id	sid	tid	token	lemma	pos
ejpam-4755	1	1	european	european	PROPN
ejpam-4755	1	2	journal	journal	PROPN
ejpam-4755	1	3	of	of	ADP
ejpam-4755	1	4	pure	pure	ADJ
ejpam-4755	1	5	and	and	CCONJ
ejpam-4755	1	6	applied	apply	VERB
ejpam-4755	1	7	mathematics	mathematic	NOUN
ejpam-4755	1	8	vol	vol	NOUN
ejpam-4755	1	9	.	.	PUNCT
ejpam-4755	2	1	16	16	NUM
ejpam-4755	2	2	,	,	PUNCT
ejpam-4755	2	3	no	no	INTJ
ejpam-4755	2	4	.	.	NOUN
ejpam-4755	2	5	2	2	NUM
ejpam-4755	2	6	,	,	PUNCT
ejpam-4755	2	7	2023	2023	NUM
ejpam-4755	2	8	,	,	PUNCT
ejpam-4755	2	9	1118	1118	NUM
ejpam-4755	2	10	-	-	SYM
ejpam-4755	2	11	1127	1127	NUM
ejpam-4755	2	12	issn	issn	PROPN
ejpam-4755	2	13	1307	1307	NUM
ejpam-4755	2	14	-	-	SYM
ejpam-4755	2	15	5543	5543	NUM
ejpam-4755	2	16	–	–	PUNCT
ejpam-4755	2	17	ejpam.com	ejpam.com	X
ejpam-4755	2	18	published	publish	VERB
ejpam-4755	2	19	by	by	ADP
ejpam-4755	2	20	new	new	PROPN
ejpam-4755	2	21	york	york	PROPN
ejpam-4755	2	22	business	business	PROPN
ejpam-4755	2	23	global	global	ADJ
ejpam-4755	2	24	nonabelian	nonabelian	ADJ
ejpam-4755	2	25	case	case	NOUN
ejpam-4755	2	26	of	of	ADP
ejpam-4755	2	27	hopf	hopf	ADJ
ejpam-4755	2	28	galois	galois	PROPN
ejpam-4755	2	29	structures	structure	NOUN
ejpam-4755	2	30	on	on	ADP
ejpam-4755	2	31	nonnormal	nonnormal	ADJ
ejpam-4755	2	32	extensions	extension	NOUN
ejpam-4755	2	33	of	of	ADP
ejpam-4755	2	34	degree	degree	NOUN
ejpam-4755	2	35	pqw	pqw	ADJ
ejpam-4755	2	36	baraa	baraa	ADJ
ejpam-4755	2	37	m.	m.	NOUN
ejpam-4755	3	1	jamal1	jamal1	PROPN
ejpam-4755	3	2	,	,	PUNCT
ejpam-4755	3	3	ali	ali	PROPN
ejpam-4755	3	4	a.	a.	PROPN
ejpam-4755	3	5	alabdali1,∗	alabdali1,∗	PROPN
ejpam-4755	3	6	1	1	NUM
ejpam-4755	3	7	department	department	PROPN
ejpam-4755	3	8	of	of	ADP
ejpam-4755	3	9	mathematics	mathematic	NOUN
ejpam-4755	3	10	,	,	PUNCT
ejpam-4755	3	11	college	college	NOUN
ejpam-4755	3	12	of	of	ADP
ejpam-4755	3	13	education	education	NOUN
ejpam-4755	3	14	for	for	ADP
ejpam-4755	3	15	pure	pure	ADJ
ejpam-4755	3	16	science	science	NOUN
ejpam-4755	3	17	,	,	PUNCT
ejpam-4755	3	18	university	university	NOUN
ejpam-4755	3	19	of	of	ADP
ejpam-4755	3	20	mosul	mosul	PROPN
ejpam-4755	3	21	,	,	PUNCT
ejpam-4755	3	22	mosul	mosul	PROPN
ejpam-4755	3	23	,	,	PUNCT
ejpam-4755	3	24	iraq	iraq	PROPN
ejpam-4755	3	25	abstract	abstract	NOUN
ejpam-4755	3	26	.	.	PUNCT
ejpam-4755	4	1	we	we	PRON
ejpam-4755	4	2	look	look	VERB
ejpam-4755	4	3	at	at	ADP
ejpam-4755	4	4	hopf	hopf	X
ejpam-4755	4	5	galois	galois	PROPN
ejpam-4755	4	6	structures	structure	NOUN
ejpam-4755	4	7	with	with	ADP
ejpam-4755	4	8	square	square	ADJ
ejpam-4755	4	9	free	free	ADJ
ejpam-4755	4	10	pqw	pqw	NOUN
ejpam-4755	4	11	degree	degree	NOUN
ejpam-4755	4	12	on	on	ADP
ejpam-4755	4	13	separable	separable	ADJ
ejpam-4755	4	14	field	field	NOUN
ejpam-4755	4	15	extensions	extension	NOUN
ejpam-4755	4	16	(	(	PUNCT
ejpam-4755	4	17	nonnormal	nonnormal	ADJ
ejpam-4755	4	18	)	)	PUNCT
ejpam-4755	5	1	l	l	NOUN
ejpam-4755	5	2	/	/	SYM
ejpam-4755	5	3	k.	k.	PROPN
ejpam-4755	5	4	where	where	SCONJ
ejpam-4755	5	5	e	e	X
ejpam-4755	5	6	/	/	SYM
ejpam-4755	5	7	k	k	PROPN
ejpam-4755	5	8	is	be	AUX
ejpam-4755	5	9	the	the	DET
ejpam-4755	5	10	normal	normal	ADJ
ejpam-4755	5	11	closure	closure	NOUN
ejpam-4755	5	12	of	of	ADP
ejpam-4755	5	13	l	l	NOUN
ejpam-4755	5	14	/	/	SYM
ejpam-4755	5	15	k	k	NOUN
ejpam-4755	5	16	,	,	PUNCT
ejpam-4755	5	17	the	the	DET
ejpam-4755	5	18	group	group	NOUN
ejpam-4755	5	19	permutation	permutation	NOUN
ejpam-4755	5	20	of	of	ADP
ejpam-4755	5	21	degree	degree	NOUN
ejpam-4755	5	22	pqw	pqw	NOUN
ejpam-4755	5	23	is	be	AUX
ejpam-4755	5	24	g	g	NOUN
ejpam-4755	5	25	=	=	SYM
ejpam-4755	5	26	gal(e	gal(e	PROPN
