
ejpam-3118	45	20	/	/	SYM
ejpam-3118	45	21	g	g	PROPN
ejpam-3118	45	22	′	′	NOUN
ejpam-3118	45	23	2	2	NUM
ejpam-3118	45	24	=	=	SYM
ejpam-3118	45	25			NUM
ejpam-3118	45	26	1	1	NUM
ejpam-3118	45	27	,	,	PUNCT
ejpam-3118	45	28	b	b	X
ejpam-3118	45	29	,	,	PUNCT
ejpam-3118	45	30	u	u	NOUN
ejpam-3118	45	31	,	,	PUNCT
ejpam-3118	45	32	v	v	NOUN
ejpam-3118	45	33	,	,	PUNCT
ejpam-3118	45	34	b1	b1	NOUN
ejpam-3118	45	35	,	,	PUNCT
ejpam-3118	45	36	u1	u1	NOUN
ejpam-3118	45	37	,	,	PUNCT
ejpam-3118	45	38	v1	v1	NOUN
ejpam-3118	45	39	,	,	PUNCT
ejpam-3118	45	40	b2	b2	NOUN
ejpam-3118	45	41	,	,	PUNCT
ejpam-3118	45	42	u2	u2	NOUN
ejpam-3118	45	43	,	,	PUNCT
ejpam-3118	45	44	v2	v2	PROPN
ejpam-3118	45	45	,	,	PUNCT
ejpam-3118	45	46	bb1	bb1	NOUN
ejpam-3118	45	47	,	,	PUNCT
ejpam-3118	45	48	bu1	bu1	NOUN
ejpam-3118	45	49	,	,	PUNCT
ejpam-3118	45	50	bv1	bv1	PROPN
ejpam-3118	45	51	,	,	PUNCT
ejpam-3118	45	52	bb2	bb2	PROPN
ejpam-3118	45	53	,	,	PUNCT
ejpam-3118	45	54	bu2	bu2	PROPN
ejpam-3118	45	55	,	,	PUNCT
ejpam-3118	45	56	bv2	bv2	PROPN
ejpam-3118	45	57	,	,	PUNCT
ejpam-3118	45	58	ub1	ub1	PROPN
ejpam-3118	45	59	,	,	PUNCT
ejpam-3118	45	60	uu1	uu1	PROPN
ejpam-3118	45	61	,	,	PUNCT
ejpam-3118	45	62	uv1	uv1	PROPN
ejpam-3118	45	63	,	,	PUNCT
ejpam-3118	45	64	ub2	ub2	PROPN
ejpam-3118	45	65	,	,	PUNCT
ejpam-3118	45	66	uu2	uu2	ADJ
ejpam-3118	45	67	,	,	PUNCT
ejpam-3118	45	68	uv2	uv2	INTJ
ejpam-3118	45	69	,	,	PUNCT
ejpam-3118	45	70	vb1	vb1	NOUN
ejpam-3118	45	71	,	,	PUNCT
ejpam-3118	45	72	vu1	vu1	X
ejpam-3118	45	73	,	,	PUNCT
ejpam-3118	45	74	vv1	vv1	NOUN
ejpam-3118	45	75	,	,	PUNCT
ejpam-3118	45	76	vb2	vb2	NOUN
ejpam-3118	45	77	,	,	PUNCT
ejpam-3118	45	78	vu2	vu2	NOUN
ejpam-3118	45	79	,	,	PUNCT
ejpam-3118	45	80	vv2	vv2	PROPN
ejpam-3118	45	81	,	,	PUNCT
ejpam-3118	45	82	b1b2	b1b2	PROPN
ejpam-3118	45	83	,	,	PUNCT
ejpam-3118	45	84	b1u2	b1u2	NOUN
ejpam-3118	45	85	,	,	PUNCT
ejpam-3118	45	86	b1v2	b1v2	NOUN
ejpam-3118	45	87	,	,	PUNCT
ejpam-3118	45	88	u1b2	u1b2	ADP
ejpam-3118	45	89	,	,	PUNCT
ejpam-3118	45	90	u1u2	u1u2	NOUN
ejpam-3118	45	91	,	,	PUNCT
ejpam-3118	45	92	u1v2	u1v2	NOUN
ejpam-3118	45	93	,	,	PUNCT
ejpam-3118	45	94	v1b2	v1b2	NOUN
ejpam-3118	45	95	,	,	PUNCT
ejpam-3118	45	96	v1u2	v1u2	X
ejpam-3118	45	97	,	,	PUNCT
ejpam-3118	45	98	v1v2	v1v2	NOUN
ejpam-3118	45	99	,	,	PUNCT
ejpam-3118	45	100	bb1b2	bb1b2	PROPN
ejpam-3118	45	101	,	,	PUNCT
ejpam-3118	45	102	bb1u2	bb1u2	PROPN
ejpam-3118	45	103	,	,	PUNCT
ejpam-3118	45	104	bb1v2	bb1v2	PROPN
ejpam-3118	45	105	,	,	PUNCT
ejpam-3118	45	106	bu1b2	bu1b2	PROPN
ejpam-3118	45	107	,	,	PUNCT
ejpam-3118	45	108	bu1u2	bu1u2	NOUN
ejpam-3118	45	109	,	,	PUNCT
ejpam-3118	45	110	bu1v2	bu1v2	PROPN
ejpam-3118	45	111	,	,	PUNCT
ejpam-3118	45	112	bv1b2	bv1b2	PROPN
ejpam-3118	45	113	,	,	PUNCT
ejpam-3118	45	114	bv1u2	bv1u2	PROPN
ejpam-3118	45	115	,	,	PUNCT
ejpam-3118	45	116	bv1v2	bv1v2	NOUN
ejpam-3118	45	117	,	,	PUNCT
ejpam-3118	45	118	ub1b2	ub1b2	PROPN
ejpam-3118	45	119	,	,	PUNCT
ejpam-3118	45	120	ub1u2	ub1u2	PROPN
ejpam-3118	45	121	,	,	PUNCT
ejpam-3118	45	122	ub1v2	ub1v2	PROPN
ejpam-3118	45	123	,	,	PUNCT
ejpam-3118	45	124	uu1b2	uu1b2	PROPN
ejpam-3118	45	125	,	,	PUNCT
ejpam-3118	45	126	uu1u2	uu1u2	PROPN
ejpam-3118	45	127	,	,	PUNCT
ejpam-3118	45	128	uu1v2	uu1v2	PROPN
ejpam-3118	45	129	,	,	PUNCT
ejpam-3118	45	130	uv1b2	uv1b2	PROPN
ejpam-3118	45	131	,	,	PUNCT
ejpam-3118	45	132	uv1u2	uv1u2	PROPN
ejpam-3118	45	133	,	,	PUNCT
ejpam-3118	45	134	uv1v2	uv1v2	PROPN
ejpam-3118	45	135	,	,	PUNCT
ejpam-3118	45	136	vb1b2	vb1b2	PROPN
ejpam-3118	45	137	,	,	PUNCT
ejpam-3118	45	138	vb1u2	vb1u2	PROPN
ejpam-3118	45	139	,	,	PUNCT
ejpam-3118	45	140	vb1v2	vb1v2	PROPN
ejpam-3118	45	141	,	,	PUNCT
ejpam-3118	45	142	vu1b2	vu1b2	PROPN
ejpam-3118	45	143	,	,	PUNCT
ejpam-3118	45	144	vu1u2	vu1u2	PROPN
ejpam-3118	45	145	,	,	PUNCT
ejpam-3118	45	146	vu1v2	vu1v2	PROPN
ejpam-3118	45	147	,	,	PUNCT
ejpam-3118	45	148	vv1b2	vv1b2	PROPN
ejpam-3118	45	149	,	,	PUNCT
ejpam-3118	45	150	vv1u2	vv1u2	PROPN
ejpam-3118	45	151	,	,	PUNCT
ejpam-3118	45	152	vv1v2	vv1v2	PROPN
ejpam-3118	45	153			NUM
ejpam-3118	45	154	.	.	PUNCT
ejpam-3118	46	1	in	in	ADP
ejpam-3118	46	2	this	this	DET
ejpam-3118	46	3	paper	paper	NOUN
ejpam-3118	46	4	we	we	PRON
ejpam-3118	46	5	describe	describe	VERB
ejpam-3118	46	6	u(zg1	u(zg1	NOUN
ejpam-3118	46	7	)	)	PUNCT
ejpam-3118	46	8	and	and	CCONJ
ejpam-3118	46	9	u(zg2	u(zg2	PROPN
ejpam-3118	46	10	)	)	PUNCT
ejpam-3118	46	11	,	,	PUNCT
ejpam-3118	46	12	the	the	DET
ejpam-3118	46	13	group	group	NOUN
ejpam-3118	46	14	of	of	ADP
ejpam-3118	46	15	units	unit	NOUN
ejpam-3118	46	16	of	of	ADP
ejpam-3118	46	17	zg1	zg1	NOUN
ejpam-3118	46	18	and	and	CCONJ
ejpam-3118	46	19	zg2	zg2	NOUN
ejpam-3118	46	20	,	,	PUNCT
ejpam-3118	46	21	respectively	respectively	ADV
ejpam-3118	46	22	.	.	PUNCT
ejpam-3118	47	1	to	to	ADP
ejpam-3118	47	2	this	this	DET
ejpam-3118	47	3	end	end	NOUN
ejpam-3118	47	4	,	,	PUNCT
ejpam-3118	47	5	we	we	PRON
ejpam-3118	47	6	still	still	ADV
ejpam-3118	47	7	need	need	VERB
ejpam-3118	47	8	to	to	PART
ejpam-3118	47	9	fixe	fixe	VERB
ejpam-3118	47	10	more	more	ADJ
ejpam-3118	47	11	notations	notation	NOUN
ejpam-3118	47	12	:	:	PUNCT
ejpam-3118	47	13	(	(	PUNCT
ejpam-3118	47	14	i	i	NOUN
ejpam-3118	47	15	)	)	PUNCT
ejpam-3118	47	16	if	if	SCONJ
ejpam-3118	47	17	g	g	PROPN
ejpam-3118	47	18	is	be	AUX
ejpam-3118	47	19	a	a	DET
ejpam-3118	47	20	finite	finite	ADJ
ejpam-3118	47	21	extra	extra	ADJ
ejpam-3118	47	22	-	-	ADJ
ejpam-3118	47	23	special	special	ADJ
ejpam-3118	47	24	2	2	NUM
ejpam-3118	47	25	-	-	PUNCT
ejpam-3118	47	26	group	group	NOUN
ejpam-3118	47	27	and	and	CCONJ
ejpam-3118	47	28	g′	g′	NOUN
ejpam-3118	47	29	=	=	SYM
ejpam-3118	47	30	{	{	PUNCT
ejpam-3118	47	31	1	1	NUM
ejpam-3118	47	32	,	,	PUNCT
ejpam-3118	47	33	s	s	AUX
ejpam-3118	47	34	}	}	PUNCT
ejpam-3118	47	35	is	be	AUX
ejpam-3118	47	36	its	its	PRON
ejpam-3118	47	37	commutator	commutator	NOUN
ejpam-3118	47	38	subgroup	subgroup	NOUN
ejpam-3118	47	39	,	,	PUNCT
ejpam-3118	47	40	then	then	ADV
ejpam-3118	47	41	u2	u2	PROPN
ejpam-3118	47	42	denotes	denote	VERB
ejpam-3118	47	43	the	the	DET
ejpam-3118	47	44	subgroup	subgroup	NOUN
ejpam-3118	47	45	of	of	ADP
ejpam-3118	47	46	u(zg	u(zg	NUM
ejpam-3118	47	47	)	)	PUNCT
ejpam-3118	47	48	defined	define	VERB
ejpam-3118	47	49	by	by	ADP
ejpam-3118	47	50	u2	u2	PROPN
ejpam-3118	47	51	=	=	SYM
ejpam-3118	47	52	u(zg	u(zg	NOUN
ejpam-3118	47	53	)	)	PUNCT
ejpam-3118	47	54	∩	∩	NOUN
ejpam-3118	47	55	(	(	PUNCT
ejpam-3118	47	56	qg	qg	PROPN
ejpam-3118	47	57	(	(	PUNCT
ejpam-3118	47	58	1−	1−	NUM
ejpam-3118	47	59	s	s	NOUN
ejpam-3118	47	60	2	2	NUM
ejpam-3118	47	61	)	)	PUNCT
ejpam-3118	47	62	+	+	CCONJ
ejpam-3118	48	1	(	(	PUNCT
ejpam-3118	48	2	1	1	NUM
ejpam-3118	48	3	+	+	SYM
ejpam-3118	48	4	s	s	NOUN
ejpam-3118	48	5	2	2	NUM
ejpam-3118	48	6	)	)	PUNCT
ejpam-3118	48	7	)	)	PUNCT
ejpam-3118	48	8	.	.	PUNCT
ejpam-3118	49	1	(	(	PUNCT
ejpam-3118	49	2	ii	ii	X
ejpam-3118	49	3	)	)	PUNCT
ejpam-3118	49	4	let	let	VERB
ejpam-3118	49	5	r	r	PRON
ejpam-3118	49	6	be	be	AUX
ejpam-3118	49	7	a	a	DET
ejpam-3118	49	8	domain	domain	NOUN
ejpam-3118	49	9	and	and	CCONJ
ejpam-3118	49	10	gln(r	gln(r	NOUN
ejpam-3118	49	11	)	)	PUNCT
ejpam-3118	49	12	the	the	DET
ejpam-3118	49	13	group	group	NOUN
ejpam-3118	49	14	of	of	ADP
ejpam-3118	49	15	invertible	invertible	ADJ
ejpam-3118	49	16	n	n	X
ejpam-3118	49	17	by	by	ADP
ejpam-3118	49	18	n	n	PRON
ejpam-3118	49	19	matrices	matrix	NOUN
ejpam-3118	49	20	with	with	ADP
ejpam-3118	49	21	coeficients	coeficient	NOUN
ejpam-3118	49	22	in	in	ADP
ejpam-3118	49	23	r.	r.	PROPN
ejpam-3118	49	24	if	if	SCONJ
ejpam-3118	49	25	s	s	PROPN
ejpam-3118	49	26	is	be	AUX
ejpam-3118	49	27	a	a	DET
ejpam-3118	49	28	subset	subset	NOUN
ejpam-3118	49	29	of	of	ADP
ejpam-3118	49	30	gln(r	gln(r	NOUN
ejpam-3118	49	31	)	)	PUNCT
ejpam-3118	49	32	,	,	PUNCT
ejpam-3118	49	33	then	then	ADV
ejpam-3118	49	34	sdet=1	sdet=1	PROPN
ejpam-3118	49	35	denotes	denote	VERB
ejpam-3118	49	36	a	a	DET
ejpam-3118	49	37	set	set	NOUN
ejpam-3118	49	38	of	of	ADP
ejpam-3118	49	39	matrix	matrix	NOUN
ejpam-3118	49	40	units	unit	NOUN
ejpam-3118	49	41	of	of	ADP
ejpam-3118	49	42	s	s	PRON
ejpam-3118	49	43	with	with	ADP
ejpam-3118	49	44	determinant	determinant	ADJ
ejpam-3118	49	45	1	1	NUM
ejpam-3118	49	46	.	.	PUNCT
ejpam-3118	49	47	similarly	similarly	ADV
ejpam-3118	49	48	,	,	PUNCT
ejpam-3118	49	49	sdet=±1	sdet=±1	PROPN
ejpam-3118	49	50	denotes	denote	VERB
ejpam-3118	49	51	a	a	DET
ejpam-3118	49	52	set	set	NOUN
ejpam-3118	49	53	of	of	ADP
ejpam-3118	49	54	matrix	matrix	NOUN
ejpam-3118	49	55	units	unit	NOUN
ejpam-3118	49	56	of	of	ADP
ejpam-3118	49	57	s	s	PRON
ejpam-3118	49	58	with	with	ADP
ejpam-3118	49	59	determinant	determinant	ADJ
ejpam-3118	49	60	±1	±1	NOUN
ejpam-3118	49	61	.	.	PUNCT
ejpam-3118	50	1	by	by	ADP
ejpam-3118	50	2	in	in	ADP
ejpam-3118	50	3	we	we	PRON
ejpam-3118	50	4	denote	denote	VERB
ejpam-3118	50	5	the	the	DET
ejpam-3118	50	6	identity	identity	NOUN
ejpam-3118	50	7	matrix	matrix	NOUN
ejpam-3118	50	8	in	in	ADP
ejpam-3118	50	9	gln(r	gln(r	NOUN
ejpam-3118	50	10	)	)	PUNCT
ejpam-3118	50	11	,	,	PUNCT
ejpam-3118	50	12	and	and	CCONJ
ejpam-3118	50	13	if	if	SCONJ
ejpam-3118	50	14	sdet=1	sdet=1	PROPN
ejpam-3118	50	15	is	be	AUX
ejpam-3118	50	16	a	a	DET
ejpam-3118	50	17	multiplicative	multiplicative	ADJ
ejpam-3118	50	18	group	group	NOUN
ejpam-3118	50	19	,	,	PUNCT
ejpam-3118	50	20	then	then	ADV
ejpam-3118	50	21	s	s	VERB
ejpam-3118	50	22	det=1	det=1	NOUN
ejpam-3118	50	23	=	=	SYM
ejpam-3118	50	24	sdet=1/({in,−in	sdet=1/({in,−in	NOUN
ejpam-3118	50	25	}	}	PUNCT
ejpam-3118	50	26	∩	∩	ADJ
ejpam-3118	50	27	sdet=1	sdet=1	PROPN
ejpam-3118	50	28	)	)	PUNCT
ejpam-3118	50	29	.	.	PUNCT
ejpam-3118	51	1	similarly	similarly	ADV
ejpam-3118	51	2	,	,	PUNCT
ejpam-3118	51	3	s	s	VERB
ejpam-3118	51	4	det=±1	det=±1	PROPN
ejpam-3118	51	5	=	=	PUNCT
ejpam-3118	51	6	sdet=±1/({in,−in	sdet=±1/({in,−in	NOUN
ejpam-3118	51	7	}	}	PUNCT
ejpam-3118	51	8	∩	∩	ADJ
ejpam-3118	51	9	sdet=±1	sdet=±1	NOUN
ejpam-3118	51	10	)	)	PUNCT
ejpam-3118	51	11	.	.	PUNCT
ejpam-3118	52	1	3	3	X
ejpam-3118	52	2	.	.	X
ejpam-3118	52	3	auxiliary	auxiliary	ADJ
ejpam-3118	52	4	results	result	NOUN
ejpam-3118	52	5	for	for	ADP
ejpam-3118	52	6	the	the	DET
ejpam-3118	52	7	main	main	ADJ
ejpam-3118	52	8	results	result	NOUN
ejpam-3118	52	9	,	,	PUNCT
ejpam-3118	52	10	we	we	PRON
ejpam-3118	52	11	will	will	AUX
ejpam-3118	52	12	need	need	VERB
ejpam-3118	52	13	the	the	DET
ejpam-3118	52	14	following	following	NOUN
ejpam-3118	52	15	:	:	PUNCT
ejpam-3118	52	16	proposition	proposition	NOUN
ejpam-3118	52	17	1	1	NUM
ejpam-3118	52	18	.	.	PUNCT
ejpam-3118	53	1	[	[	X
ejpam-3118	53	2	6	6	NUM
ejpam-3118	53	3	,	,	PUNCT
ejpam-3118	53	4	lemma	lemma	PROPN
ejpam-3118	53	5	4.2	4.2	NUM
ejpam-3118	53	6	]	]	PUNCT
ejpam-3118	53	7	the	the	DET
ejpam-3118	53	8	group	group	NOUN
ejpam-3118	53	9	ring	ring	NOUN
ejpam-3118	53	10	qd4	qd4	PROPN
ejpam-3118	53	11	admits	admit	VERB
ejpam-3118	53	12	the	the	DET
ejpam-3118	53	13	following	follow	VERB
ejpam-3118	53	14	decomposition	decomposition	NOUN
ejpam-3118	53	15	:	:	PUNCT
ejpam-3118	53	16	qd4	qd4	NOUN
ejpam-3118	53	17	=	=	SYM
ejpam-3118	53	18	qd4	qd4	NOUN
ejpam-3118	53	19	(	(	PUNCT
ejpam-3118	53	20	1	1	NUM
ejpam-3118	53	21	+	+	SYM
ejpam-3118	53	22	s	s	NOUN
ejpam-3118	53	23	2	2	NUM
ejpam-3118	53	24	)	)	PUNCT
ejpam-3118	53	25	⊕qd4	⊕qd4	NOUN
ejpam-3118	53	26	(	(	PUNCT
ejpam-3118	53	27	1−	1−	NUM
ejpam-3118	53	28	s	s	NOUN
ejpam-3118	53	29	2	2	NUM
ejpam-3118	53	30	)	)	PUNCT
ejpam-3118	53	31	,	,	PUNCT
ejpam-3118	53	32	where	where	SCONJ
ejpam-3118	53	33	qd4	qd4	NOUN
ejpam-3118	53	34	(	(	PUNCT
ejpam-3118	53	35	1	1	NUM
ejpam-3118	53	36	+	+	SYM
ejpam-3118	53	37	s	s	X
ejpam-3118	53	38	2	2	NUM
ejpam-3118	53	39	)	)	PUNCT
ejpam-3118	53	40	∼=	∼=	PROPN
ejpam-3118	53	41	q4	q4	NOUN
ejpam-3118	53	42	and	and	CCONJ
ejpam-3118	53	43	qd4	qd4	NOUN
ejpam-3118	53	44	(	(	PUNCT
ejpam-3118	53	45	1−	1−	NUM
ejpam-3118	53	46	s	s	NOUN
ejpam-3118	53	47	2	2	NUM
ejpam-3118	53	48	)	)	PUNCT
ejpam-3118	53	49	∼=	∼=	PROPN
ejpam-3118	53	50	m2(q	m2(q	NOUN
ejpam-3118	53	51	)	)	PUNCT
ejpam-3118	53	52	.	.	PUNCT
ejpam-3118	54	1	for	for	ADP
ejpam-3118	54	2	the	the	DET
ejpam-3118	54	3	sequence	sequence	NOUN
ejpam-3118	54	4	of	of	ADP
ejpam-3118	54	5	this	this	DET
ejpam-3118	54	6	work	work	NOUN
ejpam-3118	54	7	,	,	PUNCT
ejpam-3118	54	8	we	we	PRON
ejpam-3118	54	9	will	will	AUX
ejpam-3118	54	10	fix	fix	VERB
ejpam-3118	54	11	the	the	DET
ejpam-3118	54	12	following	follow	VERB
ejpam-3118	54	13	representation	representation	NOUN
ejpam-3118	54	14	of	of	ADP
ejpam-3118	54	15	d4	d4	PROPN
ejpam-3118	54	16	on	on	ADP
ejpam-3118	54	17	m2(q	m2(q	NOUN
ejpam-3118	54	18	):	):	PUNCT
ejpam-3118	54	19	•	•	NUM
ejpam-3118	54	20	b	b	X
ejpam-3118	54	21	7→	7→	NUM
ejpam-3118	54	22	e11	e11	NOUN
ejpam-3118	54	23	−	−	PROPN
ejpam-3118	54	24	e22	e22	NOUN
ejpam-3118	54	25	=	=	PUNCT
ejpam-3118	55	1	[	[	PUNCT
ejpam-3118	55	2	1	1	NUM
ejpam-3118	55	3	0	0	NUM
ejpam-3118	55	4	0	0	NUM
ejpam-3118	55	5	−1	−1	NOUN
ejpam-3118	55	6	]	]	PUNCT
ejpam-3118	55	7	;	;	PUNCT
ejpam-3118	56	1	•	•	NUM
ejpam-3118	56	2	v	v	X
ejpam-3118	56	3	7→	7→	NUM
ejpam-3118	57	1	−e12	−e12	NOUN
ejpam-3118	58	1	+	+	CCONJ
ejpam-3118	58	2	e21	e21	NUM
ejpam-3118	58	3	=	=	SYM
ejpam-3118	58	4	[	[	PUNCT
ejpam-3118	58	5	0	0	NUM
ejpam-3118	58	6	−1	−1	NOUN
ejpam-3118	58	7	1	1	NUM
ejpam-3118	58	8	0	0	NUM
ejpam-3118	58	9	]	]	PUNCT
ejpam-3118	58	10	.	.	PUNCT
ejpam-3118	59	1	proposition	proposition	NOUN
ejpam-3118	59	2	2	2	NUM
ejpam-3118	59	3	.	.	PUNCT
ejpam-3118	60	1	[	[	X
ejpam-3118	60	2	6	6	NUM
ejpam-3118	60	3	,	,	PUNCT
ejpam-3118	60	4	p	p	PRON
ejpam-3118	60	5	roposition	roposition	NOUN
ejpam-3118	60	6	3.2	3.2	NUM
ejpam-3118	60	7	]	]	PUNCT
ejpam-3118	60	8	writing	write	VERB
ejpam-3118	60	9	e	e	NOUN
ejpam-3118	60	10	=	=	SYM
ejpam-3118	60	11	1−	1−	NUM
ejpam-3118	60	12	s	s	NOUN
ejpam-3118	60	13	2	2	NUM
ejpam-3118	60	14	and	and	CCONJ
ejpam-3118	60	15	using	use	VERB
ejpam-3118	60	16	the	the	DET
ejpam-3118	60	17	above	above	ADJ
ejpam-3118	60	18	fixed	fix	VERB
ejpam-3118	60	19	representation	representation	NOUN
ejpam-3118	60	20	,	,	PUNCT
ejpam-3118	60	21	an	an	DET
ejpam-3118	60	22	elementary	elementary	ADJ
ejpam-3118	60	23	q	q	ADJ
ejpam-3118	60	24	-	-	PUNCT
ejpam-3118	60	25	basis	basis	NOUN
ejpam-3118	60	26	matrix	matrix	NOUN
ejpam-3118	60	27	of	of	ADP
ejpam-3118	60	28	qd4	qd4	NOUN
ejpam-3118	60	29	(	(	PUNCT
ejpam-3118	60	30	1−	1−	NUM
ejpam-3118	60	31	s	s	NOUN
ejpam-3118	60	32	2	2	NUM
ejpam-3118	60	33	)	)	PUNCT
ejpam-3118	60	34	∼=	∼=	PROPN
ejpam-3118	60	35	m2(q	m2(q	NOUN
ejpam-3118	60	36	)	)	PUNCT
ejpam-3118	60	37	is	be	AUX
ejpam-3118	60	38	:	:	PUNCT
ejpam-3118	60	39	c.	c.	PROPN
ejpam-3118	60	40	mello	mello	PROPN
ejpam-3118	60	41	/	/	SYM
ejpam-3118	60	42	eur	eur	PROPN
ejpam-3118	60	43	.	.	PUNCT
ejpam-3118	61	1	j.	j.	PROPN
ejpam-3118	61	2	pure	pure	PROPN
ejpam-3118	61	3	appl	appl	PROPN
ejpam-3118	61	4	.	.	PROPN
ejpam-3118	61	5	math	math	PROPN
ejpam-3118	61	6	,	,	PUNCT
ejpam-3118	61	7	10	10	NUM
ejpam-3118	61	8	(	(	PUNCT
ejpam-3118	61	9	5	5	NUM
ejpam-3118	61	10	)	)	PUNCT
ejpam-3118	61	11	(	(	PUNCT
ejpam-3118	61	12	2017	2017	NUM
ejpam-3118	61	13	)	)	PUNCT
ejpam-3118	61	14	,	,	PUNCT
ejpam-3118	61	15	955	955	NUM
ejpam-3118	61	16	-	-	SYM
ejpam-3118	61	17	966	966	NUM
ejpam-3118	61	18	958	958	NUM
ejpam-3118	61	19	e11	e11	NOUN
ejpam-3118	61	20	=	=	SYM
ejpam-3118	61	21	(	(	PUNCT
ejpam-3118	61	22	1	1	NUM
ejpam-3118	61	23	+	+	SYM
ejpam-3118	61	24	b	b	SYM
ejpam-3118	61	25	2	2	NUM
ejpam-3118	61	26	)	)	PUNCT
ejpam-3118	61	27	e	e	NOUN
ejpam-3118	61	28	,	,	PUNCT
ejpam-3118	61	29	e12	e12	NOUN
ejpam-3118	61	30	=	=	SYM
ejpam-3118	61	31	(	(	PUNCT
ejpam-3118	61	32	vb−	vb−	NUM
ejpam-3118	61	33	v	v	ADP
ejpam-3118	61	34	2	2	NUM
ejpam-3118	61	35	)	)	PUNCT
ejpam-3118	61	36	e	e	NOUN
ejpam-3118	61	37	,	,	PUNCT
ejpam-3118	61	38	e21	e21	PROPN
ejpam-3118	61	39	=	=	SYM
ejpam-3118	61	40	(	(	PUNCT
ejpam-3118	61	41	v	v	NOUN
ejpam-3118	61	42	+	+	NUM
ejpam-3118	61	43	vb	vb	NOUN
ejpam-3118	61	44	2	2	NUM
ejpam-3118	61	45	)	)	PUNCT
ejpam-3118	61	46	e	e	NOUN
ejpam-3118	61	47	,	,	PUNCT
ejpam-3118	61	48	e22	e22	NOUN
ejpam-3118	61	49	=	=	SYM
ejpam-3118	61	50	(	(	PUNCT
ejpam-3118	61	51	1−	1−	NUM
ejpam-3118	61	52	b	b	SYM
ejpam-3118	61	53	2	2	NUM
ejpam-3118	61	54	)	)	PUNCT
ejpam-3118	61	55	e.	e.	PROPN
ejpam-3118	61	56	proposition	proposition	PROPN
ejpam-3118	61	57	3	3	X
ejpam-3118	61	58	.	.	PUNCT
ejpam-3118	62	1	[	[	X
ejpam-3118	62	2	6	6	NUM
ejpam-3118	62	3	,	,	PUNCT
ejpam-3118	62	4	p	p	PRON
ejpam-3118	62	5	roposition	roposition	NOUN
ejpam-3118	62	6	2.4	2.4	NUM
ejpam-3118	62	7	]	]	PUNCT
ejpam-3118	62	8	let	let	VERB
ejpam-3118	62	9	g	g	PRON
ejpam-3118	62	10	be	be	AUX
ejpam-3118	62	11	an	an	DET
ejpam-3118	62	12	finite	finite	NOUN
ejpam-3118	62	13	extra	extra	ADJ
ejpam-3118	62	14	-	-	ADJ
ejpam-3118	62	15	special	special	ADJ
ejpam-3118	62	16	2	2	NUM
ejpam-3118	62	17	-	-	PUNCT
ejpam-3118	62	18	group	group	NOUN
ejpam-3118	62	19	,	,	PUNCT
ejpam-3118	62	20	g′	g′	NOUN
ejpam-3118	62	21	=	=	PUNCT
ejpam-3118	62	22	{	{	PUNCT
ejpam-3118	62	23	1	1	NUM
ejpam-3118	62	24	,	,	PUNCT
ejpam-3118	62	25	s	s	X
ejpam-3118	62	26	}	}	PUNCT
ejpam-3118	62	27	the	the	DET
ejpam-3118	62	28	commutator	commutator	NOUN
ejpam-3118	62	29	subgroup	subgroup	NOUN
ejpam-3118	62	30	of	of	ADP
ejpam-3118	62	31	g	g	PROPN
ejpam-3118	62	32	and	and	CCONJ
ejpam-3118	62	33	ε	ε	VERB
ejpam-3118	62	34	the	the	DET
ejpam-3118	62	35	augmentation	augmentation	NOUN
ejpam-3118	62	36	mapping	mapping	NOUN
ejpam-3118	62	37	on	on	ADP
ejpam-3118	62	38	qg	qg	PROPN
ejpam-3118	62	39	.	.	PUNCT
ejpam-3118	63	1	then	then	ADV
ejpam-3118	63	2	:	:	PUNCT
ejpam-3118	63	3	(	(	PUNCT
ejpam-3118	63	4	i	i	NOUN
ejpam-3118	63	5	)	)	PUNCT
ejpam-3118	63	6	u2	u2	PROPN
ejpam-3118	63	7	=	=	PUNCT
ejpam-3118	63	8	{	{	PUNCT
ejpam-3118	63	9	u	u	NOUN
ejpam-3118	63	10	=	=	NOUN
ejpam-3118	63	11	1	1	NUM
ejpam-3118	63	12	+	+	NUM
ejpam-3118	63	13	α(1−	α(1−	PROPN
ejpam-3118	63	14	s)|u	s)|u	PROPN
ejpam-3118	63	15	∈	∈	PROPN
ejpam-3118	63	16	u(zg	u(zg	NOUN
ejpam-3118	63	17	)	)	PUNCT
ejpam-3118	63	18	,	,	PUNCT
ejpam-3118	63	19	α	α	PROPN
ejpam-3118	63	20	∈	∈	PROPN
ejpam-3118	63	21	zg	zg	PROPN
ejpam-3118	63	22	}	}	PUNCT
ejpam-3118	63	23	;	;	PUNCT
ejpam-3118	63	24	(	(	PUNCT
ejpam-3118	63	25	ii	ii	NOUN
ejpam-3118	63	26	)	)	PUNCT
ejpam-3118	63	27	if	if	SCONJ
ejpam-3118	63	28	v	v	NOUN
ejpam-3118	63	29	=	=	SYM
ejpam-3118	63	30	{	{	PUNCT
ejpam-3118	63	31	u	u	NOUN
ejpam-3118	63	32	=	=	NOUN
ejpam-3118	63	33	1	1	NUM
ejpam-3118	63	34	+	+	NUM
ejpam-3118	63	35	α	α	PROPN
ejpam-3118	63	36	(	(	PUNCT
ejpam-3118	63	37	1−	1−	NUM
ejpam-3118	63	38	s)|u	s)|u	PROPN
ejpam-3118	63	39	∈	∈	PROPN
ejpam-3118	63	40	u(zg	u(zg	NOUN
ejpam-3118	63	41	)	)	PUNCT
ejpam-3118	63	42	,	,	PUNCT
ejpam-3118	63	43	α	α	PROPN
ejpam-3118	63	44	∈	∈	PROPN
ejpam-3118	63	45	zg	zg	PROPN
ejpam-3118	63	46	and	and	CCONJ
ejpam-3118	63	47	ε(α	ε(α	PROPN
ejpam-3118	63	48	)	)	PUNCT
ejpam-3118	63	49	is	be	AUX
ejpam-3118	63	50	even	even	ADV
ejpam-3118	63	51	}	}	PUNCT
ejpam-3118	63	52	,	,	PUNCT
ejpam-3118	63	53	then	then	ADV
ejpam-3118	63	54	v	v	ADP
ejpam-3118	63	55	∼=	∼=	NOUN
ejpam-3118	63	56	u2	u2	NOUN
ejpam-3118	63	57	/	/	SYM
ejpam-3118	63	58	g	g	NOUN
ejpam-3118	63	59	′	′	NUM
ejpam-3118	63	60	;	;	PUNCT
ejpam-3118	63	61	(	(	PUNCT
ejpam-3118	63	62	iii	iii	X
ejpam-3118	63	63	)	)	PUNCT
ejpam-3118	63	64	if	if	SCONJ
ejpam-3118	63	65	g	g	NOUN
ejpam-3118	63	66	/	/	SYM
ejpam-3118	63	67	g′	g′	NOUN
ejpam-3118	63	68	has	have	AUX
ejpam-3118	63	69	exponent	exponent	NOUN
ejpam-3118	63	70	at	at	ADP
ejpam-3118	63	71	most	most	ADV
ejpam-3118	63	72	4	4	NUM
ejpam-3118	63	73	,	,	PUNCT
ejpam-3118	63	74	then	then	ADV
