id	sid	tid	token	lemma	pos
ejpam-4871	1	1	european	european	PROPN
ejpam-4871	1	2	journal	journal	PROPN
ejpam-4871	1	3	of	of	ADP
ejpam-4871	1	4	pure	pure	ADJ
ejpam-4871	1	5	and	and	CCONJ
ejpam-4871	1	6	applied	apply	VERB
ejpam-4871	1	7	mathematics	mathematic	NOUN
ejpam-4871	1	8	vol	vol	NOUN
ejpam-4871	1	9	.	.	PUNCT
ejpam-4871	2	1	16	16	NUM
ejpam-4871	2	2	,	,	PUNCT
ejpam-4871	2	3	no	no	INTJ
ejpam-4871	2	4	.	.	NOUN
ejpam-4871	2	5	3	3	NUM
ejpam-4871	2	6	,	,	PUNCT
ejpam-4871	2	7	2023	2023	NUM
ejpam-4871	2	8	,	,	PUNCT
ejpam-4871	2	9	1970	1970	NUM
ejpam-4871	2	10	-	-	SYM
ejpam-4871	2	11	1979	1979	NUM
ejpam-4871	2	12	issn	issn	PROPN
ejpam-4871	2	13	1307	1307	NUM
ejpam-4871	2	14	-	-	SYM
ejpam-4871	2	15	5543	5543	NUM
ejpam-4871	2	16	–	–	PUNCT
ejpam-4871	2	17	ejpam.com	ejpam.com	X
ejpam-4871	2	18	published	publish	VERB
ejpam-4871	2	19	by	by	ADP
ejpam-4871	2	20	new	new	PROPN
ejpam-4871	2	21	york	york	PROPN
ejpam-4871	2	22	business	business	PROPN
ejpam-4871	2	23	global	global	PROPN
ejpam-4871	2	24	finite	finite	PROPN
ejpam-4871	2	25	minimal	minimal	ADJ
ejpam-4871	2	26	simple	simple	ADJ
ejpam-4871	2	27	groups	group	NOUN
ejpam-4871	2	28	non	non	X
ejpam-4871	2	29	satisfying	satisfy	VERB
ejpam-4871	2	30	the	the	DET
ejpam-4871	2	31	basis	basis	NOUN
ejpam-4871	2	32	property	property	NOUN
ejpam-4871	2	33	ahmad	ahmad	PROPN
ejpam-4871	2	34	al	al	PROPN
ejpam-4871	2	35	khalaf1,∗	khalaf1,∗	PROPN
ejpam-4871	2	36	,	,	PUNCT
ejpam-4871	2	37	iman	iman	NOUN
ejpam-4871	2	38	taha1	taha1	NOUN
ejpam-4871	2	39	1	1	NUM
ejpam-4871	2	40	department	department	NOUN
ejpam-4871	2	41	of	of	ADP
ejpam-4871	2	42	mathematics	mathematic	NOUN
ejpam-4871	2	43	and	and	CCONJ
ejpam-4871	2	44	statistics	statistic	NOUN
ejpam-4871	2	45	,	,	PUNCT
ejpam-4871	2	46	faculty	faculty	NOUN
ejpam-4871	2	47	of	of	ADP
ejpam-4871	2	48	sciences	science	NOUN
ejpam-4871	2	49	,	,	PUNCT
ejpam-4871	2	50	imam	imam	PROPN
ejpam-4871	2	51	mohammad	mohammad	PROPN
ejpam-4871	2	52	ibn	ibn	PROPN
ejpam-4871	2	53	saud	saud	PROPN
ejpam-4871	2	54	islamic	islamic	PROPN
ejpam-4871	2	55	university	university	PROPN
ejpam-4871	2	56	,	,	PUNCT
ejpam-4871	2	57	riyadh	riyadh	PROPN
ejpam-4871	2	58	,	,	PUNCT
ejpam-4871	2	59	saudi	saudi	PROPN
ejpam-4871	2	60	arabia	arabia	PROPN
ejpam-4871	2	61	abstract	abstract	NOUN
ejpam-4871	2	62	.	.	PUNCT
ejpam-4871	3	1	let	let	VERB
ejpam-4871	3	2	g	g	PRON
ejpam-4871	3	3	be	be	AUX
ejpam-4871	3	4	a	a	DET
ejpam-4871	3	5	finite	finite	ADJ
ejpam-4871	3	6	group	group	NOUN
ejpam-4871	3	7	.	.	PUNCT
ejpam-4871	4	1	we	we	PRON
ejpam-4871	4	2	say	say	VERB
ejpam-4871	4	3	that	that	SCONJ
ejpam-4871	4	4	g	g	PROPN
ejpam-4871	4	5	has	have	VERB
ejpam-4871	4	6	the	the	DET
ejpam-4871	4	7	basis	basis	NOUN
ejpam-4871	4	8	property	property	NOUN
ejpam-4871	4	9	if	if	SCONJ
ejpam-4871	4	10	every	every	DET
ejpam-4871	4	11	subgroup	subgroup	NOUN
ejpam-4871	4	12	h	h	NOUN
ejpam-4871	4	13	of	of	ADP
ejpam-4871	4	14	g	g	PROPN
ejpam-4871	4	15	has	have	VERB
ejpam-4871	4	16	a	a	DET
ejpam-4871	4	17	minimal	minimal	ADJ
ejpam-4871	4	18	generating	generating	NOUN
ejpam-4871	4	19	set	set	NOUN
ejpam-4871	4	20	(	(	PUNCT
ejpam-4871	4	21	basis	basis	NOUN
ejpam-4871	4	22	)	)	PUNCT
ejpam-4871	4	23	,	,	PUNCT
ejpam-4871	4	24	and	and	CCONJ
ejpam-4871	4	25	any	any	DET
ejpam-4871	4	26	two	two	NUM
ejpam-4871	4	27	bases	basis	NOUN
ejpam-4871	4	28	of	of	ADP
ejpam-4871	4	29	h	h	NOUN
ejpam-4871	4	30	have	have	VERB
ejpam-4871	4	31	the	the	DET
ejpam-4871	4	32	same	same	ADJ
ejpam-4871	4	33	cardinality	cardinality	NOUN
ejpam-4871	4	34	.	.	PUNCT
ejpam-4871	5	1	a	a	DET
ejpam-4871	5	2	group	group	NOUN
ejpam-4871	5	3	g	g	NOUN
ejpam-4871	5	4	is	be	AUX
ejpam-4871	5	5	called	call	VERB
ejpam-4871	5	6	minimal	minimal	ADJ
ejpam-4871	5	7	not	not	PART
ejpam-4871	5	8	satisfying	satisfy	VERB
ejpam-4871	5	9	the	the	DET
ejpam-4871	5	10	basis	basis	NOUN
ejpam-4871	5	11	property	property	NOUN
ejpam-4871	5	12	if	if	SCONJ
ejpam-4871	5	13	it	it	PRON
ejpam-4871	5	14	does	do	AUX
ejpam-4871	5	15	not	not	PART
ejpam-4871	5	16	satisfy	satisfy	VERB
ejpam-4871	5	17	the	the	DET
ejpam-4871	5	18	basis	basis	NOUN
ejpam-4871	5	19	property	property	NOUN
ejpam-4871	5	20	,	,	PUNCT
ejpam-4871	5	21	but	but	CCONJ
ejpam-4871	5	22	all	all	DET
ejpam-4871	5	23	its	its	PRON
ejpam-4871	5	24	proper	proper	ADJ
ejpam-4871	5	25	subgroups	subgroup	NOUN
ejpam-4871	5	26	satisfy	satisfy	VERB
ejpam-4871	5	27	the	the	DET
ejpam-4871	5	28	basis	basis	NOUN
ejpam-4871	5	29	property	property	NOUN
ejpam-4871	5	30	.	.	PUNCT
ejpam-4871	6	1	we	we	PRON
ejpam-4871	6	2	prove	prove	VERB
ejpam-4871	6	3	that	that	SCONJ
ejpam-4871	6	4	the	the	DET
ejpam-4871	6	5	following	follow	VERB
ejpam-4871	6	6	groups	group	NOUN
ejpam-4871	6	7	psl(2	psl(2	NOUN
ejpam-4871	6	8	,	,	PUNCT
ejpam-4871	6	9	5	5	X
ejpam-4871	6	10	)	)	PUNCT
ejpam-4871	6	11	∼=	∼=	PROPN
ejpam-4871	6	12	a5	a5	NOUN
ejpam-4871	6	13	,	,	PUNCT
ejpam-4871	6	14	psl(2	psl(2	NOUN
ejpam-4871	6	15	,	,	PUNCT
ejpam-4871	6	16	8)	8)	NUM
ejpam-4871	6	17	,	,	PUNCT
ejpam-4871	6	18	are	be	AUX
ejpam-4871	6	19	minimal	minimal	ADJ
ejpam-4871	6	20	groups	group	NOUN
ejpam-4871	6	21	non	non	X
ejpam-4871	6	22	satisfying	satisfy	VERB
ejpam-4871	6	23	the	the	DET
ejpam-4871	6	24	basis	basis	NOUN
ejpam-4871	6	25	property	property	NOUN
ejpam-4871	6	26	,	,	PUNCT
ejpam-4871	6	27	but	but	CCONJ
ejpam-4871	6	28	the	the	DET
ejpam-4871	6	29	groups	group	NOUN
ejpam-4871	6	30	psl(2	psl(2	NOUN
ejpam-4871	6	31	,	,	PUNCT
ejpam-4871	6	32	9	9	NUM
ejpam-4871	6	33	)	)	PUNCT
ejpam-4871	6	34	,	,	PUNCT
ejpam-4871	6	35	psl(2	psl(2	NOUN
ejpam-4871	6	36	,	,	PUNCT
ejpam-4871	6	37	17	17	NUM
ejpam-4871	6	38	)	)	PUNCT
ejpam-4871	6	39	and	and	CCONJ
ejpam-4871	6	40	psl(3	psl(3	NOUN
ejpam-4871	6	41	,	,	PUNCT
ejpam-4871	6	42	4	4	NUM
ejpam-4871	6	43	)	)	PUNCT
ejpam-4871	6	44	are	be	AUX
ejpam-4871	6	45	not	not	PART
ejpam-4871	6	46	minimal	minimal	ADJ
ejpam-4871	6	47	and	and	CCONJ
ejpam-4871	6	48	not	not	PART
ejpam-4871	6	49	satisfying	satisfy	VERB
ejpam-4871	6	50	the	the	DET
ejpam-4871	6	51	basis	basis	NOUN
ejpam-4871	6	52	property	property	NOUN
ejpam-4871	6	53	.	.	PUNCT
ejpam-4871	7	1	2020	2020	NUM
ejpam-4871	7	2	mathematics	mathematic	NOUN
ejpam-4871	7	3	subject	subject	NOUN
ejpam-4871	7	4	classifications	classification	NOUN
ejpam-4871	7	5	:	:	PUNCT
ejpam-4871	7	6	20m05	20m05	NUM
ejpam-4871	7	7	,	,	PUNCT
ejpam-4871	7	8	03d40	03d40	X
ejpam-4871	7	9	key	key	ADJ
ejpam-4871	7	10	words	word	NOUN
ejpam-4871	7	11	and	and	CCONJ
ejpam-4871	7	12	phrases	phrase	NOUN
ejpam-4871	7	13	:	:	PUNCT
ejpam-4871	7	14	simple	simple	ADJ
ejpam-4871	7	15	group	group	NOUN
ejpam-4871	7	16	,	,	PUNCT
ejpam-4871	7	17	minimal	minimal	ADJ
ejpam-4871	7	18	group	group	NOUN
ejpam-4871	7	19	,	,	PUNCT
ejpam-4871	7	20	group	group	NOUN
ejpam-4871	7	21	with	with	ADP
ejpam-4871	7	22	the	the	DET
ejpam-4871	7	23	basis	basis	NOUN
ejpam-4871	7	24	property	property	NOUN
ejpam-4871	7	25	1	1	NUM
ejpam-4871	7	26	.	.	PUNCT
ejpam-4871	8	1	introduction	introduction	NOUN
ejpam-4871	8	2	the	the	DET
ejpam-4871	8	3	burnside	burnside	NOUN
ejpam-4871	8	4	basis	basis	NOUN
ejpam-4871	8	5	theorem	theorem	NOUN
ejpam-4871	8	6	tells	tell	VERB
ejpam-4871	8	7	us	we	PRON
ejpam-4871	8	8	that	that	SCONJ
ejpam-4871	8	9	the	the	DET
ejpam-4871	8	10	generating	generating	NOUN
ejpam-4871	8	11	sets	set	NOUN
ejpam-4871	8	12	for	for	ADP
ejpam-4871	8	13	p	p	NOUN
ejpam-4871	8	14	-	-	PUNCT
ejpam-4871	8	15	groups	group	NOUN
ejpam-4871	8	16	shares	share	VERB
ejpam-4871	8	17	many	many	ADJ
ejpam-4871	8	18	property	property	NOUN
ejpam-4871	8	19	with	with	ADP
ejpam-4871	8	20	the	the	DET
ejpam-4871	8	21	bases	basis	NOUN
ejpam-4871	8	22	of	of	ADP
ejpam-4871	8	23	vector	vector	NOUN
ejpam-4871	8	24	spaces	space	NOUN
ejpam-4871	8	25	.	.	PUNCT
ejpam-4871	9	1	in	in	ADP
ejpam-4871	9	2	particular	particular	ADJ
ejpam-4871	9	3	,	,	PUNCT
ejpam-4871	9	4	if	if	SCONJ
ejpam-4871	9	5	g	g	PROPN
ejpam-4871	9	6	is	be	AUX
ejpam-4871	9	7	a	a	DET
ejpam-4871	9	8	finite	finite	NOUN
ejpam-4871	9	9	p	p	NOUN
ejpam-4871	9	10	-	-	PUNCT
ejpam-4871	9	11	group	group	NOUN
ejpam-4871	9	12	,	,	PUNCT
ejpam-4871	9	13	then	then	ADV
ejpam-4871	9	14	the	the	DET
ejpam-4871	9	15	minimal	minimal	ADJ
ejpam-4871	9	16	generating	generating	NOUN
ejpam-4871	9	17	sets	set	NOUN
ejpam-4871	9	18	(	(	PUNCT
ejpam-4871	9	19	sets	set	VERB
ejpam-4871	9	20	that	that	SCONJ
ejpam-4871	9	21	no	no	DET
ejpam-4871	9	22	smaller	small	ADJ
ejpam-4871	9	23	proper	proper	ADJ
ejpam-4871	9	24	subset	subset	NOUN
ejpam-4871	9	25	can	can	AUX
ejpam-4871	9	26	generate	generate	VERB
ejpam-4871	9	27	g	g	NOUN
ejpam-4871	9	28	as	as	ADV
ejpam-4871	9	29	well	well	ADV
ejpam-4871	9	30	)	)	PUNCT
ejpam-4871	9	31	have	have	VERB
ejpam-4871	9	32	the	the	DET
ejpam-4871	9	33	same	same	ADJ
ejpam-4871	9	34	cardinality	cardinality	NOUN
ejpam-4871	9	35	.	.	PUNCT
ejpam-4871	10	1	we	we	PRON
ejpam-4871	10	2	will	will	AUX
ejpam-4871	10	3	say	say	VERB
ejpam-4871	10	4	that	that	SCONJ
ejpam-4871	10	5	an	an	DET
ejpam-4871	10	6	arbitrary	arbitrary	ADJ
ejpam-4871	10	7	finite	finite	NOUN
ejpam-4871	10	8	group	group	NOUN
ejpam-4871	10	9	has	have	VERB
ejpam-4871	10	10	the	the	DET
ejpam-4871	10	11	generation	generation	NOUN
ejpam-4871	10	12	property	property	NOUN
ejpam-4871	10	13	if	if	SCONJ
ejpam-4871	10	14	its	its	PRON
ejpam-4871	10	15	minimal	minimal	ADJ
ejpam-4871	10	16	generating	generating	NOUN
ejpam-4871	10	17	sets	set	NOUN
ejpam-4871	10	18	have	have	VERB
ejpam-4871	10	19	the	the	DET
ejpam-4871	10	20	same	same	ADJ
ejpam-4871	10	21	cardinality	cardinality	NOUN
ejpam-4871	10	22	.	.	PUNCT
ejpam-4871	11	1	a	a	DET
ejpam-4871	11	2	finite	finite	ADJ
ejpam-4871	11	3	group	group	NOUN
ejpam-4871	11	4	g	g	PROPN
ejpam-4871	11	5	has	have	VERB
ejpam-4871	11	6	the	the	DET
ejpam-4871	11	7	basis	basis	NOUN
ejpam-4871	11	8	property	property	NOUN
ejpam-4871	11	9	if	if	SCONJ
ejpam-4871	11	10	g	g	PROPN
ejpam-4871	11	11	and	and	CCONJ
ejpam-4871	11	12	all	all	DET
ejpam-4871	11	13	its	its	PRON
ejpam-4871	11	14	subgroups	subgroup	NOUN
ejpam-4871	11	15	have	have	VERB
ejpam-4871	11	16	the	the	DET
ejpam-4871	11	17	generation	generation	NOUN
ejpam-4871	11	18	property	property	NOUN
ejpam-4871	11	19	.	.	PUNCT
ejpam-4871	12	1	in	in	ADP
ejpam-4871	12	2	[	[	X
ejpam-4871	12	3	12	12	NUM
ejpam-4871	12	4	]	]	PUNCT
ejpam-4871	12	5	,	,	PUNCT
ejpam-4871	12	6	jones	jones	PROPN
ejpam-4871	12	7	has	have	AUX
ejpam-4871	12	8	introduced	introduce	VERB
ejpam-4871	12	9	the	the	DET
ejpam-4871	12	10	basis	basis	NOUN
ejpam-4871	12	11	property	property	NOUN
ejpam-4871	12	12	and	and	CCONJ
ejpam-4871	12	13	considered	consider	VERB
ejpam-4871	12	14	it	it	PRON
ejpam-4871	12	15	in	in	ADP
ejpam-4871	12	16	the	the	DET
ejpam-4871	12	17	context	context	NOUN
ejpam-4871	12	18	of	of	ADP
ejpam-4871	12	19	inverse	inverse	NOUN
ejpam-4871	12	20	semigroups	semigroup	NOUN
ejpam-4871	12	21	.	.	PUNCT
ejpam-4871	13	1	also	also	ADV
ejpam-4871	13	2	,	,	PUNCT
ejpam-4871	13	3	jones	jones	PROPN
ejpam-4871	13	4	in	in	ADP
ejpam-4871	13	5	[	[	X
ejpam-4871	13	6	13	13	NUM
ejpam-4871	13	7	]	]	PUNCT
ejpam-4871	13	8	proved	prove	VERB
ejpam-4871	13	9	that	that	SCONJ
ejpam-4871	13	10	if	if	SCONJ
ejpam-4871	13	11	g	g	PROPN
ejpam-4871	13	12	is	be	AUX
ejpam-4871	13	13	a	a	DET
ejpam-4871	13	14	group	group	NOUN
ejpam-4871	13	15	with	with	ADP
ejpam-4871	13	16	the	the	DET
ejpam-4871	13	17	basis	basis	NOUN
ejpam-4871	13	18	property	property	NOUN
ejpam-4871	13	19	,	,	PUNCT
ejpam-4871	13	20	then	then	ADV
ejpam-4871	13	21	every	every	DET
ejpam-4871	13	22	element	element	NOUN
ejpam-4871	13	23	of	of	ADP
ejpam-4871	13	24	g	g	PROPN
ejpam-4871	13	25	must	must	AUX
ejpam-4871	13	26	has	have	VERB
ejpam-4871	13	27	a	a	DET
ejpam-4871	13	28	prime	prime	ADJ
ejpam-4871	13	29	power	power	NOUN
ejpam-4871	13	30	order	order	NOUN
ejpam-4871	13	31	,	,	PUNCT
ejpam-4871	13	32	after	after	ADP
ejpam-4871	13	33	that	that	PRON
ejpam-4871	13	34	,	,	PUNCT
ejpam-4871	13	35	he	he	PRON
ejpam-4871	13	36	established	establish	VERB
ejpam-4871	13	37	that	that	SCONJ
ejpam-4871	13	38	the	the	DET
ejpam-4871	13	39	basis	basis	NOUN
ejpam-4871	13	40	property	property	NOUN
ejpam-4871	13	41	is	be	AUX
ejpam-4871	13	42	inherited	inherit	VERB
ejpam-4871	13	43	by	by	ADP
ejpam-4871	13	44	quotients	quotient	NOUN
ejpam-4871	13	45	and	and	CCONJ
ejpam-4871	13	46	a	a	DET
ejpam-4871	13	47	group	group	NOUN
ejpam-4871	13	48	with	with	ADP
ejpam-4871	13	49	the	the	DET
ejpam-4871	13	50	basis	basis	NOUN
ejpam-4871	13	51	property	property	NOUN
ejpam-4871	13	52	is	be	AUX
ejpam-4871	13	53	soluble	soluble	ADJ
ejpam-4871	13	54	as	as	ADV
ejpam-4871	13	55	well	well	ADV
ejpam-4871	13	56	.	.	PUNCT
ejpam-4871	14	1	the	the	DET
ejpam-4871	14	2	basis	basis	NOUN
ejpam-4871	14	3	property	property	NOUN
ejpam-4871	14	4	for	for	ADP
ejpam-4871	14	5	groups	group	NOUN
ejpam-4871	14	6	has	have	AUX
ejpam-4871	14	7	been	be	AUX
ejpam-4871	14	8	developed	develop	VERB
ejpam-4871	14	9	by	by	ADP
ejpam-4871	14	10	many	many	ADJ
ejpam-4871	14	11	authors	author	NOUN
ejpam-4871	14	12	as	as	ADP
ejpam-4871	14	13	in	in	ADP
ejpam-4871	14	14	the	the	DET
ejpam-4871	14	15	articles	article	NOUN
ejpam-4871	14	16	[	[	X
ejpam-4871	14	17	1	1	NUM
ejpam-4871	14	18	,	,	PUNCT
ejpam-4871	14	19	2	2	NUM
ejpam-4871	14	20	,	,	PUNCT
ejpam-4871	14	21	4	4	NUM
ejpam-4871	14	22	,	,	PUNCT
ejpam-4871	14	23	11	11	NUM
ejpam-4871	14	24	,	,	PUNCT
ejpam-4871	14	25	14	14	NUM
ejpam-4871	14	26	,	,	PUNCT
ejpam-4871	14	27	15	15	NUM
ejpam-4871	14	28	]	]	PUNCT
ejpam-4871	14	29	and	and	CCONJ
ejpam-4871	14	30	we	we	PRON
ejpam-4871	14	31	shall	shall	AUX
ejpam-4871	14	32	mention	mention	VERB
ejpam-4871	14	33	some	some	PRON
ejpam-4871	14	34	of	of	ADP
ejpam-4871	14	35	this	this	DET
ejpam-4871	14	36	work	work	NOUN
ejpam-4871	14	37	below	below	ADV
ejpam-4871	14	38	.	.	PUNCT
ejpam-4871	15	1	a	a	DET
ejpam-4871	15	2	variant	variant	NOUN
ejpam-4871	15	3	of	of	ADP
ejpam-4871	15	4	these	these	DET
ejpam-4871	15	5	properties	property	NOUN
ejpam-4871	15	6	is	be	AUX
ejpam-4871	15	7	the	the	DET
ejpam-4871	15	8	concept	concept	NOUN
ejpam-4871	15	9	of	of	ADP
ejpam-4871	15	10	a	a	DET
ejpam-4871	15	11	matroid	matroid	ADJ
ejpam-4871	15	12	group	group	NOUN
ejpam-4871	15	13	,	,	PUNCT
ejpam-4871	15	14	which	which	PRON
ejpam-4871	15	15	is	be	AUX
ejpam-4871	15	16	a	a	DET
ejpam-4871	15	17	group	group	NOUN
ejpam-4871	15	18	that	that	PRON
ejpam-4871	15	19	satisfies	satisfy	VERB
ejpam-4871	15	20	the	the	DET
ejpam-4871	15	21	generation	generation	NOUN
ejpam-4871	15	22	property	property	NOUN
ejpam-4871	15	23	and	and	CCONJ
ejpam-4871	15	24	the	the	DET
ejpam-4871	15	25	additional	additional	ADJ
ejpam-4871	15	26	condition	condition	NOUN
ejpam-4871	15	27	that	that	SCONJ
ejpam-4871	15	28	every	every	DET
ejpam-4871	15	29	independent	independent	ADJ
ejpam-4871	15	30	subset	subset	NOUN
ejpam-4871	15	31	of	of	ADP
ejpam-4871	15	32	g	g	PROPN
ejpam-4871	15	33	∗corresponding	∗corresponde	VERB
ejpam-4871	15	34	author	author	NOUN
ejpam-4871	15	35	.	.	PUNCT
ejpam-4871	16	1	doi	doi	NOUN
ejpam-4871	16	2	:	:	PUNCT
ejpam-4871	16	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4871	https://doi.org/10.29020/nybg.ejpam.v16i3.4871	NUM
ejpam-4871	16	4	email	email	NOUN
ejpam-4871	16	5	addresses	address	NOUN
ejpam-4871	16	6	:	:	PUNCT
ejpam-4871	16	7	ajalkalaf@imamu.edu.sa	ajalkalaf@imamu.edu.sa	NOUN
ejpam-4871	16	8	(	(	PUNCT
ejpam-4871	16	9	a.	a.	PROPN
ejpam-4871	16	10	al	al	PROPN
ejpam-4871	16	11	khalaf	khalaf	PROPN
ejpam-4871	16	12	)	)	PUNCT
ejpam-4871	16	13	,	,	PUNCT
ejpam-4871	16	14	tfaith80gmail.com	tfaith80gmail.com	X
ejpam-4871	16	15	(	(	PUNCT
ejpam-4871	16	16	i.	i.	PROPN
ejpam-4871	16	17	taha	taha	PROPN
ejpam-4871	16	18	)	)	PUNCT
ejpam-4871	16	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4871	16	20	1970	1970	NUM
ejpam-4871	17	1	©	©	PROPN
ejpam-4871	17	2	2023	2023	NUM
ejpam-4871	17	3	ejpam	ejpam	NOUN
ejpam-4871	17	4	all	all	DET
ejpam-4871	17	5	rights	right	NOUN
ejpam-4871	17	6	reserved	reserve	VERB
ejpam-4871	17	7	.	.	PUNCT
ejpam-4871	18	1	a.	a.	PROPN
ejpam-4871	18	2	al	al	PROPN
ejpam-4871	18	3	khalaf	khalaf	PROPN
ejpam-4871	18	4	,	,	PUNCT
ejpam-4871	18	5	i.	i.	PROPN
ejpam-4871	18	6	taha	taha	PROPN
ejpam-4871	18	7	/	/	PUNCT
ejpam-4871	18	8	eur	eur	PROPN
ejpam-4871	18	9	.	.	PUNCT
ejpam-4871	19	1	j.	j.	PROPN
ejpam-4871	19	2	pure	pure	PROPN
ejpam-4871	19	3	appl	appl	PROPN
ejpam-4871	19	4	.	.	PROPN
ejpam-4871	19	5	math	math	PROPN
ejpam-4871	19	6	,	,	PUNCT
ejpam-4871	19	7	16	16	NUM
ejpam-4871	19	8	(	(	PUNCT
ejpam-4871	19	9	3	3	NUM
ejpam-4871	19	10	)	)	PUNCT
ejpam-4871	19	11	(	(	PUNCT
ejpam-4871	19	12	2023	2023	NUM
ejpam-4871	19	13	)	)	PUNCT
ejpam-4871	19	14	,	,	PUNCT
ejpam-4871	19	15	1970	1970	NUM
ejpam-4871	19	16	-	-	SYM
ejpam-4871	19	17	1979	1979	NUM
ejpam-4871	19	18	1971	1971	NUM
ejpam-4871	19	19	is	be	AUX
ejpam-4871	19	20	contained	contain	VERB
ejpam-4871	19	21	in	in	ADP
ejpam-4871	19	22	a	a	DET
ejpam-4871	19	23	minimal	minimal	ADJ
ejpam-4871	19	24	generating	generating	NOUN
ejpam-4871	19	25	set	set	NOUN
ejpam-4871	19	26	.	.	PUNCT
ejpam-4871	20	1	scapellato	scapellato	PROPN
ejpam-4871	20	2	and	and	CCONJ
ejpam-4871	20	3	verardi	verardi	VERB
ejpam-4871	20	4	through	through	ADP
ejpam-4871	20	5	the	the	DET
ejpam-4871	20	6	articles	article	NOUN
ejpam-4871	20	7	[	[	X
ejpam-4871	20	8	17	17	NUM
ejpam-4871	20	9	,	,	PUNCT
ejpam-4871	20	10	18	18	NUM
ejpam-4871	20	11	]	]	PUNCT
ejpam-4871	20	12	have	have	AUX
ejpam-4871	20	13	studied	study	VERB
ejpam-4871	20	14	matroid	matroid	ADJ
ejpam-4871	20	15	groups	group	NOUN
ejpam-4871	20	16	.	.	PUNCT
ejpam-4871	21	1	in	in	ADP
ejpam-4871	21	2	more	more	ADJ
ejpam-4871	21	3	details	detail	NOUN
ejpam-4871	21	4	,	,	PUNCT
ejpam-4871	21	5	they	they	PRON
ejpam-4871	21	6	provide	provide	VERB
ejpam-4871	21	7	a	a	DET
ejpam-4871	21	8	full	full	ADJ
ejpam-4871	21	9	characterization	characterization	NOUN
ejpam-4871	21	10	of	of	ADP
ejpam-4871	21	11	matroid	matroid	ADJ
ejpam-4871	21	12	groups	group	NOUN
ejpam-4871	21	13	that	that	PRON
ejpam-4871	21	14	a	a	DET
ejpam-4871	21	15	matroid	matroid	PROPN
ejpam-4871	21	16	group	group	NOUN
ejpam-4871	21	17	has	have	VERB
ejpam-4871	21	18	the	the	DET
ejpam-4871	21	19	basis	basis	NOUN
ejpam-4871	21	20	property	property	NOUN
ejpam-4871	21	21	.	.	PUNCT
ejpam-4871	22	1	alkhalaf	alkhalaf	PROPN
ejpam-4871	22	2	in	in	ADP
ejpam-4871	22	3	[	[	X
ejpam-4871	22	4	3	3	NUM
ejpam-4871	22	5	]	]	PUNCT
ejpam-4871	22	6	has	have	AUX
ejpam-4871	22	7	provided	provide	VERB
ejpam-4871	22	8	a	a	DET
ejpam-4871	22	9	pleasant	pleasant	ADJ
ejpam-4871	22	10	characterization	characterization	NOUN
ejpam-4871	22	11	of	of	ADP
ejpam-4871	22	12	groups	group	NOUN
ejpam-4871	22	13	with	with	ADP
ejpam-4871	22	14	the	the	DET
ejpam-4871	22	15	basis	basis	NOUN
ejpam-4871	22	16	property	property	NOUN
ejpam-4871	22	17	based	base	VERB
ejpam-4871	22	18	on	on	ADP
ejpam-4871	22	19	results	result	NOUN
ejpam-4871	22	20	of	of	ADP
ejpam-4871	22	21	higman	higman	NOUN
ejpam-4871	22	22	[	[	X
ejpam-4871	22	23	7	7	NUM
ejpam-4871	22	24	]	]	PUNCT
ejpam-4871	22	25	,	,	PUNCT
ejpam-4871	22	26	who	who	PRON
ejpam-4871	22	27	has	have	AUX
ejpam-4871	22	28	classified	classify	VERB
ejpam-4871	22	29	the	the	DET
ejpam-4871	22	30	soluble	soluble	ADJ
ejpam-4871	22	31	groups	group	NOUN
ejpam-4871	22	32	with	with	ADP
ejpam-4871	22	33	all	all	DET
ejpam-4871	22	34	elements	element	NOUN
ejpam-4871	22	35	of	of	ADP
ejpam-4871	22	36	prime	prime	ADJ
ejpam-4871	22	37	-	-	PUNCT
ejpam-4871	22	38	power	power	NOUN
ejpam-4871	22	39	order	order	NOUN
ejpam-4871	22	40	.	.	PUNCT
ejpam-4871	23	1	also	also	ADV
ejpam-4871	23	2	a.	a.	PROPN
ejpam-4871	23	3	alkhalaf	alkhalaf	PROPN
ejpam-4871	23	4	generalized	generalize	VERB
ejpam-4871	23	5	many	many	ADJ
ejpam-4871	23	6	of	of	ADP
ejpam-4871	23	7	the	the	DET
ejpam-4871	23	8	results	result	NOUN
ejpam-4871	23	9	related	relate	VERB
ejpam-4871	23	10	to	to	ADP
ejpam-4871	23	11	groups	group	NOUN
ejpam-4871	23	12	that	that	PRON
ejpam-4871	23	13	satisfies	satisfy	VERB
ejpam-4871	23	14	the	the	DET
ejpam-4871	23	15	basis	basis	NOUN
ejpam-4871	23	16	property	property	NOUN
ejpam-4871	23	17	,	,	PUNCT
ejpam-4871	23	18	and	and	CCONJ
ejpam-4871	23	19	we	we	PRON
ejpam-4871	23	20	can	can	AUX
ejpam-4871	23	21	find	find	VERB
ejpam-4871	23	22	them	they	PRON
ejpam-4871	23	23	in	in	ADP
ejpam-4871	23	24	[	[	X
ejpam-4871	23	25	5	5	NUM
ejpam-4871	23	26	,	,	PUNCT
ejpam-4871	23	27	6	6	NUM
ejpam-4871	23	28	]	]	PUNCT
ejpam-4871	23	29	.	.	PUNCT
ejpam-4871	24	1	the	the	DET
ejpam-4871	24	2	purpose	purpose	NOUN
ejpam-4871	24	3	of	of	ADP
ejpam-4871	24	4	this	this	DET
ejpam-4871	24	5	research	research	NOUN
ejpam-4871	24	6	is	be	AUX
ejpam-4871	24	7	to	to	PART
ejpam-4871	24	8	initiate	initiate	VERB