ejpam-4755	5	27	/	/	SYM
ejpam-4755	5	28	k	k	NOUN
ejpam-4755	5	29	)	)	PUNCT
ejpam-4755	5	30	.	.	PUNCT
ejpam-4755	6	1	we	we	PRON
ejpam-4755	6	2	study	study	VERB
ejpam-4755	6	3	details	detail	NOUN
ejpam-4755	6	4	of	of	ADP
ejpam-4755	6	5	the	the	DET
ejpam-4755	6	6	nonabelian	nonabelian	ADJ
ejpam-4755	6	7	case	case	NOUN
ejpam-4755	6	8	,	,	PUNCT
ejpam-4755	6	9	where	where	SCONJ
ejpam-4755	6	10	jl	jl	NOUN
ejpam-4755	6	11	=	=	SYM
ejpam-4755	6	12	⟨σ	⟨σ	NOUN
ejpam-4755	6	13	,	,	PUNCT
ejpam-4755	6	14	[	[	X
ejpam-4755	6	15	τ	τ	X
ejpam-4755	6	16	,	,	PUNCT
ejpam-4755	6	17	αl]⟩	αl]⟩	ADJ
ejpam-4755	6	18	is	be	AUX
ejpam-4755	6	19	a	a	DET
ejpam-4755	6	20	nonabelian	nonabelian	ADJ
ejpam-4755	6	21	regular	regular	ADJ
ejpam-4755	6	22	subgroup	subgroup	NOUN
ejpam-4755	6	23	of	of	ADP
ejpam-4755	6	24	hol(n	hol(n	PROPN
ejpam-4755	6	25	)	)	PUNCT
ejpam-4755	6	26	for	for	ADP
ejpam-4755	6	27	1	1	NUM
ejpam-4755	6	28	≤	≤	NUM
ejpam-4755	6	29	l	l	NOUN
ejpam-4755	6	30	≤	≤	NUM
ejpam-4755	7	1	w	w	ADP
ejpam-4755	7	2	−	−	NOUN
ejpam-4755	8	1	1	1	X
ejpam-4755	8	2	.	.	PUNCT
ejpam-4755	8	3	we	we	PRON
ejpam-4755	8	4	first	first	ADV
ejpam-4755	8	5	find	find	VERB
ejpam-4755	8	6	the	the	DET
ejpam-4755	8	7	group	group	NOUN
ejpam-4755	8	8	permutation	permutation	NOUN
ejpam-4755	8	9	g	g	NOUN
ejpam-4755	8	10	,	,	PUNCT
ejpam-4755	8	11	and	and	CCONJ
ejpam-4755	8	12	then	then	ADV
ejpam-4755	8	13	the	the	DET
ejpam-4755	8	14	hopf	hopf	ADJ
ejpam-4755	8	15	galois	galois	PROPN
ejpam-4755	8	16	structures	structure	NOUN
ejpam-4755	8	17	for	for	ADP
ejpam-4755	8	18	each	each	DET
ejpam-4755	8	19	g.	g.	NOUN
ejpam-4755	8	20	in	in	ADP
ejpam-4755	8	21	this	this	DET
ejpam-4755	8	22	case	case	NOUN
ejpam-4755	8	23	,	,	PUNCT
ejpam-4755	8	24	there	there	PRON
ejpam-4755	8	25	exists	exist	VERB
ejpam-4755	8	26	four	four	NUM
ejpam-4755	8	27	g	g	NOUN
ejpam-4755	8	28	such	such	ADJ
ejpam-4755	8	29	that	that	SCONJ
ejpam-4755	8	30	the	the	DET
ejpam-4755	8	31	hopf	hopf	ADJ
ejpam-4755	8	32	galois	galois	PROPN
ejpam-4755	8	33	structures	structure	NOUN
ejpam-4755	8	34	are	be	AUX
ejpam-4755	8	35	admissible	admissible	ADJ
ejpam-4755	8	36	within	within	ADP
ejpam-4755	8	37	the	the	DET
ejpam-4755	8	38	field	field	NOUN
ejpam-4755	8	39	extensions	extension	NOUN
ejpam-4755	8	40	l	l	PROPN
ejpam-4755	8	41	/	/	SYM
ejpam-4755	8	42	k.	k.	NOUN
ejpam-4755	8	43	2020	2020	NUM
ejpam-4755	8	44	mathematics	mathematics	PROPN
ejpam-4755	8	45	subject	subject	NOUN
ejpam-4755	8	46	classifications	classification	NOUN
ejpam-4755	8	47	:	:	PUNCT
ejpam-4755	8	48	12f10	12f10	NUM
ejpam-4755	8	49	,	,	PUNCT
ejpam-4755	8	50	16t05	16t05	NUM
ejpam-4755	8	51	key	key	ADJ
ejpam-4755	8	52	words	word	NOUN
ejpam-4755	8	53	and	and	CCONJ
ejpam-4755	8	54	phrases	phrase	NOUN
ejpam-4755	8	55	:	:	PUNCT
ejpam-4755	8	56	hopf	hopf	PROPN
ejpam-4755	8	57	galois	galois	PROPN
ejpam-4755	8	58	structures	structure	NOUN
ejpam-4755	8	59	,	,	PUNCT
ejpam-4755	8	60	field	field	NOUN
ejpam-4755	8	61	extensions	extension	NOUN
ejpam-4755	8	62	,	,	PUNCT
ejpam-4755	8	63	groups	group	NOUN
ejpam-4755	8	64	of	of	ADP
ejpam-4755	8	65	square	square	ADJ
ejpam-4755	8	66	free	free	ADJ
ejpam-4755	8	67	order	order	NOUN
ejpam-4755	8	68	,	,	PUNCT
ejpam-4755	8	69	sophie	sophie	PROPN
ejpam-4755	8	70	germain	germain	PROPN
ejpam-4755	8	71	primes	prime	NOUN
ejpam-4755	8	72	1	1	NUM
ejpam-4755	8	73	.	.	PUNCT
ejpam-4755	8	74	introduction	introduction	NOUN
ejpam-4755	8	75	chase	chase	NOUN
ejpam-4755	8	76	and	and	CCONJ
ejpam-4755	8	77	sweedler	sweedler	NOUN
ejpam-4755	8	78	[	[	X
ejpam-4755	8	79	7	7	NUM
ejpam-4755	8	80	]	]	PUNCT
ejpam-4755	8	81	proposed	propose	VERB
ejpam-4755	8	82	the	the	DET