ejpam-3118	63	75	u(zg	u(zg	NUM
ejpam-3118	63	76	)	)	PUNCT
ejpam-3118	63	77	=	=	X
ejpam-3118	63	78	±gv	±gv	PROPN
ejpam-3118	63	79	.	.	PUNCT
ejpam-3118	64	1	theorem	theorem	VERB
ejpam-3118	64	2	1	1	NUM
ejpam-3118	64	3	.	.	PUNCT
ejpam-3118	65	1	[	[	X
ejpam-3118	65	2	6	6	NUM
ejpam-3118	65	3	,	,	PUNCT
ejpam-3118	65	4	theorem	theorem	VERB
ejpam-3118	65	5	4.3	4.3	NUM
ejpam-3118	65	6	]	]	SYM
ejpam-3118	65	7	u(zd4	u(zd4	NOUN
ejpam-3118	65	8	)	)	PUNCT
ejpam-3118	65	9	=	=	SYM
ejpam-3118	66	1	±d4v	±d4v	NOUN
ejpam-3118	66	2	and	and	CCONJ
ejpam-3118	66	3	v	v	NOUN
ejpam-3118	66	4	is	be	AUX
ejpam-3118	66	5	isomorphic	isomorphic	ADJ
ejpam-3118	66	6	to	to	ADP
ejpam-3118	66	7	the	the	DET
ejpam-3118	66	8	group	group	NOUN
ejpam-3118	66	9	of	of	ADP
ejpam-3118	66	10	2	2	NUM
ejpam-3118	66	11	-	-	PUNCT
ejpam-3118	66	12	by-2	by-2	NOUN
ejpam-3118	66	13	matrices	matrix	NOUN
ejpam-3118	66	14	[	[	PUNCT
ejpam-3118	66	15	2z	2z	NUM
ejpam-3118	66	16	+	+	NOUN
ejpam-3118	66	17	1	1	NUM
ejpam-3118	66	18	4z	4z	NOUN
ejpam-3118	66	19	2z	2z	NOUN
ejpam-3118	66	20	2z	2z	NOUN
ejpam-3118	66	21	+	+	CCONJ
ejpam-3118	66	22	1	1	NUM
ejpam-3118	66	23	]	]	PUNCT
ejpam-3118	66	24	det=1	det=1	NOUN
ejpam-3118	66	25	.	.	PUNCT
ejpam-3118	67	1	proposition	proposition	NOUN
ejpam-3118	67	2	4	4	NUM
ejpam-3118	67	3	.	.	PUNCT
ejpam-3118	68	1	let	let	VERB
ejpam-3118	68	2	g	g	PRON
ejpam-3118	68	3	be	be	AUX
ejpam-3118	68	4	an	an	DET
ejpam-3118	68	5	finite	finite	NOUN
ejpam-3118	68	6	extra	extra	ADJ
ejpam-3118	68	7	-	-	ADJ
ejpam-3118	68	8	special	special	ADJ
ejpam-3118	68	9	2	2	NUM
ejpam-3118	68	10	-	-	PUNCT
ejpam-3118	68	11	group	group	NOUN
ejpam-3118	68	12	and	and	CCONJ
ejpam-3118	68	13	g′	g′	NOUN
ejpam-3118	68	14	=	=	SYM
ejpam-3118	68	15	{	{	PUNCT
ejpam-3118	68	16	1	1	NUM
ejpam-3118	68	17	,	,	PUNCT
ejpam-3118	68	18	s	s	X
ejpam-3118	68	19	}	}	PUNCT
ejpam-3118	68	20	its	its	PRON
ejpam-3118	68	21	commutator	commutator	NOUN
ejpam-3118	68	22	subgroup	subgroup	NOUN
ejpam-3118	68	23	.	.	PUNCT
ejpam-3118	69	1	se	se	PROPN
ejpam-3118	69	2	ĝ′	ĝ′	PROPN
ejpam-3118	69	3	=	=	NOUN
ejpam-3118	69	4	1	1	NUM
ejpam-3118	69	5	+	+	SYM
ejpam-3118	69	6	s	s	X
ejpam-3118	69	7	2	2	NUM
ejpam-3118	69	8	,	,	PUNCT
ejpam-3118	69	9	then	then	ADV
ejpam-3118	69	10	the	the	DET
ejpam-3118	69	11	component	component	NOUN
ejpam-3118	69	12	qg(1−	qg(1−	ADJ
ejpam-3118	69	13	ĝ′	ĝ′	PROPN
ejpam-3118	69	14	)	)	PUNCT
ejpam-3118	69	15	=	=	SYM
ejpam-3118	69	16	qg	qg	PROPN
ejpam-3118	69	17	(	(	PUNCT
ejpam-3118	69	18	1−	1−	NUM
ejpam-3118	69	19	s	s	NOUN
ejpam-3118	69	20	2	2	NUM
ejpam-3118	69	21	)	)	PUNCT
ejpam-3118	69	22	in	in	ADP
ejpam-3118	69	23	the	the	DET
ejpam-3118	69	24	decomposition	decomposition	NOUN
ejpam-3118	69	25	of	of	ADP
ejpam-3118	69	26	qg	qg	PROPN
ejpam-3118	69	27	is	be	AUX
ejpam-3118	69	28	simple	simple	ADJ
ejpam-3118	69	29	.	.	PUNCT
ejpam-3118	70	1	proof	proof	NOUN
ejpam-3118	70	2	.	.	PUNCT
ejpam-3118	71	1	let	let	VERB
ejpam-3118	71	2	e	e	NOUN
ejpam-3118	71	3	=	=	SYM
ejpam-3118	71	4	1−	1−	NUM
ejpam-3118	71	5	s	s	NOUN
ejpam-3118	71	6	2	2	NUM
ejpam-3118	71	7	and	and	CCONJ
ejpam-3118	71	8	e	e	NOUN
ejpam-3118	71	9	be	be	AUX
ejpam-3118	71	10	a	a	DET
ejpam-3118	71	11	non	non	ADJ
ejpam-3118	71	12	-	-	ADJ
ejpam-3118	71	13	trivial	trivial	ADJ
ejpam-3118	71	14	central	central	ADJ
ejpam-3118	71	15	idempotent	idempotent	NOUN
ejpam-3118	71	16	of	of	ADP
ejpam-3118	71	17	qg(e	qg(e	NUM
ejpam-3118	71	18	)	)	PUNCT
ejpam-3118	71	19	.	.	PUNCT
ejpam-3118	72	1	if	if	SCONJ
ejpam-3118	72	2	z(g	z(g	NOUN
ejpam-3118	72	3	)	)	PUNCT
ejpam-3118	72	4	denotes	denote	VERB
ejpam-3118	72	5	the	the	DET
ejpam-3118	72	6	center	center	NOUN
ejpam-3118	72	7	of	of	ADP
ejpam-3118	72	8	g	g	PROPN
ejpam-3118	72	9	and	and	CCONJ
ejpam-3118	72	10	cg	cg	NOUN
ejpam-3118	72	11	denotes	denote	VERB
ejpam-3118	72	12	the	the	DET
ejpam-3118	72	13	class	class	NOUN
ejpam-3118	72	14	of	of	ADP
ejpam-3118	72	15	conjugation	conjugation	NOUN
ejpam-3118	72	16	of	of	ADP
ejpam-3118	72	17	g	g	PROPN
ejpam-3118	72	18	∈	∈	PROPN
ejpam-3118	72	19	g	g	PROPN
ejpam-3118	72	20	,	,	PUNCT
ejpam-3118	72	21	then	then	ADV
ejpam-3118	72	22	e	e	X
ejpam-3118	72	23	=	=	SYM
ejpam-3118	72	24	∑	∑	PUNCT
ejpam-3118	72	25	g∈z(g	g∈z(g	NOUN
ejpam-3118	72	26	)	)	PUNCT
ejpam-3118	72	27	αgg	αgg	NOUN
ejpam-3118	72	28	+	+	CCONJ
ejpam-3118	72	29	∑	∑	ADV
ejpam-3118	72	30	g/∈z(g	g/∈z(g	ADJ
ejpam-3118	72	31	)	)	PUNCT
ejpam-3118	72	32	αgcg	αgcg	NOUN
ejpam-3118	72	33	,	,	PUNCT
ejpam-3118	72	34	where	where	SCONJ
ejpam-3118	72	35	cg	cg	NOUN
ejpam-3118	72	36	=	=	PUNCT
ejpam-3118	72	37	∑	∑	PROPN
ejpam-3118	72	38	x∈cg	x∈cg	PROPN
ejpam-3118	72	39	x.	x.	PROPN
ejpam-3118	72	40	since	since	SCONJ
ejpam-3118	72	41	g	g	NOUN
ejpam-3118	72	42	′	′	NUM
ejpam-3118	72	43	=	=	PUNCT
ejpam-3118	72	44	{	{	PUNCT
ejpam-3118	72	45	1	1	NUM
ejpam-3118	72	46	,	,	PUNCT
ejpam-3118	72	47	s	s	PART
ejpam-3118	72	48	}	}	PUNCT
ejpam-3118	72	49	,	,	PUNCT
ejpam-3118	72	50	if	if	SCONJ
ejpam-3118	72	51	g	g	PROPN
ejpam-3118	72	52	is	be	AUX
ejpam-3118	72	53	not	not	PART
ejpam-3118	72	54	central	central	ADJ
ejpam-3118	72	55	,	,	PUNCT
ejpam-3118	72	56	then	then	ADV
ejpam-3118	72	57	cg	cg	NOUN
ejpam-3118	72	58	=	=	PUNCT
ejpam-3118	72	59	{	{	PUNCT
ejpam-3118	72	60	g	g	PROPN
ejpam-3118	72	61	,	,	PUNCT
ejpam-3118	72	62	gs	gs	NOUN
ejpam-3118	72	63	}	}	PUNCT
ejpam-3118	72	64	.	.	PUNCT
ejpam-3118	73	1	consequently	consequently	ADV
ejpam-3118	73	2	,	,	PUNCT
ejpam-3118	73	3	e	e	PROPN
ejpam-3118	73	4	=	=	SYM
ejpam-3118	73	5	∑	∑	PUNCT
ejpam-3118	73	6	g∈z(g	g∈z(g	NOUN
ejpam-3118	73	7	)	)	PUNCT
ejpam-3118	73	8	αgg	αgg	NOUN
ejpam-3118	73	9	+	+	CCONJ
ejpam-3118	73	10	∑	∑	ADV
ejpam-3118	73	11	g/∈z(g	g/∈z(g	NOUN
ejpam-3118	73	12	)	)	PUNCT
ejpam-3118	73	13	αg(g	αg(g	NOUN
ejpam-3118	74	1	+	+	NUM
ejpam-3118	74	2	gs	gs	X
ejpam-3118	74	3	)	)	PUNCT
ejpam-3118	74	4	=	=	SYM
ejpam-3118	74	5	∑	∑	PUNCT
ejpam-3118	74	6	g∈z(g	g∈z(g	NOUN
ejpam-3118	74	7	)	)	PUNCT
ejpam-3118	74	8	αgg	αgg	NOUN
ejpam-3118	74	9	+	+	CCONJ
ejpam-3118	74	10	(	(	PUNCT
ejpam-3118	74	11	1	1	NUM
ejpam-3118	74	12	+	+	NUM
ejpam-3118	74	13	s	s	X
ejpam-3118	74	14	)	)	PUNCT
ejpam-3118	74	15	∑	∑	PUNCT
ejpam-3118	74	16	g/∈z(g	g/∈z(g	NOUN
ejpam-3118	74	17	)	)	PUNCT
ejpam-3118	74	18	αgg	αgg	NOUN
ejpam-3118	74	19	.	.	PUNCT
ejpam-3118	75	1	since	since	SCONJ
ejpam-3118	75	2	e	e	PROPN
ejpam-3118	75	3	is	be	AUX
ejpam-3118	75	4	an	an	DET
ejpam-3118	75	5	idempotent	idempotent	NOUN
ejpam-3118	75	6	of	of	ADP
ejpam-3118	75	7	qg(e	qg(e	NUM
ejpam-3118	75	8	)	)	PUNCT
ejpam-3118	75	9	,	,	PUNCT
ejpam-3118	75	10	it	it	PRON
ejpam-3118	75	11	follows	follow	VERB
ejpam-3118	75	12	ee	ee	PROPN
ejpam-3118	75	13	=	=	PROPN
ejpam-3118	75	14	e.	e.	PROPN
ejpam-3118	75	15	hence	hence	ADV
ejpam-3118	75	16	,	,	PUNCT
ejpam-3118	75	17	as	as	ADP
ejpam-3118	75	18	(	(	PUNCT
ejpam-3118	75	19	1	1	NUM
ejpam-3118	75	20	+	+	CCONJ
ejpam-3118	75	21	s)e	s)e	NOUN
ejpam-3118	75	22	=	=	SYM
ejpam-3118	75	23	0	0	NUM
ejpam-3118	75	24	,	,	PUNCT
ejpam-3118	75	25	e	e	X
ejpam-3118	75	26	=	=	PUNCT
ejpam-3118	75	27	(	(	PUNCT
ejpam-3118	75	28	∑	∑	INTJ
ejpam-3118	75	29	g∈z(g	g∈z(g	NOUN
ejpam-3118	75	30	)	)	PUNCT
ejpam-3118	75	31	αgg	αgg	NOUN
ejpam-3118	75	32	)	)	PUNCT
ejpam-3118	75	33	e	e	NOUN
ejpam-3118	75	34	and	and	CCONJ
ejpam-3118	75	35	e	e	PROPN
ejpam-3118	75	36	∈	∈	PROPN
ejpam-3118	75	37	q(z(g	q(z(g	NOUN
ejpam-3118	75	38	)	)	PUNCT
ejpam-3118	75	39	)	)	PUNCT
ejpam-3118	75	40	.	.	PUNCT
ejpam-3118	76	1	since	since	SCONJ
ejpam-3118	76	2	z(g	z(g	NOUN
ejpam-3118	76	3	)	)	PUNCT
ejpam-3118	76	4	=	=	PRON
ejpam-3118	76	5	{	{	PUNCT
ejpam-3118	76	6	1	1	NUM
ejpam-3118	76	7	,	,	PUNCT
ejpam-3118	76	8	s	s	PART
ejpam-3118	76	9	}	}	PUNCT
ejpam-3118	76	10	,	,	PUNCT
ejpam-3118	76	11	the	the	DET
ejpam-3118	76	12	only	only	ADJ
ejpam-3118	76	13	possibilities	possibility	NOUN
ejpam-3118	76	14	for	for	ADP
ejpam-3118	76	15	e	e	NOUN
ejpam-3118	76	16	are	be	AUX
ejpam-3118	76	17	0	0	NUM
ejpam-3118	76	18	,	,	PUNCT
ejpam-3118	76	19	1	1	NUM
ejpam-3118	76	20	,	,	PUNCT
ejpam-3118	76	21	1	1	NUM
ejpam-3118	76	22	+	+	SYM
ejpam-3118	76	23	s	s	X
ejpam-3118	76	24	2	2	NUM
ejpam-3118	76	25	and	and	CCONJ
ejpam-3118	76	26	1−	1−	NUM
ejpam-3118	76	27	s	s	NOUN
ejpam-3118	76	28	2	2	NUM
ejpam-3118	76	29	.	.	PUNCT
ejpam-3118	77	1	therefore	therefore	ADV
ejpam-3118	77	2	,	,	PUNCT
ejpam-3118	77	3	e	e	X
ejpam-3118	77	4	=	=	SYM
ejpam-3118	77	5	e	e	PROPN
ejpam-3118	77	6	and	and	CCONJ
ejpam-3118	77	7	the	the	DET
ejpam-3118	77	8	component	component	NOUN
ejpam-3118	77	9	qg(1−	qg(1−	ADJ
ejpam-3118	77	10	ĝ′	ĝ′	PROPN
ejpam-3118	77	11	)	)	PUNCT
ejpam-3118	77	12	=	=	PUNCT
ejpam-3118	77	13	qg(e	qg(e	ADV
ejpam-3118	77	14	)	)	PUNCT
ejpam-3118	77	15	is	be	AUX
ejpam-3118	77	16	simple	simple	ADJ
ejpam-3118	77	17	,	,	PUNCT
ejpam-3118	77	18	as	as	SCONJ
ejpam-3118	77	19	we	we	PRON
ejpam-3118	77	20	wanted	want	VERB
ejpam-3118	77	21	to	to	PART
ejpam-3118	77	22	prove	prove	VERB
ejpam-3118	77	23	.	.	PUNCT
ejpam-3118	78	1	4	4	X
ejpam-3118	78	2	.	.	X
ejpam-3118	78	3	main	main	ADJ
ejpam-3118	78	4	results	result	NOUN
ejpam-3118	78	5	now	now	ADV
ejpam-3118	78	6	that	that	SCONJ
ejpam-3118	78	7	we	we	PRON
ejpam-3118	78	8	have	have	AUX
ejpam-3118	78	9	introduced	introduce	VERB
ejpam-3118	78	10	the	the	DET
ejpam-3118	78	11	terminology	terminology	NOUN
ejpam-3118	78	12	,	,	PUNCT
ejpam-3118	78	13	fix	fix	VERB
ejpam-3118	78	14	the	the	DET
ejpam-3118	78	15	notation	notation	NOUN
ejpam-3118	78	16	and	and	CCONJ
ejpam-3118	78	17	display	display	VERB
ejpam-3118	78	18	the	the	DET
ejpam-3118	78	19	auxiliary	auxiliary	ADJ
ejpam-3118	78	20	results	result	NOUN
ejpam-3118	78	21	,	,	PUNCT
ejpam-3118	78	22	we	we	PRON
ejpam-3118	78	23	are	be	AUX
ejpam-3118	78	24	able	able	ADJ
ejpam-3118	78	25	to	to	PART
ejpam-3118	78	26	present	present	VERB
ejpam-3118	78	27	the	the	DET
ejpam-3118	78	28	main	main	ADJ
ejpam-3118	78	29	results	result	NOUN
ejpam-3118	78	30	.	.	PUNCT
ejpam-3118	79	1	we	we	PRON
ejpam-3118	79	2	begin	begin	VERB
ejpam-3118	79	3	describing	describe	VERB
ejpam-3118	79	4	u(zg1	u(zg1	PROPN
ejpam-3118	79	5	)	)	PUNCT
ejpam-3118	79	6	,	,	PUNCT
ejpam-3118	79	7	the	the	DET
ejpam-3118	79	8	group	group	NOUN
ejpam-3118	79	9	of	of	ADP
ejpam-3118	79	10	units	unit	NOUN
ejpam-3118	79	11	of	of	ADP
ejpam-3118	79	12	zg1	zg1	PROPN
ejpam-3118	79	13	.	.	PUNCT
ejpam-3118	80	1	c.	c.	PROPN
ejpam-3118	80	2	mello	mello	PROPN
ejpam-3118	80	3	/	/	SYM
ejpam-3118	80	4	eur	eur	PROPN
ejpam-3118	80	5	.	.	PUNCT
ejpam-3118	81	1	j.	j.	PROPN
ejpam-3118	81	2	pure	pure	PROPN
ejpam-3118	81	3	appl	appl	PROPN
ejpam-3118	81	4	.	.	PROPN
ejpam-3118	81	5	math	math	PROPN
ejpam-3118	81	6	,	,	PUNCT
ejpam-3118	81	7	10	10	NUM
ejpam-3118	81	8	(	(	PUNCT
ejpam-3118	81	9	5	5	NUM
ejpam-3118	81	10	)	)	PUNCT
ejpam-3118	81	11	(	(	PUNCT
ejpam-3118	81	12	2017	2017	NUM
ejpam-3118	81	13	)	)	PUNCT
ejpam-3118	81	14	,	,	PUNCT
ejpam-3118	81	15	955	955	NUM
ejpam-3118	81	16	-	-	SYM
ejpam-3118	81	17	966	966	NUM
ejpam-3118	81	18	959	959	NUM
ejpam-3118	81	19	4.1	4.1	NUM
ejpam-3118	81	20	.	.	PUNCT
ejpam-3118	82	1	the	the	DET
ejpam-3118	82	2	group	group	NOUN
ejpam-3118	82	3	of	of	ADP
ejpam-3118	82	4	units	unit	NOUN
ejpam-3118	82	5	of	of	ADP
ejpam-3118	82	6	group	group	NOUN
ejpam-3118	82	7	ring	ring	NOUN
ejpam-3118	82	8	zg1	zg1	NOUN
ejpam-3118	82	9	proposition	proposition	NOUN
ejpam-3118	82	10	5	5	NUM
ejpam-3118	82	11	.	.	PUNCT
ejpam-3118	83	1	the	the	DET
ejpam-3118	83	2	group	group	NOUN
ejpam-3118	83	3	ring	ring	NOUN
ejpam-3118	83	4	qg1	qg1	ADV
ejpam-3118	83	5	admits	admit	VERB
ejpam-3118	83	6	the	the	DET
ejpam-3118	83	7	following	follow	VERB
ejpam-3118	83	8	decomposition	decomposition	NOUN
ejpam-3118	83	9	:	:	PUNCT
ejpam-3118	84	1	qg1	qg1	ADV
ejpam-3118	84	2	=	=	PUNCT
ejpam-3118	85	1	qg1	qg1	ADJ
ejpam-3118	85	2	(	(	PUNCT
ejpam-3118	85	3	1	1	NUM
ejpam-3118	85	4	+	+	SYM
ejpam-3118	85	5	s	s	X
ejpam-3118	85	6	2	2	NUM
ejpam-3118	85	7	)	)	PUNCT
ejpam-3118	85	8	⊕qg1	⊕qg1	VERB
ejpam-3118	85	9	(	(	PUNCT
ejpam-3118	85	10	1−	1−	NUM
ejpam-3118	85	11	s	s	NOUN
ejpam-3118	85	12	2	2	NUM
ejpam-3118	85	13	)	)	PUNCT
ejpam-3118	85	14	,	,	PUNCT
ejpam-3118	85	15	where	where	SCONJ
ejpam-3118	85	16	qg1	qg1	ADV
ejpam-3118	85	17	(	(	PUNCT
ejpam-3118	85	18	1	1	NUM
ejpam-3118	85	19	+	+	SYM
ejpam-3118	85	20	s	s	X
ejpam-3118	85	21	2	2	NUM
ejpam-3118	85	22	)	)	PUNCT
ejpam-3118	85	23	∼=	∼=	PART
ejpam-3118	85	24	q16	q16	NOUN
ejpam-3118	86	1	and	and	CCONJ
ejpam-3118	86	2	qg1	qg1	ADV
ejpam-3118	86	3	(	(	PUNCT
ejpam-3118	86	4	1−	1−	NUM
ejpam-3118	86	5	s	s	NOUN
ejpam-3118	86	6	2	2	NUM
ejpam-3118	86	7	)	)	PUNCT
ejpam-3118	86	8	∼=	∼=	PROPN
ejpam-3118	86	9	m4(q	m4(q	NOUN
ejpam-3118	86	10	)	)	PUNCT
ejpam-3118	86	11	.	.	PUNCT
ejpam-3118	87	1	proof	proof	NOUN
ejpam-3118	87	2	.	.	PUNCT
ejpam-3118	88	1	it	it	PRON
ejpam-3118	88	2	follows	follow	VERB
ejpam-3118	88	3	from	from	ADP
ejpam-3118	88	4	proposition	proposition	NOUN
ejpam-3118	88	5	1	1	NUM
ejpam-3118	88	6	and	and	CCONJ
ejpam-3118	88	7	proposition	proposition	NOUN
ejpam-3118	88	8	4	4	NUM
ejpam-3118	88	9	.	.	X
ejpam-3118	89	1	for	for	ADP
ejpam-3118	89	2	the	the	DET
ejpam-3118	89	3	next	next	ADJ
ejpam-3118	89	4	results	result	NOUN
ejpam-3118	89	5	,	,	PUNCT
ejpam-3118	89	6	⊗	⊗	PROPN
ejpam-3118	89	7	denotes	denote	VERB
ejpam-3118	89	8	the	the	DET
ejpam-3118	89	9	kronecker	kronecker	NOUN
ejpam-3118	89	10	product	product	NOUN
ejpam-3118	89	11	and	and	CCONJ
ejpam-3118	89	12	we	we	PRON
ejpam-3118	89	13	use	use	VERB
ejpam-3118	89	14	the	the	DET
ejpam-3118	89	15	representation	representation	NOUN
ejpam-3118	89	16	of	of	ADP
ejpam-3118	89	17	d4	d4	PROPN
ejpam-3118	89	18	on	on	ADP
ejpam-3118	89	19	m2(q	m2(q	NOUN
ejpam-3118	89	20	)	)	PUNCT
ejpam-3118	89	21	previously	previously	ADV
ejpam-3118	89	22	fixed	fix	VERB
ejpam-3118	89	23	and	and	CCONJ
ejpam-3118	89	24	we	we	PRON
ejpam-3118	89	25	obtain	obtain	VERB
ejpam-3118	89	26	a	a	DET
ejpam-3118	89	27	representation	representation	NOUN
ejpam-3118	89	28	of	of	ADP
ejpam-3118	89	29	g1	g1	PROPN
ejpam-3118	89	30	on	on	ADP
ejpam-3118	89	31	m4(q	m4(q	PRON
ejpam-3118	89	32	):	):	PUNCT
ejpam-3118	89	33	•	•	NUM
ejpam-3118	89	34	b	b	SYM
ejpam-3118	89	35	7→	7→	NUM
ejpam-3118	89	36	e11	e11	NOUN
ejpam-3118	89	37	+	+	CCONJ
ejpam-3118	89	38	e22	e22	PROPN
ejpam-3118	89	39	−	−	PROPN
ejpam-3118	89	40	e33	e33	PROPN
ejpam-3118	89	41	−	−	PROPN
ejpam-3118	89	42	e44	e44	NOUN
ejpam-3118	90	1	=	=	PUNCT
ejpam-3118	90	2	[	[	PUNCT
ejpam-3118	90	3	1	1	NUM
ejpam-3118	90	4	0	0	NUM
ejpam-3118	90	5	0	0	NUM
ejpam-3118	90	6	1	1	NUM
ejpam-3118	90	7	]	]	PUNCT
ejpam-3118	91	1	⊗	⊗	PROPN
ejpam-3118	91	2	[	[	PUNCT
ejpam-3118	91	3	1	1	NUM
ejpam-3118	91	4	0	0	NUM
ejpam-3118	91	5	0	0	NUM
ejpam-3118	91	6	−1	−1	NOUN
ejpam-3118	91	7	]	]	PUNCT
ejpam-3118	91	8	,	,	PUNCT
ejpam-3118	91	9	•	•	NOUN
ejpam-3118	91	10	v	v	ADP
ejpam-3118	91	11	7→	7→	NUM
ejpam-3118	91	12	−e13	−e13	NUM
ejpam-3118	91	13	−	−	PROPN
ejpam-3118	91	14	e24	e24	PROPN
ejpam-3118	91	15	+	+	CCONJ
ejpam-3118	91	16	e31	e31	PROPN
ejpam-3118	91	17	+	+	CCONJ
ejpam-3118	91	18	e42	e42	NUM
ejpam-3118	91	19	=	=	NOUN
ejpam-3118	91	20	[	[	PUNCT
ejpam-3118	91	21	1	1	NUM
ejpam-3118	91	22	0	0	NUM
ejpam-3118	91	23	0	0	NUM
ejpam-3118	91	24	1	1	NUM
ejpam-3118	91	25	]	]	PUNCT
ejpam-3118	91	26	⊗	⊗	PROPN
ejpam-3118	91	27	[	[	PUNCT
ejpam-3118	91	28	0	0	NUM
ejpam-3118	91	29	−1	−1	NOUN
ejpam-3118	91	30	1	1	NUM
ejpam-3118	91	31	0	0	NUM
ejpam-3118	91	32	]	]	PUNCT
ejpam-3118	91	33	,	,	PUNCT
ejpam-3118	91	34	•	•	NUM
ejpam-3118	91	35	b1	b1	NOUN
ejpam-3118	91	36	7→	7→	NUM
ejpam-3118	91	37	e11	e11	NOUN
ejpam-3118	91	38	−	−	PROPN
ejpam-3118	91	39	e22	e22	NOUN
ejpam-3118	91	40	+	+	CCONJ
ejpam-3118	91	41	e33	e33	PROPN
ejpam-3118	91	42	−	−	PROPN
ejpam-3118	91	43	e44	e44	NOUN
ejpam-3118	91	44	=	=	PUNCT
ejpam-3118	91	45	[	[	PUNCT
ejpam-3118	91	46	1	1	NUM
ejpam-3118	91	47	0	0	NUM
ejpam-3118	91	48	0	0	NUM
ejpam-3118	91	49	−1	−1	NOUN
ejpam-3118	91	50	]	]	PUNCT
ejpam-3118	92	1	⊗	⊗	X
ejpam-3118	92	2	[	[	PUNCT
ejpam-3118	92	3	1	1	NUM
ejpam-3118	92	4	0	0	NUM
ejpam-3118	92	5	0	0	NUM
ejpam-3118	92	6	1	1	NUM
ejpam-3118	92	7	]	]	PUNCT
ejpam-3118	92	8	,	,	PUNCT
ejpam-3118	92	9	•	•	NUM
ejpam-3118	92	10	v1	v1	VERB
ejpam-3118	92	11	7→	7→	NUM
ejpam-3118	93	1	−e12	−e12	NOUN
ejpam-3118	94	1	+	+	CCONJ
ejpam-3118	94	2	e21	e21	NUM
ejpam-3118	94	3	−	−	NUM
ejpam-3118	94	4	e34	e34	NOUN
ejpam-3118	94	5	+	+	CCONJ
ejpam-3118	94	6	e43	e43	NOUN
ejpam-3118	94	7	=	=	SYM
ejpam-3118	94	8	[	[	PUNCT
ejpam-3118	94	9	0	0	NUM
ejpam-3118	94	10	−1	−1	NOUN
ejpam-3118	94	11	1	1	NUM
ejpam-3118	94	12	0	0	NUM
ejpam-3118	94	13	]	]	PUNCT
ejpam-3118	95	1	⊗	⊗	PROPN
ejpam-3118	95	2	[	[	PUNCT
ejpam-3118	95	3	1	1	NUM
ejpam-3118	95	4	0	0	NUM
ejpam-3118	95	5	0	0	NUM
ejpam-3118	95	6	1	1	NUM
ejpam-3118	95	7	]	]	PUNCT
ejpam-3118	95	8	.	.	PUNCT
ejpam-3118	96	1	thus	thus	ADV
ejpam-3118	96	2	,	,	PUNCT
ejpam-3118	96	3	the	the	DET
ejpam-3118	96	4	following	follow	VERB
ejpam-3118	96	5	proposition	proposition	NOUN
ejpam-3118	96	6	gives	give	VERB
ejpam-3118	96	7	us	we	PRON
ejpam-3118	96	8	an	an	DET
ejpam-3118	96	9	elementary	elementary	ADJ
ejpam-3118	96	10	q	q	ADJ
ejpam-3118	96	11	-	-	PUNCT
ejpam-3118	96	12	basis	basis	NOUN
ejpam-3118	96	13	matrix	matrix	NOUN
ejpam-3118	96	14	of	of	ADP
ejpam-3118	96	15	qg1	qg1	ADV
ejpam-3118	96	16	(	(	PUNCT
ejpam-3118	96	17	1−	1−	NUM
ejpam-3118	96	18	s	s	NOUN
ejpam-3118	96	19	2	2	NUM
ejpam-3118	96	20	)	)	PUNCT
ejpam-3118	96	21	∼=	∼=	PROPN
ejpam-3118	96	22	m4(q	m4(q	NOUN
ejpam-3118	96	23	)	)	PUNCT
ejpam-3118	96	24	.	.	PUNCT
ejpam-3118	97	1	proposition	proposition	NOUN
ejpam-3118	97	2	6	6	NUM
ejpam-3118	97	3	.	.	PUNCT
ejpam-3118	98	1	writing	write	VERB
ejpam-3118	98	2	e	e	NOUN
ejpam-3118	98	3	=	=	SYM
ejpam-3118	98	4	1−	1−	NUM
ejpam-3118	98	5	s	s	NOUN
ejpam-3118	98	6	2	2	NUM
ejpam-3118	98	7	and	and	CCONJ
ejpam-3118	98	8	using	use	VERB
ejpam-3118	98	9	the	the	DET
ejpam-3118	98	10	above	above	ADJ
ejpam-3118	98	11	representation	representation	NOUN
ejpam-3118	98	12	,	,	PUNCT
ejpam-3118	98	13	an	an	DET
ejpam-3118	98	14	elementary	elementary	ADJ
ejpam-3118	98	15	q	q	ADJ
ejpam-3118	98	16	-	-	PUNCT
ejpam-3118	98	17	basis	basis	NOUN
ejpam-3118	98	18	matrix	matrix	NOUN
ejpam-3118	98	19	of	of	ADP
ejpam-3118	98	20	qg1	qg1	ADV
ejpam-3118	98	21	(	(	PUNCT
ejpam-3118	98	22	1−	1−	NUM
ejpam-3118	98	23	s	s	NOUN
ejpam-3118	98	24	2	2	NUM
ejpam-3118	98	25	)	)	PUNCT
ejpam-3118	98	26	∼=	∼=	PROPN
ejpam-3118	98	27	m4(q	m4(q	PART
ejpam-3118	98	28	)	)	PUNCT
ejpam-3118	98	29	is	be	AUX
ejpam-3118	98	30	:	:	PUNCT
ejpam-3118	98	31	e11	e11	NUM
ejpam-3118	98	32	=	=	SYM
ejpam-3118	98	33	(	(	PUNCT
ejpam-3118	98	34	1	1	NUM
ejpam-3118	98	35	+	+	NUM
ejpam-3118	98	36	b	b	NOUN
ejpam-3118	98	37	2	2	NUM
ejpam-3118	98	38	)	)	PUNCT
ejpam-3118	98	39	(	(	PUNCT
ejpam-3118	98	40	1	1	NUM
ejpam-3118	98	41	+	+	NUM
ejpam-3118	98	42	b1	b1	NOUN
ejpam-3118	98	43	2	2	NUM
ejpam-3118	98	44	)	)	PUNCT
ejpam-3118	98	45	e	e	NOUN
ejpam-3118	98	46	,	,	PUNCT
ejpam-3118	98	47	e12	e12	NOUN
ejpam-3118	98	48	=	=	SYM
ejpam-3118	98	49	(	(	PUNCT
ejpam-3118	98	50	1	1	NUM
ejpam-3118	98	51	+	+	NUM
ejpam-3118	98	52	b	b	NOUN
ejpam-3118	98	53	2	2	NUM
ejpam-3118	98	54	)	)	PUNCT
ejpam-3118	98	55	(	(	PUNCT
ejpam-3118	98	56	v1b1	v1b1	VERB
ejpam-3118	98	57	−	−	PROPN
ejpam-3118	98	58	v1	v1	NOUN
ejpam-3118	98	59	2	2	NUM
ejpam-3118	98	60	)	)	PUNCT
ejpam-3118	98	61	e	e	NOUN
ejpam-3118	98	62	,	,	PUNCT
ejpam-3118	98	63	e13	e13	PROPN
ejpam-3118	98	64	=	=	SYM
ejpam-3118	98	65	(	(	PUNCT
ejpam-3118	98	66	vb−	vb−	NUM
ejpam-3118	98	67	v	v	ADP
ejpam-3118	98	68	2	2	NUM
ejpam-3118	98	69	)	)	PUNCT
ejpam-3118	98	70	(	(	PUNCT
ejpam-3118	98	71	1	1	NUM
ejpam-3118	98	72	+	+	NUM
ejpam-3118	98	73	b1	b1	NOUN
