id	sid	tid	token	lemma	pos
ejpam-5258	1	1	european	european	PROPN
ejpam-5258	1	2	journal	journal	PROPN
ejpam-5258	1	3	of	of	ADP
ejpam-5258	1	4	pure	pure	ADJ
ejpam-5258	1	5	and	and	CCONJ
ejpam-5258	1	6	applied	apply	VERB
ejpam-5258	1	7	mathematics	mathematic	NOUN
ejpam-5258	1	8	vol	vol	NOUN
ejpam-5258	1	9	.	.	PROPN
ejpam-5258	2	1	17	17	NUM
ejpam-5258	2	2	,	,	PUNCT
ejpam-5258	2	3	no	no	INTJ
ejpam-5258	2	4	.	.	NOUN
ejpam-5258	2	5	3	3	NUM
ejpam-5258	2	6	,	,	PUNCT
ejpam-5258	2	7	2024	2024	NUM
ejpam-5258	2	8	,	,	PUNCT
ejpam-5258	2	9	2329	2329	NUM
ejpam-5258	2	10	-	-	SYM
ejpam-5258	2	11	2335	2335	NUM
ejpam-5258	2	12	issn	issn	VERB
ejpam-5258	2	13	1307	1307	NUM
ejpam-5258	2	14	-	-	SYM
ejpam-5258	2	15	5543	5543	NUM
ejpam-5258	2	16	–	–	PUNCT
ejpam-5258	2	17	ejpam.com	ejpam.com	X
ejpam-5258	2	18	published	publish	VERB
ejpam-5258	2	19	by	by	ADP
ejpam-5258	2	20	new	new	PROPN
ejpam-5258	2	21	york	york	PROPN
ejpam-5258	2	22	business	business	PROPN
ejpam-5258	2	23	global	global	PROPN
ejpam-5258	2	24	exploring	explore	VERB
ejpam-5258	2	25	the	the	DET
ejpam-5258	2	26	associated	associated	ADJ
ejpam-5258	2	27	groups	group	NOUN
ejpam-5258	2	28	of	of	ADP
ejpam-5258	2	29	quasi	quasi	ADJ
ejpam-5258	2	30	-	-	ADJ
ejpam-5258	2	31	free	free	ADJ
ejpam-5258	2	32	groups	group	NOUN
ejpam-5258	2	33	abdulaziz	abdulaziz	PROPN
ejpam-5258	2	34	mutlaq	mutlaq	PROPN
ejpam-5258	2	35	alotaibi1	alotaibi1	PROPN
ejpam-5258	2	36	,	,	PUNCT
ejpam-5258	2	37	khaled	khaled	PROPN
ejpam-5258	2	38	mustafa	mustafa	PROPN
ejpam-5258	2	39	aljamal2,∗	aljamal2,∗	PROPN
ejpam-5258	2	40	1	1	NUM
ejpam-5258	2	41	department	department	NOUN
ejpam-5258	2	42	of	of	ADP
ejpam-5258	2	43	mathematics	mathematic	NOUN
ejpam-5258	2	44	,	,	PUNCT
ejpam-5258	2	45	college	college	NOUN
ejpam-5258	2	46	of	of	ADP
ejpam-5258	2	47	science	science	NOUN
ejpam-5258	2	48	and	and	CCONJ
ejpam-5258	2	49	humanities	humanity	NOUN
ejpam-5258	2	50	in	in	ADP
ejpam-5258	2	51	al	al	PROPN
ejpam-5258	2	52	-	-	PUNCT
ejpam-5258	2	53	kharj	kharj	PROPN
ejpam-5258	2	54	,	,	PUNCT
ejpam-5258	2	55	prince	prince	PROPN
ejpam-5258	2	56	sattam	sattam	PROPN
ejpam-5258	2	57	bin	bin	PROPN
ejpam-5258	2	58	abdulaziz	abdulaziz	PROPN
ejpam-5258	2	59	university	university	PROPN
ejpam-5258	2	60	,	,	PUNCT
ejpam-5258	2	61	al	al	PROPN
ejpam-5258	2	62	-	-	PUNCT
ejpam-5258	2	63	kharj	kharj	PROPN
ejpam-5258	2	64	11942	11942	NUM
ejpam-5258	2	65	,	,	PUNCT
ejpam-5258	3	1	saudi	saudi	PROPN
ejpam-5258	3	2	arabia	arabia	PROPN
ejpam-5258	3	3	2	2	NUM
ejpam-5258	3	4	faculty	faculty	NOUN
ejpam-5258	3	5	of	of	ADP
ejpam-5258	3	6	ocean	ocean	NOUN
ejpam-5258	3	7	engineering	engineering	NOUN
ejpam-5258	3	8	technology	technology	NOUN
ejpam-5258	3	9	and	and	CCONJ
ejpam-5258	3	10	informatics	informatic	NOUN
ejpam-5258	3	11	,	,	PUNCT
ejpam-5258	3	12	university	university	PROPN
ejpam-5258	3	13	malaysia	malaysia	PROPN
ejpam-5258	3	14	terengganu	terengganu	PROPN
ejpam-5258	3	15	,	,	PUNCT
ejpam-5258	3	16	21030	21030	NUM
ejpam-5258	3	17	kuala	kuala	PROPN
ejpam-5258	3	18	nerus	nerus	PROPN
ejpam-5258	3	19	,	,	PUNCT
ejpam-5258	3	20	terengganu	terengganu	PROPN
ejpam-5258	3	21	abstract	abstract	NOUN
ejpam-5258	3	22	.	.	PUNCT
ejpam-5258	4	1	let	let	VERB
ejpam-5258	4	2	g	g	PROPN
ejpam-5258	4	3	is	be	AUX
ejpam-5258	4	4	a	a	DET
ejpam-5258	4	5	cyclic	cyclic	ADJ
ejpam-5258	4	6	group	group	NOUN
ejpam-5258	4	7	.	.	PUNCT
ejpam-5258	5	1	then	then	ADV
ejpam-5258	5	2	h(g	h(g	VERB
ejpam-5258	5	3	)	)	PUNCT
ejpam-5258	5	4	is	be	AUX
ejpam-5258	5	5	a	a	DET
ejpam-5258	5	6	trivial	trivial	ADJ
ejpam-5258	5	7	group	group	NOUN
ejpam-5258	5	8	and	and	CCONJ
ejpam-5258	5	9	if	if	SCONJ
ejpam-5258	5	10	g	g	NOUN
ejpam-5258	5	11	=	=	PUNCT
ejpam-5258	5	12	g1∗	g1∗	PROPN
ejpam-5258	5	13	.	.	PUNCT
ejpam-5258	5	14	.	.	PUNCT
ejpam-5258	5	15	.	.	PUNCT
ejpam-5258	6	1	∗gn	∗gn	NOUN
ejpam-5258	6	2	is	be	AUX
ejpam-5258	6	3	the	the	DET
ejpam-5258	6	4	free	free	ADJ
ejpam-5258	6	5	product	product	NOUN
ejpam-5258	6	6	of	of	ADP
ejpam-5258	6	7	the	the	DET
ejpam-5258	6	8	groups	group	NOUN
ejpam-5258	6	9	g1	g1	VERB
ejpam-5258	6	10	,	,	PUNCT
ejpam-5258	6	11	.	.	PUNCT
ejpam-5258	6	12	.	.	PUNCT
ejpam-5258	7	1	.	.	PUNCT
ejpam-5258	8	1	,	,	PUNCT
ejpam-5258	8	2	gn	gn	PROPN
ejpam-5258	8	3	,	,	PUNCT
ejpam-5258	8	4	then	then	ADV
ejpam-5258	8	5	h(g	h(g	VERB
ejpam-5258	8	6	)	)	PUNCT
ejpam-5258	9	1	=	=	SYM
ejpam-5258	9	2	h(g1	h(g1	X
ejpam-5258	9	3	∗	∗	NOUN
ejpam-5258	9	4	.	.	PUNCT
ejpam-5258	9	5	.	.	PUNCT
ejpam-5258	9	6	.	.	PUNCT
ejpam-5258	10	1	∗	∗	NOUN
ejpam-5258	10	2	g∗	g∗	PROPN
ejpam-5258	10	3	)	)	PUNCT
ejpam-5258	10	4	≊	≊	NOUN
ejpam-5258	10	5	h(g1	h(g1	NOUN
ejpam-5258	10	6	)	)	PUNCT
ejpam-5258	10	7	×	×	NOUN
ejpam-5258	10	8	.	.	PUNCT
ejpam-5258	10	9	.	.	PUNCT
ejpam-5258	10	10	.	.	PUNCT
ejpam-5258	11	1	×	×	PROPN
ejpam-5258	11	2	h(gn	h(gn	NOUN
ejpam-5258	11	3	)	)	PUNCT
ejpam-5258	11	4	.	.	PUNCT
ejpam-5258	12	1	furthermore	furthermore	ADV
ejpam-5258	12	2	,	,	PUNCT
ejpam-5258	12	3	if	if	SCONJ
ejpam-5258	12	4	the	the	DET
ejpam-5258	12	5	groups	group	NOUN
ejpam-5258	12	6	g1	g1	VERB
ejpam-5258	12	7	,	,	PUNCT
ejpam-5258	12	8	g2	g2	PROPN
ejpam-5258	12	9	,	,	PUNCT
ejpam-5258	12	10	.	.	PUNCT
ejpam-5258	12	11	.	.	PUNCT
ejpam-5258	13	1	.	.	PUNCT
ejpam-5258	14	1	,	,	PUNCT
ejpam-5258	14	2	gnare	gnare	ADJ
ejpam-5258	14	3	cyclic	cyclic	ADJ
ejpam-5258	14	4	groups	group	NOUN
ejpam-5258	14	5	,	,	PUNCT
ejpam-5258	14	6	then	then	ADV
ejpam-5258	14	7	h(g	h(g	NOUN
ejpam-5258	14	8	)	)	PUNCT
ejpam-5258	14	9	is	be	AUX
ejpam-5258	14	10	a	a	DET
ejpam-5258	14	11	trivial	trivial	ADJ
ejpam-5258	14	12	group	group	NOUN
ejpam-5258	14	13	.	.	PUNCT
ejpam-5258	15	1	in	in	ADP
ejpam-5258	15	2	this	this	DET
ejpam-5258	15	3	paper	paper	NOUN
ejpam-5258	15	4	we	we	PRON
ejpam-5258	15	5	show	show	VERB
ejpam-5258	15	6	that	that	SCONJ
ejpam-5258	15	7	for	for	ADP
ejpam-5258	15	8	every	every	DET
ejpam-5258	15	9	group	group	NOUN
ejpam-5258	15	10	g	g	PROPN
ejpam-5258	15	11	there	there	PRON
ejpam-5258	15	12	exists	exist	VERB
ejpam-5258	15	13	a	a	DET
ejpam-5258	15	14	group	group	NOUN
ejpam-5258	15	15	denoted	denote	VERB
ejpam-5258	15	16	h(g	h(g	NOUN
ejpam-5258	15	17	)	)	PUNCT
ejpam-5258	15	18	and	and	CCONJ
ejpam-5258	15	19	is	be	AUX
ejpam-5258	15	20	called	call	VERB
ejpam-5258	15	21	the	the	DET
ejpam-5258	15	22	associated	associated	ADJ
ejpam-5258	15	23	group	group	NOUN
ejpam-5258	15	24	of	of	ADP
ejpam-5258	15	25	g	g	PROPN
ejpam-5258	15	26	satisfying	satisfy	VERB
ejpam-5258	15	27	some	some	DET
ejpam-5258	15	28	important	important	ADJ
ejpam-5258	15	29	properties	property	NOUN
ejpam-5258	15	30	that	that	PRON
ejpam-5258	15	31	as	as	ADP
ejpam-5258	15	32	application	application	NOUN
ejpam-5258	15	33	we	we	PRON
ejpam-5258	15	34	show	show	VERB
ejpam-5258	15	35	that	that	SCONJ
ejpam-5258	15	36	if	if	SCONJ
ejpam-5258	15	37	f	f	PROPN
ejpam-5258	15	38	is	be	AUX
ejpam-5258	15	39	a	a	DET
ejpam-5258	15	40	quasi	quasi	ADJ
ejpam-5258	15	41	-	-	ADJ
ejpam-5258	15	42	free	free	ADJ
ejpam-5258	15	43	group	group	NOUN
ejpam-5258	15	44	and	and	CCONJ
ejpam-5258	15	45	g	g	PROPN
ejpam-5258	15	46	is	be	AUX
ejpam-5258	15	47	any	any	DET
ejpam-5258	15	48	group	group	NOUN
ejpam-5258	15	49	,	,	PUNCT
ejpam-5258	15	50	then	then	ADV
ejpam-5258	15	51	h(f	h(f	PROPN
ejpam-5258	15	52	)	)	PUNCT
ejpam-5258	15	53	is	be	AUX
ejpam-5258	15	54	trivial	trivial	ADJ
ejpam-5258	15	55	and	and	CCONJ
ejpam-5258	15	56	h(f	h(f	NOUN
ejpam-5258	15	57	∗	∗	NOUN
ejpam-5258	15	58	g	g	NOUN
ejpam-5258	15	59	)	)	PUNCT
ejpam-5258	15	60	≊	≊	NOUN
ejpam-5258	15	61	h(g	h(g	NOUN
ejpam-5258	15	62	)	)	PUNCT
ejpam-5258	15	63	,	,	PUNCT
ejpam-5258	15	64	where	where	SCONJ
ejpam-5258	15	65	a	a	DET
ejpam-5258	15	66	group	group	NOUN
ejpam-5258	15	67	is	be	AUX
ejpam-5258	15	68	termed	term	VERB
ejpam-5258	15	69	a	a	DET
ejpam-5258	15	70	quasi	quasi	ADJ
ejpam-5258	15	71	-	-	ADJ
ejpam-5258	15	72	free	free	ADJ
ejpam-5258	15	73	group	group	NOUN
ejpam-5258	15	74	if	if	SCONJ
ejpam-5258	15	75	it	it	PRON
ejpam-5258	15	76	is	be	AUX
ejpam-5258	15	77	a	a	DET
ejpam-5258	15	78	free	free	ADJ
ejpam-5258	15	79	product	product	NOUN
ejpam-5258	15	80	of	of	ADP
ejpam-5258	15	81	cyclic	cyclic	ADJ
ejpam-5258	15	82	groups	group	NOUN
ejpam-5258	15	83	of	of	ADP
ejpam-5258	15	84	any	any	DET
ejpam-5258	15	85	order	order	NOUN
ejpam-5258	15	86	.	.	PUNCT
ejpam-5258	16	1	2020	2020	NUM
ejpam-5258	16	2	mathematics	mathematic	NOUN
ejpam-5258	16	3	subject	subject	NOUN
ejpam-5258	16	4	classifications	classification	NOUN
ejpam-5258	16	5	:	:	PUNCT
ejpam-5258	16	6	16u60	16u60	NUM
ejpam-5258	16	7	,	,	PUNCT
ejpam-5258	16	8	20c05	20c05	NUM
ejpam-5258	16	9	,	,	PUNCT
ejpam-5258	16	10	16s34	16s34	NUM
ejpam-5258	16	11	,	,	PUNCT
ejpam-5258	16	12	20e06	20e06	NUM
ejpam-5258	16	13	key	key	ADJ
ejpam-5258	16	14	words	word	NOUN
ejpam-5258	16	15	and	and	CCONJ
ejpam-5258	16	16	phrases	phrase	NOUN
ejpam-5258	16	17	:	:	PUNCT
ejpam-5258	16	18	free	free	ADJ
ejpam-5258	16	19	groups	group	NOUN
ejpam-5258	16	20	,	,	PUNCT
ejpam-5258	16	21	cyclic	cyclic	ADJ
ejpam-5258	16	22	groups	group	NOUN
ejpam-5258	16	23	,	,	PUNCT
ejpam-5258	16	24	quasi	quasi	ADJ
ejpam-5258	16	25	-	-	ADJ
ejpam-5258	16	26	free	free	ADJ
ejpam-5258	16	27	group	group	NOUN
ejpam-5258	16	28	,	,	PUNCT
ejpam-5258	16	29	free	free	ADJ
ejpam-5258	16	30	product	product	NOUN
ejpam-5258	16	31	of	of	ADP
ejpam-5258	16	32	groups	group	NOUN
ejpam-5258	16	33	and	and	CCONJ
ejpam-5258	16	34	associated	associated	ADJ
ejpam-5258	16	35	groups	group	NOUN
ejpam-5258	16	36	.	.	PUNCT
ejpam-5258	17	1	1	1	X
ejpam-5258	17	2	.	.	X
ejpam-5258	17	3	introduction	introduction	NOUN
ejpam-5258	17	4	we	we	PRON
ejpam-5258	17	5	introduce	introduce	VERB
ejpam-5258	17	6	the	the	DET
ejpam-5258	17	7	following	following	ADJ
ejpam-5258	17	8	basic	basic	ADJ
ejpam-5258	17	9	concepts	concept	NOUN
ejpam-5258	17	10	needed	need	VERB
ejpam-5258	17	11	for	for	ADP
ejpam-5258	17	12	the	the	DET
ejpam-5258	17	13	definition	definition	NOUN
ejpam-5258	17	14	of	of	ADP
ejpam-5258	17	15	associated	associated	ADJ
ejpam-5258	17	16	groups	group	NOUN
ejpam-5258	17	17	of	of	ADP
ejpam-5258	17	18	given	give	VERB
ejpam-5258	17	19	groups	group	NOUN
ejpam-5258	17	20	[	[	X
ejpam-5258	17	21	1	1	NUM
ejpam-5258	17	22	]	]	PUNCT
ejpam-5258	17	23	.	.	PUNCT
ejpam-5258	18	1	(	(	PUNCT
ejpam-5258	18	2	1	1	X
ejpam-5258	18	3	)	)	PUNCT
ejpam-5258	18	4	let	let	VERB
ejpam-5258	18	5	g	g	NOUN
ejpam-5258	18	6	be	be	AUX
ejpam-5258	18	7	a	a	DET
ejpam-5258	18	8	group	group	NOUN
ejpam-5258	18	9	.	.	PUNCT
ejpam-5258	19	1	i.	i.	PROPN
ejpam-5258	19	2	if	if	SCONJ
ejpam-5258	19	3	a	a	PRON
ejpam-5258	19	4	and	and	CCONJ
ejpam-5258	19	5	b	b	NOUN
ejpam-5258	19	6	are	be	AUX
ejpam-5258	19	7	two	two	NUM
ejpam-5258	19	8	subsets	subset	NOUN
ejpam-5258	19	9	of	of	ADP
ejpam-5258	19	10	g	g	NOUN
ejpam-5258	19	11	,	,	PUNCT
ejpam-5258	19	12	let	let	VERB
ejpam-5258	19	13	[	[	X
ejpam-5258	19	14	a	a	X
ejpam-5258	19	15	,	,	PUNCT
ejpam-5258	19	16	b	b	NOUN
ejpam-5258	19	17	]	]	PUNCT
ejpam-5258	19	18	be	be	AUX
ejpam-5258	19	19	the	the	DET
ejpam-5258	19	20	subgroup	subgroup	NOUN
ejpam-5258	19	21	of	of	ADP
ejpam-5258	19	22	g	g	PROPN
ejpam-5258	19	23	generated	generate	VERB
ejpam-5258	19	24	by	by	ADP
ejpam-5258	19	25	the	the	DET
ejpam-5258	19	26	elements	element	NOUN
ejpam-5258	19	27	[	[	X
ejpam-5258	19	28	a	a	X
ejpam-5258	19	29	,	,	PUNCT
ejpam-5258	19	30	b	b	NOUN
ejpam-5258	19	31	]	]	X
ejpam-5258	19	32	=	=	PUNCT
ejpam-5258	19	33	aba−1b−1	aba−1b−1	PROPN
ejpam-5258	19	34	with	with	ADP
ejpam-5258	19	35	a	a	DET
ejpam-5258	19	36	∈	∈	PROPN
ejpam-5258	19	37	a	a	DET
ejpam-5258	19	38	and	and	CCONJ
ejpam-5258	19	39	b	b	PROPN
ejpam-5258	19	40	∈	∈	PROPN
ejpam-5258	19	41	b.	b.	PROPN
ejpam-5258	19	42	define	define	VERB
ejpam-5258	19	43	g′	g′	NOUN
ejpam-5258	19	44	=	=	PUNCT
ejpam-5258	20	1	[	[	X
ejpam-5258	20	2	g	g	NOUN
ejpam-5258	20	3	,	,	PUNCT
ejpam-5258	20	4	g	g	NOUN
ejpam-5258	20	5	]	]	PUNCT
ejpam-5258	20	6	to	to	PART
ejpam-5258	20	7	be	be	AUX
ejpam-5258	20	8	the	the	DET
ejpam-5258	20	9	derived	derived	ADJ
ejpam-5258	20	10	subgroup	subgroup	NOUN
ejpam-5258	20	11	of	of	ADP
ejpam-5258	20	12	g	g	PROPN
ejpam-5258	20	13	generated	generate	VERB
ejpam-5258	20	14	by	by	ADP
ejpam-5258	20	15	the	the	DET
ejpam-5258	20	16	elements	element	NOUN
ejpam-5258	20	17	[	[	X
ejpam-5258	20	18	x	x	X
ejpam-5258	20	19	,	,	PUNCT
ejpam-5258	20	20	y	y	PROPN
ejpam-5258	20	21	]	]	X
ejpam-5258	20	22	=	=	PUNCT
ejpam-5258	20	23	xyx−1y−1	xyx−1y−1	PROPN
ejpam-5258	20	24	with	with	ADP
ejpam-5258	20	25	x	x	PROPN
ejpam-5258	20	26	,	,	PUNCT
ejpam-5258	20	27	y	y	PROPN
ejpam-5258	20	28	∈	∈	PROPN
ejpam-5258	20	29	g.	g.	NOUN
ejpam-5258	21	1	it	it	PRON
ejpam-5258	21	2	is	be	AUX
ejpam-5258	21	3	clear	clear	ADJ
ejpam-5258	21	4	that	that	SCONJ
ejpam-5258	21	5	g′	g′	NOUN
ejpam-5258	21	6	is	be	AUX
ejpam-5258	21	7	a	a	DET
ejpam-5258	21	8	normal	normal	ADJ
ejpam-5258	21	9	subgroup	subgroup	NOUN
ejpam-5258	21	10	of	of	ADP
ejpam-5258	21	11	g.	g.	PROPN
ejpam-5258	21	12	for	for	SCONJ
ejpam-5258	21	13	more	more	ADJ
ejpam-5258	21	14	details	detail	NOUN
ejpam-5258	21	15	see	see	VERB
ejpam-5258	21	16	[	[	X
ejpam-5258	21	17	8	8	NUM
ejpam-5258	21	18	]	]	PUNCT
ejpam-5258	21	19	.	.	PUNCT
ejpam-5258	22	1	ii	ii	PROPN
ejpam-5258	22	2	.	.	PUNCT
ejpam-5258	23	1	if	if	SCONJ
ejpam-5258	23	2	r	r	NOUN
ejpam-5258	23	3	is	be	AUX
ejpam-5258	23	4	a	a	DET
ejpam-5258	23	5	subset	subset	NOUN
ejpam-5258	23	6	of	of	ADP
ejpam-5258	23	7	g	g	NOUN
ejpam-5258	23	8	,	,	PUNCT
ejpam-5258	23	9	let	let	VERB
ejpam-5258	23	10	rg	rg	PRON
ejpam-5258	23	11	to	to	PART
ejpam-5258	23	12	be	be	AUX
ejpam-5258	23	13	the	the	DET
ejpam-5258	23	14	intersection	intersection	NOUN
ejpam-5258	23	15	of	of	ADP
ejpam-5258	23	16	all	all	DET
ejpam-5258	23	17	normal	normal	ADJ
ejpam-5258	23	18	subgroups	subgroup	NOUN
ejpam-5258	23	19	of	of	ADP
ejpam-5258	23	20	g	g	NOUN
ejpam-5258	23	21	containing	contain	VERB
ejpam-5258	23	22	r.	r.	PROPN
ejpam-5258	23	23	it	it	PRON
ejpam-5258	23	24	is	be	AUX
ejpam-5258	23	25	clear	clear	ADJ
ejpam-5258	23	26	that	that	SCONJ
ejpam-5258	23	27	r	r	NOUN
ejpam-5258	23	28	⊆	⊆	NUM
ejpam-5258	23	29	rg	rg	PROPN
ejpam-5258	23	30	and	and	CCONJ
ejpam-5258	23	31	rg	rg	PROPN
ejpam-5258	23	32	is	be	AUX
ejpam-5258	23	33	a	a	DET
ejpam-5258	23	34	normal	normal	ADJ
ejpam-5258	23	35	subgroup	subgroup	NOUN
ejpam-5258	23	36	of	of	ADP
ejpam-5258	23	37	g	g	PROPN
ejpam-5258	24	1	[	[	X
ejpam-5258	24	2	7	7	NUM
ejpam-5258	24	3	]	]	PUNCT
ejpam-5258	24	4	.	.	PUNCT
ejpam-5258	25	1	∗corresponding	∗corresponde	VERB
ejpam-5258	25	2	author	author	NOUN
ejpam-5258	25	3	.	.	PUNCT
ejpam-5258	26	1	doi	doi	NOUN
ejpam-5258	26	2	:	:	PUNCT
ejpam-5258	26	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5258	https://doi.org/10.29020/nybg.ejpam.v17i3.5258	NOUN
ejpam-5258	26	4	email	email	NOUN
ejpam-5258	26	5	addresses	address	NOUN
ejpam-5258	26	6	:	:	PUNCT
ejpam-5258	26	7	am.alotaibi@psau.edu.sa	am.alotaibi@psau.edu.sa	PROPN
ejpam-5258	26	8	(	(	PUNCT
ejpam-5258	26	9	a.	a.	NOUN
ejpam-5258	26	10	m.	m.	NOUN
ejpam-5258	26	11	alotaibi	alotaibi	PROPN
ejpam-5258	26	12	)	)	PUNCT
ejpam-5258	26	13	,	,	PUNCT
ejpam-5258	26	14	khaled	khale	VERB
ejpam-5258	26	15	aljammal@yahoo.com	aljammal@yahoo.com	PROPN
ejpam-5258	27	1	(	(	PUNCT
ejpam-5258	27	2	k.	k.	PROPN
ejpam-5258	27	3	m.	m.	PROPN
ejpam-5258	27	4	aljamal	aljamal	PROPN
ejpam-5258	27	5	)	)	PUNCT
ejpam-5258	27	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5258	27	7	2329	2329	NUM
ejpam-5258	28	1	©	©	ADP
ejpam-5258	28	2	2024	2024	NUM
ejpam-5258	28	3	ejpam	ejpam	NOUN
ejpam-5258	28	4	all	all	DET
ejpam-5258	28	5	rights	right	NOUN
ejpam-5258	28	6	reserved	reserve	VERB
ejpam-5258	28	7	.	.	PUNCT
ejpam-5258	29	1	a.	a.	PROPN
ejpam-5258	29	2	m.	m.	PROPN
ejpam-5258	29	3	alotaibi	alotaibi	PROPN
ejpam-5258	29	4	,	,	PUNCT
ejpam-5258	29	5	k.	k.	PROPN
ejpam-5258	29	6	m.	m.	PROPN
ejpam-5258	29	7	aljamal	aljamal	PROPN
ejpam-5258	29	8	/	/	SYM
ejpam-5258	29	9	eur	eur	PROPN
ejpam-5258	29	10	.	.	PUNCT
ejpam-5258	30	1	j.	j.	PROPN
ejpam-5258	30	2	pure	pure	PROPN
ejpam-5258	30	3	appl	appl	PROPN