ejpam-4755	8	83	hopf	hopf	ADJ
ejpam-4755	8	84	galois	galois	PROPN
ejpam-4755	8	85	theory	theory	NOUN
ejpam-4755	8	86	by	by	ADP
ejpam-4755	8	87	investigating	investigate	VERB
ejpam-4755	8	88	inseparable	inseparable	ADJ
ejpam-4755	8	89	field	field	NOUN
ejpam-4755	8	90	extensions	extension	NOUN
ejpam-4755	8	91	.	.	PUNCT
ejpam-4755	9	1	their	their	PRON
ejpam-4755	9	2	work	work	NOUN
ejpam-4755	9	3	marks	mark	VERB
ejpam-4755	9	4	the	the	DET
ejpam-4755	9	5	start	start	NOUN
ejpam-4755	9	6	of	of	ADP
ejpam-4755	9	7	a	a	DET
ejpam-4755	9	8	slew	slew	NOUN
ejpam-4755	9	9	of	of	ADP
ejpam-4755	9	10	new	new	ADJ
ejpam-4755	9	11	problems	problem	NOUN
ejpam-4755	9	12	about	about	ADP
ejpam-4755	9	13	separable	separable	ADJ
ejpam-4755	9	14	field	field	NOUN
ejpam-4755	9	15	extensions	extension	NOUN
ejpam-4755	9	16	(	(	PUNCT
ejpam-4755	9	17	sfes	sfe	NOUN
ejpam-4755	9	18	)	)	PUNCT
ejpam-4755	9	19	.	.	PUNCT
ejpam-4755	10	1	in	in	ADP
ejpam-4755	10	2	[	[	X
ejpam-4755	10	3	14	14	NUM
ejpam-4755	10	4	]	]	X
ejpam-4755	10	5	greither	greither	NOUN
ejpam-4755	10	6	and	and	CCONJ
ejpam-4755	10	7	pareigis	pareigis	NOUN
ejpam-4755	10	8	showed	show	VERB
ejpam-4755	10	9	that	that	SCONJ
ejpam-4755	10	10	an	an	DET
ejpam-4755	10	11	sfe	sfe	PROPN
ejpam-4755	10	12	can	can	AUX
ejpam-4755	10	13	generate	generate	VERB
ejpam-4755	10	14	a	a	DET
ejpam-4755	10	15	large	large	ADJ
ejpam-4755	10	16	number	number	NOUN
ejpam-4755	10	17	of	of	ADP
ejpam-4755	10	18	hopf	hopf	ADJ
ejpam-4755	10	19	galois	galois	PROPN
ejpam-4755	10	20	structures	structure	NOUN
ejpam-4755	10	21	(	(	PUNCT
ejpam-4755	10	22	hgss	hgss	ADJ
ejpam-4755	10	23	)	)	PUNCT
ejpam-4755	10	24	,	,	PUNCT
ejpam-4755	10	25	and	and	CCONJ
ejpam-4755	10	26	hgss	hgss	PROPN
ejpam-4755	10	27	can	can	AUX
ejpam-4755	10	28	be	be	AUX
ejpam-4755	10	29	used	use	VERB
ejpam-4755	10	30	by	by	ADP
ejpam-4755	10	31	the	the	DET
ejpam-4755	10	32	group	group	NOUN
ejpam-4755	10	33	theoretic	theoretic	NOUN
ejpam-4755	10	34	in	in	ADP
ejpam-4755	10	35	issues	issue	NOUN
ejpam-4755	10	36	.	.	PUNCT
ejpam-4755	11	1	if	if	SCONJ
ejpam-4755	11	2	the	the	DET
ejpam-4755	11	3	field	field	NOUN
ejpam-4755	11	4	extension	extension	NOUN
ejpam-4755	11	5	l	l	PROPN
ejpam-4755	11	6	/	/	SYM
ejpam-4755	11	7	k	k	PROPN
ejpam-4755	11	8	is	be	AUX
ejpam-4755	11	9	normal	normal	ADJ
ejpam-4755	11	10	and	and	CCONJ
ejpam-4755	11	11	separable	separable	VERB
ejpam-4755	11	12	with	with	ADP
ejpam-4755	11	13	degree	degree	NOUN
ejpam-4755	11	14	n	n	CCONJ
ejpam-4755	11	15	,	,	PUNCT
ejpam-4755	11	16	then	then	ADV
ejpam-4755	11	17	the	the	DET
ejpam-4755	11	18	galois	galois	PROPN
ejpam-4755	11	19	extension	extension	NOUN
ejpam-4755	11	20	l	l	PROPN
ejpam-4755	11	21	/	/	SYM
ejpam-4755	11	22	k	k	PROPN
ejpam-4755	11	23	is	be	AUX
ejpam-4755	11	24	classical	classical	ADJ
ejpam-4755	11	25	galois	galois	NOUN
ejpam-4755	11	26	.	.	PUNCT
ejpam-4755	12	1	let	let	VERB
ejpam-4755	12	2	its	its	PRON
ejpam-4755	12	3	galois	galois	PROPN
ejpam-4755	12	4	group	group	NOUN
ejpam-4755	12	5	be	be	AUX
ejpam-4755	12	6	g	g	NOUN
ejpam-4755	12	7	=	=	PUNCT
ejpam-4755	12	8	gal(l	gal(l	PROPN
ejpam-4755	12	9	/	/	SYM
ejpam-4755	12	10	k	k	NOUN
ejpam-4755	12	11	)	)	PUNCT
ejpam-4755	12	12	.	.	PUNCT
ejpam-4755	13	1	the	the	DET
ejpam-4755	13	2	group	group	NOUN
ejpam-4755	13	3	algebra	algebra	PROPN
ejpam-4755	13	4	k[g	k[g	PROPN
ejpam-4755	13	5	]	]	PUNCT
ejpam-4755	13	6	then	then	ADV
ejpam-4755	13	7	operates	operate	VERB
ejpam-4755	13	8	on	on	ADP
ejpam-4755	13	9	l	l	PROPN
ejpam-4755	13	10	/	/	SYM
ejpam-4755	13	11	k	k	NOUN
ejpam-4755	13	12	,	,	PUNCT
ejpam-4755	13	13	yielding	yield	VERB
ejpam-4755	13	14	at	at	ADV
ejpam-4755	13	15	least	least	ADV