ejpam-3118	98	74	2	2	NUM
ejpam-3118	98	75	)	)	PUNCT
ejpam-3118	98	76	e	e	NOUN
ejpam-3118	98	77	,	,	PUNCT
ejpam-3118	98	78	e14	e14	NOUN
ejpam-3118	98	79	=	=	SYM
ejpam-3118	98	80	(	(	PUNCT
ejpam-3118	98	81	vb−	vb−	NUM
ejpam-3118	98	82	v	v	ADP
ejpam-3118	98	83	2	2	NUM
ejpam-3118	98	84	)	)	PUNCT
ejpam-3118	98	85	(	(	PUNCT
ejpam-3118	98	86	v1b1	v1b1	VERB
ejpam-3118	98	87	−	−	PROPN
ejpam-3118	98	88	v1	v1	NOUN
ejpam-3118	98	89	2	2	NUM
ejpam-3118	98	90	)	)	PUNCT
ejpam-3118	98	91	e	e	NOUN
ejpam-3118	98	92	,	,	PUNCT
ejpam-3118	98	93	e21	e21	PROPN
ejpam-3118	98	94	=	=	SYM
ejpam-3118	98	95	(	(	PUNCT
ejpam-3118	98	96	1	1	NUM
ejpam-3118	98	97	+	+	NUM
ejpam-3118	98	98	b	b	NOUN
ejpam-3118	98	99	2	2	NUM
ejpam-3118	98	100	)	)	PUNCT
ejpam-3118	98	101	(	(	PUNCT
ejpam-3118	98	102	v1	v1	VERB
ejpam-3118	98	103	+	+	CCONJ
ejpam-3118	98	104	v1b1	v1b1	NUM
ejpam-3118	98	105	2	2	NUM
ejpam-3118	98	106	)	)	PUNCT
ejpam-3118	98	107	e	e	NOUN
ejpam-3118	98	108	,	,	PUNCT
ejpam-3118	98	109	e22	e22	PROPN
ejpam-3118	98	110	=	=	SYM
ejpam-3118	98	111	(	(	PUNCT
ejpam-3118	98	112	1	1	NUM
ejpam-3118	98	113	+	+	NUM
ejpam-3118	98	114	b	b	NOUN
ejpam-3118	98	115	2	2	NUM
ejpam-3118	98	116	)	)	PUNCT
ejpam-3118	98	117	(	(	PUNCT
ejpam-3118	98	118	1−	1−	NUM
ejpam-3118	98	119	b1	b1	NOUN
ejpam-3118	98	120	2	2	NUM
ejpam-3118	98	121	)	)	PUNCT
ejpam-3118	98	122	e	e	NOUN
ejpam-3118	98	123	,	,	PUNCT
ejpam-3118	98	124	e23	e23	NOUN
ejpam-3118	98	125	=	=	SYM
ejpam-3118	98	126	(	(	PUNCT
ejpam-3118	98	127	vb−	vb−	NUM
ejpam-3118	98	128	v	v	ADP
ejpam-3118	98	129	2	2	NUM
ejpam-3118	98	130	)	)	PUNCT
ejpam-3118	98	131	(	(	PUNCT
ejpam-3118	98	132	v1	v1	VERB
ejpam-3118	98	133	+	+	CCONJ
ejpam-3118	98	134	v1b1	v1b1	NUM
ejpam-3118	98	135	2	2	NUM
ejpam-3118	98	136	)	)	PUNCT
ejpam-3118	98	137	e	e	NOUN
ejpam-3118	98	138	,	,	PUNCT
ejpam-3118	98	139	e24	e24	NOUN
ejpam-3118	98	140	=	=	SYM
ejpam-3118	98	141	(	(	PUNCT
ejpam-3118	98	142	vb−	vb−	NUM
ejpam-3118	98	143	v	v	ADP
ejpam-3118	98	144	2	2	NUM
ejpam-3118	98	145	)	)	PUNCT
ejpam-3118	98	146	(	(	PUNCT
ejpam-3118	98	147	1−	1−	NUM
ejpam-3118	98	148	b1	b1	NOUN
ejpam-3118	98	149	2	2	NUM
ejpam-3118	98	150	)	)	PUNCT
ejpam-3118	98	151	e	e	NOUN
ejpam-3118	98	152	,	,	PUNCT
ejpam-3118	98	153	e31	e31	PROPN
ejpam-3118	98	154	=	=	PUNCT
ejpam-3118	98	155	(	(	PUNCT
ejpam-3118	98	156	v	v	NOUN
ejpam-3118	98	157	+	+	NUM
ejpam-3118	98	158	vb	vb	NOUN
ejpam-3118	98	159	2	2	NUM
ejpam-3118	98	160	)	)	PUNCT
ejpam-3118	98	161	(	(	PUNCT
ejpam-3118	98	162	1	1	NUM
ejpam-3118	98	163	+	+	NUM
ejpam-3118	98	164	b1	b1	NOUN
ejpam-3118	98	165	2	2	NUM
ejpam-3118	98	166	)	)	PUNCT
ejpam-3118	98	167	e	e	NOUN
ejpam-3118	98	168	,	,	PUNCT
ejpam-3118	98	169	e32	e32	NOUN
ejpam-3118	98	170	=	=	SYM
ejpam-3118	98	171	(	(	PUNCT
ejpam-3118	98	172	v	v	NOUN
ejpam-3118	98	173	+	+	NUM
ejpam-3118	98	174	vb	vb	NOUN
ejpam-3118	98	175	2	2	NUM
ejpam-3118	98	176	)	)	PUNCT
ejpam-3118	98	177	(	(	PUNCT
ejpam-3118	98	178	v1b1	v1b1	VERB
ejpam-3118	98	179	−	−	PROPN
ejpam-3118	98	180	v1	v1	NOUN
ejpam-3118	98	181	2	2	NUM
ejpam-3118	98	182	)	)	PUNCT
ejpam-3118	98	183	e	e	NOUN
ejpam-3118	98	184	,	,	PUNCT
ejpam-3118	98	185	e33	e33	PROPN
ejpam-3118	98	186	=	=	SYM
ejpam-3118	98	187	(	(	PUNCT
ejpam-3118	98	188	1−	1−	NUM
ejpam-3118	98	189	b	b	SYM
ejpam-3118	98	190	2	2	NUM
ejpam-3118	98	191	)	)	PUNCT
ejpam-3118	98	192	(	(	PUNCT
ejpam-3118	98	193	1	1	NUM
ejpam-3118	98	194	+	+	NUM
ejpam-3118	98	195	b1	b1	NOUN
ejpam-3118	98	196	2	2	NUM
ejpam-3118	98	197	)	)	PUNCT
ejpam-3118	98	198	e	e	NOUN
ejpam-3118	98	199	,	,	PUNCT
ejpam-3118	98	200	e34	e34	NOUN
ejpam-3118	98	201	=	=	SYM
ejpam-3118	98	202	(	(	PUNCT
ejpam-3118	98	203	1−	1−	NUM
ejpam-3118	98	204	b	b	SYM
ejpam-3118	98	205	2	2	NUM
ejpam-3118	98	206	)	)	PUNCT
ejpam-3118	98	207	(	(	PUNCT
ejpam-3118	98	208	v1b1	v1b1	VERB
ejpam-3118	98	209	−	−	PROPN
ejpam-3118	98	210	v1	v1	NOUN
ejpam-3118	98	211	2	2	NUM
ejpam-3118	98	212	)	)	PUNCT
ejpam-3118	98	213	e	e	NOUN
ejpam-3118	98	214	,	,	PUNCT
ejpam-3118	98	215	e41	e41	NOUN
ejpam-3118	98	216	=	=	SYM
ejpam-3118	98	217	(	(	PUNCT
ejpam-3118	98	218	v	v	NOUN
ejpam-3118	98	219	+	+	NUM
ejpam-3118	98	220	vb	vb	NOUN
ejpam-3118	98	221	2	2	NUM
ejpam-3118	98	222	)	)	PUNCT
ejpam-3118	98	223	(	(	PUNCT
ejpam-3118	98	224	v1	v1	VERB
ejpam-3118	98	225	+	+	CCONJ
ejpam-3118	98	226	v1b1	v1b1	NUM
ejpam-3118	98	227	2	2	NUM
ejpam-3118	98	228	)	)	PUNCT
ejpam-3118	98	229	e	e	NOUN
ejpam-3118	98	230	,	,	PUNCT
ejpam-3118	98	231	e42	e42	NOUN
ejpam-3118	98	232	=	=	SYM
ejpam-3118	98	233	(	(	PUNCT
ejpam-3118	98	234	v	v	NOUN
ejpam-3118	98	235	+	+	NUM
ejpam-3118	98	236	vb	vb	NOUN
ejpam-3118	98	237	2	2	NUM
ejpam-3118	98	238	)	)	PUNCT
ejpam-3118	98	239	(	(	PUNCT
ejpam-3118	98	240	1−	1−	NUM
ejpam-3118	98	241	b1	b1	NOUN
ejpam-3118	98	242	2	2	NUM
ejpam-3118	98	243	)	)	PUNCT
ejpam-3118	98	244	e	e	NOUN
ejpam-3118	98	245	,	,	PUNCT
ejpam-3118	98	246	e43	e43	NOUN
ejpam-3118	98	247	=	=	SYM
ejpam-3118	98	248	(	(	PUNCT
ejpam-3118	98	249	1−	1−	NUM
ejpam-3118	98	250	b	b	SYM
ejpam-3118	98	251	2	2	NUM
ejpam-3118	98	252	)	)	PUNCT
ejpam-3118	98	253	(	(	PUNCT
ejpam-3118	98	254	v1	v1	VERB
ejpam-3118	98	255	+	+	CCONJ
ejpam-3118	98	256	v1b1	v1b1	NUM
ejpam-3118	98	257	2	2	NUM
ejpam-3118	98	258	)	)	PUNCT
ejpam-3118	98	259	e	e	NOUN
ejpam-3118	98	260	,	,	PUNCT
ejpam-3118	98	261	e44	e44	NOUN
ejpam-3118	98	262	=	=	SYM
ejpam-3118	98	263	(	(	PUNCT
ejpam-3118	98	264	1−	1−	NUM
ejpam-3118	98	265	b	b	SYM
ejpam-3118	98	266	2	2	NUM
ejpam-3118	98	267	)	)	PUNCT
ejpam-3118	98	268	(	(	PUNCT
ejpam-3118	98	269	1−	1−	NUM
ejpam-3118	98	270	b1	b1	NOUN
ejpam-3118	98	271	2	2	NUM
ejpam-3118	98	272	)	)	PUNCT
ejpam-3118	98	273	e.	e.	PROPN
ejpam-3118	98	274	c.	c.	PROPN
ejpam-3118	98	275	mello	mello	PROPN
ejpam-3118	98	276	/	/	SYM
ejpam-3118	98	277	eur	eur	PROPN
ejpam-3118	98	278	.	.	PUNCT
ejpam-3118	99	1	j.	j.	PROPN
ejpam-3118	99	2	pure	pure	PROPN
ejpam-3118	99	3	appl	appl	PROPN
ejpam-3118	99	4	.	.	PROPN
ejpam-3118	99	5	math	math	PROPN
ejpam-3118	99	6	,	,	PUNCT
ejpam-3118	99	7	10	10	NUM
ejpam-3118	99	8	(	(	PUNCT
ejpam-3118	99	9	5	5	NUM
ejpam-3118	99	10	)	)	PUNCT
ejpam-3118	99	11	(	(	PUNCT
ejpam-3118	99	12	2017	2017	NUM
ejpam-3118	99	13	)	)	PUNCT
ejpam-3118	100	1	,	,	PUNCT
ejpam-3118	100	2	955	955	NUM
ejpam-3118	100	3	-	-	SYM
ejpam-3118	100	4	966	966	NUM
ejpam-3118	100	5	960	960	NUM
ejpam-3118	100	6	for	for	ADP
ejpam-3118	100	7	the	the	DET
ejpam-3118	100	8	next	next	ADJ
ejpam-3118	100	9	result	result	NOUN
ejpam-3118	100	10	,	,	PUNCT
ejpam-3118	100	11	we	we	PRON
ejpam-3118	100	12	will	will	AUX
ejpam-3118	100	13	need	need	VERB
ejpam-3118	100	14	the	the	DET
ejpam-3118	100	15	following	following	NOUN
ejpam-3118	100	16	:	:	PUNCT
ejpam-3118	100	17	definition	definition	NOUN
ejpam-3118	100	18	2	2	NUM
ejpam-3118	100	19	.	.	PUNCT
ejpam-3118	100	20	let	let	VERB
ejpam-3118	100	21	a	a	DET
ejpam-3118	100	22	=	=	X
ejpam-3118	100	23	[	[	PUNCT
ejpam-3118	100	24	2[xij	2[xij	NUM
ejpam-3118	100	25	]	]	PUNCT
ejpam-3118	100	26	+	+	CCONJ
ejpam-3118	100	27	i4	i4	PROPN
ejpam-3118	100	28	]	]	PUNCT
ejpam-3118	100	29	be	be	AUX
ejpam-3118	100	30	a	a	DET
ejpam-3118	100	31	4	4	NUM
ejpam-3118	100	32	-	-	PUNCT
ejpam-3118	100	33	by-4	by-4	NOUN
ejpam-3118	100	34	matrix	matrix	NOUN
ejpam-3118	100	35	with	with	ADP
ejpam-3118	100	36	xij	xij	PROPN
ejpam-3118	100	37	∈	∈	PROPN
ejpam-3118	100	38	z	z	PROPN
ejpam-3118	100	39	,	,	PUNCT
ejpam-3118	100	40	for	for	ADP
ejpam-3118	100	41	all	all	DET
ejpam-3118	100	42	i	i	PROPN
ejpam-3118	100	43	,	,	PUNCT
ejpam-3118	100	44	j	j	PROPN
ejpam-3118	100	45	,	,	PUNCT
ejpam-3118	100	46	1	1	NUM
ejpam-3118	100	47	≤	≤	NUM
ejpam-3118	100	48	i	i	PRON
ejpam-3118	100	49	,	,	PUNCT
ejpam-3118	100	50	j	j	PROPN
ejpam-3118	100	51	≤	≤	ADV
ejpam-3118	100	52	4	4	NUM
ejpam-3118	100	53	.	.	PUNCT
ejpam-3118	101	1	we	we	PRON
ejpam-3118	101	2	define	define	VERB
ejpam-3118	101	3	4	4	NUM
ejpam-3118	101	4	distinct	distinct	ADJ
ejpam-3118	101	5	blocks	block	NOUN
ejpam-3118	101	6	of	of	ADP
ejpam-3118	101	7	a	a	DET
ejpam-3118	101	8	:	:	PUNCT
ejpam-3118	101	9	b1	b1	NOUN
ejpam-3118	101	10	=	=	SYM
ejpam-3118	101	11	{	{	PUNCT
ejpam-3118	101	12	x11	x11	PROPN
ejpam-3118	101	13	,	,	PUNCT
ejpam-3118	101	14	x22	x22	NUM
ejpam-3118	101	15	,	,	PUNCT
ejpam-3118	101	16	x33	x33	PROPN
ejpam-3118	101	17	,	,	PUNCT
ejpam-3118	101	18	x44	x44	NOUN
ejpam-3118	101	19	}	}	PUNCT
ejpam-3118	101	20	,	,	PUNCT
ejpam-3118	101	21	b2	b2	NOUN
ejpam-3118	101	22	=	=	SYM
ejpam-3118	101	23	{	{	PUNCT
ejpam-3118	101	24	x12	x12	PROPN
ejpam-3118	101	25	,	,	PUNCT
ejpam-3118	101	26	x21	x21	PROPN
ejpam-3118	101	27	,	,	PUNCT
ejpam-3118	101	28	x34	x34	NUM
ejpam-3118	101	29	,	,	PUNCT
ejpam-3118	101	30	x43	x43	NUM
ejpam-3118	101	31	}	}	PUNCT
ejpam-3118	101	32	,	,	PUNCT
ejpam-3118	101	33	b3	b3	PROPN
ejpam-3118	101	34	=	=	SYM
ejpam-3118	101	35	{	{	PUNCT
ejpam-3118	101	36	x13	x13	PROPN
ejpam-3118	101	37	,	,	PUNCT
ejpam-3118	101	38	x24	x24	PROPN
ejpam-3118	101	39	,	,	PUNCT
ejpam-3118	101	40	x31	x31	NUM
ejpam-3118	101	41	,	,	PUNCT
ejpam-3118	101	42	x42	x42	NOUN
ejpam-3118	101	43	}	}	PUNCT
ejpam-3118	101	44	,	,	PUNCT
ejpam-3118	101	45	b4	b4	NOUN
ejpam-3118	101	46	=	=	SYM
ejpam-3118	101	47	{	{	PUNCT
ejpam-3118	101	48	x14	x14	PROPN
ejpam-3118	101	49	,	,	PUNCT
ejpam-3118	101	50	x23	x23	NUM
ejpam-3118	101	51	,	,	PUNCT
ejpam-3118	101	52	x32	x32	PROPN
ejpam-3118	101	53	,	,	PUNCT
ejpam-3118	101	54	x41	x41	PROPN
ejpam-3118	101	55	}	}	PUNCT
ejpam-3118	101	56	.	.	PUNCT
ejpam-3118	102	1	in	in	ADP
ejpam-3118	102	2	particular	particular	ADJ
ejpam-3118	102	3	,	,	PUNCT
ejpam-3118	102	4	bk	bk	PROPN
ejpam-3118	102	5	=	=	PUNCT
ejpam-3118	102	6	{	{	PUNCT
ejpam-3118	102	7	xiji	xiji	NOUN
ejpam-3118	102	8	|	|	ADV
ejpam-3118	102	9	1	1	NUM
ejpam-3118	102	10	≤	≤	NUM
ejpam-3118	102	11	i	i	PRON
ejpam-3118	102	12	≤	≤	NOUN
ejpam-3118	102	13	4	4	NUM
ejpam-3118	102	14	and	and	CCONJ
ejpam-3118	102	15	ji	ji	PROPN
ejpam-3118	103	1	6=	6=	PROPN
ejpam-3118	103	2	ji′	ji′	ADV
ejpam-3118	103	3	,	,	PUNCT
ejpam-3118	103	4	if	if	SCONJ
ejpam-3118	103	5	i	i	PRON
ejpam-3118	103	6	6=	6=	ADP
ejpam-3118	103	7	i′	i′	NOUN
ejpam-3118	103	8	}	}	PUNCT
ejpam-3118	103	9	,	,	PUNCT
ejpam-3118	103	10	1	1	NUM
ejpam-3118	103	11	≤	≤	NUM
ejpam-3118	103	12	k	k	X
ejpam-3118	103	13	≤	≤	NUM
ejpam-3118	103	14	4	4	NUM
ejpam-3118	103	15	.	.	PUNCT
ejpam-3118	104	1	finally	finally	ADV
ejpam-3118	104	2	we	we	PRON
ejpam-3118	104	3	are	be	AUX
ejpam-3118	104	4	in	in	ADP
ejpam-3118	104	5	a	a	DET
ejpam-3118	104	6	position	position	NOUN
ejpam-3118	104	7	to	to	PART
ejpam-3118	104	8	give	give	VERB
ejpam-3118	104	9	a	a	DET
ejpam-3118	104	10	description	description	NOUN
ejpam-3118	104	11	of	of	ADP
ejpam-3118	104	12	u(zg1	u(zg1	NOUN
ejpam-3118	104	13	)	)	PUNCT
ejpam-3118	104	14	in	in	ADP
ejpam-3118	104	15	a	a	DET
ejpam-3118	104	16	similar	similar	ADJ
ejpam-3118	104	17	vein	vein	NOUN
ejpam-3118	104	18	as	as	ADP
ejpam-3118	104	19	the	the	DET
ejpam-3118	104	20	description	description	NOUN
ejpam-3118	104	21	given	give	VERB
ejpam-3118	104	22	for	for	ADP
ejpam-3118	104	23	u(zd4	u(zd4	NOUN
ejpam-3118	104	24	)	)	PUNCT
ejpam-3118	104	25	in	in	ADP
ejpam-3118	104	26	theorem	theorem	NOUN
ejpam-3118	104	27	1	1	NUM
ejpam-3118	104	28	:	:	PUNCT
ejpam-3118	104	29	theorem	theorem	NOUN
ejpam-3118	104	30	2	2	NUM
ejpam-3118	104	31	.	.	PUNCT
ejpam-3118	105	1	let	let	VERB
ejpam-3118	105	2	g1	g1	PROPN
ejpam-3118	105	3	=	=	PUNCT
ejpam-3118	105	4	d×d1	d×d1	PROPN
ejpam-3118	105	5	/	/	SYM
ejpam-3118	105	6	{	{	PUNCT
ejpam-3118	105	7	1	1	PROPN
ejpam-3118	105	8	,	,	PUNCT
ejpam-3118	105	9	ss1	ss1	PROPN
ejpam-3118	105	10	}	}	PUNCT
ejpam-3118	105	11	be	be	VERB
ejpam-3118	105	12	the	the	DET
ejpam-3118	105	13	extra	extra	ADJ
ejpam-3118	105	14	-	-	ADJ
ejpam-3118	105	15	special	special	ADJ
ejpam-3118	105	16	2	2	NUM
ejpam-3118	105	17	-	-	PUNCT
ejpam-3118	105	18	group	group	NOUN
ejpam-3118	105	19	of	of	ADP
ejpam-3118	105	20	order	order	NOUN
ejpam-3118	105	21	32	32	NUM
ejpam-3118	105	22	,	,	PUNCT
ejpam-3118	105	23	the	the	DET
ejpam-3118	105	24	central	central	ADJ
ejpam-3118	105	25	product	product	NOUN
ejpam-3118	105	26	of	of	ADP
ejpam-3118	105	27	two	two	NUM
ejpam-3118	105	28	copies	copy	NOUN
ejpam-3118	105	29	of	of	ADP
ejpam-3118	105	30	d4	d4	PROPN
ejpam-3118	105	31	=	=	SYM
ejpam-3118	105	32	〈	〈	PROPN
ejpam-3118	105	33	b	b	PROPN
ejpam-3118	105	34	,	,	PUNCT
ejpam-3118	105	35	v|	v|	NOUN
ejpam-3118	105	36	b2	b2	NOUN
ejpam-3118	105	37	=	=	SYM
ejpam-3118	105	38	v4	v4	NOUN
ejpam-3118	105	39	=	=	SYM
ejpam-3118	105	40	1	1	NUM
ejpam-3118	105	41	and	and	CCONJ
ejpam-3118	105	42	bvbv	bvbv	NOUN
ejpam-3118	105	43	=	=	SYM
ejpam-3118	105	44	1	1	NUM
ejpam-3118	105	45	〉	〉	NOUN
ejpam-3118	105	46	.	.	PUNCT
ejpam-3118	106	1	then	then	ADV
ejpam-3118	106	2	u(zg1	u(zg1	X
ejpam-3118	106	3	)	)	PUNCT
ejpam-3118	106	4	=	=	PUNCT
ejpam-3118	106	5	±g1v1	±g1v1	NOUN
ejpam-3118	106	6	and	and	CCONJ
ejpam-3118	106	7	v1	v1	NOUN
ejpam-3118	106	8	is	be	AUX
ejpam-3118	106	9	isomorphic	isomorphic	ADJ
ejpam-3118	106	10	to	to	ADP
ejpam-3118	106	11	the	the	DET
ejpam-3118	106	12	group	group	NOUN
ejpam-3118	106	13	[	[	PUNCT
ejpam-3118	106	14	2	2	NUM
ejpam-3118	107	1	[	[	X
ejpam-3118	107	2	xij	xij	X
ejpam-3118	107	3	]	]	PUNCT
ejpam-3118	107	4	+	+	CCONJ
ejpam-3118	107	5	i4	i4	PROPN
ejpam-3118	107	6	]	]	PUNCT
ejpam-3118	107	7	det=1	det=1	NOUN
ejpam-3118	107	8	of	of	ADP
ejpam-3118	107	9	4	4	NUM
ejpam-3118	107	10	-	-	PUNCT
ejpam-3118	107	11	by-4	by-4	NOUN
ejpam-3118	107	12	matrices	matrix	NOUN
ejpam-3118	107	13	,	,	PUNCT
ejpam-3118	107	14	where	where	SCONJ
ejpam-3118	107	15	,	,	PUNCT
ejpam-3118	107	16	for	for	ADP
ejpam-3118	107	17	each	each	DET
ejpam-3118	107	18	k	k	NOUN
ejpam-3118	107	19	,	,	PUNCT
ejpam-3118	107	20	1	1	NUM
ejpam-3118	107	21	≤	≤	NUM
ejpam-3118	107	22	k	k	X
ejpam-3118	107	23	≤	≤	NUM
ejpam-3118	107	24	4	4	NUM
ejpam-3118	107	25	,	,	PUNCT
ejpam-3118	107	26	the	the	DET
ejpam-3118	107	27	integers	integer	NOUN
ejpam-3118	107	28	xiji	xiji	VERB
ejpam-3118	107	29	∈	∈	PROPN
ejpam-3118	107	30	bk	bk	NOUN
ejpam-3118	107	31	have	have	VERB
ejpam-3118	107	32	the	the	DET
ejpam-3118	107	33	same	same	ADJ
ejpam-3118	107	34	parity	parity	NOUN
ejpam-3118	107	35	and	and	CCONJ
ejpam-3118	107	36	4	4	NUM
ejpam-3118	107	37	divides	divide	VERB
ejpam-3118	107	38	the	the	DET
ejpam-3118	107	39	sum	sum	NOUN
ejpam-3118	107	40	x1j1	x1j1	PUNCT
ejpam-3118	108	1	+	+	ADJ
ejpam-3118	108	2	x2j2	x2j2	PROPN
ejpam-3118	108	3	+	+	ADJ
ejpam-3118	108	4	x3j3	x3j3	PROPN
ejpam-3118	108	5	+	+	ADJ
ejpam-3118	108	6	x4j4	x4j4	NOUN
ejpam-3118	108	7	.	.	PUNCT
ejpam-3118	108	8	proof	proof	NOUN
ejpam-3118	108	9	.	.	PUNCT
ejpam-3118	109	1	by	by	ADP
ejpam-3118	109	2	proposition	proposition	NOUN
ejpam-3118	109	3	3	3	NUM
ejpam-3118	109	4	,	,	PUNCT
ejpam-3118	109	5	u(zg1	u(zg1	NOUN
ejpam-3118	109	6	)	)	PUNCT
ejpam-3118	109	7	=	=	PUNCT
ejpam-3118	109	8	±g1v1	±g1v1	PROPN
ejpam-3118	109	9	,	,	PUNCT
ejpam-3118	109	10	where	where	SCONJ
ejpam-3118	109	11	v1	v1	VERB
ejpam-3118	109	12	∼=	∼=	NOUN
ejpam-3118	109	13	u2	u2	NOUN
ejpam-3118	109	14	/	/	SYM
ejpam-3118	109	15	g	g	NOUN
ejpam-3118	109	16	′	′	NUM
ejpam-3118	109	17	1	1	NUM
ejpam-3118	109	18	and	and	CCONJ
ejpam-3118	109	19	u2	u2	PROPN
ejpam-3118	109	20	=	=	SYM
ejpam-3118	109	21	u(zg1	u(zg1	ADJ
ejpam-3118	109	22	)	)	PUNCT
ejpam-3118	109	23	∩	∩	NOUN
ejpam-3118	109	24	(	(	PUNCT
ejpam-3118	109	25	qg1	qg1	ADV
ejpam-3118	109	26	(	(	PUNCT
ejpam-3118	109	27	1−	1−	NUM
ejpam-3118	109	28	s	s	NOUN
ejpam-3118	109	29	2	2	NUM
ejpam-3118	109	30	)	)	PUNCT
ejpam-3118	109	31	+	+	CCONJ
ejpam-3118	109	32	(	(	PUNCT
ejpam-3118	109	33	1	1	NUM
ejpam-3118	109	34	+	+	SYM
ejpam-3118	109	35	s	s	NOUN
ejpam-3118	109	36	2	2	NUM
ejpam-3118	109	37	)	)	PUNCT
ejpam-3118	109	38	)	)	PUNCT
ejpam-3118	110	1	=	=	PUNCT
ejpam-3118	110	2	=	=	PRON
ejpam-3118	110	3	{	{	PUNCT
ejpam-3118	110	4	u	u	NOUN
ejpam-3118	110	5	=	=	NOUN
ejpam-3118	110	6	1	1	NUM
ejpam-3118	110	7	+	+	NUM
ejpam-3118	110	8	α(1−	α(1−	PROPN
ejpam-3118	110	9	s)|u	s)|u	PROPN
ejpam-3118	110	10	∈	∈	PROPN
ejpam-3118	110	11	u(zg1	u(zg1	PROPN
ejpam-3118	110	12	)	)	PUNCT
ejpam-3118	110	13	,	,	PUNCT
ejpam-3118	110	14	α	α	PROPN
ejpam-3118	110	15	∈	∈	PROPN
ejpam-3118	110	16	zg1	zg1	NOUN
ejpam-3118	110	17	}	}	PUNCT
ejpam-3118	110	18	.	.	PUNCT
ejpam-3118	111	1	thus	thus	ADV
ejpam-3118	111	2	,	,	PUNCT
ejpam-3118	111	3	to	to	PART
ejpam-3118	111	4	describe	describe	VERB
ejpam-3118	111	5	u(zg1	u(zg1	NOUN
ejpam-3118	111	6	)	)	PUNCT
ejpam-3118	111	7	we	we	PRON
ejpam-3118	111	8	need	need	VERB
ejpam-3118	111	9	a	a	DET
ejpam-3118	111	10	complete	complete	ADJ
ejpam-3118	111	11	description	description	NOUN
ejpam-3118	111	12	of	of	ADP
ejpam-3118	111	13	v1	v1	NOUN
ejpam-3118	111	14	∼=	∼=	PART
ejpam-3118	111	15	u2	u2	NOUN
ejpam-3118	111	16	/	/	SYM
ejpam-3118	111	17	g	g	NOUN
ejpam-3118	111	18	′	′	NUM
ejpam-3118	111	19	1	1	NUM
ejpam-3118	111	20	of	of	ADP
ejpam-3118	111	21	the	the	DET
ejpam-3118	111	22	u2	u2	NOUN
ejpam-3118	111	23	,	,	PUNCT
ejpam-3118	111	24	that	that	ADV
ejpam-3118	111	25	is	is	ADV
ejpam-3118	111	26	,	,	PUNCT
ejpam-3118	111	27	we	we	PRON
ejpam-3118	111	28	need	need	VERB
ejpam-3118	111	29	to	to	PART
ejpam-3118	111	30	describe	describe	VERB
ejpam-3118	111	31	completly	completly	ADV
ejpam-3118	111	32	the	the	DET
ejpam-3118	111	33	subgroup	subgroup	NOUN
ejpam-3118	111	34	u2	u2	NOUN
ejpam-3118	111	35	of	of	ADP
ejpam-3118	111	36	the	the	DET
ejpam-3118	111	37	u(zg1	u(zg1	NOUN
ejpam-3118	111	38	)	)	PUNCT
ejpam-3118	111	39	.	.	PUNCT
ejpam-3118	112	1	let	let	VERB
ejpam-3118	112	2	u	u	PRON
ejpam-3118	112	3	∈	∈	PROPN
ejpam-3118	112	4	u2	u2	PROPN
ejpam-3118	112	5	.	.	PUNCT
ejpam-3118	113	1	then	then	ADV
ejpam-3118	113	2	,	,	PUNCT
ejpam-3118	113	3	by	by	ADP
ejpam-3118	113	4	proposition	proposition	NOUN
ejpam-3118	113	5	3	3	NUM
ejpam-3118	113	6	and	and	CCONJ
ejpam-3118	113	7	writing	write	VERB
ejpam-3118	113	8	e	e	NOUN
ejpam-3118	113	9	=	=	SYM
ejpam-3118	113	10	1−	1−	NUM
ejpam-3118	113	11	s	s	NOUN
ejpam-3118	113	12	2	2	NUM
ejpam-3118	113	13	,	,	PUNCT
ejpam-3118	113	14	u	u	NOUN
ejpam-3118	113	15	=	=	NOUN
ejpam-3118	113	16	1	1	NUM
ejpam-3118	113	17	+	+	CCONJ
ejpam-3118	113	18	α(1	α(1	PROPN
ejpam-3118	113	19	−	−	PROPN
ejpam-3118	113	20	s	s	PART
ejpam-3118	113	21	)	)	PUNCT
ejpam-3118	113	22	=	=	SYM
ejpam-3118	114	1	1	1	NUM
ejpam-3118	114	2	+	+	NUM
ejpam-3118	114	3	2(α1	2(α1	NUM
ejpam-3118	114	4	+	+	CCONJ
ejpam-3118	114	5	α2	α2	PROPN
ejpam-3118	114	6	b	b	PROPN
ejpam-3118	115	1	+	+	NUM
ejpam-3118	115	2	α3	α3	NOUN
ejpam-3118	115	3	v	v	NOUN
ejpam-3118	115	4	+	+	NUM
ejpam-3118	115	5	α4	α4	NOUN
ejpam-3118	115	6	b1	b1	NOUN
ejpam-3118	115	7	+	+	CCONJ
ejpam-3118	115	8	α5	α5	PROPN
ejpam-3118	115	9	v1	v1	NOUN
ejpam-3118	115	10	+	+	CCONJ
ejpam-3118	115	11	α6	α6	NOUN
ejpam-3118	115	12	u	u	NOUN
ejpam-3118	115	13	+	+	CCONJ
ejpam-3118	115	14	α7	α7	NOUN
ejpam-3118	115	15	u1	u1	NOUN
ejpam-3118	115	16	+	+	SYM
ejpam-3118	115	17	α8	α8	PROPN
ejpam-3118	115	18	bb1	bb1	PROPN
ejpam-3118	115	19	+	+	ADP
ejpam-3118	115	20	α9	α9	PROPN
ejpam-3118	115	21	bu1	bu1	NOUN
ejpam-3118	115	22	+	+	CCONJ
ejpam-3118	115	23	α10	α10	ADJ
ejpam-3118	115	24	bv1	bv1	NOUN
ejpam-3118	116	1	+	+	CCONJ
ejpam-3118	117	1	+	+	X
ejpam-3118	117	2	α11	α11	ADJ
ejpam-3118	117	3	ub1	ub1	PROPN
ejpam-3118	117	4	+	+	CCONJ
ejpam-3118	117	5	α12	α12	PROPN
ejpam-3118	117	6	uu1	uu1	NOUN
ejpam-3118	117	7	+	+	CCONJ
ejpam-3118	117	8	α13	α13	VERB
ejpam-3118	117	9	uv1	uv1	NOUN
ejpam-3118	117	10	+	+	CCONJ
ejpam-3118	117	11	α14	α14	NUM
ejpam-3118	117	12	vb1	vb1	NOUN
ejpam-3118	117	13	+	+	X
ejpam-3118	117	14	α15	α15	NOUN
ejpam-3118	117	15	vu1	vu1	X
ejpam-3118	117	16	+	+	CCONJ
ejpam-3118	117	17	α16	α16	PROPN
ejpam-3118	117	18	vv1)e	vv1)e	PROPN