ejpam-5258	30	4	.	.	PROPN
ejpam-5258	30	5	math	math	PROPN
ejpam-5258	30	6	,	,	PUNCT
ejpam-5258	30	7	17	17	NUM
ejpam-5258	30	8	(	(	PUNCT
ejpam-5258	30	9	3	3	NUM
ejpam-5258	30	10	)	)	PUNCT
ejpam-5258	30	11	(	(	PUNCT
ejpam-5258	30	12	2024	2024	NUM
ejpam-5258	30	13	)	)	PUNCT
ejpam-5258	30	14	,	,	PUNCT
ejpam-5258	30	15	2329	2329	NUM
ejpam-5258	30	16	-	-	SYM
ejpam-5258	30	17	2335	2335	NUM
ejpam-5258	30	18	2330	2330	NUM
ejpam-5258	30	19	(	(	PUNCT
ejpam-5258	30	20	2	2	X
ejpam-5258	30	21	)	)	PUNCT
ejpam-5258	30	22	let	let	VERB
ejpam-5258	30	23	x	x	PRON
ejpam-5258	30	24	be	be	AUX
ejpam-5258	30	25	a	a	DET
ejpam-5258	30	26	set	set	NOUN
ejpam-5258	30	27	and	and	CCONJ
ejpam-5258	30	28	let	let	VERB
ejpam-5258	30	29	fx	fx	NOUN
ejpam-5258	30	30	be	be	AUX
ejpam-5258	30	31	the	the	DET
ejpam-5258	30	32	free	free	ADJ
ejpam-5258	30	33	group	group	NOUN
ejpam-5258	30	34	of	of	ADP
ejpam-5258	30	35	the	the	DET
ejpam-5258	30	36	reduced	reduce	VERB
ejpam-5258	30	37	words	word	NOUN
ejpam-5258	30	38	of	of	ADP
ejpam-5258	30	39	x	x	PUNCT
ejpam-5258	30	40	generated	generate	VERB
ejpam-5258	30	41	by	by	ADP
ejpam-5258	30	42	x.	x.	NOUN
ejpam-5258	30	43	then	then	ADV
ejpam-5258	30	44	any	any	DET
ejpam-5258	30	45	element	element	NOUN
ejpam-5258	30	46	f	f	PROPN
ejpam-5258	30	47	∈	∈	PROPN
ejpam-5258	30	48	fx	fx	PROPN
ejpam-5258	30	49	,	,	PUNCT
ejpam-5258	30	50	f	f	PROPN
ejpam-5258	30	51	̸=	̸=	PROPN
ejpam-5258	30	52	1	1	NUM
ejpam-5258	30	53	is	be	AUX
ejpam-5258	30	54	uniquely	uniquely	ADV
ejpam-5258	30	55	written	write	VERB
ejpam-5258	30	56	as	as	ADP
ejpam-5258	30	57	f	f	PROPN
ejpam-5258	30	58	=	=	SYM
ejpam-5258	30	59	x1	x1	PROPN
ejpam-5258	30	60	α1χ2	α1χ2	X
ejpam-5258	30	61	α2	α2	ADJ
ejpam-5258	30	62	.	.	PUNCT
ejpam-5258	30	63	.	.	PUNCT
ejpam-5258	30	64	.	.	PUNCT
ejpam-5258	31	1	xn	xn	PROPN
ejpam-5258	31	2	αn	αn	NUM
ejpam-5258	31	3	,	,	PUNCT
ejpam-5258	31	4	xα+1	xα+1	PROPN
ejpam-5258	32	1	i+1	i+1	ADJ
ejpam-5258	32	2	̸=	̸=	PROPN
ejpam-5258	32	3	−αi	−αi	NOUN
ejpam-5258	32	4	,	,	PUNCT
ejpam-5258	32	5	xi	xi	ADP
ejpam-5258	32	6	∈	∈	PROPN
ejpam-5258	32	7	x	x	X
ejpam-5258	32	8	,	,	PUNCT
ejpam-5258	32	9	αi	αi	X
ejpam-5258	32	10	=	=	SYM
ejpam-5258	32	11	±1	±1	PROPN
ejpam-5258	32	12	,	,	PUNCT
ejpam-5258	32	13	i	i	PRON
ejpam-5258	32	14	=	=	NOUN
ejpam-5258	32	15	1	1	NUM
ejpam-5258	32	16	,	,	PUNCT
ejpam-5258	32	17	2	2	NUM
ejpam-5258	32	18	,	,	PUNCT
ejpam-5258	32	19	.	.	PUNCT
ejpam-5258	32	20	.	.	PUNCT
ejpam-5258	32	21	.	.	PUNCT
ejpam-5258	33	1	,	,	PUNCT
ejpam-5258	33	2	n.	n.	PROPN
ejpam-5258	33	3	a	a	DET
ejpam-5258	33	4	group	group	NOUN
ejpam-5258	33	5	h	h	NOUN
ejpam-5258	33	6	is	be	AUX
ejpam-5258	33	7	called	call	VERB
ejpam-5258	33	8	a	a	DET
ejpam-5258	33	9	free	free	ADJ
ejpam-5258	33	10	group	group	NOUN
ejpam-5258	33	11	of	of	ADP
ejpam-5258	33	12	base	base	NOUN
ejpam-5258	33	13	s	s	PART
ejpam-5258	33	14	⊆	⊆	NUM
ejpam-5258	33	15	h	h	NOUN
ejpam-5258	33	16	if	if	SCONJ
ejpam-5258	33	17	h	h	NOUN
ejpam-5258	33	18	is	be	AUX
ejpam-5258	33	19	isomorphic	isomorphic	ADJ
ejpam-5258	33	20	to	to	ADP
ejpam-5258	33	21	fs	fs	ADP
ejpam-5258	33	22	that	that	PRON
ejpam-5258	33	23	is	be	AUX
ejpam-5258	33	24	,	,	PUNCT
ejpam-5258	34	1	h	h	NOUN
ejpam-5258	34	2	∼=	∼=	PART
ejpam-5258	34	3	fs	f	NOUN
ejpam-5258	34	4	.	.	PUNCT
ejpam-5258	35	1	the	the	DET
ejpam-5258	35	2	universal	universal	ADJ
ejpam-5258	35	3	property	property	NOUN
ejpam-5258	35	4	of	of	ADP
ejpam-5258	35	5	the	the	DET
ejpam-5258	35	6	free	free	ADJ
ejpam-5258	35	7	group	group	NOUN
ejpam-5258	35	8	f	f	PROPN
ejpam-5258	35	9	of	of	ADP
ejpam-5258	35	10	base	base	NOUN
ejpam-5258	35	11	s	s	PART
ejpam-5258	36	1	[	[	X
ejpam-5258	36	2	4	4	NUM
ejpam-5258	36	3	]	]	PUNCT
ejpam-5258	36	4	,	,	PUNCT
ejpam-5258	36	5	states	state	VERB
ejpam-5258	36	6	that	that	SCONJ
ejpam-5258	36	7	given	give	VERB
ejpam-5258	36	8	any	any	DET
ejpam-5258	36	9	function	function	NOUN
ejpam-5258	36	10	f	f	NOUN
ejpam-5258	36	11	:	:	PUNCT
ejpam-5258	36	12	s	s	X
ejpam-5258	36	13	→	→	SYM
ejpam-5258	36	14	g	g	NOUN
ejpam-5258	36	15	from	from	ADP
ejpam-5258	36	16	s	s	PRON
ejpam-5258	36	17	to	to	ADP
ejpam-5258	36	18	a	a	DET
ejpam-5258	36	19	group	group	NOUN
ejpam-5258	36	20	g	g	NOUN
ejpam-5258	36	21	,	,	PUNCT
ejpam-5258	36	22	there	there	PRON
ejpam-5258	36	23	exists	exist	VERB
ejpam-5258	36	24	a	a	DET
ejpam-5258	36	25	unique	unique	ADJ
ejpam-5258	36	26	homomorphism	homomorphism	NOUN
ejpam-5258	36	27	φ	φ	X
ejpam-5258	36	28	:	:	PUNCT
ejpam-5258	36	29	fs	fs	X
ejpam-5258	36	30	→	→	SYM
ejpam-5258	36	31	g	g	NOUN
ejpam-5258	36	32	called	call	VERB
ejpam-5258	36	33	the	the	DET
ejpam-5258	36	34	universal	universal	ADJ
ejpam-5258	36	35	extension	extension	NOUN
ejpam-5258	36	36	of	of	ADP
ejpam-5258	36	37	f	f	PROPN
ejpam-5258	36	38	,	,	PUNCT
ejpam-5258	36	39	that	that	ADV
ejpam-5258	36	40	is	is	ADV
ejpam-5258	36	41	,	,	PUNCT
ejpam-5258	36	42	if	if	SCONJ
ejpam-5258	36	43	a	a	DET
ejpam-5258	36	44	∈	∈	PROPN
ejpam-5258	36	45	s	s	NOUN
ejpam-5258	36	46	,	,	PUNCT
ejpam-5258	36	47	then	then	ADV
ejpam-5258	36	48	φ(a	φ(a	ADJ
ejpam-5258	36	49	)	)	PUNCT
ejpam-5258	36	50	=	=	SYM
ejpam-5258	36	51	f(a	f(a	PROPN
ejpam-5258	36	52	)	)	PUNCT
ejpam-5258	36	53	.	.	PUNCT
ejpam-5258	37	1	also	also	ADV
ejpam-5258	37	2	,	,	PUNCT
ejpam-5258	37	3	φ	φ	PROPN
ejpam-5258	37	4	is	be	AUX
ejpam-5258	37	5	an	an	DET
ejpam-5258	37	6	epimorphism	epimorphism	NOUN
ejpam-5258	37	7	if	if	SCONJ
ejpam-5258	37	8	and	and	CCONJ
ejpam-5258	37	9	only	only	ADV
ejpam-5258	37	10	if	if	SCONJ
ejpam-5258	37	11	f(s	f(	NOUN
ejpam-5258	37	12	)	)	PUNCT
ejpam-5258	37	13	generates	generate	VERB
ejpam-5258	37	14	g.	g.	NOUN
ejpam-5258	37	15	(	(	PUNCT
ejpam-5258	37	16	3	3	X
ejpam-5258	37	17	)	)	PUNCT
ejpam-5258	37	18	let	let	VERB
ejpam-5258	37	19	x	x	PRON
ejpam-5258	37	20	be	be	AUX
ejpam-5258	37	21	a	a	DET
ejpam-5258	37	22	set	set	NOUN
ejpam-5258	37	23	and	and	CCONJ
ejpam-5258	37	24	let	let	VERB
ejpam-5258	37	25	r	r	PRON
ejpam-5258	37	26	⊆	⊆	NUM
ejpam-5258	37	27	fx	fx	ADP
ejpam-5258	37	28	a	a	DET
ejpam-5258	37	29	subset	subset	NOUN
ejpam-5258	37	30	of	of	ADP
ejpam-5258	37	31	fx	fx	PROPN
ejpam-5258	37	32	.	.	PUNCT
ejpam-5258	38	1	let	let	VERB
ejpam-5258	38	2	⟨x	⟨x	AUX
ejpam-5258	38	3	|	|	ADV
ejpam-5258	38	4	r⟩	r⟩	ADV
ejpam-5258	38	5	stand	stand	VERB
ejpam-5258	38	6	for	for	ADP
ejpam-5258	38	7	the	the	DET
ejpam-5258	38	8	quotient	quotient	NOUN
ejpam-5258	38	9	group	group	NOUN
ejpam-5258	38	10	,	,	PUNCT
ejpam-5258	38	11	such	such	ADJ
ejpam-5258	38	12	that	that	SCONJ
ejpam-5258	38	13	⟨x	⟨x	VERB
ejpam-5258	38	14	|	|	ADV
ejpam-5258	39	1	r⟩	r⟩	NOUN
ejpam-5258	39	2	=	=	ADJ
ejpam-5258	39	3	fx	fx	PROPN
ejpam-5258	39	4	/	/	SYM
ejpam-5258	39	5	r̄	r̄	NOUN
ejpam-5258	39	6	,	,	PUNCT
ejpam-5258	39	7	where	where	SCONJ
ejpam-5258	39	8	r̄	r̄	NOUN
ejpam-5258	39	9	=	=	SYM
ejpam-5258	39	10	rfx	rfx	PROPN
ejpam-5258	39	11	is	be	AUX
ejpam-5258	39	12	the	the	DET
ejpam-5258	39	13	normal	normal	ADJ
ejpam-5258	39	14	closure	closure	NOUN
ejpam-5258	39	15	of	of	ADP
ejpam-5258	39	16	r	r	NOUN
ejpam-5258	39	17	in	in	ADP
ejpam-5258	39	18	fx	fx	NOUN
ejpam-5258	39	19	.⟨x	.⟨x	PUNCT
ejpam-5258	40	1	|	|	ADV
ejpam-5258	40	2	r⟩	r⟩	INTJ
ejpam-5258	40	3	is	be	AUX
ejpam-5258	40	4	called	call	VERB
ejpam-5258	40	5	a	a	DET
ejpam-5258	40	6	presentation	presentation	NOUN
ejpam-5258	40	7	.	.	PUNCT
ejpam-5258	41	1	we	we	PRON
ejpam-5258	41	2	say	say	VERB
ejpam-5258	41	3	that	that	SCONJ
ejpam-5258	41	4	the	the	DET
ejpam-5258	41	5	group	group	NOUN
ejpam-5258	41	6	g	g	PROPN
ejpam-5258	41	7	has	have	VERB
ejpam-5258	41	8	the	the	DET
ejpam-5258	41	9	presentation	presentation	NOUN
ejpam-5258	41	10	⟨x	⟨x	VERB
ejpam-5258	42	1	|	|	ADV
ejpam-5258	42	2	r⟩	r⟩	INTJ
ejpam-5258	42	3	if	if	SCONJ
ejpam-5258	42	4	g	g	PROPN
ejpam-5258	42	5	∼=	∼=	PROPN
ejpam-5258	42	6	⟨x	⟨x	VERB
ejpam-5258	42	7	|	|	ADV
ejpam-5258	42	8	r⟩.	r⟩.	NOUN
ejpam-5258	42	9	from	from	ADP
ejpam-5258	42	10	above	above	ADP
ejpam-5258	42	11	we	we	PRON
ejpam-5258	42	12	see	see	VERB
ejpam-5258	42	13	that	that	SCONJ
ejpam-5258	42	14	a	a	DET
ejpam-5258	42	15	group	group	NOUN
ejpam-5258	42	16	g	g	PROPN
ejpam-5258	42	17	has	have	VERB
ejpam-5258	42	18	the	the	DET
ejpam-5258	42	19	presentation	presentation	NOUN
ejpam-5258	42	20	⟨x	⟨x	VERB
ejpam-5258	43	1	|	|	ADV
ejpam-5258	43	2	r⟩	r⟩	INTJ
ejpam-5258	43	3	if	if	SCONJ
ejpam-5258	43	4	and	and	CCONJ
ejpam-5258	43	5	only	only	ADV
ejpam-5258	43	6	if	if	SCONJ
ejpam-5258	43	7	there	there	PRON
ejpam-5258	43	8	exists	exist	VERB
ejpam-5258	43	9	an	an	DET
ejpam-5258	43	10	onto	onto	ADP
ejpam-5258	43	11	function	function	NOUN
ejpam-5258	43	12	f	f	NOUN
ejpam-5258	43	13	:	:	PUNCT
ejpam-5258	43	14	x	x	X
ejpam-5258	43	15	→	→	SYM
ejpam-5258	43	16	g	g	PROPN
ejpam-5258	43	17	,	,	PUNCT
ejpam-5258	43	18	such	such	ADJ
ejpam-5258	43	19	that	that	SCONJ
ejpam-5258	43	20	f(x	f(x	PROPN
ejpam-5258	43	21	)	)	PUNCT
ejpam-5258	43	22	generates	generate	VERB
ejpam-5258	43	23	g	g	NOUN
ejpam-5258	43	24	and	and	CCONJ
ejpam-5258	43	25	the	the	DET
ejpam-5258	43	26	normal	normal	ADJ
ejpam-5258	43	27	closure	closure	NOUN
ejpam-5258	43	28	rfx	rfx	NOUN
ejpam-5258	43	29	of	of	ADP
ejpam-5258	43	30	r	r	NOUN
ejpam-5258	43	31	in	in	ADP
ejpam-5258	43	32	fx	fx	NOUN
ejpam-5258	43	33	satisfies	satisfy	VERB
ejpam-5258	43	34	the	the	DET
ejpam-5258	43	35	condition	condition	NOUN
ejpam-5258	43	36	that	that	SCONJ
ejpam-5258	43	37	rfx	rfx	PROPN
ejpam-5258	43	38	=	=	SYM
ejpam-5258	43	39	ker(φ	ker(φ	NOUN
ejpam-5258	43	40	)	)	PUNCT
ejpam-5258	43	41	,	,	PUNCT
ejpam-5258	43	42	where	where	SCONJ
ejpam-5258	43	43	φ	φ	NOUN
ejpam-5258	43	44	:	:	PUNCT
ejpam-5258	43	45	fx	fx	PROPN
ejpam-5258	43	46	→	→	SYM
ejpam-5258	43	47	g	g	PROPN
ejpam-5258	43	48	is	be	AUX
ejpam-5258	43	49	the	the	DET
ejpam-5258	43	50	universal	universal	ADJ
ejpam-5258	43	51	extension	extension	NOUN
ejpam-5258	43	52	of	of	ADP
ejpam-5258	43	53	f	f	PROPN
ejpam-5258	43	54	.	.	PUNCT
ejpam-5258	44	1	2	2	X
ejpam-5258	44	2	.	.	X
ejpam-5258	44	3	the	the	DET
ejpam-5258	44	4	associated	associated	ADJ
ejpam-5258	44	5	groups	group	NOUN
ejpam-5258	44	6	the	the	DET
ejpam-5258	44	7	concept	concept	NOUN
ejpam-5258	44	8	of	of	ADP
ejpam-5258	44	9	the	the	DET
ejpam-5258	44	10	associated	associated	ADJ
ejpam-5258	44	11	group	group	NOUN
ejpam-5258	44	12	of	of	ADP
ejpam-5258	44	13	a	a	DET
ejpam-5258	44	14	given	give	VERB
ejpam-5258	44	15	group	group	NOUN
ejpam-5258	44	16	is	be	AUX
ejpam-5258	44	17	introduced	introduce	VERB
ejpam-5258	44	18	in	in	ADP
ejpam-5258	44	19	[	[	X
ejpam-5258	44	20	3	3	NUM
ejpam-5258	44	21	]	]	PUNCT
ejpam-5258	44	22	and	and	CCONJ
ejpam-5258	44	23	[	[	X
ejpam-5258	44	24	6	6	NUM
ejpam-5258	44	25	]	]	PUNCT
ejpam-5258	44	26	is	be	AUX
ejpam-5258	44	27	defined	define	VERB
ejpam-5258	44	28	as	as	SCONJ
ejpam-5258	44	29	follows	follow	VERB
ejpam-5258	44	30	.	.	PUNCT
ejpam-5258	45	1	let	let	VERB
ejpam-5258	45	2	g	g	NOUN
ejpam-5258	45	3	denote	denote	VERB
ejpam-5258	45	4	an	an	DET
ejpam-5258	45	5	arbitrary	arbitrary	ADJ
ejpam-5258	45	6	group	group	NOUN
ejpam-5258	45	7	.	.	PUNCT
ejpam-5258	46	1	for	for	ADP
ejpam-5258	46	2	x	x	SYM
ejpam-5258	46	3	,	,	PUNCT
ejpam-5258	46	4	y	y	PROPN
ejpam-5258	46	5	∈	∈	PROPN
ejpam-5258	46	6	g	g	PROPN
ejpam-5258	46	7	,	,	PUNCT
ejpam-5258	46	8	let	let	VERB
ejpam-5258	46	9	⟨x	⟨x	VERB
ejpam-5258	46	10	,	,	PUNCT
ejpam-5258	46	11	y⟩	y⟩	NOUN
ejpam-5258	46	12	and	and	CCONJ
ejpam-5258	46	13	let	let	VERB
ejpam-5258	46	14	⟨g	⟨g	NOUN
ejpam-5258	46	15	,	,	PUNCT
ejpam-5258	46	16	g⟩	g⟩	PUNCT
ejpam-5258	46	17	=	=	X
ejpam-5258	46	18	{	{	PUNCT
ejpam-5258	46	19	⟨x	⟨x	NUM
ejpam-5258	46	20	,	,	PUNCT
ejpam-5258	46	21	y⟩	y⟩	NOUN
ejpam-5258	46	22	:	:	PUNCT
ejpam-5258	46	23	x	x	X
ejpam-5258	46	24	,	,	PUNCT
ejpam-5258	46	25	y	y	PROPN
ejpam-5258	46	26	∈	∈	PROPN
ejpam-5258	46	27	g	g	PROPN
ejpam-5258	46	28	}	}	PUNCT
ejpam-5258	46	29	and	and	CCONJ
ejpam-5258	46	30	f⟨g	f⟨g	NUM
ejpam-5258	46	31	,	,	PUNCT
ejpam-5258	46	32	g⟩	g⟩	AUX
ejpam-5258	46	33	be	be	AUX
ejpam-5258	46	34	the	the	DET
ejpam-5258	46	35	free	free	ADJ
ejpam-5258	46	36	group	group	NOUN
ejpam-5258	46	37	freely	freely	ADV
ejpam-5258	46	38	generated	generate	VERB
ejpam-5258	46	39	by	by	ADP
ejpam-5258	46	40	all	all	DET
ejpam-5258	46	41	pairs	pair	NOUN
ejpam-5258	46	42	⟨x	⟨x	VERB
ejpam-5258	46	43	,	,	PUNCT
ejpam-5258	46	44	y⟩	y⟩	NOUN
ejpam-5258	46	45	with	with	ADP
ejpam-5258	46	46	x	x	PROPN
ejpam-5258	46	47	,	,	PUNCT
ejpam-5258	46	48	y	y	PROPN
ejpam-5258	46	49	∈	∈	PROPN
ejpam-5258	46	50	g.	g.	NOUN
ejpam-5258	46	51	then	then	ADV
ejpam-5258	46	52	any	any	DET
ejpam-5258	46	53	element	element	NOUN
ejpam-5258	46	54	α	α	PROPN
ejpam-5258	46	55	∈	∈	PROPN
ejpam-5258	46	56	f⟨g	f⟨g	PROPN
ejpam-5258	46	57	,	,	PUNCT
ejpam-5258	46	58	g⟩	g⟩	NOUN
ejpam-5258	46	59	,	,	PUNCT
ejpam-5258	46	60	α	α	PROPN
ejpam-5258	46	61	̸=	̸=	PROPN
ejpam-5258	46	62	1	1	NUM
ejpam-5258	46	63	is	be	AUX
ejpam-5258	46	64	uniquely	uniquely	ADV
ejpam-5258	46	65	written	write	VERB
ejpam-5258	46	66	as	as	ADP
ejpam-5258	46	67	α	α	NOUN
ejpam-5258	46	68	=	=	SYM
ejpam-5258	46	69	⟨x1	⟨x1	PROPN
ejpam-5258	46	70	,	,	PUNCT
ejpam-5258	46	71	y1⟩α1	y1⟩α1	NOUN
ejpam-5258	46	72	⟨x2	⟨x2	PROPN
ejpam-5258	46	73	,	,	PUNCT
ejpam-5258	46	74	y2⟩α2	y2⟩α2	PROPN
ejpam-5258	46	75	.	.	PUNCT
ejpam-5258	46	76	.	.	PUNCT
ejpam-5258	46	77	.	.	PUNCT
ejpam-5258	47	1	⟨xn	⟨xn	NOUN
ejpam-5258	47	2	,	,	PUNCT
ejpam-5258	47	3	yn⟩αn	yn⟩αn	PROPN
ejpam-5258	47	4	⟨xi+1	⟨xi+1	PROPN
ejpam-5258	47	5	,	,	PUNCT
ejpam-5258	47	6	yi+1⟩αi+1	yi+1⟩αi+1	PROPN
ejpam-5258	47	7	̸=	̸=	PROPN
ejpam-5258	47	8	⟨xi	⟨xi	PROPN
ejpam-5258	47	9	,	,	PUNCT
ejpam-5258	47	10	yi⟩−αi	yi⟩−αi	PROPN
ejpam-5258	47	11	,	,	PUNCT
ejpam-5258	47	12	where	where	SCONJ
ejpam-5258	47	13	xi	xi	X
ejpam-5258	47	14	,	,	PUNCT
ejpam-5258	47	15	yi	yi	PROPN
ejpam-5258	47	16	∈	∈	PROPN
ejpam-5258	47	17	g	g	PROPN
ejpam-5258	47	18	,	,	PUNCT
ejpam-5258	47	19	αi	αi	X
ejpam-5258	47	20	=	=	SYM
ejpam-5258	47	21	±1	±1	PROPN
ejpam-5258	47	22	,	,	PUNCT
ejpam-5258	47	23	i	i	PRON
ejpam-5258	47	24	=	=	NOUN
ejpam-5258	47	25	1	1	NUM
ejpam-5258	47	26	,	,	PUNCT
ejpam-5258	47	27	2	2	NUM
ejpam-5258	47	28	,	,	PUNCT
ejpam-5258	47	29	.	.	PUNCT
ejpam-5258	47	30	.	.	PUNCT
ejpam-5258	47	31	.	.	PUNCT
ejpam-5258	48	1	,	,	PUNCT
ejpam-5258	48	2	n.	n.	NOUN
ejpam-5258	48	3	proposition	proposition	NOUN
ejpam-5258	48	4	1	1	NUM
ejpam-5258	48	5	.	.	PUNCT
ejpam-5258	49	1	for	for	ADP
ejpam-5258	49	2	any	any	DET
ejpam-5258	49	3	group	group	NOUN
ejpam-5258	49	4	g	g	NOUN
ejpam-5258	49	5	there	there	PRON
ejpam-5258	49	6	is	be	VERB
ejpam-5258	49	7	a	a	DET
ejpam-5258	49	8	unique	unique	ADJ
ejpam-5258	49	9	epimorphism	epimorphism	NOUN
ejpam-5258	49	10	from	from	ADP
ejpam-5258	49	11	f⟨g	f⟨g	NUM
ejpam-5258	49	12	,	,	PUNCT
ejpam-5258	49	13	g⟩	g⟩	VERB
ejpam-5258	49	14	to	to	ADP
ejpam-5258	49	15	[	[	X
ejpam-5258	49	16	g	g	NOUN
ejpam-5258	49	17	,	,	PUNCT
ejpam-5258	49	18	g	g	NOUN
ejpam-5258	49	19	]	]	PUNCT
ejpam-5258	49	20	taking	take	VERB
ejpam-5258	49	21	each	each	DET
ejpam-5258	49	22	element	element	NOUN
ejpam-5258	49	23	⟨x	⟨x	VERB
ejpam-5258	49	24	,	,	PUNCT
ejpam-5258	49	25	y⟩	y⟩	NOUN
ejpam-5258	49	26	∈	∈	PROPN
ejpam-5258	49	27	f⟨g	f⟨g	PROPN
ejpam-5258	49	28	,	,	PUNCT
ejpam-5258	49	29	g⟩	g⟩	NOUN
ejpam-5258	49	30	,	,	PUNCT
ejpam-5258	49	31	x	x	PRON
ejpam-5258	49	32	,	,	PUNCT
ejpam-5258	49	33	y	y	PROPN
ejpam-5258	49	34	∈	∈	PROPN
ejpam-5258	49	35	g	g	NOUN
ejpam-5258	49	36	to	to	ADP
ejpam-5258	49	37	the	the	DET
ejpam-5258	49	38	element	element	NOUN
ejpam-5258	49	39	[	[	X
ejpam-5258	49	40	x	x	X
ejpam-5258	49	41	,	,	PUNCT
ejpam-5258	49	42	y	y	PROPN
ejpam-5258	49	43	]	]	X
ejpam-5258	49	44	=	=	PUNCT
ejpam-5258	49	45	xyx−1y−1	xyx−1y−1	PROPN
ejpam-5258	49	46	∈	∈	PROPN
ejpam-5258	49	47	[	[	X
ejpam-5258	49	48	g	g	NOUN
ejpam-5258	49	49	,	,	PUNCT
ejpam-5258	49	50	g	g	NOUN
ejpam-5258	49	51	]	]	PUNCT
ejpam-5258	49	52	.	.	PUNCT
ejpam-5258	50	1	proof	proof	NOUN
ejpam-5258	50	2	.	.	PUNCT
ejpam-5258	51	1	let	let	VERB
ejpam-5258	51	2	f	f	PRON
ejpam-5258	51	3	:	:	PUNCT
ejpam-5258	51	4	⟨g	⟨g	NOUN
ejpam-5258	51	5	,	,	PUNCT
ejpam-5258	51	6	g⟩	g⟩	VERB
ejpam-5258	51	7	→	→	PUNCT
ejpam-5258	51	8	[	[	X