ejpam-4871	24	9	a	a	DET
ejpam-4871	24	10	study	study	NOUN
ejpam-4871	24	11	of	of	ADP
ejpam-4871	24	12	groups	group	NOUN
ejpam-4871	24	13	with	with	ADP
ejpam-4871	24	14	minimal	minimal	ADJ
ejpam-4871	24	15	group	group	NOUN
ejpam-4871	24	16	that	that	PRON
ejpam-4871	24	17	not	not	PART
ejpam-4871	24	18	satisfying	satisfy	VERB
ejpam-4871	24	19	the	the	DET
ejpam-4871	24	20	basis	basis	NOUN
ejpam-4871	24	21	property	property	NOUN
ejpam-4871	24	22	.	.	PUNCT
ejpam-4871	25	1	since	since	SCONJ
ejpam-4871	25	2	every	every	DET
ejpam-4871	25	3	image	image	NOUN
ejpam-4871	25	4	of	of	ADP
ejpam-4871	25	5	a	a	DET
ejpam-4871	25	6	homomorphism	homomorphism	NOUN
ejpam-4871	25	7	group	group	NOUN
ejpam-4871	25	8	with	with	ADP
ejpam-4871	25	9	the	the	DET
ejpam-4871	25	10	basis	basis	NOUN
ejpam-4871	25	11	property	property	NOUN
ejpam-4871	25	12	is	be	AUX
ejpam-4871	25	13	a	a	DET
ejpam-4871	25	14	group	group	NOUN
ejpam-4871	25	15	with	with	ADP
ejpam-4871	25	16	the	the	DET
ejpam-4871	25	17	basis	basis	NOUN
ejpam-4871	25	18	property	property	NOUN
ejpam-4871	25	19	,	,	PUNCT
ejpam-4871	25	20	then	then	ADV
ejpam-4871	25	21	the	the	DET
ejpam-4871	25	22	group	group	NOUN
ejpam-4871	25	23	g	g	PROPN
ejpam-4871	25	24	can	can	AUX
ejpam-4871	25	25	be	be	AUX
ejpam-4871	25	26	a	a	DET
ejpam-4871	25	27	minimal	minimal	ADJ
ejpam-4871	25	28	group	group	NOUN
ejpam-4871	25	29	not	not	PART
ejpam-4871	25	30	satisfying	satisfy	VERB
ejpam-4871	25	31	the	the	DET
ejpam-4871	25	32	basis	basis	NOUN
ejpam-4871	25	33	property	property	NOUN
ejpam-4871	25	34	if	if	SCONJ
ejpam-4871	25	35	its	its	PRON
ejpam-4871	25	36	image	image	NOUN
ejpam-4871	25	37	under	under	ADP
ejpam-4871	25	38	a	a	DET
ejpam-4871	25	39	homomorphism	homomorphism	NOUN
ejpam-4871	25	40	of	of	ADP
ejpam-4871	25	41	every	every	DET
ejpam-4871	25	42	proper	proper	ADJ
ejpam-4871	25	43	subgroup	subgroup	NOUN
ejpam-4871	25	44	h	h	NOUN
ejpam-4871	25	45	from	from	ADP
ejpam-4871	25	46	g	g	PROPN
ejpam-4871	25	47	must	must	AUX
ejpam-4871	25	48	be	be	AUX
ejpam-4871	25	49	satisfied	satisfy	VERB
ejpam-4871	25	50	the	the	DET
ejpam-4871	25	51	basis	basis	NOUN
ejpam-4871	25	52	property	property	NOUN
ejpam-4871	25	53	.	.	PUNCT
ejpam-4871	26	1	likewise	likewise	ADV
ejpam-4871	26	2	,	,	PUNCT
ejpam-4871	26	3	all	all	DET
ejpam-4871	26	4	subgroups	subgroup	NOUN
ejpam-4871	26	5	of	of	ADP
ejpam-4871	26	6	a	a	DET
ejpam-4871	26	7	group	group	NOUN
ejpam-4871	26	8	g	g	NOUN
ejpam-4871	26	9	must	must	AUX
ejpam-4871	26	10	satisfy	satisfy	VERB
ejpam-4871	26	11	that	that	PRON
ejpam-4871	26	12	.	.	PUNCT
ejpam-4871	27	1	it	it	PRON
ejpam-4871	27	2	follows	follow	VERB
ejpam-4871	27	3	,	,	PUNCT
ejpam-4871	27	4	from	from	ADP
ejpam-4871	27	5	all	all	PRON
ejpam-4871	27	6	of	of	ADP
ejpam-4871	27	7	these	these	DET
ejpam-4871	27	8	previous	previous	ADJ
ejpam-4871	27	9	results	result	NOUN
ejpam-4871	27	10	,	,	PUNCT
ejpam-4871	27	11	a	a	DET
ejpam-4871	27	12	minimal	minimal	ADJ
ejpam-4871	27	13	simple	simple	ADJ
ejpam-4871	27	14	group	group	NOUN
ejpam-4871	27	15	does	do	AUX
ejpam-4871	27	16	not	not	PART
ejpam-4871	27	17	satisfy	satisfy	VERB
ejpam-4871	27	18	the	the	DET
ejpam-4871	27	19	basis	basis	NOUN
ejpam-4871	27	20	property	property	NOUN
ejpam-4871	27	21	if	if	SCONJ
ejpam-4871	27	22	and	and	CCONJ
ejpam-4871	27	23	only	only	ADV
ejpam-4871	27	24	if	if	SCONJ
ejpam-4871	27	25	every	every	DET
ejpam-4871	27	26	maximal	maximal	ADJ
ejpam-4871	27	27	subgroups	subgroup	NOUN
ejpam-4871	27	28	is	be	AUX
ejpam-4871	27	29	a	a	DET
ejpam-4871	27	30	group	group	NOUN
ejpam-4871	27	31	with	with	ADP
ejpam-4871	27	32	the	the	DET
ejpam-4871	27	33	basis	basis	NOUN
ejpam-4871	27	34	property	property	NOUN
ejpam-4871	27	35	.	.	PUNCT
ejpam-4871	28	1	be	be	AUX
ejpam-4871	28	2	noted	note	VERB
ejpam-4871	28	3	that	that	SCONJ
ejpam-4871	28	4	,	,	PUNCT
ejpam-4871	28	5	along	along	ADP
ejpam-4871	28	6	this	this	DET
ejpam-4871	28	7	paper	paper	NOUN
ejpam-4871	28	8	,	,	PUNCT
ejpam-4871	28	9	the	the	DET
ejpam-4871	28	10	finite	finite	ADJ
ejpam-4871	28	11	groups	group	NOUN
ejpam-4871	28	12	will	will	AUX
ejpam-4871	28	13	be	be	AUX
ejpam-4871	28	14	considered	consider	VERB
ejpam-4871	28	15	only	only	ADV
ejpam-4871	28	16	,	,	PUNCT
ejpam-4871	28	17	hence	hence	ADV
ejpam-4871	28	18	any	any	DET
ejpam-4871	28	19	proper	proper	ADJ
ejpam-4871	28	20	subgroup	subgroup	NOUN
ejpam-4871	28	21	will	will	AUX
ejpam-4871	28	22	be	be	AUX
ejpam-4871	28	23	contained	contain	VERB
ejpam-4871	28	24	in	in	ADP
ejpam-4871	28	25	a	a	DET
ejpam-4871	28	26	maximal	maximal	ADJ
ejpam-4871	28	27	subgroup	subgroup	NOUN
ejpam-4871	28	28	and	and	CCONJ
ejpam-4871	28	29	we	we	PRON
ejpam-4871	28	30	can	can	AUX
ejpam-4871	28	31	see	see	VERB
ejpam-4871	28	32	that	that	SCONJ
ejpam-4871	28	33	in	in	ADP
ejpam-4871	28	34	[	[	X
ejpam-4871	28	35	9	9	NUM
ejpam-4871	28	36	]	]	PUNCT
ejpam-4871	28	37	and	and	CCONJ
ejpam-4871	28	38	since	since	SCONJ
ejpam-4871	28	39	the	the	DET
ejpam-4871	28	40	basis	basis	NOUN
ejpam-4871	28	41	property	property	NOUN
ejpam-4871	28	42	is	be	AUX
ejpam-4871	28	43	an	an	DET
ejpam-4871	28	44	inherited	inherit	VERB
ejpam-4871	28	45	property	property	NOUN
ejpam-4871	28	46	as	as	ADP
ejpam-4871	28	47	in	in	ADP
ejpam-4871	28	48	[	[	X
ejpam-4871	28	49	13	13	NUM
ejpam-4871	28	50	]	]	PUNCT
ejpam-4871	28	51	,	,	PUNCT
ejpam-4871	28	52	then	then	ADV
ejpam-4871	28	53	it	it	PRON
ejpam-4871	28	54	is	be	AUX
ejpam-4871	28	55	enough	enough	ADJ
ejpam-4871	28	56	to	to	PART
ejpam-4871	28	57	verify	verify	VERB
ejpam-4871	28	58	that	that	SCONJ
ejpam-4871	28	59	the	the	DET
ejpam-4871	28	60	maximal	maximal	ADJ
ejpam-4871	28	61	subgroups	subgroup	NOUN
ejpam-4871	28	62	satisfies	satisfy	VERB
ejpam-4871	28	63	the	the	DET
ejpam-4871	28	64	basis	basis	NOUN
ejpam-4871	28	65	property	property	NOUN
ejpam-4871	28	66	.	.	PUNCT
ejpam-4871	29	1	it	it	PRON
ejpam-4871	29	2	should	should	AUX
ejpam-4871	29	3	be	be	AUX
ejpam-4871	29	4	mentioned	mention	VERB
ejpam-4871	29	5	that	that	SCONJ
ejpam-4871	29	6	simple	simple	ADJ
ejpam-4871	29	7	groups	group	NOUN
ejpam-4871	29	8	are	be	AUX
ejpam-4871	29	9	not	not	PART
ejpam-4871	29	10	soluble	soluble	ADJ
ejpam-4871	29	11	groups	group	NOUN
ejpam-4871	29	12	,	,	PUNCT
ejpam-4871	29	13	unless	unless	SCONJ
ejpam-4871	29	14	the	the	DET
ejpam-4871	29	15	simple	simple	ADJ
ejpam-4871	29	16	groups	group	NOUN
ejpam-4871	29	17	with	with	ADP
ejpam-4871	29	18	prime	prime	ADJ
ejpam-4871	29	19	orders	order	NOUN
ejpam-4871	29	20	.	.	PUNCT
ejpam-4871	30	1	therefore	therefore	ADV
ejpam-4871	30	2	,	,	PUNCT
ejpam-4871	30	3	they	they	PRON
ejpam-4871	30	4	can	can	AUX
ejpam-4871	30	5	not	not	PART
ejpam-4871	30	6	be	be	AUX
ejpam-4871	30	7	simple	simple	ADJ
ejpam-4871	30	8	and	and	CCONJ
ejpam-4871	30	9	non	non	ADJ
ejpam-4871	30	10	-	-	ADJ
ejpam-4871	30	11	prime	prime	ADJ
ejpam-4871	30	12	and	and	CCONJ
ejpam-4871	30	13	satisfying	satisfy	VERB
ejpam-4871	30	14	the	the	DET
ejpam-4871	30	15	basis	basis	NOUN
ejpam-4871	30	16	property	property	NOUN
ejpam-4871	30	17	at	at	ADP
ejpam-4871	30	18	the	the	DET
ejpam-4871	30	19	same	same	ADJ
ejpam-4871	30	20	time	time	NOUN
ejpam-4871	30	21	,	,	PUNCT
ejpam-4871	30	22	but	but	CCONJ
ejpam-4871	30	23	here	here	ADV
ejpam-4871	30	24	we	we	PRON
ejpam-4871	30	25	are	be	AUX
ejpam-4871	30	26	trying	try	VERB
ejpam-4871	30	27	to	to	PART
ejpam-4871	30	28	obtain	obtain	VERB
ejpam-4871	30	29	a	a	DET
ejpam-4871	30	30	description	description	NOUN
ejpam-4871	30	31	of	of	ADP
ejpam-4871	30	32	simple	simple	ADJ
ejpam-4871	30	33	groups	group	NOUN
ejpam-4871	30	34	close	close	ADJ
ejpam-4871	30	35	to	to	ADP
ejpam-4871	30	36	groups	group	NOUN
ejpam-4871	30	37	that	that	PRON
ejpam-4871	30	38	are	be	AUX
ejpam-4871	30	39	satisfying	satisfy	VERB
ejpam-4871	30	40	the	the	DET
ejpam-4871	30	41	basis	basis	NOUN
ejpam-4871	30	42	property	property	NOUN
ejpam-4871	30	43	,	,	PUNCT
ejpam-4871	30	44	in	in	ADP
ejpam-4871	30	45	other	other	ADJ
ejpam-4871	30	46	words	word	NOUN
ejpam-4871	30	47	,	,	PUNCT
ejpam-4871	30	48	we	we	PRON
ejpam-4871	30	49	will	will	AUX
ejpam-4871	30	50	study	study	VERB
ejpam-4871	30	51	the	the	DET
ejpam-4871	30	52	simple	simple	ADJ
ejpam-4871	30	53	groups	group	NOUN
ejpam-4871	30	54	that	that	PRON
ejpam-4871	30	55	are	be	AUX
ejpam-4871	30	56	not	not	PART
ejpam-4871	30	57	satisfying	satisfy	VERB
ejpam-4871	30	58	the	the	DET
ejpam-4871	30	59	basis	basis	NOUN
ejpam-4871	30	60	property	property	NOUN
ejpam-4871	30	61	.	.	PUNCT
ejpam-4871	31	1	a	a	DET
ejpam-4871	31	2	finite	finite	ADJ
ejpam-4871	31	3	group	group	NOUN
ejpam-4871	31	4	g	g	PROPN
ejpam-4871	31	5	is	be	AUX
ejpam-4871	31	6	called	call	VERB
ejpam-4871	31	7	a	a	DET
ejpam-4871	31	8	semi	semi	ADJ
ejpam-4871	31	9	prime	prime	NOUN
ejpam-4871	31	10	if	if	SCONJ
ejpam-4871	31	11	the	the	DET
ejpam-4871	31	12	order	order	NOUN
ejpam-4871	31	13	of	of	ADP
ejpam-4871	31	14	every	every	DET
ejpam-4871	31	15	element	element	NOUN
ejpam-4871	31	16	is	be	AUX
ejpam-4871	31	17	a	a	DET
ejpam-4871	31	18	power	power	NOUN
ejpam-4871	31	19	of	of	ADP
ejpam-4871	31	20	a	a	DET
ejpam-4871	31	21	prime	prime	ADJ
ejpam-4871	31	22	number	number	NOUN
ejpam-4871	31	23	,	,	PUNCT
ejpam-4871	31	24	this	this	PRON
ejpam-4871	31	25	means	mean	VERB
ejpam-4871	31	26	,	,	PUNCT
ejpam-4871	31	27	every	every	DET
ejpam-4871	31	28	element	element	NOUN
ejpam-4871	31	29	will	will	AUX
ejpam-4871	31	30	be	be	AUX
ejpam-4871	31	31	either	either	CCONJ
ejpam-4871	31	32	p	p	NOUN
ejpam-4871	31	33	-	-	PUNCT
ejpam-4871	31	34	element	element	NOUN
ejpam-4871	31	35	or	or	CCONJ
ejpam-4871	31	36	q	q	NOUN
ejpam-4871	31	37	-	-	NOUN
ejpam-4871	31	38	element	element	NOUN
ejpam-4871	31	39	.	.	PUNCT
ejpam-4871	32	1	therefore	therefore	ADV
ejpam-4871	32	2	,	,	PUNCT
ejpam-4871	32	3	every	every	DET
ejpam-4871	32	4	cyclic	cyclic	ADJ
ejpam-4871	32	5	subgroup	subgroup	NOUN
ejpam-4871	32	6	of	of	ADP
ejpam-4871	32	7	a	a	DET
ejpam-4871	32	8	group	group	NOUN
ejpam-4871	32	9	g	g	NOUN
ejpam-4871	32	10	is	be	AUX
ejpam-4871	32	11	a	a	DET
ejpam-4871	32	12	primary	primary	NOUN
ejpam-4871	32	13	.	.	PUNCT
ejpam-4871	33	1	a	a	DET
ejpam-4871	33	2	finite	finite	ADJ
ejpam-4871	33	3	group	group	NOUN
ejpam-4871	33	4	g	g	PROPN
ejpam-4871	33	5	is	be	AUX
ejpam-4871	33	6	called	call	VERB
ejpam-4871	33	7	a	a	DET
ejpam-4871	33	8	semi	semi	ADJ
ejpam-4871	33	9	simple	simple	ADJ
ejpam-4871	33	10	if	if	SCONJ
ejpam-4871	33	11	it	it	PRON
ejpam-4871	33	12	does	do	AUX
ejpam-4871	33	13	not	not	PART
ejpam-4871	33	14	have	have	VERB
ejpam-4871	33	15	any	any	DET
ejpam-4871	33	16	soluble	soluble	ADJ
ejpam-4871	33	17	normal	normal	ADJ
ejpam-4871	33	18	non	non	ADJ
ejpam-4871	33	19	-	-	ADJ
ejpam-4871	33	20	trivial	trivial	ADJ
ejpam-4871	33	21	subgroups	subgroup	NOUN
ejpam-4871	33	22	.	.	PUNCT
ejpam-4871	34	1	a	a	DET
ejpam-4871	34	2	finite	finite	ADJ
ejpam-4871	34	3	group	group	NOUN
ejpam-4871	34	4	g	g	PROPN
ejpam-4871	34	5	is	be	AUX
ejpam-4871	34	6	called	call	VERB
ejpam-4871	34	7	a	a	DET
ejpam-4871	34	8	completely	completely	ADV
ejpam-4871	34	9	decomposable	decomposable	ADJ
ejpam-4871	34	10	if	if	SCONJ
ejpam-4871	34	11	it	it	PRON
ejpam-4871	34	12	is	be	AUX
ejpam-4871	34	13	decomposed	decompose	VERB
ejpam-4871	34	14	into	into	ADP
ejpam-4871	34	15	a	a	DET
ejpam-4871	34	16	direct	direct	ADJ
ejpam-4871	34	17	product	product	NOUN
ejpam-4871	34	18	of	of	ADP
ejpam-4871	34	19	a	a	DET
ejpam-4871	34	20	finite	finite	ADJ
ejpam-4871	34	21	number	number	NOUN
ejpam-4871	34	22	of	of	ADP
ejpam-4871	34	23	simple	simple	ADJ
ejpam-4871	34	24	groups	group	NOUN
ejpam-4871	34	25	.	.	PUNCT
ejpam-4871	35	1	[	[	X
ejpam-4871	35	2	16	16	NUM
ejpam-4871	35	3	]	]	SYM
ejpam-4871	35	4	2	2	NUM
ejpam-4871	35	5	.	.	PUNCT
ejpam-4871	35	6	preliminaries	preliminary	NOUN
ejpam-4871	35	7	the	the	DET
ejpam-4871	35	8	previous	previous	ADJ
ejpam-4871	35	9	concepts	concept	NOUN
ejpam-4871	35	10	have	have	AUX
ejpam-4871	35	11	studied	study	VERB
ejpam-4871	35	12	by	by	ADP
ejpam-4871	35	13	many	many	ADJ
ejpam-4871	35	14	authors	author	NOUN
ejpam-4871	35	15	,	,	PUNCT
ejpam-4871	35	16	which	which	PRON
ejpam-4871	35	17	they	they	PRON
ejpam-4871	35	18	considered	consider	VERB
ejpam-4871	35	19	the	the	DET
ejpam-4871	35	20	basis	basis	NOUN
ejpam-4871	35	21	properties	property	NOUN
ejpam-4871	35	22	of	of	ADP
ejpam-4871	35	23	groups	group	NOUN
ejpam-4871	35	24	in	in	ADP
ejpam-4871	35	25	their	their	PRON
ejpam-4871	35	26	works	work	NOUN
ejpam-4871	35	27	,	,	PUNCT
ejpam-4871	35	28	as	as	SCONJ
ejpam-4871	35	29	written	write	VERB
ejpam-4871	35	30	in	in	ADP
ejpam-4871	35	31	[	[	X
ejpam-4871	35	32	2–5	2–5	NOUN
ejpam-4871	35	33	]	]	PUNCT
ejpam-4871	35	34	.	.	PUNCT
ejpam-4871	36	1	now	now	ADV
ejpam-4871	36	2	,	,	PUNCT
ejpam-4871	36	3	we	we	PRON
ejpam-4871	36	4	are	be	AUX
ejpam-4871	36	5	willing	willing	ADJ
ejpam-4871	36	6	to	to	PART
ejpam-4871	36	7	prove	prove	VERB
ejpam-4871	36	8	our	our	PRON
ejpam-4871	36	9	theorems	theorem	NOUN
ejpam-4871	36	10	,	,	PUNCT
ejpam-4871	36	11	for	for	ADP
ejpam-4871	36	12	that	that	PRON
ejpam-4871	36	13	,	,	PUNCT
ejpam-4871	36	14	we	we	PRON
ejpam-4871	36	15	need	need	VERB
ejpam-4871	36	16	to	to	PART
ejpam-4871	36	17	state	state	VERB
ejpam-4871	36	18	some	some	DET
ejpam-4871	36	19	lemmas	lemma	NOUN
ejpam-4871	36	20	as	as	ADP
ejpam-4871	36	21	the	the	DET
ejpam-4871	36	22	following	following	NOUN
ejpam-4871	36	23	.	.	PUNCT
ejpam-4871	37	1	lemma	lemma	PROPN
ejpam-4871	37	2	1	1	NUM
ejpam-4871	37	3	.	.	PUNCT
ejpam-4871	38	1	[	[	X
ejpam-4871	38	2	3	3	NUM
ejpam-4871	38	3	,	,	PUNCT
ejpam-4871	38	4	theorem(2.5	theorem(2.5	NOUN
ejpam-4871	38	5	)	)	PUNCT
ejpam-4871	38	6	]	]	PUNCT
ejpam-4871	38	7	let	let	VERB
ejpam-4871	38	8	a	a	DET
ejpam-4871	38	9	finite	finite	ADJ
ejpam-4871	38	10	group	group	NOUN
ejpam-4871	38	11	g	g	PROPN
ejpam-4871	38	12	be	be	AUX
ejpam-4871	38	13	a	a	DET
ejpam-4871	38	14	semi	semi	ADJ
ejpam-4871	38	15	direct	direct	ADJ
ejpam-4871	38	16	product	product	NOUN
ejpam-4871	38	17	of	of	ADP
ejpam-4871	38	18	a	a	DET
ejpam-4871	38	19	p	p	NOUN
ejpam-4871	38	20	-	-	PUNCT
ejpam-4871	38	21	group	group	NOUN
ejpam-4871	38	22	p	p	X
ejpam-4871	38	23	=	=	SYM
ejpam-4871	38	24	fit(g	fit(g	PROPN
ejpam-4871	38	25	)	)	PUNCT
ejpam-4871	38	26	(	(	PUNCT
ejpam-4871	38	27	fitting	fitting	ADJ
ejpam-4871	38	28	subgroup	subgroup	NOUN
ejpam-4871	38	29	of	of	ADP
ejpam-4871	38	30	g	g	NOUN
ejpam-4871	38	31	)	)	PUNCT
ejpam-4871	38	32	by	by	ADP
ejpam-4871	38	33	a	a	DET
ejpam-4871	38	34	cyclic	cyclic	ADJ
ejpam-4871	38	35	q	q	NOUN
ejpam-4871	38	36	-	-	NOUN
ejpam-4871	38	37	group	group	NOUN
ejpam-4871	38	38	<	<	X
ejpam-4871	38	39	y	y	PROPN
ejpam-4871	38	40	>	>	X
ejpam-4871	38	41	of	of	ADP
ejpam-4871	38	42	order	order	NOUN
ejpam-4871	38	43	qb	qb	PROPN
ejpam-4871	38	44	,	,	PUNCT
ejpam-4871	38	45	where	where	SCONJ
ejpam-4871	38	46	p	p	PROPN
ejpam-4871	38	47	̸=	̸=	PROPN
ejpam-4871	38	48	q	q	PROPN
ejpam-4871	38	49	(	(	PUNCT
ejpam-4871	38	50	p	p	NOUN
ejpam-4871	38	51	and	and	CCONJ
ejpam-4871	38	52	q	q	NOUN
ejpam-4871	38	53	are	be	AUX
ejpam-4871	38	54	prime	prime	ADJ
ejpam-4871	38	55	numbers	number	NOUN
ejpam-4871	38	56	)	)	PUNCT
ejpam-4871	38	57	,	,	PUNCT
ejpam-4871	38	58	b	b	X
ejpam-4871	38	59	∈	∈	PROPN
ejpam-4871	38	60	n	n	ADV
ejpam-4871	38	61	.	.	PUNCT
ejpam-4871	39	1	then	then	ADV
ejpam-4871	39	2	the	the	DET
ejpam-4871	39	3	group	group	NOUN
ejpam-4871	39	4	g	g	PROPN
ejpam-4871	39	5	has	have	VERB
ejpam-4871	39	6	the	the	DET
ejpam-4871	39	7	basis	basis	NOUN
ejpam-4871	39	8	property	property	NOUN
ejpam-4871	39	9	if	if	SCONJ
ejpam-4871	39	10	and	and	CCONJ
ejpam-4871	39	11	only	only	ADV
ejpam-4871	39	12	if	if	SCONJ
ejpam-4871	39	13	for	for	ADP
ejpam-4871	39	14	any	any	DET
ejpam-4871	39	15	element	element	NOUN
ejpam-4871	39	16	u	u	NOUN
ejpam-4871	39	17	∈	∈	PROPN
ejpam-4871	39	18	<	<	X
ejpam-4871	39	19	y	y	PROPN
ejpam-4871	39	20	>	>	X
ejpam-4871	39	21	,	,	PUNCT
ejpam-4871	39	22	u	u	PROPN
ejpam-4871	39	23	̸=	̸=	PROPN
ejpam-4871	39	24	e	e	NOUN
ejpam-4871	39	25	and	and	CCONJ
ejpam-4871	39	26	for	for	ADP
ejpam-4871	39	27	any	any	DET
ejpam-4871	39	28	invariant	invariant	ADJ
ejpam-4871	39	29	subgroup	subgroup	NOUN
ejpam-4871	39	30	h	h	NOUN
ejpam-4871	39	31	of	of	ADP
ejpam-4871	39	32	p	p	NOUN
ejpam-4871	39	33	,	,	PUNCT
ejpam-4871	39	34	the	the	DET
ejpam-4871	39	35	automorphism	automorphism	NOUN
ejpam-4871	39	36	φu	φu	PRON
ejpam-4871	39	37	must	must	AUX
ejpam-4871	39	38	define	define	VERB
ejpam-4871	39	39	an	an	DET
ejpam-4871	39	40	isotopic	isotopic	ADJ
ejpam-4871	39	41	representation	representation	NOUN
ejpam-4871	39	42	on	on	ADP
ejpam-4871	39	43	every	every	DET
ejpam-4871	39	44	quotient	quotient	NOUN
ejpam-4871	39	45	frattini	frattini	PROPN
ejpam-4871	39	46	subgroup	subgroup	PROPN
ejpam-4871	39	47	h.	h.	PROPN
ejpam-4871	39	48	in	in	ADP
ejpam-4871	39	49	[	[	X
ejpam-4871	39	50	5	5	NUM
ejpam-4871	39	51	]	]	PUNCT
ejpam-4871	39	52	,	,	PUNCT
ejpam-4871	39	53	the	the	DET
ejpam-4871	39	54	author	author	NOUN
ejpam-4871	39	55	used	use	VERB
ejpam-4871	39	56	known	know	VERB
ejpam-4871	39	57	results	result	NOUN
ejpam-4871	39	58	for	for	ADP
ejpam-4871	39	59	the	the	DET
ejpam-4871	39	60	nilpotency	nilpotency	NOUN
ejpam-4871	39	61	class	class	NOUN
ejpam-4871	39	62	of	of	ADP
ejpam-4871	39	63	the	the	DET
ejpam-4871	39	64	kernel	kernel	NOUN
ejpam-4871	39	65	of	of	ADP
ejpam-4871	39	66	a	a	DET
ejpam-4871	39	67	frobenius	frobenius	ADJ
ejpam-4871	39	68	group	group	NOUN
ejpam-4871	39	69	to	to	PART
ejpam-4871	39	70	describe	describe	VERB
ejpam-4871	39	71	the	the	DET
ejpam-4871	39	72	nilpotency	nilpotency	NOUN
ejpam-4871	39	73	class	class	NOUN
ejpam-4871	39	74	of	of	ADP
ejpam-4871	39	75	the	the	DET
ejpam-4871	39	76	fitting	fitting	ADJ
ejpam-4871	39	77	subgroup	subgroup	NOUN
ejpam-4871	39	78	of	of	ADP
ejpam-4871	39	79	the	the	DET
ejpam-4871	39	80	group	group	NOUN
ejpam-4871	39	81	with	with	ADP
ejpam-4871	39	82	the	the	DET
ejpam-4871	39	83	basis	basis	NOUN
ejpam-4871	39	84	property	property	NOUN
ejpam-4871	39	85	.	.	PUNCT
ejpam-4871	40	1	a.	a.	PROPN
ejpam-4871	40	2	al	al	PROPN
ejpam-4871	40	3	khalaf	khalaf	PROPN
ejpam-4871	40	4	,	,	PUNCT
ejpam-4871	40	5	i.	i.	PROPN
ejpam-4871	40	6	taha	taha	PROPN
ejpam-4871	40	7	/	/	PUNCT
ejpam-4871	40	8	eur	eur	PROPN
ejpam-4871	40	9	.	.	PUNCT
ejpam-4871	41	1	j.	j.	PROPN
ejpam-4871	41	2	pure	pure	PROPN
ejpam-4871	41	3	appl	appl	PROPN
ejpam-4871	41	4	.	.	PROPN
ejpam-4871	41	5	math	math	PROPN
ejpam-4871	41	6	,	,	PUNCT
ejpam-4871	41	7	16	16	NUM
ejpam-4871	41	8	(	(	PUNCT
ejpam-4871	41	9	3	3	NUM
ejpam-4871	41	10	)	)	PUNCT
ejpam-4871	41	11	(	(	PUNCT
ejpam-4871	41	12	2023	2023	NUM
ejpam-4871	41	13	)	)	PUNCT
ejpam-4871	41	14	,	,	PUNCT
ejpam-4871	41	15	1970	1970	NUM
ejpam-4871	41	16	-	-	SYM
ejpam-4871	41	17	1979	1979	NUM
ejpam-4871	41	18	1972	1972	NUM
ejpam-4871	41	19	lemma	lemma	PROPN
ejpam-4871	41	20	2	2	NUM
ejpam-4871	41	21	.	.	PUNCT
ejpam-4871	42	1	[	[	X
ejpam-4871	42	2	19	19	NUM
ejpam-4871	42	3	,	,	PUNCT
ejpam-4871	42	4	theorem	theorem	VERB
ejpam-4871	42	5	16	16	NUM
ejpam-4871	42	6	]	]	PUNCT
ejpam-4871	42	7	let	let	VERB
ejpam-4871	42	8	g	g	PRON
ejpam-4871	42	9	be	be	AUX
ejpam-4871	42	10	a	a	DET
ejpam-4871	42	11	simple	simple	ADJ
ejpam-4871	42	12	group	group	NOUN
ejpam-4871	42	13	,	,	PUNCT
ejpam-4871	42	14	assume	assume	VERB
ejpam-4871	42	15	that	that	SCONJ
ejpam-4871	42	16	every	every	DET
ejpam-4871	42	17	nonidentity	nonidentity	NOUN
ejpam-4871	42	18	element	element	NOUN
ejpam-4871	42	19	composite	composite	ADJ
ejpam-4871	42	20	order	order	NOUN
ejpam-4871	42	21	of	of	ADP
ejpam-4871	42	22	g	g	PROPN
ejpam-4871	42	23	is	be	AUX
ejpam-4871	42	24	a	a	DET
ejpam-4871	42	25	prime	prime	ADJ
ejpam-4871	42	26	power	power	NOUN
ejpam-4871	42	27	order	order	NOUN
ejpam-4871	42	28	.	.	PUNCT
ejpam-4871	43	1	then	then	ADV
ejpam-4871	43	2	g	g	PROPN
ejpam-4871	43	3	is	be	AUX
ejpam-4871	43	4	isomorphic	isomorphic	ADJ
ejpam-4871	43	5	with	with	ADP
ejpam-4871	43	6	one	one	NUM
ejpam-4871	43	7	of	of	ADP
ejpam-4871	43	8	the	the	DET
ejpam-4871	43	9	following	follow	VERB
ejpam-4871	43	10	groups	group	NOUN
ejpam-4871	43	11	psl(2	psl(2	NOUN
ejpam-4871	43	12	,	,	PUNCT
ejpam-4871	43	13	5	5	NUM
ejpam-4871	43	14	)	)	PUNCT
ejpam-4871	43	15	,	,	PUNCT
ejpam-4871	43	16	psl(2	psl(2	NOUN
ejpam-4871	43	17	,	,	PUNCT
ejpam-4871	43	18	7	7	NUM
ejpam-4871	43	19	)	)	PUNCT
ejpam-4871	43	20	,	,	PUNCT
ejpam-4871	43	21	psl(2	psl(2	NOUN
ejpam-4871	43	22	,	,	PUNCT
ejpam-4871	43	23	23	23	NUM
ejpam-4871	43	24	)	)	PUNCT
ejpam-4871	43	25	,	,	PUNCT
ejpam-4871	43	26	psl(2	psl(2	NOUN
ejpam-4871	43	27	,	,	PUNCT
ejpam-4871	43	28	32	32	NUM
ejpam-4871	43	29	)	)	PUNCT
ejpam-4871	43	30	,	,	PUNCT
ejpam-4871	43	31	psl(2	psl(2	NOUN
ejpam-4871	43	32	,	,	PUNCT
ejpam-4871	43	33	17	17	NUM
ejpam-4871	43	34	)	)	PUNCT
ejpam-4871	43	35	,	,	PUNCT