ejpam-3118	117	19	.	.	PUNCT
ejpam-3118	118	1	the	the	DET
ejpam-3118	118	2	proposition	proposition	NOUN
ejpam-3118	118	3	5	5	NUM
ejpam-3118	118	4	gives	give	VERB
ejpam-3118	118	5	qg1(e	qg1(e	PRON
ejpam-3118	118	6	)	)	PUNCT
ejpam-3118	118	7	∼=	∼=	PROPN
ejpam-3118	118	8	m4(q	m4(q	NUM
ejpam-3118	118	9	)	)	PUNCT
ejpam-3118	118	10	and	and	CCONJ
ejpam-3118	118	11	using	use	VERB
ejpam-3118	118	12	the	the	DET
ejpam-3118	118	13	elementary	elementary	ADJ
ejpam-3118	118	14	basis	basis	NOUN
ejpam-3118	118	15	matrix	matrix	NOUN
ejpam-3118	118	16	of	of	ADP
ejpam-3118	118	17	qg1(e	qg1(e	NOUN
ejpam-3118	118	18	)	)	PUNCT
ejpam-3118	118	19	∼=	∼=	PROPN
ejpam-3118	118	20	m4(q	m4(q	NUM
ejpam-3118	118	21	)	)	PUNCT
ejpam-3118	118	22	and	and	CCONJ
ejpam-3118	118	23	the	the	DET
ejpam-3118	118	24	given	give	VERB
ejpam-3118	118	25	representation	representation	NOUN
ejpam-3118	118	26	of	of	ADP
ejpam-3118	118	27	g1	g1	PROPN
ejpam-3118	118	28	in	in	ADP
ejpam-3118	118	29	m4(q	m4(q	NOUN
ejpam-3118	118	30	)	)	PUNCT
ejpam-3118	118	31	,	,	PUNCT
ejpam-3118	118	32	we	we	PRON
ejpam-3118	118	33	obtain	obtain	VERB
ejpam-3118	118	34	u	u	NOUN
ejpam-3118	118	35	=	=	PUNCT
ejpam-3118	118	36	(	(	PUNCT
ejpam-3118	118	37	1	1	NUM
ejpam-3118	118	38	+	+	SYM
ejpam-3118	118	39	s	s	X
ejpam-3118	118	40	2	2	NUM
ejpam-3118	118	41	)	)	PUNCT
ejpam-3118	118	42	+	+	CCONJ
ejpam-3118	118	43	(	(	PUNCT
ejpam-3118	118	44	e11	e11	X
ejpam-3118	118	45	+	+	NUM
ejpam-3118	118	46	e22	e22	NOUN
ejpam-3118	118	47	+	+	CCONJ
ejpam-3118	118	48	e33	e33	PROPN
ejpam-3118	118	49	+	+	CCONJ
ejpam-3118	118	50	e44	e44	PROPN
ejpam-3118	118	51	)	)	PUNCT
ejpam-3118	119	1	+	+	CCONJ
ejpam-3118	119	2	2[α1(e11	2[α1(e11	NUM
ejpam-3118	120	1	+	+	NUM
ejpam-3118	120	2	e22	e22	NOUN
ejpam-3118	120	3	+	+	CCONJ
ejpam-3118	120	4	e33	e33	PROPN
ejpam-3118	120	5	+	+	CCONJ
ejpam-3118	120	6	e44	e44	PROPN
ejpam-3118	120	7	)	)	PUNCT
ejpam-3118	121	1	+	+	VERB
ejpam-3118	121	2	α2(e11	α2(e11	X
ejpam-3118	121	3	+	+	CCONJ
ejpam-3118	121	4	e22−	e22−	PROPN
ejpam-3118	121	5	e33−	e33−	PROPN
ejpam-3118	121	6	e44	e44	NOUN
ejpam-3118	121	7	)	)	PUNCT
ejpam-3118	122	1	+	+	NOUN
ejpam-3118	122	2	α3(−e13−	α3(−e13−	NUM
ejpam-3118	122	3	e24	e24	NOUN
ejpam-3118	122	4	+	+	CCONJ
ejpam-3118	122	5	e31	e31	PROPN
ejpam-3118	122	6	+	+	CCONJ
ejpam-3118	122	7	e42	e42	NUM
ejpam-3118	122	8	)	)	PUNCT
ejpam-3118	123	1	+	+	ADJ
ejpam-3118	123	2	α4(e11−	α4(e11−	PROPN
ejpam-3118	123	3	e22	e22	NOUN
ejpam-3118	123	4	+	+	CCONJ
ejpam-3118	123	5	e33−	e33−	PROPN
ejpam-3118	123	6	e44	e44	NOUN
ejpam-3118	123	7	)	)	PUNCT
ejpam-3118	124	1	+	+	NOUN
ejpam-3118	124	2	α5(−e12	α5(−e12	PROPN
ejpam-3118	124	3	+	+	CCONJ
ejpam-3118	124	4	e21−	e21−	PROPN
ejpam-3118	124	5	e34	e34	NOUN
ejpam-3118	124	6	+	+	CCONJ
ejpam-3118	124	7	e43	e43	NOUN
ejpam-3118	124	8	)	)	PUNCT
ejpam-3118	124	9	+	+	CCONJ
ejpam-3118	124	10	α6(e13	α6(e13	NOUN
ejpam-3118	124	11	+	+	CCONJ
ejpam-3118	124	12	e24	e24	NOUN
ejpam-3118	124	13	+	+	CCONJ
ejpam-3118	124	14	e31	e31	PROPN
ejpam-3118	124	15	+	+	CCONJ
ejpam-3118	124	16	e42	e42	NUM
ejpam-3118	124	17	)	)	PUNCT
ejpam-3118	125	1	+	+	CCONJ
ejpam-3118	125	2	α7(e12	α7(e12	ADJ
ejpam-3118	125	3	+	+	CCONJ
ejpam-3118	125	4	e21	e21	NUM
ejpam-3118	125	5	+	+	CCONJ
ejpam-3118	125	6	e34	e34	NOUN
ejpam-3118	125	7	+	+	CCONJ
ejpam-3118	125	8	e43	e43	NOUN
ejpam-3118	125	9	)	)	PUNCT
ejpam-3118	126	1	+	+	CCONJ
ejpam-3118	126	2	α8(e11	α8(e11	PRON
ejpam-3118	126	3	−	−	PROPN
ejpam-3118	126	4	e22	e22	PROPN
ejpam-3118	126	5	−	−	PROPN
ejpam-3118	126	6	e33	e33	PROPN
ejpam-3118	126	7	+	+	CCONJ
ejpam-3118	126	8	e44	e44	PROPN
ejpam-3118	126	9	)	)	PUNCT
ejpam-3118	127	1	+	+	CCONJ
ejpam-3118	127	2	α9(e12	α9(e12	NOUN
ejpam-3118	127	3	+	+	CCONJ
ejpam-3118	127	4	e21−	e21−	PROPN
ejpam-3118	127	5	e34−	e34−	PROPN
ejpam-3118	127	6	e43	e43	NOUN
ejpam-3118	127	7	)	)	PUNCT
ejpam-3118	128	1	+	+	NOUN
ejpam-3118	128	2	α10(−e12	α10(−e12	NOUN
ejpam-3118	128	3	+	+	CCONJ
ejpam-3118	128	4	e21	e21	PROPN
ejpam-3118	128	5	+	+	NUM
ejpam-3118	128	6	e34−	e34−	PROPN
ejpam-3118	128	7	e43	e43	NOUN
ejpam-3118	128	8	)	)	PUNCT
ejpam-3118	129	1	+	+	NOUN
ejpam-3118	129	2	α11(e13−	α11(e13−	NOUN
ejpam-3118	129	3	e24	e24	NOUN
ejpam-3118	129	4	+	+	CCONJ
ejpam-3118	129	5	e31−	e31−	NOUN
ejpam-3118	129	6	e42	e42	NUM
ejpam-3118	129	7	)	)	PUNCT
ejpam-3118	130	1	+	+	ADJ
ejpam-3118	130	2	α12(e14	α12(e14	ADJ
ejpam-3118	130	3	+	+	CCONJ
ejpam-3118	130	4	e23	e23	ADJ
ejpam-3118	130	5	+	+	CCONJ
ejpam-3118	130	6	e32	e32	NOUN
ejpam-3118	130	7	+	+	CCONJ
ejpam-3118	130	8	e41	e41	NOUN
ejpam-3118	130	9	)	)	PUNCT
ejpam-3118	130	10	+	+	CCONJ
ejpam-3118	130	11	α13(−e14	α13(−e14	ADJ
ejpam-3118	130	12	+	+	CCONJ
ejpam-3118	130	13	e23	e23	ADJ
ejpam-3118	130	14	−	−	PROPN
ejpam-3118	130	15	e32	e32	NOUN
ejpam-3118	130	16	+	+	CCONJ
ejpam-3118	130	17	e41	e41	NOUN
ejpam-3118	130	18	)	)	PUNCT
ejpam-3118	130	19	+	+	NUM
ejpam-3118	130	20	α14(−e13	α14(−e13	NOUN
ejpam-3118	130	21	+	+	CCONJ
ejpam-3118	130	22	e24	e24	PROPN
ejpam-3118	130	23	+	+	CCONJ
ejpam-3118	130	24	e31	e31	PROPN
ejpam-3118	130	25	−	−	PROPN
ejpam-3118	130	26	e42	e42	NOUN
ejpam-3118	130	27	)	)	PUNCT
ejpam-3118	130	28	+	+	CCONJ
ejpam-3118	130	29	α15(−e14	α15(−e14	NUM
ejpam-3118	130	30	−	−	NOUN
ejpam-3118	130	31	e23	e23	NOUN
ejpam-3118	130	32	+	+	CCONJ
ejpam-3118	130	33	e32	e32	NOUN
ejpam-3118	130	34	+	+	CCONJ
ejpam-3118	130	35	e41	e41	NOUN
ejpam-3118	130	36	)	)	PUNCT
ejpam-3118	130	37	+	+	CCONJ
ejpam-3118	130	38	α16(e14	α16(e14	ADJ
ejpam-3118	130	39	−	−	PROPN
ejpam-3118	130	40	e23	e23	PROPN
ejpam-3118	130	41	−	−	PROPN
ejpam-3118	130	42	e32	e32	NOUN
ejpam-3118	130	43	+	+	CCONJ
ejpam-3118	130	44	e41	e41	NOUN
ejpam-3118	130	45	)	)	PUNCT
ejpam-3118	130	46	]	]	PUNCT
ejpam-3118	130	47	.	.	PUNCT
ejpam-3118	131	1	hence	hence	ADV
ejpam-3118	131	2	c.	c.	PROPN
ejpam-3118	131	3	mello	mello	PROPN
ejpam-3118	131	4	/	/	SYM
ejpam-3118	131	5	eur	eur	PROPN
ejpam-3118	131	6	.	.	PUNCT
ejpam-3118	132	1	j.	j.	PROPN
ejpam-3118	132	2	pure	pure	PROPN
ejpam-3118	132	3	appl	appl	PROPN
ejpam-3118	132	4	.	.	PROPN
ejpam-3118	132	5	math	math	PROPN
ejpam-3118	132	6	,	,	PUNCT
ejpam-3118	132	7	10	10	NUM
ejpam-3118	132	8	(	(	PUNCT
ejpam-3118	132	9	5	5	NUM
ejpam-3118	132	10	)	)	PUNCT
ejpam-3118	132	11	(	(	PUNCT
ejpam-3118	132	12	2017	2017	NUM
ejpam-3118	132	13	)	)	PUNCT
ejpam-3118	132	14	,	,	PUNCT
ejpam-3118	132	15	955	955	NUM
ejpam-3118	132	16	-	-	SYM
ejpam-3118	132	17	966	966	NUM
ejpam-3118	132	18	961	961	NUM
ejpam-3118	132	19	u	u	NOUN
ejpam-3118	132	20	=	=	PUNCT
ejpam-3118	132	21	(	(	PUNCT
ejpam-3118	132	22	1	1	NUM
ejpam-3118	132	23	+	+	SYM
ejpam-3118	132	24	s	s	X
ejpam-3118	132	25	2	2	NUM
ejpam-3118	132	26	)	)	PUNCT
ejpam-3118	133	1	+	+	PROPN
ejpam-3118	133	2	[	[	X
ejpam-3118	133	3	2(α1+α2+α4+α8)+1]e11	2(α1+α2+α4+α8)+1]e11	ADJ
ejpam-3118	133	4	+	+	NOUN
ejpam-3118	133	5	2(−α5+α7+α9−α10)e12	2(−α5+α7+α9−α10)e12	NOUN
ejpam-3118	133	6	+	+	NOUN
ejpam-3118	133	7	2(−α3+α6+α11−	2(−α3+α6+α11−	NUM
ejpam-3118	133	8	α14)e13	α14)e13	NUM
ejpam-3118	133	9	+	+	NOUN
ejpam-3118	133	10	2(α12−α13−α15+α16)e14	2(α12−α13−α15+α16)e14	ADJ
ejpam-3118	133	11	+	+	SYM
ejpam-3118	133	12	2(α5+α7+α9+α10)e21+[2(α1+α2−α4−α8)+1]e22	2(α5+α7+α9+α10)e21+[2(α1+α2−α4−α8)+1]e22	NUM
ejpam-3118	133	13	+	+	NOUN
ejpam-3118	133	14	2(α12+α13−α15−α16)e23	2(α12+α13−α15−α16)e23	NUM
ejpam-3118	133	15	+	+	NOUN
ejpam-3118	133	16	2(−α3+α6−α11+α14)e24	2(−α3+α6−α11+α14)e24	NUM
ejpam-3118	133	17	+	+	NOUN
ejpam-3118	133	18	2(α3+α6+α11+α14)e31	2(α3+α6+α11+α14)e31	NUM
ejpam-3118	133	19	+	+	NOUN
ejpam-3118	133	20	2(α12−	2(α12−	PROPN
ejpam-3118	133	21	α13+α15−α16)e32+[2(α1−α2+α4−α8)+1]e33	α13+α15−α16)e32+[2(α1−α2+α4−α8)+1]e33	ADV
ejpam-3118	133	22	+	+	NOUN
ejpam-3118	133	23	2(−α5+α7−α9+α10)e34	2(−α5+α7−α9+α10)e34	NOUN
ejpam-3118	133	24	+	+	ADJ
ejpam-3118	133	25	2(α12+α13	2(α12+α13	PROPN
ejpam-3118	133	26	+	+	SYM
ejpam-3118	133	27	α15+α16)e41	α15+α16)e41	NOUN
ejpam-3118	133	28	+	+	NOUN
ejpam-3118	133	29	2(α3+α6−α11−α14)e42	2(α3+α6−α11−α14)e42	NUM
ejpam-3118	133	30	+	+	NOUN
ejpam-3118	133	31	2(α5+α7−α9−α10)e43+[2(α1−α2−α4+α8)+1]e44	2(α5+α7−α9−α10)e43+[2(α1−α2−α4+α8)+1]e44	NUM
ejpam-3118	133	32	.	.	PUNCT
ejpam-3118	134	1	therefore	therefore	ADV
ejpam-3118	134	2	u	u	PRON
ejpam-3118	134	3	can	can	AUX
ejpam-3118	134	4	be	be	AUX
ejpam-3118	134	5	written	write	VERB
ejpam-3118	134	6	as	as	ADP
ejpam-3118	134	7	an	an	DET
ejpam-3118	134	8	integral	integral	ADJ
ejpam-3118	134	9	invertible	invertible	ADJ
ejpam-3118	134	10	matrix	matrix	NOUN
ejpam-3118	134	11	u	u	NOUN
ejpam-3118	134	12	=	=	PUNCT
ejpam-3118	135	1	[	[	X
ejpam-3118	135	2	uij	uij	X
ejpam-3118	135	3	]	]	PUNCT
ejpam-3118	135	4	,	,	PUNCT
ejpam-3118	135	5	1	1	NUM
ejpam-3118	135	6	≤	≤	X
ejpam-3118	135	7	i	i	PRON
ejpam-3118	135	8	,	,	PUNCT
ejpam-3118	135	9	j	j	PROPN
ejpam-3118	135	10	≤	≤	PROPN
ejpam-3118	135	11	4	4	NUM
ejpam-3118	135	12	,	,	PUNCT
ejpam-3118	135	13	where	where	SCONJ
ejpam-3118	135	14	u11	u11	ADJ
ejpam-3118	135	15	=	=	SYM
ejpam-3118	135	16	2(α1	2(α1	PROPN
ejpam-3118	135	17	+	+	CCONJ
ejpam-3118	135	18	α2	α2	ADJ
ejpam-3118	135	19	+	+	CCONJ
ejpam-3118	135	20	α4	α4	NOUN
ejpam-3118	135	21	+	+	CCONJ
ejpam-3118	135	22	α8	α8	NOUN
ejpam-3118	135	23	)	)	PUNCT
ejpam-3118	135	24	+	+	CCONJ
ejpam-3118	135	25	1	1	NUM
ejpam-3118	135	26	,	,	PUNCT
ejpam-3118	135	27	u12	u12	PROPN
ejpam-3118	135	28	=	=	SYM
ejpam-3118	135	29	2(−α5	2(−α5	NUM
ejpam-3118	135	30	+	+	CCONJ
ejpam-3118	135	31	α7	α7	NOUN
ejpam-3118	135	32	+	+	CCONJ
ejpam-3118	135	33	α9	α9	PROPN
ejpam-3118	135	34	−	−	PROPN
ejpam-3118	135	35	α10	α10	NOUN
ejpam-3118	135	36	)	)	PUNCT
ejpam-3118	135	37	,	,	PUNCT
ejpam-3118	135	38	u13	u13	PROPN
ejpam-3118	135	39	=	=	SYM
ejpam-3118	135	40	2(−α3	2(−α3	NUM
ejpam-3118	135	41	+	+	NUM
ejpam-3118	135	42	α6	α6	NOUN
ejpam-3118	135	43	+	+	CCONJ
ejpam-3118	135	44	α11	α11	NOUN
ejpam-3118	135	45	−	−	PROPN
ejpam-3118	135	46	α14	α14	NOUN
ejpam-3118	135	47	)	)	PUNCT
ejpam-3118	135	48	,	,	PUNCT
ejpam-3118	135	49	u14	u14	NOUN
ejpam-3118	135	50	=	=	SYM
ejpam-3118	135	51	2(α12	2(α12	NUM
ejpam-3118	135	52	−	−	PROPN
ejpam-3118	135	53	α13	α13	PROPN
ejpam-3118	135	54	−	−	PROPN
ejpam-3118	135	55	α15	α15	NOUN
ejpam-3118	135	56	+	+	CCONJ
ejpam-3118	135	57	α16	α16	VERB
ejpam-3118	135	58	)	)	PUNCT
ejpam-3118	135	59	,	,	PUNCT
ejpam-3118	135	60	u21	u21	PROPN
ejpam-3118	135	61	=	=	SYM
ejpam-3118	135	62	2(α5	2(α5	NUM
ejpam-3118	135	63	+	+	NUM
ejpam-3118	135	64	α7	α7	NOUN
ejpam-3118	135	65	+	+	CCONJ
ejpam-3118	135	66	α9	α9	PROPN
ejpam-3118	135	67	+	+	CCONJ
ejpam-3118	135	68	α10	α10	NOUN
ejpam-3118	135	69	)	)	PUNCT
ejpam-3118	135	70	,	,	PUNCT
ejpam-3118	135	71	u22	u22	PROPN
ejpam-3118	135	72	=	=	SYM
ejpam-3118	135	73	2(α1	2(α1	PROPN
ejpam-3118	135	74	+	+	CCONJ
ejpam-3118	135	75	α2	α2	ADJ
ejpam-3118	135	76	−	−	NOUN
ejpam-3118	135	77	α4	α4	NOUN
ejpam-3118	135	78	−	−	PROPN
ejpam-3118	135	79	α8	α8	NOUN
ejpam-3118	135	80	)	)	PUNCT
ejpam-3118	135	81	+	+	CCONJ
ejpam-3118	135	82	1	1	NUM
ejpam-3118	135	83	,	,	PUNCT
ejpam-3118	135	84	u23	u23	NOUN
ejpam-3118	135	85	=	=	SYM
ejpam-3118	135	86	2(α12	2(α12	PROPN
ejpam-3118	135	87	+	+	NUM
ejpam-3118	135	88	α13	α13	PROPN
ejpam-3118	135	89	−	−	PROPN
ejpam-3118	135	90	α15	α15	NOUN
ejpam-3118	135	91	−	−	PROPN
ejpam-3118	135	92	α16	α16	PROPN
ejpam-3118	135	93	)	)	PUNCT
ejpam-3118	135	94	,	,	PUNCT
ejpam-3118	135	95	u24	u24	NOUN
ejpam-3118	135	96	=	=	SYM
ejpam-3118	135	97	2(−α3	2(−α3	NUM
ejpam-3118	135	98	+	+	NUM
ejpam-3118	135	99	α6	α6	NOUN
ejpam-3118	135	100	−	−	PROPN
ejpam-3118	135	101	α11	α11	NOUN
ejpam-3118	135	102	+	+	CCONJ
ejpam-3118	135	103	α14	α14	NUM
ejpam-3118	135	104	)	)	PUNCT
ejpam-3118	135	105	,	,	PUNCT
ejpam-3118	135	106	u31	u31	NOUN
ejpam-3118	135	107	=	=	SYM
ejpam-3118	135	108	2(α3	2(α3	NUM
ejpam-3118	135	109	+	+	NUM
ejpam-3118	135	110	α6	α6	NOUN
ejpam-3118	135	111	+	+	CCONJ
ejpam-3118	135	112	α11	α11	NOUN
ejpam-3118	135	113	+	+	CCONJ
ejpam-3118	135	114	α14	α14	NUM
ejpam-3118	135	115	)	)	PUNCT
ejpam-3118	135	116	,	,	PUNCT
ejpam-3118	135	117	u32	u32	PROPN
ejpam-3118	135	118	=	=	SYM
ejpam-3118	135	119	2(α12	2(α12	NUM
ejpam-3118	135	120	−	−	PROPN
ejpam-3118	135	121	α13	α13	PROPN
ejpam-3118	135	122	+	+	NUM
ejpam-3118	135	123	α15	α15	NOUN
ejpam-3118	135	124	−	−	PROPN
ejpam-3118	135	125	α16	α16	PROPN
ejpam-3118	135	126	)	)	PUNCT
ejpam-3118	135	127	,	,	PUNCT
ejpam-3118	135	128	u33	u33	NOUN
ejpam-3118	135	129	=	=	SYM
ejpam-3118	135	130	2(α1	2(α1	PROPN
ejpam-3118	135	131	−	−	NOUN
ejpam-3118	135	132	α2	α2	ADJ
ejpam-3118	135	133	+	+	CCONJ
ejpam-3118	135	134	α4	α4	NOUN
ejpam-3118	135	135	−	−	PROPN
ejpam-3118	135	136	α8	α8	NOUN
ejpam-3118	135	137	)	)	PUNCT
ejpam-3118	135	138	+	+	CCONJ
ejpam-3118	135	139	1	1	NUM
ejpam-3118	135	140	,	,	PUNCT
ejpam-3118	135	141	u34	u34	PROPN
ejpam-3118	135	142	=	=	SYM
ejpam-3118	135	143	2(−α5	2(−α5	NUM
ejpam-3118	135	144	+	+	CCONJ
ejpam-3118	135	145	α7	α7	NOUN
ejpam-3118	135	146	−	−	PROPN
ejpam-3118	135	147	α9	α9	PROPN
ejpam-3118	135	148	+	+	CCONJ
ejpam-3118	135	149	α10	α10	NOUN
ejpam-3118	135	150	)	)	PUNCT
ejpam-3118	135	151	,	,	PUNCT
ejpam-3118	135	152	u41	u41	ADJ
ejpam-3118	135	153	=	=	SYM
ejpam-3118	135	154	2(α12	2(α12	NUM
ejpam-3118	135	155	+	+	NUM
ejpam-3118	135	156	α13	α13	PROPN
ejpam-3118	135	157	+	+	NUM
ejpam-3118	135	158	α15	α15	NOUN
ejpam-3118	135	159	+	+	CCONJ
ejpam-3118	135	160	α16	α16	VERB
ejpam-3118	135	161	)	)	PUNCT
ejpam-3118	135	162	,	,	PUNCT
ejpam-3118	135	163	u42	u42	NOUN
ejpam-3118	135	164	=	=	SYM
ejpam-3118	135	165	2(α3	2(α3	NUM
ejpam-3118	135	166	+	+	NUM
ejpam-3118	135	167	α6	α6	NOUN
ejpam-3118	135	168	−	−	NOUN
ejpam-3118	135	169	α11	α11	NOUN
ejpam-3118	135	170	−	−	PROPN
ejpam-3118	135	171	α14	α14	PROPN
ejpam-3118	135	172	)	)	PUNCT
ejpam-3118	135	173	,	,	PUNCT
ejpam-3118	135	174	u43	u43	PROPN
ejpam-3118	135	175	=	=	SYM
ejpam-3118	135	176	2(α5	2(α5	NUM
ejpam-3118	135	177	+	+	NUM
ejpam-3118	135	178	α7	α7	NOUN
ejpam-3118	135	179	−	−	PROPN
ejpam-3118	135	180	α9	α9	PROPN
ejpam-3118	135	181	−	−	PROPN
ejpam-3118	135	182	α10	α10	NOUN
ejpam-3118	135	183	)	)	PUNCT
ejpam-3118	135	184	,	,	PUNCT
ejpam-3118	135	185	u44	u44	NOUN
ejpam-3118	135	186	=	=	SYM
ejpam-3118	135	187	2(α1	2(α1	NOUN
ejpam-3118	135	188	−	−	NOUN
ejpam-3118	135	189	α2	α2	ADJ
ejpam-3118	135	190	−	−	NOUN
ejpam-3118	135	191	α4	α4	NOUN
ejpam-3118	135	192	+	+	CCONJ
ejpam-3118	135	193	α8	α8	NOUN
ejpam-3118	135	194	)	)	PUNCT
ejpam-3118	135	195	+	+	CCONJ
ejpam-3118	135	196	1	1	X
ejpam-3118	135	197	.	.	PUNCT
ejpam-3118	135	198	thus	thus	ADV
ejpam-3118	135	199	we	we	PRON
ejpam-3118	135	200	produce	produce	VERB
ejpam-3118	135	201	the	the	DET
ejpam-3118	135	202	monomorphism	monomorphism	NOUN
ejpam-3118	135	203	ϕ	ϕ	X
ejpam-3118	135	204	:	:	PUNCT
ejpam-3118	135	205	u2	u2	NOUN
ejpam-3118	135	206	→	→	SYM
ejpam-3118	135	207			NOUN
ejpam-3118	135	208	2z	2z	NOUN
ejpam-3118	135	209	+	+	NOUN
ejpam-3118	135	210	1	1	NUM
ejpam-3118	135	211	2z	2z	NUM
ejpam-3118	135	212	2z	2z	NUM
ejpam-3118	135	213	2z	2z	NUM
ejpam-3118	135	214	2z	2z	NUM
ejpam-3118	135	215	2z	2z	NOUN
ejpam-3118	135	216	+	+	CCONJ
ejpam-3118	135	217	1	1	NUM
ejpam-3118	135	218	2z	2z	NUM
ejpam-3118	135	219	2z	2z	NUM
ejpam-3118	135	220	2z	2z	NUM
ejpam-3118	135	221	2z	2z	NUM
ejpam-3118	135	222	2z	2z	NOUN
ejpam-3118	135	223	+	+	CCONJ
ejpam-3118	135	224	1	1	NUM
ejpam-3118	135	225	2z	2z	NUM
ejpam-3118	135	226	2z	2z	NUM
ejpam-3118	135	227	2z	2z	NUM
ejpam-3118	135	228	2z	2z	NUM
ejpam-3118	135	229	2z	2z	NOUN
ejpam-3118	135	230	+	+	CCONJ
ejpam-3118	135	231	1	1	NUM
ejpam-3118	135	232			PROPN
ejpam-3118	135	233	det=±1	det=±1	PROPN
ejpam-3118	135	234	defined	define	VERB
ejpam-3118	135	235	by	by	ADP
ejpam-3118	135	236	ϕ(u	ϕ(u	PROPN
ejpam-3118	135	237	)	)	PUNCT
ejpam-3118	136	1	=	=	PUNCT
ejpam-3118	136	2	[	[	PUNCT
ejpam-3118	136	3	2(xij	2(xij	NUM
ejpam-3118	136	4	)	)	PUNCT
ejpam-3118	137	1	+	+	CCONJ
ejpam-3118	137	2	i4	i4	PROPN
ejpam-3118	137	3	]	]	PUNCT
ejpam-3118	137	4	,	,	PUNCT
ejpam-3118	137	5	where	where	SCONJ
ejpam-3118	137	6	x11	x11	NOUN
ejpam-3118	137	7	=	=	SYM
ejpam-3118	137	8	α1	α1	PROPN
ejpam-3118	137	9	+	+	CCONJ
ejpam-3118	137	10	α2	α2	ADJ
ejpam-3118	137	11	+	+	NUM
ejpam-3118	137	12	α4	α4	NOUN
ejpam-3118	137	13	+	+	CCONJ
ejpam-3118	137	14	α8	α8	NOUN
ejpam-3118	137	15	,	,	PUNCT
ejpam-3118	137	16	x12	x12	NUM
ejpam-3118	137	17	=	=	SYM
ejpam-3118	137	18	−α5	−α5	PROPN
ejpam-3118	137	19	+	+	NUM
ejpam-3118	137	20	α7	α7	NOUN
ejpam-3118	138	1	+	+	CCONJ
ejpam-3118	138	2	α9	α9	PROPN
ejpam-3118	138	3	−	−	PROPN
ejpam-3118	138	4	α10	α10	NOUN
ejpam-3118	138	5	,	,	PUNCT
ejpam-3118	138	6	x13	x13	NOUN
ejpam-3118	138	7	=	=	SYM
ejpam-3118	138	8	−α3	−α3	PROPN
ejpam-3118	138	9	+	+	CCONJ
ejpam-3118	138	10	α6	α6	NOUN
ejpam-3118	138	11	+	+	CCONJ
ejpam-3118	138	12	α11	α11	NOUN
ejpam-3118	138	13	−	−	PROPN
ejpam-3118	138	14	α14	α14	PROPN
ejpam-3118	138	15	,	,	PUNCT
ejpam-3118	138	16	x14	x14	PROPN
ejpam-3118	138	17	=	=	PROPN
ejpam-3118	138	18	α12	α12	PROPN
ejpam-3118	138	19	−	−	PROPN
ejpam-3118	138	20	α13	α13	PROPN
ejpam-3118	138	21	−	−	PROPN
ejpam-3118	138	22	α15	α15	NOUN
ejpam-3118	138	23	+	+	CCONJ
ejpam-3118	138	24	α16	α16	VERB
ejpam-3118	138	25	,	,	PUNCT
ejpam-3118	138	26	x21	x21	PROPN
ejpam-3118	138	27	=	=	SYM
ejpam-3118	138	28	α5	α5	PROPN
ejpam-3118	138	29	+	+	CCONJ
ejpam-3118	138	30	α7	α7	NOUN
ejpam-3118	139	1	+	+	CCONJ
ejpam-3118	139	2	α9	α9	PROPN
ejpam-3118	139	3	+	+	CCONJ
ejpam-3118	139	4	α10	α10	PROPN
ejpam-3118	139	5	,	,	PUNCT
ejpam-3118	139	6	x22	x22	NOUN
ejpam-3118	139	7	=	=	SYM
ejpam-3118	139	8	α1	α1	PROPN
ejpam-3118	139	9	+	+	CCONJ
ejpam-3118	139	10	α2	α2	ADJ
ejpam-3118	139	11	−	−	NOUN
ejpam-3118	139	12	α4	α4	NOUN
ejpam-3118	139	13	−	−	PROPN
ejpam-3118	139	14	α8	α8	NOUN
ejpam-3118	139	15	,	,	PUNCT
ejpam-3118	139	16	x23	x23	PROPN
ejpam-3118	139	17	=	=	SYM
ejpam-3118	139	18	α12	α12	PROPN
ejpam-3118	139	19	+	+	CCONJ
ejpam-3118	139	20	α13	α13	PROPN
ejpam-3118	139	21	−	−	PROPN
ejpam-3118	139	22	α15	α15	PROPN
ejpam-3118	139	23	−	−	PROPN
ejpam-3118	139	24	α16	α16	PROPN
ejpam-3118	139	25	,	,	PUNCT
ejpam-3118	139	26	x24	x24	NOUN
ejpam-3118	139	27	=	=	SYM
ejpam-3118	139	28	−α3	−α3	PROPN
ejpam-3118	139	29	+	+	CCONJ
ejpam-3118	139	30	α6	α6	NOUN
ejpam-3118	139	31	−	−	PROPN
ejpam-3118	139	32	α11	α11	NOUN
ejpam-3118	139	33	+	+	CCONJ
ejpam-3118	139	34	α14	α14	NUM
ejpam-3118	139	35	,	,	PUNCT
ejpam-3118	139	36	x31	x31	NOUN
ejpam-3118	139	37	=	=	SYM
ejpam-3118	139	38	α3	α3	PROPN
ejpam-3118	139	39	+	+	CCONJ
ejpam-3118	139	40	α6	α6	NOUN
ejpam-3118	139	41	+	+	CCONJ
ejpam-3118	139	42	α11	α11	NOUN
ejpam-3118	139	43	+	+	CCONJ
ejpam-3118	139	44	α14	α14	NUM
ejpam-3118	139	45	,	,	PUNCT
ejpam-3118	139	46	x32	x32	NOUN
ejpam-3118	139	47	=	=	SYM
ejpam-3118	139	48	α12	α12	PROPN
ejpam-3118	139	49	−	−	PROPN
ejpam-3118	139	50	α13	α13	PROPN
ejpam-3118	139	51	+	+	NUM
ejpam-3118	139	52	α15	α15	NOUN
ejpam-3118	139	53	−	−	PROPN
ejpam-3118	139	54	α16	α16	PROPN
ejpam-3118	139	55	,	,	PUNCT
ejpam-3118	139	56	x33	x33	NOUN
ejpam-3118	139	57	=	=	SYM
ejpam-3118	139	58	α1	α1	PROPN
ejpam-3118	139	59	−	−	PROPN
ejpam-3118	139	60	α2	α2	ADJ
ejpam-3118	139	61	+	+	CCONJ
ejpam-3118	139	62	α4	α4	PROPN
ejpam-3118	139	63	−	−	PROPN
ejpam-3118	139	64	α8	α8	NOUN
ejpam-3118	139	65	,	,	PUNCT
ejpam-3118	139	66	x34	x34	NOUN
ejpam-3118	140	1	=	=	SYM
ejpam-3118	140	2	−α5	−α5	PROPN
ejpam-3118	140	3	+	+	NUM
ejpam-3118	140	4	α7	α7	NOUN
ejpam-3118	140	5	−	−	PROPN
ejpam-3118	140	6	α9	α9	PROPN
ejpam-3118	140	7	+	+	CCONJ
ejpam-3118	140	8	α10	α10	PROPN
ejpam-3118	140	9	,	,	PUNCT
ejpam-3118	140	10	x41	x41	PROPN
ejpam-3118	140	11	=	=	SYM
ejpam-3118	140	12	α12	α12	PROPN
ejpam-3118	140	13	+	+	CCONJ
ejpam-3118	140	14	α13	α13	PROPN
ejpam-3118	140	15	+	+	NUM