ejpam-5258	51	9	g	g	NOUN
ejpam-5258	51	10	,	,	PUNCT
ejpam-5258	51	11	g	g	NOUN
ejpam-5258	51	12	]	]	PUNCT
ejpam-5258	51	13	be	be	AUX
ejpam-5258	51	14	the	the	DET
ejpam-5258	51	15	function	function	NOUN
ejpam-5258	51	16	given	give	VERB
ejpam-5258	51	17	by	by	ADP
ejpam-5258	51	18	f(⟨x	f(⟨x	NOUN
ejpam-5258	51	19	,	,	PUNCT
ejpam-5258	51	20	y⟩	y⟩	NOUN
ejpam-5258	51	21	)	)	PUNCT
ejpam-5258	51	22	=	=	PUNCT
ejpam-5258	52	1	[	[	X
ejpam-5258	52	2	x	x	X
ejpam-5258	52	3	,	,	PUNCT
ejpam-5258	52	4	y	y	PROPN
ejpam-5258	52	5	]	]	X
ejpam-5258	52	6	=	=	PUNCT
ejpam-5258	52	7	xyx−1y−1	xyx−1y−1	PROPN
ejpam-5258	52	8	with	with	ADP
ejpam-5258	52	9	x	x	PROPN
ejpam-5258	52	10	,	,	PUNCT
ejpam-5258	52	11	y	y	PROPN
ejpam-5258	52	12	∈	∈	PROPN
ejpam-5258	52	13	g.	g.	PROPN
ejpam-5258	52	14	since	since	SCONJ
ejpam-5258	52	15	f	f	PROPN
ejpam-5258	52	16	⟨g	⟨g	PROPN
ejpam-5258	52	17	,	,	PUNCT
ejpam-5258	52	18	g⟩	g⟩	AUX
ejpam-5258	52	19	is	be	AUX
ejpam-5258	52	20	a	a	DET
ejpam-5258	52	21	free	free	ADJ
ejpam-5258	52	22	group	group	NOUN
ejpam-5258	52	23	on	on	ADP
ejpam-5258	52	24	⟨g	⟨g	NOUN
ejpam-5258	52	25	,	,	PUNCT
ejpam-5258	52	26	g⟩	g⟩	VERB
ejpam-5258	52	27	,	,	PUNCT
ejpam-5258	52	28	the	the	DET
ejpam-5258	52	29	universal	universal	ADJ
ejpam-5258	52	30	property	property	NOUN
ejpam-5258	52	31	shows	show	VERB
ejpam-5258	52	32	that	that	SCONJ
ejpam-5258	52	33	there	there	PRON
ejpam-5258	52	34	exists	exist	VERB
ejpam-5258	52	35	a	a	DET
ejpam-5258	52	36	unique	unique	ADJ
ejpam-5258	52	37	homomorphism	homomorphism	NOUN
ejpam-5258	52	38	the	the	DET
ejpam-5258	52	39	function	function	NOUN
ejpam-5258	52	40	φg	φg	VERB
ejpam-5258	52	41	:	:	PUNCT
ejpam-5258	52	42	f⟨g	f⟨g	NUM
ejpam-5258	52	43	,	,	PUNCT
ejpam-5258	52	44	g⟩	g⟩	PUNCT
ejpam-5258	52	45	→	→	PUNCT
ejpam-5258	52	46	[	[	X
ejpam-5258	52	47	g	g	NOUN
ejpam-5258	52	48	,	,	PUNCT
ejpam-5258	52	49	g	g	NOUN
ejpam-5258	52	50	]	]	PUNCT
ejpam-5258	52	51	satisfying	satisfy	VERB
ejpam-5258	52	52	the	the	DET
ejpam-5258	52	53	condition	condition	NOUN
ejpam-5258	52	54	that	that	SCONJ
ejpam-5258	52	55	⟨x1	⟨x1	NOUN
ejpam-5258	52	56	,	,	PUNCT
ejpam-5258	52	57	y1⟩φg(⟨x	y1⟩φg(⟨x	NOUN
ejpam-5258	52	58	,	,	PUNCT
ejpam-5258	52	59	y⟩	y⟩	NOUN
ejpam-5258	52	60	)	)	PUNCT
ejpam-5258	52	61	=	=	PUNCT
ejpam-5258	53	1	[	[	X
ejpam-5258	53	2	x	x	X
ejpam-5258	53	3	,	,	PUNCT
ejpam-5258	53	4	y	y	PROPN
ejpam-5258	53	5	]	]	X
ejpam-5258	53	6	=	=	PUNCT
ejpam-5258	53	7	xyx−1y−1	xyx−1y−1	PROPN
ejpam-5258	53	8	with	with	ADP
ejpam-5258	53	9	x	x	PROPN
ejpam-5258	53	10	,	,	PUNCT
ejpam-5258	53	11	y	y	PROPN
ejpam-5258	53	12	∈	∈	PROPN
ejpam-5258	53	13	g.	g.	NOUN
ejpam-5258	53	14	this	this	PRON
ejpam-5258	53	15	shows	show	VERB
ejpam-5258	53	16	that	that	SCONJ
ejpam-5258	53	17	f	f	PROPN
ejpam-5258	53	18	is	be	AUX
ejpam-5258	53	19	the	the	DET
ejpam-5258	53	20	restriction	restriction	NOUN
ejpam-5258	53	21	of	of	ADP
ejpam-5258	53	22	φg	φg	VERB
ejpam-5258	53	23	on	on	ADP
ejpam-5258	53	24	f	f	PROPN
ejpam-5258	53	25	.	.	PUNCT
ejpam-5258	54	1	that	that	PRON
ejpam-5258	54	2	is	is	ADV
ejpam-5258	54	3	,	,	PUNCT
ejpam-5258	54	4	φg	φg	VERB
ejpam-5258	54	5	|	|	ADV
ejpam-5258	54	6	⟨g	⟨g	NOUN
ejpam-5258	54	7	,	,	PUNCT
ejpam-5258	54	8	g⟩	g⟩	VERB
ejpam-5258	54	9	=	=	SYM
ejpam-5258	54	10	f	f	PROPN
ejpam-5258	54	11	,	,	PUNCT
ejpam-5258	54	12	or	or	CCONJ
ejpam-5258	54	13	φg(⟨x	φg(⟨x	NUM
ejpam-5258	54	14	,	,	PUNCT
ejpam-5258	54	15	y⟩	y⟩	NOUN
ejpam-5258	54	16	)	)	PUNCT
ejpam-5258	54	17	=	=	SYM
ejpam-5258	54	18	f(⟨x	f(⟨x	PROPN
ejpam-5258	54	19	,	,	PUNCT
ejpam-5258	54	20	y⟩	y⟩	NOUN
ejpam-5258	54	21	)	)	PUNCT
ejpam-5258	54	22	for	for	ADP
ejpam-5258	54	23	all	all	PRON
ejpam-5258	54	24	,	,	PUNCT
ejpam-5258	54	25	y	y	PROPN
ejpam-5258	54	26	∈	∈	PROPN
ejpam-5258	54	27	g.	g.	NOUN
ejpam-5258	55	1	so	so	ADV
ejpam-5258	55	2	for	for	ADP
ejpam-5258	55	3	any	any	DET
ejpam-5258	55	4	element	element	NOUN
ejpam-5258	55	5	α	α	PROPN
ejpam-5258	55	6	∈	∈	PROPN
ejpam-5258	55	7	f⟨g	f⟨g	PROPN
ejpam-5258	55	8	,	,	PUNCT
ejpam-5258	55	9	g⟩	g⟩	NOUN
ejpam-5258	55	10	,	,	PUNCT
ejpam-5258	55	11	α	α	PROPN
ejpam-5258	55	12	̸=	̸=	PROPN
ejpam-5258	55	13	1	1	NUM
ejpam-5258	55	14	,	,	PUNCT
ejpam-5258	55	15	α	α	PROPN
ejpam-5258	55	16	can	can	AUX
ejpam-5258	55	17	be	be	AUX
ejpam-5258	55	18	written	write	VERB
ejpam-5258	55	19	uniquely	uniquely	ADV
ejpam-5258	55	20	as	as	ADP
ejpam-5258	55	21	α	α	NUM
ejpam-5258	55	22	=	=	SYM
ejpam-5258	55	23	⟨x1	⟨x1	PROPN
ejpam-5258	55	24	,	,	PUNCT
ejpam-5258	55	25	y1⟩α1	y1⟩α1	NOUN
ejpam-5258	55	26	⟨x2	⟨x2	PROPN
ejpam-5258	55	27	,	,	PUNCT
ejpam-5258	55	28	y2⟩α2	y2⟩α2	PROPN
ejpam-5258	55	29	.	.	PUNCT
ejpam-5258	55	30	.	.	PUNCT
ejpam-5258	55	31	.	.	PUNCT
ejpam-5258	56	1	⟨xn	⟨xn	NOUN
ejpam-5258	56	2	,	,	PUNCT
ejpam-5258	56	3	yn⟩αn	yn⟩αn	PROPN
ejpam-5258	56	4	.	.	PROPN
ejpam-5258	56	5	and	and	CCONJ
ejpam-5258	56	6	the	the	DET
ejpam-5258	56	7	value	value	NOUN
ejpam-5258	56	8	of	of	ADP
ejpam-5258	56	9	α	α	NOUN
ejpam-5258	56	10	under	under	ADP
ejpam-5258	56	11	φg	φg	VERB
ejpam-5258	56	12	is	be	AUX
ejpam-5258	56	13	given	give	VERB
ejpam-5258	56	14	by	by	ADP
ejpam-5258	56	15	φg(α	φg(α	NOUN
ejpam-5258	56	16	)	)	PUNCT
ejpam-5258	56	17	=	=	SYM
ejpam-5258	57	1	⟨x1	⟨x1	NOUN
ejpam-5258	57	2	,	,	PUNCT
ejpam-5258	57	3	y1⟩α1	y1⟩α1	NOUN
ejpam-5258	57	4	⟨x2	⟨x2	PROPN
ejpam-5258	57	5	,	,	PUNCT
ejpam-5258	57	6	y2⟩α2	y2⟩α2	PROPN
ejpam-5258	57	7	.	.	PUNCT
ejpam-5258	57	8	.	.	PUNCT
ejpam-5258	57	9	.	.	PUNCT
ejpam-5258	58	1	⟨xn	⟨xn	NOUN
ejpam-5258	58	2	,	,	PUNCT
ejpam-5258	58	3	yn⟩αn	yn⟩αn	PROPN
ejpam-5258	58	4	.	.	PUNCT
ejpam-5258	59	1	now	now	ADV
ejpam-5258	59	2	if	if	SCONJ
ejpam-5258	59	3	φ	φ	PROPN
ejpam-5258	59	4	:	:	PUNCT
ejpam-5258	59	5	f⟨g	f⟨g	NUM
ejpam-5258	59	6	,	,	PUNCT
ejpam-5258	59	7	g⟩	g⟩	PUNCT
ejpam-5258	59	8	→	→	PUNCT
ejpam-5258	59	9	[	[	X
ejpam-5258	59	10	g	g	NOUN
ejpam-5258	59	11	,	,	PUNCT
ejpam-5258	59	12	g	g	NOUN
ejpam-5258	59	13	]	]	PUNCT
ejpam-5258	59	14	is	be	AUX
ejpam-5258	59	15	a	a	DET
ejpam-5258	59	16	homomorphism	homomorphism	NOUN
ejpam-5258	59	17	,	,	PUNCT
ejpam-5258	59	18	such	such	ADJ
ejpam-5258	59	19	that	that	DET
ejpam-5258	59	20	φ(⟨x	φ(⟨x	NOUN
ejpam-5258	59	21	,	,	PUNCT
ejpam-5258	59	22	y⟩	y⟩	NOUN
ejpam-5258	59	23	)	)	PUNCT
ejpam-5258	60	1	=	=	PUNCT
ejpam-5258	61	1	[	[	X
ejpam-5258	61	2	x	x	X
ejpam-5258	61	3	,	,	PUNCT
ejpam-5258	61	4	y	y	PROPN
ejpam-5258	61	5	]	]	X
ejpam-5258	61	6	=	=	PUNCT
ejpam-5258	61	7	xyx−1y−1	xyx−1y−1	PROPN
ejpam-5258	61	8	with	with	ADP
ejpam-5258	61	9	x	x	PROPN
ejpam-5258	61	10	,	,	PUNCT
ejpam-5258	61	11	y	y	PROPN
ejpam-5258	61	12	∈	∈	PROPN
ejpam-5258	61	13	g	g	PROPN
ejpam-5258	61	14	,	,	PUNCT
ejpam-5258	61	15	then	then	ADV
ejpam-5258	61	16	φ	φ	PROPN
ejpam-5258	61	17	=	=	SYM
ejpam-5258	61	18	φg	φg	PROPN
ejpam-5258	61	19	.	.	PUNCT
ejpam-5258	61	20	consequently	consequently	ADV
ejpam-5258	61	21	,	,	PUNCT
ejpam-5258	61	22	φg	φg	VERB
ejpam-5258	61	23	is	be	AUX
ejpam-5258	61	24	the	the	DET
ejpam-5258	61	25	unique	unique	ADJ
ejpam-5258	61	26	required	required	ADJ
ejpam-5258	61	27	homomorphism	homomorphism	NOUN
ejpam-5258	61	28	.	.	PUNCT
ejpam-5258	62	1	a.	a.	PROPN
ejpam-5258	62	2	m.	m.	PROPN
ejpam-5258	62	3	alotaibi	alotaibi	PROPN
ejpam-5258	62	4	,	,	PUNCT
ejpam-5258	62	5	k.	k.	PROPN
ejpam-5258	62	6	m.	m.	PROPN
ejpam-5258	62	7	aljamal	aljamal	PROPN
ejpam-5258	62	8	/	/	SYM
ejpam-5258	62	9	eur	eur	PROPN
ejpam-5258	62	10	.	.	PUNCT
ejpam-5258	63	1	j.	j.	PROPN
ejpam-5258	63	2	pure	pure	PROPN
ejpam-5258	63	3	appl	appl	PROPN
ejpam-5258	63	4	.	.	PROPN
ejpam-5258	63	5	math	math	PROPN
ejpam-5258	63	6	,	,	PUNCT
ejpam-5258	63	7	17	17	NUM
ejpam-5258	63	8	(	(	PUNCT
ejpam-5258	63	9	3	3	NUM
ejpam-5258	63	10	)	)	PUNCT
ejpam-5258	63	11	(	(	PUNCT
ejpam-5258	63	12	2024	2024	NUM
ejpam-5258	63	13	)	)	PUNCT
ejpam-5258	63	14	,	,	PUNCT
ejpam-5258	63	15	2329	2329	NUM
ejpam-5258	63	16	-	-	SYM
ejpam-5258	63	17	2335	2335	NUM
ejpam-5258	63	18	2331	2331	NUM
ejpam-5258	63	19	since	since	SCONJ
ejpam-5258	63	20	f(⟨g	f(⟨g	NOUN
ejpam-5258	63	21	,	,	PUNCT
ejpam-5258	63	22	g⟩	g⟩	ADV
ejpam-5258	63	23	)	)	PUNCT
ejpam-5258	63	24	=	=	PUNCT
ejpam-5258	64	1	[	[	X
ejpam-5258	64	2	g	g	NOUN
ejpam-5258	64	3	,	,	PUNCT
ejpam-5258	64	4	g	g	NOUN
ejpam-5258	64	5	]	]	PUNCT
ejpam-5258	64	6	generates	generate	VERB
ejpam-5258	64	7	[	[	X
ejpam-5258	64	8	g	g	NOUN
ejpam-5258	64	9	,	,	PUNCT
ejpam-5258	64	10	g	g	NOUN
ejpam-5258	64	11	]	]	X
ejpam-5258	64	12	,	,	PUNCT
ejpam-5258	64	13	this	this	PRON
ejpam-5258	64	14	implies	imply	VERB
ejpam-5258	64	15	that	that	SCONJ
ejpam-5258	64	16	φg	φg	VERB
ejpam-5258	64	17	is	be	AUX
ejpam-5258	64	18	an	an	DET
ejpam-5258	64	19	epimorphism	epimorphism	NOUN
ejpam-5258	64	20	.	.	PUNCT
ejpam-5258	65	1	this	this	PRON
ejpam-5258	65	2	complete	complete	VERB
ejpam-5258	65	3	the	the	DET
ejpam-5258	65	4	proof	proof	NOUN
ejpam-5258	65	5	.	.	PUNCT
ejpam-5258	66	1	definition	definition	NOUN
ejpam-5258	66	2	1	1	NUM
ejpam-5258	66	3	.	.	PUNCT
ejpam-5258	67	1	for	for	ADP
ejpam-5258	67	2	any	any	DET
ejpam-5258	67	3	group	group	NOUN
ejpam-5258	67	4	g	g	NOUN
ejpam-5258	67	5	,	,	PUNCT
ejpam-5258	67	6	let	let	VERB
ejpam-5258	67	7	φg	φg	VERB
ejpam-5258	67	8	:	:	PUNCT
ejpam-5258	67	9	f⟨g	f⟨g	NUM
ejpam-5258	67	10	,	,	PUNCT
ejpam-5258	67	11	g⟩	g⟩	PUNCT
ejpam-5258	67	12	→	→	PUNCT
ejpam-5258	67	13	[	[	X
ejpam-5258	67	14	g	g	NOUN
ejpam-5258	67	15	,	,	PUNCT
ejpam-5258	67	16	g	g	NOUN
ejpam-5258	67	17	]	]	PUNCT
ejpam-5258	67	18	be	be	AUX
ejpam-5258	67	19	the	the	DET
ejpam-5258	67	20	unique	unique	ADJ
ejpam-5258	67	21	epimorphism	epimorphism	NOUN
ejpam-5258	67	22	of	of	ADP
ejpam-5258	67	23	proposition	proposition	NOUN
ejpam-5258	67	24	1	1	NUM
ejpam-5258	67	25	satisfying	satisfy	VERB
ejpam-5258	67	26	the	the	DET
ejpam-5258	67	27	condition	condition	NOUN
ejpam-5258	67	28	that	that	SCONJ
ejpam-5258	67	29	φg(⟨x	φg(⟨x	ADP
ejpam-5258	67	30	,	,	PUNCT
ejpam-5258	67	31	y⟩	y⟩	NOUN
ejpam-5258	67	32	)	)	PUNCT
ejpam-5258	67	33	=	=	PUNCT
ejpam-5258	68	1	[	[	X
ejpam-5258	68	2	x	x	X
ejpam-5258	68	3	,	,	PUNCT
ejpam-5258	68	4	y	y	PROPN
ejpam-5258	68	5	]	]	X
ejpam-5258	68	6	=	=	PUNCT
ejpam-5258	68	7	xyx−1y−1	xyx−1y−1	PROPN
ejpam-5258	68	8	with	with	ADP
ejpam-5258	68	9	x	x	PROPN
ejpam-5258	68	10	,	,	PUNCT
ejpam-5258	68	11	y	y	PROPN
ejpam-5258	68	12	∈	∈	PROPN
ejpam-5258	68	13	g.	g.	NOUN
ejpam-5258	68	14	we	we	PRON
ejpam-5258	68	15	denote	denote	VERB
ejpam-5258	68	16	by	by	ADP
ejpam-5258	68	17	c(g	c(g	PROPN
ejpam-5258	68	18	)	)	PUNCT
ejpam-5258	68	19	=	=	SYM
ejpam-5258	68	20	kerφg	kerφg	PROPN
ejpam-5258	68	21	)	)	PUNCT
ejpam-5258	68	22	the	the	DET
ejpam-5258	68	23	kernel	kernel	NOUN
ejpam-5258	68	24	of	of	ADP
ejpam-5258	68	25	φg	φg	NOUN
ejpam-5258	68	26	.	.	PUNCT
ejpam-5258	69	1	then	then	ADV
ejpam-5258	69	2	it	it	PRON
ejpam-5258	69	3	is	be	AUX
ejpam-5258	69	4	clear	clear	ADJ
ejpam-5258	69	5	that	that	SCONJ
ejpam-5258	69	6	c(g	c(g	PROPN
ejpam-5258	69	7	)	)	PUNCT
ejpam-5258	69	8	is	be	AUX
ejpam-5258	69	9	a	a	DET
ejpam-5258	69	10	normal	normal	ADJ
ejpam-5258	69	11	subgroup	subgroup	NOUN
ejpam-5258	69	12	of	of	ADP
ejpam-5258	69	13	f⟨g	f⟨g	PROPN
ejpam-5258	69	14	,	,	PUNCT
ejpam-5258	69	15	g⟩.	g⟩.	ADJ
ejpam-5258	69	16	definition	definition	NOUN
ejpam-5258	69	17	2	2	NUM
ejpam-5258	69	18	.	.	X
ejpam-5258	70	1	for	for	ADP
ejpam-5258	70	2	any	any	DET
ejpam-5258	70	3	group	group	NOUN
ejpam-5258	70	4	g	g	NOUN
ejpam-5258	70	5	,	,	PUNCT
ejpam-5258	70	6	let	let	VERB
ejpam-5258	70	7	r(g	r(g	NUM
ejpam-5258	70	8	)	)	PUNCT
ejpam-5258	70	9	⊆	⊆	NUM
ejpam-5258	70	10	f⟨g	f⟨g	NUM
ejpam-5258	70	11	,	,	PUNCT
ejpam-5258	70	12	g⟩	g⟩	AUX
ejpam-5258	70	13	be	be	AUX
ejpam-5258	70	14	the	the	DET
ejpam-5258	70	15	set	set	NOUN
ejpam-5258	70	16	of	of	ADP
ejpam-5258	70	17	the	the	DET
ejpam-5258	70	18	following	follow	VERB
ejpam-5258	70	19	elements	element	NOUN
ejpam-5258	70	20	of	of	ADP
ejpam-5258	70	21	⟨x	⟨x	NUM
ejpam-5258	70	22	,	,	PUNCT
ejpam-5258	70	23	x⟩	x⟩	PUNCT
ejpam-5258	70	24	⟨x	⟨x	NUM
ejpam-5258	70	25	,	,	PUNCT
ejpam-5258	70	26	y⟩⟨y	y⟩⟨y	PROPN
ejpam-5258	70	27	,	,	PUNCT
ejpam-5258	70	28	x⟩	x⟩	PUNCT
ejpam-5258	71	1	⟨y	⟨y	X
ejpam-5258	71	2	,	,	PUNCT
ejpam-5258	71	3	z⟩x⟨x	z⟩x⟨x	PROPN
ejpam-5258	71	4	,	,	PUNCT
ejpam-5258	71	5	z⟩⟨xy	z⟩⟨xy	NOUN
ejpam-5258	71	6	,	,	PUNCT
ejpam-5258	71	7	z⟩−1	z⟩−1	NOUN
ejpam-5258	71	8	⟨y	⟨y	X
ejpam-5258	71	9	,	,	PUNCT
ejpam-5258	71	10	z⟩x⟨y	z⟩x⟨y	NUM
ejpam-5258	71	11	,	,	PUNCT
ejpam-5258	71	12	z⟩−1⟨x	z⟩−1⟨x	PROPN
ejpam-5258	71	13	,	,	PUNCT
ejpam-5258	71	14	[	[	X
ejpam-5258	71	15	y	y	X
ejpam-5258	71	16	,	,	PUNCT
ejpam-5258	71	17	z]⟩−1	z]⟩−1	PROPN
ejpam-5258	71	18			PROPN
ejpam-5258	71	19	for	for	ADP
ejpam-5258	71	20	x	x	PROPN
ejpam-5258	71	21	,	,	PUNCT
ejpam-5258	71	22	y	y	PROPN
ejpam-5258	71	23	,	,	PUNCT
ejpam-5258	71	24	z	z	PROPN
ejpam-5258	71	25	∈	∈	PROPN
ejpam-5258	71	26	g	g	NOUN
ejpam-5258	71	27	,	,	PUNCT
ejpam-5258	71	28	where	where	SCONJ
ejpam-5258	71	29	⟨y	⟨y	NOUN
ejpam-5258	71	30	,	,	PUNCT
ejpam-5258	71	31	z⟩x	z⟩x	NUM
ejpam-5258	71	32	=	=	SYM
ejpam-5258	71	33	⟨yx	⟨yx	PROPN
ejpam-5258	71	34	,	,	PUNCT
ejpam-5258	71	35	zx⟩	zx⟩	X
ejpam-5258	71	36	=	=	PUNCT
ejpam-5258	71	37	〈	〈	PROPN
ejpam-5258	71	38	xyx−1	xyx−1	PROPN
ejpam-5258	71	39	,	,	PUNCT
ejpam-5258	71	40	xzx−1	xzx−1	PROPN
ejpam-5258	71	41	〉	〉	NOUN
ejpam-5258	71	42	.	.	PUNCT
ejpam-5258	72	1	lemma	lemma	PROPN
ejpam-5258	72	2	1	1	X
ejpam-5258	72	3	.	.	PUNCT
ejpam-5258	73	1	let	let	VERB
ejpam-5258	73	2	g	g	PRON
ejpam-5258	73	3	be	be	AUX
ejpam-5258	73	4	a	a	DET
ejpam-5258	73	5	group	group	NOUN
ejpam-5258	73	6	of	of	ADP
ejpam-5258	73	7	presentation	presentation	NOUN
ejpam-5258	73	8	⟨x	⟨x	VERB
ejpam-5258	73	9	|	|	ADV
ejpam-5258	73	10	r⟩.	r⟩.	NOUN
ejpam-5258	73	11	then	then	ADV
ejpam-5258	73	12	h(g	h(g	PRON
ejpam-5258	73	13	)	)	PUNCT
ejpam-5258	73	14	∼=	∼=	PART
ejpam-5258	73	15	r̄∩[fx	r̄∩[fx	PROPN
ejpam-5258	73	16	,	,	PUNCT
ejpam-5258	73	17	fx	fx	NOUN
ejpam-5258	73	18	]	]	PUNCT
ejpam-5258	73	19	/	/	SYM
ejpam-5258	73	20	[	[	PUNCT
ejpam-5258	73	21	fx	fx	NOUN
ejpam-5258	73	22	,	,	PUNCT
ejpam-5258	73	23	r̄	r̄	NOUN
ejpam-5258	73	24	]	]	PUNCT
ejpam-5258	73	25	.	.	PUNCT
ejpam-5258	74	1	proof	proof	NOUN
ejpam-5258	74	2	.	.	PUNCT
ejpam-5258	75	1	see	see	VERB
ejpam-5258	75	2	[	[	X
ejpam-5258	75	3	3	3	NUM
ejpam-5258	75	4	]	]	PUNCT
ejpam-5258	75	5	.	.	PUNCT
ejpam-5258	76	1	theorem	theorem	NOUN
ejpam-5258	76	2	1	1	NUM
ejpam-5258	76	3	.	.	X
ejpam-5258	77	1	for	for	ADP
ejpam-5258	77	2	any	any	DET
ejpam-5258	77	3	group	group	NOUN
ejpam-5258	77	4	g	g	NOUN
ejpam-5258	77	5	,	,	PUNCT
ejpam-5258	77	6	the	the	DET
ejpam-5258	77	7	normal	normal	ADJ
ejpam-5258	77	8	closure	closure	NOUN
ejpam-5258	77	9	[	[	X
ejpam-5258	77	10	r(g)]f	r(g)]f	NOUN
ejpam-5258	77	11	⟨g	⟨g	NOUN
ejpam-5258	77	12	,	,	PUNCT
ejpam-5258	77	13	g	g	ADP
ejpam-5258	77	14	〉	〉	NOUN
ejpam-5258	77	15	of	of	ADP
ejpam-5258	77	16	r(g	r(g	NUM
ejpam-5258	77	17	)	)	PUNCT
ejpam-5258	77	18	in	in	ADP
ejpam-5258	77	19	f⟨g	f⟨g	NUM
ejpam-5258	77	20	,	,	PUNCT
ejpam-5258	77	21	g⟩	g⟩	VERB
ejpam-5258	77	22	is	be	AUX
ejpam-5258	77	23	contained	contain	VERB
ejpam-5258	77	24	in	in	ADP
ejpam-5258	77	25	c(g	c(g	PROPN
ejpam-5258	77	26	)	)	PUNCT
ejpam-5258	77	27	.	.	PUNCT
ejpam-5258	78	1	proof	proof	NOUN
ejpam-5258	78	2	.	.	PUNCT
ejpam-5258	79	1	first	first	ADV
ejpam-5258	79	2	we	we	PRON
ejpam-5258	79	3	show	show	VERB
ejpam-5258	79	4	that	that	SCONJ
ejpam-5258	79	5	r(g	r(g	NUM
ejpam-5258	79	6	)	)	PUNCT
ejpam-5258	79	7	⊆	⊆	NUM
ejpam-5258	79	8	c(g	c(g	PROPN
ejpam-5258	79	9	)	)	PUNCT
ejpam-5258	79	10	.	.	PUNCT
ejpam-5258	80	1	this	this	PRON
ejpam-5258	80	2	is	be	AUX
ejpam-5258	80	3	equivalent	equivalent	ADJ
ejpam-5258	80	4	of	of	ADP
ejpam-5258	80	5	showing	show	VERB
ejpam-5258	80	6	that	that	SCONJ
ejpam-5258	80	7	the	the	DET
ejpam-5258	80	8	value	value	NOUN
ejpam-5258	80	9	of	of	ADP
ejpam-5258	80	10	any	any	DET
ejpam-5258	80	11	element	element	NOUN
ejpam-5258	80	12	α	α	PROPN
ejpam-5258	80	13	∈	∈	PROPN
ejpam-5258	80	14	r(g	r(g	NUM
ejpam-5258	80	15	)	)	PUNCT
ejpam-5258	80	16	under	under	ADP
ejpam-5258	80	17	the	the	DET
ejpam-5258	80	18	epimorphism	epimorphism	NOUN
ejpam-5258	80	19	φg	φg	ADP