ejpam-4755	13	16	one	one	NUM
ejpam-4755	13	17	hgs	hgs	NOUN
ejpam-4755	13	18	.	.	PUNCT
ejpam-4755	14	1	on	on	ADP
ejpam-4755	14	2	the	the	DET
ejpam-4755	14	3	other	other	ADJ
ejpam-4755	14	4	hand	hand	NOUN
ejpam-4755	14	5	,	,	PUNCT
ejpam-4755	14	6	there	there	PRON
ejpam-4755	14	7	could	could	AUX
ejpam-4755	14	8	be	be	AUX
ejpam-4755	14	9	a	a	DET
ejpam-4755	14	10	slew	slew	NOUN
ejpam-4755	14	11	of	of	ADP
ejpam-4755	14	12	more	more	ADV
ejpam-4755	14	13	hgss	hgss	ADJ
ejpam-4755	14	14	on	on	ADP
ejpam-4755	14	15	l	l	PROPN
ejpam-4755	14	16	/	/	SYM
ejpam-4755	14	17	k.	k.	PROPN
ejpam-4755	15	1	we	we	PRON
ejpam-4755	15	2	have	have	VERB
ejpam-4755	15	3	l	l	NOUN
ejpam-4755	15	4	as	as	ADP
ejpam-4755	15	5	hopf	hopf	PROPN
ejpam-4755	15	6	algebras	algebras	PROPN
ejpam-4755	15	7	l⊗k	l⊗k	NOUN
ejpam-4755	15	8	h	h	NOUN
ejpam-4755	15	9	∼=	∼=	PROPN
ejpam-4755	15	10	l[n	l[n	NOUN
ejpam-4755	15	11	]	]	PUNCT
ejpam-4755	15	12	for	for	ADP
ejpam-4755	15	13	every	every	DET
ejpam-4755	15	14	group	group	NOUN
ejpam-4755	15	15	n	n	CCONJ
ejpam-4755	15	16	of	of	ADP
ejpam-4755	15	17	order	order	NOUN
ejpam-4755	15	18	n	n	NOUN
ejpam-4755	15	19	if	if	SCONJ
ejpam-4755	15	20	the	the	DET
ejpam-4755	15	21	k	k	PROPN
ejpam-4755	15	22	hopf	hopf	PROPN
ejpam-4755	15	23	algebra	algebra	NOUN
ejpam-4755	15	24	h	h	NOUN
ejpam-4755	15	25	generates	generate	VERB
ejpam-4755	15	26	one	one	NUM
ejpam-4755	15	27	of	of	ADP
ejpam-4755	15	28	these	these	DET
ejpam-4755	15	29	hgss	hgss	ADJ
ejpam-4755	15	30	on	on	ADP
ejpam-4755	15	31	l	l	PROPN
ejpam-4755	15	32	/	/	SYM
ejpam-4755	15	33	k.	k.	PROPN
ejpam-4755	16	1	we	we	PRON
ejpam-4755	16	2	have	have	VERB
ejpam-4755	16	3	the	the	DET
ejpam-4755	16	4	type	type	NOUN
ejpam-4755	16	5	of	of	ADP
ejpam-4755	16	6	hgs	hgs	PROPN
ejpam-4755	16	7	by	by	ADP
ejpam-4755	16	8	the	the	DET
ejpam-4755	16	9	isomorphism	isomorphism	NOUN
ejpam-4755	16	10	type	type	NOUN
ejpam-4755	16	11	of	of	ADP
ejpam-4755	16	12	the	the	DET
ejpam-4755	16	13	group	group	NOUN
ejpam-4755	16	14	n	n	NOUN
ejpam-4755	16	15	.	.	PUNCT
ejpam-4755	17	1	the	the	DET
ejpam-4755	17	2	group	group	NOUN
ejpam-4755	17	3	g	g	PROPN
ejpam-4755	17	4	determinates	determinate	VERB
ejpam-4755	17	5	the	the	DET
ejpam-4755	17	6	different	different	ADJ
ejpam-4755	17	7	types	type	NOUN
ejpam-4755	17	8	of	of	ADP
ejpam-4755	17	9	hgs	hgs	PROPN
ejpam-4755	17	10	as	as	ADV
ejpam-4755	17	11	well	well	ADV
ejpam-4755	17	12	as	as	ADP
ejpam-4755	17	13	the	the	DET
ejpam-4755	17	14	number	number	NOUN
ejpam-4755	17	15	of	of	ADP
ejpam-4755	17	16	each	each	DET
ejpam-4755	17	17	type	type	NOUN
ejpam-4755	17	18	.	.	PUNCT
ejpam-4755	18	1	consider	consider	VERB
ejpam-4755	18	2	l	l	NOUN
ejpam-4755	18	3	/	/	SYM
ejpam-4755	18	4	k	k	NOUN
ejpam-4755	18	5	to	to	PART
ejpam-4755	18	6	be	be	AUX
ejpam-4755	18	7	an	an	DET
ejpam-4755	18	8	sfe	sfe	PROPN
ejpam-4755	18	9	(	(	PUNCT
ejpam-4755	18	10	presumably	presumably	ADV
ejpam-4755	18	11	nonnormal	nonnormal	ADJ
ejpam-4755	18	12	)	)	PUNCT
ejpam-4755	18	13	of	of	ADP
ejpam-4755	18	14	degree	degree	NOUN
ejpam-4755	18	15	n	n	NOUN
ejpam-4755	18	16	in	in	ADP
ejpam-4755	18	17	general	general	ADJ
ejpam-4755	18	18	.	.	PUNCT
ejpam-4755	19	1	let	let	VERB
ejpam-4755	19	2	the	the	DET
ejpam-4755	19	3	normal	normal	ADJ
ejpam-4755	19	4	closure	closure	NOUN
ejpam-4755	19	5	of	of	ADP
ejpam-4755	19	6	l	l	PROPN
ejpam-4755	19	7	/	/	SYM
ejpam-4755	19	8	k	k	PROPN
ejpam-4755	19	9	is	be	AUX
ejpam-4755	19	10	f	f	PROPN
ejpam-4755	19	11	/	/	SYM
ejpam-4755	19	12	k	k	NOUN
ejpam-4755	19	13	,	,	PUNCT
ejpam-4755	19	14	while	while	SCONJ
ejpam-4755	19	15	the	the	DET
ejpam-4755	19	16	galois	galois	PROPN
ejpam-4755	19	17	groups	group	NOUN