ejpam-3118	140	16	α15	α15	NOUN
ejpam-3118	140	17	+	+	CCONJ
ejpam-3118	140	18	α16	α16	VERB
ejpam-3118	140	19	,	,	PUNCT
ejpam-3118	140	20	x42	x42	NOUN
ejpam-3118	140	21	=	=	SYM
ejpam-3118	140	22	α3	α3	PROPN
ejpam-3118	140	23	+	+	CCONJ
ejpam-3118	140	24	α6	α6	NOUN
ejpam-3118	140	25	−	−	PROPN
ejpam-3118	140	26	α11	α11	NOUN
ejpam-3118	140	27	−	−	PROPN
ejpam-3118	140	28	α14	α14	PROPN
ejpam-3118	140	29	,	,	PUNCT
ejpam-3118	140	30	x43	x43	PROPN
ejpam-3118	140	31	=	=	SYM
ejpam-3118	140	32	α5	α5	PROPN
ejpam-3118	140	33	+	+	CCONJ
ejpam-3118	140	34	α7	α7	NOUN
ejpam-3118	140	35	−	−	PROPN
ejpam-3118	140	36	α9	α9	PROPN
ejpam-3118	140	37	−	−	PROPN
ejpam-3118	140	38	α10	α10	NOUN
ejpam-3118	140	39	,	,	PUNCT
ejpam-3118	140	40	x44	x44	NOUN
ejpam-3118	140	41	=	=	PROPN
ejpam-3118	140	42	α1	α1	PROPN
ejpam-3118	140	43	−	−	PROPN
ejpam-3118	140	44	α2	α2	ADJ
ejpam-3118	140	45	−	−	NOUN
ejpam-3118	140	46	α4	α4	NOUN
ejpam-3118	140	47	+	+	NUM
ejpam-3118	140	48	α8	α8	NOUN
ejpam-3118	140	49	.	.	PUNCT
ejpam-3118	141	1	let	let	VERB
ejpam-3118	141	2	a	a	PRON
ejpam-3118	141	3	=	=	PUNCT
ejpam-3118	142	1	[	[	X
ejpam-3118	142	2	2(xij	2(xij	NUM
ejpam-3118	142	3	)	)	PUNCT
ejpam-3118	142	4	+	+	CCONJ
ejpam-3118	143	1	i4	i4	PROPN
ejpam-3118	143	2	]	]	PUNCT
ejpam-3118	143	3	,	,	PUNCT
ejpam-3118	143	4	with	with	ADP
ejpam-3118	143	5	xij	xij	PROPN
ejpam-3118	143	6	∈	∈	PROPN
ejpam-3118	143	7	z	z	PROPN
ejpam-3118	143	8	,	,	PUNCT
ejpam-3118	143	9	for	for	ADP
ejpam-3118	143	10	all	all	DET
ejpam-3118	143	11	i	i	PROPN
ejpam-3118	143	12	,	,	PUNCT
ejpam-3118	143	13	j	j	PROPN
ejpam-3118	143	14	,	,	PUNCT
ejpam-3118	143	15	1	1	NUM
ejpam-3118	143	16	≤	≤	NUM
ejpam-3118	143	17	i	i	PRON
ejpam-3118	143	18	,	,	PUNCT
ejpam-3118	143	19	j	j	PROPN
ejpam-3118	143	20	≤	≤	ADV
ejpam-3118	143	21	4	4	NUM
ejpam-3118	143	22	.	.	PUNCT
ejpam-3118	143	23	then	then	ADV
ejpam-3118	143	24	deta	deta	VERB
ejpam-3118	143	25	=	=	NOUN
ejpam-3118	143	26	1	1	NUM
ejpam-3118	143	27	+	+	NUM
ejpam-3118	143	28	2β1	2β1	NUM
ejpam-3118	143	29	+	+	CCONJ
ejpam-3118	143	30	4β2	4β2	NUM
ejpam-3118	144	1	+	+	NUM
ejpam-3118	144	2	8β3	8β3	NUM
ejpam-3118	144	3	+	+	CCONJ
ejpam-3118	144	4	16β4	16β4	NUM
ejpam-3118	144	5	,	,	PUNCT
ejpam-3118	144	6	where	where	SCONJ
ejpam-3118	144	7	βr	βr	ADP
ejpam-3118	144	8	∈	∈	PROPN
ejpam-3118	144	9	z	z	PROPN
ejpam-3118	144	10	,	,	PUNCT
ejpam-3118	144	11	1	1	NUM
ejpam-3118	144	12	≤	≤	NOUN
ejpam-3118	144	13	r	r	NOUN
ejpam-3118	144	14	≤	≤	NUM
ejpam-3118	144	15	4	4	NUM
ejpam-3118	144	16	.	.	PUNCT
ejpam-3118	145	1	in	in	ADP
ejpam-3118	145	2	particular	particular	ADJ
ejpam-3118	145	3	,	,	PUNCT
ejpam-3118	145	4	β1	β1	PROPN
ejpam-3118	145	5	=	=	PUNCT
ejpam-3118	145	6	x11	x11	PROPN
ejpam-3118	145	7	+	+	CCONJ
ejpam-3118	145	8	x22	x22	NUM
ejpam-3118	146	1	+	+	CCONJ
ejpam-3118	146	2	x33	x33	PROPN
ejpam-3118	146	3	+	+	CCONJ
ejpam-3118	146	4	x44	x44	NOUN
ejpam-3118	146	5	.	.	PUNCT
ejpam-3118	147	1	furthermore	furthermore	ADV
ejpam-3118	147	2	,	,	PUNCT
ejpam-3118	147	3	a	a	DET
ejpam-3118	147	4	∈	∈	PROPN
ejpam-3118	147	5	ϕ(u2	ϕ(u2	NOUN
ejpam-3118	147	6	)	)	PUNCT
ejpam-3118	148	1	if	if	SCONJ
ejpam-3118	148	2	and	and	CCONJ
ejpam-3118	148	3	only	only	ADV
ejpam-3118	148	4	if	if	SCONJ
ejpam-3118	148	5	deta	deta	NOUN
ejpam-3118	148	6	=	=	NOUN
ejpam-3118	148	7	1	1	NUM
ejpam-3118	148	8	and	and	CCONJ
ejpam-3118	148	9	,	,	PUNCT
ejpam-3118	148	10	for	for	ADP
ejpam-3118	148	11	each	each	DET
ejpam-3118	148	12	k	k	NOUN
ejpam-3118	148	13	,	,	PUNCT
ejpam-3118	148	14	1	1	NUM
ejpam-3118	148	15	≤	≤	NUM
ejpam-3118	148	16	k	k	X
ejpam-3118	148	17	≤	≤	NUM
ejpam-3118	148	18	4	4	NUM
ejpam-3118	148	19	,	,	PUNCT
ejpam-3118	148	20	the	the	DET
ejpam-3118	148	21	integers	integer	NOUN
ejpam-3118	148	22	xiji	xiji	VERB
ejpam-3118	148	23	∈	∈	PROPN
ejpam-3118	148	24	bk	bk	NOUN
ejpam-3118	148	25	have	have	VERB
ejpam-3118	148	26	the	the	DET
ejpam-3118	148	27	same	same	ADJ
ejpam-3118	148	28	parity	parity	NOUN
ejpam-3118	148	29	and	and	CCONJ
ejpam-3118	148	30	4	4	NUM
ejpam-3118	148	31	divides	divide	VERB
ejpam-3118	148	32	the	the	DET
ejpam-3118	148	33	sum	sum	NOUN
ejpam-3118	148	34	x1j1	x1j1	PUNCT
ejpam-3118	149	1	+	+	CCONJ
ejpam-3118	149	2	x2j2	x2j2	PUNCT
ejpam-3118	150	1	+	+	CCONJ
ejpam-3118	150	2	x3j3	x3j3	PUNCT
ejpam-3118	151	1	+	+	CCONJ
ejpam-3118	151	2	x4j4	x4j4	X
ejpam-3118	151	3	.	.	PUNCT
ejpam-3118	151	4	indeed	indeed	ADV
ejpam-3118	151	5	,	,	PUNCT
ejpam-3118	151	6	a	a	DET
ejpam-3118	151	7	∈	∈	PROPN
ejpam-3118	151	8	ϕ(u2	ϕ(u2	NOUN
ejpam-3118	151	9	)	)	PUNCT
ejpam-3118	152	1	if	if	SCONJ
ejpam-3118	152	2	and	and	CCONJ
ejpam-3118	152	3	only	only	ADV
ejpam-3118	152	4	if	if	SCONJ
ejpam-3118	152	5	deta	deta	NOUN
ejpam-3118	152	6	=	=	SYM
ejpam-3118	152	7	±1	±1	VERB
ejpam-3118	152	8	and	and	CCONJ
ejpam-3118	152	9	,	,	PUNCT
ejpam-3118	152	10	for	for	ADP
ejpam-3118	152	11	each	each	DET
ejpam-3118	152	12	k	k	NOUN
ejpam-3118	152	13	,	,	PUNCT
ejpam-3118	152	14	1	1	NUM
ejpam-3118	152	15	≤	≤	NUM
ejpam-3118	152	16	k	k	X
ejpam-3118	152	17	≤	≤	NUM
ejpam-3118	152	18	4	4	NUM
ejpam-3118	152	19	,	,	PUNCT
ejpam-3118	152	20	with	with	ADP
ejpam-3118	152	21	xiji	xiji	PROPN
ejpam-3118	152	22	∈	∈	PROPN
ejpam-3118	152	23	bk	bk	PROPN
ejpam-3118	152	24	,	,	PUNCT
ejpam-3118	152	25	4	4	NUM
ejpam-3118	152	26	divides	divide	VERB
ejpam-3118	152	27	the	the	DET
ejpam-3118	152	28	sum	sum	NOUN
ejpam-3118	152	29	c.	c.	PROPN
ejpam-3118	152	30	mello	mello	PROPN
ejpam-3118	152	31	/	/	SYM
ejpam-3118	152	32	eur	eur	PROPN
ejpam-3118	152	33	.	.	PUNCT
ejpam-3118	153	1	j.	j.	PROPN
ejpam-3118	153	2	pure	pure	PROPN
ejpam-3118	153	3	appl	appl	PROPN
ejpam-3118	153	4	.	.	PROPN
ejpam-3118	153	5	math	math	PROPN
ejpam-3118	153	6	,	,	PUNCT
ejpam-3118	153	7	10	10	NUM
ejpam-3118	153	8	(	(	PUNCT
ejpam-3118	153	9	5	5	NUM
ejpam-3118	153	10	)	)	PUNCT
ejpam-3118	153	11	(	(	PUNCT
ejpam-3118	153	12	2017	2017	NUM
ejpam-3118	153	13	)	)	PUNCT
ejpam-3118	153	14	,	,	PUNCT
ejpam-3118	153	15	955	955	NUM
ejpam-3118	153	16	-	-	SYM
ejpam-3118	153	17	966	966	NUM
ejpam-3118	153	18	962	962	NUM
ejpam-3118	153	19	x1j1	x1j1	PUNCT
ejpam-3118	154	1	+	+	CCONJ
ejpam-3118	154	2	x2j2	x2j2	PUNCT
ejpam-3118	155	1	+	+	CCONJ
ejpam-3118	155	2	x3j3	x3j3	PUNCT
ejpam-3118	156	1	+	+	CCONJ
ejpam-3118	156	2	x4j4	x4j4	INTJ
ejpam-3118	156	3	,	,	PUNCT
ejpam-3118	156	4	this	this	PRON
ejpam-3118	156	5	is	be	AUX
ejpam-3118	156	6	,	,	PUNCT
ejpam-3118	156	7	4|(x1j1	4|(x1j1	PROPN
ejpam-3118	157	1	+	+	CCONJ
ejpam-3118	157	2	x2j2	x2j2	PUNCT
ejpam-3118	158	1	+	+	CCONJ
ejpam-3118	158	2	x3j3	x3j3	PUNCT
ejpam-3118	159	1	+	+	NUM
ejpam-3118	159	2	x4j4	x4j4	X
ejpam-3118	159	3	)	)	PUNCT
ejpam-3118	159	4	,	,	PUNCT
ejpam-3118	159	5	and	and	CCONJ
ejpam-3118	159	6	2|(x1j1	2|(x1j1	NUM
ejpam-3118	159	7	+	+	CCONJ
ejpam-3118	159	8	x2j2	x2j2	PROPN
ejpam-3118	159	9	)	)	PUNCT
ejpam-3118	159	10	,	,	PUNCT
ejpam-3118	160	1	2|(x1j1	2|(x1j1	PROPN
ejpam-3118	160	2	+	+	NOUN
ejpam-3118	160	3	x3j3	x3j3	PROPN
ejpam-3118	160	4	)	)	PUNCT
ejpam-3118	160	5	,	,	PUNCT
ejpam-3118	161	1	2|(x1j1	2|(x1j1	PROPN
ejpam-3118	161	2	+	+	NOUN
ejpam-3118	161	3	x4j4	x4j4	NOUN
ejpam-3118	161	4	)	)	PUNCT
ejpam-3118	161	5	,	,	PUNCT
ejpam-3118	161	6	2|(x2j2	2|(x2j2	PROPN
ejpam-3118	161	7	+	+	PROPN
ejpam-3118	161	8	x3j3	x3j3	PROPN
ejpam-3118	161	9	)	)	PUNCT
ejpam-3118	161	10	,	,	PUNCT
ejpam-3118	161	11	2|(x2j2	2|(x2j2	PROPN
ejpam-3118	161	12	+	+	NOUN
ejpam-3118	161	13	x4j4	x4j4	NOUN
ejpam-3118	161	14	)	)	PUNCT
ejpam-3118	161	15	and	and	CCONJ
ejpam-3118	161	16	2|(x3j3	2|(x3j3	PROPN
ejpam-3118	161	17	+	+	NOUN
ejpam-3118	161	18	x4j4	x4j4	NOUN
ejpam-3118	161	19	)	)	PUNCT
ejpam-3118	161	20	.	.	PUNCT
ejpam-3118	162	1	in	in	ADP
ejpam-3118	162	2	particular	particular	ADJ
ejpam-3118	162	3	,	,	PUNCT
ejpam-3118	162	4	as	as	ADP
ejpam-3118	162	5	4|(x11	4|(x11	NUM
ejpam-3118	162	6	+	+	NOUN
ejpam-3118	162	7	x22	x22	NOUN
ejpam-3118	162	8	+	+	ADJ
ejpam-3118	162	9	x33	x33	ADJ
ejpam-3118	162	10	+	+	NOUN
ejpam-3118	162	11	x44	x44	NOUN
ejpam-3118	162	12	)	)	PUNCT
ejpam-3118	162	13	,	,	PUNCT
ejpam-3118	162	14	it	it	PRON
ejpam-3118	162	15	follows	follow	VERB
ejpam-3118	162	16	that	that	SCONJ
ejpam-3118	162	17	deta	deta	NOUN
ejpam-3118	162	18	=	=	NOUN
ejpam-3118	162	19	1	1	X
ejpam-3118	162	20	.	.	PUNCT
ejpam-3118	163	1	so	so	ADV
ejpam-3118	163	2	ϕ(u2	ϕ(u2	ADV
ejpam-3118	163	3	)	)	PUNCT
ejpam-3118	164	1	=	=	PUNCT
ejpam-3118	164	2	[	[	PUNCT
ejpam-3118	164	3	2(xij	2(xij	NUM
ejpam-3118	164	4	)	)	PUNCT
ejpam-3118	164	5	+	+	CCONJ
ejpam-3118	165	1	i4	i4	PROPN
ejpam-3118	165	2	]	]	PUNCT
ejpam-3118	165	3	det=1	det=1	PROPN
ejpam-3118	165	4	is	be	AUX
ejpam-3118	165	5	a	a	DET
ejpam-3118	165	6	group	group	NOUN
ejpam-3118	165	7	of	of	ADP
ejpam-3118	165	8	4	4	NUM
ejpam-3118	165	9	-	-	PUNCT
ejpam-3118	165	10	by-4	by-4	NOUN
ejpam-3118	165	11	matrices	matrix	NOUN
ejpam-3118	165	12	,	,	PUNCT
ejpam-3118	165	13	where	where	SCONJ
ejpam-3118	165	14	for	for	ADP
ejpam-3118	165	15	each	each	DET
ejpam-3118	165	16	k	k	NOUN
ejpam-3118	165	17	,	,	PUNCT
ejpam-3118	165	18	1	1	NUM
ejpam-3118	165	19	≤	≤	NUM
ejpam-3118	165	20	k	k	X
ejpam-3118	165	21	≤	≤	NUM
ejpam-3118	165	22	4	4	NUM
ejpam-3118	165	23	,	,	PUNCT
ejpam-3118	165	24	the	the	DET
ejpam-3118	165	25	integers	integer	NOUN
ejpam-3118	165	26	xiji	xiji	VERB
ejpam-3118	165	27	∈	∈	PROPN
ejpam-3118	165	28	bk	bk	NOUN
ejpam-3118	165	29	have	have	VERB
ejpam-3118	165	30	the	the	DET
ejpam-3118	165	31	same	same	ADJ
ejpam-3118	165	32	parity	parity	NOUN
ejpam-3118	165	33	and	and	CCONJ
ejpam-3118	165	34	4	4	NUM
ejpam-3118	165	35	divides	divide	VERB
ejpam-3118	165	36	the	the	DET
ejpam-3118	165	37	sum	sum	NOUN
ejpam-3118	165	38	x1j1	x1j1	PUNCT
ejpam-3118	166	1	+	+	ADJ
ejpam-3118	166	2	x2j2	x2j2	PROPN
ejpam-3118	167	1	+	+	ADJ
ejpam-3118	167	2	x3j3	x3j3	PROPN
ejpam-3118	168	1	+	+	ADJ
ejpam-3118	168	2	x4j4	x4j4	PROPN
ejpam-3118	168	3	.	.	PUNCT
ejpam-3118	169	1	since	since	SCONJ
ejpam-3118	169	2	ϕ(s	ϕ(s	PRON
ejpam-3118	169	3	)	)	PUNCT
ejpam-3118	169	4	=	=	SYM
ejpam-3118	169	5	ϕ(1	ϕ(1	PROPN
ejpam-3118	169	6	+	+	CCONJ
ejpam-3118	169	7	s(1−	s(1−	PROPN
ejpam-3118	169	8	s	s	PART
ejpam-3118	169	9	)	)	PUNCT
ejpam-3118	169	10	)	)	PUNCT
ejpam-3118	170	1	=	=	PUNCT
ejpam-3118	170	2	−i4	−i4	ADJ
ejpam-3118	170	3	,	,	PUNCT
ejpam-3118	170	4	it	it	PRON
ejpam-3118	170	5	follows	follow	VERB
ejpam-3118	170	6	that	that	SCONJ
ejpam-3118	170	7	the	the	DET
ejpam-3118	170	8	mapping	mapping	NOUN
ejpam-3118	170	9	ϕ	ϕ	NOUN
ejpam-3118	170	10	induces	induce	VERB
ejpam-3118	170	11	an	an	DET
ejpam-3118	170	12	isomorphism	isomorphism	NOUN
ejpam-3118	170	13	from	from	ADP
ejpam-3118	170	14	v1	v1	PROPN
ejpam-3118	170	15	onto	onto	ADP
ejpam-3118	170	16	the	the	DET
ejpam-3118	170	17	group	group	NOUN
ejpam-3118	170	18	[	[	PUNCT
ejpam-3118	170	19	2(xij	2(xij	NUM
ejpam-3118	170	20	)	)	PUNCT
ejpam-3118	171	1	+	+	CCONJ
ejpam-3118	172	1	i4	i4	PROPN
ejpam-3118	172	2	]	]	PUNCT
ejpam-3118	172	3	det=1	det=1	NOUN
ejpam-3118	172	4	of	of	ADP
ejpam-3118	172	5	4	4	NUM
ejpam-3118	172	6	-	-	PUNCT
ejpam-3118	172	7	by-4	by-4	NOUN
ejpam-3118	172	8	matrices	matrix	NOUN
ejpam-3118	172	9	,	,	PUNCT
ejpam-3118	172	10	where	where	SCONJ
ejpam-3118	172	11	for	for	ADP
ejpam-3118	172	12	each	each	DET
ejpam-3118	172	13	k	k	NOUN
ejpam-3118	172	14	,	,	PUNCT
ejpam-3118	172	15	1	1	NUM
ejpam-3118	172	16	≤	≤	NUM
ejpam-3118	172	17	k	k	X
ejpam-3118	172	18	≤	≤	NUM
ejpam-3118	172	19	4	4	NUM
ejpam-3118	172	20	,	,	PUNCT
ejpam-3118	172	21	the	the	DET
ejpam-3118	172	22	integers	integer	NOUN
ejpam-3118	172	23	xiji	xiji	VERB
ejpam-3118	172	24	∈	∈	PROPN
ejpam-3118	172	25	bk	bk	NOUN
ejpam-3118	172	26	have	have	VERB
ejpam-3118	172	27	the	the	DET
ejpam-3118	172	28	same	same	ADJ
ejpam-3118	172	29	parity	parity	NOUN
ejpam-3118	172	30	and	and	CCONJ
ejpam-3118	172	31	4	4	NUM
ejpam-3118	172	32	divides	divide	VERB
ejpam-3118	172	33	the	the	DET
ejpam-3118	172	34	sum	sum	NOUN
ejpam-3118	172	35	x1j1	x1j1	PUNCT
ejpam-3118	173	1	+	+	ADJ
ejpam-3118	173	2	x2j2	x2j2	PROPN
ejpam-3118	174	1	+	+	ADJ
ejpam-3118	174	2	x3j3	x3j3	PROPN
ejpam-3118	174	3	+	+	ADJ
ejpam-3118	174	4	x4j4	x4j4	PROPN
ejpam-3118	174	5	.	.	PUNCT
ejpam-3118	175	1	4.2	4.2	NUM
ejpam-3118	175	2	.	.	PUNCT
ejpam-3118	176	1	the	the	DET
ejpam-3118	176	2	group	group	NOUN
ejpam-3118	176	3	of	of	ADP
ejpam-3118	176	4	units	unit	NOUN
ejpam-3118	176	5	of	of	ADP
ejpam-3118	176	6	group	group	NOUN
ejpam-3118	176	7	ring	ring	NOUN
ejpam-3118	176	8	zg2	zg2	NOUN
ejpam-3118	176	9	proposition	proposition	NOUN
ejpam-3118	176	10	7	7	NUM
ejpam-3118	176	11	.	.	PUNCT
ejpam-3118	177	1	the	the	DET
ejpam-3118	177	2	group	group	NOUN
ejpam-3118	177	3	ring	ring	NOUN
ejpam-3118	177	4	qg2	qg2	PROPN
ejpam-3118	177	5	admits	admit	VERB
ejpam-3118	177	6	the	the	DET
ejpam-3118	177	7	following	follow	VERB
ejpam-3118	177	8	decomposition	decomposition	NOUN
ejpam-3118	177	9	:	:	PUNCT
ejpam-3118	177	10	qg2	qg2	NOUN
ejpam-3118	177	11	=	=	NOUN
ejpam-3118	177	12	qg2	qg2	NOUN
ejpam-3118	177	13	(	(	PUNCT
ejpam-3118	177	14	1	1	NUM
ejpam-3118	177	15	+	+	SYM
ejpam-3118	177	16	s	s	NOUN
ejpam-3118	177	17	2	2	NUM
ejpam-3118	177	18	)	)	PUNCT
ejpam-3118	177	19	⊕qg2	⊕qg2	NOUN
ejpam-3118	177	20	(	(	PUNCT
ejpam-3118	177	21	1−	1−	NUM
ejpam-3118	177	22	s	s	NOUN
ejpam-3118	177	23	2	2	NUM
ejpam-3118	177	24	)	)	PUNCT
ejpam-3118	177	25	,	,	PUNCT
ejpam-3118	177	26	where	where	SCONJ
ejpam-3118	177	27	qg2	qg2	NOUN
ejpam-3118	177	28	(	(	PUNCT
ejpam-3118	177	29	1	1	NUM
ejpam-3118	177	30	+	+	SYM
ejpam-3118	177	31	s	s	AUX
ejpam-3118	177	32	2	2	NUM
ejpam-3118	177	33	)	)	PUNCT
ejpam-3118	177	34	∼=	∼=	PROPN
ejpam-3118	177	35	q64	q64	NOUN
ejpam-3118	177	36	and	and	CCONJ
ejpam-3118	177	37	qg2	qg2	NOUN
ejpam-3118	177	38	(	(	PUNCT
ejpam-3118	177	39	1−	1−	NUM
ejpam-3118	177	40	s	s	NOUN
ejpam-3118	177	41	2	2	NUM
ejpam-3118	177	42	)	)	PUNCT
ejpam-3118	177	43	∼=	∼=	PROPN
ejpam-3118	177	44	m8(q	m8(q	NOUN
ejpam-3118	177	45	)	)	PUNCT
ejpam-3118	177	46	.	.	PUNCT
ejpam-3118	178	1	proof	proof	NOUN
ejpam-3118	178	2	.	.	PUNCT
ejpam-3118	179	1	it	it	PRON
ejpam-3118	179	2	follows	follow	VERB
ejpam-3118	179	3	from	from	ADP
ejpam-3118	179	4	proposition	proposition	NOUN
ejpam-3118	179	5	4	4	NUM
ejpam-3118	179	6	and	and	CCONJ
ejpam-3118	179	7	proposition	proposition	NOUN
ejpam-3118	179	8	5	5	NUM
ejpam-3118	179	9	.	.	PUNCT
ejpam-3118	180	1	for	for	ADP
ejpam-3118	180	2	the	the	DET
ejpam-3118	180	3	next	next	ADJ
ejpam-3118	180	4	results	result	NOUN
ejpam-3118	180	5	,	,	PUNCT
ejpam-3118	180	6	we	we	PRON
ejpam-3118	180	7	use	use	VERB
ejpam-3118	180	8	the	the	DET
ejpam-3118	180	9	representation	representation	NOUN
ejpam-3118	180	10	of	of	ADP
ejpam-3118	180	11	d4	d4	PROPN
ejpam-3118	180	12	on	on	ADP
ejpam-3118	180	13	m2(q	m2(q	NOUN
ejpam-3118	180	14	)	)	PUNCT
ejpam-3118	180	15	previously	previously	ADV
ejpam-3118	180	16	fixed	fix	VERB
ejpam-3118	180	17	and	and	CCONJ
ejpam-3118	180	18	we	we	PRON
ejpam-3118	180	19	obtain	obtain	VERB
ejpam-3118	180	20	a	a	DET
ejpam-3118	180	21	representation	representation	NOUN
ejpam-3118	180	22	of	of	ADP
ejpam-3118	180	23	g2	g2	PROPN
ejpam-3118	180	24	on	on	ADP
ejpam-3118	180	25	m8(q	m8(q	NOUN
ejpam-3118	180	26	):	):	PUNCT
ejpam-3118	180	27	•	•	NUM
ejpam-3118	180	28	b	b	SYM
ejpam-3118	180	29	7→	7→	NUM
ejpam-3118	180	30	e11	e11	NOUN
ejpam-3118	180	31	+	+	CCONJ
ejpam-3118	180	32	e22	e22	NOUN
ejpam-3118	180	33	+	+	CCONJ
ejpam-3118	180	34	e33	e33	PROPN
ejpam-3118	180	35	+	+	CCONJ
ejpam-3118	180	36	e44−	e44−	PROPN
ejpam-3118	180	37	e55−	e55−	PROPN
ejpam-3118	180	38	e66−	e66−	PROPN
ejpam-3118	181	1	e77−	e77−	NOUN
ejpam-3118	181	2	e88	e88	NOUN
ejpam-3118	181	3	=	=	PUNCT
ejpam-3118	181	4	[	[	PUNCT
ejpam-3118	181	5	1	1	NUM
ejpam-3118	181	6	0	0	NUM
ejpam-3118	181	7	0	0	NUM
ejpam-3118	181	8	1	1	NUM
ejpam-3118	181	9	]	]	PUNCT
ejpam-3118	182	1	⊗	⊗	PROPN
ejpam-3118	182	2	[	[	PUNCT
ejpam-3118	182	3	1	1	NUM
ejpam-3118	182	4	0	0	NUM
ejpam-3118	182	5	0	0	NUM
ejpam-3118	182	6	1	1	NUM
ejpam-3118	182	7	]	]	PUNCT
ejpam-3118	182	8	⊗	⊗	PROPN
ejpam-3118	182	9	[	[	PUNCT
ejpam-3118	182	10	1	1	NUM
ejpam-3118	182	11	0	0	NUM
ejpam-3118	182	12	0	0	NUM
ejpam-3118	182	13	−1	−1	NOUN
ejpam-3118	182	14	]	]	PUNCT
ejpam-3118	182	15	,	,	PUNCT
ejpam-3118	182	16	•	•	NOUN
ejpam-3118	182	17	v	v	NOUN
ejpam-3118	182	18	7→	7→	NUM
ejpam-3118	182	19	−e15−e26−e37−e48+e51+e62+e73+e84	−e15−e26−e37−e48+e51+e62+e73+e84	NOUN
ejpam-3118	182	20	=	=	PUNCT
ejpam-3118	183	1	[	[	PUNCT
ejpam-3118	183	2	1	1	NUM
ejpam-3118	183	3	0	0	NUM
ejpam-3118	183	4	0	0	NUM
ejpam-3118	183	5	1	1	NUM
ejpam-3118	183	6	]	]	PUNCT
ejpam-3118	184	1	⊗	⊗	PROPN
ejpam-3118	184	2	[	[	PUNCT
ejpam-3118	184	3	1	1	NUM
ejpam-3118	184	4	0	0	NUM
ejpam-3118	184	5	0	0	NUM
ejpam-3118	184	6	1	1	NUM
ejpam-3118	184	7	]	]	PUNCT
ejpam-3118	184	8	⊗	⊗	PROPN
ejpam-3118	184	9	[	[	PUNCT
ejpam-3118	184	10	0	0	NUM
ejpam-3118	184	11	−1	−1	NOUN
ejpam-3118	184	12	1	1	NUM
ejpam-3118	184	13	0	0	NUM
ejpam-3118	184	14	]	]	PUNCT
ejpam-3118	184	15	,	,	PUNCT
ejpam-3118	184	16	•	•	NUM
ejpam-3118	184	17	b1	b1	NOUN
ejpam-3118	184	18	7→	7→	NUM
ejpam-3118	184	19	e11+e22−e33−e44+e55+e66−e77−e88	e11+e22−e33−e44+e55+e66−e77−e88	NOUN
ejpam-3118	184	20	=	=	PUNCT
ejpam-3118	184	21	[	[	PUNCT
ejpam-3118	184	22	1	1	NUM
ejpam-3118	184	23	0	0	NUM
ejpam-3118	184	24	0	0	NUM
ejpam-3118	184	25	1	1	NUM
ejpam-3118	184	26	]	]	PUNCT
ejpam-3118	184	27	⊗	⊗	PROPN
ejpam-3118	184	28	[	[	PUNCT
ejpam-3118	184	29	1	1	NUM
ejpam-3118	184	30	0	0	NUM
ejpam-3118	184	31	0	0	NUM
ejpam-3118	184	32	−1	−1	NOUN
ejpam-3118	184	33	]	]	PUNCT
ejpam-3118	185	1	⊗	⊗	X
ejpam-3118	185	2	[	[	PUNCT
ejpam-3118	185	3	1	1	NUM
ejpam-3118	185	4	0	0	NUM
ejpam-3118	185	5	0	0	NUM
ejpam-3118	185	6	1	1	NUM
ejpam-3118	185	7	]	]	PUNCT
ejpam-3118	185	8	,	,	PUNCT
ejpam-3118	185	9	•	•	NUM
ejpam-3118	185	10	v1	v1	NOUN
ejpam-3118	185	11	7→	7→	NUM
ejpam-3118	185	12	−e13−e24+e31+e42−e57−e68+e75+e86	−e13−e24+e31+e42−e57−e68+e75+e86	NOUN
ejpam-3118	186	1	=	=	PUNCT
ejpam-3118	187	1	[	[	PUNCT
ejpam-3118	187	2	1	1	NUM
ejpam-3118	187	3	0	0	NUM
ejpam-3118	187	4	0	0	NUM
ejpam-3118	187	5	1	1	NUM
ejpam-3118	187	6	]	]	PUNCT
ejpam-3118	188	1	⊗	⊗	PROPN
ejpam-3118	188	2	[	[	PUNCT
ejpam-3118	188	3	0	0	NUM
ejpam-3118	188	4	−1	−1	NOUN
ejpam-3118	188	5	1	1	NUM
ejpam-3118	188	6	0	0	NUM
ejpam-3118	188	7	]	]	PUNCT
ejpam-3118	189	1	⊗	⊗	PROPN
ejpam-3118	189	2	[	[	PUNCT
ejpam-3118	189	3	1	1	NUM
ejpam-3118	189	4	0	0	NUM
ejpam-3118	189	5	0	0	NUM
ejpam-3118	189	6	1	1	NUM
ejpam-3118	189	7	]	]	PUNCT
ejpam-3118	189	8	,	,	PUNCT
ejpam-3118	189	9	•	•	NUM
ejpam-3118	189	10	b2	b2	NOUN
ejpam-3118	189	11	7→	7→	NUM
ejpam-3118	189	12	e11−e22+e33−e44+e55−e66+e77−e88	e11−e22+e33−e44+e55−e66+e77−e88	NOUN
ejpam-3118	189	13	=	=	PUNCT
ejpam-3118	190	1	[	[	PUNCT
ejpam-3118	190	2	1	1	NUM
ejpam-3118	190	3	0	0	NUM
ejpam-3118	190	4	0	0	NUM
ejpam-3118	190	5	−1	−1	NOUN
ejpam-3118	190	6	]	]	PUNCT
ejpam-3118	191	1	⊗	⊗	X
ejpam-3118	191	2	[	[	PUNCT
ejpam-3118	191	3	1	1	NUM
ejpam-3118	191	4	0	0	NUM
ejpam-3118	191	5	0	0	NUM
ejpam-3118	191	6	1	1	NUM
ejpam-3118	191	7	]	]	PUNCT
ejpam-3118	191	8	⊗	⊗	PROPN
ejpam-3118	191	9	[	[	PUNCT
ejpam-3118	191	10	1	1	NUM
ejpam-3118	191	11	0	0	NUM
ejpam-3118	191	12	0	0	NUM
ejpam-3118	191	13	1	1	NUM
ejpam-3118	191	14	]	]	PUNCT
ejpam-3118	191	15	,	,	PUNCT
ejpam-3118	191	16	•	•	NUM
ejpam-3118	191	17	v2	v2	VERB
ejpam-3118	191	18	7→	7→	NUM
ejpam-3118	191	19	−e12+e21−e34+e43−e56+e65−e78+e87	−e12+e21−e34+e43−e56+e65−e78+e87	NOUN
ejpam-3118	191	20	=	=	PUNCT
ejpam-3118	191	21	[	[	PUNCT
ejpam-3118	191	22	0	0	NUM
ejpam-3118	191	23	−1	−1	NOUN
ejpam-3118	191	24	1	1	NUM
ejpam-3118	191	25	0	0	NUM
ejpam-3118	191	26	]	]	PUNCT
ejpam-3118	191	27	⊗	⊗	PROPN
ejpam-3118	191	28	[	[	PUNCT
ejpam-3118	191	29	1	1	NUM