ejpam-4871	43	36	psl(3	psl(3	NOUN
ejpam-4871	43	37	,	,	PUNCT
ejpam-4871	43	38	22	22	NUM
ejpam-4871	43	39	)	)	PUNCT
ejpam-4871	43	40	,	,	PUNCT
ejpam-4871	43	41	sz(23	sz(23	NOUN
ejpam-4871	43	42	)	)	PUNCT
ejpam-4871	43	43	,	,	PUNCT
ejpam-4871	43	44	sz(26	sz(26	NOUN
ejpam-4871	43	45	)	)	PUNCT
ejpam-4871	43	46	.	.	PUNCT
ejpam-4871	44	1	3	3	X
ejpam-4871	44	2	.	.	X
ejpam-4871	45	1	the	the	DET
ejpam-4871	45	2	properties	property	NOUN
ejpam-4871	45	3	of	of	ADP
ejpam-4871	45	4	simple	simple	ADJ
ejpam-4871	45	5	groups	group	NOUN
ejpam-4871	45	6	lemma	lemma	PROPN
ejpam-4871	45	7	3	3	X
ejpam-4871	45	8	.	.	PUNCT
ejpam-4871	46	1	let	let	VERB
ejpam-4871	46	2	g	g	PRON
ejpam-4871	46	3	be	be	AUX
ejpam-4871	46	4	a	a	DET
ejpam-4871	46	5	minimal	minimal	ADJ
ejpam-4871	46	6	simple	simple	ADJ
ejpam-4871	46	7	group	group	NOUN
ejpam-4871	46	8	that	that	PRON
ejpam-4871	46	9	does	do	AUX
ejpam-4871	46	10	not	not	PART
ejpam-4871	46	11	satisfy	satisfy	VERB
ejpam-4871	46	12	the	the	DET
ejpam-4871	46	13	basis	basis	NOUN
ejpam-4871	46	14	property	property	NOUN
ejpam-4871	46	15	.	.	PUNCT
ejpam-4871	47	1	then	then	ADV
ejpam-4871	47	2	g	g	PROPN
ejpam-4871	47	3	is	be	AUX
ejpam-4871	47	4	a	a	DET
ejpam-4871	47	5	semi	semi	ADJ
ejpam-4871	47	6	-	-	ADJ
ejpam-4871	47	7	prime	prime	ADJ
ejpam-4871	47	8	.	.	PUNCT
ejpam-4871	48	1	proof	proof	NOUN
ejpam-4871	48	2	.	.	PUNCT
ejpam-4871	49	1	suppose	suppose	VERB
ejpam-4871	49	2	the	the	DET
ejpam-4871	49	3	group	group	NOUN
ejpam-4871	49	4	g	g	PROPN
ejpam-4871	49	5	is	be	AUX
ejpam-4871	49	6	a	a	DET
ejpam-4871	49	7	simple	simple	ADJ
ejpam-4871	49	8	and	and	CCONJ
ejpam-4871	49	9	non	non	ADJ
ejpam-4871	49	10	semi	semi	ADJ
ejpam-4871	49	11	-	-	ADJ
ejpam-4871	49	12	prime	prime	ADJ
ejpam-4871	49	13	.	.	PUNCT
ejpam-4871	50	1	then	then	ADV
ejpam-4871	50	2	,	,	PUNCT
ejpam-4871	50	3	for	for	ADP
ejpam-4871	50	4	the	the	DET
ejpam-4871	50	5	two	two	NUM
ejpam-4871	50	6	prime	prime	ADJ
ejpam-4871	50	7	numbers	number	NOUN
ejpam-4871	50	8	p	p	NOUN
ejpam-4871	50	9	and	and	CCONJ
ejpam-4871	50	10	q	q	PROPN
ejpam-4871	50	11	(	(	PUNCT
ejpam-4871	50	12	p	p	PROPN
ejpam-4871	50	13	̸=	̸=	PROPN
ejpam-4871	50	14	q	q	PROPN
ejpam-4871	50	15	)	)	PUNCT
ejpam-4871	50	16	,	,	PUNCT
ejpam-4871	50	17	there	there	PRON
ejpam-4871	50	18	is	be	VERB
ejpam-4871	50	19	a	a	DET
ejpam-4871	50	20	cyclic	cyclic	ADJ
ejpam-4871	50	21	subgroup	subgroup	NOUN
ejpam-4871	50	22	<	<	X
ejpam-4871	50	23	y	y	PROPN
ejpam-4871	50	24	>	>	X
ejpam-4871	50	25	of	of	ADP
ejpam-4871	50	26	g	g	NOUN
ejpam-4871	50	27	with	with	ADP
ejpam-4871	50	28	order	order	NOUN
ejpam-4871	50	29	pq	pq	NOUN
ejpam-4871	50	30	,	,	PUNCT
ejpam-4871	50	31	which	which	PRON
ejpam-4871	50	32	does	do	AUX
ejpam-4871	50	33	not	not	PART
ejpam-4871	50	34	satisfy	satisfy	VERB
ejpam-4871	50	35	the	the	DET
ejpam-4871	50	36	basis	basis	NOUN
ejpam-4871	50	37	property	property	NOUN
ejpam-4871	50	38	,	,	PUNCT
ejpam-4871	50	39	also	also	ADV
ejpam-4871	50	40	,	,	PUNCT
ejpam-4871	50	41	since	since	SCONJ
ejpam-4871	50	42	g	g	PROPN
ejpam-4871	50	43	is	be	AUX
ejpam-4871	50	44	the	the	DET
ejpam-4871	50	45	minimal	minimal	ADJ
ejpam-4871	50	46	group	group	NOUN
ejpam-4871	50	47	,	,	PUNCT
ejpam-4871	50	48	which	which	PRON
ejpam-4871	50	49	does	do	AUX
ejpam-4871	50	50	not	not	PART
ejpam-4871	50	51	satisfy	satisfy	VERB
ejpam-4871	50	52	the	the	DET
ejpam-4871	50	53	basis	basis	NOUN
ejpam-4871	50	54	property	property	NOUN
ejpam-4871	50	55	,	,	PUNCT
ejpam-4871	50	56	hence	hence	ADV
ejpam-4871	50	57	the	the	DET
ejpam-4871	50	58	group	group	NOUN
ejpam-4871	50	59	g	g	PROPN
ejpam-4871	50	60	is	be	AUX
ejpam-4871	50	61	a	a	DET
ejpam-4871	50	62	biprimary	biprimary	ADJ
ejpam-4871	50	63	cyclic	cyclic	NOUN
ejpam-4871	50	64	group	group	NOUN
ejpam-4871	50	65	whose	whose	DET
ejpam-4871	50	66	order	order	NOUN
ejpam-4871	50	67	is	be	AUX
ejpam-4871	50	68	pq	pq	NOUN
ejpam-4871	50	69	,	,	PUNCT
ejpam-4871	50	70	and	and	CCONJ
ejpam-4871	50	71	this	this	PRON
ejpam-4871	50	72	contradicts	contradict	VERB
ejpam-4871	50	73	the	the	DET
ejpam-4871	50	74	hypothesis	hypothesis	NOUN
ejpam-4871	50	75	.	.	PUNCT
ejpam-4871	51	1	therefore	therefore	ADV
ejpam-4871	51	2	,	,	PUNCT
ejpam-4871	51	3	g	g	PROPN
ejpam-4871	51	4	is	be	AUX
ejpam-4871	51	5	a	a	DET
ejpam-4871	51	6	semi	semi	ADJ
ejpam-4871	51	7	-	-	ADJ
ejpam-4871	51	8	prime	prime	ADJ
ejpam-4871	51	9	group	group	NOUN
ejpam-4871	51	10	.	.	PUNCT
ejpam-4871	52	1	lemma	lemma	PROPN
ejpam-4871	52	2	4	4	X
ejpam-4871	52	3	.	.	PUNCT
ejpam-4871	53	1	let	let	VERB
ejpam-4871	53	2	g	g	PRON
ejpam-4871	53	3	be	be	AUX
ejpam-4871	53	4	a	a	DET
ejpam-4871	53	5	minimal	minimal	ADJ
ejpam-4871	53	6	group	group	NOUN
ejpam-4871	53	7	neither	neither	CCONJ
ejpam-4871	53	8	satisfying	satisfy	VERB
ejpam-4871	53	9	the	the	DET
ejpam-4871	53	10	basis	basis	NOUN
ejpam-4871	53	11	property	property	NOUN
ejpam-4871	53	12	,	,	PUNCT
ejpam-4871	53	13	nor	nor	CCONJ
ejpam-4871	53	14	soluble	soluble	ADJ
ejpam-4871	53	15	.	.	PUNCT
ejpam-4871	54	1	then	then	ADV
ejpam-4871	54	2	g	g	PROPN
ejpam-4871	54	3	is	be	AUX
ejpam-4871	54	4	not	not	PART
ejpam-4871	54	5	a	a	DET
ejpam-4871	54	6	commutative	commutative	ADJ
ejpam-4871	54	7	simple	simple	ADJ
ejpam-4871	54	8	group	group	NOUN
ejpam-4871	54	9	.	.	PUNCT
ejpam-4871	55	1	proof	proof	NOUN
ejpam-4871	55	2	.	.	PUNCT
ejpam-4871	56	1	suppose	suppose	VERB
ejpam-4871	56	2	g	g	NOUN
ejpam-4871	56	3	is	be	AUX
ejpam-4871	56	4	not	not	PART
ejpam-4871	56	5	a	a	DET
ejpam-4871	56	6	soluble	soluble	ADJ
ejpam-4871	56	7	group	group	NOUN
ejpam-4871	56	8	and	and	CCONJ
ejpam-4871	56	9	let	let	VERB
ejpam-4871	56	10	h	h	PRON
ejpam-4871	56	11	be	be	AUX
ejpam-4871	56	12	a	a	DET
ejpam-4871	56	13	maximal	maximal	ADJ
ejpam-4871	56	14	normal	normal	ADJ
ejpam-4871	56	15	subgroup	subgroup	NOUN
ejpam-4871	56	16	,	,	PUNCT
ejpam-4871	56	17	which	which	PRON
ejpam-4871	56	18	is	be	AUX
ejpam-4871	56	19	a	a	DET
ejpam-4871	56	20	soluble	soluble	ADJ
ejpam-4871	56	21	subgroup	subgroup	NOUN
ejpam-4871	56	22	of	of	ADP
ejpam-4871	56	23	g.	g.	PROPN
ejpam-4871	57	1	if	if	SCONJ
ejpam-4871	57	2	|h|	|h|	PROPN
ejpam-4871	57	3	=	=	AUX
ejpam-4871	57	4	̸	̸	NUM
ejpam-4871	57	5	e	e	NOUN
ejpam-4871	57	6	and	and	CCONJ
ejpam-4871	57	7	since	since	SCONJ
ejpam-4871	57	8	g	g	PROPN
ejpam-4871	57	9	is	be	AUX
ejpam-4871	57	10	a	a	DET
ejpam-4871	57	11	minimal	minimal	ADJ
ejpam-4871	57	12	that	that	PRON
ejpam-4871	57	13	is	be	AUX
ejpam-4871	57	14	not	not	PART
ejpam-4871	57	15	satisfying	satisfy	VERB
ejpam-4871	57	16	the	the	DET
ejpam-4871	57	17	basis	basis	NOUN
ejpam-4871	57	18	property	property	NOUN
ejpam-4871	57	19	,	,	PUNCT
ejpam-4871	57	20	then	then	ADV
ejpam-4871	57	21	g	g	PROPN
ejpam-4871	57	22	/	/	SYM
ejpam-4871	57	23	h	h	PROPN
ejpam-4871	57	24	is	be	AUX
ejpam-4871	57	25	a	a	DET
ejpam-4871	57	26	group	group	NOUN
ejpam-4871	57	27	the	the	DET
ejpam-4871	57	28	basis	basis	NOUN
ejpam-4871	57	29	property	property	NOUN
ejpam-4871	57	30	,	,	PUNCT
ejpam-4871	57	31	therefore	therefore	ADV
ejpam-4871	57	32	g	g	PROPN
ejpam-4871	57	33	/	/	SYM
ejpam-4871	57	34	h	h	NOUN
ejpam-4871	57	35	is	be	AUX
ejpam-4871	57	36	a	a	DET
ejpam-4871	57	37	soluble	soluble	ADJ
ejpam-4871	57	38	,	,	PUNCT
ejpam-4871	57	39	see	see	VERB
ejpam-4871	57	40	the	the	DET
ejpam-4871	57	41	book	book	NOUN
ejpam-4871	57	42	[	[	X
ejpam-4871	57	43	16	16	NUM
ejpam-4871	57	44	]	]	PUNCT
ejpam-4871	57	45	and	and	CCONJ
ejpam-4871	57	46	g	g	PROPN
ejpam-4871	57	47	must	must	AUX
ejpam-4871	57	48	be	be	AUX
ejpam-4871	57	49	a	a	DET
ejpam-4871	57	50	soluble	soluble	ADJ
ejpam-4871	57	51	group	group	NOUN
ejpam-4871	57	52	as	as	ADP
ejpam-4871	57	53	an	an	DET
ejpam-4871	57	54	extension	extension	NOUN
ejpam-4871	57	55	of	of	ADP
ejpam-4871	57	56	a	a	DET
ejpam-4871	57	57	soluble	soluble	ADJ
ejpam-4871	57	58	subgroup	subgroup	NOUN
ejpam-4871	57	59	by	by	ADP
ejpam-4871	57	60	the	the	DET
ejpam-4871	57	61	soluble	soluble	ADJ
ejpam-4871	57	62	group	group	NOUN
ejpam-4871	57	63	,	,	PUNCT
ejpam-4871	57	64	but	but	CCONJ
ejpam-4871	57	65	this	this	PRON
ejpam-4871	57	66	contradicts	contradict	VERB
ejpam-4871	57	67	the	the	DET
ejpam-4871	57	68	hypothesis	hypothesis	NOUN
ejpam-4871	57	69	that	that	PRON
ejpam-4871	57	70	g	g	PROPN
ejpam-4871	57	71	is	be	AUX
ejpam-4871	57	72	not	not	PART
ejpam-4871	57	73	soluble	soluble	ADJ
ejpam-4871	57	74	.	.	PUNCT
ejpam-4871	58	1	so	so	ADV
ejpam-4871	58	2	g	g	PROPN
ejpam-4871	58	3	does	do	AUX
ejpam-4871	58	4	not	not	PART
ejpam-4871	58	5	contain	contain	VERB
ejpam-4871	58	6	any	any	DET
ejpam-4871	58	7	soluble	soluble	ADJ
ejpam-4871	58	8	normal	normal	ADJ
ejpam-4871	58	9	subgroup	subgroup	NOUN
ejpam-4871	58	10	,	,	PUNCT
ejpam-4871	58	11	hence	hence	ADV
ejpam-4871	58	12	it	it	PRON
ejpam-4871	58	13	is	be	AUX
ejpam-4871	58	14	a	a	DET
ejpam-4871	58	15	semisimple	semisimple	NOUN
ejpam-4871	58	16	,	,	PUNCT
ejpam-4871	58	17	by	by	ADP
ejpam-4871	58	18	using	use	VERB
ejpam-4871	58	19	[	[	X
ejpam-4871	58	20	9	9	NUM
ejpam-4871	58	21	]	]	PUNCT
ejpam-4871	58	22	.	.	PUNCT
ejpam-4871	59	1	thus	thus	ADV
ejpam-4871	59	2	g	g	PROPN
ejpam-4871	59	3	contains	contain	VERB
ejpam-4871	59	4	a	a	DET
ejpam-4871	59	5	maximal	maximal	ADJ
ejpam-4871	59	6	normal	normal	ADJ
ejpam-4871	59	7	subgroup	subgroup	NOUN
ejpam-4871	59	8	a	a	PRON
ejpam-4871	59	9	that	that	PRON
ejpam-4871	59	10	is	be	AUX
ejpam-4871	59	11	completely	completely	ADV
ejpam-4871	59	12	decompose	decompose	VERB
ejpam-4871	59	13	without	without	ADP
ejpam-4871	59	14	center	center	NOUN
ejpam-4871	59	15	,	,	PUNCT
ejpam-4871	59	16	so	so	ADV
ejpam-4871	59	17	the	the	DET
ejpam-4871	59	18	group	group	NOUN
ejpam-4871	59	19	g	g	PROPN
ejpam-4871	59	20	is	be	AUX
ejpam-4871	59	21	embedding	embed	VERB
ejpam-4871	59	22	in	in	ADP
ejpam-4871	59	23	the	the	DET
ejpam-4871	59	24	group	group	NOUN
ejpam-4871	59	25	automorphisms	automorphisms	PROPN
ejpam-4871	59	26	auta	auta	PROPN
ejpam-4871	59	27	.	.	PUNCT
ejpam-4871	60	1	if	if	SCONJ
ejpam-4871	60	2	a	a	PRON
ejpam-4871	60	3	coincides	coincide	VERB
ejpam-4871	60	4	the	the	DET
ejpam-4871	60	5	group	group	NOUN
ejpam-4871	60	6	of	of	ADP
ejpam-4871	60	7	inner	inner	ADJ
ejpam-4871	60	8	automorphisms	automorphism	NOUN
ejpam-4871	60	9	of	of	ADP
ejpam-4871	60	10	a	a	DET
ejpam-4871	60	11	,	,	PUNCT
ejpam-4871	60	12	then	then	ADV
ejpam-4871	60	13	a	a	DET
ejpam-4871	60	14	=	=	PUNCT
ejpam-4871	60	15	a1	a1	PROPN
ejpam-4871	60	16	·	·	PUNCT
ejpam-4871	60	17	a2	a2	PROPN
ejpam-4871	60	18	·	·	PUNCT
ejpam-4871	60	19	.	.	PUNCT
ejpam-4871	60	20	.	.	PUNCT
ejpam-4871	61	1	.	.	PUNCT
ejpam-4871	62	1	·	·	PUNCT
ejpam-4871	62	2	am	be	AUX
ejpam-4871	62	3	,	,	PUNCT
ejpam-4871	62	4	where	where	SCONJ
ejpam-4871	62	5	ai	ai	NOUN
ejpam-4871	62	6	are	be	AUX
ejpam-4871	62	7	simple	simple	ADJ
ejpam-4871	62	8	groups	group	NOUN
ejpam-4871	62	9	.	.	PUNCT
ejpam-4871	63	1	since	since	SCONJ
ejpam-4871	63	2	a	a	DET
ejpam-4871	63	3	group	group	NOUN
ejpam-4871	63	4	a	a	PRON
ejpam-4871	63	5	without	without	ADP
ejpam-4871	63	6	center	center	NOUN
ejpam-4871	63	7	,	,	PUNCT
ejpam-4871	63	8	then	then	ADV
ejpam-4871	63	9	a	a	PRON
ejpam-4871	63	10	has	have	VERB
ejpam-4871	63	11	no	no	DET
ejpam-4871	63	12	a	a	DET
ejpam-4871	63	13	subgroup	subgroup	NOUN
ejpam-4871	63	14	of	of	ADP
ejpam-4871	63	15	a	a	DET
ejpam-4871	63	16	prime	prime	ADJ
ejpam-4871	63	17	order	order	NOUN
ejpam-4871	63	18	.	.	PUNCT
ejpam-4871	64	1	thus	thus	ADV
ejpam-4871	64	2	ai	ai	VERB
ejpam-4871	64	3	are	be	AUX
ejpam-4871	64	4	simple	simple	ADJ
ejpam-4871	64	5	and	and	CCONJ
ejpam-4871	64	6	non	non	ADJ
ejpam-4871	64	7	commutative	commutative	ADJ
ejpam-4871	64	8	subgroups	subgroup	NOUN
ejpam-4871	64	9	.	.	PUNCT
ejpam-4871	65	1	in	in	ADP
ejpam-4871	65	2	the	the	DET
ejpam-4871	65	3	case	case	NOUN
ejpam-4871	65	4	of	of	ADP
ejpam-4871	65	5	m	m	PROPN
ejpam-4871	65	6	>	>	X
ejpam-4871	65	7	1	1	NUM
ejpam-4871	65	8	,	,	PUNCT
ejpam-4871	65	9	then	then	ADV
ejpam-4871	65	10	a1	a1	NOUN
ejpam-4871	65	11	is	be	AUX
ejpam-4871	65	12	a	a	DET
ejpam-4871	65	13	proper	proper	ADJ
ejpam-4871	65	14	subgroup	subgroup	NOUN
ejpam-4871	65	15	of	of	ADP
ejpam-4871	65	16	g	g	PROPN
ejpam-4871	65	17	,	,	PUNCT
ejpam-4871	65	18	therefore	therefore	ADV
ejpam-4871	65	19	,	,	PUNCT
ejpam-4871	65	20	according	accord	VERB
ejpam-4871	65	21	to	to	ADP
ejpam-4871	65	22	the	the	DET
ejpam-4871	65	23	definition	definition	NOUN
ejpam-4871	65	24	of	of	ADP
ejpam-4871	65	25	a	a	DET
ejpam-4871	65	26	minimal	minimal	ADJ
ejpam-4871	65	27	simple	simple	ADJ
ejpam-4871	65	28	group	group	NOUN
ejpam-4871	65	29	that	that	PRON
ejpam-4871	65	30	does	do	AUX
ejpam-4871	65	31	not	not	PART
ejpam-4871	65	32	satisfy	satisfy	VERB
ejpam-4871	65	33	the	the	DET
ejpam-4871	65	34	basis	basis	NOUN
ejpam-4871	65	35	property	property	NOUN
ejpam-4871	65	36	,	,	PUNCT
ejpam-4871	65	37	hence	hence	ADV
ejpam-4871	65	38	a1	a1	NOUN
ejpam-4871	65	39	is	be	AUX
ejpam-4871	65	40	a	a	DET
ejpam-4871	65	41	group	group	NOUN
ejpam-4871	65	42	with	with	ADP
ejpam-4871	65	43	the	the	DET
ejpam-4871	65	44	basis	basis	NOUN
ejpam-4871	65	45	property	property	NOUN
ejpam-4871	65	46	,	,	PUNCT
ejpam-4871	65	47	but	but	CCONJ
ejpam-4871	65	48	this	this	PRON
ejpam-4871	65	49	contradicts	contradict	VERB
ejpam-4871	65	50	the	the	DET
ejpam-4871	65	51	concept	concept	NOUN
ejpam-4871	65	52	that	that	SCONJ
ejpam-4871	65	53	the	the	DET
ejpam-4871	65	54	group	group	NOUN
ejpam-4871	65	55	that	that	PRON
ejpam-4871	65	56	achieves	achieve	VERB
ejpam-4871	65	57	the	the	DET
ejpam-4871	65	58	basis	basis	NOUN
ejpam-4871	65	59	property	property	NOUN
ejpam-4871	65	60	is	be	AUX
ejpam-4871	65	61	a	a	DET
ejpam-4871	65	62	soluble	soluble	ADJ
ejpam-4871	65	63	as	as	ADP
ejpam-4871	65	64	in	in	ADP
ejpam-4871	65	65	[	[	X
ejpam-4871	65	66	13	13	NUM
ejpam-4871	65	67	]	]	PUNCT
ejpam-4871	65	68	.	.	PUNCT
ejpam-4871	66	1	so	so	ADV
ejpam-4871	66	2	the	the	DET
ejpam-4871	66	3	group	group	NOUN
ejpam-4871	66	4	a	a	PROPN
ejpam-4871	66	5	is	be	AUX
ejpam-4871	66	6	simple	simple	ADJ
ejpam-4871	66	7	.	.	PUNCT
ejpam-4871	67	1	suppose	suppose	VERB
ejpam-4871	67	2	that	that	SCONJ
ejpam-4871	67	3	g	g	PROPN
ejpam-4871	67	4	̸=	̸=	PROPN
ejpam-4871	67	5	a.	a.	NOUN
ejpam-4871	67	6	then	then	ADV
ejpam-4871	67	7	a	a	PRON
ejpam-4871	67	8	is	be	AUX
ejpam-4871	67	9	a	a	DET
ejpam-4871	67	10	proper	proper	ADJ
ejpam-4871	67	11	subgroup	subgroup	NOUN
ejpam-4871	67	12	of	of	ADP
ejpam-4871	67	13	the	the	DET
ejpam-4871	67	14	group	group	NOUN
ejpam-4871	67	15	g	g	NOUN
ejpam-4871	67	16	,	,	PUNCT
ejpam-4871	67	17	therefore	therefore	ADV
ejpam-4871	67	18	,	,	PUNCT
ejpam-4871	67	19	it	it	PRON
ejpam-4871	67	20	is	be	AUX
ejpam-4871	67	21	a	a	DET
ejpam-4871	67	22	group	group	NOUN
ejpam-4871	67	23	with	with	ADP
ejpam-4871	67	24	the	the	DET
ejpam-4871	67	25	basis	basis	NOUN
ejpam-4871	67	26	property	property	NOUN
ejpam-4871	67	27	.	.	PUNCT
ejpam-4871	68	1	this	this	PRON
ejpam-4871	68	2	is	be	AUX
ejpam-4871	68	3	a	a	DET
ejpam-4871	68	4	contradiction	contradiction	NOUN
ejpam-4871	68	5	of	of	ADP
ejpam-4871	68	6	the	the	DET
ejpam-4871	68	7	solubility	solubility	NOUN
ejpam-4871	68	8	of	of	ADP
ejpam-4871	68	9	the	the	DET
ejpam-4871	68	10	group	group	NOUN
ejpam-4871	68	11	with	with	ADP
ejpam-4871	68	12	the	the	DET
ejpam-4871	68	13	basis	basis	NOUN
ejpam-4871	68	14	property	property	NOUN
ejpam-4871	68	15	.	.	PUNCT
ejpam-4871	69	1	corollary	corollary	ADJ
ejpam-4871	69	2	1	1	NUM
ejpam-4871	69	3	.	.	PUNCT
ejpam-4871	70	1	let	let	VERB
ejpam-4871	70	2	g	g	PRON
ejpam-4871	70	3	be	be	AUX
ejpam-4871	70	4	a	a	DET
ejpam-4871	70	5	minimal	minimal	ADJ
ejpam-4871	70	6	group	group	NOUN
ejpam-4871	70	7	that	that	PRON
ejpam-4871	70	8	does	do	AUX
ejpam-4871	70	9	not	not	PART
ejpam-4871	70	10	satisfy	satisfy	VERB
ejpam-4871	70	11	the	the	DET
ejpam-4871	70	12	basis	basis	NOUN
ejpam-4871	70	13	property	property	NOUN
ejpam-4871	70	14	,	,	PUNCT
ejpam-4871	70	15	then	then	ADV
ejpam-4871	70	16	g	g	PROPN
ejpam-4871	70	17	is	be	AUX
ejpam-4871	70	18	semi	semi	ADJ
ejpam-4871	70	19	-	-	ADJ
ejpam-4871	70	20	prime	prime	ADJ
ejpam-4871	70	21	,	,	PUNCT
ejpam-4871	70	22	and	and	CCONJ
ejpam-4871	70	23	if	if	SCONJ
ejpam-4871	70	24	g	g	PROPN
ejpam-4871	70	25	is	be	AUX
ejpam-4871	70	26	a	a	DET
ejpam-4871	70	27	not	not	PART
ejpam-4871	70	28	soluble	soluble	ADJ
ejpam-4871	70	29	,	,	PUNCT
ejpam-4871	70	30	then	then	ADV
ejpam-4871	70	31	it	it	PRON
ejpam-4871	70	32	must	must	AUX
ejpam-4871	70	33	be	be	AUX
ejpam-4871	70	34	simple	simple	ADJ
ejpam-4871	70	35	and	and	CCONJ
ejpam-4871	70	36	noncommutative	noncommutative	ADJ
ejpam-4871	70	37	.	.	PUNCT
ejpam-4871	71	1	a.	a.	PROPN
ejpam-4871	71	2	al	al	PROPN
ejpam-4871	71	3	khalaf	khalaf	PROPN
ejpam-4871	71	4	,	,	PUNCT
ejpam-4871	71	5	i.	i.	PROPN
ejpam-4871	71	6	taha	taha	PROPN
ejpam-4871	71	7	/	/	PUNCT
ejpam-4871	71	8	eur	eur	PROPN
ejpam-4871	71	9	.	.	PUNCT
ejpam-4871	72	1	j.	j.	PROPN
ejpam-4871	72	2	pure	pure	PROPN
ejpam-4871	72	3	appl	appl	PROPN
ejpam-4871	72	4	.	.	PROPN
ejpam-4871	72	5	math	math	PROPN
ejpam-4871	72	6	,	,	PUNCT
ejpam-4871	72	7	16	16	NUM
ejpam-4871	72	8	(	(	PUNCT
ejpam-4871	72	9	3	3	NUM
ejpam-4871	72	10	)	)	PUNCT
ejpam-4871	72	11	(	(	PUNCT
ejpam-4871	72	12	2023	2023	NUM
ejpam-4871	72	13	)	)	PUNCT
ejpam-4871	72	14	,	,	PUNCT
ejpam-4871	72	15	1970	1970	NUM
ejpam-4871	72	16	-	-	SYM
ejpam-4871	72	17	1979	1979	NUM
ejpam-4871	72	18	1973	1973	NUM
ejpam-4871	72	19	remark	remark	NOUN
ejpam-4871	72	20	1	1	NUM
ejpam-4871	72	21	.	.	PUNCT
ejpam-4871	73	1	the	the	DET
ejpam-4871	73	2	general	general	ADJ
ejpam-4871	73	3	linear	linear	PROPN
ejpam-4871	73	4	projective	projective	ADJ
ejpam-4871	73	5	groups	group	NOUN
ejpam-4871	73	6	pgl(2	pgl(2	NOUN
ejpam-4871	73	7	,	,	PUNCT
ejpam-4871	73	8	q	q	NOUN
ejpam-4871	73	9	)	)	PUNCT
ejpam-4871	73	10	,	,	PUNCT
ejpam-4871	73	11	where	where	SCONJ
ejpam-4871	73	12	q	q	PROPN
ejpam-4871	73	13	≥	≥	NUM
ejpam-4871	73	14	5	5	NUM
ejpam-4871	73	15	,	,	PUNCT
ejpam-4871	73	16	which	which	PRON
ejpam-4871	73	17	q	q	NOUN
ejpam-4871	73	18	is	be	AUX
ejpam-4871	73	19	an	an	DET
ejpam-4871	73	20	odd	odd	ADJ
ejpam-4871	73	21	number	number	NOUN
ejpam-4871	73	22	,	,	PUNCT
ejpam-4871	73	23	are	be	AUX
ejpam-4871	73	24	not	not	PART
ejpam-4871	73	25	simple	simple	ADJ
ejpam-4871	73	26	,	,	PUNCT
ejpam-4871	73	27	see	see	VERB
ejpam-4871	73	28	that	that	SCONJ
ejpam-4871	73	29	in	in	ADP
ejpam-4871	73	30	[	[	X
ejpam-4871	73	31	19	19	NUM
ejpam-4871	73	32	,	,	PUNCT
ejpam-4871	73	33	20	20	NUM
ejpam-4871	73	34	]	]	PUNCT
ejpam-4871	73	35	,	,	PUNCT
ejpam-4871	73	36	but	but	CCONJ
ejpam-4871	73	37	,	,	PUNCT
ejpam-4871	73	38	psl(2	psl(2	NOUN
ejpam-4871	73	39	,	,	PUNCT
ejpam-4871	73	40	q	q	X
ejpam-4871	73	41	)	)	PUNCT
ejpam-4871	73	42	is	be	AUX
ejpam-4871	73	43	simple	simple	ADJ
ejpam-4871	73	44	for	for	ADP
ejpam-4871	73	45	q	q	PROPN
ejpam-4871	73	46	≥	≥	NUM
ejpam-4871	73	47	4	4	NUM
ejpam-4871	73	48	.	.	PUNCT
ejpam-4871	74	1	we	we	PRON
ejpam-4871	74	2	can	can	AUX
ejpam-4871	74	3	also	also	ADV
ejpam-4871	74	4	getting	get	VERB
ejpam-4871	74	5	on	on	ADP
ejpam-4871	74	6	more	more	ADJ
ejpam-4871	74	7	details	detail	NOUN
ejpam-4871	74	8	about	about	ADP
ejpam-4871	74	9	this	this	DET
ejpam-4871	74	10	kind	kind	NOUN
ejpam-4871	74	11	of	of	ADP
ejpam-4871	74	12	groups	group	NOUN
ejpam-4871	74	13	in	in	ADP
ejpam-4871	74	14	[	[	X
ejpam-4871	74	15	19	19	NUM
ejpam-4871	74	16	]	]	PUNCT
ejpam-4871	74	17	.	.	PUNCT
ejpam-4871	75	1	since	since	SCONJ
ejpam-4871	75	2	the	the	DET
ejpam-4871	75	3	groups	group	NOUN
ejpam-4871	75	4	pgl(2	pgl(2	NOUN
ejpam-4871	75	5	,	,	PUNCT
ejpam-4871	75	6	q	q	X
ejpam-4871	75	7	)	)	PUNCT
ejpam-4871	75	8	for	for	ADP
ejpam-4871	75	9	each	each	DET
ejpam-4871	75	10	q	q	ADJ
ejpam-4871	75	11	≥	≥	NUM
ejpam-4871	75	12	5	5	NUM
ejpam-4871	75	13	and	and	CCONJ
ejpam-4871	75	14	q	q	NOUN
ejpam-4871	75	15	is	be	AUX
ejpam-4871	75	16	odd	odd	ADJ
ejpam-4871	75	17	are	be	AUX
ejpam-4871	75	18	not	not	PART
ejpam-4871	75	19	simple	simple	ADJ
ejpam-4871	75	20	.	.	PUNCT
ejpam-4871	76	1	so	so	ADV
ejpam-4871	76	2	,	,	PUNCT
ejpam-4871	76	3	we	we	PRON
ejpam-4871	76	4	can	can	AUX
ejpam-4871	76	5	remove	remove	VERB
ejpam-4871	76	6	it	it	PRON
ejpam-4871	76	7	from	from	ADP
ejpam-4871	76	8	the	the	DET
ejpam-4871	76	9	class	class	NOUN
ejpam-4871	76	10	of	of	ADP
ejpam-4871	76	11	the	the	DET
ejpam-4871	76	12	minimal	minimal	ADJ
ejpam-4871	76	13	simple	simple	ADJ
ejpam-4871	76	14	group	group	NOUN
ejpam-4871	76	15	that	that	PRON
ejpam-4871	76	16	does	do	AUX
ejpam-4871	76	17	not	not	PART
ejpam-4871	76	18	satisfy	satisfy	VERB
ejpam-4871	76	19	the	the	DET
ejpam-4871	76	20	basis	basis	NOUN
ejpam-4871	76	21	property	property	NOUN
ejpam-4871	76	22	.	.	PUNCT
ejpam-4871	77	1	example	example	NOUN
ejpam-4871	78	1	1	1	NUM
ejpam-4871	78	2	.	.	PUNCT
ejpam-4871	79	1	if	if	SCONJ
ejpam-4871	79	2	g	g	PROPN