ejpam-4755	19	18	of	of	ADP
ejpam-4755	19	19	f	f	PROPN
ejpam-4755	19	20	/	/	SYM
ejpam-4755	19	21	k	k	PROPN
ejpam-4755	19	22	and	and	CCONJ
ejpam-4755	19	23	f	f	PROPN
ejpam-4755	19	24	/	/	SYM
ejpam-4755	19	25	l	l	NOUN
ejpam-4755	19	26	are	be	AUX
ejpam-4755	19	27	g	g	PROPN
ejpam-4755	19	28	=	=	PROPN
ejpam-4755	19	29	gal(f	gal(f	PROPN
ejpam-4755	19	30	/	/	SYM
ejpam-4755	19	31	k	k	NOUN
ejpam-4755	19	32	)	)	PUNCT
ejpam-4755	19	33	∗corresponding	∗corresponde	VERB
ejpam-4755	19	34	author	author	NOUN
ejpam-4755	19	35	.	.	PUNCT
ejpam-4755	20	1	doi	doi	NOUN
ejpam-4755	20	2	:	:	PUNCT
ejpam-4755	20	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4755	https://doi.org/10.29020/nybg.ejpam.v16i2.4755	ADJ
ejpam-4755	20	4	email	email	NOUN
ejpam-4755	20	5	addresses	address	NOUN
ejpam-4755	20	6	:	:	PUNCT
ejpam-4755	20	7	baraa.20esp7@student.uomosul.edu.iq	baraa.20esp7@student.uomosul.edu.iq	PROPN
ejpam-4755	20	8	(	(	PUNCT
ejpam-4755	20	9	b.	b.	PROPN
ejpam-4755	20	10	jamal	jamal	PROPN
ejpam-4755	20	11	)	)	PUNCT
ejpam-4755	20	12	,	,	PUNCT
ejpam-4755	20	13	ali.alabdali@uomosul.edu.iq	ali.alabdali@uomosul.edu.iq	PROPN
ejpam-4755	20	14	(	(	PUNCT
ejpam-4755	20	15	a.	a.	PROPN
ejpam-4755	20	16	alabdali	alabdali	PROPN
ejpam-4755	20	17	)	)	PUNCT
ejpam-4755	20	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4755	20	19	1118	1118	NUM
ejpam-4755	21	1	©	©	ADP
ejpam-4755	21	2	2023	2023	NUM
ejpam-4755	21	3	ejpam	ejpam	NOUN
ejpam-4755	21	4	all	all	DET
ejpam-4755	21	5	rights	right	NOUN
ejpam-4755	21	6	reserved	reserve	VERB
ejpam-4755	21	7	.	.	PUNCT
ejpam-4755	22	1	b.	b.	PROPN
ejpam-4755	22	2	jamal	jamal	PROPN
ejpam-4755	22	3	,	,	PUNCT
ejpam-4755	22	4	a.	a.	PROPN
ejpam-4755	22	5	alabdali	alabdali	VERB
ejpam-4755	22	6	/	/	SYM
ejpam-4755	22	7	eur	eur	PROPN
ejpam-4755	22	8	.	.	PUNCT
ejpam-4755	23	1	j.	j.	PROPN
ejpam-4755	23	2	pure	pure	PROPN
ejpam-4755	23	3	appl	appl	PROPN
ejpam-4755	23	4	.	.	PROPN
ejpam-4755	23	5	math	math	PROPN
ejpam-4755	23	6	,	,	PUNCT
ejpam-4755	23	7	16	16	NUM
ejpam-4755	23	8	(	(	PUNCT
ejpam-4755	23	9	2	2	NUM
ejpam-4755	23	10	)	)	PUNCT
ejpam-4755	23	11	(	(	PUNCT
ejpam-4755	23	12	2023	2023	NUM
ejpam-4755	23	13	)	)	PUNCT
ejpam-4755	23	14	,	,	PUNCT
ejpam-4755	23	15	1118	1118	NUM
ejpam-4755	23	16	-	-	SYM
ejpam-4755	23	17	1127	1127	NUM
ejpam-4755	23	18	1119	1119	NUM
ejpam-4755	23	19	and	and	CCONJ
ejpam-4755	23	20	g	g	NOUN
ejpam-4755	23	21	′	′	NUM
ejpam-4755	24	1	=	=	PUNCT
ejpam-4755	24	2	gal(f	gal(f	PROPN
ejpam-4755	24	3	/	/	SYM
ejpam-4755	24	4	l	l	NOUN
ejpam-4755	24	5	)	)	PUNCT
ejpam-4755	24	6	,	,	PUNCT
ejpam-4755	25	1	respectively	respectively	ADV
ejpam-4755	25	2	.	.	PUNCT
ejpam-4755	26	1	in	in	ADP
ejpam-4755	26	2	each	each	DET
ejpam-4755	26	3	type	type	NOUN
ejpam-4755	26	4	the	the	DET
ejpam-4755	26	5	number	number	NOUN
ejpam-4755	26	6	of	of	ADP
ejpam-4755	26	7	hgss	hgss	PROPN
ejpam-4755	26	8	is	be	AUX
ejpam-4755	26	9	determined	determine	VERB
ejpam-4755	26	10	by	by	ADP
ejpam-4755	26	11	the	the	DET
ejpam-4755	26	12	group	group	NOUN
ejpam-4755	26	13	g	g	PROPN
ejpam-4755	26	14	and	and	CCONJ
ejpam-4755	26	15	its	its	PRON
ejpam-4755	26	16	subgroup	subgroup	NOUN
ejpam-4755	26	17	g	g	NOUN
ejpam-4755	26	18	′	′	NUM
ejpam-4755	26	19	.	.	PUNCT
ejpam-4755	27	1	the	the	DET
ejpam-4755	27	2	primary	primary	ADJ
ejpam-4755	27	3	finding	finding	NOUN
ejpam-4755	27	4	of	of	ADP
ejpam-4755	27	5	greither	greither	NOUN
ejpam-4755	27	6	and	and	CCONJ
ejpam-4755	27	7	pareigis	pareigis	ADJ
ejpam-4755	27	8	[	[	X
ejpam-4755	27	9	14	14	NUM
ejpam-4755	27	10	]	]	PUNCT
ejpam-4755	27	11	is	be	AUX
ejpam-4755	27	12	that	that	PRON
ejpam-4755	27	13	hgss	hgss	ADJ