ejpam-3118	191	30	0	0	NUM
ejpam-3118	191	31	0	0	NUM
ejpam-3118	191	32	1	1	NUM
ejpam-3118	191	33	]	]	PUNCT
ejpam-3118	192	1	⊗	⊗	PROPN
ejpam-3118	193	1	[	[	PUNCT
ejpam-3118	193	2	1	1	NUM
ejpam-3118	193	3	0	0	NUM
ejpam-3118	193	4	0	0	NUM
ejpam-3118	193	5	1	1	NUM
ejpam-3118	193	6	]	]	PUNCT
ejpam-3118	193	7	.	.	PUNCT
ejpam-3118	194	1	c.	c.	PROPN
ejpam-3118	194	2	mello	mello	PROPN
ejpam-3118	194	3	/	/	SYM
ejpam-3118	194	4	eur	eur	PROPN
ejpam-3118	194	5	.	.	PUNCT
ejpam-3118	195	1	j.	j.	PROPN
ejpam-3118	195	2	pure	pure	PROPN
ejpam-3118	195	3	appl	appl	PROPN
ejpam-3118	195	4	.	.	PROPN
ejpam-3118	195	5	math	math	PROPN
ejpam-3118	195	6	,	,	PUNCT
ejpam-3118	195	7	10	10	NUM
ejpam-3118	195	8	(	(	PUNCT
ejpam-3118	195	9	5	5	NUM
ejpam-3118	195	10	)	)	PUNCT
ejpam-3118	195	11	(	(	PUNCT
ejpam-3118	195	12	2017	2017	NUM
ejpam-3118	195	13	)	)	PUNCT
ejpam-3118	195	14	,	,	PUNCT
ejpam-3118	195	15	955	955	NUM
ejpam-3118	195	16	-	-	SYM
ejpam-3118	195	17	966	966	NUM
ejpam-3118	195	18	963	963	NUM
ejpam-3118	195	19	just	just	ADV
ejpam-3118	195	20	as	as	SCONJ
ejpam-3118	195	21	extend	extend	VERB
ejpam-3118	195	22	the	the	DET
ejpam-3118	195	23	proposition	proposition	NOUN
ejpam-3118	195	24	2	2	NUM
ejpam-3118	195	25	can	can	AUX
ejpam-3118	195	26	also	also	ADV
ejpam-3118	195	27	extend	extend	VERB
ejpam-3118	195	28	the	the	DET
ejpam-3118	195	29	proposition	proposition	NOUN
ejpam-3118	195	30	6	6	NUM
ejpam-3118	195	31	and	and	CCONJ
ejpam-3118	195	32	get	get	VERB
ejpam-3118	195	33	an	an	DET
ejpam-3118	195	34	elementary	elementary	ADJ
ejpam-3118	195	35	q	q	ADJ
ejpam-3118	195	36	-	-	PUNCT
ejpam-3118	195	37	basis	basis	NOUN
ejpam-3118	195	38	matrix	matrix	NOUN
ejpam-3118	195	39	of	of	ADP
ejpam-3118	195	40	qg2	qg2	NOUN
ejpam-3118	195	41	(	(	PUNCT
ejpam-3118	195	42	1−	1−	NUM
ejpam-3118	195	43	s	s	NOUN
ejpam-3118	195	44	2	2	NUM
ejpam-3118	195	45	)	)	PUNCT
ejpam-3118	195	46	∼=	∼=	PROPN
ejpam-3118	195	47	m8(q	m8(q	NOUN
ejpam-3118	195	48	)	)	PUNCT
ejpam-3118	195	49	,	,	PUNCT
ejpam-3118	195	50	that	that	PRON
ejpam-3118	195	51	will	will	AUX
ejpam-3118	195	52	be	be	AUX
ejpam-3118	195	53	used	use	VERB
ejpam-3118	195	54	in	in	ADP
ejpam-3118	195	55	next	next	ADJ
ejpam-3118	195	56	result	result	NOUN
ejpam-3118	195	57	.	.	PUNCT
ejpam-3118	196	1	even	even	ADV
ejpam-3118	196	2	to	to	ADP
ejpam-3118	196	3	the	the	DET
ejpam-3118	196	4	next	next	ADJ
ejpam-3118	196	5	result	result	NOUN
ejpam-3118	196	6	,	,	PUNCT
ejpam-3118	196	7	we	we	PRON
ejpam-3118	196	8	will	will	AUX
ejpam-3118	196	9	need	need	VERB
ejpam-3118	196	10	the	the	DET
ejpam-3118	196	11	following	follow	VERB
ejpam-3118	196	12	definition	definition	NOUN
ejpam-3118	196	13	:	:	PUNCT
ejpam-3118	196	14	definition	definition	NOUN
ejpam-3118	196	15	3	3	X
ejpam-3118	196	16	.	.	PUNCT
ejpam-3118	197	1	let	let	VERB
ejpam-3118	197	2	a	a	PRON
ejpam-3118	197	3	=	=	X
ejpam-3118	197	4	[	[	PUNCT
ejpam-3118	197	5	2(xij	2(xij	NUM
ejpam-3118	197	6	)	)	PUNCT
ejpam-3118	198	1	+	+	NUM
ejpam-3118	198	2	i8	i8	NOUN
ejpam-3118	198	3	]	]	PUNCT
ejpam-3118	198	4	be	be	AUX
ejpam-3118	198	5	a	a	DET
ejpam-3118	198	6	8	8	NUM
ejpam-3118	198	7	-	-	PUNCT
ejpam-3118	198	8	by-8	by-8	NOUN
ejpam-3118	198	9	matrix	matrix	NOUN
ejpam-3118	198	10	with	with	ADP
ejpam-3118	198	11	xij	xij	PROPN
ejpam-3118	198	12	∈	∈	PROPN
ejpam-3118	198	13	z	z	PROPN
ejpam-3118	198	14	,	,	PUNCT
ejpam-3118	198	15	for	for	ADP
ejpam-3118	198	16	all	all	DET
ejpam-3118	198	17	i	i	PROPN
ejpam-3118	198	18	,	,	PUNCT
ejpam-3118	198	19	j	j	PROPN
ejpam-3118	198	20	,	,	PUNCT
ejpam-3118	198	21	1	1	NUM
ejpam-3118	198	22	≤	≤	NUM
ejpam-3118	198	23	i	i	PRON
ejpam-3118	198	24	,	,	PUNCT
ejpam-3118	198	25	j	j	PROPN
ejpam-3118	198	26	≤	≤	ADV
ejpam-3118	198	27	8	8	NUM
ejpam-3118	198	28	.	.	PUNCT
ejpam-3118	199	1	we	we	PRON
ejpam-3118	199	2	define	define	VERB
ejpam-3118	199	3	8	8	NUM
ejpam-3118	199	4	distinct	distinct	ADJ
ejpam-3118	199	5	blocks	block	NOUN
ejpam-3118	199	6	of	of	ADP
ejpam-3118	199	7	a	a	DET
ejpam-3118	199	8	:	:	PUNCT
ejpam-3118	199	9	b1	b1	NOUN
ejpam-3118	199	10	=	=	SYM
ejpam-3118	199	11	{	{	PUNCT
ejpam-3118	199	12	x11	x11	PROPN
ejpam-3118	199	13	,	,	PUNCT
ejpam-3118	199	14	x22	x22	NUM
ejpam-3118	199	15	,	,	PUNCT
ejpam-3118	199	16	x33	x33	PROPN
ejpam-3118	199	17	,	,	PUNCT
ejpam-3118	199	18	x44	x44	PROPN
ejpam-3118	199	19	,	,	PUNCT
ejpam-3118	199	20	x55	x55	PROPN
ejpam-3118	199	21	,	,	PUNCT
ejpam-3118	199	22	x66	x66	PROPN
ejpam-3118	199	23	,	,	PUNCT
ejpam-3118	199	24	x77	x77	PROPN
ejpam-3118	199	25	,	,	PUNCT
ejpam-3118	199	26	x88	x88	PROPN
ejpam-3118	199	27	}	}	PUNCT
ejpam-3118	199	28	,	,	PUNCT
ejpam-3118	199	29	b2	b2	NOUN
ejpam-3118	199	30	=	=	SYM
ejpam-3118	199	31	{	{	PUNCT
ejpam-3118	199	32	x12	x12	PROPN
ejpam-3118	199	33	,	,	PUNCT
ejpam-3118	199	34	x21	x21	PROPN
ejpam-3118	199	35	,	,	PUNCT
ejpam-3118	199	36	x34	x34	NUM
ejpam-3118	199	37	,	,	PUNCT
ejpam-3118	199	38	x43	x43	PROPN
ejpam-3118	199	39	,	,	PUNCT
ejpam-3118	199	40	x56	x56	PROPN
ejpam-3118	199	41	,	,	PUNCT
ejpam-3118	199	42	x65	x65	PROPN
ejpam-3118	199	43	,	,	PUNCT
ejpam-3118	199	44	x78	x78	NUM
ejpam-3118	199	45	,	,	PUNCT
ejpam-3118	199	46	x87	x87	PROPN
ejpam-3118	199	47	}	}	PUNCT
ejpam-3118	199	48	,	,	PUNCT
ejpam-3118	199	49	b3	b3	PROPN
ejpam-3118	199	50	=	=	SYM
ejpam-3118	199	51	{	{	PUNCT
ejpam-3118	199	52	x13	x13	PROPN
ejpam-3118	199	53	,	,	PUNCT
ejpam-3118	199	54	x24	x24	PROPN
ejpam-3118	199	55	,	,	PUNCT
ejpam-3118	199	56	x31	x31	NUM
ejpam-3118	199	57	,	,	PUNCT
ejpam-3118	199	58	x42	x42	NOUN
ejpam-3118	199	59	,	,	PUNCT
ejpam-3118	199	60	x57	x57	NUM
ejpam-3118	199	61	,	,	PUNCT
ejpam-3118	199	62	x68	x68	PROPN
ejpam-3118	199	63	,	,	PUNCT
ejpam-3118	199	64	x75	x75	PROPN
ejpam-3118	199	65	,	,	PUNCT
ejpam-3118	199	66	x86	x86	PROPN
ejpam-3118	199	67	}	}	PUNCT
ejpam-3118	199	68	,	,	PUNCT
ejpam-3118	199	69	b4	b4	NOUN
ejpam-3118	199	70	=	=	SYM
ejpam-3118	199	71	{	{	PUNCT
ejpam-3118	199	72	x14	x14	PROPN
ejpam-3118	199	73	,	,	PUNCT
ejpam-3118	199	74	x23	x23	NUM
ejpam-3118	199	75	,	,	PUNCT
ejpam-3118	199	76	x32	x32	PROPN
ejpam-3118	199	77	,	,	PUNCT
ejpam-3118	199	78	x41	x41	PROPN
ejpam-3118	199	79	,	,	PUNCT
ejpam-3118	199	80	x58	x58	PROPN
ejpam-3118	199	81	,	,	PUNCT
ejpam-3118	199	82	x67	x67	PROPN
ejpam-3118	199	83	,	,	PUNCT
ejpam-3118	199	84	x76	x76	PROPN
ejpam-3118	199	85	,	,	PUNCT
ejpam-3118	199	86	x85	x85	PROPN
ejpam-3118	199	87	}	}	PUNCT
ejpam-3118	199	88	,	,	PUNCT
ejpam-3118	199	89	b5	b5	PROPN
ejpam-3118	199	90	=	=	SYM
ejpam-3118	199	91	{	{	PUNCT
ejpam-3118	199	92	x15	x15	PROPN
ejpam-3118	199	93	,	,	PUNCT
ejpam-3118	199	94	x26	x26	PROPN
ejpam-3118	199	95	,	,	PUNCT
ejpam-3118	199	96	x37	x37	NUM
ejpam-3118	199	97	,	,	PUNCT
ejpam-3118	199	98	x48	x48	NUM
ejpam-3118	199	99	,	,	PUNCT
ejpam-3118	199	100	x51	x51	PROPN
ejpam-3118	199	101	,	,	PUNCT
ejpam-3118	199	102	x62	x62	NOUN
ejpam-3118	199	103	,	,	PUNCT
ejpam-3118	199	104	x73	x73	PROPN
ejpam-3118	199	105	,	,	PUNCT
ejpam-3118	199	106	x84	x84	NOUN
ejpam-3118	199	107	}	}	PUNCT
ejpam-3118	199	108	,	,	PUNCT
ejpam-3118	199	109	b6	b6	NOUN
ejpam-3118	199	110	=	=	SYM
ejpam-3118	199	111	{	{	PUNCT
ejpam-3118	199	112	x16	x16	PROPN
ejpam-3118	199	113	,	,	PUNCT
ejpam-3118	199	114	x25	x25	NUM
ejpam-3118	199	115	,	,	PUNCT
ejpam-3118	199	116	x38	x38	NOUN
ejpam-3118	199	117	,	,	PUNCT
ejpam-3118	199	118	x47	x47	PROPN
ejpam-3118	199	119	,	,	PUNCT
ejpam-3118	199	120	x52	x52	PROPN
ejpam-3118	199	121	,	,	PUNCT
ejpam-3118	199	122	x61	x61	PROPN
ejpam-3118	199	123	,	,	PUNCT
ejpam-3118	199	124	x74	x74	PROPN
ejpam-3118	199	125	,	,	PUNCT
ejpam-3118	199	126	x83	x83	PROPN
ejpam-3118	199	127	}	}	PUNCT
ejpam-3118	199	128	,	,	PUNCT
ejpam-3118	199	129	b7	b7	PROPN
ejpam-3118	199	130	=	=	PUNCT
ejpam-3118	199	131	{	{	PUNCT
ejpam-3118	199	132	x17	x17	PROPN
ejpam-3118	199	133	,	,	PUNCT
ejpam-3118	199	134	x28	x28	PROPN
ejpam-3118	199	135	,	,	PUNCT
ejpam-3118	199	136	x35	x35	NOUN
ejpam-3118	199	137	,	,	PUNCT
ejpam-3118	199	138	x46	x46	PROPN
ejpam-3118	199	139	,	,	PUNCT
ejpam-3118	199	140	x53	x53	NOUN
ejpam-3118	199	141	,	,	PUNCT
ejpam-3118	199	142	x64	x64	PROPN
ejpam-3118	199	143	,	,	PUNCT
ejpam-3118	199	144	x71	x71	NOUN
ejpam-3118	199	145	,	,	PUNCT
ejpam-3118	199	146	x82	x82	PUNCT
ejpam-3118	199	147	}	}	PUNCT
ejpam-3118	199	148	,	,	PUNCT
ejpam-3118	199	149	b8	b8	PROPN
ejpam-3118	199	150	=	=	SYM
ejpam-3118	199	151	{	{	PUNCT
ejpam-3118	199	152	x18	x18	NOUN
ejpam-3118	199	153	,	,	PUNCT
ejpam-3118	199	154	x27	x27	PROPN
ejpam-3118	199	155	,	,	PUNCT
ejpam-3118	199	156	x36	x36	NUM
ejpam-3118	199	157	,	,	PUNCT
ejpam-3118	199	158	x45	x45	PROPN
ejpam-3118	199	159	,	,	PUNCT
ejpam-3118	199	160	x54	x54	PROPN
ejpam-3118	199	161	,	,	PUNCT
ejpam-3118	199	162	x63	x63	NUM
ejpam-3118	199	163	,	,	PUNCT
ejpam-3118	199	164	x72	x72	NUM
ejpam-3118	199	165	,	,	PUNCT
ejpam-3118	199	166	x81	x81	PROPN
ejpam-3118	199	167	}	}	PUNCT
ejpam-3118	199	168	.	.	PUNCT
ejpam-3118	200	1	in	in	ADP
ejpam-3118	200	2	particular	particular	ADJ
ejpam-3118	200	3	,	,	PUNCT
ejpam-3118	200	4	bk	bk	PROPN
ejpam-3118	200	5	=	=	PUNCT
ejpam-3118	200	6	{	{	PUNCT
ejpam-3118	200	7	xiji	xiji	NOUN
ejpam-3118	200	8	|	|	ADV
ejpam-3118	200	9	1	1	NUM
ejpam-3118	200	10	≤	≤	NUM
ejpam-3118	200	11	i	i	PRON
ejpam-3118	200	12	≤	≤	NOUN
ejpam-3118	200	13	8	8	NUM
ejpam-3118	200	14	and	and	CCONJ
ejpam-3118	200	15	ji	ji	PROPN
ejpam-3118	201	1	6=	6=	PROPN
ejpam-3118	201	2	ji′	ji′	ADV
ejpam-3118	201	3	,	,	PUNCT
ejpam-3118	201	4	if	if	SCONJ
ejpam-3118	201	5	i	i	PRON
ejpam-3118	201	6	6=	6=	ADP
ejpam-3118	201	7	i′	i′	NOUN
ejpam-3118	201	8	}	}	PUNCT
ejpam-3118	201	9	,	,	PUNCT
ejpam-3118	201	10	1	1	NUM
ejpam-3118	201	11	≤	≤	NUM
ejpam-3118	201	12	k	k	X
ejpam-3118	201	13	≤	≤	NUM
ejpam-3118	201	14	8	8	NUM
ejpam-3118	201	15	.	.	PUNCT
ejpam-3118	202	1	finally	finally	ADV
ejpam-3118	202	2	,	,	PUNCT
ejpam-3118	202	3	with	with	ADP
ejpam-3118	202	4	the	the	DET
ejpam-3118	202	5	same	same	ADJ
ejpam-3118	202	6	idea	idea	NOUN
ejpam-3118	202	7	that	that	SCONJ
ejpam-3118	202	8	we	we	PRON
ejpam-3118	202	9	use	use	VERB
ejpam-3118	202	10	to	to	PART
ejpam-3118	202	11	extend	extend	VERB
ejpam-3118	202	12	the	the	DET
ejpam-3118	202	13	theorem	theorem	NOUN
ejpam-3118	202	14	1	1	NUM
ejpam-3118	202	15	,	,	PUNCT
ejpam-3118	202	16	extend	extend	VERB
ejpam-3118	202	17	the	the	DET
ejpam-3118	202	18	theorem	theorem	NOUN
ejpam-3118	202	19	2	2	NUM
ejpam-3118	202	20	and	and	CCONJ
ejpam-3118	202	21	describe	describe	VERB
ejpam-3118	202	22	completly	completly	ADV
ejpam-3118	202	23	u(zg2	u(zg2	PRON
ejpam-3118	202	24	):	):	PUNCT
ejpam-3118	202	25	theorem	theorem	ADJ
ejpam-3118	202	26	3	3	X
ejpam-3118	202	27	.	.	PUNCT
ejpam-3118	203	1	let	let	VERB
ejpam-3118	203	2	g2	g2	PROPN
ejpam-3118	203	3	=	=	PUNCT
ejpam-3118	204	1	d	d	PRON
ejpam-3118	204	2	×	×	NOUN
ejpam-3118	204	3	d1	d1	PROPN
ejpam-3118	204	4	×	×	PROPN
ejpam-3118	204	5	d2	d2	PROPN
ejpam-3118	204	6	/	/	SYM
ejpam-3118	204	7	{	{	PUNCT
ejpam-3118	204	8	1	1	PROPN
ejpam-3118	204	9	,	,	PUNCT
ejpam-3118	204	10	ss1	ss1	PROPN
ejpam-3118	204	11	,	,	PUNCT
ejpam-3118	204	12	ss2	ss2	PROPN
ejpam-3118	204	13	,	,	PUNCT
ejpam-3118	204	14	s1s2	s1s2	PROPN
ejpam-3118	204	15	}	}	PUNCT
ejpam-3118	204	16	be	be	AUX
ejpam-3118	204	17	the	the	DET
ejpam-3118	204	18	extra	extra	ADJ
ejpam-3118	204	19	-	-	ADJ
ejpam-3118	204	20	special	special	ADJ
ejpam-3118	204	21	2	2	NUM
ejpam-3118	204	22	-	-	PUNCT
ejpam-3118	204	23	group	group	NOUN
ejpam-3118	204	24	of	of	ADP
ejpam-3118	204	25	order	order	NOUN
ejpam-3118	204	26	128	128	NUM
ejpam-3118	204	27	,	,	PUNCT
ejpam-3118	204	28	the	the	DET
ejpam-3118	204	29	central	central	ADJ
ejpam-3118	204	30	product	product	NOUN
ejpam-3118	204	31	of	of	ADP
ejpam-3118	204	32	three	three	NUM
ejpam-3118	204	33	copies	copy	NOUN
ejpam-3118	204	34	of	of	ADP
ejpam-3118	204	35	d4	d4	PROPN
ejpam-3118	204	36	=	=	SYM
ejpam-3118	204	37	〈	〈	PROPN
ejpam-3118	204	38	b	b	PROPN
ejpam-3118	204	39	,	,	PUNCT
ejpam-3118	204	40	v|	v|	NOUN
ejpam-3118	204	41	b2	b2	NOUN
ejpam-3118	204	42	=	=	SYM
ejpam-3118	204	43	v4	v4	NOUN
ejpam-3118	204	44	=	=	SYM
ejpam-3118	204	45	1	1	NUM
ejpam-3118	204	46	and	and	CCONJ
ejpam-3118	204	47	bvbv	bvbv	NOUN
ejpam-3118	204	48	=	=	SYM
ejpam-3118	204	49	1	1	NUM
ejpam-3118	204	50	〉	〉	NOUN
ejpam-3118	204	51	.	.	PUNCT
ejpam-3118	205	1	then	then	ADV
ejpam-3118	205	2	u(zg2	u(zg2	PRON
ejpam-3118	205	3	)	)	PUNCT
ejpam-3118	205	4	=	=	SYM
ejpam-3118	205	5	±g2v2	±g2v2	NOUN
ejpam-3118	205	6	and	and	CCONJ
ejpam-3118	205	7	v2	v2	NOUN
ejpam-3118	205	8	is	be	AUX
ejpam-3118	205	9	isomorphic	isomorphic	ADJ
ejpam-3118	205	10	to	to	ADP
ejpam-3118	205	11	the	the	DET
ejpam-3118	205	12	group	group	NOUN
ejpam-3118	205	13	[	[	PUNCT
ejpam-3118	205	14	2(xij	2(xij	NUM
ejpam-3118	205	15	)	)	PUNCT
ejpam-3118	206	1	+	+	NUM
ejpam-3118	206	2	i8	i8	NOUN
ejpam-3118	206	3	]	]	PUNCT
ejpam-3118	206	4	det=1	det=1	NOUN
ejpam-3118	206	5	of	of	ADP
ejpam-3118	206	6	8	8	NUM
ejpam-3118	206	7	-	-	PUNCT
ejpam-3118	206	8	by-8	by-8	NOUN
ejpam-3118	206	9	matrices	matrix	NOUN
ejpam-3118	206	10	,	,	PUNCT
ejpam-3118	206	11	where	where	SCONJ
ejpam-3118	206	12	,	,	PUNCT
ejpam-3118	206	13	for	for	ADP
ejpam-3118	206	14	each	each	DET
ejpam-3118	206	15	k	k	NOUN
ejpam-3118	206	16	,	,	PUNCT
ejpam-3118	206	17	1	1	NUM
ejpam-3118	206	18	≤	≤	NUM
ejpam-3118	207	1	k	k	X
ejpam-3118	207	2	≤	≤	NUM
ejpam-3118	207	3	8	8	NUM
ejpam-3118	207	4	,	,	PUNCT
ejpam-3118	207	5	the	the	DET
ejpam-3118	207	6	integers	integer	NOUN
ejpam-3118	207	7	xiji	xiji	VERB
ejpam-3118	207	8	∈	∈	PROPN
ejpam-3118	207	9	bk	bk	NOUN
ejpam-3118	207	10	satisfy	satisfy	VERB
ejpam-3118	207	11	the	the	DET
ejpam-3118	207	12	following	follow	VERB
ejpam-3118	207	13	conditions	condition	NOUN
ejpam-3118	207	14	:	:	PUNCT
ejpam-3118	207	15	(	(	PUNCT
ejpam-3118	207	16	i	i	NOUN
ejpam-3118	207	17	)	)	PUNCT
ejpam-3118	207	18	all	all	DET
ejpam-3118	207	19	integers	integer	NOUN
ejpam-3118	207	20	xiji	xiji	VERB
ejpam-3118	207	21	,	,	PUNCT
ejpam-3118	207	22	1	1	NUM
ejpam-3118	207	23	≤	≤	NUM
ejpam-3118	207	24	i	i	PRON
ejpam-3118	207	25	≤	≤	NOUN
ejpam-3118	207	26	8	8	NUM
ejpam-3118	207	27	,	,	PUNCT
ejpam-3118	207	28	have	have	VERB
ejpam-3118	207	29	the	the	DET
ejpam-3118	207	30	same	same	ADJ
ejpam-3118	207	31	parity	parity	NOUN
ejpam-3118	207	32	;	;	PUNCT
ejpam-3118	207	33	(	(	PUNCT
ejpam-3118	207	34	ii	ii	NOUN
ejpam-3118	207	35	)	)	PUNCT
ejpam-3118	207	36	4	4	NUM
ejpam-3118	207	37	divides	divide	VERB
ejpam-3118	207	38	the	the	DET
ejpam-3118	207	39	sums	sum	NOUN
ejpam-3118	207	40	x1j1	x1j1	PUNCT
ejpam-3118	208	1	+	+	NOUN
ejpam-3118	208	2	x2j2	x2j2	PROPN
ejpam-3118	209	1	+	+	ADJ
ejpam-3118	209	2	x3j3	x3j3	PROPN
ejpam-3118	210	1	+	+	ADJ
ejpam-3118	210	2	x4j4	x4j4	PROPN
ejpam-3118	210	3	and	and	CCONJ
ejpam-3118	210	4	x5j5	x5j5	PUNCT
ejpam-3118	211	1	+	+	NOUN
ejpam-3118	211	2	x6j6	x6j6	X
ejpam-3118	211	3	+	+	NOUN
ejpam-3118	211	4	x7j7	x7j7	PUNCT
ejpam-3118	211	5	+	+	NOUN
ejpam-3118	211	6	x8j8	x8j8	X
ejpam-3118	211	7	;	;	PUNCT
ejpam-3118	211	8	(	(	PUNCT
ejpam-3118	211	9	iii	iii	X
ejpam-3118	211	10	)	)	PUNCT
ejpam-3118	211	11	if	if	SCONJ
ejpam-3118	211	12	x1j1	x1j1	PRON
ejpam-3118	211	13	and	and	CCONJ
ejpam-3118	211	14	x(1+k)j(1+k	x(1+k)j(1+k	NUM
ejpam-3118	211	15	)	)	PUNCT
ejpam-3118	211	16	,	,	PUNCT
ejpam-3118	211	17	1	1	NUM
ejpam-3118	211	18	≤	≤	NUM
ejpam-3118	211	19	k	k	X
ejpam-3118	211	20	≤	≤	NUM
ejpam-3118	211	21	3	3	NUM
ejpam-3118	211	22	,	,	PUNCT
ejpam-3118	211	23	are	be	AUX
ejpam-3118	211	24	congruentes	congruente	NOUN
ejpam-3118	211	25	module	module	NOUN
ejpam-3118	211	26	4	4	NUM
ejpam-3118	211	27	,	,	PUNCT
ejpam-3118	211	28	then	then	ADV
ejpam-3118	211	29	x5j5	x5j5	PROPN
ejpam-3118	211	30	e	e	PROPN
ejpam-3118	211	31	x(5+k)j(5+k	x(5+k)j(5+k	PROPN
ejpam-3118	211	32	)	)	PUNCT
ejpam-3118	211	33	also	also	ADV
ejpam-3118	211	34	are	be	AUX
ejpam-3118	211	35	;	;	PUNCT
ejpam-3118	211	36	(	(	PUNCT
ejpam-3118	211	37	iv	iv	X
ejpam-3118	211	38	)	)	PUNCT
ejpam-3118	211	39	8	8	NUM
ejpam-3118	211	40	divides	divide	VERB
ejpam-3118	211	41	the	the	DET
ejpam-3118	211	42	sum	sum	NOUN
ejpam-3118	211	43	x1j1	x1j1	PUNCT
ejpam-3118	212	1	+	+	ADJ
ejpam-3118	212	2	x2j2	x2j2	PROPN
ejpam-3118	213	1	+	+	ADJ
ejpam-3118	213	2	x3j3	x3j3	PROPN
ejpam-3118	214	1	+	+	ADJ
ejpam-3118	214	2	x4j4	x4j4	X
ejpam-3118	215	1	+	+	ADJ
ejpam-3118	215	2	x5j5	x5j5	ADJ
ejpam-3118	215	3	+	+	ADJ
ejpam-3118	215	4	x6j6	x6j6	X
ejpam-3118	215	5	+	+	NOUN
ejpam-3118	215	6	x7j7	x7j7	PROPN
ejpam-3118	215	7	+	+	NOUN
ejpam-3118	215	8	x8j8	x8j8	X
ejpam-3118	215	9	.	.	PUNCT
ejpam-3118	215	10	proof	proof	NOUN
ejpam-3118	215	11	.	.	PUNCT
ejpam-3118	216	1	by	by	ADP
ejpam-3118	216	2	proposition	proposition	NOUN
ejpam-3118	216	3	3	3	NUM
ejpam-3118	216	4	,	,	PUNCT
ejpam-3118	216	5	u(zg2	u(zg2	NOUN
ejpam-3118	216	6	)	)	PUNCT
ejpam-3118	216	7	=	=	SYM
ejpam-3118	216	8	±g2v2	±g2v2	PROPN
ejpam-3118	216	9	,	,	PUNCT
ejpam-3118	216	10	where	where	SCONJ
ejpam-3118	216	11	v2	v2	VERB
ejpam-3118	216	12	∼=	∼=	NOUN
ejpam-3118	216	13	u2	u2	NOUN
ejpam-3118	216	14	/	/	SYM
ejpam-3118	216	15	g	g	NOUN
ejpam-3118	216	16	′	′	NUM
ejpam-3118	216	17	2	2	NUM
ejpam-3118	216	18	and	and	CCONJ
ejpam-3118	216	19	u2	u2	PROPN
ejpam-3118	216	20	=	=	PUNCT
ejpam-3118	216	21	u(zg2	u(zg2	NOUN
ejpam-3118	216	22	)	)	PUNCT
ejpam-3118	216	23	∩	∩	NOUN
ejpam-3118	216	24	(	(	PUNCT
ejpam-3118	216	25	qg2	qg2	NOUN
ejpam-3118	216	26	(	(	PUNCT
ejpam-3118	216	27	1−	1−	NUM
ejpam-3118	216	28	s	s	NOUN
ejpam-3118	216	29	2	2	NUM
ejpam-3118	216	30	)	)	PUNCT
ejpam-3118	216	31	+	+	CCONJ
ejpam-3118	216	32	(	(	PUNCT
ejpam-3118	216	33	1	1	NUM
ejpam-3118	216	34	+	+	SYM
ejpam-3118	216	35	s	s	NOUN
ejpam-3118	216	36	2	2	NUM
ejpam-3118	216	37	)	)	PUNCT
ejpam-3118	216	38	)	)	PUNCT
ejpam-3118	217	1	=	=	PUNCT
ejpam-3118	217	2	=	=	PRON
ejpam-3118	217	3	{	{	PUNCT
ejpam-3118	217	4	u	u	NOUN
ejpam-3118	217	5	=	=	NOUN
ejpam-3118	217	6	1	1	NUM
ejpam-3118	217	7	+	+	NUM
ejpam-3118	217	8	α(1−	α(1−	PROPN
ejpam-3118	217	9	s)|u	s)|u	PROPN
ejpam-3118	217	10	∈	∈	PROPN
ejpam-3118	217	11	u(zg2	u(zg2	PROPN
ejpam-3118	217	12	)	)	PUNCT
ejpam-3118	217	13	,	,	PUNCT
ejpam-3118	217	14	α	α	PROPN
ejpam-3118	217	15	∈	∈	PROPN
ejpam-3118	217	16	zg2	zg2	NOUN
ejpam-3118	217	17	}	}	PUNCT
ejpam-3118	217	18	.	.	PUNCT
ejpam-3118	218	1	thus	thus	ADV
ejpam-3118	218	2	,	,	PUNCT
ejpam-3118	218	3	to	to	PART
ejpam-3118	218	4	describe	describe	VERB
ejpam-3118	218	5	u(zg2	u(zg2	PRON
ejpam-3118	218	6	)	)	PUNCT
ejpam-3118	218	7	we	we	PRON
ejpam-3118	218	8	need	need	VERB
ejpam-3118	218	9	a	a	DET
ejpam-3118	218	10	complet	complet	NOUN
ejpam-3118	218	11	description	description	NOUN
ejpam-3118	218	12	of	of	ADP
ejpam-3118	218	13	v2	v2	PROPN
ejpam-3118	218	14	∼=	∼=	PROPN
ejpam-3118	218	15	u2	u2	NOUN
ejpam-3118	218	16	/	/	SYM
ejpam-3118	218	17	g	g	NOUN
ejpam-3118	218	18	′	′	NUM
ejpam-3118	218	19	2	2	NUM
ejpam-3118	218	20	of	of	ADP
ejpam-3118	218	21	the	the	DET
ejpam-3118	218	22	u2	u2	NOUN
ejpam-3118	218	23	,	,	PUNCT
ejpam-3118	218	24	that	that	ADV
ejpam-3118	218	25	is	is	ADV
ejpam-3118	218	26	,	,	PUNCT
ejpam-3118	218	27	we	we	PRON
ejpam-3118	218	28	need	need	VERB
ejpam-3118	218	29	to	to	PART
ejpam-3118	218	30	describe	describe	VERB
ejpam-3118	218	31	completly	completly	ADV
ejpam-3118	218	32	the	the	DET
ejpam-3118	218	33	subgroup	subgroup	NOUN
ejpam-3118	218	34	u2	u2	NOUN
ejpam-3118	218	35	of	of	ADP
ejpam-3118	218	36	the	the	DET
ejpam-3118	218	37	u(zg2	u(zg2	NOUN
ejpam-3118	218	38	)	)	PUNCT
ejpam-3118	218	39	.	.	PUNCT
ejpam-3118	219	1	c.	c.	PROPN
ejpam-3118	219	2	mello	mello	PROPN
ejpam-3118	219	3	/	/	SYM
ejpam-3118	219	4	eur	eur	PROPN
ejpam-3118	219	5	.	.	PUNCT
ejpam-3118	220	1	j.	j.	PROPN
ejpam-3118	220	2	pure	pure	PROPN
ejpam-3118	220	3	appl	appl	PROPN