ejpam-4871	79	3	=	=	SYM
ejpam-4871	79	4	s4	s4	PROPN
ejpam-4871	79	5	=	=	SYM
ejpam-4871	79	6	<	<	X
ejpam-4871	79	7	α	α	PROPN
ejpam-4871	79	8	,	,	PUNCT
ejpam-4871	79	9	β	β	X
ejpam-4871	79	10	>	>	X
ejpam-4871	79	11	is	be	AUX
ejpam-4871	79	12	a	a	DET
ejpam-4871	79	13	symmetric	symmetric	ADJ
ejpam-4871	79	14	group	group	NOUN
ejpam-4871	79	15	s4	s4	NOUN
ejpam-4871	79	16	does	do	AUX
ejpam-4871	79	17	not	not	PART
ejpam-4871	79	18	satisfy	satisfy	VERB
ejpam-4871	79	19	the	the	DET
ejpam-4871	79	20	basis	basis	NOUN
ejpam-4871	79	21	property	property	NOUN
ejpam-4871	79	22	,	,	PUNCT
ejpam-4871	79	23	such	such	ADJ
ejpam-4871	79	24	that	that	SCONJ
ejpam-4871	79	25	α	α	NOUN
ejpam-4871	79	26	=	=	X
ejpam-4871	79	27	(	(	PUNCT
ejpam-4871	79	28	1234	1234	NUM
ejpam-4871	79	29	)	)	PUNCT
ejpam-4871	79	30	,	,	PUNCT
ejpam-4871	79	31	β	β	X
ejpam-4871	79	32	=	=	SYM
ejpam-4871	79	33	(	(	PUNCT
ejpam-4871	79	34	142	142	NUM
ejpam-4871	79	35	)	)	PUNCT
ejpam-4871	79	36	,	,	PUNCT
ejpam-4871	79	37	then	then	ADV
ejpam-4871	79	38	α2	α2	PROPN
ejpam-4871	79	39	=	=	SYM
ejpam-4871	79	40	(	(	PUNCT
ejpam-4871	79	41	13)(24	13)(24	NUM
ejpam-4871	79	42	)	)	PUNCT
ejpam-4871	79	43	and	and	CCONJ
ejpam-4871	79	44	α2β	α2β	PROPN
ejpam-4871	79	45	=	=	SYM
ejpam-4871	79	46	(	(	PUNCT
ejpam-4871	79	47	34	34	NUM
ejpam-4871	79	48	)	)	PUNCT
ejpam-4871	79	49	,	,	PUNCT
ejpam-4871	79	50	βα3β	βα3β	PROPN
ejpam-4871	79	51	=	=	SYM
ejpam-4871	79	52	(	(	PUNCT
ejpam-4871	79	53	13	13	NUM
ejpam-4871	79	54	)	)	PUNCT
ejpam-4871	79	55	.	.	PUNCT
ejpam-4871	80	1	for	for	ADP
ejpam-4871	80	2	more	more	ADJ
ejpam-4871	80	3	,	,	PUNCT
ejpam-4871	80	4	we	we	PRON
ejpam-4871	80	5	can	can	AUX
ejpam-4871	80	6	find	find	VERB
ejpam-4871	80	7	that	that	SCONJ
ejpam-4871	80	8	g	g	PROPN
ejpam-4871	80	9	=	=	PUNCT
ejpam-4871	80	10	s4	s4	PROPN
ejpam-4871	80	11	=	=	X
ejpam-4871	80	12	<	<	X
ejpam-4871	80	13	α2	α2	PROPN
ejpam-4871	80	14	,	,	PUNCT
ejpam-4871	80	15	α2β	α2β	NOUN
ejpam-4871	80	16	,	,	PUNCT
ejpam-4871	80	17	βα3β	βα3β	PROPN
ejpam-4871	80	18	>	>	PUNCT
ejpam-4871	80	19	that	that	PRON
ejpam-4871	80	20	means	mean	VERB
ejpam-4871	80	21	,	,	PUNCT
ejpam-4871	80	22	there	there	PRON
ejpam-4871	80	23	are	be	VERB
ejpam-4871	80	24	two	two	NUM
ejpam-4871	80	25	bases	basis	NOUN
ejpam-4871	80	26	for	for	ADP
ejpam-4871	80	27	the	the	DET
ejpam-4871	80	28	symmetric	symmetric	ADJ
ejpam-4871	80	29	group	group	NOUN
ejpam-4871	80	30	s4	s4	PROPN
ejpam-4871	80	31	,	,	PUNCT
ejpam-4871	80	32	first	first	ADV
ejpam-4871	80	33	of	of	ADP
ejpam-4871	80	34	them	they	PRON
ejpam-4871	80	35	consists	consist	VERB
ejpam-4871	80	36	of	of	ADP
ejpam-4871	80	37	three	three	NUM
ejpam-4871	80	38	elements	element	NOUN
ejpam-4871	80	39	and	and	CCONJ
ejpam-4871	80	40	the	the	DET
ejpam-4871	80	41	other	other	ADJ
ejpam-4871	80	42	one	one	NOUN
ejpam-4871	80	43	has	have	VERB
ejpam-4871	80	44	two	two	NUM
ejpam-4871	80	45	elements	element	NOUN
ejpam-4871	80	46	,	,	PUNCT
ejpam-4871	80	47	but	but	CCONJ
ejpam-4871	80	48	,	,	PUNCT
ejpam-4871	80	49	this	this	PRON
ejpam-4871	80	50	contradicts	contradict	VERB
ejpam-4871	80	51	the	the	DET
ejpam-4871	80	52	concept	concept	NOUN
ejpam-4871	80	53	of	of	ADP
ejpam-4871	80	54	the	the	DET
ejpam-4871	80	55	basis	basis	NOUN
ejpam-4871	80	56	property	property	NOUN
ejpam-4871	80	57	.	.	PUNCT
ejpam-4871	81	1	so	so	ADV
ejpam-4871	81	2	the	the	DET
ejpam-4871	81	3	group	group	NOUN
ejpam-4871	81	4	does	do	AUX
ejpam-4871	81	5	not	not	PART
ejpam-4871	81	6	satisfy	satisfy	VERB
ejpam-4871	81	7	the	the	DET
ejpam-4871	81	8	basis	basis	NOUN
ejpam-4871	81	9	property	property	NOUN
ejpam-4871	81	10	.	.	PUNCT
ejpam-4871	82	1	lemma	lemma	PROPN
ejpam-4871	82	2	5	5	NUM
ejpam-4871	82	3	.	.	PUNCT
ejpam-4871	83	1	the	the	DET
ejpam-4871	83	2	groups	group	NOUN
ejpam-4871	83	3	psl(2	psl(2	NOUN
ejpam-4871	83	4	,	,	PUNCT
ejpam-4871	83	5	7	7	NUM
ejpam-4871	83	6	)	)	PUNCT
ejpam-4871	83	7	,	,	PUNCT
ejpam-4871	83	8	psl(2	psl(2	NOUN
ejpam-4871	83	9	,	,	PUNCT
ejpam-4871	83	10	32	32	NUM
ejpam-4871	83	11	)	)	PUNCT
ejpam-4871	83	12	,	,	PUNCT
ejpam-4871	83	13	psl(2	psl(2	NOUN
ejpam-4871	83	14	,	,	PUNCT
ejpam-4871	83	15	17	17	NUM
ejpam-4871	83	16	)	)	PUNCT
ejpam-4871	83	17	,	,	PUNCT
ejpam-4871	83	18	are	be	AUX
ejpam-4871	83	19	semi	semi	ADJ
ejpam-4871	83	20	-	-	ADJ
ejpam-4871	83	21	prime	prime	ADJ
ejpam-4871	83	22	that	that	PRON
ejpam-4871	83	23	not	not	PART
ejpam-4871	83	24	satisfy	satisfy	VERB
ejpam-4871	83	25	the	the	DET
ejpam-4871	83	26	basis	basis	NOUN
ejpam-4871	83	27	property	property	NOUN
ejpam-4871	83	28	,	,	PUNCT
ejpam-4871	83	29	but	but	CCONJ
ejpam-4871	83	30	,	,	PUNCT
ejpam-4871	83	31	they	they	PRON
ejpam-4871	83	32	are	be	AUX
ejpam-4871	83	33	not	not	PART
ejpam-4871	83	34	minimal	minimal	ADJ
ejpam-4871	83	35	.	.	PUNCT
ejpam-4871	84	1	proof	proof	NOUN
ejpam-4871	84	2	.	.	PUNCT
ejpam-4871	85	1	according	accord	VERB
ejpam-4871	85	2	to	to	ADP
ejpam-4871	85	3	the	the	DET
ejpam-4871	85	4	article	article	NOUN
ejpam-4871	85	5	[	[	X
ejpam-4871	85	6	19	19	NUM
ejpam-4871	85	7	]	]	PUNCT
ejpam-4871	85	8	,	,	PUNCT
ejpam-4871	85	9	we	we	PRON
ejpam-4871	85	10	saw	see	VERB
ejpam-4871	85	11	that	that	SCONJ
ejpam-4871	85	12	the	the	DET
ejpam-4871	85	13	three	three	NUM
ejpam-4871	85	14	previous	previous	ADJ
ejpam-4871	85	15	groups	group	NOUN
ejpam-4871	85	16	are	be	AUX
ejpam-4871	85	17	semiprime	semiprime	ADJ
ejpam-4871	85	18	,	,	PUNCT
ejpam-4871	85	19	also	also	ADV
ejpam-4871	85	20	,	,	PUNCT
ejpam-4871	85	21	since	since	SCONJ
ejpam-4871	85	22	they	they	PRON
ejpam-4871	85	23	are	be	AUX
ejpam-4871	85	24	simple	simple	ADJ
ejpam-4871	85	25	,	,	PUNCT
ejpam-4871	85	26	then	then	ADV
ejpam-4871	85	27	,	,	PUNCT
ejpam-4871	85	28	they	they	PRON
ejpam-4871	85	29	must	must	AUX
ejpam-4871	85	30	not	not	PART
ejpam-4871	85	31	to	to	PART
ejpam-4871	85	32	be	be	AUX
ejpam-4871	85	33	a	a	DET
ejpam-4871	85	34	soluble	soluble	ADJ
ejpam-4871	85	35	.	.	PUNCT
ejpam-4871	86	1	according	accord	VERB
ejpam-4871	86	2	to	to	ADP
ejpam-4871	86	3	[	[	X
ejpam-4871	86	4	13	13	NUM
ejpam-4871	86	5	]	]	PUNCT
ejpam-4871	86	6	,	,	PUNCT
ejpam-4871	86	7	the	the	DET
ejpam-4871	86	8	groups	group	NOUN
ejpam-4871	86	9	do	do	AUX
ejpam-4871	86	10	not	not	PART
ejpam-4871	86	11	satisfy	satisfy	VERB
ejpam-4871	86	12	the	the	DET
ejpam-4871	86	13	basis	basis	NOUN
ejpam-4871	86	14	property	property	NOUN
ejpam-4871	86	15	.	.	PUNCT
ejpam-4871	87	1	now	now	ADV
ejpam-4871	87	2	by	by	ADP
ejpam-4871	87	3	[	[	X
ejpam-4871	87	4	19	19	NUM
ejpam-4871	87	5	]	]	PUNCT
ejpam-4871	87	6	,	,	PUNCT
ejpam-4871	87	7	the	the	DET
ejpam-4871	87	8	order	order	NOUN
ejpam-4871	87	9	of	of	ADP
ejpam-4871	87	10	the	the	DET
ejpam-4871	87	11	field	field	NOUN
ejpam-4871	87	12	gf	gf	X
ejpam-4871	87	13	(	(	PUNCT
ejpam-4871	87	14	q	q	X
ejpam-4871	87	15	)	)	PUNCT
ejpam-4871	87	16	has	have	VERB
ejpam-4871	87	17	the	the	DET
ejpam-4871	87	18	form	form	NOUN
ejpam-4871	87	19	q	q	NOUN
ejpam-4871	87	20	=	=	SYM
ejpam-4871	87	21	8h	8h	NUM
ejpam-4871	87	22	±	±	NUM
ejpam-4871	87	23	1	1	NUM
ejpam-4871	87	24	,	,	PUNCT
ejpam-4871	87	25	where	where	SCONJ
ejpam-4871	87	26	q	q	NOUN
ejpam-4871	87	27	=	=	SYM
ejpam-4871	87	28	7	7	NUM
ejpam-4871	87	29	,	,	PUNCT
ejpam-4871	87	30	q	q	NOUN
ejpam-4871	87	31	=	=	SYM
ejpam-4871	87	32	9	9	NUM
ejpam-4871	87	33	or	or	CCONJ
ejpam-4871	87	34	q	q	NOUN
ejpam-4871	87	35	=	=	SYM
ejpam-4871	87	36	17	17	NUM
ejpam-4871	87	37	,	,	PUNCT
ejpam-4871	87	38	then	then	ADV
ejpam-4871	87	39	each	each	PRON
ejpam-4871	87	40	of	of	ADP
ejpam-4871	87	41	the	the	DET
ejpam-4871	87	42	previous	previous	ADJ
ejpam-4871	87	43	groups	group	NOUN
ejpam-4871	87	44	must	must	AUX
ejpam-4871	87	45	contains	contain	VERB
ejpam-4871	87	46	a	a	DET
ejpam-4871	87	47	proper	proper	ADJ
ejpam-4871	87	48	subgroup	subgroup	NOUN
ejpam-4871	87	49	that	that	PRON
ejpam-4871	87	50	is	be	AUX
ejpam-4871	87	51	isomorphic	isomorphic	ADJ
ejpam-4871	87	52	to	to	ADP
ejpam-4871	87	53	the	the	DET
ejpam-4871	87	54	symmetric	symmetric	ADJ
ejpam-4871	87	55	group	group	NOUN
ejpam-4871	87	56	s4	s4	PROPN
ejpam-4871	87	57	,	,	PUNCT
ejpam-4871	87	58	and	and	CCONJ
ejpam-4871	87	59	according	accord	VERB
ejpam-4871	87	60	to	to	ADP
ejpam-4871	87	61	example	example	NOUN
ejpam-4871	87	62	1	1	NUM
ejpam-4871	87	63	,	,	PUNCT
ejpam-4871	87	64	the	the	DET
ejpam-4871	87	65	group	group	NOUN
ejpam-4871	87	66	s4	s4	PROPN
ejpam-4871	87	67	does	do	AUX
ejpam-4871	87	68	not	not	PART
ejpam-4871	87	69	satisfy	satisfy	VERB
ejpam-4871	87	70	the	the	DET
ejpam-4871	87	71	basis	basis	NOUN
ejpam-4871	87	72	property	property	NOUN
ejpam-4871	87	73	,	,	PUNCT
ejpam-4871	87	74	therefore	therefore	ADV
ejpam-4871	87	75	the	the	DET
ejpam-4871	87	76	groups	group	NOUN
ejpam-4871	87	77	q	q	X
ejpam-4871	87	78	=	=	SYM
ejpam-4871	87	79	7	7	NUM
ejpam-4871	87	80	,	,	PUNCT
ejpam-4871	87	81	q	q	NOUN
ejpam-4871	87	82	=	=	SYM
ejpam-4871	87	83	9	9	NUM
ejpam-4871	87	84	or	or	CCONJ
ejpam-4871	87	85	q	q	NOUN
ejpam-4871	87	86	=	=	NOUN
ejpam-4871	87	87	17	17	NUM
ejpam-4871	87	88	where	where	SCONJ
ejpam-4871	87	89	q	q	NOUN
ejpam-4871	88	1	=	=	SYM
ejpam-4871	88	2	7	7	NUM
ejpam-4871	88	3	,	,	PUNCT
ejpam-4871	88	4	q	q	NOUN
ejpam-4871	88	5	=	=	SYM
ejpam-4871	88	6	9	9	NUM
ejpam-4871	88	7	or	or	CCONJ
ejpam-4871	88	8	q	q	NOUN
ejpam-4871	89	1	=	=	SYM
ejpam-4871	89	2	17	17	NUM
ejpam-4871	89	3	are	be	AUX
ejpam-4871	89	4	not	not	PART
ejpam-4871	89	5	minimal	minimal	ADJ
ejpam-4871	89	6	.	.	PUNCT
ejpam-4871	90	1	4	4	X
ejpam-4871	90	2	.	.	X
ejpam-4871	90	3	the	the	DET
ejpam-4871	90	4	minimal	minimal	ADJ
ejpam-4871	90	5	simple	simple	ADJ
ejpam-4871	90	6	groups	group	NOUN
ejpam-4871	90	7	theorem	theorem	VERB
ejpam-4871	90	8	1	1	NUM
ejpam-4871	90	9	.	.	PUNCT
ejpam-4871	91	1	a	a	DET
ejpam-4871	91	2	group	group	NOUN
ejpam-4871	91	3	g	g	NOUN
ejpam-4871	91	4	=	=	NOUN
ejpam-4871	91	5	psl(2	psl(2	NOUN
ejpam-4871	91	6	,	,	PUNCT
ejpam-4871	91	7	5	5	NUM
ejpam-4871	91	8	)	)	PUNCT
ejpam-4871	91	9	is	be	AUX
ejpam-4871	91	10	a	a	DET
ejpam-4871	91	11	minimal	minimal	ADJ
ejpam-4871	91	12	does	do	AUX
ejpam-4871	91	13	not	not	PART
ejpam-4871	91	14	satisfy	satisfy	VERB
ejpam-4871	91	15	the	the	DET
ejpam-4871	91	16	basis	basis	NOUN
ejpam-4871	91	17	property	property	NOUN
ejpam-4871	91	18	.	.	PUNCT
ejpam-4871	92	1	proof	proof	NOUN
ejpam-4871	92	2	.	.	PUNCT
ejpam-4871	93	1	according	accord	VERB
ejpam-4871	93	2	to	to	ADP
ejpam-4871	93	3	[	[	X
ejpam-4871	93	4	19	19	NUM
ejpam-4871	93	5	]	]	PUNCT
ejpam-4871	93	6	,	,	PUNCT
ejpam-4871	93	7	the	the	DET
ejpam-4871	93	8	groups	group	NOUN
ejpam-4871	93	9	,	,	PUNCT
ejpam-4871	93	10	which	which	PRON
ejpam-4871	93	11	of	of	ADP
ejpam-4871	93	12	the	the	DET
ejpam-4871	93	13	form	form	NOUN
ejpam-4871	93	14	psl(2	psl(2	NOUN
ejpam-4871	93	15	,	,	PUNCT
ejpam-4871	93	16	qn	qn	NOUN
ejpam-4871	93	17	)	)	PUNCT
ejpam-4871	93	18	,	,	PUNCT
ejpam-4871	93	19	where	where	SCONJ
ejpam-4871	93	20	q	q	NOUN
ejpam-4871	93	21	is	be	AUX
ejpam-4871	93	22	a	a	DET
ejpam-4871	93	23	prime	prime	NOUN
ejpam-4871	93	24	have	have	VERB
ejpam-4871	93	25	a	a	DET
ejpam-4871	93	26	subgroup	subgroup	NOUN
ejpam-4871	93	27	of	of	ADP
ejpam-4871	93	28	the	the	DET
ejpam-4871	93	29	form	form	NOUN
ejpam-4871	93	30	a5	a5	NOUN
ejpam-4871	93	31	,	,	PUNCT
ejpam-4871	93	32	and	and	CCONJ
ejpam-4871	93	33	since	since	SCONJ
ejpam-4871	93	34	a5	a5	PROPN
ejpam-4871	93	35	is	be	AUX
ejpam-4871	93	36	a	a	DET
ejpam-4871	93	37	simple	simple	NOUN
ejpam-4871	93	38	,	,	PUNCT
ejpam-4871	93	39	then	then	ADV
ejpam-4871	93	40	,	,	PUNCT
ejpam-4871	93	41	it	it	PRON
ejpam-4871	93	42	is	be	AUX
ejpam-4871	93	43	non	non	X
ejpam-4871	93	44	a	a	DET
ejpam-4871	93	45	soluble	soluble	ADJ
ejpam-4871	93	46	and	and	CCONJ
ejpam-4871	93	47	since	since	SCONJ
ejpam-4871	93	48	every	every	DET
ejpam-4871	93	49	a	a	DET
ejpam-4871	93	50	non	non	ADJ
ejpam-4871	93	51	soluble	soluble	ADJ
ejpam-4871	93	52	group	group	NOUN
ejpam-4871	93	53	does	do	AUX
ejpam-4871	93	54	not	not	PART
ejpam-4871	93	55	satisfy	satisfy	VERB
ejpam-4871	93	56	the	the	DET
ejpam-4871	93	57	basis	basis	NOUN
ejpam-4871	93	58	property	property	NOUN
ejpam-4871	93	59	,	,	PUNCT
ejpam-4871	93	60	depending	depend	VERB
ejpam-4871	93	61	on	on	ADP
ejpam-4871	93	62	[	[	X
ejpam-4871	93	63	13	13	NUM
ejpam-4871	93	64	]	]	PUNCT
ejpam-4871	93	65	.	.	PUNCT
ejpam-4871	94	1	on	on	ADP
ejpam-4871	94	2	the	the	DET
ejpam-4871	94	3	other	other	ADJ
ejpam-4871	94	4	hand	hand	NOUN
ejpam-4871	94	5	,	,	PUNCT
ejpam-4871	94	6	the	the	DET
ejpam-4871	94	7	order	order	NOUN
ejpam-4871	94	8	of	of	ADP
ejpam-4871	94	9	the	the	DET
ejpam-4871	94	10	group	group	NOUN
ejpam-4871	94	11	psl(2	psl(2	NOUN
ejpam-4871	94	12	,	,	PUNCT
ejpam-4871	94	13	q	q	X
ejpam-4871	94	14	)	)	PUNCT
ejpam-4871	94	15	is	be	AUX
ejpam-4871	94	16	given	give	VERB
ejpam-4871	94	17	by	by	ADP
ejpam-4871	94	18	the	the	DET
ejpam-4871	94	19	following	follow	VERB
ejpam-4871	94	20	relationship	relationship	NOUN
ejpam-4871	94	21	.	.	PUNCT
ejpam-4871	95	1	|psl(2	|psl(2	PROPN
ejpam-4871	95	2	,	,	PUNCT
ejpam-4871	95	3	q)|	q)|	NOUN
ejpam-4871	95	4	=	=	PUNCT
ejpam-4871	95	5	q(q2	q(q2	NOUN
ejpam-4871	95	6	−	−	NOUN
ejpam-4871	95	7	1	1	NUM
ejpam-4871	95	8	)	)	PUNCT
ejpam-4871	95	9	2	2	NUM
ejpam-4871	95	10	.	.	PUNCT
ejpam-4871	96	1	hence	hence	ADV
ejpam-4871	96	2	,	,	PUNCT
ejpam-4871	96	3	|psl(2	|psl(2	PROPN
ejpam-4871	96	4	,	,	PUNCT
ejpam-4871	96	5	5)|	5)|	NUM
ejpam-4871	96	6	=	=	SYM
ejpam-4871	96	7	5(52	5(52	NUM
ejpam-4871	96	8	−	−	NOUN
ejpam-4871	96	9	1	1	NUM
ejpam-4871	96	10	)	)	SYM
ejpam-4871	96	11	2	2	NUM
ejpam-4871	96	12	=	=	SYM
ejpam-4871	96	13	60	60	NUM
ejpam-4871	96	14	.	.	PUNCT
ejpam-4871	97	1	since	since	SCONJ
ejpam-4871	97	2	|a5|	|a5|	VERB
ejpam-4871	97	3	=	=	NOUN
ejpam-4871	97	4	60	60	NUM
ejpam-4871	97	5	,	,	PUNCT
ejpam-4871	97	6	so	so	ADV
ejpam-4871	97	7	psl(2	psl(2	NOUN
ejpam-4871	97	8	,	,	PUNCT
ejpam-4871	97	9	5	5	NUM
ejpam-4871	97	10	)	)	PUNCT
ejpam-4871	97	11	≈	≈	PROPN
ejpam-4871	97	12	a5	a5	PROPN
ejpam-4871	97	13	(	(	PUNCT
ejpam-4871	97	14	is	be	AUX
ejpam-4871	97	15	equal	equal	ADJ
ejpam-4871	97	16	to	to	ADP
ejpam-4871	97	17	its	its	PRON
ejpam-4871	97	18	subgroup	subgroup	NOUN
ejpam-4871	97	19	of	of	ADP
ejpam-4871	97	20	the	the	DET
ejpam-4871	97	21	same	same	ADJ
ejpam-4871	97	22	order	order	NOUN
ejpam-4871	97	23	)	)	PUNCT
ejpam-4871	97	24	.	.	PUNCT
ejpam-4871	98	1	a.	a.	PROPN
ejpam-4871	98	2	al	al	PROPN
ejpam-4871	98	3	khalaf	khalaf	PROPN
ejpam-4871	98	4	,	,	PUNCT
ejpam-4871	98	5	i.	i.	PROPN
ejpam-4871	98	6	taha	taha	PROPN
ejpam-4871	98	7	/	/	PUNCT
ejpam-4871	98	8	eur	eur	PROPN
ejpam-4871	98	9	.	.	PUNCT
ejpam-4871	99	1	j.	j.	PROPN
ejpam-4871	99	2	pure	pure	PROPN
ejpam-4871	99	3	appl	appl	PROPN
ejpam-4871	99	4	.	.	PROPN
ejpam-4871	99	5	math	math	PROPN
ejpam-4871	99	6	,	,	PUNCT
ejpam-4871	99	7	16	16	NUM
ejpam-4871	99	8	(	(	PUNCT
ejpam-4871	99	9	3	3	NUM
ejpam-4871	99	10	)	)	PUNCT
ejpam-4871	99	11	(	(	PUNCT
ejpam-4871	99	12	2023	2023	NUM
ejpam-4871	99	13	)	)	PUNCT
ejpam-4871	99	14	,	,	PUNCT
ejpam-4871	99	15	1970	1970	NUM
ejpam-4871	99	16	-	-	SYM
ejpam-4871	99	17	1979	1979	NUM
ejpam-4871	99	18	1974	1974	NUM
ejpam-4871	99	19	theorem	theorem	NOUN
ejpam-4871	99	20	2	2	NUM
ejpam-4871	99	21	.	.	PUNCT
ejpam-4871	100	1	let	let	VERB
ejpam-4871	100	2	a5	a5	PROPN
ejpam-4871	100	3	be	be	AUX
ejpam-4871	100	4	the	the	DET
ejpam-4871	100	5	alternating	alternate	VERB
ejpam-4871	100	6	group	group	NOUN
ejpam-4871	100	7	.	.	PUNCT
ejpam-4871	101	1	then	then	ADV
ejpam-4871	101	2	a5	a5	PROPN
ejpam-4871	101	3	is	be	AUX
ejpam-4871	101	4	minimal	minimal	ADJ
ejpam-4871	101	5	not	not	PART
ejpam-4871	101	6	satisfy	satisfy	VERB
ejpam-4871	101	7	the	the	DET
ejpam-4871	101	8	basis	basis	NOUN
ejpam-4871	101	9	property	property	NOUN
ejpam-4871	101	10	.	.	PUNCT
ejpam-4871	102	1	proof	proof	NOUN
ejpam-4871	102	2	.	.	PUNCT
ejpam-4871	103	1	we	we	PRON
ejpam-4871	103	2	will	will	AUX
ejpam-4871	103	3	find	find	VERB
ejpam-4871	103	4	all	all	DET
ejpam-4871	103	5	subgroups	subgroup	NOUN
ejpam-4871	103	6	of	of	ADP
ejpam-4871	103	7	the	the	DET
ejpam-4871	103	8	alternating	alternate	VERB
ejpam-4871	103	9	group	group	NOUN
ejpam-4871	103	10	a5	a5	PROPN
ejpam-4871	103	11	.	.	PUNCT
ejpam-4871	104	1	according	accord	VERB
ejpam-4871	104	2	to	to	ADP
ejpam-4871	104	3	[	[	X
ejpam-4871	104	4	19	19	NUM
ejpam-4871	104	5	]	]	PUNCT
ejpam-4871	104	6	,	,	PUNCT
ejpam-4871	104	7	the	the	DET
ejpam-4871	104	8	subgroups	subgroup	NOUN
ejpam-4871	104	9	of	of	ADP
ejpam-4871	104	10	the	the	DET
ejpam-4871	104	11	group	group	NOUN
ejpam-4871	104	12	psl(2	psl(2	NOUN
ejpam-4871	104	13	,	,	PUNCT
ejpam-4871	104	14	5	5	NUM
ejpam-4871	104	15	)	)	PUNCT
ejpam-4871	104	16	≈	≈	PROPN
ejpam-4871	104	17	a5	a5	PROPN
ejpam-4871	104	18	can	can	AUX
ejpam-4871	104	19	be	be	AUX
ejpam-4871	104	20	one	one	NUM
ejpam-4871	104	21	of	of	ADP
ejpam-4871	104	22	the	the	DET
ejpam-4871	104	23	following	follow	VERB
ejpam-4871	104	24	groups	group	NOUN
ejpam-4871	104	25	:	:	PUNCT
ejpam-4871	104	26	•	•	ADP
ejpam-4871	104	27	the	the	DET
ejpam-4871	104	28	order	order	NOUN
ejpam-4871	104	29	of	of	ADP
ejpam-4871	104	30	the	the	DET
ejpam-4871	104	31	even	even	ADJ
ejpam-4871	104	32	groups	group	NOUN
ejpam-4871	104	33	d2	d2	PROPN
ejpam-4871	104	34	or	or	CCONJ
ejpam-4871	104	35	d3	d3	PROPN
ejpam-4871	104	36	(	(	PUNCT
ejpam-4871	104	37	dihedral	dihedral	ADJ
ejpam-4871	104	38	groups	group	NOUN
ejpam-4871	104	39	)	)	PUNCT
ejpam-4871	104	40	,	,	PUNCT
ejpam-4871	104	41	where	where	SCONJ
ejpam-4871	104	42	q	q	NOUN
ejpam-4871	104	43	=	=	SYM
ejpam-4871	104	44	5	5	NUM
ejpam-4871	104	45	̸=	̸=	PROPN
ejpam-4871	104	46	1	1	NUM
ejpam-4871	104	47	are	be	AUX
ejpam-4871	104	48	4	4	NUM
ejpam-4871	104	49	or	or	CCONJ
ejpam-4871	104	50	6	6	NUM
ejpam-4871	104	51	respectively	respectively	ADV
ejpam-4871	104	52	and	and	CCONJ
ejpam-4871	104	53	the	the	DET
ejpam-4871	104	54	2	2	NUM
ejpam-4871	104	55	-	-	PUNCT
ejpam-4871	104	56	group	group	NOUN
ejpam-4871	104	57	d2	d2	NOUN
ejpam-4871	104	58	satisfies	satisfy	VERB
ejpam-4871	104	59	the	the	DET
ejpam-4871	104	60	basis	basis	NOUN
ejpam-4871	104	61	property	property	NOUN
ejpam-4871	104	62	,	,	PUNCT
ejpam-4871	104	63	because	because	SCONJ
ejpam-4871	104	64	it	it	PRON
ejpam-4871	104	65	is	be	AUX
ejpam-4871	104	66	a	a	DET
ejpam-4871	104	67	primary	primary	ADJ
ejpam-4871	104	68	group	group	NOUN
ejpam-4871	104	69	,	,	PUNCT
ejpam-4871	104	70	see	see	VERB
ejpam-4871	104	71	[	[	X
ejpam-4871	104	72	3	3	NUM
ejpam-4871	104	73	]	]	PUNCT
ejpam-4871	104	74	.	.	PUNCT
ejpam-4871	105	1	likewise	likewise	ADV
ejpam-4871	105	2	,	,	PUNCT
ejpam-4871	105	3	the	the	DET
ejpam-4871	105	4	2	2	NUM
ejpam-4871	105	5	-	-	PUNCT
ejpam-4871	105	6	group	group	NOUN
ejpam-4871	105	7	d3	d3	PROPN
ejpam-4871	105	8	satisfies	satisfy	VERB
ejpam-4871	105	9	the	the	DET
ejpam-4871	105	10	basis	basis	NOUN
ejpam-4871	105	11	property	property	NOUN
ejpam-4871	105	12	,	,	PUNCT
ejpam-4871	105	13	because	because	SCONJ
ejpam-4871	105	14	it	it	PRON
ejpam-4871	105	15	is	be	AUX
ejpam-4871	105	16	a	a	DET
ejpam-4871	105	17	metacyclic	metacyclic	ADJ
ejpam-4871	105	18	group	group	NOUN
ejpam-4871	105	19	,	,	PUNCT
ejpam-4871	105	20	depending	depend	VERB
ejpam-4871	105	21	on	on	ADP
ejpam-4871	105	22	[	[	X
ejpam-4871	105	23	3	3	NUM
ejpam-4871	105	24	]	]	PUNCT
ejpam-4871	105	25	.	.	PUNCT
ejpam-4871	106	1	•	•	NUM
ejpam-4871	106	2	the	the	DET
ejpam-4871	106	3	subgroup	subgroup	NOUN
ejpam-4871	106	4	of	of	ADP
ejpam-4871	106	5	a	a	DET
ejpam-4871	106	6	non	non	ADJ
ejpam-4871	106	7	-	-	ADJ
ejpam-4871	106	8	commutative	commutative	ADJ
ejpam-4871	106	9	group	group	NOUN
ejpam-4871	106	10	h	h	NOUN
ejpam-4871	106	11	with	with	ADP
ejpam-4871	106	12	the	the	DET
ejpam-4871	106	13	order	order	NOUN
ejpam-4871	106	14	5(5−1	5(5−1	NUM
ejpam-4871	106	15	)	)	PUNCT
ejpam-4871	106	16	2	2	NUM
ejpam-4871	106	17	=	=	SYM
ejpam-4871	106	18	10	10	NUM
ejpam-4871	106	19	,	,	PUNCT
ejpam-4871	106	20	is	be	AUX
ejpam-4871	106	21	a	a	DET
ejpam-4871	106	22	5sylow	5sylow	NUM
ejpam-4871	106	23	subgroup	subgroup	NOUN
ejpam-4871	106	24	q	q	X
ejpam-4871	106	25	,	,	PUNCT
ejpam-4871	106	26	which	which	PRON
ejpam-4871	106	27	is	be	AUX
ejpam-4871	106	28	a	a	DET
ejpam-4871	106	29	primary	primary	ADJ
ejpam-4871	106	30	commutative	commutative	ADJ
ejpam-4871	106	31	group	group	NOUN
ejpam-4871	106	32	isomorphic	isomorphic	ADJ
ejpam-4871	106	33	to	to	ADP
ejpam-4871	106	34	c5	c5	PROPN
ejpam-4871	106	35	,	,	PUNCT
ejpam-4871	106	36	and	and	CCONJ
ejpam-4871	106	37	since|h	since|h	NOUN
ejpam-4871	106	38	:	:	PUNCT
ejpam-4871	106	39	q|	q|	NOUN
ejpam-4871	106	40	=	=	SYM
ejpam-4871	106	41	2	2	X
ejpam-4871	106	42	.	.	PUNCT
ejpam-4871	106	43	then	then	ADV
ejpam-4871	106	44	q	q	X
ejpam-4871	106	45	⊴	⊴	PROPN
ejpam-4871	106	46	h	h	NOUN
ejpam-4871	106	47	that	that	PRON