ejpam-4755	27	14	on	on	ADP
ejpam-4755	27	15	l	l	PROPN
ejpam-4755	27	16	/	/	SYM
ejpam-4755	27	17	k	k	PROPN
ejpam-4755	27	18	are	be	AUX
ejpam-4755	27	19	congruent	congruent	ADJ
ejpam-4755	27	20	to	to	PART
ejpam-4755	27	21	order	order	VERB
ejpam-4755	27	22	n	n	PRON
ejpam-4755	27	23	groups	group	NOUN
ejpam-4755	27	24	and	and	CCONJ
ejpam-4755	27	25	act	act	VERB
ejpam-4755	27	26	transitively	transitively	PROPN
ejpam-4755	27	27	as	as	ADP
ejpam-4755	27	28	a	a	DET
ejpam-4755	27	29	permutation	permutation	NOUN
ejpam-4755	27	30	group	group	NOUN
ejpam-4755	27	31	(	(	PUNCT
ejpam-4755	27	32	pg	pg	NOUN
ejpam-4755	27	33	)	)	PUNCT
ejpam-4755	27	34	on	on	ADP
ejpam-4755	27	35	the	the	DET
ejpam-4755	27	36	space	space	NOUN
ejpam-4755	27	37	of	of	ADP
ejpam-4755	27	38	left	left	ADJ
ejpam-4755	27	39	coset	coset	NOUN
ejpam-4755	27	40	x	x	X
ejpam-4755	27	41	=	=	SYM
ejpam-4755	27	42	g	g	NOUN
ejpam-4755	27	43	/	/	SYM
ejpam-4755	27	44	g	g	NOUN
ejpam-4755	27	45	′	′	NOUN
ejpam-4755	27	46	.	.	PUNCT
ejpam-4755	28	1	many	many	ADJ
ejpam-4755	28	2	authors	author	NOUN
ejpam-4755	28	3	have	have	AUX
ejpam-4755	28	4	studied	study	VERB
ejpam-4755	28	5	hgss	hgss	ADJ
ejpam-4755	28	6	since	since	SCONJ
ejpam-4755	28	7	greither	greither	NOUN
ejpam-4755	28	8	and	and	CCONJ
ejpam-4755	28	9	pareigis	pareigis	ADJ
ejpam-4755	28	10	’	'	PUNCT
ejpam-4755	28	11	efforts	effort	NOUN
ejpam-4755	28	12	on	on	ADP
ejpam-4755	28	13	the	the	DET
ejpam-4755	28	14	subject	subject	NOUN
ejpam-4755	28	15	.	.	PUNCT
ejpam-4755	29	1	the	the	DET
ejpam-4755	29	2	majority	majority	NOUN
ejpam-4755	29	3	of	of	ADP
ejpam-4755	29	4	them	they	PRON
ejpam-4755	29	5	are	be	AUX
ejpam-4755	29	6	interested	interested	ADJ
ejpam-4755	29	7	in	in	ADP
ejpam-4755	29	8	galois	galois	PROPN
ejpam-4755	29	9	extensions	extension	NOUN
ejpam-4755	29	10	on	on	ADP
ejpam-4755	29	11	various	various	ADJ
ejpam-4755	29	12	forms	form	NOUN
ejpam-4755	29	13	of	of	ADP
ejpam-4755	29	14	sfes	sfe	NOUN
ejpam-4755	29	15	;	;	PUNCT
ejpam-4755	29	16	see	see	VERB
ejpam-4755	29	17	[	[	X
ejpam-4755	29	18	11	11	NUM
ejpam-4755	29	19	,	,	PUNCT
ejpam-4755	29	20	16	16	NUM
ejpam-4755	29	21	,	,	PUNCT
ejpam-4755	29	22	19	19	NUM
ejpam-4755	29	23	]	]	PUNCT
ejpam-4755	29	24	.	.	PUNCT
ejpam-4755	30	1	other	other	ADJ
ejpam-4755	30	2	authors	author	NOUN
ejpam-4755	30	3	,	,	PUNCT
ejpam-4755	30	4	such	such	ADJ
ejpam-4755	30	5	as	as	ADP
ejpam-4755	30	6	[	[	X
ejpam-4755	30	7	9	9	NUM
ejpam-4755	30	8	,	,	PUNCT
ejpam-4755	30	9	12	12	NUM
ejpam-4755	30	10	,	,	PUNCT
ejpam-4755	30	11	13	13	NUM
ejpam-4755	30	12	]	]	PUNCT
ejpam-4755	30	13	deal	deal	NOUN
ejpam-4755	30	14	with	with	ADP
ejpam-4755	30	15	nonnormal	nonnormal	ADJ
ejpam-4755	30	16	extensions	extension	NOUN
ejpam-4755	30	17	.	.	PUNCT
ejpam-4755	31	1	the	the	DET
ejpam-4755	31	2	study	study	NOUN
ejpam-4755	31	3	of	of	ADP
ejpam-4755	31	4	hgss	hgss	PROPN
ejpam-4755	31	5	on	on	ADP
ejpam-4755	31	6	galois	galois	PROPN
ejpam-4755	31	7	extensions	extension	NOUN
ejpam-4755	31	8	has	have	AUX
ejpam-4755	31	9	been	be	AUX
ejpam-4755	31	10	more	more	ADV
ejpam-4755	31	11	well	well	ADV
ejpam-4755	31	12	-	-	PUNCT
ejpam-4755	31	13	known	know	VERB
ejpam-4755	31	14	in	in	ADP
ejpam-4755	31	15	recent	recent	ADJ
ejpam-4755	31	16	years	year	NOUN
ejpam-4755	31	17	due	due	ADP
ejpam-4755	31	18	to	to	ADP
ejpam-4755	31	19	a	a	DET
ejpam-4755	31	20	link	link	NOUN
ejpam-4755	31	21	between	between	ADP
ejpam-4755	31	22	studying	study	VERB
ejpam-4755	31	23	hgss	hgss	ADJ
ejpam-4755	31	24	and	and	CCONJ
ejpam-4755	31	25	the	the	DET
ejpam-4755	31	26	solutions	solution	NOUN
ejpam-4755	31	27	of	of	ADP
ejpam-4755	31	28	the	the	DET
ejpam-4755	31	29	yang	yang	PROPN