ejpam-5258	80	20	:	:	PUNCT
ejpam-5258	80	21	f⟨g	f⟨g	NUM
ejpam-5258	80	22	,	,	PUNCT
ejpam-5258	80	23	g⟩	g⟩	PUNCT
ejpam-5258	80	24	→	→	PUNCT
ejpam-5258	80	25	[	[	X
ejpam-5258	80	26	g	g	NOUN
ejpam-5258	80	27	,	,	PUNCT
ejpam-5258	80	28	g	g	NOUN
ejpam-5258	80	29	]	]	PUNCT
ejpam-5258	80	30	equals	equal	VERB
ejpam-5258	80	31	φg(α	φg(α	NOUN
ejpam-5258	80	32	)	)	PUNCT
ejpam-5258	80	33	=	=	SYM
ejpam-5258	80	34	1	1	NUM
ejpam-5258	80	35	,	,	PUNCT
ejpam-5258	80	36	the	the	DET
ejpam-5258	80	37	identity	identity	NOUN
ejpam-5258	80	38	element	element	NOUN
ejpam-5258	80	39	of	of	ADP
ejpam-5258	80	40	g.	g.	PROPN
ejpam-5258	80	41	(	(	PUNCT
ejpam-5258	80	42	1	1	X
ejpam-5258	80	43	)	)	PUNCT
ejpam-5258	80	44	let	let	VERB
ejpam-5258	80	45	x	x	SYM
ejpam-5258	80	46	∈	∈	PROPN
ejpam-5258	80	47	g.	g.	PROPN
ejpam-5258	80	48	then	then	ADV
ejpam-5258	80	49	⟨x	⟨x	VERB
ejpam-5258	80	50	,	,	PUNCT
ejpam-5258	80	51	x⟩	x⟩	PUNCT
ejpam-5258	81	1	∈	∈	PROPN
ejpam-5258	81	2	f	f	PROPN
ejpam-5258	81	3	⟨g	⟨g	PROPN
ejpam-5258	81	4	,	,	PUNCT
ejpam-5258	81	5	g⟩	g⟩	NOUN
ejpam-5258	81	6	and	and	CCONJ
ejpam-5258	81	7	φg(⟨x	φg(⟨x	NOUN
ejpam-5258	81	8	,	,	PUNCT
ejpam-5258	81	9	x⟩	x⟩	PUNCT
ejpam-5258	81	10	)	)	PUNCT
ejpam-5258	81	11	=	=	PUNCT
ejpam-5258	82	1	[	[	X
ejpam-5258	82	2	x	x	X
ejpam-5258	82	3	,	,	PUNCT
ejpam-5258	82	4	x	x	X
ejpam-5258	82	5	]	]	X
ejpam-5258	82	6	=	=	PUNCT
ejpam-5258	82	7	xx−1x−1	xx−1x−1	PUNCT
ejpam-5258	82	8	=	=	SYM
ejpam-5258	83	1	1	1	X
ejpam-5258	83	2	.	.	PUNCT
ejpam-5258	83	3	(	(	PUNCT
ejpam-5258	83	4	2	2	X
ejpam-5258	83	5	)	)	PUNCT
ejpam-5258	83	6	let	let	VERB
ejpam-5258	83	7	x	x	PRON
ejpam-5258	83	8	,	,	PUNCT
ejpam-5258	83	9	y	y	PROPN
ejpam-5258	83	10	,	,	PUNCT
ejpam-5258	83	11	z	z	PROPN
ejpam-5258	83	12	∈	∈	PROPN
ejpam-5258	83	13	g.	g.	NOUN
ejpam-5258	83	14	then	then	ADV
ejpam-5258	83	15	the	the	DET
ejpam-5258	83	16	elements	element	NOUN
ejpam-5258	83	17	⟨y	⟨y	X
ejpam-5258	83	18	,	,	PUNCT
ejpam-5258	83	19	z⟩x	z⟩x	NUM
ejpam-5258	83	20	,	,	PUNCT
ejpam-5258	83	21	⟨x	⟨x	VERB
ejpam-5258	83	22	,	,	PUNCT
ejpam-5258	83	23	z⟩	z⟩	NOUN
ejpam-5258	83	24	,	,	PUNCT
ejpam-5258	83	25	⟨xy	⟨xy	NOUN
ejpam-5258	83	26	,	,	PUNCT
ejpam-5258	83	27	z⟩−1	z⟩−1	NOUN
ejpam-5258	83	28	and	and	CCONJ
ejpam-5258	83	29	(	(	PUNCT
ejpam-5258	83	30	⟨y	⟨y	PROPN
ejpam-5258	83	31	,	,	PUNCT
ejpam-5258	83	32	z⟩x⟨x	z⟩x⟨x	PROPN
ejpam-5258	83	33	,	,	PUNCT
ejpam-5258	83	34	z⟩⟨xy	z⟩⟨xy	NOUN
ejpam-5258	83	35	,	,	PUNCT
ejpam-5258	83	36	z⟩−1	z⟩−1	NOUN
ejpam-5258	83	37	are	be	AUX
ejpam-5258	83	38	in	in	ADP
ejpam-5258	83	39	f⟨g	f⟨g	NUM
ejpam-5258	83	40	,	,	PUNCT
ejpam-5258	83	41	g⟩	g⟩	NOUN
ejpam-5258	83	42	and	and	CCONJ
ejpam-5258	83	43	φg	φg	VERB
ejpam-5258	83	44	(	(	PUNCT
ejpam-5258	83	45	〈	〈	PROPN
ejpam-5258	83	46	y	y	PROPN
ejpam-5258	83	47	,	,	PUNCT
ejpam-5258	83	48	zx⟨x	zx⟨x	NOUN
ejpam-5258	83	49	,	,	PUNCT
ejpam-5258	83	50	z⟩⟨xy	z⟩⟨xy	NOUN
ejpam-5258	83	51	,	,	PUNCT
ejpam-5258	83	52	z⟩−1	z⟩−1	NOUN
ejpam-5258	83	53	)	)	PUNCT
ejpam-5258	84	1	=	=	PUNCT
ejpam-5258	84	2	φg	φg	X
ejpam-5258	84	3	(	(	PUNCT
ejpam-5258	84	4	⟨y	⟨y	NOUN
ejpam-5258	84	5	,	,	PUNCT
ejpam-5258	84	6	z⟩x	z⟩x	NUM
ejpam-5258	84	7	)	)	PUNCT
ejpam-5258	84	8	φg(⟨x	φg(⟨x	PROPN
ejpam-5258	84	9	,	,	PUNCT
ejpam-5258	84	10	z⟩)φg	z⟩)φg	PROPN
ejpam-5258	84	11	(	(	PUNCT
ejpam-5258	84	12	⟨xy	⟨xy	NOUN
ejpam-5258	84	13	,	,	PUNCT
ejpam-5258	84	14	z⟩−1	z⟩−1	NOUN
ejpam-5258	84	15	)	)	PUNCT
ejpam-5258	85	1	′′	′′	PROPN
ejpam-5258	85	2	(	(	PUNCT
ejpam-5258	85	3	3	3	X
ejpam-5258	85	4	)	)	PUNCT
ejpam-5258	85	5	let	let	VERB
ejpam-5258	85	6	x	x	PRON
ejpam-5258	85	7	,	,	PUNCT
ejpam-5258	85	8	y	y	PROPN
ejpam-5258	85	9	,	,	PUNCT
ejpam-5258	85	10	z	z	PROPN
ejpam-5258	85	11	∈	∈	PROPN
ejpam-5258	85	12	g.	g.	NOUN
ejpam-5258	85	13	then	then	ADV
ejpam-5258	85	14	the	the	DET
ejpam-5258	85	15	elements	element	NOUN
ejpam-5258	85	16	⟨y	⟨y	X
ejpam-5258	85	17	,	,	PUNCT
ejpam-5258	85	18	z⟩x	z⟩x	NUM
ejpam-5258	85	19	,	,	PUNCT
ejpam-5258	85	20	⟨y	⟨y	X
ejpam-5258	85	21	,	,	PUNCT
ejpam-5258	85	22	z⟩−1	z⟩−1	NOUN
ejpam-5258	85	23	,	,	PUNCT
ejpam-5258	85	24	⟨x	⟨x	VERB
ejpam-5258	85	25	,	,	PUNCT
ejpam-5258	85	26	[	[	X
ejpam-5258	85	27	y	y	X
ejpam-5258	85	28	,	,	PUNCT
ejpam-5258	85	29	z]⟩−1	z]⟩−1	PROPN
ejpam-5258	85	30	and	and	CCONJ
ejpam-5258	85	31	⟨y	⟨y	NOUN
ejpam-5258	85	32	,	,	PUNCT
ejpam-5258	85	33	z⟩x⟨y	z⟩x⟨y	NUM
ejpam-5258	85	34	,	,	PUNCT
ejpam-5258	85	35	z⟩−1⟨x	z⟩−1⟨x	PROPN
ejpam-5258	85	36	,	,	PUNCT
ejpam-5258	85	37	[	[	X
ejpam-5258	85	38	y	y	X
ejpam-5258	85	39	,	,	PUNCT
ejpam-5258	85	40	z]⟩−1	z]⟩−1	PROPN
ejpam-5258	85	41	are	be	AUX
ejpam-5258	85	42	in	in	ADP
ejpam-5258	85	43	f⟨g	f⟨g	NUM
ejpam-5258	85	44	,	,	PUNCT
ejpam-5258	85	45	g⟩	g⟩	NOUN
ejpam-5258	85	46	and	and	CCONJ
ejpam-5258	85	47	φg	φg	VERB
ejpam-5258	85	48	(	(	PUNCT
ejpam-5258	85	49	⟨y	⟨y	X
ejpam-5258	85	50	,	,	PUNCT
ejpam-5258	85	51	z⟩x⟨y	z⟩x⟨y	NUM
ejpam-5258	85	52	,	,	PUNCT
ejpam-5258	85	53	z⟩−1⟨x	z⟩−1⟨x	PROPN
ejpam-5258	85	54	,	,	PUNCT
ejpam-5258	85	55	[	[	X
ejpam-5258	85	56	y	y	PROPN
ejpam-5258	85	57	,	,	PUNCT
ejpam-5258	85	58	z]⟩−1	z]⟩−1	PROPN
ejpam-5258	85	59	)	)	PUNCT
ejpam-5258	86	1	=	=	PUNCT
ejpam-5258	86	2	φg	φg	X
ejpam-5258	86	3	(	(	PUNCT
ejpam-5258	86	4	⟨y	⟨y	X
ejpam-5258	86	5	,	,	PUNCT
ejpam-5258	86	6	z⟩x)φg	z⟩x)φg	NOUN
ejpam-5258	86	7	(	(	PUNCT
ejpam-5258	86	8	⟨y	⟨y	X
ejpam-5258	86	9	,	,	PUNCT
ejpam-5258	86	10	z⟩−1	z⟩−1	NOUN
ejpam-5258	86	11	)	)	PUNCT
ejpam-5258	86	12	φg	φg	VERB
ejpam-5258	86	13	(	(	PUNCT
ejpam-5258	86	14	⟨x	⟨x	NUM
ejpam-5258	86	15	,	,	PUNCT
ejpam-5258	86	16	[	[	X
ejpam-5258	86	17	y	y	NOUN
ejpam-5258	86	18	,	,	PUNCT
ejpam-5258	86	19	z]⟩−1	z]⟩−1	NUM
ejpam-5258	86	20	)	)	PUNCT
ejpam-5258	86	21	from	from	ADP
ejpam-5258	86	22	above	above	ADP
ejpam-5258	86	23	we	we	PRON
ejpam-5258	86	24	have	have	VERB
ejpam-5258	86	25	r(g	r(g	NUM
ejpam-5258	86	26	)	)	PUNCT
ejpam-5258	86	27	⊆	⊆	NUM
ejpam-5258	86	28	c(g	c(g	PROPN
ejpam-5258	86	29	)	)	PUNCT
ejpam-5258	86	30	.	.	PUNCT
ejpam-5258	87	1	since	since	SCONJ
ejpam-5258	87	2	c(g	c(g	PROPN
ejpam-5258	87	3	)	)	PUNCT
ejpam-5258	87	4	is	be	AUX
ejpam-5258	87	5	a	a	DET
ejpam-5258	87	6	normal	normal	ADJ
ejpam-5258	87	7	subgroup	subgroup	NOUN
ejpam-5258	87	8	of	of	ADP
ejpam-5258	87	9	f⟨g	f⟨g	PROPN
ejpam-5258	87	10	,	,	PUNCT
ejpam-5258	87	11	g⟩	g⟩	VERB
ejpam-5258	87	12	,	,	PUNCT
ejpam-5258	87	13	this	this	PRON
ejpam-5258	87	14	implies	imply	VERB
ejpam-5258	87	15	that	that	SCONJ
ejpam-5258	87	16	the	the	DET
ejpam-5258	87	17	normal	normal	ADJ
ejpam-5258	87	18	closure	closure	NOUN
ejpam-5258	87	19	[	[	X
ejpam-5258	87	20	r(g	r(g	NUM
ejpam-5258	87	21	)	)	PUNCT
ejpam-5258	87	22	]	]	PUNCT
ejpam-5258	88	1	f	f	PROPN
ejpam-5258	88	2	⟨g	⟨g	PROPN
ejpam-5258	88	3	,	,	PUNCT
ejpam-5258	88	4	g⟩	g⟩	NOUN
ejpam-5258	88	5	of	of	ADP
ejpam-5258	88	6	r(g	r(g	NUM
ejpam-5258	88	7	)	)	PUNCT
ejpam-5258	88	8	in	in	ADP
ejpam-5258	88	9	f⟨g	f⟨g	NUM
ejpam-5258	88	10	,	,	PUNCT
ejpam-5258	88	11	g⟩	g⟩	VERB
ejpam-5258	88	12	is	be	AUX
ejpam-5258	88	13	contained	contain	VERB
ejpam-5258	88	14	in	in	ADP
ejpam-5258	88	15	c(g	c(g	PROPN
ejpam-5258	88	16	)	)	PUNCT
ejpam-5258	88	17	.	.	PUNCT
ejpam-5258	89	1	this	this	PRON
ejpam-5258	89	2	complete	complete	ADJ
ejpam-5258	89	3	the	the	DET
ejpam-5258	89	4	proof	proof	NOUN
ejpam-5258	89	5	.	.	PUNCT
ejpam-5258	90	1	definition	definition	NOUN
ejpam-5258	90	2	3	3	NUM
ejpam-5258	90	3	.	.	PUNCT
ejpam-5258	91	1	[	[	X
ejpam-5258	91	2	3	3	X
ejpam-5258	91	3	]	]	PUNCT
ejpam-5258	91	4	for	for	ADP
ejpam-5258	91	5	any	any	DET
ejpam-5258	91	6	group	group	NOUN
ejpam-5258	91	7	g	g	NOUN
ejpam-5258	91	8	,	,	PUNCT
ejpam-5258	91	9	let	let	VERB
ejpam-5258	91	10	b(g	b(g	PRON
ejpam-5258	91	11	)	)	PUNCT
ejpam-5258	92	1	=	=	PUNCT
ejpam-5258	93	1	[	[	X
ejpam-5258	93	2	r(g)]f	r(g)]f	NOUN
ejpam-5258	93	3	⟨g	⟨g	NOUN
ejpam-5258	93	4	,	,	PUNCT
ejpam-5258	93	5	g⟩	g⟩	AUX
ejpam-5258	93	6	be	be	AUX
ejpam-5258	93	7	the	the	DET
ejpam-5258	93	8	normal	normal	ADJ
ejpam-5258	93	9	closure	closure	NOUN
ejpam-5258	93	10	of	of	ADP
ejpam-5258	93	11	r(g	r(g	NUM
ejpam-5258	93	12	)	)	PUNCT
ejpam-5258	93	13	in	in	ADP
ejpam-5258	93	14	f⟨g	f⟨g	NUM
ejpam-5258	93	15	,	,	PUNCT
ejpam-5258	93	16	g⟩	g⟩	NOUN
ejpam-5258	93	17	and	and	CCONJ
ejpam-5258	93	18	h(g	h(g	NOUN
ejpam-5258	93	19	)	)	PUNCT
ejpam-5258	93	20	be	be	VERB
ejpam-5258	93	21	the	the	DET
ejpam-5258	93	22	group	group	NOUN
ejpam-5258	93	23	h(g	h(g	NOUN
ejpam-5258	93	24	)	)	PUNCT
ejpam-5258	93	25	=	=	SYM
ejpam-5258	93	26	c(g)/b(g	c(g)/b(g	NOUN
ejpam-5258	93	27	)	)	PUNCT
ejpam-5258	93	28	=	=	SYM
ejpam-5258	93	29	{	{	PUNCT
ejpam-5258	93	30	αb(g	αb(g	NOUN
ejpam-5258	93	31	)	)	PUNCT
ejpam-5258	93	32	:	:	PUNCT
ejpam-5258	93	33	α	α	PROPN
ejpam-5258	93	34	∈	∈	PROPN
ejpam-5258	93	35	c(g	c(g	PROPN
ejpam-5258	93	36	)	)	PUNCT
ejpam-5258	93	37	}	}	PUNCT
ejpam-5258	93	38	,	,	PUNCT
ejpam-5258	93	39	the	the	DET
ejpam-5258	93	40	quotient	quotient	NOUN
ejpam-5258	93	41	group	group	NOUN
ejpam-5258	93	42	of	of	ADP
ejpam-5258	93	43	the	the	DET
ejpam-5258	93	44	set	set	NOUN
ejpam-5258	93	45	of	of	ADP
ejpam-5258	93	46	left	left	ADJ
ejpam-5258	93	47	cosets	coset	NOUN
ejpam-5258	93	48	of	of	ADP
ejpam-5258	93	49	b(g	b(g	PROPN
ejpam-5258	93	50	)	)	PUNCT
ejpam-5258	93	51	in	in	ADP
ejpam-5258	93	52	c(g).h(g	c(g).h(g	NOUN
ejpam-5258	93	53	)	)	PUNCT
ejpam-5258	93	54	is	be	AUX
ejpam-5258	93	55	called	call	VERB
ejpam-5258	93	56	the	the	DET
ejpam-5258	93	57	associated	associated	ADJ
ejpam-5258	93	58	group	group	NOUN
ejpam-5258	93	59	of	of	ADP
ejpam-5258	93	60	the	the	DET
ejpam-5258	93	61	group	group	NOUN
ejpam-5258	93	62	g.	g.	NOUN
ejpam-5258	93	63	proposition	proposition	PROPN
ejpam-5258	93	64	2	2	NUM
ejpam-5258	93	65	.	.	PUNCT
ejpam-5258	94	1	the	the	DET
ejpam-5258	94	2	associated	associated	ADJ
ejpam-5258	94	3	group	group	NOUN
ejpam-5258	94	4	of	of	ADP
ejpam-5258	94	5	any	any	DET
ejpam-5258	94	6	infinite	infinite	ADJ
ejpam-5258	94	7	cyclic	cyclic	NOUN
ejpam-5258	94	8	group	group	NOUN
ejpam-5258	94	9	is	be	AUX
ejpam-5258	94	10	trivial	trivial	ADJ
ejpam-5258	94	11	.	.	PUNCT
ejpam-5258	95	1	a.	a.	NOUN
ejpam-5258	95	2	m.	m.	PROPN
ejpam-5258	95	3	alotaibi	alotaibi	PROPN
ejpam-5258	95	4	,	,	PUNCT
ejpam-5258	95	5	k.	k.	PROPN
ejpam-5258	95	6	m.	m.	PROPN
ejpam-5258	95	7	aljamal	aljamal	PROPN
ejpam-5258	95	8	/	/	SYM
ejpam-5258	95	9	eur	eur	PROPN
ejpam-5258	95	10	.	.	PUNCT
ejpam-5258	96	1	j.	j.	PROPN
ejpam-5258	96	2	pure	pure	PROPN
ejpam-5258	96	3	appl	appl	PROPN
ejpam-5258	96	4	.	.	PROPN
ejpam-5258	96	5	math	math	PROPN
ejpam-5258	96	6	,	,	PUNCT
ejpam-5258	96	7	17	17	NUM
ejpam-5258	96	8	(	(	PUNCT
ejpam-5258	96	9	3	3	NUM
ejpam-5258	96	10	)	)	PUNCT
ejpam-5258	96	11	(	(	PUNCT
ejpam-5258	96	12	2024	2024	NUM
ejpam-5258	96	13	)	)	PUNCT
ejpam-5258	96	14	,	,	PUNCT
ejpam-5258	96	15	2329	2329	NUM
ejpam-5258	96	16	-	-	SYM
ejpam-5258	96	17	2335	2335	NUM
ejpam-5258	96	18	2332	2332	NUM
ejpam-5258	96	19	proof	proof	NOUN
ejpam-5258	96	20	.	.	PUNCT
ejpam-5258	97	1	if	if	SCONJ
ejpam-5258	97	2	g	g	PROPN
ejpam-5258	97	3	is	be	AUX
ejpam-5258	97	4	an	an	DET
ejpam-5258	97	5	infinite	infinite	ADJ
ejpam-5258	97	6	cyclic	cyclic	NOUN
ejpam-5258	97	7	,	,	PUNCT
ejpam-5258	97	8	then	then	ADV
ejpam-5258	97	9	g	g	PROPN
ejpam-5258	97	10	is	be	AUX
ejpam-5258	97	11	generated	generate	VERB
ejpam-5258	97	12	by	by	ADP
ejpam-5258	97	13	a	a	DET
ejpam-5258	97	14	single	single	ADJ
ejpam-5258	97	15	element	element	NOUN
ejpam-5258	97	16	g	g	PROPN
ejpam-5258	97	17	and	and	CCONJ
ejpam-5258	97	18	g	g	PROPN
ejpam-5258	97	19	has	have	VERB
ejpam-5258	97	20	the	the	DET
ejpam-5258	97	21	presentation	presentation	NOUN
ejpam-5258	97	22	g	g	NOUN
ejpam-5258	97	23	=	=	PUNCT
ejpam-5258	97	24	⟨x	⟨x	VERB
ejpam-5258	97	25	|	|	ADV
ejpam-5258	97	26	∅⟩	∅⟩	NOUN
ejpam-5258	97	27	=	=	PUNCT
ejpam-5258	97	28	⟨x	⟨x	VERB
ejpam-5258	97	29	|	|	ADV
ejpam-5258	97	30	r⟩	r⟩	NOUN
ejpam-5258	97	31	,	,	PUNCT
ejpam-5258	97	32	where	where	SCONJ
ejpam-5258	97	33	x	x	X
ejpam-5258	97	34	=	=	PRON
ejpam-5258	97	35	{	{	PUNCT
ejpam-5258	97	36	x	x	NOUN
ejpam-5258	97	37	}	}	PUNCT
ejpam-5258	97	38	and	and	CCONJ
ejpam-5258	97	39	r	r	NOUN
ejpam-5258	97	40	=	=	NOUN
ejpam-5258	97	41	∅	∅	NOUN
ejpam-5258	97	42	,	,	PUNCT
ejpam-5258	97	43	the	the	DET
ejpam-5258	97	44	empty	empty	ADJ
ejpam-5258	97	45	set	set	NOUN
ejpam-5258	97	46	.	.	PUNCT
ejpam-5258	98	1	then	then	ADV
ejpam-5258	98	2	the	the	DET
ejpam-5258	98	3	normal	normal	ADJ
ejpam-5258	98	4	closure	closure	NOUN
ejpam-5258	98	5	rfx	rfx	NOUN
ejpam-5258	98	6	of	of	ADP
ejpam-5258	98	7	r	r	NOUN
ejpam-5258	98	8	in	in	ADP
ejpam-5258	98	9	fx	fx	NOUN
ejpam-5258	98	10	is	be	AUX
ejpam-5258	98	11	{	{	PUNCT
ejpam-5258	98	12	1	1	NUM
ejpam-5258	98	13	}	}	PUNCT
ejpam-5258	98	14	,	,	PUNCT
ejpam-5258	98	15	the	the	DET
ejpam-5258	98	16	identity	identity	NOUN
ejpam-5258	98	17	subgroup	subgroup	NOUN
ejpam-5258	98	18	of	of	ADP
ejpam-5258	98	19	g.	g.	PROPN
ejpam-5258	98	20	by	by	ADP
ejpam-5258	98	21	lemma	lemma	PROPN
ejpam-5258	98	22	1	1	NUM
ejpam-5258	98	23	,	,	PUNCT
ejpam-5258	98	24	h(g	h(g	NOUN
ejpam-5258	98	25	)	)	PUNCT
ejpam-5258	99	1	∼=	∼=	PART
ejpam-5258	99	2	r̄	r̄	NOUN
ejpam-5258	99	3	∩	∩	NOUN
ejpam-5258	99	4	[	[	X
ejpam-5258	99	5	fx	fx	NOUN
ejpam-5258	99	6	,	,	PUNCT
ejpam-5258	99	7	fx	fx	NOUN
ejpam-5258	99	8	]	]	PUNCT
ejpam-5258	99	9	/	/	SYM
ejpam-5258	99	10	[	[	PUNCT
ejpam-5258	99	11	fx	fx	NOUN
ejpam-5258	99	12	,	,	PUNCT
ejpam-5258	99	13	r̄	r̄	NOUN
ejpam-5258	99	14	]	]	PUNCT
ejpam-5258	99	15	=	=	PUNCT
ejpam-5258	99	16	{	{	PUNCT
ejpam-5258	99	17	1}/{1	1}/{1	NUM
ejpam-5258	99	18	}	}	PUNCT
ejpam-5258	99	19	=	=	SYM
ejpam-5258	99	20	{	{	PUNCT
ejpam-5258	99	21	1	1	NUM
ejpam-5258	99	22	}	}	PUNCT
ejpam-5258	99	23	.	.	PUNCT
ejpam-5258	100	1	consequently	consequently	ADV
ejpam-5258	100	2	,	,	PUNCT
ejpam-5258	100	3	h(g	h(g	NOUN
ejpam-5258	100	4	)	)	PUNCT
ejpam-5258	100	5	∼=	∼=	PROPN
ejpam-5258	100	6	{	{	PUNCT
ejpam-5258	100	7	1	1	NUM
ejpam-5258	100	8	}	}	PUNCT
ejpam-5258	100	9	.	.	PUNCT
ejpam-5258	101	1	this	this	PRON
ejpam-5258	101	2	completes	complete	VERB
ejpam-5258	101	3	the	the	DET
ejpam-5258	101	4	proof	proof	NOUN
ejpam-5258	101	5	.	.	PUNCT
ejpam-5258	102	1	theorem	theorem	NOUN
ejpam-5258	102	2	2	2	NUM
ejpam-5258	102	3	.	.	PUNCT
ejpam-5258	102	4	the	the	DET
ejpam-5258	102	5	associated	associated	ADJ
ejpam-5258	102	6	group	group	NOUN
ejpam-5258	102	7	of	of	ADP
ejpam-5258	102	8	the	the	DET
ejpam-5258	102	9	free	free	ADJ
ejpam-5258	102	10	product	product	NOUN
ejpam-5258	102	11	of	of	ADP
ejpam-5258	102	12	two	two	NUM
ejpam-5258	102	13	groups	group	NOUN
ejpam-5258	102	14	is	be	AUX
ejpam-5258	102	15	the	the	DET
ejpam-5258	102	16	direct	direct	ADJ
ejpam-5258	102	17	product	product	NOUN
ejpam-5258	102	18	of	of	ADP
ejpam-5258	102	19	associated	associated	ADJ
ejpam-5258	102	20	groups	group	NOUN
ejpam-5258	102	21	of	of	ADP
ejpam-5258	102	22	the	the	DET
ejpam-5258	102	23	two	two	NUM
ejpam-5258	102	24	groups	group	NOUN
ejpam-5258	102	25	.	.	PUNCT
ejpam-5258	103	1	that	that	PRON
ejpam-5258	103	2	is	be	AUX
ejpam-5258	103	3	,	,	PUNCT
ejpam-5258	103	4	if	if	SCONJ
ejpam-5258	103	5	k	k	PROPN
ejpam-5258	103	6	and	and	CCONJ
ejpam-5258	103	7	l	l	NOUN
ejpam-5258	103	8	are	be	AUX
ejpam-5258	103	9	two	two	NUM
ejpam-5258	103	10	groups	group	NOUN
ejpam-5258	103	11	,	,	PUNCT
ejpam-5258	103	12	then	then	ADV
ejpam-5258	103	13	h(k	h(k	PROPN
ejpam-5258	103	14	∗	∗	PROPN
ejpam-5258	103	15	l	l	NOUN
ejpam-5258	103	16	)	)	PUNCT
ejpam-5258	103	17	∼=	∼=	PROPN
ejpam-5258	103	18	h(k)×h(l	h(k)×h(l	NOUN
ejpam-5258	103	19	)	)	PUNCT
ejpam-5258	103	20	.	.	PUNCT
ejpam-5258	104	1	proof	proof	NOUN
ejpam-5258	104	2	.	.	PUNCT
ejpam-5258	105	1	see	see	VERB
ejpam-5258	105	2	[	[	X
ejpam-5258	105	3	3	3	NUM
ejpam-5258	105	4	]	]	PUNCT
ejpam-5258	105	5	.	.	PUNCT
ejpam-5258	106	1	remark	remark	PROPN
ejpam-5258	106	2	1	1	NUM
ejpam-5258	106	3	.	.	PUNCT
ejpam-5258	107	1	we	we	PRON
ejpam-5258	107	2	have	have	VERB
ejpam-5258	107	3	the	the	DET
ejpam-5258	107	4	following	follow	VERB
ejpam-5258	107	5	notes	note	NOUN
ejpam-5258	107	6	regarding	regard	VERB
ejpam-5258	107	7	theorem	theorem	NOUN
ejpam-5258	107	8	2	2	NUM