ejpam-4871	106	48	means	mean	VERB
ejpam-4871	106	49	h	h	NOUN
ejpam-4871	106	50	is	be	AUX
ejpam-4871	106	51	the	the	DET
ejpam-4871	106	52	even	even	ADJ
ejpam-4871	106	53	group	group	NOUN
ejpam-4871	106	54	of	of	ADP
ejpam-4871	106	55	the	the	DET
ejpam-4871	106	56	order	order	NOUN
ejpam-4871	106	57	10	10	NUM
ejpam-4871	106	58	,	,	PUNCT
ejpam-4871	106	59	and	and	CCONJ
ejpam-4871	106	60	also	also	ADV
ejpam-4871	106	61	h	h	PROPN
ejpam-4871	106	62	is	be	AUX
ejpam-4871	106	63	metacyclic	metacyclic	ADJ
ejpam-4871	106	64	group	group	NOUN
ejpam-4871	106	65	that	that	PRON
ejpam-4871	106	66	satisfies	satisfy	VERB
ejpam-4871	106	67	the	the	DET
ejpam-4871	106	68	basis	basis	NOUN
ejpam-4871	106	69	property	property	NOUN
ejpam-4871	106	70	[	[	X
ejpam-4871	106	71	3	3	NUM
ejpam-4871	106	72	]	]	PUNCT
ejpam-4871	106	73	.	.	PUNCT
ejpam-4871	107	1	•	•	NUM
ejpam-4871	107	2	the	the	DET
ejpam-4871	107	3	groups	group	NOUN
ejpam-4871	107	4	psl(2	psl(2	NOUN
ejpam-4871	107	5	,	,	PUNCT
ejpam-4871	107	6	5	5	X
ejpam-4871	107	7	)	)	PUNCT
ejpam-4871	107	8	∼=	∼=	PROPN
ejpam-4871	107	9	a5	a5	NOUN
ejpam-4871	107	10	,	,	PUNCT
ejpam-4871	107	11	pgl(2	pgl(2	NOUN
ejpam-4871	107	12	,	,	PUNCT
ejpam-4871	107	13	5	5	NUM
ejpam-4871	107	14	)	)	PUNCT
ejpam-4871	107	15	≥	≥	NOUN
ejpam-4871	107	16	60	60	NUM
ejpam-4871	107	17	and	and	CCONJ
ejpam-4871	107	18	pgl(2	pgl(2	NOUN
ejpam-4871	107	19	,	,	PUNCT
ejpam-4871	107	20	5	5	NUM
ejpam-4871	107	21	)	)	PUNCT
ejpam-4871	107	22	are	be	AUX
ejpam-4871	107	23	not	not	PART
ejpam-4871	107	24	a	a	DET
ejpam-4871	107	25	subgroup	subgroup	NOUN
ejpam-4871	107	26	of	of	ADP
ejpam-4871	107	27	a5	a5	PROPN
ejpam-4871	107	28	.	.	PUNCT
ejpam-4871	108	1	therefore	therefore	ADV
ejpam-4871	108	2	,	,	PUNCT
ejpam-4871	108	3	we	we	PRON
ejpam-4871	108	4	find	find	VERB
ejpam-4871	108	5	that	that	SCONJ
ejpam-4871	108	6	all	all	DET
ejpam-4871	108	7	the	the	DET
ejpam-4871	108	8	proper	proper	ADJ
ejpam-4871	108	9	subgroups	subgroup	NOUN
ejpam-4871	108	10	of	of	ADP
ejpam-4871	108	11	the	the	DET
ejpam-4871	108	12	group	group	NOUN
ejpam-4871	108	13	a5	a5	PROPN
ejpam-4871	108	14	has	have	VERB
ejpam-4871	108	15	the	the	DET
ejpam-4871	108	16	basis	basis	NOUN
ejpam-4871	108	17	property	property	NOUN
ejpam-4871	108	18	,	,	PUNCT
ejpam-4871	108	19	but	but	CCONJ
ejpam-4871	108	20	a5	a5	PROPN
ejpam-4871	108	21	does	do	AUX
ejpam-4871	108	22	not	not	PART
ejpam-4871	108	23	satisfy	satisfy	VERB
ejpam-4871	108	24	the	the	DET
ejpam-4871	108	25	basis	basis	NOUN
ejpam-4871	108	26	property	property	NOUN
ejpam-4871	108	27	,	,	PUNCT
ejpam-4871	108	28	because	because	SCONJ
ejpam-4871	108	29	it	it	PRON
ejpam-4871	108	30	is	be	AUX
ejpam-4871	108	31	simple	simple	ADJ
ejpam-4871	108	32	,	,	PUNCT
ejpam-4871	108	33	as	as	SCONJ
ejpam-4871	108	34	it	it	PRON
ejpam-4871	108	35	is	be	AUX
ejpam-4871	108	36	not	not	PART
ejpam-4871	108	37	soluble	soluble	ADJ
ejpam-4871	108	38	.	.	PUNCT
ejpam-4871	109	1	•	•	NUM
ejpam-4871	109	2	the	the	DET
ejpam-4871	109	3	alternating	alternate	VERB
ejpam-4871	109	4	group	group	NOUN
ejpam-4871	109	5	a4	a4	NOUN
ejpam-4871	109	6	,	,	PUNCT
ejpam-4871	109	7	the	the	DET
ejpam-4871	109	8	symmetric	symmetric	ADJ
ejpam-4871	109	9	group	group	NOUN
ejpam-4871	109	10	s4	s4	PROPN
ejpam-4871	109	11	,	,	PUNCT
ejpam-4871	109	12	or	or	CCONJ
ejpam-4871	109	13	the	the	DET
ejpam-4871	109	14	alternating	alternate	VERB
ejpam-4871	109	15	group	group	NOUN
ejpam-4871	109	16	a5	a5	PROPN
ejpam-4871	109	17	itself	itself	PRON
ejpam-4871	109	18	.	.	PUNCT
ejpam-4871	110	1	since	since	SCONJ
ejpam-4871	110	2	|s4|	|s4|	NOUN
ejpam-4871	110	3	=	=	SYM
ejpam-4871	110	4	24	24	NUM
ejpam-4871	110	5	,	,	PUNCT
ejpam-4871	110	6	then|s4|	then|s4|	PROPN
ejpam-4871	110	7	∤	∤	PROPN
ejpam-4871	110	8	|a5|	|a5|	VERB
ejpam-4871	110	9	the	the	DET
ejpam-4871	110	10	symmetric	symmetric	ADJ
ejpam-4871	110	11	group	group	NOUN
ejpam-4871	110	12	s4	s4	PROPN
ejpam-4871	110	13	is	be	AUX
ejpam-4871	110	14	not	not	PART
ejpam-4871	110	15	a	a	DET
ejpam-4871	110	16	subgroup	subgroup	NOUN
ejpam-4871	110	17	of	of	ADP
ejpam-4871	110	18	the	the	DET
ejpam-4871	110	19	group	group	NOUN
ejpam-4871	110	20	a5	a5	PROPN
ejpam-4871	110	21	.	.	PUNCT
ejpam-4871	111	1	as	as	SCONJ
ejpam-4871	111	2	the	the	DET
ejpam-4871	111	3	group	group	NOUN
ejpam-4871	111	4	a5	a5	PROPN
ejpam-4871	111	5	is	be	AUX
ejpam-4871	111	6	not	not	PART
ejpam-4871	111	7	proper	proper	ADJ
ejpam-4871	111	8	subgroup	subgroup	NOUN
ejpam-4871	111	9	of	of	ADP
ejpam-4871	111	10	the	the	DET
ejpam-4871	111	11	groupa5	groupa5	PROPN
ejpam-4871	111	12	.	.	PUNCT
ejpam-4871	112	1	now	now	ADV
ejpam-4871	112	2	we	we	PRON
ejpam-4871	112	3	study	study	VERB
ejpam-4871	112	4	the	the	DET
ejpam-4871	112	5	alternating	alternate	VERB
ejpam-4871	112	6	group	group	NOUN
ejpam-4871	112	7	a4	a4	PROPN
ejpam-4871	112	8	where	where	SCONJ
ejpam-4871	112	9	|a4|	|a4|	ADJ
ejpam-4871	112	10	=	=	SYM
ejpam-4871	112	11	12	12	NUM
ejpam-4871	112	12	=	=	SYM
ejpam-4871	112	13	22	22	NUM
ejpam-4871	112	14	·	·	SYM
ejpam-4871	112	15	3	3	NUM
ejpam-4871	112	16	,	,	PUNCT
ejpam-4871	112	17	which	which	PRON
ejpam-4871	112	18	is	be	AUX
ejpam-4871	112	19	a	a	DET
ejpam-4871	112	20	semidirect	semidirect	ADJ
ejpam-4871	112	21	product	product	NOUN
ejpam-4871	112	22	of	of	ADP
ejpam-4871	112	23	the	the	DET
ejpam-4871	112	24	klein	klein	PROPN
ejpam-4871	112	25	group	group	PROPN
ejpam-4871	112	26	k	k	PROPN
ejpam-4871	112	27	by	by	ADP
ejpam-4871	112	28	the	the	DET
ejpam-4871	112	29	cyclic	cyclic	ADJ
ejpam-4871	112	30	group	group	NOUN
ejpam-4871	112	31	<	<	X
ejpam-4871	112	32	y	y	X
ejpam-4871	112	33	>	>	PUNCT
ejpam-4871	112	34	=	=	X
ejpam-4871	112	35	<	<	X
ejpam-4871	112	36	(	(	PUNCT
ejpam-4871	112	37	123	123	NUM
ejpam-4871	112	38	)	)	PUNCT
ejpam-4871	112	39	>	>	X
ejpam-4871	113	1	whose	whose	DET
ejpam-4871	113	2	order	order	NOUN
ejpam-4871	113	3	is	be	AUX
ejpam-4871	113	4	equal	equal	ADJ
ejpam-4871	113	5	to	to	ADP
ejpam-4871	113	6	3	3	NUM
ejpam-4871	113	7	.	.	PUNCT
ejpam-4871	114	1	on	on	ADP
ejpam-4871	114	2	the	the	DET
ejpam-4871	114	3	other	other	ADJ
ejpam-4871	114	4	hand	hand	NOUN
ejpam-4871	114	5	,	,	PUNCT
ejpam-4871	114	6	we	we	PRON
ejpam-4871	114	7	have	have	VERB
ejpam-4871	114	8	klein	klein	PROPN
ejpam-4871	114	9	’s	’s	PART
ejpam-4871	114	10	group	group	NOUN
ejpam-4871	114	11	k	k	PROPN
ejpam-4871	115	1	=	=	PUNCT
ejpam-4871	115	2	<	<	X
ejpam-4871	115	3	(	(	PUNCT
ejpam-4871	115	4	12)(34	12)(34	NUM
ejpam-4871	115	5	)	)	PUNCT
ejpam-4871	115	6	,	,	PUNCT
ejpam-4871	115	7	(	(	PUNCT
ejpam-4871	115	8	13)(24	13)(24	NUM
ejpam-4871	115	9	)	)	PUNCT
ejpam-4871	115	10	>	>	PUNCT
ejpam-4871	115	11	=	=	SYM
ejpam-4871	115	12	{	{	PUNCT
ejpam-4871	115	13	(	(	PUNCT
ejpam-4871	115	14	1	1	NUM
ejpam-4871	115	15	)	)	PUNCT
ejpam-4871	115	16	,	,	PUNCT
ejpam-4871	115	17	(	(	PUNCT
ejpam-4871	115	18	12)(34	12)(34	NUM
ejpam-4871	115	19	)	)	PUNCT
ejpam-4871	115	20	,	,	PUNCT
ejpam-4871	115	21	(	(	PUNCT
ejpam-4871	115	22	13)(24)(14)(23	13)(24)(14)(23	NUM
ejpam-4871	115	23	)	)	PUNCT
ejpam-4871	115	24	}	}	PUNCT
ejpam-4871	115	25	is	be	AUX
ejpam-4871	115	26	a	a	DET
ejpam-4871	115	27	primary	primary	ADJ
ejpam-4871	115	28	2	2	NUM
ejpam-4871	115	29	-	-	PUNCT
ejpam-4871	115	30	group	group	NOUN
ejpam-4871	115	31	of	of	ADP
ejpam-4871	115	32	order	order	NOUN
ejpam-4871	115	33	4	4	NUM
ejpam-4871	115	34	as	as	ADP
ejpam-4871	115	35	that	that	PRON
ejpam-4871	115	36	k	k	PROPN
ejpam-4871	115	37	⊴	⊴	ADP
ejpam-4871	115	38	a4	a4	NUM
ejpam-4871	115	39	.	.	PUNCT
ejpam-4871	116	1	then	then	ADV
ejpam-4871	116	2	the	the	DET
ejpam-4871	116	3	group	group	NOUN
ejpam-4871	116	4	k	k	PROPN
ejpam-4871	116	5	can	can	AUX
ejpam-4871	116	6	be	be	AUX
ejpam-4871	116	7	considered	consider	VERB
ejpam-4871	116	8	as	as	ADP
ejpam-4871	116	9	a	a	DET
ejpam-4871	116	10	vector	vector	NOUN
ejpam-4871	116	11	space	space	NOUN
ejpam-4871	116	12	of	of	ADP
ejpam-4871	116	13	dimension	dimension	NOUN
ejpam-4871	116	14	2	2	NUM
ejpam-4871	116	15	over	over	ADP
ejpam-4871	116	16	the	the	DET
ejpam-4871	116	17	field	field	NOUN
ejpam-4871	116	18	gf	gf	X
ejpam-4871	116	19	(	(	PUNCT
ejpam-4871	116	20	2	2	NUM
ejpam-4871	116	21	)	)	PUNCT
ejpam-4871	116	22	.	.	PUNCT
ejpam-4871	117	1	since	since	SCONJ
ejpam-4871	117	2	k	k	PROPN
ejpam-4871	117	3	is	be	AUX
ejpam-4871	117	4	a	a	DET
ejpam-4871	117	5	⊴	⊴	NUM
ejpam-4871	117	6	a4	a4	NUM
ejpam-4871	117	7	,	,	PUNCT
ejpam-4871	117	8	then	then	ADV
ejpam-4871	117	9	y	y	PROPN
ejpam-4871	117	10	acts	act	VERB
ejpam-4871	117	11	as	as	ADP
ejpam-4871	117	12	a	a	DET
ejpam-4871	117	13	linear	linear	ADJ
ejpam-4871	117	14	operator	operator	NOUN
ejpam-4871	117	15	on	on	ADP
ejpam-4871	117	16	a	a	DET
ejpam-4871	117	17	vector	vector	NOUN
ejpam-4871	117	18	space	space	NOUN
ejpam-4871	117	19	of	of	ADP
ejpam-4871	117	20	the	the	DET
ejpam-4871	117	21	form	form	NOUN
ejpam-4871	118	1	ϕy	ϕy	INTJ
ejpam-4871	118	2	:	:	PUNCT
ejpam-4871	118	3	α	α	PROPN
ejpam-4871	118	4	−→	−→	NOUN
ejpam-4871	118	5	y−1αy	y−1αy	NOUN
ejpam-4871	118	6	,	,	PUNCT
ejpam-4871	118	7	for	for	ADP
ejpam-4871	118	8	all	all	DET
ejpam-4871	118	9	α	α	NOUN
ejpam-4871	118	10	∈	∈	PROPN
ejpam-4871	118	11	k	k	NOUN
ejpam-4871	119	1	such	such	ADJ
ejpam-4871	119	2	that	that	SCONJ
ejpam-4871	119	3	φ3	φ3	NOUN
ejpam-4871	119	4	y	y	NOUN
ejpam-4871	119	5	=	=	PUNCT
ejpam-4871	119	6	idk	idk	PROPN
ejpam-4871	119	7	and	and	CCONJ
ejpam-4871	119	8	φ(α	φ(α	ADJ
ejpam-4871	119	9	)	)	PUNCT
ejpam-4871	119	10	̸=	̸=	PROPN
ejpam-4871	119	11	α	α	NOUN
ejpam-4871	119	12	for	for	ADP
ejpam-4871	119	13	all	all	DET
ejpam-4871	119	14	α	α	NOUN
ejpam-4871	119	15	∈	∈	PROPN
ejpam-4871	119	16	k	k	NOUN
ejpam-4871	119	17	−	−	PROPN
ejpam-4871	119	18	{	{	PUNCT
ejpam-4871	119	19	(	(	PUNCT
ejpam-4871	119	20	1	1	NUM
ejpam-4871	119	21	)	)	PUNCT
ejpam-4871	119	22	}	}	PUNCT
ejpam-4871	119	23	,	,	PUNCT
ejpam-4871	119	24	φ3	φ3	PROPN
ejpam-4871	119	25	y	y	PROPN
ejpam-4871	119	26	=	=	SYM
ejpam-4871	119	27	idk	idk	PROPN
ejpam-4871	119	28	.	.	PUNCT
ejpam-4871	120	1	in	in	ADP
ejpam-4871	120	2	fact	fact	NOUN
ejpam-4871	120	3	(	(	PUNCT
ejpam-4871	120	4	123)(12)(34)(123	123)(12)(34)(123	NUM
ejpam-4871	120	5	)	)	PUNCT
ejpam-4871	120	6	=	=	PUNCT
ejpam-4871	120	7	(	(	PUNCT
ejpam-4871	120	8	14)(32	14)(32	NUM
ejpam-4871	120	9	)	)	PUNCT
ejpam-4871	120	10	(	(	PUNCT
ejpam-4871	120	11	132)(14)(23)(123	132)(14)(23)(123	NUM
ejpam-4871	120	12	)	)	PUNCT
ejpam-4871	120	13	=	=	PRON
ejpam-4871	120	14	(	(	PUNCT
ejpam-4871	120	15	13)(24	13)(24	NUM
ejpam-4871	120	16	)	)	PUNCT
ejpam-4871	120	17	(	(	PUNCT
ejpam-4871	120	18	132)(13)(24)(123	132)(13)(24)(123	NUM
ejpam-4871	120	19	)	)	PUNCT
ejpam-4871	120	20	=	=	PUNCT
ejpam-4871	120	21	(	(	PUNCT
ejpam-4871	120	22	12)(34	12)(34	NUM
ejpam-4871	120	23	)	)	PUNCT
ejpam-4871	120	24	.	.	PUNCT
ejpam-4871	121	1	thus	thus	ADV
ejpam-4871	121	2	,	,	PUNCT
ejpam-4871	121	3	from	from	ADP
ejpam-4871	121	4	the	the	DET
ejpam-4871	121	5	equality	equality	NOUN
ejpam-4871	121	6	(	(	PUNCT
ejpam-4871	121	7	φ3	φ3	NOUN
ejpam-4871	121	8	y	y	PROPN
ejpam-4871	121	9	−	−	PROPN
ejpam-4871	121	10	idk)(α	idk)(α	NOUN
ejpam-4871	121	11	)	)	PUNCT
ejpam-4871	121	12	=	=	SYM
ejpam-4871	122	1	(	(	PUNCT
ejpam-4871	122	2	φy	φy	NOUN
ejpam-4871	122	3	−	−	PROPN
ejpam-4871	122	4	idk)(φ2	idk)(φ2	PROPN
ejpam-4871	123	1	+	+	CCONJ
ejpam-4871	123	2	φ+	φ+	NOUN
ejpam-4871	123	3	idk)(α	idk)(α	NOUN
ejpam-4871	123	4	)	)	PUNCT
ejpam-4871	124	1	=	=	SYM
ejpam-4871	124	2	0	0	NUM
ejpam-4871	124	3	,	,	PUNCT
ejpam-4871	124	4	for	for	ADP
ejpam-4871	124	5	all	all	DET
ejpam-4871	124	6	α	α	NOUN
ejpam-4871	124	7	∈	∈	PROPN
ejpam-4871	124	8	k.	k.	NOUN
ejpam-4871	124	9	a.	a.	PROPN
ejpam-4871	124	10	al	al	PROPN
ejpam-4871	124	11	khalaf	khalaf	PROPN
ejpam-4871	124	12	,	,	PUNCT
ejpam-4871	124	13	i.	i.	PROPN
ejpam-4871	124	14	taha	taha	PROPN
ejpam-4871	124	15	/	/	PUNCT
ejpam-4871	124	16	eur	eur	PROPN
ejpam-4871	124	17	.	.	PUNCT
ejpam-4871	125	1	j.	j.	PROPN
ejpam-4871	125	2	pure	pure	PROPN
ejpam-4871	125	3	appl	appl	PROPN
ejpam-4871	125	4	.	.	PROPN
ejpam-4871	125	5	math	math	PROPN
ejpam-4871	125	6	,	,	PUNCT
ejpam-4871	125	7	16	16	NUM
ejpam-4871	125	8	(	(	PUNCT
ejpam-4871	125	9	3	3	NUM
ejpam-4871	125	10	)	)	PUNCT
ejpam-4871	125	11	(	(	PUNCT
ejpam-4871	125	12	2023	2023	NUM
ejpam-4871	125	13	)	)	PUNCT
ejpam-4871	125	14	,	,	PUNCT
ejpam-4871	125	15	1970	1970	NUM
ejpam-4871	125	16	-	-	SYM
ejpam-4871	125	17	1979	1979	NUM
ejpam-4871	125	18	1975	1975	NUM
ejpam-4871	125	19	from	from	ADP
ejpam-4871	125	20	the	the	DET
ejpam-4871	125	21	fact	fact	NOUN
ejpam-4871	125	22	that	that	SCONJ
ejpam-4871	125	23	the	the	DET
ejpam-4871	125	24	operator	operator	NOUN
ejpam-4871	125	25	(	(	PUNCT
ejpam-4871	125	26	φy	φy	INTJ
ejpam-4871	125	27	−	−	PROPN
ejpam-4871	125	28	idk	idk	NOUN
ejpam-4871	125	29	)	)	PUNCT
ejpam-4871	125	30	is	be	AUX
ejpam-4871	125	31	not	not	PART
ejpam-4871	125	32	singular	singular	ADJ
ejpam-4871	125	33	,	,	PUNCT
ejpam-4871	125	34	then	then	ADV
ejpam-4871	125	35	φ2	φ2	PROPN
ejpam-4871	125	36	+	+	CCONJ
ejpam-4871	125	37	φ	φ	PROPN
ejpam-4871	125	38	+	+	CCONJ
ejpam-4871	125	39	idk	idk	PROPN
ejpam-4871	125	40	=	=	SYM
ejpam-4871	125	41	0	0	NUM
ejpam-4871	125	42	,	,	PUNCT
ejpam-4871	125	43	therefore	therefore	ADV
ejpam-4871	125	44	the	the	DET
ejpam-4871	125	45	polynomial	polynomial	ADJ
ejpam-4871	125	46	z2	z2	PROPN
ejpam-4871	125	47	+	+	CCONJ
ejpam-4871	125	48	z	z	PROPN
ejpam-4871	125	49	+	+	CCONJ
ejpam-4871	125	50	1	1	NUM
ejpam-4871	125	51	on	on	ADP
ejpam-4871	125	52	the	the	DET
ejpam-4871	125	53	field	field	NOUN
ejpam-4871	125	54	gf	gf	X
ejpam-4871	125	55	(	(	PUNCT
ejpam-4871	125	56	2	2	X
ejpam-4871	125	57	)	)	PUNCT
ejpam-4871	125	58	is	be	AUX
ejpam-4871	125	59	a	a	DET
ejpam-4871	125	60	minimal	minimal	ADJ
ejpam-4871	125	61	polynomial	polynomial	NOUN
ejpam-4871	125	62	of	of	ADP
ejpam-4871	125	63	the	the	DET
ejpam-4871	125	64	operator	operator	NOUN
ejpam-4871	125	65	φy	φy	INTJ
ejpam-4871	126	1	since	since	SCONJ
ejpam-4871	126	2	it	it	PRON
ejpam-4871	126	3	is	be	AUX
ejpam-4871	126	4	not	not	PART
ejpam-4871	126	5	decomposing	decompose	VERB
ejpam-4871	126	6	over	over	ADP
ejpam-4871	126	7	the	the	DET
ejpam-4871	126	8	field	field	NOUN
ejpam-4871	126	9	gf	gf	X
ejpam-4871	126	10	(	(	PUNCT
ejpam-4871	126	11	2	2	X
ejpam-4871	126	12	)	)	PUNCT
ejpam-4871	127	1	[	[	X
ejpam-4871	127	2	10	10	NUM
ejpam-4871	127	3	]	]	PUNCT
ejpam-4871	127	4	on	on	ADP
ejpam-4871	127	5	non	non	ADJ
ejpam-4871	127	6	zero	zero	NUM
ejpam-4871	127	7	vector	vector	NOUN
ejpam-4871	127	8	of	of	ADP
ejpam-4871	127	9	k.	k.	PROPN
ejpam-4871	127	10	thus	thus	ADV
ejpam-4871	127	11	,	,	PUNCT
ejpam-4871	127	12	the	the	DET
ejpam-4871	127	13	condition	condition	NOUN
ejpam-4871	127	14	i1	i1	PROPN
ejpam-4871	127	15	)	)	PUNCT
ejpam-4871	127	16	for	for	ADP
ejpam-4871	127	17	automorphism	automorphism	NOUN
ejpam-4871	127	18	φy	φy	NOUN
ejpam-4871	127	19	for	for	ADP
ejpam-4871	127	20	the	the	DET
ejpam-4871	127	21	group	group	NOUN
ejpam-4871	127	22	,	,	PUNCT
ejpam-4871	127	23	k	k	PROPN
ejpam-4871	127	24	is	be	AUX
ejpam-4871	127	25	fulfilled	fulfil	VERB
ejpam-4871	127	26	.	.	PUNCT
ejpam-4871	128	1	if	if	SCONJ
ejpam-4871	128	2	α	α	PROPN
ejpam-4871	128	3	∈	∈	PROPN
ejpam-4871	128	4	k	k	NOUN
ejpam-4871	128	5	and	and	CCONJ
ejpam-4871	128	6	u	u	PROPN
ejpam-4871	128	7	∈	∈	PROPN
ejpam-4871	128	8	a4	a4	NOUN
ejpam-4871	128	9	\	\	NOUN
ejpam-4871	128	10	k	k	NOUN
ejpam-4871	128	11	,	,	PUNCT
ejpam-4871	128	12	then	then	ADV
ejpam-4871	128	13	the	the	DET
ejpam-4871	128	14	vectors	vector	NOUN
ejpam-4871	128	15	α	α	NOUN
ejpam-4871	128	16	and	and	CCONJ
ejpam-4871	128	17	u−1αu	u−1αu	PROPN
ejpam-4871	128	18	are	be	AUX
ejpam-4871	128	19	linearly	linearly	ADV
ejpam-4871	128	20	independent	independent	ADJ
ejpam-4871	128	21	(	(	PUNCT
ejpam-4871	128	22	otherwise	otherwise	ADV
ejpam-4871	128	23	,	,	PUNCT
ejpam-4871	128	24	since	since	SCONJ
ejpam-4871	128	25	|u|	|u|	PROPN
ejpam-4871	128	26	=	=	SYM
ejpam-4871	128	27	3	3	NUM
ejpam-4871	128	28	and	and	CCONJ
ejpam-4871	128	29	|α|	|α|	PROPN
ejpam-4871	128	30	=	=	SYM
ejpam-4871	128	31	2	2	NUM
ejpam-4871	128	32	,	,	PUNCT
ejpam-4871	128	33	uα	uα	NOUN
ejpam-4871	128	34	=	=	SYM
ejpam-4871	128	35	αu	αu	PROPN
ejpam-4871	128	36	,	,	PUNCT
ejpam-4871	128	37	and	and	CCONJ
ejpam-4871	128	38	the	the	DET
ejpam-4871	128	39	order	order	NOUN
ejpam-4871	128	40	of	of	ADP
ejpam-4871	128	41	uα	uα	PROPN
ejpam-4871	128	42	is	be	AUX
ejpam-4871	128	43	equal	equal	ADJ
ejpam-4871	128	44	6	6	NUM
ejpam-4871	128	45	,	,	PUNCT
ejpam-4871	128	46	thus	thus	ADV
ejpam-4871	128	47	this	this	PRON
ejpam-4871	128	48	is	be	AUX
ejpam-4871	128	49	not	not	PART
ejpam-4871	128	50	possible	possible	ADJ
ejpam-4871	128	51	in	in	ADP
ejpam-4871	128	52	the	the	DET
ejpam-4871	128	53	groupa4	groupa4	NOUN
ejpam-4871	128	54	)	)	PUNCT
ejpam-4871	128	55	.	.	PUNCT
ejpam-4871	129	1	so	so	ADV
ejpam-4871	129	2	,	,	PUNCT
ejpam-4871	129	3	there	there	PRON
ejpam-4871	129	4	are	be	VERB
ejpam-4871	129	5	no	no	DET
ejpam-4871	129	6	proper	proper	ADJ
ejpam-4871	129	7	normal	normal	ADJ
ejpam-4871	129	8	subgroups	subgroup	NOUN
ejpam-4871	129	9	in	in	ADP
ejpam-4871	129	10	the	the	DET
ejpam-4871	129	11	group	group	NOUN
ejpam-4871	129	12	k	k	PROPN
ejpam-4871	129	13	with	with	ADP
ejpam-4871	129	14	respect	respect	NOUN
ejpam-4871	129	15	to	to	ADP
ejpam-4871	129	16	automorphism	automorphism	NOUN
ejpam-4871	129	17	.	.	PUNCT
ejpam-4871	130	1	therefore	therefore	ADV
ejpam-4871	130	2	,	,	PUNCT
ejpam-4871	130	3	the	the	DET
ejpam-4871	130	4	condition	condition	NOUN
ejpam-4871	130	5	i1	i1	PROPN
ejpam-4871	130	6	)	)	PUNCT
ejpam-4871	130	7	for	for	ADP
ejpam-4871	130	8	all	all	DET
ejpam-4871	130	9	elements	element	NOUN
ejpam-4871	130	10	and	and	CCONJ
ejpam-4871	130	11	for	for	ADP
ejpam-4871	130	12	any	any	DET
ejpam-4871	130	13	normal	normal	ADJ
ejpam-4871	130	14	subgroups	subgroup	NOUN
ejpam-4871	130	15	with	with	ADP
ejpam-4871	130	16	respect	respect	NOUN
ejpam-4871	130	17	to	to	ADP
ejpam-4871	130	18	automorphism	automorphism	NOUN
ejpam-4871	130	19	ϕy	ϕy	NOUN
ejpam-4871	130	20	,	,	PUNCT
ejpam-4871	130	21	because	because	SCONJ
ejpam-4871	130	22	we	we	PRON
ejpam-4871	130	23	can	can	AUX
ejpam-4871	130	24	in	in	ADP
ejpam-4871	130	25	the	the	DET
ejpam-4871	130	26	previous	previous	ADJ
ejpam-4871	130	27	study	study	NOUN
ejpam-4871	130	28	with	with	ADP
ejpam-4871	130	29	respect	respect	NOUN
ejpam-4871	130	30	to	to	ADP
ejpam-4871	130	31	automorphism	automorphism	NOUN
ejpam-4871	130	32	φy	φy	PROPN
ejpam-4871	130	33	substitute	substitute	NOUN
ejpam-4871	130	34	y	y	PROPN
ejpam-4871	130	35	by	by	ADP
ejpam-4871	130	36	u.	u.	PROPN
ejpam-4871	130	37	now	now	ADV
ejpam-4871	130	38	according	accord	VERB
ejpam-4871	130	39	to	to	ADP
ejpam-4871	130	40	[	[	X
ejpam-4871	130	41	3	3	NUM
ejpam-4871	130	42	,	,	PUNCT
ejpam-4871	130	43	theorem	theorem	VERB
ejpam-4871	130	44	2.5	2.5	NUM
ejpam-4871	130	45	]	]	PUNCT
ejpam-4871	130	46	,	,	PUNCT
ejpam-4871	130	47	the	the	DET
ejpam-4871	130	48	group	group	NOUN
ejpam-4871	130	49	has	have	VERB
ejpam-4871	130	50	the	the	DET
ejpam-4871	130	51	basis	basis	NOUN
ejpam-4871	130	52	property	property	NOUN
ejpam-4871	130	53	.	.	PUNCT
ejpam-4871	131	1	so	so	ADV
ejpam-4871	131	2	a5	a5	PROPN
ejpam-4871	131	3	is	be	AUX
ejpam-4871	131	4	a	a	DET
ejpam-4871	131	5	minimal	minimal	ADJ
ejpam-4871	131	6	that	that	PRON
ejpam-4871	131	7	not	not	PART
ejpam-4871	131	8	satisfy	satisfy	VERB
ejpam-4871	131	9	the	the	DET
ejpam-4871	131	10	basis	basis	NOUN
ejpam-4871	131	11	property	property	NOUN
ejpam-4871	131	12	.	.	PUNCT
ejpam-4871	132	1	theorem	theorem	NOUN
ejpam-4871	132	2	3	3	X
ejpam-4871	132	3	.	.	PUNCT
ejpam-4871	133	1	let	let	VERB
ejpam-4871	133	2	g	g	NOUN
ejpam-4871	133	3	=	=	NOUN
ejpam-4871	133	4	psl(3	psl(3	NOUN
ejpam-4871	133	5	,	,	PUNCT
ejpam-4871	133	6	4	4	X
ejpam-4871	133	7	)	)	PUNCT
ejpam-4871	133	8	be	be	AUX
ejpam-4871	133	9	a	a	DET
ejpam-4871	133	10	group	group	NOUN
ejpam-4871	133	11	.	.	PUNCT
ejpam-4871	134	1	then	then	ADV
ejpam-4871	134	2	,	,	PUNCT
ejpam-4871	134	3	a	a	DET
ejpam-4871	134	4	group	group	NOUN
ejpam-4871	134	5	psl(3	psl(3	NOUN
ejpam-4871	134	6	,	,	PUNCT
ejpam-4871	134	7	4	4	NUM
ejpam-4871	134	8	)	)	PUNCT
ejpam-4871	134	9	is	be	AUX
ejpam-4871	134	10	not	not	PART
ejpam-4871	134	11	minimal	minimal	ADJ
ejpam-4871	134	12	not	not	PART
ejpam-4871	134	13	satisfy	satisfy	VERB
ejpam-4871	134	14	the	the	DET
ejpam-4871	134	15	basis	basis	NOUN
ejpam-4871	134	16	property	property	NOUN
ejpam-4871	134	17	.	.	PUNCT
ejpam-4871	135	1	proof	proof	NOUN
ejpam-4871	135	2	.	.	PUNCT
ejpam-4871	136	1	we	we	PRON
ejpam-4871	136	2	study	study	VERB
ejpam-4871	136	3	the	the	DET
ejpam-4871	136	4	group	group	NOUN
ejpam-4871	136	5	sl(2	sl(2	PROPN
ejpam-4871	136	6	,	,	PUNCT
ejpam-4871	136	7	4	4	NUM
ejpam-4871	136	8	)	)	PUNCT