ejpam-3118	220	4	.	.	PROPN
ejpam-3118	220	5	math	math	PROPN
ejpam-3118	220	6	,	,	PUNCT
ejpam-3118	220	7	10	10	NUM
ejpam-3118	220	8	(	(	PUNCT
ejpam-3118	220	9	5	5	NUM
ejpam-3118	220	10	)	)	PUNCT
ejpam-3118	220	11	(	(	PUNCT
ejpam-3118	220	12	2017	2017	NUM
ejpam-3118	220	13	)	)	PUNCT
ejpam-3118	220	14	,	,	PUNCT
ejpam-3118	220	15	955	955	NUM
ejpam-3118	220	16	-	-	SYM
ejpam-3118	220	17	966	966	NUM
ejpam-3118	220	18	964	964	NUM
ejpam-3118	220	19	let	let	VERB
ejpam-3118	220	20	u	u	PRON
ejpam-3118	220	21	∈	∈	PROPN
ejpam-3118	220	22	u2	u2	PROPN
ejpam-3118	220	23	.	.	PUNCT
ejpam-3118	221	1	then	then	ADV
ejpam-3118	221	2	,	,	PUNCT
ejpam-3118	221	3	by	by	ADP
ejpam-3118	221	4	proposition	proposition	NOUN
ejpam-3118	221	5	3	3	NUM
ejpam-3118	221	6	and	and	CCONJ
ejpam-3118	221	7	writing	write	VERB
ejpam-3118	221	8	e	e	NOUN
ejpam-3118	221	9	=	=	SYM
ejpam-3118	221	10	1−	1−	NUM
ejpam-3118	221	11	s	s	NOUN
ejpam-3118	221	12	2	2	NUM
ejpam-3118	221	13	,	,	PUNCT
ejpam-3118	221	14	u	u	NOUN
ejpam-3118	221	15	=	=	NOUN
ejpam-3118	221	16	1	1	NUM
ejpam-3118	221	17	+	+	CCONJ
ejpam-3118	221	18	α(1	α(1	PROPN
ejpam-3118	221	19	−	−	PROPN
ejpam-3118	221	20	s	s	PART
ejpam-3118	221	21	)	)	PUNCT
ejpam-3118	221	22	=	=	SYM
ejpam-3118	222	1	1	1	NUM
ejpam-3118	222	2	+	+	NUM
ejpam-3118	222	3	2(α1	2(α1	NUM
ejpam-3118	222	4	+	+	CCONJ
ejpam-3118	222	5	α2	α2	PROPN
ejpam-3118	222	6	b	b	PROPN
ejpam-3118	223	1	+	+	NUM
ejpam-3118	223	2	α3	α3	NOUN
ejpam-3118	223	3	v	v	NOUN
ejpam-3118	223	4	+	+	NUM
ejpam-3118	223	5	α4	α4	NOUN
ejpam-3118	223	6	b1	b1	NOUN
ejpam-3118	223	7	+	+	CCONJ
ejpam-3118	223	8	α5	α5	PROPN
ejpam-3118	223	9	v1	v1	NOUN
ejpam-3118	223	10	+	+	CCONJ
ejpam-3118	223	11	α6	α6	NOUN
ejpam-3118	223	12	b2	b2	NOUN
ejpam-3118	223	13	+	+	CCONJ
ejpam-3118	223	14	α7	α7	NOUN
ejpam-3118	223	15	v2	v2	NOUN
ejpam-3118	223	16	+	+	NUM
ejpam-3118	223	17	α8	α8	PROPN
ejpam-3118	223	18	u	u	NOUN
ejpam-3118	223	19	+	+	CCONJ
ejpam-3118	223	20	α9	α9	NOUN
ejpam-3118	223	21	u1	u1	NOUN
ejpam-3118	223	22	+	+	CCONJ
ejpam-3118	223	23	+	+	ADJ
ejpam-3118	223	24	α10	α10	ADJ
ejpam-3118	223	25	u2	u2	NOUN
ejpam-3118	223	26	+	+	CCONJ
ejpam-3118	223	27	α11	α11	NOUN
ejpam-3118	223	28	bb1	bb1	NOUN
ejpam-3118	223	29	+	+	CCONJ
ejpam-3118	223	30	α12	α12	ADJ
ejpam-3118	223	31	bu1	bu1	NOUN
ejpam-3118	223	32	+	+	CCONJ
ejpam-3118	223	33	α13	α13	NUM
ejpam-3118	223	34	bv1	bv1	NOUN
ejpam-3118	223	35	+	+	CCONJ
ejpam-3118	223	36	α14	α14	PROPN
ejpam-3118	223	37	ub1	ub1	PROPN
ejpam-3118	224	1	+	+	PROPN
ejpam-3118	224	2	α15	α15	NOUN
ejpam-3118	224	3	uu1	uu1	ADP
ejpam-3118	224	4	+	+	CCONJ
ejpam-3118	224	5	α16	α16	VERB
ejpam-3118	224	6	uv1	uv1	NOUN
ejpam-3118	224	7	+	+	CCONJ
ejpam-3118	224	8	α17	α17	NOUN
ejpam-3118	224	9	vb1	vb1	NOUN
ejpam-3118	224	10	+	+	CCONJ
ejpam-3118	224	11	α18	α18	NOUN
ejpam-3118	224	12	vu1	vu1	NOUN
ejpam-3118	224	13	+	+	CCONJ
ejpam-3118	224	14	α19	α19	VERB
ejpam-3118	224	15	vv1	vv1	NOUN
ejpam-3118	225	1	+	+	CCONJ
ejpam-3118	225	2	+	+	ADJ
ejpam-3118	225	3	α20	α20	NOUN
ejpam-3118	225	4	bb2	bb2	NOUN
ejpam-3118	225	5	+	+	CCONJ
ejpam-3118	225	6	α21	α21	PROPN
ejpam-3118	225	7	bu2	bu2	X
ejpam-3118	225	8	+	+	CCONJ
ejpam-3118	225	9	α22	α22	NUM
ejpam-3118	225	10	bv2	bv2	NOUN
ejpam-3118	225	11	+	+	CCONJ
ejpam-3118	225	12	α23	α23	NOUN
ejpam-3118	225	13	ub2	ub2	NOUN
ejpam-3118	225	14	+	+	CCONJ
ejpam-3118	225	15	α24	α24	NUM
ejpam-3118	225	16	uu2	uu2	ADJ
ejpam-3118	225	17	+	+	CCONJ
ejpam-3118	225	18	α25	α25	NUM
ejpam-3118	225	19	uv2	uv2	ADJ
ejpam-3118	226	1	+	+	CCONJ
ejpam-3118	226	2	α26	α26	NOUN
ejpam-3118	226	3	vb2	vb2	VERB
ejpam-3118	226	4	+	+	CCONJ
ejpam-3118	226	5	α27	α27	VERB
ejpam-3118	226	6	vu2	vu2	X
ejpam-3118	226	7	+	+	NUM
ejpam-3118	226	8	α28	α28	NOUN
ejpam-3118	226	9	vv2	vv2	NOUN
ejpam-3118	226	10	+	+	CCONJ
ejpam-3118	226	11	+	+	ADJ
ejpam-3118	226	12	α29	α29	ADJ
ejpam-3118	226	13	b1b2	b1b2	NOUN
ejpam-3118	227	1	+	+	NUM
ejpam-3118	227	2	α30	α30	PROPN
ejpam-3118	227	3	b1u2	b1u2	NOUN
ejpam-3118	227	4	+	+	NOUN
ejpam-3118	227	5	α31	α31	NOUN
ejpam-3118	227	6	b1v2	b1v2	X
ejpam-3118	227	7	+	+	CCONJ
ejpam-3118	227	8	α32	α32	NUM
ejpam-3118	227	9	u1b2	u1b2	ADP
ejpam-3118	227	10	+	+	X
ejpam-3118	227	11	α33	α33	NOUN
ejpam-3118	227	12	u1u2	u1u2	X
ejpam-3118	227	13	+	+	X
ejpam-3118	227	14	α34	α34	PROPN
ejpam-3118	227	15	u1v2	u1v2	PUNCT
ejpam-3118	227	16	+	+	CCONJ
ejpam-3118	227	17	α35	α35	NUM
ejpam-3118	227	18	v1b2	v1b2	PUNCT
ejpam-3118	228	1	+	+	NOUN
ejpam-3118	228	2	α36	α36	NUM
ejpam-3118	228	3	v1u2	v1u2	X
ejpam-3118	229	1	+	+	NOUN
ejpam-3118	229	2	+	+	ADJ
ejpam-3118	229	3	α37	α37	NOUN
ejpam-3118	229	4	v1v2	v1v2	X
ejpam-3118	229	5	+	+	ADJ
ejpam-3118	229	6	α38	α38	NOUN
ejpam-3118	229	7	bb1b2	bb1b2	ADJ
ejpam-3118	229	8	+	+	NOUN
ejpam-3118	229	9	α39	α39	NOUN
ejpam-3118	229	10	bb1u2	bb1u2	NOUN
ejpam-3118	229	11	+	+	PROPN
ejpam-3118	229	12	α40	α40	NOUN
ejpam-3118	229	13	bb1v2	bb1v2	NOUN
ejpam-3118	230	1	+	+	NOUN
ejpam-3118	230	2	α41	α41	NOUN
ejpam-3118	230	3	bu1b2	bu1b2	PROPN
ejpam-3118	230	4	+	+	ADJ
ejpam-3118	230	5	α42	α42	ADJ
ejpam-3118	230	6	bu1u2	bu1u2	NOUN
ejpam-3118	230	7	+	+	PUNCT
ejpam-3118	230	8	α43	α43	ADJ
ejpam-3118	230	9	bu1v2++α44	bu1v2++α44	ADJ
ejpam-3118	230	10	bv1b2+α45	bv1b2+α45	NOUN
ejpam-3118	230	11	bv1u2+α46	bv1u2+α46	NOUN
ejpam-3118	230	12	bv1v2+α47	bv1v2+α47	NOUN
ejpam-3118	230	13	ub1b2+α48	ub1b2+α48	NOUN
ejpam-3118	230	14	ub1u2+α49	ub1u2+α49	VERB
ejpam-3118	230	15	ub1v2+α50	ub1v2+α50	PROPN
ejpam-3118	230	16	uu1b2	uu1b2	PROPN
ejpam-3118	230	17	+	+	PROPN
ejpam-3118	230	18	+	+	ADJ
ejpam-3118	230	19	α51	α51	NUM
ejpam-3118	230	20	uu1u2	uu1u2	PUNCT
ejpam-3118	230	21	+	+	NUM
ejpam-3118	230	22	α52	α52	NOUN
ejpam-3118	230	23	uu1v2	uu1v2	X
ejpam-3118	230	24	+	+	CCONJ
ejpam-3118	230	25	α53	α53	ADJ
ejpam-3118	230	26	uv1b2	uv1b2	PROPN
ejpam-3118	230	27	+	+	CCONJ
ejpam-3118	230	28	α54	α54	PROPN
ejpam-3118	230	29	uv1u2	uv1u2	NOUN
ejpam-3118	230	30	+	+	CCONJ
ejpam-3118	230	31	α55	α55	PROPN
ejpam-3118	230	32	uv1v2	uv1v2	X
ejpam-3118	230	33	+	+	CCONJ
ejpam-3118	230	34	α56	α56	NOUN
ejpam-3118	230	35	vb1b2	vb1b2	NOUN
ejpam-3118	230	36	+	+	NUM
ejpam-3118	230	37	α57	α57	ADJ
ejpam-3118	230	38	vb1u2	vb1u2	PROPN
ejpam-3118	230	39	+	+	CCONJ
ejpam-3118	230	40	+	+	ADJ
ejpam-3118	230	41	α58	α58	ADJ
ejpam-3118	230	42	vb1v2	vb1v2	NOUN
ejpam-3118	230	43	+	+	CCONJ
ejpam-3118	230	44	α59	α59	NOUN
ejpam-3118	230	45	vu1b2	vu1b2	PROPN
ejpam-3118	230	46	+	+	CCONJ
ejpam-3118	230	47	α60	α60	ADJ
ejpam-3118	230	48	vu1u2	vu1u2	PROPN
ejpam-3118	230	49	+	+	PUNCT
ejpam-3118	230	50	α61	α61	NOUN
ejpam-3118	230	51	vu1v2	vu1v2	NOUN
ejpam-3118	230	52	+	+	CCONJ
ejpam-3118	230	53	α62	α62	NUM
ejpam-3118	230	54	vv1b2	vv1b2	PROPN
ejpam-3118	230	55	+	+	NUM
ejpam-3118	230	56	α63	α63	PROPN
ejpam-3118	231	1	vv1u2	vv1u2	PROPN
ejpam-3118	231	2	+	+	CCONJ
ejpam-3118	231	3	α64	α64	PROPN
ejpam-3118	231	4	vv1v2)e	vv1v2)e	PROPN
ejpam-3118	231	5	.	.	PUNCT
ejpam-3118	232	1	the	the	DET
ejpam-3118	232	2	proposition	proposition	NOUN
ejpam-3118	232	3	7	7	NUM
ejpam-3118	232	4	gives	give	VERB
ejpam-3118	232	5	qg2(e	qg2(e	ADV
ejpam-3118	232	6	)	)	PUNCT
ejpam-3118	232	7	∼=	∼=	PART
ejpam-3118	232	8	m8(q	m8(q	NOUN
ejpam-3118	232	9	)	)	PUNCT
ejpam-3118	232	10	and	and	CCONJ
ejpam-3118	232	11	using	use	VERB
ejpam-3118	232	12	the	the	DET
ejpam-3118	232	13	elementary	elementary	ADJ
ejpam-3118	232	14	matrix	matrix	NOUN
ejpam-3118	232	15	basis	basis	NOUN
ejpam-3118	232	16	of	of	ADP
ejpam-3118	232	17	qg1(e	qg1(e	NOUN
ejpam-3118	232	18	)	)	PUNCT
ejpam-3118	232	19	∼=	∼=	PART
ejpam-3118	232	20	m8(q	m8(q	NOUN
ejpam-3118	232	21	)	)	PUNCT
ejpam-3118	232	22	and	and	CCONJ
ejpam-3118	232	23	the	the	DET
ejpam-3118	232	24	give	give	NOUN
ejpam-3118	232	25	representation	representation	NOUN
ejpam-3118	232	26	of	of	ADP
ejpam-3118	232	27	g2	g2	PROPN
ejpam-3118	232	28	in	in	ADP
ejpam-3118	232	29	m8(q	m8(q	NOUN
ejpam-3118	232	30	)	)	PUNCT
ejpam-3118	232	31	,	,	PUNCT
ejpam-3118	232	32	u	u	NOUN
ejpam-3118	232	33	can	can	AUX
ejpam-3118	232	34	be	be	AUX
ejpam-3118	232	35	written	write	VERB
ejpam-3118	232	36	as	as	ADP
ejpam-3118	232	37	an	an	DET
ejpam-3118	232	38	integral	integral	ADJ
ejpam-3118	232	39	invertible	invertible	ADJ
ejpam-3118	232	40	matrix	matrix	NOUN
ejpam-3118	232	41	[	[	X
ejpam-3118	232	42	uij	uij	X
ejpam-3118	232	43	]	]	PUNCT
ejpam-3118	232	44	,	,	PUNCT
ejpam-3118	232	45	1	1	NUM
ejpam-3118	232	46	≤	≤	X
ejpam-3118	232	47	i	i	PRON
ejpam-3118	232	48	,	,	PUNCT
ejpam-3118	232	49	j	j	PROPN
ejpam-3118	232	50	≤	≤	ADV
ejpam-3118	232	51	8	8	NUM
ejpam-3118	232	52	.	.	PUNCT
ejpam-3118	233	1	thus	thus	ADV
ejpam-3118	233	2	we	we	PRON
ejpam-3118	233	3	produce	produce	VERB
ejpam-3118	233	4	the	the	DET
ejpam-3118	233	5	monomorphism	monomorphism	NOUN
ejpam-3118	233	6	defined	define	VERB
ejpam-3118	233	7	by	by	ADP
ejpam-3118	233	8	ϕ(u	ϕ(u	PROPN
ejpam-3118	233	9	)	)	PUNCT
ejpam-3118	234	1	=	=	PUNCT
ejpam-3118	234	2	[	[	PUNCT
ejpam-3118	234	3	2(xij	2(xij	NUM
ejpam-3118	234	4	)	)	PUNCT
ejpam-3118	235	1	+	+	NUM
ejpam-3118	235	2	i8	i8	NOUN
ejpam-3118	235	3	]	]	PUNCT
ejpam-3118	235	4	.	.	PUNCT
ejpam-3118	236	1	let	let	VERB
ejpam-3118	236	2	a	a	PRON
ejpam-3118	236	3	=	=	PUNCT
ejpam-3118	237	1	[	[	X
ejpam-3118	237	2	2(xij	2(xij	NUM
ejpam-3118	237	3	)	)	PUNCT
ejpam-3118	237	4	+	+	NUM
ejpam-3118	237	5	i8	i8	NOUN
ejpam-3118	237	6	]	]	PUNCT
ejpam-3118	237	7	,	,	PUNCT
ejpam-3118	237	8	with	with	ADP
ejpam-3118	237	9	xij	xij	PROPN
ejpam-3118	237	10	∈	∈	PROPN
ejpam-3118	237	11	z	z	PROPN
ejpam-3118	237	12	,	,	PUNCT
ejpam-3118	237	13	for	for	ADP
ejpam-3118	237	14	all	all	DET
ejpam-3118	237	15	i	i	PROPN
ejpam-3118	237	16	,	,	PUNCT
ejpam-3118	237	17	j	j	PROPN
ejpam-3118	237	18	,	,	PUNCT
ejpam-3118	237	19	1	1	NUM
ejpam-3118	237	20	≤	≤	NUM
ejpam-3118	237	21	i	i	PRON
ejpam-3118	237	22	,	,	PUNCT
ejpam-3118	237	23	j	j	PROPN
ejpam-3118	237	24	≤	≤	ADV
ejpam-3118	237	25	8	8	NUM
ejpam-3118	237	26	.	.	PUNCT
ejpam-3118	238	1	then	then	ADV
ejpam-3118	238	2	deta	deta	VERB
ejpam-3118	238	3	=	=	NOUN
ejpam-3118	238	4	1	1	NUM
ejpam-3118	239	1	+	+	NUM
ejpam-3118	239	2	2β1	2β1	NUM
ejpam-3118	240	1	+	+	CCONJ
ejpam-3118	240	2	4β2	4β2	NUM
ejpam-3118	241	1	+	+	NUM
ejpam-3118	241	2	8β3	8β3	NUM
ejpam-3118	241	3	+	+	CCONJ
ejpam-3118	241	4	16β4	16β4	NUM
ejpam-3118	242	1	+	+	CCONJ
ejpam-3118	242	2	32β5	32β5	NUM
ejpam-3118	242	3	+	+	CCONJ
ejpam-3118	242	4	64β6	64β6	NUM
ejpam-3118	242	5	+	+	CCONJ
ejpam-3118	242	6	128β7	128β7	NUM
ejpam-3118	242	7	+	+	NUM
ejpam-3118	242	8	256β8	256β8	NUM
ejpam-3118	242	9	,	,	PUNCT
ejpam-3118	242	10	where	where	SCONJ
ejpam-3118	242	11	βr	βr	ADP
ejpam-3118	242	12	∈	∈	PROPN
ejpam-3118	242	13	z	z	PROPN
ejpam-3118	242	14	,	,	PUNCT
ejpam-3118	242	15	1	1	NUM
ejpam-3118	242	16	≤	≤	NOUN
ejpam-3118	242	17	r	r	NOUN
ejpam-3118	242	18	≤	≤	NUM
ejpam-3118	242	19	8	8	NUM
ejpam-3118	242	20	.	.	PUNCT
ejpam-3118	243	1	in	in	ADP
ejpam-3118	243	2	particular	particular	ADJ
ejpam-3118	243	3	,	,	PUNCT
ejpam-3118	243	4	β1	β1	PROPN
ejpam-3118	243	5	=	=	PUNCT
ejpam-3118	243	6	x11	x11	PROPN
ejpam-3118	243	7	+	+	NOUN
ejpam-3118	243	8	x22	x22	NOUN
ejpam-3118	243	9	+	+	ADJ
ejpam-3118	243	10	x33	x33	ADJ
ejpam-3118	243	11	+	+	NOUN
ejpam-3118	243	12	x44	x44	NOUN
ejpam-3118	243	13	+	+	NOUN
ejpam-3118	243	14	x55	x55	NOUN
ejpam-3118	243	15	+	+	NOUN
ejpam-3118	243	16	x66	x66	PROPN
ejpam-3118	243	17	+	+	NOUN
ejpam-3118	243	18	x77	x77	PROPN
ejpam-3118	243	19	+	+	ADJ
ejpam-3118	243	20	x88	x88	PROPN
ejpam-3118	243	21	.	.	PUNCT
ejpam-3118	244	1	furthermore	furthermore	ADV
ejpam-3118	244	2	,	,	PUNCT
ejpam-3118	244	3	a	a	DET
ejpam-3118	244	4	∈	∈	PROPN
ejpam-3118	244	5	ϕ(u2	ϕ(u2	NOUN
ejpam-3118	244	6	)	)	PUNCT
ejpam-3118	245	1	if	if	SCONJ
ejpam-3118	245	2	and	and	CCONJ
ejpam-3118	245	3	only	only	ADV
ejpam-3118	245	4	if	if	SCONJ
ejpam-3118	245	5	deta	deta	NOUN
ejpam-3118	245	6	=	=	NOUN
ejpam-3118	245	7	1	1	NUM
ejpam-3118	245	8	and	and	CCONJ
ejpam-3118	245	9	,	,	PUNCT
ejpam-3118	245	10	for	for	ADP
ejpam-3118	245	11	each	each	DET
ejpam-3118	245	12	k	k	NOUN
ejpam-3118	245	13	,	,	PUNCT
ejpam-3118	245	14	1	1	NUM
ejpam-3118	245	15	≤	≤	NUM
ejpam-3118	245	16	k	k	X
ejpam-3118	245	17	≤	≤	NUM
ejpam-3118	245	18	8	8	NUM
ejpam-3118	245	19	,	,	PUNCT
ejpam-3118	245	20	the	the	DET
ejpam-3118	245	21	integers	integer	NOUN
ejpam-3118	245	22	xiji	xiji	VERB
ejpam-3118	245	23	∈	∈	PROPN
ejpam-3118	245	24	bk	bk	NOUN
ejpam-3118	245	25	satisfy	satisfy	VERB
ejpam-3118	245	26	the	the	DET
ejpam-3118	245	27	following	follow	VERB
ejpam-3118	245	28	conditions	condition	NOUN
ejpam-3118	245	29	:	:	PUNCT
ejpam-3118	245	30	(	(	PUNCT
ejpam-3118	245	31	i	i	NOUN
ejpam-3118	245	32	)	)	PUNCT
ejpam-3118	245	33	all	all	DET
ejpam-3118	245	34	integers	integer	NOUN
ejpam-3118	245	35	xiji	xiji	VERB
ejpam-3118	245	36	,	,	PUNCT
ejpam-3118	245	37	1	1	NUM
ejpam-3118	245	38	≤	≤	NUM
ejpam-3118	245	39	i	i	PRON
ejpam-3118	245	40	≤	≤	NOUN
ejpam-3118	245	41	8	8	NUM
ejpam-3118	245	42	,	,	PUNCT
ejpam-3118	245	43	have	have	VERB
ejpam-3118	245	44	the	the	DET
ejpam-3118	245	45	same	same	ADJ
ejpam-3118	245	46	parity	parity	NOUN
ejpam-3118	245	47	;	;	PUNCT
ejpam-3118	245	48	(	(	PUNCT
ejpam-3118	245	49	ii	ii	NOUN
ejpam-3118	245	50	)	)	PUNCT
ejpam-3118	245	51	4	4	NUM
ejpam-3118	245	52	divides	divide	VERB
ejpam-3118	245	53	the	the	DET
ejpam-3118	245	54	sums	sum	NOUN
ejpam-3118	245	55	x1j1	x1j1	PUNCT
ejpam-3118	246	1	+	+	NOUN
ejpam-3118	246	2	x2j2	x2j2	PROPN
ejpam-3118	247	1	+	+	ADJ
ejpam-3118	247	2	x3j3	x3j3	PROPN
ejpam-3118	248	1	+	+	ADJ
ejpam-3118	248	2	x4j4	x4j4	PROPN
ejpam-3118	248	3	and	and	CCONJ
ejpam-3118	248	4	x5j5	x5j5	PUNCT
ejpam-3118	249	1	+	+	NOUN
ejpam-3118	249	2	x6j6	x6j6	X
ejpam-3118	249	3	+	+	NOUN
ejpam-3118	249	4	x7j7	x7j7	X
ejpam-3118	249	5	+	+	ADJ
ejpam-3118	249	6	x8j8	x8j8	NUM
ejpam-3118	249	7	;	;	PUNCT
ejpam-3118	249	8	(	(	PUNCT
ejpam-3118	249	9	iii	iii	X
ejpam-3118	249	10	)	)	PUNCT
ejpam-3118	249	11	ifx1j1	ifx1j1	NOUN
ejpam-3118	249	12	andx(1+k)j(1+k	andx(1+k)j(1+k	NOUN
ejpam-3118	249	13	)	)	PUNCT
ejpam-3118	249	14	,	,	PUNCT
ejpam-3118	249	15	1	1	NUM
ejpam-3118	249	16	≤	≤	NUM
ejpam-3118	249	17	k	k	X
ejpam-3118	249	18	≤	≤	NUM
ejpam-3118	249	19	3	3	NUM
ejpam-3118	249	20	,	,	PUNCT
ejpam-3118	249	21	are	be	AUX
ejpam-3118	249	22	congruentes	congruente	NOUN
ejpam-3118	249	23	module	module	NOUN
ejpam-3118	249	24	4	4	NUM
ejpam-3118	249	25	,	,	PUNCT
ejpam-3118	249	26	thenx5j5	thenx5j5	NUM
ejpam-3118	249	27	ex(5+k)j(5+k	ex(5+k)j(5+k	PROPN
ejpam-3118	249	28	)	)	PUNCT
ejpam-3118	249	29	also	also	ADV
ejpam-3118	249	30	are	be	AUX
ejpam-3118	249	31	;	;	PUNCT
ejpam-3118	249	32	(	(	PUNCT
ejpam-3118	249	33	iv	iv	X
ejpam-3118	249	34	)	)	PUNCT
ejpam-3118	249	35	8	8	NUM
ejpam-3118	249	36	divides	divide	VERB
ejpam-3118	249	37	the	the	DET
ejpam-3118	249	38	sum	sum	NOUN
ejpam-3118	249	39	x1j1	x1j1	PUNCT
ejpam-3118	250	1	+	+	ADJ
ejpam-3118	250	2	x2j2	x2j2	PROPN
ejpam-3118	251	1	+	+	ADJ
ejpam-3118	251	2	x3j3	x3j3	PROPN
ejpam-3118	252	1	+	+	ADJ
ejpam-3118	252	2	x4j4	x4j4	X
ejpam-3118	253	1	+	+	ADJ
ejpam-3118	253	2	x5j5	x5j5	ADJ
ejpam-3118	253	3	+	+	ADJ
ejpam-3118	253	4	x6j6	x6j6	X
ejpam-3118	253	5	+	+	NOUN
ejpam-3118	253	6	x7j7	x7j7	X
ejpam-3118	253	7	+	+	ADJ
ejpam-3118	253	8	x8j8	x8j8	X
ejpam-3118	253	9	.	.	PUNCT
ejpam-3118	254	1	indeed	indeed	ADV
ejpam-3118	254	2	,	,	PUNCT
ejpam-3118	254	3	a	a	DET
ejpam-3118	254	4	∈	∈	PROPN
ejpam-3118	254	5	ϕ(u2	ϕ(u2	NOUN
ejpam-3118	254	6	)	)	PUNCT
ejpam-3118	255	1	if	if	SCONJ
ejpam-3118	255	2	and	and	CCONJ
ejpam-3118	255	3	only	only	ADV
ejpam-3118	255	4	if	if	SCONJ
ejpam-3118	255	5	deta	deta	NOUN
ejpam-3118	255	6	=	=	NOUN
ejpam-3118	255	7	1	1	NUM
ejpam-3118	255	8	and	and	CCONJ
ejpam-3118	255	9	,	,	PUNCT
ejpam-3118	255	10	for	for	ADP
ejpam-3118	255	11	each	each	DET
ejpam-3118	255	12	k	k	NOUN
ejpam-3118	255	13	,	,	PUNCT
ejpam-3118	255	14	1	1	NUM
ejpam-3118	255	15	≤	≤	NUM
ejpam-3118	255	16	k	k	X
ejpam-3118	255	17	≤	≤	NUM
ejpam-3118	255	18	8	8	NUM
ejpam-3118	255	19	,	,	PUNCT
ejpam-3118	255	20	the	the	DET
ejpam-3118	255	21	integers	integer	NOUN
ejpam-3118	255	22	xiji	xiji	VERB
ejpam-3118	255	23	∈	∈	PROPN
ejpam-3118	255	24	bk	bk	NOUN
ejpam-3118	255	25	satisfy	satisfy	VERB
ejpam-3118	255	26	the	the	DET
ejpam-3118	255	27	following	follow	VERB
ejpam-3118	255	28	conditions	condition	NOUN
ejpam-3118	255	29	:	:	PUNCT
ejpam-3118	255	30	•	•	NUM
ejpam-3118	255	31	2	2	NUM
ejpam-3118	255	32	divides	divide	VERB
ejpam-3118	255	33	the	the	DET
ejpam-3118	255	34	sum	sum	NOUN
ejpam-3118	255	35	xiji	xiji	NOUN
ejpam-3118	256	1	+	+	PROPN
ejpam-3118	256	2	xi′ji′	xi′ji′	PROPN
ejpam-3118	256	3	,	,	PUNCT
ejpam-3118	256	4	for	for	ADP
ejpam-3118	256	5	all	all	DET
ejpam-3118	256	6	1	1	NUM
ejpam-3118	256	7	≤	≤	NOUN
ejpam-3118	256	8	i	i	PRON
ejpam-3118	256	9	,	,	PUNCT
ejpam-3118	256	10	i′	i′	VERB
ejpam-3118	256	11	≤	≤	NUM
ejpam-3118	256	12	8	8	NUM
ejpam-3118	256	13	;	;	PUNCT
ejpam-3118	256	14	•	•	NUM
ejpam-3118	256	15	4	4	NUM
ejpam-3118	256	16	divides	divide	VERB
ejpam-3118	256	17	the	the	DET
ejpam-3118	256	18	following	follow	VERB
ejpam-3118	256	19	sums	sum	NOUN
ejpam-3118	256	20	:	:	PUNCT
ejpam-3118	256	21	·	·	PUNCT
ejpam-3118	256	22	x1j1	x1j1	X
ejpam-3118	257	1	+	+	NOUN
ejpam-3118	257	2	x2j2	x2j2	PROPN
ejpam-3118	257	3	+	+	ADJ
ejpam-3118	257	4	xiji	xiji	NOUN
ejpam-3118	258	1	+	+	ADJ
ejpam-3118	258	2	x(i+1)j(i+1	x(i+1)j(i+1	PROPN
ejpam-3118	258	3	)	)	PUNCT
ejpam-3118	258	4	,	,	PUNCT
ejpam-3118	258	5	with	with	ADP
ejpam-3118	258	6	i	i	PRON
ejpam-3118	258	7	∈	∈	PROPN
ejpam-3118	258	8	{	{	PUNCT
ejpam-3118	258	9	3	3	NUM
ejpam-3118	258	10	,	,	PUNCT
ejpam-3118	258	11	5	5	NUM
ejpam-3118	258	12	,	,	PUNCT
ejpam-3118	258	13	7	7	NUM
ejpam-3118	258	14	}	}	PUNCT
ejpam-3118	258	15	;	;	PUNCT
ejpam-3118	258	16	·	·	PUNCT
ejpam-3118	258	17	x1j1	x1j1	PUNCT
ejpam-3118	259	1	+	+	ADJ
ejpam-3118	259	2	x3j3	x3j3	PROPN
ejpam-3118	259	3	+	+	ADJ
ejpam-3118	259	4	xiji	xiji	PROPN
ejpam-3118	259	5	+	+	PROPN
ejpam-3118	259	6	x(i+2)j(i+2	x(i+2)j(i+2	PROPN
ejpam-3118	259	7	)	)	PUNCT
ejpam-3118	259	8	,	,	PUNCT
ejpam-3118	259	9	with	with	ADP
ejpam-3118	259	10	i	i	PRON
ejpam-3118	259	11	∈	∈	PROPN
ejpam-3118	259	12	{	{	PUNCT
ejpam-3118	259	13	5	5	NUM
ejpam-3118	259	14	,	,	PUNCT
ejpam-3118	259	15	6	6	NUM
ejpam-3118	259	16	}	}	PUNCT
ejpam-3118	259	17	;	;	PUNCT
ejpam-3118	259	18	·	·	PUNCT
ejpam-3118	259	19	x1j1	x1j1	PUNCT
ejpam-3118	260	1	+	+	NOUN
ejpam-3118	260	2	x4j4	x4j4	X
ejpam-3118	260	3	+	+	ADJ
ejpam-3118	260	4	x5j5	x5j5	ADJ
ejpam-3118	260	5	+	+	NOUN
ejpam-3118	260	6	x8j8	x8j8	NUM
ejpam-3118	260	7	;	;	PUNCT
ejpam-3118	260	8	·	·	PUNCT
ejpam-3118	260	9	x1j1	x1j1	PUNCT
ejpam-3118	261	1	+	+	NOUN
ejpam-3118	261	2	x4j4	x4j4	X
ejpam-3118	261	3	+	+	ADJ
ejpam-3118	261	4	x6j6	x6j6	X
ejpam-3118	261	5	+	+	NOUN
ejpam-3118	261	6	x7j7	x7j7	NUM
ejpam-3118	261	7	;	;	PUNCT
ejpam-3118	261	8	·	·	PUNCT
ejpam-3118	261	9	x2j2	x2j2	PUNCT
ejpam-3118	262	1	+	+	ADJ
ejpam-3118	262	2	x3j3	x3j3	PROPN
ejpam-3118	263	1	+	+	ADJ
ejpam-3118	263	2	x5j5	x5j5	ADJ
ejpam-3118	263	3	+	+	NOUN
ejpam-3118	263	4	x8j8	x8j8	NUM
ejpam-3118	263	5	;	;	PUNCT
ejpam-3118	263	6	references	reference	NOUN
ejpam-3118	263	7	965	965	NUM
ejpam-3118	263	8	·	·	PUNCT
ejpam-3118	263	9	x2j2	x2j2	PUNCT
ejpam-3118	264	1	+	+	ADJ
ejpam-3118	264	2	x3j3	x3j3	PROPN
ejpam-3118	264	3	+	+	ADJ
ejpam-3118	264	4	x6j6	x6j6	X
ejpam-3118	264	5	+	+	NOUN
ejpam-3118	264	6	x7j7	x7j7	NUM
ejpam-3118	264	7	;	;	PUNCT
ejpam-3118	264	8	·	·	PUNCT
ejpam-3118	264	9	x2j2	x2j2	PUNCT
ejpam-3118	265	1	+	+	ADJ
ejpam-3118	265	2	x4j4	x4j4	X
ejpam-3118	265	3	+	+	ADJ
ejpam-3118	265	4	xiji	xiji	PROPN
ejpam-3118	265	5	+	+	PROPN
ejpam-3118	265	6	x(i+2)j(i+2	x(i+2)j(i+2	PROPN
ejpam-3118	265	7	)	)	PUNCT
ejpam-3118	265	8	,	,	PUNCT