ejpam-5258	107	9	,	,	PUNCT
ejpam-5258	107	10	let	let	VERB
ejpam-5258	107	11	k	k	NOUN
ejpam-5258	107	12	=	=	PUNCT
ejpam-5258	107	13	⟨x	⟨x	VERB
ejpam-5258	108	1	|	|	ADV
ejpam-5258	108	2	r⟩	r⟩	NOUN
ejpam-5258	108	3	and	and	CCONJ
ejpam-5258	108	4	l	l	NOUN
ejpam-5258	109	1	=	=	NOUN
ejpam-5258	109	2	⟨y	⟨y	X
ejpam-5258	109	3	|	|	ADV
ejpam-5258	109	4	s⟩	s⟩	ADV
ejpam-5258	109	5	be	be	AUX
ejpam-5258	109	6	presentations	presentation	NOUN
ejpam-5258	109	7	of	of	ADP
ejpam-5258	109	8	the	the	DET
ejpam-5258	109	9	groups	group	NOUN
ejpam-5258	109	10	k	k	PROPN
ejpam-5258	109	11	and	and	CCONJ
ejpam-5258	109	12	l	l	PROPN
ejpam-5258	109	13	,	,	PUNCT
ejpam-5258	109	14	such	such	ADJ
ejpam-5258	109	15	that	that	SCONJ
ejpam-5258	109	16	x	x	SYM
ejpam-5258	109	17	∩	∩	ADJ
ejpam-5258	109	18	y	y	NOUN
ejpam-5258	109	19	=	=	PUNCT
ejpam-5258	109	20	∅.	∅.	NOUN
ejpam-5258	109	21	by	by	ADP
ejpam-5258	109	22	[	[	X
ejpam-5258	109	23	5	5	NUM
ejpam-5258	109	24	]	]	PUNCT
ejpam-5258	109	25	,	,	PUNCT
ejpam-5258	109	26	k	k	PROPN
ejpam-5258	109	27	∗	∗	X
ejpam-5258	109	28	l	l	NOUN
ejpam-5258	109	29	has	have	VERB
ejpam-5258	109	30	the	the	DET
ejpam-5258	109	31	presentation	presentation	NOUN
ejpam-5258	109	32	k	k	X
ejpam-5258	109	33	∗	∗	X
ejpam-5258	109	34	l	l	NOUN
ejpam-5258	109	35	=	=	PUNCT
ejpam-5258	109	36	⟨x	⟨x	VERB
ejpam-5258	109	37	∪	∪	X
ejpam-5258	109	38	y	y	NOUN
ejpam-5258	109	39	|	|	ADV
ejpam-5258	109	40	r	r	NOUN
ejpam-5258	109	41	∪	∪	NOUN
ejpam-5258	109	42	s⟩.	s⟩.	ADJ
ejpam-5258	109	43	the	the	DET
ejpam-5258	109	44	definition	definition	NOUN
ejpam-5258	109	45	of	of	ADP
ejpam-5258	109	46	the	the	DET
ejpam-5258	109	47	presentation	presentation	NOUN
ejpam-5258	109	48	implies	imply	VERB
ejpam-5258	110	1	that	that	SCONJ
ejpam-5258	110	2	k	k	PROPN
ejpam-5258	110	3	=	=	PUNCT
ejpam-5258	110	4	⟨x	⟨x	VERB
ejpam-5258	110	5	|	|	ADV
ejpam-5258	111	1	r⟩	r⟩	NOUN
ejpam-5258	111	2	=	=	ADJ
ejpam-5258	111	3	fx	fx	PROPN
ejpam-5258	111	4	/	/	SYM
ejpam-5258	111	5	r̄	r̄	NOUN
ejpam-5258	111	6	,	,	PUNCT
ejpam-5258	111	7	where	where	SCONJ
ejpam-5258	111	8	r̄	r̄	NOUN
ejpam-5258	111	9	is	be	AUX
ejpam-5258	111	10	the	the	DET
ejpam-5258	111	11	normal	normal	ADJ
ejpam-5258	111	12	closure	closure	NOUN
ejpam-5258	111	13	of	of	ADP
ejpam-5258	111	14	r	r	NOUN
ejpam-5258	111	15	in	in	ADP
ejpam-5258	111	16	fx	fx	NOUN
ejpam-5258	111	17	,	,	PUNCT
ejpam-5258	111	18	l	l	NOUN
ejpam-5258	111	19	=	=	PUNCT
ejpam-5258	111	20	⟨y	⟨y	X
ejpam-5258	112	1	|	|	ADV
ejpam-5258	112	2	s⟩	s⟩	ADJ
ejpam-5258	112	3	=	=	SYM
ejpam-5258	112	4	fy	fy	PROPN
ejpam-5258	112	5	/s̄	/s̄	PUNCT
ejpam-5258	112	6	,	,	PUNCT
ejpam-5258	112	7	where	where	SCONJ
ejpam-5258	112	8	s̄	s̄	NOUN
ejpam-5258	112	9	is	be	AUX
ejpam-5258	112	10	the	the	DET
ejpam-5258	112	11	normal	normal	ADJ
ejpam-5258	112	12	closure	closure	NOUN
ejpam-5258	112	13	of	of	ADP
ejpam-5258	112	14	s	s	PRON
ejpam-5258	112	15	in	in	ADP
ejpam-5258	112	16	fy	fy	PROPN
ejpam-5258	112	17	,	,	PUNCT
ejpam-5258	112	18	and	and	CCONJ
ejpam-5258	112	19	k	k	PROPN
ejpam-5258	112	20	∗	∗	NOUN
ejpam-5258	112	21	l	l	NOUN
ejpam-5258	112	22	=	=	PUNCT
ejpam-5258	112	23	⟨x	⟨x	VERB
ejpam-5258	112	24	∪	∪	X
ejpam-5258	112	25	y	y	NOUN
ejpam-5258	113	1	|	|	ADV
ejpam-5258	113	2	r	r	NOUN
ejpam-5258	113	3	∪	∪	X
ejpam-5258	113	4	s⟩	s⟩	NOUN
ejpam-5258	113	5	=	=	SYM
ejpam-5258	113	6	fx∪y	fx∪y	NOUN
ejpam-5258	113	7	/	/	SYM
ejpam-5258	113	8	x∪y	x∪y	NOUN
ejpam-5258	113	9	,	,	PUNCT
ejpam-5258	113	10	where	where	SCONJ
ejpam-5258	113	11	x	x	PUNCT
ejpam-5258	113	12	∪	∪	VERB
ejpam-5258	113	13	y	y	NOUN
ejpam-5258	113	14	=	=	PUNCT
ejpam-5258	114	1	[	[	X
ejpam-5258	114	2	r∪s]fx∪y	r∪s]fx∪y	NOUN
ejpam-5258	114	3	,	,	PUNCT
ejpam-5258	114	4	normal	normal	ADJ
ejpam-5258	114	5	closure	closure	NOUN
ejpam-5258	114	6	of	of	ADP
ejpam-5258	114	7	r∪s	r∪s	NOUN
ejpam-5258	114	8	in	in	ADP
ejpam-5258	114	9	fx∪y	fx∪y	NOUN
ejpam-5258	114	10	.	.	PUNCT
ejpam-5258	115	1	lemma	lemma	PROPN
ejpam-5258	115	2	1	1	NUM
ejpam-5258	115	3	,	,	PUNCT
ejpam-5258	115	4	implies	imply	VERB
ejpam-5258	115	5	that	that	SCONJ
ejpam-5258	115	6	h(k	h(k	PROPN
ejpam-5258	115	7	)	)	PUNCT
ejpam-5258	115	8	∼=	∼=	PROPN
ejpam-5258	115	9	r̄	r̄	NOUN
ejpam-5258	115	10	∩	∩	NOUN
ejpam-5258	115	11	[	[	X
ejpam-5258	115	12	fx	fx	NOUN
ejpam-5258	115	13	,	,	PUNCT
ejpam-5258	115	14	fx	fx	NOUN
ejpam-5258	115	15	]	]	PUNCT
ejpam-5258	115	16	/	/	SYM
ejpam-5258	115	17	[	[	PUNCT
ejpam-5258	115	18	fx	fx	NOUN
ejpam-5258	115	19	,	,	PUNCT
ejpam-5258	115	20	r̄	r̄	NOUN
ejpam-5258	115	21	]	]	PUNCT
ejpam-5258	115	22	,	,	PUNCT
ejpam-5258	115	23	h(l	h(l	PROPN
ejpam-5258	115	24	)	)	PUNCT
ejpam-5258	116	1	∼=	∼=	PROPN
ejpam-5258	116	2	s̄∩[fy	s̄∩[fy	PROPN
ejpam-5258	116	3	,	,	PUNCT
ejpam-5258	116	4	fy	fy	PROPN
ejpam-5258	116	5	]	]	PUNCT
ejpam-5258	116	6	/	/	PUNCT
ejpam-5258	116	7	[	[	PUNCT
ejpam-5258	116	8	fy	fy	NOUN
ejpam-5258	116	9	,	,	PUNCT
ejpam-5258	116	10	s̄	s̄	NOUN
ejpam-5258	116	11	]	]	PUNCT
ejpam-5258	116	12	andh(k∗l	andh(k∗l	NOUN
ejpam-5258	116	13	)	)	PUNCT
ejpam-5258	116	14	∼=	∼=	PROPN
ejpam-5258	116	15	(	(	PUNCT
ejpam-5258	116	16	r	r	NOUN
ejpam-5258	116	17	∪	∪	ADP
ejpam-5258	116	18	s)∩[fx∪y	s)∩[fx∪y	NOUN
ejpam-5258	116	19	,	,	PUNCT
ejpam-5258	116	20	fx∪y	fx∪y	NOUN
ejpam-5258	116	21	]	]	PUNCT
ejpam-5258	116	22	/	/	SYM
ejpam-5258	116	23	[	[	PUNCT
ejpam-5258	116	24	fx∪y	fx∪y	NOUN
ejpam-5258	116	25	,	,	PUNCT
ejpam-5258	116	26	r	r	NOUN
ejpam-5258	116	27	∪	∪	NOUN
ejpam-5258	116	28	s	s	X
ejpam-5258	116	29	]	]	PUNCT
ejpam-5258	116	30	.	.	PUNCT
ejpam-5258	117	1	corollary	corollary	ADJ
ejpam-5258	117	2	1	1	NUM
ejpam-5258	117	3	.	.	PUNCT
ejpam-5258	117	4	consider	consider	VERB
ejpam-5258	117	5	the	the	DET
ejpam-5258	117	6	groups	group	NOUN
ejpam-5258	117	7	k	k	PROPN
ejpam-5258	117	8	and	and	CCONJ
ejpam-5258	117	9	l	l	NOUN
ejpam-5258	117	10	of	of	ADP
ejpam-5258	117	11	presentations	presentation	NOUN
ejpam-5258	117	12	k	k	X
ejpam-5258	118	1	=	=	SYM
ejpam-5258	118	2	⟨x0	⟨x0	PROPN
ejpam-5258	118	3	,	,	PUNCT
ejpam-5258	118	4	x1	x1	PROPN
ejpam-5258	118	5	,	,	PUNCT
ejpam-5258	118	6	.	.	PUNCT
ejpam-5258	118	7	.	.	PUNCT
ejpam-5258	118	8	.	.	PUNCT
ejpam-5258	119	1	,	,	PUNCT
ejpam-5258	119	2	xn+1	xn+1	PROPN
ejpam-5258	119	3	|	|	ADV
ejpam-5258	119	4	r1	r1	PROPN
ejpam-5258	119	5	,	,	PUNCT
ejpam-5258	119	6	.	.	PUNCT
ejpam-5258	119	7	.	.	PUNCT
ejpam-5258	120	1	.	.	PUNCT
ejpam-5258	121	1	,	,	PUNCT
ejpam-5258	121	2	rn	rn	PROPN
ejpam-5258	121	3	,	,	PUNCT
ejpam-5258	121	4	x0⟩	x0⟩	PRON
ejpam-5258	121	5	,	,	PUNCT
ejpam-5258	121	6	and	and	CCONJ
ejpam-5258	121	7	l	l	NOUN
ejpam-5258	122	1	=	=	SYM
ejpam-5258	122	2	⟨x0	⟨x0	PROPN
ejpam-5258	122	3	,	,	PUNCT
ejpam-5258	122	4	x1	x1	PROPN
ejpam-5258	122	5	,	,	PUNCT
ejpam-5258	122	6	.	.	PUNCT
ejpam-5258	122	7	.	.	PUNCT
ejpam-5258	122	8	.	.	PUNCT
ejpam-5258	123	1	,	,	PUNCT
ejpam-5258	123	2	xn+1	xn+1	PROPN
ejpam-5258	123	3	|	|	ADV
ejpam-5258	123	4	r1	r1	PROPN
ejpam-5258	123	5	,	,	PUNCT
ejpam-5258	123	6	.	.	PUNCT
ejpam-5258	123	7	.	.	PUNCT
ejpam-5258	123	8	.	.	PUNCT
ejpam-5258	124	1	,	,	PUNCT
ejpam-5258	124	2	rn⟩.	rn⟩.	NOUN
ejpam-5258	124	3	then	then	ADV
ejpam-5258	124	4	h(k	h(k	PROPN
ejpam-5258	124	5	)	)	PUNCT
ejpam-5258	124	6	∼=	∼=	PROPN
ejpam-5258	124	7	h(l	h(l	NUM
ejpam-5258	124	8	)	)	PUNCT
ejpam-5258	124	9	.	.	PUNCT
ejpam-5258	125	1	proof	proof	NOUN
ejpam-5258	125	2	.	.	PUNCT
ejpam-5258	126	1	by	by	ADP
ejpam-5258	126	2	[	[	X
ejpam-5258	126	3	5	5	NUM
ejpam-5258	126	4	]	]	PUNCT
ejpam-5258	126	5	,	,	PUNCT
ejpam-5258	126	6	l	l	NOUN
ejpam-5258	126	7	=	=	SYM
ejpam-5258	126	8	k	k	PROPN
ejpam-5258	126	9	∗	∗	PROPN
ejpam-5258	126	10	p	p	PROPN
ejpam-5258	126	11	is	be	AUX
ejpam-5258	126	12	the	the	DET
ejpam-5258	126	13	free	free	ADJ
ejpam-5258	126	14	product	product	NOUN
ejpam-5258	126	15	of	of	ADP
ejpam-5258	126	16	k	k	PROPN
ejpam-5258	126	17	and	and	CCONJ
ejpam-5258	126	18	p	p	NOUN
ejpam-5258	126	19	,	,	PUNCT
ejpam-5258	126	20	where	where	SCONJ
ejpam-5258	126	21	p	p	NOUN
ejpam-5258	126	22	is	be	AUX
ejpam-5258	126	23	an	an	DET
ejpam-5258	126	24	infinite	infinite	ADJ
ejpam-5258	126	25	cyclic	cyclic	NOUN
ejpam-5258	126	26	group	group	NOUN
ejpam-5258	126	27	.	.	PUNCT
ejpam-5258	127	1	by	by	ADP
ejpam-5258	127	2	theorem	theorem	NOUN
ejpam-5258	127	3	1	1	NUM
ejpam-5258	127	4	,	,	PUNCT
ejpam-5258	127	5	h(l	h(l	NUM
ejpam-5258	127	6	)	)	PUNCT
ejpam-5258	127	7	∼=	∼=	PROPN
ejpam-5258	127	8	h(k)×h(p	h(k)×h(p	NOUN
ejpam-5258	127	9	)	)	PUNCT
ejpam-5258	127	10	and	and	CCONJ
ejpam-5258	127	11	by	by	ADP
ejpam-5258	127	12	proposition	proposition	NOUN
ejpam-5258	127	13	2	2	NUM
ejpam-5258	127	14	h(p	h(p	PROPN
ejpam-5258	127	15	)	)	PUNCT
ejpam-5258	127	16	is	be	AUX
ejpam-5258	127	17	trivial	trivial	ADJ
ejpam-5258	127	18	.	.	PUNCT
ejpam-5258	128	1	that	that	PRON
ejpam-5258	128	2	is	be	AUX
ejpam-5258	128	3	,	,	PUNCT
ejpam-5258	128	4	h(p	h(p	PROPN
ejpam-5258	128	5	)	)	PUNCT
ejpam-5258	128	6	∼=	∼=	PROPN
ejpam-5258	128	7	{	{	PUNCT
ejpam-5258	128	8	1	1	NUM
ejpam-5258	128	9	}	}	PUNCT
ejpam-5258	128	10	.	.	PUNCT
ejpam-5258	129	1	this	this	PRON
ejpam-5258	129	2	implies	imply	VERB
ejpam-5258	129	3	that	that	SCONJ
ejpam-5258	129	4	h(l	h(l	PROPN
ejpam-5258	129	5	)	)	PUNCT
ejpam-5258	129	6	∼=	∼=	ADP
ejpam-5258	129	7	h(k)×{1	h(k)×{1	NOUN
ejpam-5258	129	8	}	}	PUNCT
ejpam-5258	129	9	∼=	∼=	PROPN
ejpam-5258	129	10	h(k	h(k	NOUN
ejpam-5258	129	11	)	)	PUNCT
ejpam-5258	129	12	.	.	PUNCT
ejpam-5258	130	1	this	this	PRON
ejpam-5258	130	2	complete	complete	ADJ
ejpam-5258	130	3	the	the	DET
ejpam-5258	130	4	proof	proof	NOUN
ejpam-5258	130	5	.	.	PUNCT
ejpam-5258	131	1	3	3	X
ejpam-5258	131	2	.	.	X
ejpam-5258	131	3	the	the	DET
ejpam-5258	131	4	associated	associated	ADJ
ejpam-5258	131	5	groups	group	NOUN
ejpam-5258	131	6	of	of	ADP
ejpam-5258	131	7	quasi	quasi	ADJ
ejpam-5258	131	8	-	-	ADJ
ejpam-5258	131	9	free	free	ADJ
ejpam-5258	131	10	groups	group	NOUN
ejpam-5258	131	11	recall	recall	VERB
ejpam-5258	131	12	that	that	SCONJ
ejpam-5258	131	13	a	a	DET
ejpam-5258	131	14	group	group	NOUN
ejpam-5258	131	15	is	be	AUX
ejpam-5258	131	16	termed	term	VERB
ejpam-5258	131	17	a	a	DET
ejpam-5258	131	18	quasi	quasi	ADJ
ejpam-5258	131	19	-	-	ADJ
ejpam-5258	131	20	free	free	ADJ
ejpam-5258	131	21	group	group	NOUN
ejpam-5258	131	22	if	if	SCONJ
ejpam-5258	131	23	it	it	PRON
ejpam-5258	131	24	is	be	AUX
ejpam-5258	131	25	a	a	DET
ejpam-5258	131	26	free	free	ADJ
ejpam-5258	131	27	product	product	NOUN
ejpam-5258	131	28	of	of	ADP
ejpam-5258	131	29	cyclic	cyclic	ADJ
ejpam-5258	131	30	groups	group	NOUN
ejpam-5258	131	31	of	of	ADP
ejpam-5258	131	32	any	any	DET
ejpam-5258	131	33	order	order	NOUN
ejpam-5258	131	34	.	.	PUNCT
ejpam-5258	132	1	in	in	ADP
ejpam-5258	132	2	this	this	DET
ejpam-5258	132	3	section	section	NOUN
ejpam-5258	132	4	we	we	PRON
ejpam-5258	132	5	show	show	VERB
ejpam-5258	132	6	that	that	SCONJ
ejpam-5258	132	7	if	if	SCONJ
ejpam-5258	132	8	f	f	PROPN
ejpam-5258	132	9	is	be	AUX
ejpam-5258	132	10	a	a	DET
ejpam-5258	132	11	quasi	quasi	ADJ
ejpam-5258	132	12	-	-	ADJ
ejpam-5258	132	13	free	free	ADJ
ejpam-5258	132	14	group	group	NOUN
ejpam-5258	132	15	and	and	CCONJ
ejpam-5258	132	16	g	g	PROPN
ejpam-5258	132	17	is	be	AUX
ejpam-5258	132	18	any	any	DET
ejpam-5258	132	19	group	group	NOUN
ejpam-5258	132	20	then	then	ADV
ejpam-5258	132	21	the	the	DET
ejpam-5258	132	22	associated	associated	ADJ
ejpam-5258	132	23	group	group	NOUN
ejpam-5258	132	24	h(f	h(f	PROPN
ejpam-5258	132	25	)	)	PUNCT
ejpam-5258	132	26	of	of	ADP
ejpam-5258	132	27	f	f	PROPN
ejpam-5258	132	28	is	be	AUX
ejpam-5258	132	29	trivial	trivial	ADJ
ejpam-5258	132	30	and	and	CCONJ
ejpam-5258	132	31	the	the	DET
ejpam-5258	132	32	associated	associated	ADJ
ejpam-5258	132	33	group	group	NOUN
ejpam-5258	132	34	h(f	h(f	PROPN
ejpam-5258	132	35	∗g	∗g	NUM
ejpam-5258	132	36	)	)	PUNCT
ejpam-5258	132	37	of	of	ADP
ejpam-5258	132	38	the	the	DET
ejpam-5258	132	39	free	free	ADJ
ejpam-5258	132	40	product	product	NOUN
ejpam-5258	132	41	f	f	PROPN
ejpam-5258	132	42	∗g	∗g	NOUN
ejpam-5258	132	43	of	of	ADP
ejpam-5258	132	44	f	f	PROPN
ejpam-5258	132	45	and	and	CCONJ
ejpam-5258	132	46	g	g	PROPN
ejpam-5258	132	47	satisfies	satisfy	VERB
ejpam-5258	132	48	the	the	DET
ejpam-5258	132	49	condition	condition	NOUN
ejpam-5258	132	50	h(f	h(f	X
ejpam-5258	132	51	∗g	∗g	NUM
ejpam-5258	132	52	)	)	PUNCT
ejpam-5258	132	53	∼=	∼=	PROPN
ejpam-5258	132	54	h(g	h(g	NOUN
ejpam-5258	132	55	)	)	PUNCT
ejpam-5258	132	56	.	.	PUNCT
ejpam-5258	133	1	first	first	ADV
ejpam-5258	133	2	we	we	PRON
ejpam-5258	133	3	introduce	introduce	VERB
ejpam-5258	133	4	the	the	DET
ejpam-5258	133	5	following	follow	VERB
ejpam-5258	133	6	concept	concept	NOUN
ejpam-5258	133	7	.	.	PUNCT
ejpam-5258	134	1	if	if	SCONJ
ejpam-5258	134	2	g	g	PROPN
ejpam-5258	134	3	is	be	AUX
ejpam-5258	134	4	a	a	DET
ejpam-5258	134	5	finite	finite	ADJ
ejpam-5258	134	6	group	group	NOUN
ejpam-5258	134	7	,	,	PUNCT
ejpam-5258	134	8	the	the	DET
ejpam-5258	134	9	schur	schur	PROPN
ejpam-5258	134	10	multiplier	multiplier	NOUN
ejpam-5258	134	11	of	of	ADP
ejpam-5258	134	12	g	g	PROPN
ejpam-5258	134	13	introduced	introduce	VERB
ejpam-5258	134	14	in	in	ADP
ejpam-5258	134	15	[	[	X
ejpam-5258	134	16	8	8	NUM
ejpam-5258	134	17	,	,	PUNCT
ejpam-5258	134	18	p.	p.	NOUN
ejpam-5258	134	19	14	14	NUM
ejpam-5258	134	20	]	]	PUNCT
ejpam-5258	134	21	is	be	AUX
ejpam-5258	134	22	denoted	denote	VERB
ejpam-5258	134	23	by	by	ADP
ejpam-5258	134	24	m(g	m(g	PROPN
ejpam-5258	134	25	)	)	PUNCT
ejpam-5258	134	26	and	and	CCONJ
ejpam-5258	134	27	is	be	AUX
ejpam-5258	134	28	defined	define	VERB
ejpam-5258	134	29	to	to	PART
ejpam-5258	134	30	be	be	AUX
ejpam-5258	134	31	the	the	DET
ejpam-5258	134	32	second	second	ADJ
ejpam-5258	134	33	cohomology	cohomology	NOUN
ejpam-5258	134	34	group	group	NOUN
ejpam-5258	134	35	h2	h2	PROPN
ejpam-5258	134	36	(	(	PUNCT
ejpam-5258	134	37	g	g	NOUN
ejpam-5258	134	38	,	,	PUNCT
ejpam-5258	134	39	c∗	c∗	NOUN
ejpam-5258	134	40	)	)	PUNCT
ejpam-5258	134	41	of	of	ADP
ejpam-5258	134	42	g	g	PROPN
ejpam-5258	134	43	,	,	PUNCT
ejpam-5258	134	44	where	where	SCONJ
ejpam-5258	134	45	c∗	c∗	PROPN
ejpam-5258	134	46	is	be	AUX
ejpam-5258	134	47	the	the	DET
ejpam-5258	134	48	set	set	NOUN
ejpam-5258	134	49	of	of	ADP
ejpam-5258	134	50	nonzero	nonzero	NOUN
ejpam-5258	134	51	complex	complex	ADJ
ejpam-5258	134	52	numbers	number	NOUN
ejpam-5258	134	53	.	.	PUNCT
ejpam-5258	135	1	proposition	proposition	NOUN
ejpam-5258	135	2	3	3	NUM
ejpam-5258	135	3	.	.	PUNCT
ejpam-5258	136	1	let	let	VERB
ejpam-5258	136	2	g	g	PRON
ejpam-5258	136	3	be	be	AUX
ejpam-5258	136	4	a	a	DET
ejpam-5258	136	5	finite	finite	ADJ
ejpam-5258	136	6	group	group	NOUN
ejpam-5258	136	7	.	.	PUNCT
ejpam-5258	137	1	then	then	ADV
ejpam-5258	137	2	h(g	h(g	VERB
ejpam-5258	137	3	)	)	PUNCT
ejpam-5258	137	4	∼=	∼=	PROPN
ejpam-5258	137	5	m(g	m(g	NOUN
ejpam-5258	137	6	)	)	PUNCT
ejpam-5258	137	7	.	.	PUNCT
ejpam-5258	138	1	furthermore	furthermore	ADV
ejpam-5258	138	2	,	,	PUNCT
ejpam-5258	138	3	if	if	SCONJ
ejpam-5258	138	4	g	g	PROPN
ejpam-5258	138	5	has	have	VERB
ejpam-5258	138	6	the	the	DET
ejpam-5258	138	7	presentation	presentation	NOUN
ejpam-5258	138	8	⟨x	⟨x	VERB
ejpam-5258	138	9	|	|	ADV
ejpam-5258	138	10	r⟩	r⟩	NOUN
ejpam-5258	138	11	,	,	PUNCT
ejpam-5258	138	12	where	where	SCONJ
ejpam-5258	138	13	x	x	PRON
ejpam-5258	138	14	has	have	VERB
ejpam-5258	138	15	cardinality	cardinality	PROPN
ejpam-5258	138	16	m	m	PROPN
ejpam-5258	138	17	and	and	CCONJ
ejpam-5258	138	18	r	r	NOUN
ejpam-5258	138	19	has	have	VERB
ejpam-5258	138	20	cardinality	cardinality	NOUN
ejpam-5258	138	21	n	n	CCONJ
ejpam-5258	138	22	,	,	PUNCT
ejpam-5258	138	23	then	then	ADV
ejpam-5258	138	24	h(g	h(g	VERB
ejpam-5258	138	25	)	)	PUNCT
ejpam-5258	139	1	∼=	∼=	PROPN
ejpam-5258	139	2	{	{	PUNCT
ejpam-5258	139	3	1	1	NUM
ejpam-5258	139	4	}	}	PUNCT
ejpam-5258	139	5	if	if	SCONJ
ejpam-5258	139	6	m	m	VERB
ejpam-5258	139	7	=	=	SYM
ejpam-5258	139	8	n	n	NOUN
ejpam-5258	139	9	and	and	CCONJ
ejpam-5258	139	10	h(g	h(g	NOUN
ejpam-5258	139	11	)	)	PUNCT
ejpam-5258	139	12	is	be	AUX
ejpam-5258	139	13	cyclic	cyclic	ADJ
ejpam-5258	139	14	if	if	SCONJ
ejpam-5258	139	15	n	n	NUM
ejpam-5258	139	16	=	=	SYM