ejpam-4871	136	9	.	.	PUNCT
ejpam-4871	137	1	since	since	SCONJ
ejpam-4871	137	2	the	the	DET
ejpam-4871	137	3	identity	identity	NOUN
ejpam-4871	137	4	x2−1	x2−1	PUNCT
ejpam-4871	137	5	=	=	SYM
ejpam-4871	137	6	0	0	PROPN
ejpam-4871	137	7	has	have	VERB
ejpam-4871	137	8	unique	unique	ADJ
ejpam-4871	137	9	solution	solution	NOUN
ejpam-4871	137	10	on	on	ADP
ejpam-4871	137	11	the	the	DET
ejpam-4871	137	12	field	field	NOUN
ejpam-4871	137	13	gf	gf	X
ejpam-4871	137	14	(	(	PUNCT
ejpam-4871	137	15	2	2	NUM
ejpam-4871	137	16	)	)	PUNCT
ejpam-4871	137	17	,	,	PUNCT
ejpam-4871	137	18	then	then	ADV
ejpam-4871	137	19	the	the	DET
ejpam-4871	137	20	center	center	NOUN
ejpam-4871	137	21	of	of	ADP
ejpam-4871	137	22	the	the	DET
ejpam-4871	137	23	group	group	NOUN
ejpam-4871	137	24	sl(2	sl(2	PROPN
ejpam-4871	137	25	,	,	PUNCT
ejpam-4871	137	26	4	4	NUM
ejpam-4871	137	27	)	)	PUNCT
ejpam-4871	137	28	coincides	coincide	VERB
ejpam-4871	137	29	with	with	ADP
ejpam-4871	137	30	the	the	DET
ejpam-4871	137	31	identity	identity	NOUN
ejpam-4871	137	32	,	,	PUNCT
ejpam-4871	137	33	so	so	ADV
ejpam-4871	137	34	psl(2	psl(2	NOUN
ejpam-4871	137	35	,	,	PUNCT
ejpam-4871	137	36	4	4	NUM
ejpam-4871	137	37	)	)	PUNCT
ejpam-4871	137	38	≈	≈	PROPN
ejpam-4871	137	39	sl(2	sl(2	PROPN
ejpam-4871	137	40	,	,	PUNCT
ejpam-4871	137	41	4	4	NUM
ejpam-4871	137	42	)	)	PUNCT
ejpam-4871	138	1	[	[	X
ejpam-4871	138	2	19	19	NUM
ejpam-4871	138	3	,	,	PUNCT
ejpam-4871	138	4	theorem6.14	theorem6.14	PRON
ejpam-4871	138	5	]	]	X
ejpam-4871	138	6	and	and	CCONJ
ejpam-4871	138	7	psl(2	psl(2	NOUN
ejpam-4871	138	8	,	,	PUNCT
ejpam-4871	138	9	4	4	NUM
ejpam-4871	138	10	)	)	PUNCT
ejpam-4871	138	11	≈	≈	PROPN
ejpam-4871	138	12	a5	a5	PROPN
ejpam-4871	138	13	,	,	PUNCT
ejpam-4871	138	14	since	since	SCONJ
ejpam-4871	138	15	|psl(2	|psl(2	PROPN
ejpam-4871	138	16	,	,	PUNCT
ejpam-4871	138	17	4)|	4)|	NUM
ejpam-4871	138	18	=	=	SYM
ejpam-4871	138	19	4(42	4(42	NUM
ejpam-4871	138	20	−	−	NOUN
ejpam-4871	138	21	1	1	X
ejpam-4871	138	22	)	)	PUNCT
ejpam-4871	138	23	=	=	SYM
ejpam-4871	138	24	60	60	NUM
ejpam-4871	138	25	.	.	PUNCT
ejpam-4871	138	26	define	define	VERB
ejpam-4871	138	27	the	the	DET
ejpam-4871	138	28	mapping	mapping	NOUN
ejpam-4871	138	29	ξ	ξ	X
ejpam-4871	138	30	:	:	PUNCT
ejpam-4871	139	1	sl(2	sl(2	PROPN
ejpam-4871	139	2	,	,	PUNCT
ejpam-4871	139	3	4	4	NUM
ejpam-4871	139	4	)	)	PUNCT
ejpam-4871	139	5	→	→	SYM
ejpam-4871	139	6	sl(3	sl(3	PROPN
ejpam-4871	139	7	,	,	PUNCT
ejpam-4871	139	8	4	4	NUM
ejpam-4871	139	9	)	)	PUNCT
ejpam-4871	139	10	by	by	ADP
ejpam-4871	139	11	:	:	PUNCT
ejpam-4871	139	12	ξ	ξ	X
ejpam-4871	139	13	(	(	PUNCT
ejpam-4871	139	14	[	[	PUNCT
ejpam-4871	139	15	α	α	X
ejpam-4871	139	16	β	β	X
ejpam-4871	139	17	γ	γ	X
ejpam-4871	139	18	δ	δ	PROPN
ejpam-4871	139	19	]	]	PUNCT
ejpam-4871	139	20	)	)	PUNCT
ejpam-4871	139	21	=	=	PUNCT
ejpam-4871	139	22			NOUN
ejpam-4871	139	23	1	1	NUM
ejpam-4871	139	24	0	0	NUM
ejpam-4871	139	25	0	0	NUM
ejpam-4871	139	26	0	0	NUM
ejpam-4871	139	27	α	α	PRON
ejpam-4871	139	28	β	β	NOUN
ejpam-4871	139	29	0	0	PUNCT
ejpam-4871	139	30	γ	γ	PROPN
ejpam-4871	139	31	δ	δ	PROPN
ejpam-4871	139	32			NOUN
ejpam-4871	139	33	let	let	VERB
ejpam-4871	139	34	’s	’s	PRON
ejpam-4871	139	35	define	define	VERB
ejpam-4871	139	36	the	the	DET
ejpam-4871	139	37	natural	natural	ADJ
ejpam-4871	139	38	homomorphism	homomorphism	NOUN
ejpam-4871	139	39	η	η	PROPN
ejpam-4871	139	40	:	:	PUNCT
ejpam-4871	139	41	sl(3	sl(3	PROPN
ejpam-4871	139	42	,	,	PUNCT
ejpam-4871	139	43	4	4	NUM
ejpam-4871	139	44	)	)	PUNCT
ejpam-4871	139	45	→	→	SYM
ejpam-4871	139	46	sl(3,4	sl(3,4	ADJ
ejpam-4871	139	47	)	)	PUNCT
ejpam-4871	139	48	z(sl(3,4	z(sl(3,4	NUM
ejpam-4871	139	49	)	)	PUNCT
ejpam-4871	139	50	≈	≈	PROPN
ejpam-4871	139	51	psl(3	psl(3	NOUN
ejpam-4871	139	52	,	,	PUNCT
ejpam-4871	139	53	4	4	NUM
ejpam-4871	139	54	)	)	PUNCT
ejpam-4871	139	55	.	.	PUNCT
ejpam-4871	140	1	thus	thus	ADV
ejpam-4871	140	2	ϕ	ϕ	X
ejpam-4871	140	3	=	=	SYM
ejpam-4871	140	4	η	η	PROPN
ejpam-4871	140	5	◦	◦	PROPN
ejpam-4871	140	6	ξ	ξ	X
ejpam-4871	140	7	|sl(2,4	|sl(2,4	NOUN
ejpam-4871	140	8	)	)	PUNCT
ejpam-4871	140	9	is	be	AUX
ejpam-4871	140	10	a	a	DET
ejpam-4871	140	11	subgroup	subgroup	NOUN
ejpam-4871	140	12	of	of	ADP
ejpam-4871	140	13	a	a	DET
ejpam-4871	140	14	group	group	NOUN
ejpam-4871	140	15	t	t	NOUN
ejpam-4871	140	16	=	=	PUNCT
ejpam-4871	140	17	psl(3	psl(3	NOUN
ejpam-4871	140	18	,	,	PUNCT
ejpam-4871	140	19	4	4	NUM
ejpam-4871	140	20	)	)	PUNCT
ejpam-4871	140	21	,	,	PUNCT
ejpam-4871	140	22	let	let	VERB
ejpam-4871	140	23	ϕ	ϕ	NOUN
ejpam-4871	140	24	=	=	PUNCT
ejpam-4871	140	25	η	η	PROPN
ejpam-4871	140	26	◦	◦	PROPN
ejpam-4871	140	27	ξ	ξ	X
ejpam-4871	140	28	|sl(2,4	|sl(2,4	NOUN
ejpam-4871	140	29	)	)	PUNCT
ejpam-4871	140	30	and	and	CCONJ
ejpam-4871	140	31	since	since	SCONJ
ejpam-4871	140	32	the	the	DET
ejpam-4871	140	33	group	group	NOUN
ejpam-4871	140	34	sl(2	sl(2	PROPN
ejpam-4871	140	35	,	,	PUNCT
ejpam-4871	140	36	4	4	NUM
ejpam-4871	140	37	)	)	PUNCT
ejpam-4871	140	38	is	be	AUX
ejpam-4871	140	39	a	a	DET
ejpam-4871	140	40	simple	simple	NOUN
ejpam-4871	140	41	,	,	PUNCT
ejpam-4871	140	42	then	then	ADV
ejpam-4871	140	43	either	either	CCONJ
ejpam-4871	140	44	|t	|t	VERB
ejpam-4871	141	1	|	|	ADV
ejpam-4871	141	2	=	=	SYM
ejpam-4871	141	3	1	1	NUM
ejpam-4871	141	4	or	or	CCONJ
ejpam-4871	141	5	ϕ	ϕ	NOUN
ejpam-4871	141	6	is	be	AUX
ejpam-4871	141	7	onto	onto	ADP
ejpam-4871	141	8	,	,	PUNCT
ejpam-4871	141	9	but	but	CCONJ
ejpam-4871	141	10	ϕ	ϕ	X
ejpam-4871	141	11	(	(	PUNCT
ejpam-4871	141	12	[	[	PUNCT
ejpam-4871	141	13	0	0	NUM
ejpam-4871	141	14	1	1	NUM
ejpam-4871	141	15	−1	−1	NOUN
ejpam-4871	141	16	0	0	NUM
ejpam-4871	141	17	]	]	PUNCT
ejpam-4871	141	18	)	)	PUNCT
ejpam-4871	142	1	=	=	PUNCT
ejpam-4871	142	2			NOUN
ejpam-4871	142	3	1	1	NUM
ejpam-4871	142	4	0	0	NUM
ejpam-4871	142	5	0	0	NUM
ejpam-4871	142	6	0	0	NUM
ejpam-4871	142	7	0	0	NUM
ejpam-4871	142	8	1	1	NUM
ejpam-4871	142	9	0	0	NUM
ejpam-4871	142	10	−1	−1	NOUN
ejpam-4871	142	11	0	0	NUM
ejpam-4871	142	12			NOUN
ejpam-4871	142	13	⊈	⊈	NUM
ejpam-4871	142	14	z(sl(3	z(sl(3	NOUN
ejpam-4871	142	15	,	,	PUNCT
ejpam-4871	142	16	4	4	NUM
ejpam-4871	142	17	)	)	PUNCT
ejpam-4871	142	18	therefore	therefore	ADV
ejpam-4871	142	19	,	,	PUNCT
ejpam-4871	142	20	the	the	DET
ejpam-4871	142	21	situation	situation	NOUN
ejpam-4871	142	22	|t	|t	VERB
ejpam-4871	143	1	|	|	ADV
ejpam-4871	143	2	=	=	SYM
ejpam-4871	143	3	1	1	NUM
ejpam-4871	143	4	is	be	AUX
ejpam-4871	143	5	not	not	PART
ejpam-4871	143	6	possible	possible	ADJ
ejpam-4871	143	7	,	,	PUNCT
ejpam-4871	143	8	and	and	CCONJ
ejpam-4871	143	9	ϕ	ϕ	NOUN
ejpam-4871	143	10	is	be	AUX
ejpam-4871	143	11	onto	onto	ADP
ejpam-4871	143	12	and	and	CCONJ
ejpam-4871	143	13	within	within	ADP
ejpam-4871	143	14	the	the	DET
ejpam-4871	143	15	subgroups	subgroup	NOUN
ejpam-4871	143	16	of	of	ADP
ejpam-4871	143	17	the	the	DET
ejpam-4871	143	18	group	group	NOUN
ejpam-4871	143	19	t	t	PROPN
ejpam-4871	143	20	=	=	PUNCT
ejpam-4871	143	21	psl(3	psl(3	NOUN
ejpam-4871	143	22	,	,	PUNCT
ejpam-4871	143	23	4	4	NUM
ejpam-4871	143	24	)	)	PUNCT
ejpam-4871	143	25	,	,	PUNCT
ejpam-4871	143	26	there	there	PRON
ejpam-4871	143	27	is	be	VERB
ejpam-4871	143	28	a	a	DET
ejpam-4871	143	29	group	group	NOUN
ejpam-4871	143	30	isomorphic	isomorphic	ADJ
ejpam-4871	143	31	to	to	ADP
ejpam-4871	143	32	a5	a5	PROPN
ejpam-4871	143	33	,	,	PUNCT
ejpam-4871	143	34	and	and	CCONJ
ejpam-4871	143	35	so	so	ADV
ejpam-4871	143	36	|psl(3	|psl(3	ADV
ejpam-4871	143	37	,	,	PUNCT
ejpam-4871	143	38	4)|	4)|	NOUN
ejpam-4871	143	39	=	=	SYM
ejpam-4871	143	40	|sl(3	|sl(3	NUM
ejpam-4871	143	41	,	,	PUNCT
ejpam-4871	143	42	4)|	4)|	NOUN
ejpam-4871	143	43	3	3	NUM
ejpam-4871	143	44	=	=	SYM
ejpam-4871	143	45	(	(	PUNCT
ejpam-4871	143	46	26	26	NUM
ejpam-4871	143	47	−	−	NOUN
ejpam-4871	143	48	1)(26	1)(26	NUM
ejpam-4871	143	49	−	−	NOUN
ejpam-4871	143	50	22)22	22)22	NUM
ejpam-4871	143	51	3	3	NUM
ejpam-4871	143	52	>	>	SYM
ejpam-4871	143	53	60	60	NUM
ejpam-4871	143	54	.	.	PUNCT
ejpam-4871	144	1	hence	hence	ADV
ejpam-4871	144	2	psl(3	psl(3	NOUN
ejpam-4871	144	3	,	,	PUNCT
ejpam-4871	144	4	4	4	NUM
ejpam-4871	144	5	)	)	PUNCT
ejpam-4871	144	6	has	have	VERB
ejpam-4871	144	7	a	a	DET
ejpam-4871	144	8	proper	proper	ADJ
ejpam-4871	144	9	subgroup	subgroup	NOUN
ejpam-4871	144	10	not	not	PART
ejpam-4871	144	11	satisfying	satisfy	VERB
ejpam-4871	144	12	the	the	DET
ejpam-4871	144	13	basis	basis	NOUN
ejpam-4871	144	14	property	property	NOUN
ejpam-4871	144	15	and	and	CCONJ
ejpam-4871	144	16	psl(3	psl(3	NOUN
ejpam-4871	144	17	,	,	PUNCT
ejpam-4871	144	18	4	4	NUM
ejpam-4871	144	19	)	)	PUNCT
ejpam-4871	144	20	is	be	AUX
ejpam-4871	144	21	not	not	PART
ejpam-4871	144	22	minimal	minimal	ADJ
ejpam-4871	144	23	and	and	CCONJ
ejpam-4871	144	24	does	do	AUX
ejpam-4871	144	25	not	not	PART
ejpam-4871	144	26	satisfy	satisfy	VERB
ejpam-4871	144	27	the	the	DET
ejpam-4871	144	28	basis	basis	NOUN
ejpam-4871	144	29	property	property	NOUN
ejpam-4871	144	30	.	.	PUNCT
ejpam-4871	145	1	theorem	theorem	VERB
ejpam-4871	145	2	4	4	NUM
ejpam-4871	145	3	.	.	PUNCT
ejpam-4871	146	1	let	let	VERB
ejpam-4871	146	2	g	g	NOUN
ejpam-4871	146	3	=	=	PUNCT
ejpam-4871	146	4	psl(2	psl(2	NOUN
ejpam-4871	146	5	,	,	PUNCT
ejpam-4871	146	6	8)	8)	NUM
ejpam-4871	146	7	be	be	AUX
ejpam-4871	146	8	a	a	DET
ejpam-4871	146	9	group	group	NOUN
ejpam-4871	146	10	.	.	PUNCT
ejpam-4871	147	1	then	then	ADV
ejpam-4871	147	2	,	,	PUNCT
ejpam-4871	147	3	a	a	DET
ejpam-4871	147	4	group	group	NOUN
ejpam-4871	147	5	psl(2	psl(2	NOUN
ejpam-4871	147	6	,	,	PUNCT
ejpam-4871	147	7	8)	8)	NUM
ejpam-4871	147	8	is	be	AUX
ejpam-4871	147	9	minimal	minimal	ADJ
ejpam-4871	147	10	not	not	PART
ejpam-4871	147	11	satisfying	satisfy	VERB
ejpam-4871	147	12	the	the	DET
ejpam-4871	147	13	basis	basis	NOUN
ejpam-4871	147	14	property	property	NOUN
ejpam-4871	147	15	.	.	PUNCT
ejpam-4871	148	1	a.	a.	PROPN
ejpam-4871	148	2	al	al	PROPN
ejpam-4871	148	3	khalaf	khalaf	PROPN
ejpam-4871	148	4	,	,	PUNCT
ejpam-4871	148	5	i.	i.	PROPN
ejpam-4871	148	6	taha	taha	PROPN
ejpam-4871	148	7	/	/	PUNCT
ejpam-4871	148	8	eur	eur	PROPN
ejpam-4871	148	9	.	.	PUNCT
ejpam-4871	149	1	j.	j.	PROPN
ejpam-4871	149	2	pure	pure	PROPN
ejpam-4871	149	3	appl	appl	PROPN
ejpam-4871	149	4	.	.	PROPN
ejpam-4871	149	5	math	math	PROPN
ejpam-4871	149	6	,	,	PUNCT
ejpam-4871	149	7	16	16	NUM
ejpam-4871	149	8	(	(	PUNCT
ejpam-4871	149	9	3	3	NUM
ejpam-4871	149	10	)	)	PUNCT
ejpam-4871	149	11	(	(	PUNCT
ejpam-4871	149	12	2023	2023	NUM
ejpam-4871	149	13	)	)	PUNCT
ejpam-4871	149	14	,	,	PUNCT
ejpam-4871	149	15	1970	1970	NUM
ejpam-4871	149	16	-	-	SYM
ejpam-4871	149	17	1979	1979	NUM
ejpam-4871	149	18	1976	1976	NUM
ejpam-4871	149	19	proof	proof	NOUN
ejpam-4871	149	20	.	.	PUNCT
ejpam-4871	150	1	consider	consider	VERB
ejpam-4871	150	2	the	the	DET
ejpam-4871	150	3	group	group	NOUN
ejpam-4871	150	4	psl(2	psl(2	NOUN
ejpam-4871	150	5	,	,	PUNCT
ejpam-4871	150	6	8)	8)	NUM
ejpam-4871	150	7	.	.	PUNCT
ejpam-4871	150	8	from	from	ADP
ejpam-4871	150	9	[	[	X
ejpam-4871	150	10	8	8	NUM
ejpam-4871	150	11	]	]	SYM
ejpam-4871	150	12	|psl(2	|psl(2	PROPN
ejpam-4871	150	13	,	,	PUNCT
ejpam-4871	150	14	8)|	8)|	NUM
ejpam-4871	150	15	=	=	SYM
ejpam-4871	150	16	(	(	PUNCT
ejpam-4871	150	17	8	8	NUM
ejpam-4871	150	18	+	+	NUM
ejpam-4871	150	19	1)8(8−	1)8(8−	NOUN
ejpam-4871	150	20	1	1	NUM
ejpam-4871	150	21	)	)	PUNCT
ejpam-4871	150	22	=	=	SYM
ejpam-4871	150	23	9	9	NUM
ejpam-4871	150	24	·	·	SYM
ejpam-4871	150	25	8	8	NUM
ejpam-4871	150	26	·	·	SYM
ejpam-4871	150	27	7	7	NUM
ejpam-4871	150	28	=	=	SYM
ejpam-4871	150	29	504	504	NUM
ejpam-4871	150	30	.	.	PUNCT
ejpam-4871	151	1	now	now	ADV
ejpam-4871	151	2	,	,	PUNCT
ejpam-4871	151	3	by	by	ADP
ejpam-4871	151	4	using	use	VERB
ejpam-4871	151	5	[	[	X
ejpam-4871	151	6	19	19	NUM
ejpam-4871	151	7	,	,	PUNCT
ejpam-4871	151	8	theorem	theorem	VERB
ejpam-4871	151	9	6.25	6.25	NUM
ejpam-4871	151	10	]	]	PUNCT
ejpam-4871	151	11	the	the	DET
ejpam-4871	151	12	subgroups	subgroup	NOUN
ejpam-4871	151	13	of	of	ADP
ejpam-4871	151	14	the	the	DET
ejpam-4871	151	15	group	group	NOUN
ejpam-4871	151	16	psl(2	psl(2	NOUN
ejpam-4871	151	17	,	,	PUNCT
ejpam-4871	151	18	8)	8)	NUM
ejpam-4871	151	19	can	can	AUX
ejpam-4871	151	20	be	be	AUX
ejpam-4871	151	21	one	one	NUM
ejpam-4871	151	22	of	of	ADP
ejpam-4871	151	23	the	the	DET
ejpam-4871	151	24	following	follow	VERB
ejpam-4871	151	25	groups	group	NOUN
ejpam-4871	151	26	.	.	PUNCT
ejpam-4871	152	1	•	•	NUM
ejpam-4871	152	2	the	the	DET
ejpam-4871	152	3	even	even	ADJ
ejpam-4871	152	4	groups	group	NOUN
ejpam-4871	152	5	(	(	PUNCT
ejpam-4871	152	6	dihedral	dihedral	ADJ
ejpam-4871	152	7	groups	group	NOUN
ejpam-4871	152	8	)	)	PUNCT
ejpam-4871	152	9	with	with	ADP
ejpam-4871	152	10	orders	order	NOUN
ejpam-4871	152	11	2(q	2(q	NUM
ejpam-4871	152	12	±	±	NUM
ejpam-4871	152	13	1	1	NUM
ejpam-4871	152	14	)	)	PUNCT
ejpam-4871	152	15	i.e.	i.e.	X
ejpam-4871	152	16	the	the	DET
ejpam-4871	152	17	groups	group	NOUN
ejpam-4871	152	18	with	with	ADP
ejpam-4871	152	19	orders	order	NOUN
ejpam-4871	152	20	2	2	NUM
ejpam-4871	152	21	·	·	SYM
ejpam-4871	152	22	7	7	NUM
ejpam-4871	152	23	or	or	CCONJ
ejpam-4871	152	24	2	2	NUM
ejpam-4871	152	25	·	·	SYM
ejpam-4871	152	26	9	9	NUM
ejpam-4871	152	27	which	which	PRON
ejpam-4871	152	28	form	form	VERB
ejpam-4871	152	29	groups	group	NOUN
ejpam-4871	152	30	the	the	DET
ejpam-4871	152	31	basis	basis	NOUN
ejpam-4871	152	32	property	property	NOUN
ejpam-4871	152	33	,	,	PUNCT
ejpam-4871	152	34	because	because	SCONJ
ejpam-4871	152	35	they	they	PRON
ejpam-4871	152	36	are	be	AUX
ejpam-4871	152	37	metacyclic	metacyclic	ADJ
ejpam-4871	152	38	groups	group	NOUN
ejpam-4871	152	39	.	.	PUNCT
ejpam-4871	153	1	•	•	NUM
ejpam-4871	153	2	the	the	DET
ejpam-4871	153	3	group	group	NOUN
ejpam-4871	153	4	h	h	NOUN
ejpam-4871	153	5	of	of	ADP
ejpam-4871	153	6	order	order	NOUN
ejpam-4871	153	7	q(q−1	q(q−1	NOUN
ejpam-4871	153	8	)	)	PUNCT
ejpam-4871	154	1	d	d	NOUN
ejpam-4871	154	2	,	,	PUNCT
ejpam-4871	154	3	where	where	SCONJ
ejpam-4871	154	4	d	d	NOUN
ejpam-4871	154	5	=	=	SYM
ejpam-4871	154	6	(	(	PUNCT
ejpam-4871	154	7	2	2	NUM
ejpam-4871	154	8	,	,	PUNCT
ejpam-4871	154	9	q	q	NOUN
ejpam-4871	154	10	−	−	PROPN
ejpam-4871	154	11	1	1	NUM
ejpam-4871	154	12	)	)	PUNCT
ejpam-4871	154	13	=	=	NOUN
ejpam-4871	154	14	(	(	PUNCT
ejpam-4871	154	15	2	2	NUM
ejpam-4871	154	16	,	,	PUNCT
ejpam-4871	154	17	7	7	NUM
ejpam-4871	154	18	)	)	PUNCT
ejpam-4871	154	19	=	=	SYM
ejpam-4871	154	20	1	1	X
ejpam-4871	154	21	.	.	PUNCT
ejpam-4871	155	1	thus	thus	ADV
ejpam-4871	155	2	the	the	DET
ejpam-4871	155	3	group	group	NOUN
ejpam-4871	155	4	h	h	NOUN
ejpam-4871	155	5	of	of	ADP
ejpam-4871	155	6	order	order	NOUN
ejpam-4871	155	7	(	(	PUNCT
ejpam-4871	155	8	8)(7	8)(7	NUM
ejpam-4871	155	9	)	)	PUNCT
ejpam-4871	155	10	=	=	SYM
ejpam-4871	155	11	56	56	NUM
ejpam-4871	155	12	and	and	CCONJ
ejpam-4871	155	13	it	it	PRON
ejpam-4871	155	14	is	be	AUX
ejpam-4871	155	15	an	an	DET
ejpam-4871	155	16	extension	extension	NOUN
ejpam-4871	155	17	of	of	ADP
ejpam-4871	155	18	the	the	DET
ejpam-4871	155	19	primary	primary	ADJ
ejpam-4871	155	20	abelian	abelian	ADJ
ejpam-4871	155	21	2	2	NUM
ejpam-4871	155	22	-	-	PUNCT
ejpam-4871	155	23	group	group	NOUN
ejpam-4871	155	24	q	q	NOUN
ejpam-4871	155	25	such	such	ADJ
ejpam-4871	155	26	that	that	DET
ejpam-4871	155	27	|q|	|q|	NOUN
ejpam-4871	155	28	=	=	SYM
ejpam-4871	155	29	8	8	NUM
ejpam-4871	155	30	,	,	PUNCT
ejpam-4871	155	31	where	where	SCONJ
ejpam-4871	155	32	q▷h	q▷h	PUNCT
ejpam-4871	155	33	by	by	ADP
ejpam-4871	155	34	a	a	DET
ejpam-4871	155	35	group	group	NOUN
ejpam-4871	155	36	with	with	ADP
ejpam-4871	155	37	order	order	NOUN
ejpam-4871	155	38	7	7	NUM
ejpam-4871	155	39	.	.	PUNCT
ejpam-4871	155	40	since	since	SCONJ
ejpam-4871	155	41	|psl(2	|psl(2	PROPN
ejpam-4871	155	42	,	,	PUNCT
ejpam-4871	155	43	8)|	8)|	NUM
ejpam-4871	155	44	=	=	SYM
ejpam-4871	155	45	(	(	PUNCT
ejpam-4871	155	46	7)(8)(9	7)(8)(9	NOUN
ejpam-4871	155	47	)	)	PUNCT
ejpam-4871	155	48	,	,	PUNCT
ejpam-4871	155	49	then	then	ADV
ejpam-4871	155	50	the	the	DET
ejpam-4871	155	51	group	group	NOUN
ejpam-4871	155	52	q	q	NOUN
ejpam-4871	155	53	is	be	AUX
ejpam-4871	155	54	a	a	DET
ejpam-4871	155	55	2	2	NUM
ejpam-4871	155	56	-	-	PUNCT
ejpam-4871	155	57	sylow	sylow	NOUN
ejpam-4871	155	58	subgroup	subgroup	NOUN
ejpam-4871	155	59	of	of	ADP
ejpam-4871	155	60	psl(2	psl(2	NOUN
ejpam-4871	155	61	,	,	PUNCT
ejpam-4871	155	62	8)	8)	NUM
ejpam-4871	155	63	.	.	PUNCT
ejpam-4871	156	1	according	accord	VERB
ejpam-4871	156	2	to	to	ADP
ejpam-4871	156	3	[	[	X
ejpam-4871	156	4	8	8	NUM
ejpam-4871	156	5	,	,	PUNCT
ejpam-4871	156	6	theorem7.1	theorem7.1	X
ejpam-4871	156	7	]	]	PUNCT
ejpam-4871	156	8	2sylow	2sylow	NUM
ejpam-4871	156	9	subgroup	subgroup	NOUN
ejpam-4871	156	10	of	of	ADP
ejpam-4871	156	11	psl(2	psl(2	NOUN
ejpam-4871	156	12	,	,	PUNCT
ejpam-4871	156	13	8)	8)	NUM
ejpam-4871	156	14	is	be	AUX
ejpam-4871	156	15	composed	compose	VERB
ejpam-4871	156	16	of	of	ADP
ejpam-4871	156	17	matrices	matrix	NOUN
ejpam-4871	156	18	of	of	ADP
ejpam-4871	156	19	the	the	DET
ejpam-4871	156	20	form	form	NOUN
ejpam-4871	156	21	bβ	bβ	NOUN
ejpam-4871	156	22	=	=	PUNCT
ejpam-4871	156	23	[	[	PUNCT
ejpam-4871	156	24	1	1	NUM
ejpam-4871	156	25	β	β	NOUN
ejpam-4871	156	26	0	0	NUM
ejpam-4871	156	27	1	1	NUM
ejpam-4871	156	28	]	]	PUNCT
ejpam-4871	156	29	β	β	X
ejpam-4871	156	30	∈	∈	X
ejpam-4871	156	31	gf	gf	X
ejpam-4871	156	32	(	(	PUNCT
ejpam-4871	156	33	8)	8)	NUM
ejpam-4871	156	34	.	.	PUNCT
ejpam-4871	157	1	(	(	PUNCT
ejpam-4871	157	2	note	note	VERB
ejpam-4871	157	3	that	that	SCONJ
ejpam-4871	157	4	the	the	DET
ejpam-4871	157	5	center	center	NOUN
ejpam-4871	157	6	of	of	ADP
ejpam-4871	157	7	the	the	DET
ejpam-4871	157	8	group	group	NOUN
ejpam-4871	157	9	sl(2	sl(2	PROPN
ejpam-4871	157	10	,	,	PUNCT
ejpam-4871	157	11	8)	8)	NUM
ejpam-4871	157	12	is	be	AUX
ejpam-4871	157	13	equal	equal	ADJ
ejpam-4871	157	14	to	to	ADP
ejpam-4871	157	15	the	the	DET
ejpam-4871	157	16	identity	identity	NOUN
ejpam-4871	157	17	,	,	PUNCT
ejpam-4871	157	18	therefore	therefore	ADV
ejpam-4871	157	19	,	,	PUNCT
ejpam-4871	157	20	we	we	PRON
ejpam-4871	157	21	can	can	AUX
ejpam-4871	157	22	be	be	AUX
ejpam-4871	157	23	considered	consider	VERB
ejpam-4871	157	24	sl(2	sl(2	PROPN
ejpam-4871	157	25	,	,	PUNCT
ejpam-4871	157	26	8)	8)	NUM
ejpam-4871	157	27	=	=	SYM
ejpam-4871	157	28	psl(2	psl(2	NOUN
ejpam-4871	157	29	,	,	PUNCT
ejpam-4871	157	30	8)).thus	8)).thu	NOUN
ejpam-4871	157	31	we	we	PRON
ejpam-4871	157	32	can	can	AUX
ejpam-4871	157	33	write	write	VERB
ejpam-4871	157	34	that	that	DET
ejpam-4871	157	35	q	q	NOUN
ejpam-4871	158	1	=	=	PRON
ejpam-4871	158	2	{	{	PUNCT
ejpam-4871	158	3	bβ	bβ	NOUN
ejpam-4871	158	4	:	:	PUNCT
ejpam-4871	158	5	β	β	X
ejpam-4871	158	6	∈	∈	PRON
ejpam-4871	158	7	gf	gf	X
ejpam-4871	158	8	(	(	PUNCT
ejpam-4871	158	9	8)	8)	NUM
ejpam-4871	158	10	}	}	PUNCT
ejpam-4871	158	11	.	.	PUNCT
ejpam-4871	159	1	thus	thus	ADV
ejpam-4871	159	2	,	,	PUNCT
ejpam-4871	159	3	according	accord	VERB
ejpam-4871	159	4	to	to	ADP
ejpam-4871	159	5	the	the	DET
ejpam-4871	159	6	same	same	ADJ
ejpam-4871	159	7	theory	theory	NOUN
ejpam-4871	159	8	the	the	DET
ejpam-4871	159	9	normalizer	normalizer	PROPN
ejpam-4871	159	10	n(q	n(q	PROPN
ejpam-4871	159	11	)	)	PUNCT
ejpam-4871	159	12	is	be	AUX
ejpam-4871	159	13	composed	compose	VERB
ejpam-4871	159	14	of	of	ADP
ejpam-4871	159	15	matrices	matrix	NOUN
ejpam-4871	159	16	of	of	ADP
ejpam-4871	159	17	the	the	DET
ejpam-4871	159	18	form	form	NOUN
ejpam-4871	159	19	bβ	bβ	NOUN
ejpam-4871	159	20	=	=	PUNCT
ejpam-4871	159	21	[	[	PUNCT
ejpam-4871	159	22	1	1	NUM
ejpam-4871	159	23	β	β	NOUN
ejpam-4871	159	24	0	0	NUM
ejpam-4871	159	25	1	1	NUM
ejpam-4871	159	26	]	]	PUNCT
ejpam-4871	159	27	β	β	X
ejpam-4871	159	28	∈	∈	X
ejpam-4871	159	29	gf	gf	X
ejpam-4871	159	30	(	(	PUNCT
ejpam-4871	159	31	8)	8)	NUM
ejpam-4871	159	32	.	.	PUNCT
ejpam-4871	159	33	[	[	PUNCT
ejpam-4871	159	34	α	α	X
ejpam-4871	159	35	β	β	NOUN
ejpam-4871	159	36	0	0	PUNCT
ejpam-4871	159	37	δ	δ	NOUN
ejpam-4871	159	38	]	]	PUNCT
ejpam-4871	159	39	,	,	PUNCT
ejpam-4871	159	40	α	α	X
ejpam-4871	159	41	̸=	̸=	PROPN
ejpam-4871	159	42	0	0	NUM
ejpam-4871	159	43	,	,	PUNCT
ejpam-4871	159	44	δ	δ	PROPN
ejpam-4871	159	45	̸=	̸=	PROPN
ejpam-4871	159	46	0	0	NUM
ejpam-4871	159	47	.	.	PUNCT
ejpam-4871	160	1	since	since	SCONJ
ejpam-4871	160	2	det	det	PROPN
ejpam-4871	160	3	[	[	PUNCT
ejpam-4871	160	4	α	α	X
ejpam-4871	160	5	β	β	NOUN
ejpam-4871	160	6	0	0	PUNCT
ejpam-4871	160	7	δ	δ	NOUN
ejpam-4871	160	8	]	]	PUNCT
ejpam-4871	160	9	=	=	PUNCT
ejpam-4871	160	10	αδ	αδ	ADP
ejpam-4871	160	11	=	=	SYM
ejpam-4871	160	12	1	1	NUM
ejpam-4871	160	13	then	then	ADV
ejpam-4871	160	14	δ	δ	PROPN
ejpam-4871	160	15	=	=	SYM
ejpam-4871	160	16	α−1	α−1	PROPN
ejpam-4871	160	17	and	and	CCONJ