ejpam-4755	31	30	baxter	baxter	PROPN
ejpam-4755	31	31	equation	equation	NOUN
ejpam-4755	31	32	as	as	ADP
ejpam-4755	31	33	set	set	VERB
ejpam-4755	31	34	theoretic	theoretic	NOUN
ejpam-4755	31	35	(	(	PUNCT
ejpam-4755	31	36	skew	skew	ADJ
ejpam-4755	31	37	braces	brace	NOUN
ejpam-4755	31	38	and	and	CCONJ
ejpam-4755	31	39	braces	brace	NOUN
ejpam-4755	31	40	)	)	PUNCT
ejpam-4755	31	41	,	,	PUNCT
ejpam-4755	31	42	for	for	ADP
ejpam-4755	31	43	more	more	ADJ
ejpam-4755	31	44	information	information	NOUN
ejpam-4755	31	45	,	,	PUNCT
ejpam-4755	31	46	see	see	VERB
ejpam-4755	31	47	[	[	X
ejpam-4755	31	48	2	2	NUM
ejpam-4755	31	49	,	,	PUNCT
ejpam-4755	31	50	18	18	NUM
ejpam-4755	31	51	]	]	PUNCT
ejpam-4755	31	52	.	.	PUNCT
ejpam-4755	32	1	byott	byott	PROPN
ejpam-4755	32	2	shows	show	VERB
ejpam-4755	32	3	in	in	ADP
ejpam-4755	32	4	[	[	X
ejpam-4755	32	5	4	4	X
ejpam-4755	32	6	]	]	PUNCT
ejpam-4755	32	7	that	that	SCONJ
ejpam-4755	32	8	there	there	PRON
ejpam-4755	32	9	exists	exist	VERB
ejpam-4755	32	10	a	a	DET
ejpam-4755	32	11	cg	cg	NOUN
ejpam-4755	32	12	of	of	ADP
ejpam-4755	32	13	order	order	NOUN
ejpam-4755	32	14	pq	pq	INTJ
ejpam-4755	32	15	and	and	CCONJ
ejpam-4755	32	16	a	a	DET
ejpam-4755	32	17	nonabelian	nonabelian	ADJ
ejpam-4755	32	18	group	group	NOUN
ejpam-4755	32	19	of	of	ADP
ejpam-4755	32	20	the	the	DET
ejpam-4755	32	21	same	same	ADJ
ejpam-4755	32	22	order	order	NOUN
ejpam-4755	32	23	such	such	ADJ
ejpam-4755	32	24	that	that	SCONJ
ejpam-4755	32	25	a	a	DET
ejpam-4755	32	26	galois	galois	PROPN
ejpam-4755	32	27	extension	extension	NOUN
ejpam-4755	32	28	of	of	ADP
ejpam-4755	32	29	degree	degree	NOUN
ejpam-4755	32	30	pq	pq	NOUN
ejpam-4755	32	31	allows	allow	VERB
ejpam-4755	32	32	the	the	DET
ejpam-4755	32	33	number	number	NOUN
ejpam-4755	32	34	of	of	ADP
ejpam-4755	32	35	hgss	hgss	ADJ
ejpam-4755	32	36	,	,	PUNCT
ejpam-4755	32	37	based	base	VERB
ejpam-4755	32	38	on	on	ADP
ejpam-4755	32	39	the	the	DET
ejpam-4755	32	40	condition	condition	NOUN
ejpam-4755	32	41	p	p	X
ejpam-4755	32	42	≡	≡	PROPN
ejpam-4755	32	43	1	1	NUM
ejpam-4755	32	44	(	(	PUNCT
ejpam-4755	32	45	mod	mod	PROPN
ejpam-4755	32	46	q	q	NOUN
ejpam-4755	32	47	)	)	PUNCT
ejpam-4755	32	48	where	where	SCONJ
ejpam-4755	32	49	p	p	NOUN
ejpam-4755	32	50	and	and	CCONJ
ejpam-4755	32	51	q	q	NOUN
ejpam-4755	32	52	are	be	AUX
ejpam-4755	32	53	distinct	distinct	ADJ
ejpam-4755	32	54	primes	prime	NOUN
ejpam-4755	32	55	.	.	PUNCT
ejpam-4755	33	1	a	a	DET
ejpam-4755	33	2	galois	galois	PROPN
ejpam-4755	33	3	extension	extension	NOUN
ejpam-4755	33	4	with	with	ADP
ejpam-4755	33	5	kinds	kind	NOUN
ejpam-4755	33	6	of	of	ADP
ejpam-4755	33	7	groups	group	NOUN
ejpam-4755	33	8	admits	admit	VERB
ejpam-4755	33	9	the	the	DET
ejpam-4755	33	10	cyclic	cyclic	ADJ
ejpam-4755	33	11	and	and	CCONJ
ejpam-4755	33	12	nonabelian	nonabelian	ADJ
ejpam-4755	33	13	hgss	hgss	PROPN
ejpam-4755	33	14	.	.	PUNCT
ejpam-4755	34	1	furthermore	furthermore	ADV
ejpam-4755	34	2	,	,	PUNCT
ejpam-4755	34	3	when	when	SCONJ
ejpam-4755	34	4	the	the	DET
ejpam-4755	34	5	degree	degree	NOUN
ejpam-4755	34	6	is	be	AUX
ejpam-4755	34	7	2pq	2pq	ADJ
ejpam-4755	34	8	with	with	ADP
ejpam-4755	34	9	odd	odd	ADJ
ejpam-4755	34	10	primes	prime	NOUN
ejpam-4755	34	11	p	p	X
ejpam-4755	34	12	,	,	PUNCT
ejpam-4755	34	13	q	q	NOUN
ejpam-4755	34	14	and	and	CCONJ
ejpam-4755	34	15	p	p	NOUN
ejpam-4755	34	16	=	=	NOUN
ejpam-4755	34	17	2q	2q	NOUN
ejpam-4755	35	1	+	+	SYM
ejpam-4755	35	2	1	1	X
ejpam-4755	35	3	(	(	PUNCT
ejpam-4755	35	4	p	p	NOUN
ejpam-4755	35	5	is	be	AUX
ejpam-4755	35	6	safe	safe	ADJ
ejpam-4755	35	7	prime	prime	NOUN
ejpam-4755	35	8	and	and	CCONJ
ejpam-4755	35	9	q	q	NOUN
ejpam-4755	35	10	is	be	AUX