ejpam-5258	139	17	m+	m+	NUM
ejpam-5258	139	18	1	1	NUM
ejpam-5258	139	19	.	.	PUNCT
ejpam-5258	140	1	proof	proof	NOUN
ejpam-5258	140	2	.	.	PUNCT
ejpam-5258	141	1	if	if	SCONJ
ejpam-5258	141	2	g	g	PROPN
ejpam-5258	141	3	is	be	AUX
ejpam-5258	141	4	finite	finite	ADJ
ejpam-5258	141	5	,	,	PUNCT
ejpam-5258	141	6	then	then	ADV
ejpam-5258	141	7	by	by	ADP
ejpam-5258	141	8	[	[	X
ejpam-5258	141	9	2	2	X
ejpam-5258	141	10	]	]	PUNCT
ejpam-5258	141	11	we	we	PRON
ejpam-5258	141	12	have	have	VERB
ejpam-5258	141	13	h(g	h(g	NOUN
ejpam-5258	141	14	)	)	PUNCT
ejpam-5258	141	15	=	=	SYM
ejpam-5258	141	16	m(g	m(g	NOUN
ejpam-5258	141	17	)	)	PUNCT
ejpam-5258	141	18	.	.	PUNCT
ejpam-5258	142	1	if	if	SCONJ
ejpam-5258	142	2	m	m	PROPN
ejpam-5258	142	3	=	=	SYM
ejpam-5258	142	4	n	n	CCONJ
ejpam-5258	142	5	,	,	PUNCT
ejpam-5258	142	6	then	then	ADV
ejpam-5258	142	7	by	by	ADP
ejpam-5258	142	8	[	[	X
ejpam-5258	142	9	3	3	NUM
ejpam-5258	142	10	]	]	PUNCT
ejpam-5258	142	11	,	,	PUNCT
ejpam-5258	142	12	m(g	m(g	PROPN
ejpam-5258	142	13	)	)	PUNCT
ejpam-5258	142	14	=	=	SYM
ejpam-5258	143	1	1	1	X
ejpam-5258	143	2	.	.	PUNCT
ejpam-5258	143	3	consequently	consequently	ADV
ejpam-5258	143	4	,	,	PUNCT
ejpam-5258	143	5	h(h	h(h	X
ejpam-5258	143	6	)	)	PUNCT
ejpam-5258	143	7	=	=	SYM
ejpam-5258	143	8	1	1	X
ejpam-5258	143	9	.	.	PUNCT
ejpam-5258	144	1	if	if	SCONJ
ejpam-5258	144	2	n	n	NOUN
ejpam-5258	144	3	=	=	SYM
ejpam-5258	144	4	m+	m+	NUM
ejpam-5258	144	5	1	1	NUM
ejpam-5258	144	6	,	,	PUNCT
ejpam-5258	144	7	then	then	ADV
ejpam-5258	144	8	m(g	m(g	NOUN
ejpam-5258	144	9	)	)	PUNCT
ejpam-5258	144	10	is	be	AUX
ejpam-5258	144	11	cyclic	cyclic	ADJ
ejpam-5258	144	12	.	.	PUNCT
ejpam-5258	145	1	this	this	PRON
ejpam-5258	145	2	implies	imply	VERB
ejpam-5258	145	3	that	that	SCONJ
ejpam-5258	145	4	h(g	h(g	NOUN
ejpam-5258	145	5	)	)	PUNCT
ejpam-5258	145	6	is	be	AUX
ejpam-5258	145	7	cyclic	cyclic	ADJ
ejpam-5258	145	8	.	.	PUNCT
ejpam-5258	146	1	this	this	PRON
ejpam-5258	146	2	complete	complete	ADJ
ejpam-5258	146	3	the	the	DET
ejpam-5258	146	4	proof	proof	NOUN
ejpam-5258	146	5	.	.	PUNCT
ejpam-5258	147	1	a.	a.	PROPN
ejpam-5258	147	2	m.	m.	PROPN
ejpam-5258	147	3	alotaibi	alotaibi	PROPN
ejpam-5258	147	4	,	,	PUNCT
ejpam-5258	147	5	k.	k.	PROPN
ejpam-5258	147	6	m.	m.	PROPN
ejpam-5258	147	7	aljamal	aljamal	PROPN
ejpam-5258	147	8	/	/	SYM
ejpam-5258	147	9	eur	eur	PROPN
ejpam-5258	147	10	.	.	PUNCT
ejpam-5258	148	1	j.	j.	PROPN
ejpam-5258	148	2	pure	pure	PROPN
ejpam-5258	148	3	appl	appl	PROPN
ejpam-5258	148	4	.	.	PROPN
ejpam-5258	148	5	math	math	PROPN
ejpam-5258	148	6	,	,	PUNCT
ejpam-5258	148	7	17	17	NUM
ejpam-5258	148	8	(	(	PUNCT
ejpam-5258	148	9	3	3	NUM
ejpam-5258	148	10	)	)	PUNCT
ejpam-5258	148	11	(	(	PUNCT
ejpam-5258	148	12	2024	2024	NUM
ejpam-5258	148	13	)	)	PUNCT
ejpam-5258	148	14	,	,	PUNCT
ejpam-5258	148	15	2329	2329	NUM
ejpam-5258	148	16	-	-	SYM
ejpam-5258	148	17	2335	2335	NUM
ejpam-5258	148	18	2333	2333	NUM
ejpam-5258	148	19	lemma	lemma	PROPN
ejpam-5258	148	20	2	2	NUM
ejpam-5258	148	21	.	.	PUNCT
ejpam-5258	149	1	the	the	DET
ejpam-5258	149	2	associated	associated	ADJ
ejpam-5258	149	3	group	group	NOUN
ejpam-5258	149	4	of	of	ADP
ejpam-5258	149	5	any	any	DET
ejpam-5258	149	6	cyclic	cyclic	ADJ
ejpam-5258	149	7	group	group	NOUN
ejpam-5258	149	8	is	be	AUX
ejpam-5258	149	9	trivial	trivial	ADJ
ejpam-5258	149	10	.	.	PUNCT
ejpam-5258	150	1	proof	proof	NOUN
ejpam-5258	150	2	.	.	PUNCT
ejpam-5258	151	1	let	let	VERB
ejpam-5258	151	2	g	g	NOUN
ejpam-5258	151	3	be	be	AUX
ejpam-5258	151	4	any	any	DET
ejpam-5258	151	5	cyclic	cyclic	ADJ
ejpam-5258	151	6	group	group	NOUN
ejpam-5258	151	7	.	.	PUNCT
ejpam-5258	152	1	we	we	PRON
ejpam-5258	152	2	need	need	VERB
ejpam-5258	152	3	to	to	PART
ejpam-5258	152	4	show	show	VERB
ejpam-5258	152	5	that	that	SCONJ
ejpam-5258	152	6	h(g	h(g	NOUN
ejpam-5258	152	7	)	)	PUNCT
ejpam-5258	152	8	is	be	AUX
ejpam-5258	152	9	trivial	trivial	ADJ
ejpam-5258	152	10	.	.	PUNCT
ejpam-5258	153	1	if	if	SCONJ
ejpam-5258	153	2	g	g	PROPN
ejpam-5258	153	3	is	be	AUX
ejpam-5258	153	4	an	an	DET
ejpam-5258	153	5	infinite	infinite	ADJ
ejpam-5258	153	6	cyclic	cyclic	NOUN
ejpam-5258	153	7	group	group	NOUN
ejpam-5258	153	8	,	,	PUNCT
ejpam-5258	153	9	then	then	ADV
ejpam-5258	153	10	by	by	ADP
ejpam-5258	153	11	proposition	proposition	NOUN
ejpam-5258	153	12	2	2	NUM
ejpam-5258	153	13	,	,	PUNCT
ejpam-5258	153	14	h(g	h(g	NOUN
ejpam-5258	153	15	)	)	PUNCT
ejpam-5258	153	16	∼=	∼=	PROPN
ejpam-5258	153	17	{	{	PUNCT
ejpam-5258	153	18	1	1	NUM
ejpam-5258	153	19	}	}	PUNCT
ejpam-5258	153	20	.	.	PUNCT
ejpam-5258	154	1	if	if	SCONJ
ejpam-5258	154	2	g	g	PROPN
ejpam-5258	154	3	is	be	AUX
ejpam-5258	154	4	a	a	DET
ejpam-5258	154	5	finite	finite	ADJ
ejpam-5258	154	6	cyclic	cyclic	ADJ
ejpam-5258	154	7	group	group	NOUN
ejpam-5258	154	8	of	of	ADP
ejpam-5258	154	9	order	order	NOUN
ejpam-5258	154	10	n	n	X
ejpam-5258	154	11	then	then	ADV
ejpam-5258	154	12	g	g	PROPN
ejpam-5258	154	13	has	have	VERB
ejpam-5258	154	14	the	the	DET
ejpam-5258	154	15	presentation	presentation	NOUN
ejpam-5258	154	16	g	g	NOUN
ejpam-5258	154	17	=	=	PUNCT
ejpam-5258	154	18	⟨x	⟨x	VERB
ejpam-5258	154	19	|	|	ADV
ejpam-5258	154	20	xn⟩	xn⟩	PROPN
ejpam-5258	154	21	of	of	ADP
ejpam-5258	154	22	one	one	NUM
ejpam-5258	154	23	generator	generator	NOUN
ejpam-5258	154	24	x	x	NOUN
ejpam-5258	154	25	and	and	CCONJ
ejpam-5258	154	26	one	one	NUM
ejpam-5258	154	27	relater	relater	NOUN
ejpam-5258	154	28	xn	xn	PUNCT
ejpam-5258	155	1	=	=	SYM
ejpam-5258	155	2	1	1	X
ejpam-5258	155	3	.	.	PUNCT
ejpam-5258	156	1	so	so	ADV
ejpam-5258	156	2	the	the	DET
ejpam-5258	156	3	number	number	NOUN
ejpam-5258	156	4	of	of	ADP
ejpam-5258	156	5	the	the	DET
ejpam-5258	156	6	generators	generator	NOUN
ejpam-5258	156	7	of	of	ADP
ejpam-5258	156	8	g	g	PROPN
ejpam-5258	156	9	is	be	AUX
ejpam-5258	156	10	the	the	DET
ejpam-5258	156	11	same	same	ADJ
ejpam-5258	156	12	number	number	NOUN
ejpam-5258	156	13	of	of	ADP
ejpam-5258	156	14	relaters	relater	NOUN
ejpam-5258	156	15	=	=	SYM
ejpam-5258	156	16	1	1	X
ejpam-5258	156	17	.	.	PUNCT
ejpam-5258	156	18	then	then	ADV
ejpam-5258	156	19	proposition	proposition	NOUN
ejpam-5258	156	20	3	3	NUM
ejpam-5258	156	21	,	,	PUNCT
ejpam-5258	156	22	shows	show	VERB
ejpam-5258	156	23	that	that	SCONJ
ejpam-5258	156	24	h(g	h(g	NOUN
ejpam-5258	156	25	)	)	PUNCT
ejpam-5258	156	26	∼=	∼=	PROPN
ejpam-5258	156	27	{	{	PUNCT
ejpam-5258	156	28	1	1	NUM
ejpam-5258	156	29	}	}	PUNCT
ejpam-5258	156	30	.	.	PUNCT
ejpam-5258	157	1	this	this	PRON
ejpam-5258	157	2	complete	complete	VERB
ejpam-5258	157	3	the	the	DET
ejpam-5258	157	4	proof	proof	NOUN
ejpam-5258	157	5	.	.	PUNCT
ejpam-5258	158	1	theorem	theorem	NOUN
ejpam-5258	158	2	3	3	NUM
ejpam-5258	158	3	.	.	PUNCT
ejpam-5258	159	1	the	the	DET
ejpam-5258	159	2	associated	associated	ADJ
ejpam-5258	159	3	group	group	NOUN
ejpam-5258	159	4	of	of	ADP
ejpam-5258	159	5	a	a	DET
ejpam-5258	159	6	quasi	quasi	ADJ
ejpam-5258	159	7	-	-	ADJ
ejpam-5258	159	8	free	free	ADJ
ejpam-5258	159	9	group	group	NOUN
ejpam-5258	159	10	is	be	AUX
ejpam-5258	159	11	trivial	trivial	ADJ
ejpam-5258	159	12	.	.	PUNCT
ejpam-5258	160	1	proof	proof	NOUN
ejpam-5258	160	2	.	.	PUNCT
ejpam-5258	161	1	let	let	VERB
ejpam-5258	161	2	f	f	PRON
ejpam-5258	161	3	be	be	AUX
ejpam-5258	161	4	a	a	DET
ejpam-5258	161	5	quasi	quasi	ADJ
ejpam-5258	161	6	-	-	ADJ
ejpam-5258	161	7	free	free	ADJ
ejpam-5258	161	8	group	group	NOUN
ejpam-5258	161	9	and	and	CCONJ
ejpam-5258	161	10	g	g	PROPN
ejpam-5258	161	11	be	be	AUX
ejpam-5258	161	12	any	any	DET
ejpam-5258	161	13	group	group	NOUN
ejpam-5258	161	14	.	.	PUNCT
ejpam-5258	162	1	then	then	ADV
ejpam-5258	162	2	h(f	h(f	VERB
ejpam-5258	162	3	)	)	PUNCT
ejpam-5258	163	1	∼=	∼=	PROPN
ejpam-5258	163	2	{	{	PUNCT
ejpam-5258	163	3	1	1	NUM
ejpam-5258	163	4	}	}	PUNCT
ejpam-5258	163	5	and	and	CCONJ
ejpam-5258	163	6	h(f	h(f	ADV
ejpam-5258	163	7	∗g	∗g	NUM
ejpam-5258	163	8	)	)	PUNCT
ejpam-5258	163	9	∼=	∼=	PROPN
ejpam-5258	163	10	h(g	h(g	NOUN
ejpam-5258	163	11	)	)	PUNCT
ejpam-5258	163	12	.	.	PUNCT
ejpam-5258	164	1	let	let	VERB
ejpam-5258	164	2	f	f	PRON
ejpam-5258	164	3	be	be	AUX
ejpam-5258	164	4	a	a	DET
ejpam-5258	164	5	quasi	quasi	ADJ
ejpam-5258	164	6	-	-	ADJ
ejpam-5258	164	7	free	free	ADJ
ejpam-5258	164	8	group	group	NOUN
ejpam-5258	164	9	.	.	PUNCT
ejpam-5258	165	1	then	then	ADV
ejpam-5258	165	2	f	f	PROPN
ejpam-5258	165	3	can	can	AUX
ejpam-5258	165	4	be	be	AUX
ejpam-5258	165	5	written	write	VERB
ejpam-5258	165	6	as	as	ADP
ejpam-5258	165	7	f	f	PROPN
ejpam-5258	165	8	=	=	SYM
ejpam-5258	165	9	c∞	c∞	PROPN
ejpam-5258	165	10	∗	∗	NOUN
ejpam-5258	165	11	c∞	c∞	PROPN
ejpam-5258	165	12	∗	∗	NOUN
ejpam-5258	165	13	.	.	PUNCT
ejpam-5258	165	14	.	.	PUNCT
ejpam-5258	165	15	.	.	PUNCT
ejpam-5258	166	1	∗	∗	NOUN
ejpam-5258	166	2	c∞︸	c∞︸	X
ejpam-5258	166	3	︷︷	︷︷	PROPN
ejpam-5258	166	4	︸	︸	ADP
ejpam-5258	167	1	p−	p−	NOUN
ejpam-5258	167	2	factors	factor	NOUN
ejpam-5258	167	3	∗cα1	∗cα1	NOUN
ejpam-5258	167	4	∗	∗	NOUN
ejpam-5258	167	5	cα2	cα2	NOUN
ejpam-5258	167	6	∗	∗	NOUN
ejpam-5258	167	7	.	.	PUNCT
ejpam-5258	167	8	.	.	PUNCT
ejpam-5258	168	1	.	.	PUNCT
ejpam-5258	169	1	∗	∗	NOUN
ejpam-5258	169	2	cαn︸	cαn︸	PROPN
ejpam-5258	169	3	︷︷	︷︷	PROPN
ejpam-5258	169	4	︸	︸	ADP
ejpam-5258	169	5	q−	q−	PROPN
ejpam-5258	169	6	factors	factor	NOUN
ejpam-5258	169	7	,	,	PUNCT
ejpam-5258	169	8	where	where	SCONJ
ejpam-5258	169	9	c∞	c∞	PROPN
ejpam-5258	169	10	stands	stand	VERB
ejpam-5258	169	11	for	for	ADP
ejpam-5258	169	12	an	an	DET
ejpam-5258	169	13	infinite	infinite	ADJ
ejpam-5258	169	14	cyclic	cyclic	NOUN
ejpam-5258	169	15	group	group	NOUN
ejpam-5258	169	16	and	and	CCONJ
ejpam-5258	169	17	cα1	cα1	NOUN
ejpam-5258	169	18	,	,	PUNCT
ejpam-5258	169	19	cα2	cα2	PROPN
ejpam-5258	169	20	,	,	PUNCT
ejpam-5258	169	21	.	.	PUNCT
ejpam-5258	169	22	.	.	PUNCT
ejpam-5258	169	23	.	.	PUNCT
ejpam-5258	170	1	,	,	PUNCT
ejpam-5258	170	2	cαn	cαn	PROPN
ejpam-5258	170	3	stand	stand	VERB
ejpam-5258	170	4	for	for	ADP
ejpam-5258	170	5	finite	finite	ADJ
ejpam-5258	170	6	cyclic	cyclic	ADJ
ejpam-5258	170	7	groups	group	NOUN
ejpam-5258	170	8	of	of	ADP
ejpam-5258	170	9	orders	order	NOUN
ejpam-5258	170	10	α1	α1	PROPN
ejpam-5258	170	11	,	,	PUNCT
ejpam-5258	170	12	α2	α2	ADJ
ejpam-5258	170	13	,	,	PUNCT
ejpam-5258	170	14	.	.	PUNCT
ejpam-5258	170	15	.	.	PUNCT
ejpam-5258	171	1	.	.	PUNCT
ejpam-5258	172	1	,	,	PUNCT
ejpam-5258	172	2	αn	αn	NOUN
ejpam-5258	172	3	respectively	respectively	ADV
ejpam-5258	172	4	.	.	PUNCT
ejpam-5258	173	1	from	from	ADP
ejpam-5258	173	2	proposition	proposition	NOUN
ejpam-5258	173	3	1	1	NUM
ejpam-5258	173	4	,	,	PUNCT
ejpam-5258	173	5	we	we	PRON
ejpam-5258	173	6	have	have	VERB
ejpam-5258	173	7	lemma	lemma	PROPN
ejpam-5258	173	8	2	2	NUM
ejpam-5258	173	9	,	,	PUNCT
ejpam-5258	173	10	implies	imply	VERB
ejpam-5258	173	11	that	that	SCONJ
ejpam-5258	173	12	h(f	h(f	NOUN
ejpam-5258	173	13	)	)	PUNCT
ejpam-5258	174	1	∼=	∼=	PROPN
ejpam-5258	174	2	(	(	PUNCT
ejpam-5258	174	3	1)×	1)×	NUM
ejpam-5258	174	4	(	(	PUNCT
ejpam-5258	174	5	1)×	1)×	NUM
ejpam-5258	174	6	.	.	PUNCT
ejpam-5258	174	7	.	.	PUNCT
ejpam-5258	175	1	.×	.×	NOUN
ejpam-5258	175	2	(	(	PUNCT
ejpam-5258	175	3	1)︸	1)︸	NUM
ejpam-5258	175	4	︷︷	︷︷	VERB
ejpam-5258	175	5	︸	︸	ADP
ejpam-5258	175	6	p−	p−	NOUN
ejpam-5258	175	7	factors	factor	NOUN
ejpam-5258	175	8	×	×	NOUN
ejpam-5258	175	9	(	(	PUNCT
ejpam-5258	175	10	1)×	1)×	NUM
ejpam-5258	175	11	(	(	PUNCT
ejpam-5258	175	12	1)×	1)×	NUM
ejpam-5258	175	13	.	.	PUNCT
ejpam-5258	175	14	.	.	PUNCT
ejpam-5258	176	1	.×	.×	NOUN
ejpam-5258	176	2	(	(	PUNCT
ejpam-5258	176	3	1)︸	1)︸	NUM
ejpam-5258	176	4	︷︷	︷︷	VERB
ejpam-5258	176	5	︸	︸	PRON
ejpam-5258	176	6	q−	q−	PROPN
ejpam-5258	176	7	factors	factor	VERB
ejpam-5258	176	8	∼=	∼=	ADV
ejpam-5258	176	9	1	1	NUM
ejpam-5258	176	10	.	.	PUNCT
ejpam-5258	177	1	this	this	PRON
ejpam-5258	177	2	completes	complete	VERB
ejpam-5258	177	3	the	the	DET
ejpam-5258	177	4	proof	proof	NOUN
ejpam-5258	177	5	.	.	PUNCT
ejpam-5258	178	1	corollary	corollary	ADJ
ejpam-5258	178	2	2	2	NUM
ejpam-5258	178	3	.	.	PUNCT
ejpam-5258	179	1	let	let	VERB
ejpam-5258	179	2	z	z	NOUN
ejpam-5258	179	3	=	=	PRON
ejpam-5258	179	4	{	{	PUNCT
ejpam-5258	179	5	.	.	PUNCT
ejpam-5258	179	6	.	.	PUNCT
ejpam-5258	179	7	.	.	PUNCT
ejpam-5258	180	1	,	,	PUNCT
ejpam-5258	180	2	−3,−2,−1	−3,−2,−1	PROPN
ejpam-5258	180	3	,	,	PUNCT
ejpam-5258	180	4	0	0	NUM
ejpam-5258	180	5	,	,	PUNCT
ejpam-5258	180	6	1	1	NUM
ejpam-5258	180	7	,	,	PUNCT
ejpam-5258	180	8	2	2	NUM
ejpam-5258	180	9	,	,	PUNCT
ejpam-5258	180	10	3	3	NUM
ejpam-5258	180	11	,	,	PUNCT
ejpam-5258	180	12	.	.	PUNCT
ejpam-5258	180	13	.	.	PUNCT
ejpam-5258	181	1	.	.	PUNCT
ejpam-5258	181	2	}	}	PUNCT
ejpam-5258	181	3	be	be	AUX
ejpam-5258	181	4	the	the	DET
ejpam-5258	181	5	group	group	NOUN
ejpam-5258	181	6	of	of	ADP
ejpam-5258	181	7	integers	integer	NOUN
ejpam-5258	181	8	and	and	CCONJ
ejpam-5258	181	9	zn	zn	NUM
ejpam-5258	181	10	=	=	SYM
ejpam-5258	181	11	{	{	PUNCT
ejpam-5258	181	12	0	0	NUM
ejpam-5258	181	13	,	,	PUNCT
ejpam-5258	181	14	1	1	NUM
ejpam-5258	181	15	,	,	PUNCT
ejpam-5258	181	16	.	.	PUNCT
ejpam-5258	181	17	.	.	PUNCT
ejpam-5258	182	1	.	.	PUNCT
ejpam-5258	183	1	,	,	PUNCT
ejpam-5258	183	2	n−	n−	NOUN
ejpam-5258	183	3	1	1	NUM
ejpam-5258	183	4	}	}	PUNCT
ejpam-5258	183	5	be	be	AUX
ejpam-5258	183	6	the	the	DET
ejpam-5258	183	7	group	group	NOUN
ejpam-5258	183	8	of	of	ADP
ejpam-5258	183	9	integers	integer	NOUN
ejpam-5258	183	10	modulo	modulo	VERB
ejpam-5258	183	11	n.	n.	PROPN
ejpam-5258	183	12	then	then	ADV
ejpam-5258	183	13	h(z	h(z	NOUN
ejpam-5258	183	14	)	)	PUNCT
ejpam-5258	183	15	∼=	∼=	PROPN
ejpam-5258	183	16	{	{	PUNCT
ejpam-5258	183	17	1	1	NUM
ejpam-5258	183	18	}	}	PUNCT
ejpam-5258	183	19	and	and	CCONJ
ejpam-5258	183	20	h	h	PROPN
ejpam-5258	183	21	(	(	PUNCT
ejpam-5258	183	22	zn	zn	X
ejpam-5258	183	23	)	)	PUNCT
ejpam-5258	183	24	∼=	∼=	PROPN
ejpam-5258	183	25	{	{	PUNCT
ejpam-5258	183	26	1	1	NUM
ejpam-5258	183	27	}	}	PUNCT
ejpam-5258	183	28	.	.	PUNCT
ejpam-5258	184	1	corollary	corollary	ADJ
ejpam-5258	184	2	3	3	X
ejpam-5258	184	3	.	.	PUNCT
ejpam-5258	185	1	if	if	SCONJ
ejpam-5258	185	2	k	k	PROPN
ejpam-5258	185	3	is	be	AUX
ejpam-5258	185	4	a	a	DET
ejpam-5258	185	5	free	free	ADJ
ejpam-5258	185	6	group	group	NOUN
ejpam-5258	185	7	and	and	CCONJ
ejpam-5258	185	8	g	g	NOUN
ejpam-5258	185	9	is	be	AUX
ejpam-5258	185	10	any	any	DET
ejpam-5258	185	11	group	group	NOUN
ejpam-5258	185	12	,	,	PUNCT
ejpam-5258	185	13	then	then	ADV
ejpam-5258	185	14	h(k	h(k	PROPN
ejpam-5258	185	15	)	)	PUNCT
ejpam-5258	185	16	∼=	∼=	PROPN
ejpam-5258	185	17	{	{	PUNCT
ejpam-5258	185	18	1	1	NUM
ejpam-5258	185	19	}	}	PUNCT
ejpam-5258	185	20	,	,	PUNCT
ejpam-5258	185	21	h(f	h(f	PROPN
ejpam-5258	185	22	⟨g	⟨g	NOUN
ejpam-5258	185	23	,	,	PUNCT
ejpam-5258	185	24	g⟩	g⟩	NOUN
ejpam-5258	185	25	)	)	PUNCT
ejpam-5258	185	26	∼=	∼=	PROPN
ejpam-5258	185	27	{	{	PUNCT
ejpam-5258	185	28	1	1	NUM
ejpam-5258	185	29	}	}	PUNCT
ejpam-5258	185	30	and	and	CCONJ
ejpam-5258	185	31	h	h	NOUN
ejpam-5258	185	32	(	(	PUNCT
ejpam-5258	185	33	f⟨g	f⟨g	NUM
ejpam-5258	185	34	,	,	PUNCT
ejpam-5258	185	35	g⟩	g⟩	VERB
ejpam-5258	185	36	∗g	∗g	NOUN
ejpam-5258	185	37	)	)	PUNCT
ejpam-5258	185	38	∼=	∼=	VERB
ejpam-5258	185	39	h(g	h(g	NOUN
ejpam-5258	185	40	)	)	PUNCT
ejpam-5258	185	41	.	.	PUNCT
ejpam-5258	186	1	as	as	ADP
ejpam-5258	186	2	an	an	DET
ejpam-5258	186	3	example	example	NOUN
ejpam-5258	186	4	of	of	ADP
ejpam-5258	186	5	a	a	DET
ejpam-5258	186	6	quasi	quasi	ADJ
ejpam-5258	186	7	-	-	ADJ
ejpam-5258	186	8	free	free	ADJ
ejpam-5258	186	9	group	group	NOUN
ejpam-5258	186	10	we	we	PRON
ejpam-5258	186	11	have	have	VERB
ejpam-5258	186	12	the	the	DET
ejpam-5258	186	13	following	following	NOUN
ejpam-5258	186	14	.	.	PUNCT
ejpam-5258	186	15	example	example	NOUN
ejpam-5258	187	1	1	1	NUM
ejpam-5258	187	2	.	.	PUNCT
ejpam-5258	187	3	let	let	VERB
ejpam-5258	187	4	z	z	NOUN
ejpam-5258	187	5	be	be	AUX
ejpam-5258	187	6	the	the	DET
ejpam-5258	187	7	group	group	NOUN
ejpam-5258	187	8	of	of	ADP
ejpam-5258	187	9	integers	integer	NOUN
ejpam-5258	187	10	and	and	CCONJ
ejpam-5258	187	11	g	g	NOUN
ejpam-5258	187	12	=	=	SYM