ejpam-4871	160	18	n(q	n(q	PROPN
ejpam-4871	160	19	)	)	PUNCT
ejpam-4871	161	1	=	=	PRON
ejpam-4871	161	2	{	{	PUNCT
ejpam-4871	161	3	[	[	PUNCT
ejpam-4871	161	4	α	α	X
ejpam-4871	161	5	β	β	NOUN
ejpam-4871	161	6	0	0	PUNCT
ejpam-4871	161	7	δ	δ	NOUN
ejpam-4871	161	8	]	]	X
ejpam-4871	161	9	:	:	PUNCT
ejpam-4871	161	10	α	α	PROPN
ejpam-4871	161	11	∈	∈	PROPN
ejpam-4871	161	12	f	f	PROPN
ejpam-4871	161	13	∗	∗	NOUN
ejpam-4871	161	14	,	,	PUNCT
ejpam-4871	161	15	β	β	X
ejpam-4871	161	16	∈	∈	X
ejpam-4871	161	17	gf	gf	X
ejpam-4871	161	18	(	(	PUNCT
ejpam-4871	161	19	8)	8)	NUM
ejpam-4871	161	20	}	}	PUNCT
ejpam-4871	161	21	.	.	PUNCT
ejpam-4871	162	1	we	we	PRON
ejpam-4871	162	2	study	study	VERB
ejpam-4871	162	3	the	the	DET
ejpam-4871	162	4	matrix	matrix	NOUN
ejpam-4871	162	5	aα	aα	NOUN
ejpam-4871	162	6	,	,	PUNCT
ejpam-4871	162	7	α	α	PROPN
ejpam-4871	162	8	̸=	̸=	PROPN
ejpam-4871	162	9	0	0	NUM
ejpam-4871	162	10	,	,	PUNCT
ejpam-4871	162	11	α	α	PROPN
ejpam-4871	162	12	∈	∈	ADJ
ejpam-4871	162	13	gf	gf	X
ejpam-4871	162	14	(	(	PUNCT
ejpam-4871	162	15	8)	8)	NUM
ejpam-4871	162	16	aα	aα	NOUN
ejpam-4871	162	17	=	=	PUNCT
ejpam-4871	162	18	[	[	PUNCT
ejpam-4871	162	19	α	α	NOUN
ejpam-4871	162	20	0	0	NUM
ejpam-4871	162	21	0	0	NUM
ejpam-4871	162	22	α−1	α−1	PROPN
ejpam-4871	162	23	]	]	PUNCT
ejpam-4871	162	24	.	.	PUNCT
ejpam-4871	163	1	a.	a.	PROPN
ejpam-4871	163	2	al	al	PROPN
ejpam-4871	163	3	khalaf	khalaf	PROPN
ejpam-4871	163	4	,	,	PUNCT
ejpam-4871	163	5	i.	i.	PROPN
ejpam-4871	163	6	taha	taha	PROPN
ejpam-4871	163	7	/	/	PUNCT
ejpam-4871	163	8	eur	eur	PROPN
ejpam-4871	163	9	.	.	PUNCT
ejpam-4871	164	1	j.	j.	PROPN
ejpam-4871	164	2	pure	pure	PROPN
ejpam-4871	164	3	appl	appl	PROPN
ejpam-4871	164	4	.	.	PROPN
ejpam-4871	164	5	math	math	PROPN
ejpam-4871	164	6	,	,	PUNCT
ejpam-4871	164	7	16	16	NUM
ejpam-4871	164	8	(	(	PUNCT
ejpam-4871	164	9	3	3	NUM
ejpam-4871	164	10	)	)	PUNCT
ejpam-4871	164	11	(	(	PUNCT
ejpam-4871	164	12	2023	2023	NUM
ejpam-4871	164	13	)	)	PUNCT
ejpam-4871	164	14	,	,	PUNCT
ejpam-4871	164	15	1970	1970	NUM
ejpam-4871	164	16	-	-	SYM
ejpam-4871	164	17	1979	1979	NUM
ejpam-4871	164	18	1977	1977	NUM
ejpam-4871	164	19	it	it	PRON
ejpam-4871	164	20	is	be	AUX
ejpam-4871	164	21	clear	clear	ADJ
ejpam-4871	164	22	that	that	SCONJ
ejpam-4871	164	23	|α|	|α|	NOUN
ejpam-4871	164	24	=	=	SYM
ejpam-4871	164	25	8	8	NUM
ejpam-4871	164	26	−	−	NUM
ejpam-4871	164	27	1	1	NUM
ejpam-4871	164	28	=	=	SYM
ejpam-4871	164	29	7	7	NUM
ejpam-4871	164	30	and	and	CCONJ
ejpam-4871	164	31	|aα|	|aα|	ADV
ejpam-4871	164	32	=	=	SYM
ejpam-4871	164	33	7	7	NUM
ejpam-4871	164	34	,	,	PUNCT
ejpam-4871	164	35	a7	a7	PROPN
ejpam-4871	164	36	α	α	NOUN
ejpam-4871	164	37	=	=	NOUN
ejpam-4871	164	38	1	1	NUM
ejpam-4871	164	39	now	now	ADV
ejpam-4871	164	40	,	,	PUNCT
ejpam-4871	164	41	the	the	DET
ejpam-4871	164	42	matrix	matrix	NOUN
ejpam-4871	164	43	of	of	ADP
ejpam-4871	164	44	the	the	DET
ejpam-4871	164	45	form	form	NOUN
ejpam-4871	164	46	aα	aα	NOUN
ejpam-4871	164	47	generate	generate	VERB
ejpam-4871	164	48	a	a	DET
ejpam-4871	164	49	cyclic	cyclic	ADJ
ejpam-4871	164	50	group	group	NOUN
ejpam-4871	164	51	of	of	ADP
ejpam-4871	164	52	order	order	NOUN
ejpam-4871	164	53	7	7	NUM
ejpam-4871	164	54	,	,	PUNCT
ejpam-4871	164	55	and	and	CCONJ
ejpam-4871	164	56	so	so	ADV
ejpam-4871	164	57	on	on	ADV
ejpam-4871	164	58	...	...	PUNCT
ejpam-4871	164	59	aαbβ	aαbβ	NOUN
ejpam-4871	164	60	=	=	PUNCT
ejpam-4871	164	61	[	[	PUNCT
ejpam-4871	164	62	α	α	NOUN
ejpam-4871	164	63	0	0	NUM
ejpam-4871	164	64	0	0	NUM
ejpam-4871	164	65	α−1	α−1	PROPN
ejpam-4871	164	66	]	]	PUNCT
ejpam-4871	165	1	[	[	PUNCT
ejpam-4871	165	2	1	1	NUM
ejpam-4871	165	3	β	β	NOUN
ejpam-4871	165	4	0	0	NUM
ejpam-4871	165	5	1	1	NUM
ejpam-4871	165	6	]	]	PUNCT
ejpam-4871	165	7	=	=	PUNCT
ejpam-4871	165	8	[	[	PUNCT
ejpam-4871	165	9	α	α	NOUN
ejpam-4871	165	10	αβ	αβ	NOUN
ejpam-4871	165	11	0	0	NUM
ejpam-4871	165	12	α−1	α−1	PROPN
ejpam-4871	165	13	]	]	PUNCT
ejpam-4871	165	14	.	.	PUNCT
ejpam-4871	166	1	then	then	ADV
ejpam-4871	166	2	n(q	n(q	PROPN
ejpam-4871	166	3	)	)	PUNCT
ejpam-4871	166	4	=	=	PUNCT
ejpam-4871	167	1	<	<	X
ejpam-4871	167	2	aα	aα	X
ejpam-4871	167	3	>	>	X
ejpam-4871	167	4	q	q	X
ejpam-4871	167	5	,	,	PUNCT
ejpam-4871	167	6	since	since	SCONJ
ejpam-4871	167	7	aαbβaα−1	aαbβaα−1	NOUN
ejpam-4871	167	8	=	=	SYM
ejpam-4871	167	9	[	[	PUNCT
ejpam-4871	167	10	α	α	NOUN
ejpam-4871	167	11	αβ	αβ	INTJ
ejpam-4871	167	12	0	0	NUM
ejpam-4871	167	13	α−1	α−1	NOUN
ejpam-4871	167	14	]	]	PUNCT
ejpam-4871	167	15	[	[	PUNCT
ejpam-4871	167	16	α−1	α−1	NOUN
ejpam-4871	167	17	0	0	NUM
ejpam-4871	167	18	0	0	NUM
ejpam-4871	168	1	α	α	NOUN
ejpam-4871	168	2	]	]	PUNCT
ejpam-4871	169	1	=	=	PUNCT
ejpam-4871	169	2	[	[	PUNCT
ejpam-4871	169	3	1	1	NUM
ejpam-4871	169	4	α2β	α2β	PROPN
ejpam-4871	169	5	0	0	NUM
ejpam-4871	169	6	1	1	NUM
ejpam-4871	169	7	]	]	PUNCT
ejpam-4871	169	8	,	,	PUNCT
ejpam-4871	169	9	and	and	CCONJ
ejpam-4871	169	10	<	<	X
ejpam-4871	169	11	aα	aα	X
ejpam-4871	169	12	>	>	X
ejpam-4871	169	13	∩q	∩q	PROPN
ejpam-4871	169	14	=	=	PUNCT
ejpam-4871	169	15	{	{	PUNCT
ejpam-4871	169	16	1	1	NUM
ejpam-4871	169	17	}	}	PUNCT
ejpam-4871	169	18	,	,	PUNCT
ejpam-4871	169	19	q	q	NOUN
ejpam-4871	169	20	⊴	⊴	ADP
ejpam-4871	169	21	n(q	n(q	PROPN
ejpam-4871	169	22	)	)	PUNCT
ejpam-4871	169	23	,	,	PUNCT
ejpam-4871	169	24	n(q	n(q	PROPN
ejpam-4871	169	25	)	)	PUNCT
ejpam-4871	169	26	=	=	SYM
ejpam-4871	169	27	qλ	qλ	PROPN
ejpam-4871	169	28	<	<	NOUN
ejpam-4871	169	29	aα	aα	NOUN
ejpam-4871	169	30	>	>	X
ejpam-4871	169	31	.	.	PUNCT
ejpam-4871	170	1	thus	thus	ADV
ejpam-4871	170	2	,	,	PUNCT
ejpam-4871	170	3	we	we	PRON
ejpam-4871	170	4	can	can	AUX
ejpam-4871	170	5	consider	consider	VERB
ejpam-4871	170	6	that	that	DET
ejpam-4871	170	7	h	h	NOUN
ejpam-4871	170	8	=	=	SYM
ejpam-4871	170	9	n(q	n(q	PROPN
ejpam-4871	170	10	)	)	PUNCT
ejpam-4871	170	11	,	,	PUNCT
ejpam-4871	170	12	and	and	CCONJ
ejpam-4871	170	13	k	k	X
ejpam-4871	170	14	=	=	PUNCT
ejpam-4871	171	1	<	<	X
ejpam-4871	171	2	aα	aα	X
ejpam-4871	171	3	>	>	PUNCT
ejpam-4871	171	4	.	.	PUNCT
ejpam-4871	172	1	since	since	SCONJ
ejpam-4871	172	2	bβbγ	bβbγ	NOUN
ejpam-4871	172	3	=	=	SYM
ejpam-4871	172	4	bβ+γ	bβ+γ	PROPN
ejpam-4871	172	5	.	.	PUNCT
ejpam-4871	173	1	(	(	PUNCT
ejpam-4871	173	2	1	1	X
ejpam-4871	173	3	)	)	PUNCT
ejpam-4871	173	4	then	then	ADV
ejpam-4871	173	5	it	it	PRON
ejpam-4871	173	6	can	can	AUX
ejpam-4871	173	7	be	be	AUX
ejpam-4871	173	8	considered	consider	VERB
ejpam-4871	173	9	that	that	PRON
ejpam-4871	173	10	q	q	NOUN
ejpam-4871	173	11	is	be	AUX
ejpam-4871	173	12	a	a	DET
ejpam-4871	173	13	vector	vector	NOUN
ejpam-4871	173	14	space	space	NOUN
ejpam-4871	173	15	over	over	ADP
ejpam-4871	173	16	the	the	DET
ejpam-4871	173	17	field	field	NOUN
ejpam-4871	173	18	gf	gf	X
ejpam-4871	173	19	(	(	PUNCT
ejpam-4871	173	20	8)	8)	NUM
ejpam-4871	173	21	and	and	CCONJ
ejpam-4871	173	22	the	the	DET
ejpam-4871	173	23	element	element	NOUN
ejpam-4871	173	24	aα	aα	NOUN
ejpam-4871	173	25	of	of	ADP
ejpam-4871	173	26	order	order	NOUN
ejpam-4871	173	27	7	7	NUM
ejpam-4871	173	28	acts	act	NOUN
ejpam-4871	173	29	on	on	ADP
ejpam-4871	173	30	q	q	NOUN
ejpam-4871	173	31	by	by	ADP
ejpam-4871	173	32	the	the	DET
ejpam-4871	173	33	rule	rule	NOUN
ejpam-4871	173	34	according	accord	VERB
ejpam-4871	173	35	to	to	ADP
ejpam-4871	173	36	(	(	PUNCT
ejpam-4871	173	37	1	1	NUM
ejpam-4871	173	38	)	)	PUNCT
ejpam-4871	174	1	ϕα	ϕα	ADV
ejpam-4871	174	2	:	:	PUNCT
ejpam-4871	174	3	bβ	bβ	NOUN
ejpam-4871	174	4	→	→	SYM
ejpam-4871	174	5	bα−2β	bα−2β	PROPN
ejpam-4871	174	6	,	,	PUNCT
ejpam-4871	174	7	f(α	f(α	NOUN
ejpam-4871	174	8	2	2	NUM
ejpam-4871	174	9	)	)	PUNCT
ejpam-4871	174	10	=	=	SYM
ejpam-4871	174	11	0	0	X
ejpam-4871	174	12	.	.	PUNCT
ejpam-4871	175	1	thus	thus	ADV
ejpam-4871	175	2	if	if	SCONJ
ejpam-4871	175	3	g(z	g(z	PROPN
ejpam-4871	175	4	)	)	PUNCT
ejpam-4871	175	5	is	be	AUX
ejpam-4871	175	6	a	a	DET
ejpam-4871	175	7	minimum	minimum	ADJ
ejpam-4871	175	8	polynomial	polynomial	NOUN
ejpam-4871	175	9	on	on	ADP
ejpam-4871	175	10	the	the	DET
ejpam-4871	175	11	field	field	NOUN
ejpam-4871	175	12	gf	gf	X
ejpam-4871	175	13	(	(	PUNCT
ejpam-4871	175	14	2	2	NUM
ejpam-4871	175	15	)	)	PUNCT
ejpam-4871	175	16	,	,	PUNCT
ejpam-4871	175	17	then	then	ADV
ejpam-4871	175	18	if	if	SCONJ
ejpam-4871	175	19	β	β	X
ejpam-4871	175	20	̸=	̸=	PROPN
ejpam-4871	175	21	0	0	NUM
ejpam-4871	175	22	,	,	PUNCT
ejpam-4871	175	23	then	then	ADV
ejpam-4871	175	24	g(ϕα)bβ	g(ϕα)bβ	NOUN
ejpam-4871	175	25	=	=	SYM
ejpam-4871	175	26	0	0	NUM
ejpam-4871	175	27	⇔	⇔	PROPN
ejpam-4871	175	28	g(α−2)β	g(α−2)β	PROPN
ejpam-4871	175	29	=	=	SYM
ejpam-4871	175	30	0	0	NUM
ejpam-4871	175	31	⇔	⇔	PROPN
ejpam-4871	175	32	g(α−2	g(α−2	PROPN
ejpam-4871	175	33	)	)	PUNCT
ejpam-4871	175	34	=	=	SYM
ejpam-4871	176	1	0	0	X
ejpam-4871	176	2	.	.	PUNCT
ejpam-4871	177	1	since	since	SCONJ
ejpam-4871	177	2	α−2	α−2	PROPN
ejpam-4871	177	3	̸=	̸=	PROPN
ejpam-4871	177	4	0	0	NUM
ejpam-4871	177	5	,	,	PUNCT
ejpam-4871	177	6	α−2	α−2	PROPN
ejpam-4871	177	7	is	be	AUX
ejpam-4871	177	8	the	the	DET
ejpam-4871	177	9	element	element	NOUN
ejpam-4871	177	10	of	of	ADP
ejpam-4871	177	11	the	the	DET
ejpam-4871	177	12	field	field	NOUN
ejpam-4871	177	13	gf	gf	X
ejpam-4871	177	14	(	(	PUNCT
ejpam-4871	177	15	8)	8)	NUM
ejpam-4871	177	16	has	have	AUX
ejpam-4871	177	17	a	a	DET
ejpam-4871	177	18	minimal	minimal	ADJ
ejpam-4871	177	19	polynomial	polynomial	NOUN
ejpam-4871	177	20	over	over	ADP
ejpam-4871	177	21	the	the	DET
ejpam-4871	177	22	field	field	NOUN
ejpam-4871	177	23	gf	gf	X
ejpam-4871	177	24	(	(	PUNCT
ejpam-4871	177	25	2	2	NUM
ejpam-4871	177	26	)	)	PUNCT
ejpam-4871	177	27	,	,	PUNCT
ejpam-4871	177	28	which	which	PRON
ejpam-4871	177	29	is	be	AUX
ejpam-4871	177	30	irreducible	irreducible	ADJ
ejpam-4871	177	31	over	over	ADP
ejpam-4871	177	32	the	the	DET
ejpam-4871	177	33	field	field	NOUN
ejpam-4871	177	34	gf	gf	X
ejpam-4871	177	35	(	(	PUNCT
ejpam-4871	177	36	2	2	NUM
ejpam-4871	177	37	)	)	PUNCT
ejpam-4871	177	38	and	and	CCONJ
ejpam-4871	177	39	according	accord	VERB
ejpam-4871	177	40	to	to	ADP
ejpam-4871	177	41	[	[	X
ejpam-4871	177	42	10	10	NUM
ejpam-4871	177	43	]	]	PUNCT
ejpam-4871	177	44	,	,	PUNCT
ejpam-4871	177	45	we	we	PRON
ejpam-4871	177	46	take	take	VERB
ejpam-4871	177	47	the	the	DET
ejpam-4871	177	48	minimum	minimum	ADJ
ejpam-4871	177	49	polynomial	polynomial	NOUN
ejpam-4871	177	50	of	of	ADP
ejpam-4871	177	51	the	the	DET
ejpam-4871	177	52	form	form	NOUN
ejpam-4871	177	53	f0(z	f0(z	PUNCT
ejpam-4871	177	54	)	)	PUNCT
ejpam-4871	178	1	=	=	SYM
ejpam-4871	178	2	z3	z3	PROPN
ejpam-4871	179	1	+	+	CCONJ
ejpam-4871	179	2	z	z	X
ejpam-4871	180	1	+	+	CCONJ
ejpam-4871	180	2	1	1	NUM
ejpam-4871	180	3	or	or	CCONJ
ejpam-4871	180	4	f0(z	f0(z	NUM
ejpam-4871	180	5	)	)	PUNCT
ejpam-4871	181	1	=	=	SYM
ejpam-4871	181	2	z3	z3	PROPN
ejpam-4871	181	3	+	+	CCONJ
ejpam-4871	181	4	z2	z2	PROPN
ejpam-4871	181	5	+	+	CCONJ
ejpam-4871	181	6	1	1	NUM
ejpam-4871	181	7	.	.	PUNCT
ejpam-4871	181	8	thus	thus	ADV
ejpam-4871	181	9	degf0(z	degf0(z	ADJ
ejpam-4871	181	10	)	)	PUNCT
ejpam-4871	181	11	=	=	NOUN
ejpam-4871	181	12	min{l	min{l	NOUN
ejpam-4871	181	13	∈	∈	PROPN
ejpam-4871	181	14	n	n	NOUN
ejpam-4871	181	15	:	:	PUNCT
ejpam-4871	181	16	zl	zl	PROPN
ejpam-4871	181	17	≡	≡	PROPN
ejpam-4871	181	18	1(mod7	1(mod7	NUM
ejpam-4871	181	19	)	)	PUNCT
ejpam-4871	181	20	.	.	PUNCT
ejpam-4871	182	1	hence	hence	ADV
ejpam-4871	182	2	,	,	PUNCT
ejpam-4871	182	3	the	the	DET
ejpam-4871	182	4	vector	vector	NOUN
ejpam-4871	182	5	space	space	NOUN
ejpam-4871	182	6	q	q	NOUN
ejpam-4871	182	7	is	be	AUX
ejpam-4871	182	8	not	not	PART
ejpam-4871	182	9	reducible	reducible	ADJ
ejpam-4871	182	10	,	,	PUNCT
ejpam-4871	182	11	and	and	CCONJ
ejpam-4871	182	12	it	it	PRON
ejpam-4871	182	13	follows	follow	VERB
ejpam-4871	182	14	that	that	SCONJ
ejpam-4871	182	15	all	all	DET
ejpam-4871	182	16	the	the	DET
ejpam-4871	182	17	conditions	condition	NOUN
ejpam-4871	182	18	of	of	ADP
ejpam-4871	182	19	the	the	DET
ejpam-4871	182	20	[	[	X
ejpam-4871	182	21	3	3	NUM
ejpam-4871	182	22	,	,	PUNCT
ejpam-4871	182	23	theorem	theorem	VERB
ejpam-4871	182	24	2.5	2.5	NUM
ejpam-4871	182	25	]	]	PUNCT
ejpam-4871	182	26	satisfy	satisfy	NOUN
ejpam-4871	182	27	for	for	ADP
ejpam-4871	182	28	the	the	DET
ejpam-4871	182	29	group	group	NOUN
ejpam-4871	182	30	h	h	NOUN
ejpam-4871	182	31	and	and	CCONJ
ejpam-4871	182	32	is	be	AUX
ejpam-4871	182	33	a	a	DET
ejpam-4871	182	34	group	group	NOUN
ejpam-4871	182	35	with	with	ADP
ejpam-4871	182	36	the	the	DET
ejpam-4871	182	37	basis	basis	NOUN
ejpam-4871	182	38	property	property	NOUN
ejpam-4871	182	39	.	.	PUNCT
ejpam-4871	183	1	•	•	NUM
ejpam-4871	183	2	the	the	DET
ejpam-4871	183	3	group	group	NOUN
ejpam-4871	183	4	a4	a4	PROPN
ejpam-4871	183	5	,	,	PUNCT
ejpam-4871	183	6	was	be	AUX
ejpam-4871	183	7	indicated	indicate	VERB
ejpam-4871	183	8	earlier	early	ADV
ejpam-4871	183	9	in	in	ADP
ejpam-4871	183	10	theorem	theorem	NOUN
ejpam-4871	183	11	1	1	NUM
ejpam-4871	183	12	that	that	SCONJ
ejpam-4871	183	13	it	it	PRON
ejpam-4871	183	14	is	be	AUX
ejpam-4871	183	15	a	a	DET
ejpam-4871	183	16	group	group	NOUN
ejpam-4871	183	17	with	with	ADP
ejpam-4871	183	18	the	the	DET
ejpam-4871	183	19	basis	basis	NOUN
ejpam-4871	183	20	property	property	NOUN
ejpam-4871	183	21	.	.	PUNCT
ejpam-4871	184	1	the	the	DET
ejpam-4871	184	2	group	group	NOUN
ejpam-4871	184	3	s4	s4	PROPN
ejpam-4871	184	4	does	do	AUX
ejpam-4871	184	5	not	not	PART
ejpam-4871	184	6	contain	contain	VERB
ejpam-4871	184	7	in	in	ADP
ejpam-4871	184	8	a	a	DET
ejpam-4871	184	9	group	group	NOUN
ejpam-4871	184	10	psl(2	psl(2	NOUN
ejpam-4871	184	11	,	,	PUNCT
ejpam-4871	184	12	8)	8)	NUM
ejpam-4871	184	13	,	,	PUNCT
ejpam-4871	184	14	then	then	ADV
ejpam-4871	184	15	by	by	ADP
ejpam-4871	184	16	theorem	theorem	ADJ
ejpam-4871	184	17	626	626	NUM
ejpam-4871	184	18	suzuki	suzuki	NOUN
ejpam-4871	184	19	[	[	X
ejpam-4871	184	20	20	20	NUM
ejpam-4871	184	21	]	]	PUNCT
ejpam-4871	184	22	,	,	PUNCT
ejpam-4871	184	23	since	since	SCONJ
ejpam-4871	184	24	in	in	ADP
ejpam-4871	184	25	this	this	DET
ejpam-4871	184	26	case	case	NOUN
ejpam-4871	184	27	q2	q2	NOUN
ejpam-4871	184	28	=	=	SYM
ejpam-4871	184	29	64	64	NUM
ejpam-4871	184	30	̸=	̸=	PROPN
ejpam-4871	184	31	1(mod16	1(mod16	NUM
ejpam-4871	184	32	)	)	PUNCT
ejpam-4871	184	33	also	also	ADV
ejpam-4871	184	34	the	the	DET
ejpam-4871	184	35	group	group	NOUN
ejpam-4871	184	36	psl(2	psl(2	NOUN
ejpam-4871	184	37	,	,	PUNCT
ejpam-4871	184	38	8)	8)	NUM
ejpam-4871	184	39	does	do	AUX
ejpam-4871	184	40	not	not	PART
ejpam-4871	184	41	contain	contain	VERB
ejpam-4871	184	42	a	a	DET
ejpam-4871	184	43	group	group	NOUN
ejpam-4871	184	44	a5	a5	NOUN
ejpam-4871	184	45	by	by	ADP
ejpam-4871	184	46	the	the	DET
ejpam-4871	184	47	same	same	ADJ
ejpam-4871	184	48	theorem	theorem	NOUN
ejpam-4871	184	49	,	,	PUNCT
ejpam-4871	184	50	since	since	SCONJ
ejpam-4871	184	51	q(q2	q(q2	NOUN
ejpam-4871	184	52	−	−	PROPN
ejpam-4871	184	53	1	1	NUM
ejpam-4871	184	54	)	)	PUNCT
ejpam-4871	184	55	=	=	SYM
ejpam-4871	184	56	(	(	PUNCT
ejpam-4871	184	57	8)(63	8)(63	NUM
ejpam-4871	184	58	)	)	PUNCT
ejpam-4871	184	59	̸=	̸=	PROPN
ejpam-4871	184	60	0(mod5	0(mod5	NUM
ejpam-4871	184	61	)	)	PUNCT
ejpam-4871	184	62	.	.	PUNCT
ejpam-4871	185	1	references	reference	NOUN
ejpam-4871	185	2	1978	1978	NUM
ejpam-4871	185	3	•	•	NOUN
ejpam-4871	185	4	if	if	SCONJ
ejpam-4871	185	5	r	r	NOUN
ejpam-4871	185	6	<	<	X
ejpam-4871	185	7	8	8	NUM
ejpam-4871	185	8	,	,	PUNCT
ejpam-4871	185	9	and	and	CCONJ
ejpam-4871	185	10	q	q	NOUN
ejpam-4871	185	11	=	=	PROPN
ejpam-4871	185	12	rm	rm	PROPN
ejpam-4871	185	13	,	,	PUNCT
ejpam-4871	185	14	then	then	ADV
ejpam-4871	185	15	r	r	NOUN
ejpam-4871	185	16	=	=	SYM
ejpam-4871	185	17	2	2	NUM
ejpam-4871	185	18	so	so	ADV
ejpam-4871	185	19	we	we	PRON
ejpam-4871	185	20	consider	consider	VERB
ejpam-4871	185	21	the	the	DET
ejpam-4871	185	22	groups	group	NOUN
ejpam-4871	185	23	psl(2	psl(2	ADJ
ejpam-4871	185	24	,	,	PUNCT
ejpam-4871	185	25	2	2	NUM
ejpam-4871	185	26	)	)	PUNCT
ejpam-4871	185	27	,	,	PUNCT
ejpam-4871	185	28	pgl(2	pgl(2	NOUN
ejpam-4871	185	29	,	,	PUNCT
ejpam-4871	185	30	2	2	NUM
ejpam-4871	185	31	)	)	PUNCT
ejpam-4871	185	32	.	.	PUNCT
ejpam-4871	186	1	since	since	SCONJ
ejpam-4871	186	2	the	the	DET
ejpam-4871	186	3	center	center	NOUN
ejpam-4871	186	4	of	of	ADP
ejpam-4871	186	5	the	the	DET
ejpam-4871	186	6	group	group	NOUN
ejpam-4871	186	7	gl(2	gl(2	PROPN
ejpam-4871	186	8	,	,	PUNCT
ejpam-4871	186	9	2	2	NUM
ejpam-4871	186	10	)	)	PUNCT
ejpam-4871	186	11	is	be	AUX
ejpam-4871	186	12	the	the	DET
ejpam-4871	186	13	identity	identity	NOUN
ejpam-4871	186	14	and	and	CCONJ
ejpam-4871	186	15	gf	gf	PROPN
ejpam-4871	186	16	(	(	PUNCT
ejpam-4871	186	17	2	2	NUM
ejpam-4871	186	18	)	)	PUNCT
ejpam-4871	186	19	=	=	NOUN
ejpam-4871	186	20	{	{	PUNCT
ejpam-4871	186	21	0	0	NUM
ejpam-4871	186	22	,	,	PUNCT
ejpam-4871	186	23	1	1	NUM
ejpam-4871	186	24	}	}	PUNCT
ejpam-4871	186	25	,	,	PUNCT
ejpam-4871	186	26	then	then	ADV
ejpam-4871	186	27	psl(2	psl(2	NOUN
ejpam-4871	186	28	,	,	PUNCT
ejpam-4871	186	29	2	2	X
ejpam-4871	186	30	)	)	PUNCT
ejpam-4871	186	31	∼=	∼=	PROPN
ejpam-4871	186	32	pgl(2	pgl(2	NOUN
ejpam-4871	186	33	,	,	PUNCT
ejpam-4871	186	34	2	2	X
ejpam-4871	186	35	)	)	PUNCT
ejpam-4871	186	36	∼=	∼=	PROPN
ejpam-4871	186	37	gl(2	gl(2	NOUN
ejpam-4871	186	38	,	,	PUNCT
ejpam-4871	186	39	2	2	NUM
ejpam-4871	186	40	)	)	PUNCT
ejpam-4871	186	41	=	=	SYM
ejpam-4871	186	42	2(22	2(22	NUM
ejpam-4871	187	1	−	−	NOUN
ejpam-4871	187	2	1	1	NUM
ejpam-4871	187	3	)	)	PUNCT
ejpam-4871	187	4	=	=	SYM
ejpam-4871	187	5	6	6	X
ejpam-4871	187	6	.	.	PUNCT
ejpam-4871	188	1	since	since	SCONJ
ejpam-4871	188	2	the	the	DET
ejpam-4871	188	3	group	group	NOUN
ejpam-4871	188	4	gl(2	gl(2	PROPN
ejpam-4871	188	5	,	,	PUNCT
ejpam-4871	188	6	2	2	NUM
ejpam-4871	188	7	)	)	PUNCT
ejpam-4871	188	8	is	be	AUX
ejpam-4871	188	9	not	not	PART
ejpam-4871	188	10	abelian	abelian	ADJ
ejpam-4871	188	11	of	of	ADP
ejpam-4871	188	12	order	order	NOUN
ejpam-4871	188	13	6	6	NUM
ejpam-4871	188	14	,	,	PUNCT
ejpam-4871	188	15	and	and	CCONJ
ejpam-4871	188	16	has	have	VERB
ejpam-4871	188	17	the	the	DET
ejpam-4871	188	18	form	form	NOUN
ejpam-4871	188	19	{	{	PUNCT
ejpam-4871	188	20	[	[	PUNCT
ejpam-4871	188	21	1	1	NUM
ejpam-4871	188	22	0	0	NUM
ejpam-4871	188	23	0	0	NUM
ejpam-4871	188	24	1	1	NUM
ejpam-4871	188	25	]	]	PUNCT
ejpam-4871	188	26	,	,	PUNCT
ejpam-4871	188	27	[	[	PUNCT
ejpam-4871	188	28	1	1	NUM
ejpam-4871	188	29	1	1	NUM
ejpam-4871	188	30	0	0	NUM
ejpam-4871	188	31	1	1	NUM
ejpam-4871	188	32	]	]	PUNCT
ejpam-4871	188	33	,	,	PUNCT
ejpam-4871	188	34	[	[	PUNCT
ejpam-4871	188	35	1	1	NUM
ejpam-4871	188	36	0	0	NUM
ejpam-4871	188	37	1	1	NUM
ejpam-4871	188	38	1	1	NUM
ejpam-4871	188	39	]	]	PUNCT
ejpam-4871	188	40	,	,	PUNCT
ejpam-4871	189	1	[	[	PUNCT
ejpam-4871	189	2	0	0	NUM
ejpam-4871	189	3	1	1	NUM
ejpam-4871	189	4	1	1	NUM
ejpam-4871	189	5	0	0	NUM
ejpam-4871	189	6	]	]	PUNCT
ejpam-4871	189	7	,	,	PUNCT
ejpam-4871	189	8	[	[	PUNCT
ejpam-4871	189	9	1	1	NUM
ejpam-4871	189	10	1	1	NUM
ejpam-4871	189	11	1	1	NUM
ejpam-4871	189	12	0	0	NUM
ejpam-4871	189	13	]	]	PUNCT
ejpam-4871	189	14	,	,	PUNCT
ejpam-4871	189	15	[	[	PUNCT
ejpam-4871	189	16	0	0	NUM
ejpam-4871	189	17	1	1	NUM
ejpam-4871	189	18	0	0	NUM
ejpam-4871	189	19	1	1	NUM
ejpam-4871	189	20	]	]	PUNCT
ejpam-4871	189	21	}	}	PUNCT
ejpam-4871	189	22	.	.	PUNCT
ejpam-4871	190	1	hence	hence	ADV
ejpam-4871	190	2	,	,	PUNCT
ejpam-4871	190	3	it	it	PRON
ejpam-4871	190	4	is	be	AUX
ejpam-4871	190	5	metacyclic	metacyclic	ADJ
ejpam-4871	190	6	so	so	SCONJ
ejpam-4871	190	7	it	it	PRON
ejpam-4871	190	8	is	be	AUX
ejpam-4871	190	9	a	a	DET
ejpam-4871	190	10	group	group	NOUN
ejpam-4871	190	11	with	with	ADP
ejpam-4871	190	12	the	the	DET
ejpam-4871	190	13	basis	basis	NOUN
ejpam-4871	190	14	property	property	NOUN
ejpam-4871	190	15	.	.	PUNCT
ejpam-4871	191	1	therefore	therefore	ADV
ejpam-4871	191	2	,	,	PUNCT
ejpam-4871	191	3	all	all	DET
ejpam-4871	191	4	cases	case	NOUN
ejpam-4871	191	5	have	have	AUX
ejpam-4871	191	6	been	be	AUX
ejpam-4871	191	7	studied	study	VERB
ejpam-4871	191	8	,	,	PUNCT
ejpam-4871	191	9	and	and	CCONJ
ejpam-4871	191	10	so	so	ADV
ejpam-4871	191	11	the	the	DET
ejpam-4871	191	12	group	group	NOUN
ejpam-4871	191	13	psl(2	psl(2	NOUN
ejpam-4871	191	14	,	,	PUNCT
ejpam-4871	191	15	8)	8)	NUM
ejpam-4871	191	16	is	be	AUX
ejpam-4871	191	17	minimal	minimal	ADJ
ejpam-4871	191	18	not	not	PART
ejpam-4871	191	19	satisfying	satisfy	VERB
ejpam-4871	191	20	the	the	DET
ejpam-4871	191	21	basis	basis	NOUN
ejpam-4871	191	22	property	property	NOUN
ejpam-4871	191	23	.	.	PUNCT
ejpam-4871	192	1	acknowledgements	acknowledgement	NOUN
ejpam-4871	192	2	the	the	DET
ejpam-4871	192	3	authors	author	NOUN
ejpam-4871	192	4	extend	extend	VERB
ejpam-4871	192	5	their	their	PRON