ejpam-3118	265	9	with	with	ADP
ejpam-3118	265	10	i	i	PRON
ejpam-3118	265	11	∈	∈	PROPN
ejpam-3118	265	12	{	{	PUNCT
ejpam-3118	265	13	5	5	NUM
ejpam-3118	265	14	,	,	PUNCT
ejpam-3118	265	15	6	6	NUM
ejpam-3118	265	16	}	}	PUNCT
ejpam-3118	265	17	;	;	PUNCT
ejpam-3118	265	18	·	·	PUNCT
ejpam-3118	265	19	x3j3	x3j3	PUNCT
ejpam-3118	266	1	+	+	X
ejpam-3118	266	2	x4j4	x4j4	X
ejpam-3118	266	3	+	+	ADJ
ejpam-3118	266	4	xiji	xiji	NOUN
ejpam-3118	266	5	+	+	ADJ
ejpam-3118	266	6	x(i+1)j(i+1	x(i+1)j(i+1	PROPN
ejpam-3118	266	7	)	)	PUNCT
ejpam-3118	266	8	,	,	PUNCT
ejpam-3118	266	9	with	with	ADP
ejpam-3118	266	10	i	i	PRON
ejpam-3118	266	11	∈	∈	PROPN
ejpam-3118	266	12	{	{	PUNCT
ejpam-3118	266	13	5	5	NUM
ejpam-3118	266	14	,	,	PUNCT
ejpam-3118	266	15	7	7	NUM
ejpam-3118	266	16	}	}	PUNCT
ejpam-3118	266	17	;	;	PUNCT
ejpam-3118	266	18	·	·	PUNCT
ejpam-3118	266	19	x5j5	x5j5	PUNCT
ejpam-3118	267	1	+	+	PUNCT
ejpam-3118	267	2	x6j6	x6j6	X
ejpam-3118	267	3	+	+	NOUN
ejpam-3118	267	4	x7j7	x7j7	X
ejpam-3118	267	5	+	+	ADJ
ejpam-3118	267	6	x8j8	x8j8	X
ejpam-3118	267	7	.	.	PUNCT
ejpam-3118	268	1	•	•	NOUN
ejpam-3118	268	2	8	8	NUM
ejpam-3118	268	3	divides	divide	VERB
ejpam-3118	268	4	the	the	DET
ejpam-3118	268	5	sum	sum	NOUN
ejpam-3118	268	6	x1j1	x1j1	PUNCT
ejpam-3118	269	1	+	+	ADJ
ejpam-3118	269	2	x2j2	x2j2	PROPN
ejpam-3118	270	1	+	+	ADJ
ejpam-3118	270	2	x3j3	x3j3	PROPN
ejpam-3118	271	1	+	+	ADJ
ejpam-3118	271	2	x4j4	x4j4	X
ejpam-3118	272	1	+	+	ADJ
ejpam-3118	272	2	x5j5	x5j5	ADJ
ejpam-3118	272	3	+	+	ADJ
ejpam-3118	272	4	x6j6	x6j6	X
ejpam-3118	272	5	+	+	NOUN
ejpam-3118	272	6	x7j7	x7j7	X
ejpam-3118	272	7	+	+	NOUN
ejpam-3118	272	8	x8j8	x8j8	X
ejpam-3118	272	9	.	.	PUNCT
ejpam-3118	273	1	in	in	ADP
ejpam-3118	273	2	particular	particular	ADJ
ejpam-3118	273	3	,	,	PUNCT
ejpam-3118	273	4	as	as	SCONJ
ejpam-3118	273	5	8	8	NUM
ejpam-3118	273	6	divides	divide	VERB
ejpam-3118	273	7	x11+x22+x33+x44+x55+x66+x77+x88	x11+x22+x33+x44+x55+x66+x77+x88	PROPN
ejpam-3118	273	8	,	,	PUNCT
ejpam-3118	273	9	we	we	PRON
ejpam-3118	273	10	have	have	VERB
ejpam-3118	273	11	that	that	DET
ejpam-3118	273	12	deta	deta	NOUN
ejpam-3118	273	13	=	=	NOUN
ejpam-3118	273	14	1	1	X
ejpam-3118	273	15	.	.	PUNCT
ejpam-3118	274	1	furthermore	furthermore	ADV
ejpam-3118	274	2	,	,	PUNCT
ejpam-3118	274	3	ϕ(s	ϕ(s	PROPN
ejpam-3118	274	4	)	)	PUNCT
ejpam-3118	274	5	=	=	SYM
ejpam-3118	275	1	ϕ(1	ϕ(1	PROPN
ejpam-3118	275	2	+	+	CCONJ
ejpam-3118	275	3	s(1−	s(1−	PROPN
ejpam-3118	275	4	s	s	PART
ejpam-3118	275	5	)	)	PUNCT
ejpam-3118	275	6	)	)	PUNCT
ejpam-3118	276	1	=	=	PUNCT
ejpam-3118	276	2	−i8	−i8	PROPN
ejpam-3118	276	3	.	.	PUNCT
ejpam-3118	277	1	so	so	ADV
ejpam-3118	277	2	,	,	PUNCT
ejpam-3118	277	3	it	it	PRON
ejpam-3118	277	4	follows	follow	VERB
ejpam-3118	277	5	that	that	SCONJ
ejpam-3118	277	6	the	the	DET
ejpam-3118	277	7	mapping	mapping	NOUN
ejpam-3118	277	8	ϕ	ϕ	NOUN
ejpam-3118	277	9	induces	induce	VERB
ejpam-3118	277	10	the	the	DET
ejpam-3118	277	11	isomorphism	isomorphism	NOUN
ejpam-3118	277	12	wanted	want	VERB
ejpam-3118	277	13	.	.	PUNCT
ejpam-3118	278	1	the	the	DET
ejpam-3118	278	2	reader	reader	NOUN
ejpam-3118	278	3	may	may	AUX
ejpam-3118	278	4	notice	notice	VERB
ejpam-3118	278	5	that	that	SCONJ
ejpam-3118	278	6	the	the	DET
ejpam-3118	278	7	idea	idea	NOUN
ejpam-3118	278	8	used	use	VERB
ejpam-3118	278	9	in	in	ADP
ejpam-3118	278	10	this	this	DET
ejpam-3118	278	11	paper	paper	NOUN
ejpam-3118	278	12	can	can	AUX
ejpam-3118	278	13	be	be	AUX
ejpam-3118	278	14	extended	extend	VERB
ejpam-3118	278	15	to	to	PART
ejpam-3118	278	16	describe	describe	VERB
ejpam-3118	278	17	the	the	DET
ejpam-3118	278	18	group	group	NOUN
ejpam-3118	278	19	of	of	ADP
ejpam-3118	278	20	units	unit	NOUN
ejpam-3118	278	21	of	of	ADP
ejpam-3118	278	22	any	any	DET
ejpam-3118	278	23	integral	integral	ADJ
ejpam-3118	278	24	group	group	NOUN
ejpam-3118	278	25	ring	ring	NOUN
ejpam-3118	278	26	of	of	ADP
ejpam-3118	278	27	a	a	DET
ejpam-3118	278	28	finite	finite	ADJ
ejpam-3118	278	29	extra	extra	ADJ
ejpam-3118	278	30	-	-	ADJ
ejpam-3118	278	31	special	special	ADJ
ejpam-3118	278	32	2	2	NUM
ejpam-3118	278	33	-	-	PUNCT
ejpam-3118	278	34	group	group	NOUN
ejpam-3118	278	35	of	of	ADP
ejpam-3118	278	36	order	order	NOUN
ejpam-3118	278	37	higher	high	ADJ
ejpam-3118	278	38	than	than	ADP
ejpam-3118	278	39	128	128	NUM
ejpam-3118	278	40	,	,	PUNCT
ejpam-3118	278	41	that	that	PRON
ejpam-3118	278	42	is	be	AUX
ejpam-3118	278	43	a	a	DET
ejpam-3118	278	44	central	central	ADJ
ejpam-3118	278	45	product	product	NOUN
ejpam-3118	278	46	of	of	ADP
ejpam-3118	278	47	copies	copy	NOUN
ejpam-3118	278	48	of	of	ADP
ejpam-3118	278	49	d4	d4	PROPN
ejpam-3118	278	50	.	.	PUNCT
ejpam-3118	279	1	references	reference	NOUN
ejpam-3118	279	2	[	[	X
ejpam-3118	279	3	1	1	X
ejpam-3118	279	4	]	]	PUNCT
ejpam-3118	279	5	a	a	DET
ejpam-3118	279	6	k	k	PROPN
ejpam-3118	279	7	bhandari	bhandari	NOUN
ejpam-3118	279	8	and	and	CCONJ
ejpam-3118	279	9	i	i	PRON
ejpam-3118	279	10	s	s	VERB
ejpam-3118	279	11	luthar	luthar	NOUN
ejpam-3118	279	12	.	.	PUNCT
ejpam-3118	280	1	torsion	torsion	NOUN
ejpam-3118	280	2	units	unit	NOUN
ejpam-3118	280	3	of	of	ADP
ejpam-3118	280	4	integral	integral	ADJ
ejpam-3118	280	5	group	group	NOUN
ejpam-3118	280	6	rings	ring	NOUN
ejpam-3118	280	7	of	of	ADP
ejpam-3118	280	8	metacyclic	metacyclic	ADJ
ejpam-3118	280	9	groups	group	NOUN
ejpam-3118	280	10	.	.	PUNCT
ejpam-3118	281	1	j.	j.	PROPN
ejpam-3118	281	2	number	number	PROPN
ejpam-3118	281	3	theory	theory	NOUN
ejpam-3118	281	4	,	,	PUNCT
ejpam-3118	281	5	17:170–183	17:170–183	NUM
ejpam-3118	281	6	,	,	PUNCT
ejpam-3118	281	7	1983	1983	NUM
ejpam-3118	281	8	.	.	PUNCT
ejpam-3118	282	1	[	[	X
ejpam-3118	282	2	2	2	X
ejpam-3118	282	3	]	]	PUNCT
ejpam-3118	282	4	a	a	DET
ejpam-3118	282	5	bovdi	bovdi	NOUN
ejpam-3118	282	6	and	and	CCONJ
ejpam-3118	282	7	f	f	PROPN
ejpam-3118	282	8	c	c	PROPN
ejpam-3118	282	9	polcino	polcino	NOUN
ejpam-3118	282	10	milies	milie	NOUN
ejpam-3118	282	11	.	.	PUNCT
ejpam-3118	283	1	normal	normal	ADJ
ejpam-3118	283	2	subgroups	subgroup	NOUN
ejpam-3118	283	3	of	of	ADP
ejpam-3118	283	4	the	the	DET
ejpam-3118	283	5	group	group	NOUN
ejpam-3118	283	6	of	of	ADP
ejpam-3118	283	7	units	unit	NOUN
ejpam-3118	283	8	in	in	ADP
ejpam-3118	283	9	group	group	NOUN
ejpam-3118	283	10	rings	ring	NOUN
ejpam-3118	283	11	of	of	ADP
ejpam-3118	283	12	torsion	torsion	NOUN
ejpam-3118	283	13	groups	group	NOUN
ejpam-3118	283	14	.	.	PUNCT
ejpam-3118	284	1	publ	publ	PROPN
ejpam-3118	284	2	.	.	PUNCT
ejpam-3118	285	1	math	math	NOUN
ejpam-3118	285	2	.	.	PUNCT
ejpam-3118	286	1	debrecen	debrecen	PROPN
ejpam-3118	286	2	,	,	PUNCT
ejpam-3118	286	3	59:235–242	59:235–242	PROPN
ejpam-3118	286	4	,	,	PUNCT
ejpam-3118	286	5	2001	2001	NUM
ejpam-3118	286	6	.	.	PUNCT
ejpam-3118	287	1	[	[	X
ejpam-3118	287	2	3	3	NUM
ejpam-3118	287	3	]	]	X
ejpam-3118	287	4	r	r	NOUN
ejpam-3118	287	5	a	a	DET
ejpam-3118	287	6	ferraz	ferraz	NOUN
ejpam-3118	287	7	.	.	PUNCT
ejpam-3118	288	1	groups	group	NOUN
ejpam-3118	288	2	generated	generate	VERB
ejpam-3118	288	3	by	by	ADP
ejpam-3118	288	4	a	a	DET
ejpam-3118	288	5	bass	bass	NOUN
ejpam-3118	288	6	cyclic	cyclic	ADJ
ejpam-3118	288	7	unit	unit	NOUN
ejpam-3118	288	8	and	and	CCONJ
ejpam-3118	288	9	a	a	DET
ejpam-3118	288	10	bicyclic	bicyclic	NOUN
ejpam-3118	288	11	unit	unit	NOUN
ejpam-3118	288	12	in	in	ADP
ejpam-3118	288	13	the	the	DET
ejpam-3118	288	14	units	unit	NOUN
ejpam-3118	288	15	of	of	ADP
ejpam-3118	288	16	zg	zg	PROPN
ejpam-3118	288	17	.	.	PUNCT
ejpam-3118	289	1	j.	j.	PROPN
ejpam-3118	289	2	group	group	PROPN
ejpam-3118	289	3	theory	theory	NOUN
ejpam-3118	289	4	,	,	PUNCT
ejpam-3118	289	5	7:421–430	7:421–430	PROPN
ejpam-3118	289	6	,	,	PUNCT
ejpam-3118	289	7	2004	2004	NUM
ejpam-3118	289	8	.	.	PUNCT
ejpam-3118	290	1	[	[	X
ejpam-3118	290	2	4	4	X
ejpam-3118	290	3	]	]	PUNCT
ejpam-3118	290	4	a	a	DET
ejpam-3118	290	5	giambruno	giambruno	NOUN
ejpam-3118	290	6	and	and	CCONJ
ejpam-3118	290	7	s	s	PROPN
ejpam-3118	290	8	k	k	PROPN
ejpam-3118	290	9	sehgal	sehgal	PROPN
ejpam-3118	290	10	.	.	PUNCT
ejpam-3118	291	1	generators	generator	NOUN
ejpam-3118	291	2	of	of	ADP
ejpam-3118	291	3	large	large	ADJ
ejpam-3118	291	4	subgroups	subgroup	NOUN
ejpam-3118	291	5	of	of	ADP
ejpam-3118	291	6	units	unit	NOUN
ejpam-3118	291	7	of	of	ADP
ejpam-3118	291	8	integral	integral	ADJ
ejpam-3118	291	9	group	group	NOUN
ejpam-3118	291	10	rings	ring	NOUN
ejpam-3118	291	11	of	of	ADP
ejpam-3118	291	12	nilpotent	nilpotent	ADJ
ejpam-3118	291	13	groups	group	NOUN
ejpam-3118	291	14	.	.	PUNCT
ejpam-3118	292	1	j.	j.	PROPN
ejpam-3118	292	2	of	of	ADP
ejpam-3118	292	3	algebra	algebra	PROPN
ejpam-3118	292	4	,	,	PUNCT
ejpam-3118	292	5	174:150–156	174:150–156	NUM
ejpam-3118	292	6	,	,	PUNCT
ejpam-3118	292	7	1995	1995	NUM
ejpam-3118	292	8	.	.	PUNCT
ejpam-3118	293	1	[	[	X
ejpam-3118	293	2	5	5	NUM
ejpam-3118	293	3	]	]	PUNCT
ejpam-3118	293	4	e	e	X
ejpam-3118	293	5	g	g	NOUN
ejpam-3118	293	6	goodaire	goodaire	NOUN
ejpam-3118	293	7	and	and	CCONJ
ejpam-3118	293	8	e	e	NOUN
ejpam-3118	293	9	jespers	jesper	NOUN
ejpam-3118	293	10	.	.	PUNCT
ejpam-3118	294	1	determining	determine	VERB
ejpam-3118	294	2	units	unit	NOUN
ejpam-3118	294	3	in	in	ADP
ejpam-3118	294	4	some	some	DET
ejpam-3118	294	5	integral	integral	ADJ
ejpam-3118	294	6	group	group	NOUN
ejpam-3118	294	7	rings	ring	NOUN
ejpam-3118	294	8	.	.	PUNCT
ejpam-3118	295	1	canad	canad	PROPN
ejpam-3118	295	2	.	.	PUNCT
ejpam-3118	296	1	math	math	NOUN
ejpam-3118	296	2	.	.	PUNCT
ejpam-3118	297	1	bull	bull	PROPN
ejpam-3118	297	2	.	.	PUNCT
ejpam-3118	297	3	,	,	PUNCT
ejpam-3118	297	4	33(2):242–1246	33(2):242–1246	NUM
ejpam-3118	297	5	,	,	PUNCT
ejpam-3118	297	6	1990	1990	NUM
ejpam-3118	297	7	.	.	PUNCT
ejpam-3118	298	1	[	[	X
ejpam-3118	298	2	6	6	NUM
ejpam-3118	298	3	]	]	SYM
ejpam-3118	298	4	e	e	NOUN
ejpam-3118	298	5	jespers	jesper	NOUN
ejpam-3118	298	6	and	and	CCONJ
ejpam-3118	298	7	a	a	DET
ejpam-3118	298	8	del	del	PROPN
ejpam-3118	298	9	rio	rio	PROPN
ejpam-3118	298	10	.	.	PUNCT
ejpam-3118	299	1	group	group	PROPN
ejpam-3118	299	2	ring	ring	NOUN
ejpam-3118	299	3	groups	group	NOUN
ejpam-3118	299	4	,	,	PUNCT
ejpam-3118	299	5	vol	vol	NOUN
ejpam-3118	299	6	.	.	NOUN
ejpam-3118	300	1	1	1	NUM
ejpam-3118	300	2	:	:	PUNCT
ejpam-3118	300	3	orders	order	NOUN
ejpam-3118	300	4	and	and	CCONJ
ejpam-3118	300	5	generic	generic	ADJ
ejpam-3118	300	6	constructions	construction	NOUN
ejpam-3118	300	7	of	of	ADP
ejpam-3118	300	8	units	unit	NOUN
ejpam-3118	300	9	.	.	PUNCT
ejpam-3118	301	1	de	de	ADP
ejpam-3118	301	2	gruyter	gruyter	NOUN
ejpam-3118	301	3	,	,	PUNCT
ejpam-3118	301	4	berlin	berlin	PROPN
ejpam-3118	301	5	,	,	PUNCT
ejpam-3118	301	6	2015	2015	NUM
ejpam-3118	301	7	.	.	PUNCT
ejpam-3118	302	1	[	[	X
ejpam-3118	302	2	7	7	NUM
ejpam-3118	302	3	]	]	X
ejpam-3118	302	4	e	e	NOUN
ejpam-3118	302	5	jespers	jesper	NOUN
ejpam-3118	302	6	and	and	CCONJ
ejpam-3118	302	7	a	a	DET
ejpam-3118	302	8	del	del	PROPN
ejpam-3118	302	9	rio	rio	PROPN
ejpam-3118	302	10	.	.	PUNCT
ejpam-3118	303	1	group	group	PROPN
ejpam-3118	303	2	ring	ring	NOUN
ejpam-3118	303	3	groups	group	NOUN
ejpam-3118	303	4	,	,	PUNCT
ejpam-3118	303	5	vol	vol	NOUN
ejpam-3118	303	6	.	.	NOUN
ejpam-3118	304	1	2	2	NUM
ejpam-3118	304	2	:	:	PUNCT
ejpam-3118	304	3	structure	structure	NOUN
ejpam-3118	304	4	theorems	theorem	NOUN
ejpam-3118	304	5	of	of	ADP
ejpam-3118	304	6	unit	unit	NOUN
ejpam-3118	304	7	groups	group	NOUN
ejpam-3118	304	8	.	.	PUNCT
ejpam-3118	305	1	de	de	ADP
ejpam-3118	305	2	gruyter	gruyter	NOUN
ejpam-3118	305	3	,	,	PUNCT
ejpam-3118	305	4	berlin	berlin	PROPN
ejpam-3118	305	5	,	,	PUNCT
ejpam-3118	305	6	2015	2015	NUM
ejpam-3118	305	7	.	.	PUNCT
ejpam-3118	306	1	[	[	X
ejpam-3118	306	2	8	8	NUM
ejpam-3118	306	3	]	]	SYM
ejpam-3118	306	4	e	e	NOUN
ejpam-3118	306	5	jespers	jesper	NOUN
ejpam-3118	306	6	and	and	CCONJ
ejpam-3118	306	7	g	g	PROPN
ejpam-3118	306	8	leal	leal	NOUN
ejpam-3118	306	9	.	.	PUNCT
ejpam-3118	307	1	describing	describe	VERB
ejpam-3118	307	2	units	unit	NOUN
ejpam-3118	307	3	of	of	ADP
ejpam-3118	307	4	integral	integral	ADJ
ejpam-3118	307	5	group	group	NOUN
ejpam-3118	307	6	rings	ring	NOUN
ejpam-3118	307	7	of	of	ADP
ejpam-3118	307	8	some	some	DET
ejpam-3118	307	9	2	2	NUM
ejpam-3118	307	10	-	-	PUNCT
ejpam-3118	307	11	groups	group	NOUN
ejpam-3118	307	12	.	.	PUNCT
ejpam-3118	308	1	comm	comm	NOUN
ejpam-3118	308	2	.	.	PUNCT
ejpam-3118	309	1	algebra	algebra	PROPN
ejpam-3118	309	2	,	,	PUNCT
ejpam-3118	309	3	19(6):1809–1827	19(6):1809–1827	NUM
ejpam-3118	309	4	,	,	PUNCT
ejpam-3118	309	5	1991	1991	NUM
ejpam-3118	309	6	.	.	PUNCT
ejpam-3118	310	1	[	[	X
ejpam-3118	310	2	9	9	NUM
ejpam-3118	310	3	]	]	SYM
ejpam-3118	310	4	e	e	NOUN
ejpam-3118	310	5	jespers	jesper	NOUN
ejpam-3118	310	6	and	and	CCONJ
ejpam-3118	310	7	g	g	PROPN
ejpam-3118	310	8	leal	leal	NOUN
ejpam-3118	310	9	.	.	PUNCT
ejpam-3118	311	1	generators	generator	NOUN
ejpam-3118	311	2	of	of	ADP
ejpam-3118	311	3	large	large	ADJ
ejpam-3118	311	4	subgroups	subgroup	NOUN
ejpam-3118	311	5	of	of	ADP
ejpam-3118	311	6	the	the	DET
ejpam-3118	311	7	units	unit	NOUN
ejpam-3118	311	8	of	of	ADP
ejpam-3118	311	9	integral	integral	ADJ
ejpam-3118	311	10	group	group	NOUN
ejpam-3118	311	11	rings	ring	NOUN
ejpam-3118	311	12	.	.	PUNCT
ejpam-3118	312	1	manuscripta	manuscripta	NOUN
ejpam-3118	312	2	math	math	PROPN
ejpam-3118	312	3	.	.	PUNCT
ejpam-3118	312	4	,	,	PUNCT
ejpam-3118	313	1	78:303–315	78:303–315	PROPN
ejpam-3118	313	2	,	,	PUNCT
ejpam-3118	313	3	1993	1993	NUM
ejpam-3118	313	4	.	.	PUNCT
ejpam-3118	314	1	[	[	X
ejpam-3118	314	2	10	10	NUM
ejpam-3118	314	3	]	]	X
ejpam-3118	314	4	e	e	NOUN
ejpam-3118	314	5	jespers	jesper	NOUN
ejpam-3118	314	6	,	,	PUNCT
ejpam-3118	314	7	g	g	NOUN
ejpam-3118	314	8	leal	leal	NOUN
ejpam-3118	314	9	and	and	CCONJ
ejpam-3118	314	10	f	f	PROPN
ejpam-3118	314	11	c	c	PROPN
ejpam-3118	314	12	polcino	polcino	NOUN
ejpam-3118	314	13	milies	milie	NOUN
ejpam-3118	314	14	.	.	PUNCT
ejpam-3118	315	1	units	unit	NOUN
ejpam-3118	315	2	of	of	ADP
ejpam-3118	315	3	integral	integral	ADJ
ejpam-3118	315	4	group	group	NOUN
ejpam-3118	315	5	rings	ring	NOUN
ejpam-3118	315	6	of	of	ADP
ejpam-3118	315	7	some	some	DET
ejpam-3118	315	8	metacyclic	metacyclic	ADJ
ejpam-3118	315	9	groups	group	NOUN
ejpam-3118	315	10	.	.	PUNCT
ejpam-3118	316	1	canad	canad	PROPN
ejpam-3118	316	2	.	.	PUNCT
ejpam-3118	317	1	math	math	NOUN
ejpam-3118	317	2	.	.	PUNCT
ejpam-3118	318	1	bull	bull	PROPN
ejpam-3118	318	2	.	.	PUNCT
ejpam-3118	318	3	,	,	PUNCT
ejpam-3118	319	1	37(2):228–237	37(2):228–237	PROPN
ejpam-3118	319	2	,	,	PUNCT
ejpam-3118	319	3	1994	1994	NUM
ejpam-3118	319	4	.	.	PUNCT
ejpam-3118	320	1	references	reference	NOUN
ejpam-3118	320	2	966	966	NUM
ejpam-3118	321	1	[	[	X
ejpam-3118	321	2	11	11	NUM
ejpam-3118	321	3	]	]	SYM
ejpam-3118	321	4	e	e	NOUN
ejpam-3118	321	5	jespers	jesper	NOUN
ejpam-3118	321	6	,	,	PUNCT
ejpam-3118	321	7	m	m	VERB
ejpam-3118	321	8	m	m	NOUN
ejpam-3118	321	9	parmenter	parmenter	NOUN
ejpam-3118	321	10	and	and	CCONJ
ejpam-3118	321	11	s	s	NOUN
ejpam-3118	321	12	k	k	PROPN
ejpam-3118	321	13	sehgal	sehgal	PROPN
ejpam-3118	321	14	.	.	PUNCT
ejpam-3118	322	1	central	central	ADJ
ejpam-3118	322	2	units	unit	NOUN
ejpam-3118	322	3	of	of	ADP
ejpam-3118	322	4	integral	integral	ADJ
ejpam-3118	322	5	group	group	NOUN
ejpam-3118	322	6	rings	ring	NOUN
ejpam-3118	322	7	of	of	ADP
ejpam-3118	322	8	nilpotent	nilpotent	ADJ
ejpam-3118	322	9	groups	group	NOUN
ejpam-3118	322	10	.	.	PUNCT
ejpam-3118	323	1	proc	proc	PROPN
ejpam-3118	323	2	.	.	PUNCT
ejpam-3118	324	1	amer	amer	PROPN
ejpam-3118	324	2	.	.	PUNCT
ejpam-3118	324	3	math	math	PROPN
ejpam-3118	324	4	soc	soc	PROPN
ejpam-3118	324	5	.	.	PUNCT
ejpam-3118	324	6	,	,	PUNCT
ejpam-3118	324	7	124:1007–1012	124:1007–1012	NUM
ejpam-3118	324	8	,	,	PUNCT
ejpam-3118	324	9	1996	1996	NUM
ejpam-3118	324	10	.	.	PUNCT
ejpam-3118	325	1	[	[	X
ejpam-3118	325	2	12	12	NUM
ejpam-3118	325	3	]	]	X
ejpam-3118	325	4	f	f	PROPN
ejpam-3118	325	5	c	c	PROPN
ejpam-3118	325	6	polcino	polcino	NOUN
ejpam-3118	325	7	milies	milie	NOUN
ejpam-3118	325	8	.	.	PUNCT
ejpam-3118	326	1	the	the	DET
ejpam-3118	326	2	units	unit	NOUN
ejpam-3118	326	3	of	of	ADP
ejpam-3118	326	4	integral	integral	ADJ
ejpam-3118	326	5	group	group	NOUN
ejpam-3118	326	6	ring	ring	NOUN
ejpam-3118	326	7	zd4	zd4	NOUN
ejpam-3118	326	8	.	.	PUNCT
ejpam-3118	327	1	bol	bol	NOUN
ejpam-3118	327	2	.	.	PUNCT
ejpam-3118	328	1	soc	soc	PROPN
ejpam-3118	328	2	.	.	PUNCT
ejpam-3118	329	1	brasileira	brasileira	PROPN
ejpam-3118	329	2	de	de	PROPN
ejpam-3118	329	3	mat	mat	PROPN
ejpam-3118	329	4	.	.	PROPN
ejpam-3118	329	5	,	,	PUNCT
ejpam-3118	329	6	4:85–92	4:85–92	PROPN
ejpam-3118	329	7	,	,	PUNCT
ejpam-3118	329	8	1972	1972	NUM
ejpam-3118	329	9	.	.	PUNCT
ejpam-3118	330	1	[	[	X
ejpam-3118	330	2	13	13	NUM
ejpam-3118	330	3	]	]	SYM
ejpam-3118	330	4	j	j	PROPN
ejpam-3118	330	5	ritter	ritter	PROPN
ejpam-3118	330	6	and	and	CCONJ
ejpam-3118	330	7	s	s	PROPN
ejpam-3118	330	8	k	k	PROPN
ejpam-3118	330	9	sehgal	sehgal	PROPN
ejpam-3118	330	10	.	.	PUNCT
ejpam-3118	331	1	generators	generator	NOUN
ejpam-3118	331	2	of	of	ADP
ejpam-3118	331	3	subgroups	subgroup	NOUN
ejpam-3118	331	4	of	of	ADP
ejpam-3118	331	5	u(zg	u(zg	NOUN
ejpam-3118	331	6	)	)	PUNCT
ejpam-3118	331	7	.	.	PUNCT
ejpam-3118	332	1	contemp	contemp	NOUN
ejpam-3118	332	2	.	.	PUNCT
ejpam-3118	333	1	math	math	NOUN
ejpam-3118	333	2	.	.	PUNCT
ejpam-3118	334	1	,	,	PUNCT
ejpam-3118	334	2	93:331	93:331	NUM
ejpam-3118	334	3	–	–	PUNCT
ejpam-3118	334	4	347	347	NUM
ejpam-3118	334	5	,	,	PUNCT
ejpam-3118	334	6	1989	1989	NUM
ejpam-3118	334	7	.	.	PUNCT
ejpam-3118	335	1	[	[	X
ejpam-3118	335	2	14	14	NUM
ejpam-3118	335	3	]	]	X
ejpam-3118	335	4	j	j	PROPN
ejpam-3118	335	5	ritter	ritter	PROPN
ejpam-3118	335	6	and	and	CCONJ
ejpam-3118	335	7	s	s	PROPN
ejpam-3118	335	8	k	k	PROPN
ejpam-3118	335	9	sehgal	sehgal	PROPN
ejpam-3118	335	10	.	.	PUNCT
ejpam-3118	336	1	construction	construction	NOUN
ejpam-3118	336	2	of	of	ADP
ejpam-3118	336	3	units	unit	NOUN
ejpam-3118	336	4	in	in	ADP
ejpam-3118	336	5	integral	integral	ADJ
ejpam-3118	336	6	group	group	NOUN
ejpam-3118	336	7	rings	ring	NOUN
ejpam-3118	336	8	of	of	ADP
ejpam-3118	336	9	finite	finite	ADJ
ejpam-3118	336	10	nilpotent	nilpotent	ADJ
ejpam-3118	336	11	groups	group	NOUN
ejpam-3118	336	12	.	.	PUNCT
ejpam-3118	337	1	trans	trans	PROPN
ejpam-3118	337	2	.	.	PUNCT
ejpam-3118	338	1	amer	amer	PROPN
ejpam-3118	338	2	.	.	PUNCT
ejpam-3118	338	3	math	math	PROPN
ejpam-3118	338	4	.	.	PUNCT
ejpam-3118	339	1	soc	soc	PROPN
ejpam-3118	339	2	.	.	PUNCT
ejpam-3118	339	3	,	,	PUNCT
ejpam-3118	339	4	324:602–621	324:602–621	NUM
ejpam-3118	339	5	,	,	PUNCT
ejpam-3118	339	6	1991	1991	NUM
ejpam-3118	339	7	.	.	PUNCT
ejpam-3118	340	1	[	[	X
ejpam-3118	340	2	15	15	NUM
ejpam-3118	340	3	]	]	X
ejpam-3118	340	4	j	j	PROPN
ejpam-3118	340	5	ritter	ritter	PROPN
ejpam-3118	340	6	and	and	CCONJ
ejpam-3118	340	7	s	s	PROPN
ejpam-3118	340	8	k	k	PROPN
ejpam-3118	340	9	sehgal	sehgal	PROPN
ejpam-3118	340	10	.	.	PUNCT
ejpam-3118	341	1	construction	construction	NOUN
ejpam-3118	341	2	of	of	ADP
ejpam-3118	341	3	units	unit	NOUN
ejpam-3118	341	4	in	in	ADP
ejpam-3118	341	5	integral	integral	ADJ
ejpam-3118	341	6	group	group	NOUN
ejpam-3118	341	7	rings	ring	NOUN
ejpam-3118	341	8	of	of	ADP
ejpam-3118	341	9	monomial	monomial	ADJ
ejpam-3118	341	10	and	and	CCONJ
ejpam-3118	341	11	symmetric	symmetric	ADJ
ejpam-3118	341	12	groups	group	NOUN
ejpam-3118	341	13	.	.	PUNCT
ejpam-3118	342	1	j.	j.	PROPN
ejpam-3118	342	2	algebra	algebra	PROPN
ejpam-3118	342	3	,	,	PUNCT
ejpam-3118	342	4	142:511–526	142:511–526	NUM
ejpam-3118	342	5	,	,	PUNCT
ejpam-3118	342	6	1991	1991	NUM
ejpam-3118	342	7	.	.	PUNCT