ejpam-5258	187	13	psl(2	psl(2	NOUN
ejpam-5258	187	14	,	,	PUNCT
ejpam-5258	187	15	z	z	X
ejpam-5258	187	16	)	)	PUNCT
ejpam-5258	187	17	be	be	AUX
ejpam-5258	187	18	the	the	DET
ejpam-5258	187	19	projective	projective	ADJ
ejpam-5258	187	20	special	special	ADJ
ejpam-5258	187	21	linear	linear	PROPN
ejpam-5258	187	22	group	group	NOUN
ejpam-5258	187	23	of	of	ADP
ejpam-5258	187	24	degree	degree	NOUN
ejpam-5258	187	25	2	2	NUM
ejpam-5258	187	26	over	over	ADP
ejpam-5258	187	27	z.	z.	PROPN
ejpam-5258	188	1	it	it	PRON
ejpam-5258	188	2	is	be	AUX
ejpam-5258	188	3	well	well	ADV
ejpam-5258	188	4	known	know	VERB
ejpam-5258	188	5	that[1	that[1	NOUN
ejpam-5258	188	6	]	]	PUNCT
ejpam-5258	188	7	,	,	PUNCT
ejpam-5258	188	8	g	g	PROPN
ejpam-5258	188	9	=	=	PUNCT
ejpam-5258	188	10	a	a	DET
ejpam-5258	188	11	∗	∗	NOUN
ejpam-5258	188	12	b	b	NOUN
ejpam-5258	188	13	,	,	PUNCT
ejpam-5258	188	14	the	the	DET
ejpam-5258	188	15	free	free	ADJ
ejpam-5258	188	16	product	product	NOUN
ejpam-5258	188	17	of	of	ADP
ejpam-5258	188	18	the	the	DET
ejpam-5258	188	19	cyclic	cyclic	ADJ
ejpam-5258	188	20	groups	group	NOUN
ejpam-5258	188	21	a	a	PRON
ejpam-5258	188	22	of	of	ADP
ejpam-5258	188	23	order	order	NOUN
ejpam-5258	188	24	2	2	NUM
ejpam-5258	188	25	,	,	PUNCT
ejpam-5258	188	26	and	and	CCONJ
ejpam-5258	188	27	the	the	DET
ejpam-5258	188	28	cyclic	cyclic	ADJ
ejpam-5258	188	29	group	group	NOUN
ejpam-5258	188	30	b	b	PROPN
ejpam-5258	188	31	of	of	ADP
ejpam-5258	188	32	order	order	NOUN
ejpam-5258	188	33	3	3	NUM
ejpam-5258	188	34	defined	define	VERB
ejpam-5258	188	35	g	g	NOUN
ejpam-5258	188	36	is	be	AUX
ejpam-5258	188	37	a	a	DET
ejpam-5258	188	38	quasi	quasi	ADJ
ejpam-5258	188	39	-	-	ADJ
ejpam-5258	188	40	free	free	ADJ
ejpam-5258	188	41	group	group	NOUN
ejpam-5258	188	42	,	,	PUNCT
ejpam-5258	188	43	and	and	CCONJ
ejpam-5258	188	44	theorem	theorem	VERB
ejpam-5258	188	45	3	3	NUM
ejpam-5258	188	46	,	,	PUNCT
ejpam-5258	188	47	shows	show	VERB
ejpam-5258	188	48	that	that	SCONJ
ejpam-5258	188	49	h(f	h(f	NOUN
ejpam-5258	188	50	∗g	∗g	ADV
ejpam-5258	188	51	)	)	PUNCT
ejpam-5258	188	52	∼=	∼=	PROPN
ejpam-5258	188	53	{	{	PUNCT
ejpam-5258	188	54	1	1	NUM
ejpam-5258	188	55	}	}	PUNCT
ejpam-5258	188	56	.	.	PUNCT
ejpam-5258	189	1	4	4	X
ejpam-5258	189	2	.	.	X
ejpam-5258	189	3	the	the	DET
ejpam-5258	189	4	associated	associated	ADJ
ejpam-5258	189	5	groups	group	NOUN
ejpam-5258	189	6	of	of	ADP
ejpam-5258	189	7	dihedral	dihedral	ADJ
ejpam-5258	189	8	groups	group	NOUN
ejpam-5258	189	9	and	and	CCONJ
ejpam-5258	189	10	quaternion	quaternion	NOUN
ejpam-5258	189	11	groups	group	NOUN
ejpam-5258	189	12	for	for	ADP
ejpam-5258	189	13	the	the	DET
ejpam-5258	189	14	structures	structure	NOUN
ejpam-5258	189	15	of	of	ADP
ejpam-5258	189	16	dihedral	dihedral	ADJ
ejpam-5258	189	17	groups	group	NOUN
ejpam-5258	189	18	and	and	CCONJ
ejpam-5258	189	19	quaternion	quaternion	NOUN
ejpam-5258	189	20	groups	group	NOUN
ejpam-5258	189	21	we	we	PRON
ejpam-5258	189	22	refer	refer	VERB
ejpam-5258	189	23	the	the	DET
ejpam-5258	189	24	readers	reader	NOUN
ejpam-5258	189	25	to	to	ADP
ejpam-5258	189	26	[	[	X
ejpam-5258	189	27	8	8	NUM
ejpam-5258	189	28	]	]	PUNCT
ejpam-5258	189	29	.	.	PUNCT
ejpam-5258	190	1	proposition	proposition	NOUN
ejpam-5258	190	2	4	4	NUM
ejpam-5258	190	3	.	.	PUNCT
ejpam-5258	191	1	let	let	VERB
ejpam-5258	191	2	g	g	PRON
ejpam-5258	191	3	be	be	AUX
ejpam-5258	191	4	a	a	DET
ejpam-5258	191	5	dihedral	dihedral	ADJ
ejpam-5258	191	6	group	group	NOUN
ejpam-5258	191	7	.	.	PUNCT
ejpam-5258	192	1	then	then	ADV
ejpam-5258	192	2	(	(	PUNCT
ejpam-5258	192	3	i	i	NOUN
ejpam-5258	192	4	)	)	PUNCT
ejpam-5258	192	5	if	if	SCONJ
ejpam-5258	192	6	g	g	NOUN
ejpam-5258	192	7	=	=	PUNCT
ejpam-5258	192	8	d∞	d∞	PROPN
ejpam-5258	192	9	is	be	AUX
ejpam-5258	192	10	infinite	infinite	ADJ
ejpam-5258	192	11	,	,	PUNCT
ejpam-5258	192	12	then	then	ADV
ejpam-5258	192	13	h	h	PROPN
ejpam-5258	192	14	(	(	PUNCT
ejpam-5258	192	15	d∞	d∞	NOUN
ejpam-5258	192	16	)	)	PUNCT
ejpam-5258	192	17	∼=	∼=	PROPN
ejpam-5258	192	18	{	{	PUNCT
ejpam-5258	192	19	1	1	NUM
ejpam-5258	192	20	}	}	PUNCT
ejpam-5258	192	21	.	.	PUNCT
ejpam-5258	193	1	(	(	PUNCT
ejpam-5258	193	2	ii	ii	NOUN
ejpam-5258	193	3	)	)	PUNCT
ejpam-5258	193	4	if	if	SCONJ
ejpam-5258	193	5	g	g	PROPN
ejpam-5258	193	6	=	=	VERB
ejpam-5258	193	7	dn	dn	PROPN
ejpam-5258	193	8	is	be	AUX
ejpam-5258	193	9	finite	finite	ADJ
ejpam-5258	193	10	,	,	PUNCT
ejpam-5258	193	11	then	then	ADV
ejpam-5258	193	12	h	h	PROPN
ejpam-5258	193	13	(	(	PUNCT
ejpam-5258	193	14	dn	dn	ADJ
ejpam-5258	193	15	)	)	PUNCT
ejpam-5258	193	16	is	be	AUX
ejpam-5258	193	17	cyclic	cyclic	ADJ
ejpam-5258	193	18	.	.	PUNCT
ejpam-5258	194	1	a.	a.	PROPN
ejpam-5258	194	2	m.	m.	PROPN
ejpam-5258	194	3	alotaibi	alotaibi	PROPN
ejpam-5258	194	4	,	,	PUNCT
ejpam-5258	194	5	k.	k.	PROPN
ejpam-5258	194	6	m.	m.	PROPN
ejpam-5258	194	7	aljamal	aljamal	PROPN
ejpam-5258	194	8	/	/	SYM
ejpam-5258	194	9	eur	eur	PROPN
ejpam-5258	194	10	.	.	PUNCT
ejpam-5258	195	1	j.	j.	PROPN
ejpam-5258	195	2	pure	pure	PROPN
ejpam-5258	195	3	appl	appl	PROPN
ejpam-5258	195	4	.	.	PROPN
ejpam-5258	195	5	math	math	PROPN
ejpam-5258	195	6	,	,	PUNCT
ejpam-5258	195	7	17	17	NUM
ejpam-5258	195	8	(	(	PUNCT
ejpam-5258	195	9	3	3	NUM
ejpam-5258	195	10	)	)	PUNCT
ejpam-5258	195	11	(	(	PUNCT
ejpam-5258	195	12	2024	2024	NUM
ejpam-5258	195	13	)	)	PUNCT
ejpam-5258	195	14	,	,	PUNCT
ejpam-5258	195	15	2329	2329	NUM
ejpam-5258	195	16	-	-	SYM
ejpam-5258	195	17	2335	2335	NUM
ejpam-5258	195	18	2334	2334	NUM
ejpam-5258	195	19	proof	proof	NOUN
ejpam-5258	195	20	.	.	PUNCT
ejpam-5258	196	1	(	(	PUNCT
ejpam-5258	196	2	1	1	X
ejpam-5258	196	3	)	)	PUNCT
ejpam-5258	196	4	g	g	NOUN
ejpam-5258	196	5	=	=	PUNCT
ejpam-5258	196	6	d∞	d∞	NOUN
ejpam-5258	196	7	is	be	AUX
ejpam-5258	196	8	defined	define	VERB
ejpam-5258	196	9	as	as	ADP
ejpam-5258	196	10	the	the	DET
ejpam-5258	196	11	group	group	NOUN
ejpam-5258	196	12	of	of	ADP
ejpam-5258	196	13	two	two	NUM
ejpam-5258	196	14	-	-	PUNCT
ejpam-5258	196	15	by	by	ADP
ejpam-5258	196	16	-	-	PUNCT
ejpam-5258	196	17	two	two	NUM
ejpam-5258	196	18	matrices	matrix	NOUN
ejpam-5258	196	19	with	with	ADP
ejpam-5258	196	20	entries	entry	NOUN
ejpam-5258	196	21	from	from	ADP
ejpam-5258	196	22	the	the	DET
ejpam-5258	196	23	group	group	NOUN
ejpam-5258	196	24	of	of	ADP
ejpam-5258	196	25	integers	integer	NOUN
ejpam-5258	196	26	z	z	PROPN
ejpam-5258	196	27	of	of	ADP
ejpam-5258	196	28	the	the	DET
ejpam-5258	196	29	form	form	NOUN
ejpam-5258	196	30	(	(	PUNCT
ejpam-5258	196	31	ε	ε	PROPN
ejpam-5258	196	32	k	k	PROPN
ejpam-5258	196	33	0	0	PROPN
ejpam-5258	196	34	1	1	NUM
ejpam-5258	196	35	)	)	PUNCT
ejpam-5258	196	36	where	where	SCONJ
ejpam-5258	196	37	e	e	NOUN
ejpam-5258	196	38	is	be	AUX
ejpam-5258	196	39	1	1	NUM
ejpam-5258	196	40	or	or	CCONJ
ejpam-5258	196	41	-1	-1	NOUN
ejpam-5258	196	42	,	,	PUNCT
ejpam-5258	196	43	and	and	CCONJ
ejpam-5258	196	44	k	k	PROPN
ejpam-5258	196	45	is	be	AUX
ejpam-5258	196	46	any	any	DET
ejpam-5258	196	47	integer	integer	NOUN
ejpam-5258	196	48	.	.	PUNCT
ejpam-5258	197	1	d∞	d∞	PROPN
ejpam-5258	197	2	=	=	PUNCT
ejpam-5258	197	3	a	a	DET
ejpam-5258	197	4	∗b	∗b	NOUN
ejpam-5258	197	5	,	,	PUNCT
ejpam-5258	197	6	the	the	DET
ejpam-5258	197	7	free	free	ADJ
ejpam-5258	197	8	product	product	NOUN
ejpam-5258	197	9	of	of	ADP
ejpam-5258	197	10	the	the	DET
ejpam-5258	197	11	groups	group	NOUN
ejpam-5258	197	12	a	a	PRON
ejpam-5258	197	13	=	=	X
ejpam-5258	197	14	{	{	PUNCT
ejpam-5258	197	15	(	(	PUNCT
ejpam-5258	197	16	1	1	NUM
ejpam-5258	197	17	0	0	NUM
ejpam-5258	197	18	0	0	NUM
ejpam-5258	197	19	1	1	NUM
ejpam-5258	197	20	)	)	PUNCT
ejpam-5258	197	21	,	,	PUNCT
ejpam-5258	197	22	(	(	PUNCT
ejpam-5258	197	23	1	1	NUM
ejpam-5258	197	24	1	1	NUM
ejpam-5258	197	25	0	0	NUM
ejpam-5258	197	26	1	1	NUM
ejpam-5258	197	27	)	)	PUNCT
ejpam-5258	197	28	}	}	PUNCT
ejpam-5258	197	29	,	,	PUNCT
ejpam-5258	197	30	b	b	X
ejpam-5258	197	31	=	=	PRON
ejpam-5258	197	32	{	{	PUNCT
ejpam-5258	197	33	(	(	PUNCT
ejpam-5258	197	34	1	1	NUM
ejpam-5258	197	35	0	0	NUM
ejpam-5258	197	36	0	0	NUM
ejpam-5258	197	37	1	1	NUM
ejpam-5258	197	38	)	)	PUNCT
ejpam-5258	197	39	,	,	PUNCT
ejpam-5258	197	40	(	(	PUNCT
ejpam-5258	197	41	−1	−1	NOUN
ejpam-5258	197	42	0	0	SYM
ejpam-5258	197	43	0	0	NUM
ejpam-5258	197	44	1	1	NUM
ejpam-5258	197	45	)	)	PUNCT
ejpam-5258	197	46	}	}	PUNCT
ejpam-5258	197	47	.	.	PUNCT
ejpam-5258	198	1	aand	aand	PROPN
ejpam-5258	198	2	b	b	PROPN
ejpam-5258	198	3	are	be	AUX
ejpam-5258	198	4	of	of	ADP
ejpam-5258	198	5	order	order	NOUN
ejpam-5258	198	6	2	2	NUM
ejpam-5258	198	7	which	which	PRON
ejpam-5258	198	8	implies	imply	VERB
ejpam-5258	198	9	a	a	PRON
ejpam-5258	198	10	and	and	CCONJ
ejpam-5258	198	11	b	b	NOUN
ejpam-5258	198	12	are	be	AUX
ejpam-5258	198	13	cyclic	cyclic	ADJ
ejpam-5258	198	14	groups	group	NOUN
ejpam-5258	198	15	,	,	PUNCT
ejpam-5258	198	16	then	then	ADV
ejpam-5258	198	17	d∞	d∞	NOUN
ejpam-5258	198	18	is	be	AUX
ejpam-5258	198	19	a	a	DET
ejpam-5258	198	20	quasi	quasi	ADJ
ejpam-5258	198	21	-	-	ADJ
ejpam-5258	198	22	free	free	ADJ
ejpam-5258	198	23	group	group	NOUN
ejpam-5258	198	24	and	and	CCONJ
ejpam-5258	198	25	by	by	ADP
ejpam-5258	198	26	theorem	theorem	ADJ
ejpam-5258	198	27	3.1	3.1	NUM
ejpam-5258	198	28	,	,	PUNCT
ejpam-5258	198	29	h	h	NOUN
ejpam-5258	198	30	(	(	PUNCT
ejpam-5258	198	31	d∞	d∞	NOUN
ejpam-5258	198	32	)	)	PUNCT
ejpam-5258	198	33	∼=	∼=	PROPN
ejpam-5258	198	34	{	{	PUNCT
ejpam-5258	198	35	1	1	NUM
ejpam-5258	198	36	}	}	PUNCT
ejpam-5258	198	37	.	.	PUNCT
ejpam-5258	199	1	(	(	PUNCT
ejpam-5258	199	2	2	2	X
ejpam-5258	199	3	)	)	PUNCT
ejpam-5258	199	4	if	if	SCONJ
ejpam-5258	199	5	g	g	PROPN
ejpam-5258	199	6	=	=	VERB
ejpam-5258	199	7	dn	dn	PROPN
ejpam-5258	199	8	is	be	AUX
ejpam-5258	199	9	a	a	DET
ejpam-5258	199	10	finite	finite	ADJ
ejpam-5258	199	11	dihedral	dihedral	ADJ
ejpam-5258	199	12	group	group	NOUN
ejpam-5258	199	13	,	,	PUNCT
ejpam-5258	199	14	then	then	ADV
ejpam-5258	199	15	g	g	PROPN
ejpam-5258	199	16	is	be	AUX
ejpam-5258	199	17	of	of	ADP
ejpam-5258	199	18	order	order	NOUN
ejpam-5258	199	19	2n	2n	NUM
ejpam-5258	199	20	and	and	CCONJ
ejpam-5258	199	21	is	be	AUX
ejpam-5258	199	22	defined	define	VERB
ejpam-5258	199	23	as	as	ADP
ejpam-5258	199	24	the	the	DET
ejpam-5258	199	25	group	group	NOUN
ejpam-5258	199	26	of	of	ADP
ejpam-5258	199	27	two	two	NUM
ejpam-5258	199	28	-	-	PUNCT
ejpam-5258	199	29	by	by	ADP
ejpam-5258	199	30	-	-	PUNCT
ejpam-5258	199	31	two	two	NUM
ejpam-5258	199	32	matrices	matrix	NOUN
ejpam-5258	199	33	,	,	PUNCT
ejpam-5258	199	34	with	with	ADP
ejpam-5258	199	35	entries	entry	NOUN
ejpam-5258	199	36	from	from	ADP
ejpam-5258	199	37	the	the	DET
ejpam-5258	199	38	ring	ring	NOUN
ejpam-5258	199	39	of	of	ADP
ejpam-5258	199	40	integers	integer	NOUN
ejpam-5258	199	41	zn	zn	PROPN
ejpam-5258	199	42	mod	mod	PROPN
ejpam-5258	199	43	n	n	PROPN
ejpam-5258	199	44	of	of	ADP
ejpam-5258	199	45	the	the	DET
ejpam-5258	199	46	form	form	NOUN
ejpam-5258	199	47	(	(	PUNCT
ejpam-5258	199	48	ε	ε	PROPN
ejpam-5258	199	49	k	k	PROPN
ejpam-5258	199	50	0	0	PROPN
ejpam-5258	199	51	1	1	NUM
ejpam-5258	199	52	)	)	PUNCT
ejpam-5258	199	53	,	,	PUNCT
ejpam-5258	199	54	where	where	SCONJ
ejpam-5258	199	55	ε	ε	PROPN
ejpam-5258	199	56	is	be	AUX
ejpam-5258	199	57	1	1	NUM
ejpam-5258	199	58	or	or	CCONJ
ejpam-5258	199	59	-1	-1	NOUN
ejpam-5258	199	60	,	,	PUNCT
ejpam-5258	199	61	and	and	CCONJ
ejpam-5258	199	62	k	k	PROPN
ejpam-5258	199	63	is	be	AUX
ejpam-5258	199	64	any	any	DET
ejpam-5258	199	65	integer	integer	NOUN
ejpam-5258	199	66	mod	mod	PROPN
ejpam-5258	199	67	n.	n.	PROPN
ejpam-5258	199	68	then	then	ADV
ejpam-5258	199	69	by	by	ADP
ejpam-5258	199	70	[	[	X
ejpam-5258	199	71	8	8	NUM
ejpam-5258	199	72	]	]	PUNCT
ejpam-5258	199	73	,	,	PUNCT
ejpam-5258	199	74	dn	dn	PROPN
ejpam-5258	199	75	has	have	VERB
ejpam-5258	199	76	the	the	DET
ejpam-5258	199	77	presentation	presentation	NOUN
ejpam-5258	199	78	dn	dn	NOUN
ejpam-5258	199	79	=	=	PUNCT
ejpam-5258	199	80	〈	〈	PROPN
ejpam-5258	199	81	x	x	NOUN
ejpam-5258	199	82	,	,	PUNCT
ejpam-5258	199	83	y	y	PROPN
ejpam-5258	199	84	|	|	ADV
ejpam-5258	199	85	xn	xn	PROPN
ejpam-5258	199	86	,	,	PUNCT
ejpam-5258	199	87	y2	y2	INTJ
ejpam-5258	199	88	,	,	PUNCT
ejpam-5258	199	89	(	(	PUNCT
ejpam-5258	199	90	xy)2	xy)2	X
ejpam-5258	199	91	〉	〉	PROPN
ejpam-5258	199	92	of	of	ADP
ejpam-5258	199	93	2	2	NUM
ejpam-5258	199	94	generators	generator	NOUN
ejpam-5258	199	95	and	and	CCONJ
ejpam-5258	199	96	3	3	NUM
ejpam-5258	199	97	relations	relation	NOUN
ejpam-5258	199	98	.	.	PUNCT
ejpam-5258	200	1	since	since	SCONJ
ejpam-5258	200	2	dn	dn	PROPN
ejpam-5258	200	3	is	be	AUX
ejpam-5258	200	4	finite	finite	ADJ
ejpam-5258	200	5	and	and	CCONJ
ejpam-5258	200	6	3	3	NUM
ejpam-5258	200	7	=	=	SYM
ejpam-5258	200	8	2	2	NUM
ejpam-5258	200	9	+	+	NOUN
ejpam-5258	200	10	1	1	NUM
ejpam-5258	200	11	,	,	PUNCT
ejpam-5258	200	12	proposition	proposition	NOUN
ejpam-5258	200	13	3	3	NUM
ejpam-5258	200	14	shows	show	VERB
ejpam-5258	200	15	that	that	SCONJ
ejpam-5258	200	16	h	h	NOUN
ejpam-5258	200	17	(	(	PUNCT
ejpam-5258	200	18	dn	dn	NOUN
ejpam-5258	200	19	)	)	PUNCT
ejpam-5258	200	20	is	be	AUX
ejpam-5258	200	21	cyclic	cyclic	ADJ
ejpam-5258	200	22	.	.	PUNCT
ejpam-5258	201	1	this	this	PRON
ejpam-5258	201	2	complete	complete	ADJ
ejpam-5258	201	3	the	the	DET
ejpam-5258	201	4	proof	proof	NOUN
ejpam-5258	201	5	.	.	PUNCT
ejpam-5258	202	1	example	example	NOUN
ejpam-5258	203	1	2	2	NUM
ejpam-5258	203	2	.	.	PUNCT
ejpam-5258	204	1	let	let	VERB
ejpam-5258	204	2	g	g	NOUN
ejpam-5258	204	3	=	=	NOUN
ejpam-5258	204	4	psl(2	psl(2	NOUN
ejpam-5258	204	5	,	,	PUNCT
ejpam-5258	204	6	f	f	PROPN
ejpam-5258	204	7	)	)	PUNCT
ejpam-5258	204	8	be	be	AUX
ejpam-5258	204	9	the	the	DET
ejpam-5258	204	10	projective	projective	ADJ
ejpam-5258	204	11	special	special	ADJ
ejpam-5258	204	12	linear	linear	PROPN
ejpam-5258	204	13	group	group	NOUN
ejpam-5258	204	14	of	of	ADP
ejpam-5258	204	15	degree	degree	NOUN
ejpam-5258	204	16	2	2	NUM
ejpam-5258	204	17	over	over	ADP
ejpam-5258	204	18	the	the	DET
ejpam-5258	204	19	galois	galois	PROPN
ejpam-5258	204	20	field	field	NOUN
ejpam-5258	204	21	f	f	PROPN
ejpam-5258	204	22	consisting	consist	VERB
ejpam-5258	204	23	of	of	ADP
ejpam-5258	204	24	5	5	NUM
ejpam-5258	204	25	elements	element	NOUN
ejpam-5258	204	26	.	.	PUNCT
ejpam-5258	205	1	then	then	ADV
ejpam-5258	205	2	h(g	h(g	AUX
ejpam-5258	205	3	)	)	PUNCT
ejpam-5258	205	4	∼=	∼=	PROPN
ejpam-5258	205	5	c2	c2	PROPN
ejpam-5258	205	6	and	and	CCONJ
ejpam-5258	205	7	for	for	ADP
ejpam-5258	205	8	every	every	DET
ejpam-5258	205	9	free	free	ADJ
ejpam-5258	205	10	group	group	NOUN
ejpam-5258	205	11	k	k	PROPN
ejpam-5258	205	12	have	have	VERB
ejpam-5258	205	13	h(k	h(k	PROPN
ejpam-5258	205	14	∗g	∗g	NOUN
ejpam-5258	205	15	)	)	PUNCT
ejpam-5258	205	16	∼=	∼=	PROPN
ejpam-5258	205	17	c2	c2	PROPN
ejpam-5258	205	18	,	,	PUNCT
ejpam-5258	205	19	where	where	SCONJ
ejpam-5258	205	20	c2	c2	PROPN
ejpam-5258	205	21	is	be	AUX
ejpam-5258	205	22	a	a	DET
ejpam-5258	205	23	cyclic	cyclic	ADJ
ejpam-5258	205	24	group	group	NOUN
ejpam-5258	205	25	of	of	ADP
ejpam-5258	205	26	order	order	NOUN
ejpam-5258	205	27	2	2	NUM
ejpam-5258	205	28	,	,	PUNCT
ejpam-5258	205	29	because	because	SCONJ
ejpam-5258	205	30	it	it	PRON
ejpam-5258	205	31	is	be	AUX
ejpam-5258	205	32	well	well	ADV
ejpam-5258	205	33	known	known	ADJ
ejpam-5258	205	34	that	that	SCONJ
ejpam-5258	205	35	[	[	X
ejpam-5258	205	36	3	3	NUM
ejpam-5258	205	37	]	]	PUNCT
ejpam-5258	205	38	.	.	PUNCT
ejpam-5258	206	1	now	now	ADV
ejpam-5258	206	2	by	by	ADP
ejpam-5258	206	3	[	[	X
ejpam-5258	206	4	2	2	NUM
ejpam-5258	206	5	]	]	PUNCT
ejpam-5258	206	6	,	,	PUNCT
ejpam-5258	206	7	g	g	PROPN
ejpam-5258	206	8	has	have	VERB
ejpam-5258	206	9	the	the	DET
ejpam-5258	206	10	presentation	presentation	NOUN
ejpam-5258	206	11	g	g	PROPN
ejpam-5258	206	12	=	=	PUNCT
ejpam-5258	206	13	〈	〈	PROPN
ejpam-5258	206	14	x	x	NOUN
ejpam-5258	206	15	,	,	PUNCT
ejpam-5258	206	16	y	y	PROPN
ejpam-5258	206	17	|	|	PROPN
ejpam-5258	206	18	x5	x5	PROPN
ejpam-5258	206	19	,	,	PUNCT
ejpam-5258	206	20	y3	y3	NOUN
ejpam-5258	206	21	,	,	PUNCT