ejpam-4871	192	6	appreciation	appreciation	NOUN
ejpam-4871	192	7	to	to	ADP
ejpam-4871	192	8	the	the	DET
ejpam-4871	192	9	deanship	deanship	NOUN
ejpam-4871	192	10	of	of	ADP
ejpam-4871	192	11	scientific	scientific	ADJ
ejpam-4871	192	12	research	research	NOUN
ejpam-4871	192	13	,	,	PUNCT
ejpam-4871	192	14	imam	imam	PROPN
ejpam-4871	192	15	mohammad	mohammad	PROPN
ejpam-4871	192	16	ibn	ibn	PROPN
ejpam-4871	192	17	saud	saud	PROPN
ejpam-4871	192	18	islamic	islamic	PROPN
ejpam-4871	192	19	university	university	PROPN
ejpam-4871	192	20	(	(	PUNCT
ejpam-4871	192	21	imsiu	imsiu	PROPN
ejpam-4871	192	22	)	)	PUNCT
ejpam-4871	192	23	,	,	PUNCT
ejpam-4871	192	24	saudi	saudi	PROPN
ejpam-4871	192	25	arabia	arabia	PROPN
ejpam-4871	192	26	,	,	PUNCT
ejpam-4871	192	27	for	for	ADP
ejpam-4871	192	28	funding	fund	VERB
ejpam-4871	192	29	this	this	DET
ejpam-4871	192	30	research	research	NOUN
ejpam-4871	192	31	work	work	NOUN
ejpam-4871	192	32	through	through	ADP
ejpam-4871	192	33	grant	grant	NOUN
ejpam-4871	192	34	no	no	NOUN
ejpam-4871	192	35	.	.	PUNCT
ejpam-4871	193	1	(	(	PUNCT
ejpam-4871	193	2	221412001	221412001	NUM
ejpam-4871	193	3	)	)	PUNCT
ejpam-4871	193	4	.	.	PUNCT
ejpam-4871	194	1	references	reference	NOUN
ejpam-4871	194	2	[	[	X
ejpam-4871	194	3	1	1	X
ejpam-4871	194	4	]	]	PUNCT
ejpam-4871	194	5	i	i	PROPN
ejpam-4871	194	6	al	al	PROPN
ejpam-4871	194	7	-	-	PUNCT
ejpam-4871	194	8	dayel	dayel	PROPN
ejpam-4871	194	9	and	and	CCONJ
ejpam-4871	194	10	a	a	DET
ejpam-4871	194	11	al	al	PROPN
ejpam-4871	194	12	khalaf	khalaf	PROPN
ejpam-4871	194	13	.	.	PUNCT
ejpam-4871	195	1	completely	completely	ADV
ejpam-4871	195	2	0	0	NUM
ejpam-4871	195	3	-	-	PUNCT
ejpam-4871	195	4	simple	simple	ADJ
ejpam-4871	195	5	semigroup	semigroup	NOUN
ejpam-4871	195	6	with	with	ADP
ejpam-4871	195	7	the	the	DET
ejpam-4871	195	8	basis	basis	NOUN
ejpam-4871	195	9	property	property	NOUN
ejpam-4871	195	10	.	.	PUNCT
ejpam-4871	196	1	asian	asian	ADJ
ejpam-4871	196	2	-	-	PUNCT
ejpam-4871	196	3	european	european	ADJ
ejpam-4871	196	4	journal	journal	NOUN
ejpam-4871	196	5	of	of	ADP
ejpam-4871	196	6	mathematics	mathematic	NOUN
ejpam-4871	196	7	,	,	PUNCT
ejpam-4871	196	8	14(08):2150141	14(08):2150141	NUM
ejpam-4871	196	9	,	,	PUNCT
ejpam-4871	196	10	2020	2020	NUM
ejpam-4871	196	11	.	.	PUNCT
ejpam-4871	197	1	[	[	X
ejpam-4871	197	2	2	2	X
ejpam-4871	197	3	]	]	X
ejpam-4871	197	4	i	i	PROPN
ejpam-4871	197	5	al	al	PROPN
ejpam-4871	197	6	-	-	PUNCT
ejpam-4871	197	7	dayel	dayel	PROPN
ejpam-4871	197	8	and	and	CCONJ
ejpam-4871	197	9	a	a	DET
ejpam-4871	197	10	al	al	PROPN
ejpam-4871	197	11	khalaf	khalaf	PROPN
ejpam-4871	197	12	.	.	PUNCT
ejpam-4871	198	1	generalization	generalization	NOUN
ejpam-4871	198	2	of	of	ADP
ejpam-4871	198	3	the	the	DET
ejpam-4871	198	4	basis	basis	NOUN
ejpam-4871	198	5	property	property	NOUN
ejpam-4871	198	6	on	on	ADP
ejpam-4871	198	7	finite	finite	ADJ
ejpam-4871	198	8	groups	group	NOUN
ejpam-4871	198	9	.	.	PUNCT
ejpam-4871	199	1	asian	asian	ADJ
ejpam-4871	199	2	-	-	PUNCT
ejpam-4871	199	3	european	european	ADJ
ejpam-4871	199	4	journal	journal	NOUN
ejpam-4871	199	5	of	of	ADP
ejpam-4871	199	6	mathematics	mathematic	NOUN
ejpam-4871	199	7	,	,	PUNCT
ejpam-4871	199	8	14(07):2150111	14(07):2150111	NUM
ejpam-4871	199	9	,	,	PUNCT
ejpam-4871	199	10	2021	2021	NUM
ejpam-4871	199	11	.	.	PUNCT
ejpam-4871	200	1	[	[	X
ejpam-4871	200	2	3	3	X
ejpam-4871	200	3	]	]	PUNCT
ejpam-4871	200	4	a	a	DET
ejpam-4871	200	5	alhalaf	alhalaf	NOUN
ejpam-4871	200	6	.	.	PUNCT
ejpam-4871	201	1	finite	finite	PROPN
ejpam-4871	201	2	-	-	NOUN
ejpam-4871	201	3	group	group	NOUN
ejpam-4871	201	4	with	with	ADP
ejpam-4871	201	5	the	the	DET
ejpam-4871	201	6	basis	basis	NOUN
ejpam-4871	201	7	property	property	NOUN
ejpam-4871	201	8	.	.	PUNCT
ejpam-4871	202	1	in	in	ADP
ejpam-4871	202	2	doklady	doklady	NOUN
ejpam-4871	202	3	akademii	akademii	NOUN
ejpam-4871	202	4	nauk	nauk	ADJ
ejpam-4871	202	5	belarusi	belarusi	NOUN
ejpam-4871	202	6	,	,	PUNCT
ejpam-4871	202	7	volume	volume	NOUN
ejpam-4871	202	8	33	33	NUM
ejpam-4871	202	9	,	,	PUNCT
ejpam-4871	202	10	pages	page	NOUN
ejpam-4871	202	11	972–974	972–974	NUM
ejpam-4871	202	12	,	,	PUNCT
ejpam-4871	202	13	byelarus	byelarus	NOUN
ejpam-4871	202	14	,	,	PUNCT
ejpam-4871	202	15	1989	1989	NUM
ejpam-4871	202	16	.	.	PUNCT
ejpam-4871	203	1	academii	academii	PROPN
ejpam-4871	203	2	nauk	nauk	VERB
ejpam-4871	203	3	belarusi	belarusi	PROPN
ejpam-4871	204	1	f	f	PROPN
ejpam-4871	204	2	scorina	scorina	PROPN
ejpam-4871	204	3	pr	pr	VERB
ejpam-4871	204	4	66	66	NUM
ejpam-4871	204	5	,	,	PUNCT
ejpam-4871	204	6	room	room	NOUN
ejpam-4871	204	7	403	403	NUM
ejpam-4871	204	8	,	,	PUNCT
ejpam-4871	204	9	minsk	minsk	PROPN
ejpam-4871	204	10	,	,	PUNCT
ejpam-4871	204	11	220072	220072	NUM
ejpam-4871	204	12	.	.	PUNCT
ejpam-4871	205	1	[	[	X
ejpam-4871	205	2	4	4	X
ejpam-4871	205	3	]	]	X
ejpam-4871	205	4	a	a	DET
ejpam-4871	205	5	aljouiee	aljouiee	NOUN
ejpam-4871	205	6	and	and	CCONJ
ejpam-4871	205	7	a	a	DET
ejpam-4871	205	8	al	al	PROPN
ejpam-4871	205	9	khalaf	khalaf	PROPN
ejpam-4871	205	10	.	.	PUNCT
ejpam-4871	206	1	completely	completely	ADV
ejpam-4871	206	2	simple	simple	ADJ
ejpam-4871	206	3	semigroup	semigroup	NOUN
ejpam-4871	206	4	with	with	ADP
ejpam-4871	206	5	basis	basis	NOUN
ejpam-4871	206	6	property	property	NOUN
ejpam-4871	206	7	.	.	PUNCT
ejpam-4871	207	1	j.	j.	PROPN
ejpam-4871	207	2	semigroup	semigroup	PROPN
ejpam-4871	207	3	theory	theory	PROPN
ejpam-4871	207	4	appl	appl	PROPN
ejpam-4871	207	5	.	.	PROPN
ejpam-4871	207	6	,	,	PUNCT
ejpam-4871	207	7	10:1–10	10:1–10	NUM
ejpam-4871	207	8	,	,	PUNCT
ejpam-4871	207	9	2013	2013	NUM
ejpam-4871	207	10	.	.	PUNCT
ejpam-4871	208	1	[	[	X
ejpam-4871	208	2	5	5	NUM
ejpam-4871	208	3	]	]	PUNCT
ejpam-4871	208	4	m	m	VERB
ejpam-4871	208	5	alkadhi	alkadhi	ADJ
ejpam-4871	208	6	,	,	PUNCT
ejpam-4871	208	7	a	a	DET
ejpam-4871	208	8	al	al	PROPN
ejpam-4871	208	9	khalaf	khalaf	PROPN
ejpam-4871	208	10	,	,	PUNCT
ejpam-4871	208	11	and	and	CCONJ
ejpam-4871	208	12	m	m	VERB
ejpam-4871	208	13	quick	quick	ADJ
ejpam-4871	208	14	.	.	PUNCT
ejpam-4871	209	1	the	the	DET
ejpam-4871	209	2	nilpotency	nilpotency	NOUN
ejpam-4871	209	3	class	class	NOUN
ejpam-4871	209	4	of	of	ADP
ejpam-4871	209	5	fitting	fitting	ADJ
ejpam-4871	209	6	subgroups	subgroup	NOUN
ejpam-4871	209	7	of	of	ADP
ejpam-4871	209	8	groups	group	NOUN
ejpam-4871	209	9	with	with	ADP
ejpam-4871	209	10	basis	basis	NOUN
ejpam-4871	209	11	property	property	NOUN
ejpam-4871	209	12	.	.	PUNCT
ejpam-4871	210	1	international	international	ADJ
ejpam-4871	210	2	journal	journal	PROPN
ejpam-4871	210	3	of	of	ADP
ejpam-4871	210	4	algebra	algebra	PROPN
ejpam-4871	210	5	,	,	PUNCT
ejpam-4871	210	6	6(14):697–704	6(14):697–704	NUM
ejpam-4871	210	7	,	,	PUNCT
ejpam-4871	210	8	2012	2012	NUM
ejpam-4871	210	9	.	.	PUNCT
ejpam-4871	211	1	[	[	X
ejpam-4871	211	2	6	6	NUM
ejpam-4871	211	3	]	]	PUNCT
ejpam-4871	211	4	a	a	DET
ejpam-4871	211	5	alkhalaf	alkhalaf	PROPN
ejpam-4871	211	6	and	and	CCONJ
ejpam-4871	211	7	m	m	NOUN
ejpam-4871	211	8	alkadhi	alkadhi	ADJ
ejpam-4871	211	9	.	.	PUNCT
ejpam-4871	212	1	relation	relation	NOUN
ejpam-4871	212	2	between	between	ADP
ejpam-4871	212	3	groups	group	NOUN
ejpam-4871	212	4	with	with	ADP
ejpam-4871	212	5	basis	basis	NOUN
ejpam-4871	212	6	property	property	NOUN
ejpam-4871	212	7	and	and	CCONJ
ejpam-4871	212	8	groups	group	NOUN
ejpam-4871	212	9	with	with	ADP
ejpam-4871	212	10	exchange	exchange	NOUN
ejpam-4871	212	11	property	property	NOUN
ejpam-4871	212	12	.	.	PUNCT
ejpam-4871	213	1	analele	analele	ADP
ejpam-4871	213	2	ştiinţifice	ştiinţifice	PROPN
ejpam-4871	213	3	ale	ale	NOUN
ejpam-4871	213	4	universităţii	universităţii	PROPN
ejpam-4871	213	5	”	"	PUNCT
ejpam-4871	213	6	ovidius	ovidius	ADJ
ejpam-4871	213	7	”	"	PUNCT
ejpam-4871	213	8	constanţa	constanţa	NOUN
ejpam-4871	213	9	.	.	PUNCT
ejpam-4871	214	1	seria	seria	PROPN
ejpam-4871	214	2	matematică	matematică	PROPN
ejpam-4871	214	3	,	,	PUNCT
ejpam-4871	214	4	24(2):5–14	24(2):5–14	NUM
ejpam-4871	214	5	,	,	PUNCT
ejpam-4871	214	6	2016	2016	NUM
ejpam-4871	214	7	.	.	PUNCT
ejpam-4871	215	1	[	[	X
ejpam-4871	215	2	7	7	NUM
ejpam-4871	215	3	]	]	X
ejpam-4871	215	4	g	g	PROPN
ejpam-4871	215	5	higman	higman	NOUN
ejpam-4871	215	6	.	.	PUNCT
ejpam-4871	216	1	finite	finite	ADJ
ejpam-4871	216	2	groups	group	NOUN
ejpam-4871	216	3	in	in	ADP
ejpam-4871	216	4	which	which	PRON
ejpam-4871	216	5	every	every	DET
ejpam-4871	216	6	element	element	NOUN
ejpam-4871	216	7	has	have	VERB
ejpam-4871	216	8	prime	prime	ADJ
ejpam-4871	216	9	power	power	NOUN
ejpam-4871	216	10	order	order	NOUN
ejpam-4871	216	11	.	.	PUNCT
ejpam-4871	217	1	journal	journal	NOUN
ejpam-4871	217	2	of	of	ADP
ejpam-4871	217	3	the	the	DET
ejpam-4871	217	4	london	london	PROPN
ejpam-4871	217	5	mathematical	mathematical	ADJ
ejpam-4871	217	6	society	society	NOUN
ejpam-4871	217	7	,	,	PUNCT
ejpam-4871	217	8	1(3):335–342	1(3):335–342	NUM
ejpam-4871	217	9	,	,	PUNCT
ejpam-4871	217	10	1957	1957	NUM
ejpam-4871	217	11	.	.	PUNCT
ejpam-4871	218	1	references	reference	NOUN
ejpam-4871	218	2	1979	1979	NUM
ejpam-4871	218	3	[	[	X
ejpam-4871	218	4	8	8	NUM
ejpam-4871	218	5	]	]	SYM
ejpam-4871	218	6	b	b	X
ejpam-4871	218	7	huppert	huppert	X
ejpam-4871	218	8	.	.	PUNCT
ejpam-4871	218	9	endliche	endliche	PROPN
ejpam-4871	218	10	gruppen	gruppen	PROPN
ejpam-4871	218	11	i.	i.	PROPN
ejpam-4871	218	12	springer	springer	PROPN
ejpam-4871	218	13	-	-	PUNCT
ejpam-4871	218	14	verlag	verlag	PROPN
ejpam-4871	218	15	,	,	PUNCT
ejpam-4871	218	16	2013	2013	NUM
ejpam-4871	218	17	.	.	PUNCT
ejpam-4871	219	1	[	[	X
ejpam-4871	219	2	9	9	NUM
ejpam-4871	219	3	]	]	PUNCT
ejpam-4871	219	4	a.	a.	NOUN
ejpam-4871	219	5	g.	g.	PROPN
ejpam-4871	219	6	kurosh	kurosh	PROPN
ejpam-4871	219	7	.	.	PUNCT
ejpam-4871	220	1	the	the	DET
ejpam-4871	220	2	theory	theory	NOUN
ejpam-4871	220	3	of	of	ADP
ejpam-4871	220	4	groups	group	NOUN
ejpam-4871	220	5	.	.	PUNCT
ejpam-4871	220	6	,	,	PUNCT
ejpam-4871	220	7	volume	volume	NOUN
ejpam-4871	220	8	1	1	NUM
ejpam-4871	220	9	.	.	PUNCT
ejpam-4871	220	10	chelsea	chelsea	PROPN
ejpam-4871	220	11	publishing	publishing	PROPN
ejpam-4871	220	12	company	company	NOUN
ejpam-4871	220	13	,	,	PUNCT
ejpam-4871	220	14	1955	1955	NUM
ejpam-4871	220	15	.	.	PUNCT
ejpam-4871	221	1	[	[	X
ejpam-4871	221	2	10	10	NUM
ejpam-4871	221	3	]	]	X
ejpam-4871	221	4	f.	f.	PROPN
ejpam-4871	221	5	j.	j.	PROPN
ejpam-4871	221	6	macwilliams	macwilliams	PROPN
ejpam-4871	221	7	and	and	CCONJ
ejpam-4871	221	8	n.	n.	PROPN
ejpam-4871	221	9	a.	a.	PROPN
ejpam-4871	221	10	sloane	sloane	NOUN
ejpam-4871	221	11	.	.	PUNCT
ejpam-4871	222	1	the	the	DET
ejpam-4871	222	2	theory	theory	NOUN
ejpam-4871	222	3	of	of	ADP
ejpam-4871	222	4	error	error	NOUN
ejpam-4871	222	5	-	-	PUNCT
ejpam-4871	222	6	correcting	correct	VERB
ejpam-4871	222	7	codes	code	NOUN
ejpam-4871	222	8	.	.	PUNCT
ejpam-4871	223	1	,	,	PUNCT
ejpam-4871	223	2	volume	volume	NOUN
ejpam-4871	223	3	16	16	NUM
ejpam-4871	223	4	.	.	PUNCT
ejpam-4871	224	1	elsevier	elsevier	NOUN
ejpam-4871	224	2	,	,	PUNCT
ejpam-4871	224	3	1977	1977	NUM
ejpam-4871	224	4	.	.	PUNCT
ejpam-4871	225	1	[	[	X
ejpam-4871	225	2	11	11	NUM
ejpam-4871	225	3	]	]	X
ejpam-4871	225	4	j	j	PROPN
ejpam-4871	225	5	mcdougall	mcdougall	NOUN
ejpam-4871	225	6	-	-	PUNCT
ejpam-4871	225	7	bagnall	bagnall	NOUN
ejpam-4871	225	8	and	and	CCONJ
ejpam-4871	225	9	m	m	VERB
ejpam-4871	225	10	quick	quick	ADJ
ejpam-4871	225	11	.	.	PUNCT
ejpam-4871	226	1	groups	group	NOUN
ejpam-4871	226	2	with	with	ADP
ejpam-4871	226	3	the	the	DET
ejpam-4871	226	4	basis	basis	NOUN
ejpam-4871	226	5	property	property	NOUN
ejpam-4871	226	6	.	.	PUNCT
ejpam-4871	227	1	journal	journal	NOUN
ejpam-4871	227	2	of	of	ADP
ejpam-4871	227	3	algebra	algebra	PROPN
ejpam-4871	227	4	,	,	PUNCT
ejpam-4871	227	5	346(1):332–339	346(1):332–339	PROPN
ejpam-4871	227	6	,	,	PUNCT
ejpam-4871	227	7	2011	2011	NUM
ejpam-4871	227	8	.	.	PUNCT
ejpam-4871	228	1	[	[	X
ejpam-4871	228	2	12	12	NUM
ejpam-4871	228	3	]	]	PUNCT
ejpam-4871	228	4	p.	p.	NOUN
ejpam-4871	228	5	jones	jones	PROPN
ejpam-4871	228	6	.	.	PUNCT
ejpam-4871	229	1	a	a	DET
ejpam-4871	229	2	basis	basis	NOUN
ejpam-4871	229	3	theorem	theorem	NOUN
ejpam-4871	229	4	for	for	ADP
ejpam-4871	229	5	free	free	ADJ
ejpam-4871	229	6	inverse	inverse	NOUN
ejpam-4871	229	7	semigroups	semigroup	NOUN
ejpam-4871	229	8	.	.	PUNCT
ejpam-4871	230	1	journal	journal	NOUN
ejpam-4871	230	2	of	of	ADP
ejpam-4871	230	3	algebra	algebra	PROPN
ejpam-4871	230	4	,	,	PUNCT
ejpam-4871	230	5	49(1):172	49(1):172	NOUN
ejpam-4871	230	6	–	–	PUNCT
ejpam-4871	230	7	190	190	NUM
ejpam-4871	230	8	,	,	PUNCT
ejpam-4871	230	9	1977	1977	NUM
ejpam-4871	230	10	.	.	PUNCT
ejpam-4871	231	1	[	[	X
ejpam-4871	231	2	13	13	NUM
ejpam-4871	231	3	]	]	PUNCT
ejpam-4871	231	4	p.	p.	PROPN
ejpam-4871	231	5	jones	jones	PROPN
ejpam-4871	231	6	.	.	PUNCT
ejpam-4871	232	1	basis	basis	NOUN
ejpam-4871	232	2	properties	property	NOUN
ejpam-4871	232	3	for	for	ADP
ejpam-4871	232	4	inverse	inverse	NOUN
ejpam-4871	232	5	semigroups	semigroup	NOUN
ejpam-4871	232	6	.	.	PUNCT
ejpam-4871	233	1	journal	journal	NOUN
ejpam-4871	233	2	of	of	ADP
ejpam-4871	233	3	algebra	algebra	PROPN
ejpam-4871	233	4	,	,	PUNCT
ejpam-4871	233	5	50(1):135–152	50(1):135–152	PROPN
ejpam-4871	233	6	,	,	PUNCT
ejpam-4871	233	7	1978	1978	NUM
ejpam-4871	233	8	.	.	PUNCT
ejpam-4871	234	1	[	[	X
ejpam-4871	234	2	14	14	NUM
ejpam-4871	234	3	]	]	X
ejpam-4871	234	4	p.	p.	NOUN
ejpam-4871	234	5	jones	jones	PROPN
ejpam-4871	234	6	.	.	PUNCT
ejpam-4871	235	1	basis	basis	NOUN
ejpam-4871	235	2	properties	property	NOUN
ejpam-4871	235	3	,	,	PUNCT
ejpam-4871	235	4	exchange	exchange	NOUN
ejpam-4871	235	5	properties	property	NOUN
ejpam-4871	235	6	and	and	CCONJ
ejpam-4871	235	7	embeddings	embedding	NOUN
ejpam-4871	235	8	in	in	ADP
ejpam-4871	235	9	idempotent	idempotent	NOUN
ejpam-4871	235	10	-	-	PUNCT
ejpam-4871	235	11	free	free	ADJ
ejpam-4871	235	12	semigroups	semigroup	NOUN
ejpam-4871	235	13	.	.	PUNCT
ejpam-4871	236	1	in	in	ADP
ejpam-4871	236	2	semigroups	semigroup	NOUN
ejpam-4871	236	3	and	and	CCONJ
ejpam-4871	236	4	their	their	PRON
ejpam-4871	236	5	applications	application	NOUN
ejpam-4871	236	6	:	:	PUNCT
ejpam-4871	236	7	proceedings	proceeding	NOUN
ejpam-4871	236	8	of	of	ADP
ejpam-4871	236	9	the	the	DET
ejpam-4871	236	10	international	international	ADJ
ejpam-4871	236	11	conference	conference	NOUN
ejpam-4871	236	12	“	"	PUNCT
ejpam-4871	236	13	algebraic	algebraic	ADJ
ejpam-4871	236	14	theory	theory	NOUN
ejpam-4871	236	15	of	of	ADP
ejpam-4871	236	16	semigroups	semigroup	NOUN
ejpam-4871	236	17	and	and	CCONJ
ejpam-4871	236	18	its	its	PRON
ejpam-4871	236	19	applications	application	NOUN
ejpam-4871	236	20	”	"	PUNCT
ejpam-4871	236	21	held	hold	VERB
ejpam-4871	236	22	at	at	ADP
ejpam-4871	236	23	the	the	DET
ejpam-4871	236	24	california	california	PROPN
ejpam-4871	236	25	state	state	PROPN
ejpam-4871	236	26	university	university	PROPN
ejpam-4871	236	27	,	,	PUNCT
ejpam-4871	236	28	chico	chico	PROPN
ejpam-4871	236	29	,	,	PUNCT
ejpam-4871	236	30	april	april	PROPN
ejpam-4871	236	31	10–12	10–12	NUM
ejpam-4871	236	32	,	,	PUNCT
ejpam-4871	236	33	1986	1986	NUM
ejpam-4871	236	34	,	,	PUNCT
ejpam-4871	236	35	pages	page	NOUN
ejpam-4871	236	36	69–82	69–82	NUM
ejpam-4871	236	37	.	.	PUNCT
ejpam-4871	236	38	springer	springer	NOUN
ejpam-4871	236	39	,	,	PUNCT
ejpam-4871	236	40	1987	1987	NUM
ejpam-4871	236	41	.	.	PUNCT
ejpam-4871	237	1	[	[	X
ejpam-4871	237	2	15	15	NUM
ejpam-4871	237	3	]	]	X
ejpam-4871	237	4	p.	p.	NOUN
ejpam-4871	237	5	jones	jones	PROPN
ejpam-4871	237	6	.	.	PUNCT
ejpam-4871	238	1	exchange	exchange	NOUN
ejpam-4871	238	2	properties	property	NOUN
ejpam-4871	238	3	and	and	CCONJ
ejpam-4871	238	4	basis	basis	NOUN
ejpam-4871	238	5	properties	property	NOUN
ejpam-4871	238	6	for	for	ADP
ejpam-4871	238	7	closure	closure	NOUN
ejpam-4871	238	8	operators	operator	NOUN
ejpam-4871	238	9	.	.	PUNCT
ejpam-4871	239	1	in	in	ADP
ejpam-4871	239	2	colloquium	colloquium	NOUN
ejpam-4871	239	3	mathematicum	mathematicum	NOUN
ejpam-4871	239	4	,	,	PUNCT
ejpam-4871	239	5	volume	volume	NOUN
ejpam-4871	239	6	1	1	NUM
ejpam-4871	239	7	,	,	PUNCT
ejpam-4871	239	8	pages	page	NOUN
ejpam-4871	239	9	29–33	29–33	NUM
ejpam-4871	239	10	,	,	PUNCT
ejpam-4871	239	11	1989	1989	NUM
ejpam-4871	239	12	.	.	PUNCT
ejpam-4871	240	1	[	[	X
ejpam-4871	240	2	16	16	NUM
ejpam-4871	240	3	]	]	X
ejpam-4871	240	4	d	d	X
ejpam-4871	240	5	robinson	robinson	PROPN
ejpam-4871	240	6	.	.	PUNCT
ejpam-4871	241	1	a	a	DET
ejpam-4871	241	2	course	course	NOUN
ejpam-4871	241	3	in	in	ADP
ejpam-4871	241	4	the	the	DET
ejpam-4871	241	5	theory	theory	NOUN
ejpam-4871	241	6	of	of	ADP
ejpam-4871	241	7	groups	group	NOUN
ejpam-4871	241	8	.	.	PUNCT
ejpam-4871	242	1	,	,	PUNCT
ejpam-4871	242	2	volume	volume	NOUN
ejpam-4871	242	3	80	80	NUM
ejpam-4871	242	4	.	.	PUNCT
ejpam-4871	243	1	springer	springer	NOUN
ejpam-4871	243	2	science	science	PROPN
ejpam-4871	243	3	&	&	CCONJ
ejpam-4871	243	4	business	business	NOUN
ejpam-4871	243	5	media	medium	NOUN
ejpam-4871	243	6	,	,	PUNCT
ejpam-4871	243	7	2012	2012	NUM
ejpam-4871	243	8	.	.	PUNCT
ejpam-4871	244	1	[	[	X
ejpam-4871	244	2	17	17	NUM
ejpam-4871	244	3	]	]	X
ejpam-4871	244	4	r	r	NOUN
ejpam-4871	244	5	scapellato	scapellato	NOUN
ejpam-4871	244	6	and	and	CCONJ
ejpam-4871	244	7	l	l	NOUN
ejpam-4871	244	8	verardi	verardi	NOUN
ejpam-4871	244	9	.	.	PUNCT
ejpam-4871	245	1	bases	basis	NOUN
ejpam-4871	245	2	of	of	ADP
ejpam-4871	245	3	certain	certain	ADJ
ejpam-4871	245	4	finite	finite	ADJ
ejpam-4871	245	5	groups	group	NOUN
ejpam-4871	245	6	.	.	PUNCT
ejpam-4871	246	1	in	in	ADP
ejpam-4871	246	2	annales	annale	NOUN
ejpam-4871	246	3	mathématiques	mathématiques	PROPN
ejpam-4871	246	4	blaise	blaise	PROPN
ejpam-4871	246	5	pascal	pascal	PROPN
ejpam-4871	246	6	,	,	PUNCT
ejpam-4871	246	7	pages	page	NOUN
ejpam-4871	246	8	85–93	85–93	NUM
ejpam-4871	246	9	,	,	PUNCT
ejpam-4871	246	10	1994	1994	NUM
ejpam-4871	246	11	.	.	PUNCT
ejpam-4871	247	1	[	[	X
ejpam-4871	247	2	18	18	NUM
ejpam-4871	247	3	]	]	X
ejpam-4871	247	4	r	r	NOUN
ejpam-4871	247	5	scapellato	scapellato	PROPN
ejpam-4871	247	6	,	,	PUNCT
ejpam-4871	247	7	l	l	NOUN
ejpam-4871	247	8	verardi	verardi	NOUN
ejpam-4871	247	9	,	,	PUNCT
ejpam-4871	247	10	et	et	PROPN
ejpam-4871	247	11	al	al	PROPN
ejpam-4871	247	12	.	.	PROPN
ejpam-4871	247	13	groupes	groupes	PROPN
ejpam-4871	247	14	finis	finis	PROPN
ejpam-4871	247	15	qui	qui	X
ejpam-4871	247	16	jouissent	jouissent	PROPN
ejpam-4871	247	17	d’une	d’une	ADJ
ejpam-4871	247	18	propriété	propriété	NOUN
ejpam-4871	247	19	analogue	analogue	NOUN
ejpam-4871	247	20	au	au	ADP
ejpam-4871	247	21	théorème	théorème	PROPN
ejpam-4871	247	22	des	des	PROPN
ejpam-4871	247	23	bases	basis	NOUN
ejpam-4871	247	24	de	de	X
ejpam-4871	247	25	burnside	burnside	PROPN
ejpam-4871	247	26	.	.	PUNCT
ejpam-4871	248	1	bollettino	bollettino	PROPN
ejpam-4871	248	2	dell	dell	PROPN
ejpam-4871	248	3	union	union	PROPN
ejpam-4871	248	4	matematica	matematica	PROPN
ejpam-4871	248	5	italiana	italiana	PROPN
ejpam-4871	248	6	a.	a.	PROPN
ejpam-4871	248	7	,	,	PUNCT
ejpam-4871	248	8	7:187–194	7:187–194	NOUN
ejpam-4871	248	9	,	,	PUNCT
ejpam-4871	248	10	1991	1991	NUM
ejpam-4871	248	11	.	.	PUNCT
ejpam-4871	249	1	[	[	X
ejpam-4871	249	2	19	19	NUM
ejpam-4871	249	3	]	]	X
ejpam-4871	249	4	m	m	PROPN
ejpam-4871	249	5	suzuki	suzuki	PROPN
ejpam-4871	249	6	.	.	PUNCT
ejpam-4871	250	1	a	a	DET
ejpam-4871	250	2	new	new	ADJ
ejpam-4871	250	3	type	type	NOUN
ejpam-4871	250	4	of	of	ADP
ejpam-4871	250	5	simple	simple	ADJ
ejpam-4871	250	6	groups	group	NOUN
ejpam-4871	250	7	of	of	ADP
ejpam-4871	250	8	finite	finite	ADJ
ejpam-4871	250	9	order	order	NOUN
ejpam-4871	250	10	.	.	PUNCT
ejpam-4871	251	1	proceedings	proceeding	NOUN
ejpam-4871	251	2	of	of	ADP
ejpam-4871	251	3	the	the	DET
ejpam-4871	251	4	national	national	PROPN
ejpam-4871	251	5	academy	academy	PROPN
ejpam-4871	251	6	of	of	ADP
ejpam-4871	251	7	sciences	sciences	PROPN
ejpam-4871	251	8	,	,	PUNCT
ejpam-4871	251	9	46(6):868–870	46(6):868–870	PROPN
ejpam-4871	251	10	,	,	PUNCT
ejpam-4871	251	11	1960	1960	NUM
ejpam-4871	251	12	.	.	PUNCT
ejpam-4871	252	1	[	[	X
ejpam-4871	252	2	20	20	NUM
ejpam-4871	252	3	]	]	X
ejpam-4871	252	4	m	m	PROPN
ejpam-4871	252	5	suzuki	suzuki	PROPN
ejpam-4871	252	6	.	.	PUNCT
ejpam-4871	253	1	on	on	ADP
ejpam-4871	253	2	generalized	generalized	ADJ
ejpam-4871	253	3	(	(	PUNCT
ejpam-4871	253	4	zt)-groups	zt)-group	NOUN
ejpam-4871	253	5	.	.	PUNCT
ejpam-4871	254	1	archiv	archiv	PROPN
ejpam-4871	254	2	der	der	PROPN
ejpam-4871	254	3	mathematik	mathematik	PROPN
ejpam-4871	254	4	,	,	PUNCT
ejpam-4871	254	5	13:199–202	13:199–202	PROPN
ejpam-4871	254	6	,	,	PUNCT
ejpam-4871	254	7	1962	1962	NUM
ejpam-4871	254	8	.	.	PUNCT