ejpam-5258	206	22	(	(	PUNCT
ejpam-5258	206	23	xy)2	xy)2	X
ejpam-5258	206	24	〉	〉	PROPN
ejpam-5258	206	25	of	of	ADP
ejpam-5258	206	26	two	two	NUM
ejpam-5258	206	27	generators	generator	NOUN
ejpam-5258	206	28	and	and	CCONJ
ejpam-5258	206	29	three	three	NUM
ejpam-5258	206	30	relaters	relater	NOUN
ejpam-5258	206	31	.	.	PUNCT
ejpam-5258	207	1	by	by	ADP
ejpam-5258	207	2	proposition	proposition	NOUN
ejpam-5258	207	3	3	3	NUM
ejpam-5258	207	4	,	,	PUNCT
ejpam-5258	207	5	h(g	h(g	NOUN
ejpam-5258	207	6	)	)	PUNCT
ejpam-5258	207	7	is	be	AUX
ejpam-5258	207	8	cyclic	cyclic	ADJ
ejpam-5258	207	9	.	.	PUNCT
ejpam-5258	208	1	proposition	proposition	NOUN
ejpam-5258	208	2	5	5	NUM
ejpam-5258	208	3	.	.	PUNCT
ejpam-5258	209	1	let	let	VERB
ejpam-5258	209	2	qn	qn	NOUN
ejpam-5258	209	3	be	be	AUX
ejpam-5258	209	4	the	the	DET
ejpam-5258	209	5	quaternion	quaternion	ADJ
ejpam-5258	209	6	group	group	NOUN
ejpam-5258	209	7	of	of	ADP
ejpam-5258	209	8	order	order	NOUN
ejpam-5258	209	9	4n	4n	NOUN
ejpam-5258	209	10	.	.	PUNCT
ejpam-5258	210	1	then	then	ADV
ejpam-5258	210	2	h	h	PROPN
ejpam-5258	210	3	(	(	PUNCT
ejpam-5258	210	4	qn	qn	INTJ
ejpam-5258	210	5	)	)	PUNCT
ejpam-5258	210	6	is	be	AUX
ejpam-5258	210	7	cyclic	cyclic	ADJ
ejpam-5258	210	8	.	.	PUNCT
ejpam-5258	211	1	proof	proof	NOUN
ejpam-5258	211	2	.	.	PUNCT
ejpam-5258	212	1	it	it	PRON
ejpam-5258	212	2	is	be	AUX
ejpam-5258	212	3	well	well	ADV
ejpam-5258	212	4	known	know	VERB
ejpam-5258	212	5	in	in	ADP
ejpam-5258	212	6	[	[	X
ejpam-5258	212	7	4	4	X
ejpam-5258	212	8	]	]	PUNCT
ejpam-5258	212	9	that	that	SCONJ
ejpam-5258	212	10	qn	qn	PROPN
ejpam-5258	212	11	has	have	VERB
ejpam-5258	212	12	the	the	DET
ejpam-5258	212	13	presentation	presentation	NOUN
ejpam-5258	212	14	qn	qn	NOUN
ejpam-5258	212	15	=	=	X
ejpam-5258	212	16	〈	〈	PROPN
ejpam-5258	212	17	a	a	NOUN
ejpam-5258	212	18	,	,	PUNCT
ejpam-5258	212	19	b	b	PROPN
ejpam-5258	212	20	|	|	ADV
ejpam-5258	212	21	a2n	a2n	ADJ
ejpam-5258	212	22	=	=	SYM
ejpam-5258	212	23	1	1	NUM
ejpam-5258	212	24	,	,	PUNCT
ejpam-5258	212	25	b2	b2	NOUN
ejpam-5258	212	26	=	=	SYM
ejpam-5258	212	27	an	an	PROPN
ejpam-5258	212	28	,	,	PUNCT
ejpam-5258	212	29	b−1ab	b−1ab	NOUN
ejpam-5258	212	30	=	=	SYM
ejpam-5258	212	31	a−1	a−1	PROPN
ejpam-5258	212	32	〉	〉	NOUN
ejpam-5258	212	33	.	.	PUNCT
ejpam-5258	213	1	so	so	ADV
ejpam-5258	213	2	the	the	DET
ejpam-5258	213	3	presentation	presentation	NOUN
ejpam-5258	213	4	of	of	ADP
ejpam-5258	213	5	qn	qn	NOUN
ejpam-5258	213	6	is	be	AUX
ejpam-5258	213	7	of	of	ADP
ejpam-5258	213	8	2	2	NUM
ejpam-5258	213	9	generators	generator	NOUN
ejpam-5258	213	10	3	3	NUM
ejpam-5258	213	11	relations	relation	NOUN
ejpam-5258	213	12	so	so	ADV
ejpam-5258	213	13	,	,	PUNCT
ejpam-5258	213	14	by	by	ADP
ejpam-5258	213	15	proposition	proposition	NOUN
ejpam-5258	213	16	3	3	NUM
ejpam-5258	213	17	,	,	PUNCT
ejpam-5258	213	18	h	h	NOUN
ejpam-5258	213	19	(	(	PUNCT
ejpam-5258	213	20	qn	qn	NOUN
ejpam-5258	213	21	)	)	PUNCT
ejpam-5258	213	22	is	be	AUX
ejpam-5258	213	23	cyclic	cyclic	ADJ
ejpam-5258	213	24	.	.	PUNCT
ejpam-5258	214	1	this	this	PRON
ejpam-5258	214	2	complete	complete	ADJ
ejpam-5258	214	3	the	the	DET
ejpam-5258	214	4	proof	proof	NOUN
ejpam-5258	214	5	.	.	PUNCT
ejpam-5258	215	1	5	5	X
ejpam-5258	215	2	.	.	X
ejpam-5258	215	3	conclusion	conclusion	NOUN
ejpam-5258	215	4	it	it	PRON
ejpam-5258	215	5	is	be	AUX
ejpam-5258	215	6	stated	state	VERB
ejpam-5258	215	7	and	and	CCONJ
ejpam-5258	215	8	proven	prove	VERB
ejpam-5258	215	9	associated	associated	ADJ
ejpam-5258	215	10	group	group	NOUN
ejpam-5258	215	11	of	of	ADP
ejpam-5258	215	12	any	any	DET
ejpam-5258	215	13	cyclic	cyclic	ADJ
ejpam-5258	215	14	group	group	NOUN
ejpam-5258	215	15	is	be	AUX
ejpam-5258	215	16	trivial	trivial	ADJ
ejpam-5258	215	17	.	.	PUNCT
ejpam-5258	216	1	and	and	CCONJ
ejpam-5258	216	2	associated	associated	ADJ
ejpam-5258	216	3	group	group	NOUN
ejpam-5258	216	4	of	of	ADP
ejpam-5258	216	5	a	a	DET
ejpam-5258	216	6	quasi	quasi	ADJ
ejpam-5258	216	7	-	-	ADJ
ejpam-5258	216	8	free	free	ADJ
ejpam-5258	216	9	group	group	NOUN
ejpam-5258	216	10	is	be	AUX
ejpam-5258	216	11	trivial	trivial	ADJ
ejpam-5258	216	12	.	.	PUNCT
ejpam-5258	217	1	in	in	ADP
ejpam-5258	217	2	future	future	ADJ
ejpam-5258	217	3	work	work	NOUN
ejpam-5258	217	4	,	,	PUNCT
ejpam-5258	217	5	we	we	PRON
ejpam-5258	217	6	must	must	AUX
ejpam-5258	217	7	reach	reach	VERB
ejpam-5258	217	8	facts	fact	NOUN
ejpam-5258	217	9	related	relate	VERB
ejpam-5258	217	10	to	to	ADP
ejpam-5258	217	11	the	the	DET
ejpam-5258	217	12	following	follow	VERB
ejpam-5258	217	13	(	(	PUNCT
ejpam-5258	217	14	i	i	NOUN
ejpam-5258	217	15	)	)	PUNCT
ejpam-5258	217	16	let	let	VERB
ejpam-5258	217	17	g	g	NOUN
ejpam-5258	217	18	=	=	VERB
ejpam-5258	217	19	g1∗ag2	g1∗ag2	PROPN
ejpam-5258	217	20	be	be	AUX
ejpam-5258	217	21	the	the	DET
ejpam-5258	217	22	free	free	ADJ
ejpam-5258	217	23	product	product	NOUN
ejpam-5258	217	24	of	of	ADP
ejpam-5258	217	25	the	the	DET
ejpam-5258	217	26	groups	group	NOUN
ejpam-5258	217	27	g1	g1	VERB
ejpam-5258	217	28	and	and	CCONJ
ejpam-5258	217	29	g2	g2	PROPN
ejpam-5258	217	30	with	with	ADP
ejpam-5258	217	31	an	an	DET
ejpam-5258	217	32	amalgamation	amalgamation	NOUN
ejpam-5258	217	33	subgroup	subgroup	NOUN
ejpam-5258	217	34	a	a	DET
ejpam-5258	217	35	introduced	introduce	VERB
ejpam-5258	217	36	in	in	ADP
ejpam-5258	217	37	[	[	X
ejpam-5258	217	38	5	5	NUM
ejpam-5258	217	39	]	]	PUNCT
ejpam-5258	217	40	.	.	PUNCT
ejpam-5258	218	1	find	find	VERB
ejpam-5258	218	2	h(g	h(g	NOUN
ejpam-5258	218	3	)	)	PUNCT
ejpam-5258	218	4	in	in	ADP
ejpam-5258	218	5	terms	term	NOUN
ejpam-5258	218	6	of	of	ADP
ejpam-5258	218	7	h	h	PROPN
ejpam-5258	218	8	(	(	PUNCT
ejpam-5258	218	9	g1	g1	PROPN
ejpam-5258	218	10	)	)	PUNCT
ejpam-5258	218	11	,	,	PUNCT
ejpam-5258	218	12	h	h	PROPN
ejpam-5258	218	13	(	(	PUNCT
ejpam-5258	218	14	g2	g2	PROPN
ejpam-5258	218	15	)	)	PUNCT
ejpam-5258	218	16	and	and	CCONJ
ejpam-5258	218	17	h(a	h(a	PROPN
ejpam-5258	218	18	)	)	PUNCT
ejpam-5258	218	19	.	.	PUNCT
ejpam-5258	219	1	(	(	PUNCT
ejpam-5258	219	2	ii	ii	NOUN
ejpam-5258	219	3	)	)	PUNCT
ejpam-5258	219	4	let	let	VERB
ejpam-5258	219	5	g	g	PROPN
ejpam-5258	219	6	be	be	AUX
ejpam-5258	219	7	the	the	DET
ejpam-5258	219	8	hnn	hnn	PROPN
ejpam-5258	219	9	-	-	PUNCT
ejpam-5258	219	10	group	group	NOUN
ejpam-5258	219	11	g	g	NOUN
ejpam-5258	219	12	=	=	SYM
ejpam-5258	219	13	⟨h	⟨h	PROPN
ejpam-5258	219	14	,	,	PUNCT
ejpam-5258	219	15	ti	ti	NOUN
ejpam-5258	219	16	|	|	ADV
ejpam-5258	219	17	rel(h	rel(h	PROPN
ejpam-5258	219	18	)	)	PUNCT
ejpam-5258	219	19	,	,	PUNCT
ejpam-5258	219	20	tiaiti−1	tiaiti−1	PROPN
ejpam-5258	219	21	=	=	SYM
ejpam-5258	219	22	bi	bi	PROPN
ejpam-5258	219	23	,	,	PUNCT
ejpam-5258	219	24	i	i	PRON
ejpam-5258	219	25	∈	∈	PROPN
ejpam-5258	219	26	i⟩	i⟩	NOUN
ejpam-5258	219	27	of	of	ADP
ejpam-5258	219	28	base	base	ADJ
ejpam-5258	219	29	h	h	NOUN
ejpam-5258	219	30	and	and	CCONJ
ejpam-5258	219	31	associated	associated	ADJ
ejpam-5258	219	32	pairs	pair	NOUN
ejpam-5258	219	33	(	(	PUNCT
ejpam-5258	219	34	ai	ai	NOUN
ejpam-5258	219	35	,	,	PUNCT
ejpam-5258	219	36	bi	bi	NOUN
ejpam-5258	219	37	)	)	PUNCT
ejpam-5258	219	38	,	,	PUNCT
ejpam-5258	219	39	i	i	PRON
ejpam-5258	219	40	∈	∈	VERB
ejpam-5258	219	41	i	i	PRON
ejpam-5258	219	42	of	of	ADP
ejpam-5258	219	43	subgroups	subgroup	NOUN
ejpam-5258	219	44	of	of	ADP
ejpam-5258	219	45	h	h	NOUN
ejpam-5258	219	46	introduced	introduce	VERB
ejpam-5258	219	47	in	in	ADP
ejpam-5258	219	48	[	[	X
ejpam-5258	219	49	1	1	NUM
ejpam-5258	219	50	]	]	PUNCT
ejpam-5258	219	51	.	.	PUNCT
ejpam-5258	220	1	find	find	VERB
ejpam-5258	220	2	h(g	h(g	NOUN
ejpam-5258	220	3	)	)	PUNCT
ejpam-5258	220	4	in	in	ADP
ejpam-5258	220	5	terms	term	NOUN
ejpam-5258	220	6	of	of	ADP
ejpam-5258	220	7	h(h	h(h	NOUN
ejpam-5258	220	8	)	)	PUNCT
ejpam-5258	220	9	,	,	PUNCT
ejpam-5258	220	10	h(ai	h(ai	PROPN
ejpam-5258	220	11	)	)	PUNCT
ejpam-5258	220	12	and	and	CCONJ
ejpam-5258	220	13	h(bi	h(bi	PROPN
ejpam-5258	220	14	)	)	PUNCT
ejpam-5258	220	15	,	,	PUNCT
ejpam-5258	220	16	i	i	PRON
ejpam-5258	220	17	∈	∈	PROPN
ejpam-5258	220	18	i.	i.	NOUN
ejpam-5258	220	19	references	reference	VERB
ejpam-5258	220	20	2335	2335	NUM
ejpam-5258	220	21	acknowledgements	acknowledgement	NOUN
ejpam-5258	220	22	this	this	DET
ejpam-5258	220	23	study	study	NOUN
ejpam-5258	220	24	is	be	AUX
ejpam-5258	220	25	supported	support	VERB
ejpam-5258	220	26	via	via	ADP
ejpam-5258	220	27	funding	funding	NOUN
ejpam-5258	220	28	from	from	ADP
ejpam-5258	220	29	prince	prince	PROPN
ejpam-5258	220	30	sattam	sattam	PROPN
ejpam-5258	220	31	bin	bin	PROPN
ejpam-5258	220	32	abdulaziz	abdulaziz	PROPN
ejpam-5258	220	33	university	university	PROPN
ejpam-5258	220	34	project	project	NOUN
ejpam-5258	220	35	number	number	NOUN
ejpam-5258	220	36	(	(	PUNCT
ejpam-5258	220	37	psau/2024	psau/2024	NOUN
ejpam-5258	220	38	/	/	SYM
ejpam-5258	220	39	r/1446	r/1446	PROPN
ejpam-5258	220	40	)	)	PUNCT
ejpam-5258	220	41	.	.	PUNCT
ejpam-5258	221	1	references	reference	NOUN
ejpam-5258	221	2	[	[	X
ejpam-5258	221	3	1	1	NUM
ejpam-5258	221	4	]	]	PUNCT
ejpam-5258	221	5	khaled	khaled	PROPN
ejpam-5258	221	6	mustafa	mustafa	PROPN
ejpam-5258	221	7	aljamal	aljamal	PROPN
ejpam-5258	221	8	,	,	PUNCT
ejpam-5258	221	9	ahmad	ahmad	PROPN
ejpam-5258	221	10	termimi	termimi	PROPN
ejpam-5258	221	11	ab	ab	PROPN
ejpam-5258	221	12	ghani	ghani	PROPN
ejpam-5258	221	13	,	,	PUNCT
ejpam-5258	221	14	and	and	CCONJ
ejpam-5258	221	15	rasheed	rasheed	VERB
ejpam-5258	221	16	mahmood	mahmood	PROPN
ejpam-5258	221	17	saleh	saleh	PROPN
ejpam-5258	221	18	.	.	PUNCT
ejpam-5258	222	1	on	on	ADP
ejpam-5258	222	2	preimages	preimage	NOUN
ejpam-5258	222	3	of	of	ADP
ejpam-5258	222	4	the	the	DET
ejpam-5258	222	5	quasi	quasi	NOUN
ejpam-5258	222	6	-	-	ADJ
ejpam-5258	222	7	treed	treed	ADJ
ejpam-5258	222	8	hnn	hnn	PROPN
ejpam-5258	222	9	groups	group	NOUN
ejpam-5258	222	10	.	.	PUNCT
ejpam-5258	223	1	in	in	ADP
ejpam-5258	223	2	2021	2021	NUM
ejpam-5258	223	3	international	international	ADJ
ejpam-5258	223	4	conference	conference	NOUN
ejpam-5258	223	5	on	on	ADP
ejpam-5258	223	6	information	information	NOUN
ejpam-5258	223	7	technology	technology	NOUN
ejpam-5258	223	8	(	(	PUNCT
ejpam-5258	223	9	icit	icit	PROPN
ejpam-5258	223	10	)	)	PUNCT
ejpam-5258	223	11	,	,	PUNCT
ejpam-5258	223	12	2021	2021	NUM
ejpam-5258	223	13	.	.	PUNCT
ejpam-5258	224	1	[	[	X
ejpam-5258	224	2	2	2	NUM
ejpam-5258	224	3	]	]	PUNCT
ejpam-5258	224	4	warren	warren	PROPN
ejpam-5258	224	5	dicks	dick	NOUN
ejpam-5258	224	6	and	and	CCONJ
ejpam-5258	224	7	martin	martin	PROPN
ejpam-5258	224	8	john	john	PROPN
ejpam-5258	224	9	dunwoody	dunwoody	PROPN
ejpam-5258	224	10	.	.	PUNCT
ejpam-5258	225	1	groups	group	NOUN
ejpam-5258	225	2	acting	act	VERB
ejpam-5258	225	3	on	on	ADP
ejpam-5258	225	4	graphs	graph	NOUN
ejpam-5258	225	5	.	.	PUNCT
ejpam-5258	226	1	cambridge	cambridge	PROPN
ejpam-5258	226	2	university	university	PROPN
ejpam-5258	226	3	press	press	NOUN
ejpam-5258	226	4	,	,	PUNCT
ejpam-5258	226	5	1989	1989	NUM
ejpam-5258	226	6	.	.	PUNCT
ejpam-5258	227	1	[	[	X
ejpam-5258	227	2	3	3	X
ejpam-5258	227	3	]	]	X
ejpam-5258	227	4	gregory	gregory	PROPN
ejpam-5258	227	5	karpilovsky	karpilovsky	PROPN
ejpam-5258	227	6	.	.	PUNCT
ejpam-5258	228	1	the	the	DET
ejpam-5258	228	2	schur	schur	PROPN
ejpam-5258	228	3	multiplier	multiplier	X
ejpam-5258	228	4	.	.	PUNCT
ejpam-5258	229	1	oxford	oxford	PROPN
ejpam-5258	229	2	university	university	PROPN
ejpam-5258	229	3	press	press	PROPN
ejpam-5258	229	4	,	,	PUNCT
ejpam-5258	229	5	inc	inc	PROPN
ejpam-5258	229	6	.	.	PROPN
ejpam-5258	229	7	,	,	PUNCT
ejpam-5258	229	8	1987	1987	NUM
ejpam-5258	229	9	.	.	PUNCT
ejpam-5258	230	1	[	[	X
ejpam-5258	230	2	4	4	X
ejpam-5258	230	3	]	]	X
ejpam-5258	230	4	roger	roger	PROPN
ejpam-5258	230	5	c	c	PROPN
ejpam-5258	230	6	lyndon	lyndon	PROPN
ejpam-5258	230	7	,	,	PUNCT
ejpam-5258	230	8	paul	paul	PROPN
ejpam-5258	230	9	e	e	PROPN
ejpam-5258	230	10	schupp	schupp	PROPN
ejpam-5258	230	11	,	,	PUNCT
ejpam-5258	230	12	rc	rc	PROPN
ejpam-5258	230	13	lyndon	lyndon	PROPN
ejpam-5258	230	14	,	,	PUNCT
ejpam-5258	230	15	and	and	CCONJ
ejpam-5258	230	16	pe	pe	PROPN
ejpam-5258	230	17	schupp	schupp	PROPN
ejpam-5258	230	18	.	.	PUNCT
ejpam-5258	231	1	combinatorial	combinatorial	PROPN
ejpam-5258	231	2	group	group	NOUN
ejpam-5258	231	3	theory	theory	NOUN
ejpam-5258	231	4	.	.	PUNCT
ejpam-5258	232	1	springer	springer	NOUN
ejpam-5258	232	2	,	,	PUNCT
ejpam-5258	232	3	1977	1977	NUM
ejpam-5258	232	4	.	.	PUNCT
ejpam-5258	233	1	[	[	X
ejpam-5258	233	2	5	5	NUM
ejpam-5258	233	3	]	]	PUNCT
ejpam-5258	233	4	w	w	PROPN
ejpam-5258	233	5	magnus	magnus	PROPN
ejpam-5258	233	6	,	,	PUNCT
ejpam-5258	233	7	karrass	karrass	NOUN
ejpam-5258	233	8	a	a	PRON
ejpam-5258	233	9	,	,	PUNCT
ejpam-5258	233	10	and	and	CCONJ
ejpam-5258	233	11	d.	d.	PROPN
ejpam-5258	233	12	solitar	solitar	PROPN
ejpam-5258	233	13	.	.	PUNCT
ejpam-5258	234	1	combinatorial	combinatorial	PROPN
ejpam-5258	234	2	group	group	NOUN
ejpam-5258	234	3	theory	theory	NOUN
ejpam-5258	234	4	.	.	PUNCT
ejpam-5258	235	1	dover	dover	PROPN
ejpam-5258	235	2	publ.inc	publ.inc	PROPN
ejpam-5258	235	3	.	.	PROPN
ejpam-5258	235	4	new	new	PROPN
ejpam-5258	235	5	york	york	PROPN
ejpam-5258	235	6	,	,	PUNCT
ejpam-5258	235	7	1976	1976	NUM
ejpam-5258	235	8	.	.	PUNCT
ejpam-5258	236	1	[	[	X
ejpam-5258	236	2	6	6	NUM
ejpam-5258	236	3	]	]	PUNCT
ejpam-5258	236	4	clair	clair	PROPN
ejpam-5258	236	5	miller	miller	PROPN
ejpam-5258	236	6	.	.	PUNCT
ejpam-5258	237	1	the	the	DET
ejpam-5258	237	2	second	second	ADJ
ejpam-5258	237	3	homology	homology	NOUN
ejpam-5258	237	4	group	group	NOUN
ejpam-5258	237	5	of	of	ADP
ejpam-5258	237	6	a	a	DET
ejpam-5258	237	7	group	group	NOUN
ejpam-5258	237	8	;	;	PUNCT
ejpam-5258	237	9	relations	relation	NOUN
ejpam-5258	237	10	among	among	ADP
ejpam-5258	237	11	commutators	commutator	NOUN
ejpam-5258	237	12	.	.	PUNCT
ejpam-5258	238	1	proceedings	proceeding	NOUN
ejpam-5258	238	2	of	of	ADP
ejpam-5258	238	3	the	the	DET
ejpam-5258	238	4	american	american	PROPN
ejpam-5258	238	5	mathematical	mathematical	PROPN
ejpam-5258	238	6	society	society	NOUN
ejpam-5258	238	7	,	,	PUNCT
ejpam-5258	238	8	1952	1952	NUM
ejpam-5258	238	9	.	.	PUNCT
ejpam-5258	239	1	[	[	X
ejpam-5258	239	2	7	7	X
ejpam-5258	239	3	]	]	X
ejpam-5258	239	4	khaled	khaled	PROPN
ejpam-5258	239	5	mustafa	mustafa	PROPN
ejpam-5258	239	6	al	al	PROPN
ejpam-5258	239	7	-	-	PROPN
ejpam-5258	239	8	jamal	jamal	PROPN
ejpam-5258	239	9	and	and	CCONJ
ejpam-5258	239	10	ahmad	ahmad	PROPN
ejpam-5258	239	11	termimi	termimi	PROPN
ejpam-5258	239	12	ab	ab	PROPN
ejpam-5258	239	13	ghani	ghani	PROPN
ejpam-5258	239	14	.	.	PUNCT
ejpam-5258	240	1	on	on	ADP
ejpam-5258	240	2	the	the	DET
ejpam-5258	240	3	relation	relation	NOUN
ejpam-5258	240	4	between	between	ADP
ejpam-5258	240	5	ct	ct	NOUN
ejpam-5258	240	6	-	-	PUNCT
ejpam-5258	240	7	groups	group	NOUN
ejpam-5258	240	8	and	and	CCONJ
ejpam-5258	240	9	nsp	nsp	NOUN
ejpam-5258	240	10	-	-	PUNCT
ejpam-5258	240	11	groups	group	NOUN
ejpam-5258	240	12	on	on	ADP
ejpam-5258	240	13	finite	finite	ADJ
ejpam-5258	240	14	groups	group	NOUN
ejpam-5258	240	15	.	.	PUNCT
ejpam-5258	241	1	in	in	ADP
ejpam-5258	241	2	journal	journal	PROPN
ejpam-5258	241	3	of	of	ADP
ejpam-5258	241	4	physics	physics	PROPN
ejpam-5258	241	5	:	:	PUNCT
ejpam-5258	241	6	conference	conference	NOUN
ejpam-5258	241	7	series	series	NOUN
ejpam-5258	241	8	,	,	PUNCT
ejpam-5258	241	9	2019	2019	NUM
ejpam-5258	241	10	.	.	PUNCT
ejpam-5258	242	1	[	[	X
ejpam-5258	242	2	8	8	X
ejpam-5258	242	3	]	]	PUNCT
ejpam-5258	242	4	j.	j.	PROPN
ejpam-5258	242	5	j.	j.	PROPN
ejpam-5258	242	6	rotman	rotman	PROPN
ejpam-5258	242	7	.	.	PUNCT
ejpam-5258	243	1	the	the	DET
ejpam-5258	243	2	theory	theory	NOUN
ejpam-5258	243	3	of	of	ADP
ejpam-5258	243	4	groups	group	NOUN
ejpam-5258	243	5	:	:	PUNCT
ejpam-5258	243	6	an	an	DET
ejpam-5258	243	7	introduction	introduction	NOUN
ejpam-5258	243	8	.	.	PUNCT
ejpam-5258	244	1	allyn	allyn	PROPN
ejpam-5258	244	2	and	and	CCONJ
ejpam-5258	244	3	bacon	bacon	NOUN
ejpam-5258	244	4	,	,	PUNCT
ejpam-5258	244	5	1973	1973	NUM
ejpam-5258	244	6	.	.	PUNCT