ejpam-4755	35	11	sophie	sophie	PROPN
ejpam-4755	35	12	germain	germain	PROPN
ejpam-4755	35	13	prime	prime	NOUN
ejpam-4755	35	14	)	)	PUNCT
ejpam-4755	35	15	,	,	PUNCT
ejpam-4755	35	16	there	there	PRON
ejpam-4755	35	17	is	be	VERB
ejpam-4755	35	18	research	research	NOUN
ejpam-4755	35	19	in	in	ADP
ejpam-4755	35	20	numerous	numerous	ADJ
ejpam-4755	35	21	resources	resource	NOUN
ejpam-4755	35	22	[	[	X
ejpam-4755	35	23	5	5	NUM
ejpam-4755	35	24	,	,	PUNCT
ejpam-4755	35	25	10	10	NUM
ejpam-4755	35	26	,	,	PUNCT
ejpam-4755	35	27	17	17	NUM
ejpam-4755	35	28	]	]	PUNCT
ejpam-4755	35	29	.	.	PUNCT
ejpam-4755	36	1	the	the	DET
ejpam-4755	36	2	hgss	hgss	ADJ
ejpam-4755	36	3	on	on	ADP
ejpam-4755	36	4	l	l	PROPN
ejpam-4755	36	5	/	/	SYM
ejpam-4755	36	6	k	k	NOUN
ejpam-4755	36	7	of	of	ADP
ejpam-4755	36	8	type	type	NOUN
ejpam-4755	36	9	n	n	CCONJ
ejpam-4755	36	10	with	with	ADP
ejpam-4755	36	11	an	an	DET
ejpam-4755	36	12	arbitrary	arbitrary	ADJ
ejpam-4755	36	13	square	square	ADJ
ejpam-4755	36	14	free	free	ADJ
ejpam-4755	36	15	degree	degree	NOUN
ejpam-4755	36	16	n	n	NOUN
ejpam-4755	36	17	are	be	AUX
ejpam-4755	36	18	described	describe	VERB
ejpam-4755	36	19	in	in	ADP
ejpam-4755	36	20	[	[	X
ejpam-4755	36	21	1	1	NUM
ejpam-4755	36	22	]	]	PUNCT
ejpam-4755	36	23	.	.	PUNCT
ejpam-4755	37	1	the	the	DET
ejpam-4755	37	2	hgss	hgss	PROPN
ejpam-4755	37	3	were	be	AUX
ejpam-4755	37	4	enumerated	enumerate	VERB
ejpam-4755	37	5	by	by	ADP
ejpam-4755	37	6	dividing	divide	VERB
ejpam-4755	37	7	the	the	DET
ejpam-4755	37	8	order	order	NOUN
ejpam-4755	37	9	n	n	NOUN
ejpam-4755	37	10	into	into	ADP
ejpam-4755	37	11	two	two	NUM
ejpam-4755	37	12	groups	group	NOUN
ejpam-4755	37	13	,	,	PUNCT
ejpam-4755	37	14	g	g	NOUN
ejpam-4755	37	15	and	and	CCONJ
ejpam-4755	37	16	n	n	CCONJ
ejpam-4755	37	17	,	,	PUNCT
ejpam-4755	37	18	with	with	ADP
ejpam-4755	37	19	g	g	PROPN
ejpam-4755	37	20	=	=	SYM
ejpam-4755	37	21	gal(l	gal(l	PROPN
ejpam-4755	37	22	/	/	SYM
ejpam-4755	37	23	k	k	NOUN
ejpam-4755	37	24	)	)	PUNCT
ejpam-4755	37	25	.	.	PUNCT
ejpam-4755	38	1	byott	byott	PROPN
ejpam-4755	38	2	and	and	CCONJ
ejpam-4755	38	3	lyons	lyons	PROPN
ejpam-4755	38	4	has	have	AUX
ejpam-4755	38	5	shown	show	VERB
ejpam-4755	38	6	in	in	ADP
ejpam-4755	38	7	their	their	PRON
ejpam-4755	38	8	paper	paper	NOUN
ejpam-4755	39	1	[	[	X
ejpam-4755	39	2	6	6	NUM
ejpam-4755	39	3	]	]	PUNCT
ejpam-4755	39	4	that	that	SCONJ
ejpam-4755	39	5	the	the	DET
ejpam-4755	39	6	conclusions	conclusion	NOUN
ejpam-4755	39	7	of	of	ADP
ejpam-4755	39	8	[	[	X
ejpam-4755	39	9	1	1	NUM
ejpam-4755	39	10	]	]	PUNCT
ejpam-4755	39	11	may	may	AUX
ejpam-4755	39	12	extend	extend	VERB
ejpam-4755	39	13	to	to	AUX
ejpam-4755	39	14	nonnormal	nonnormal	ADJ
ejpam-4755	39	15	but	but	CCONJ
ejpam-4755	39	16	sfes	sfe	VERB
ejpam-4755	39	17	l	l	PROPN
ejpam-4755	39	18	/	/	SYM
ejpam-4755	39	19	k	k	PROPN
ejpam-4755	39	20	of	of	ADP
ejpam-4755	39	21	square	square	ADJ
ejpam-4755	39	22	free	free	ADJ
ejpam-4755	39	23	degree	degree	NOUN
ejpam-4755	39	24	n	n	PROPN
ejpam-4755	39	25	=	=	SYM
ejpam-4755	39	26	pq	pq	X
ejpam-4755	39	27	(	(	PUNCT
ejpam-4755	39	28	p	p	NOUN
ejpam-4755	39	29	=	=	X
ejpam-4755	39	30	2q	2q	NOUN
ejpam-4755	40	1	+	+	CCONJ
ejpam-4755	40	2	1	1	NUM
ejpam-4755	40	3	is	be	AUX
ejpam-4755	40	4	a	a	DET
ejpam-4755	40	5	safe	safe	ADJ
ejpam-4755	40	6	prime	prime	NOUN
ejpam-4755	40	7	and	and	CCONJ
ejpam-4755	40	8	q	q	PROPN
ejpam-4755	40	9	≥	≥	NUM
ejpam-4755	40	10	3	3	NUM
ejpam-4755	40	11	is	be	AUX
ejpam-4755	40	12	a	a	DET
ejpam-4755	40	13	sophie	sophie	PROPN
ejpam-4755	40	14	germain	germain	NOUN
ejpam-4755	40	15	prime	prime	NOUN
ejpam-4755	40	16	)	)	PUNCT
ejpam-4755	40	17	.	.	PUNCT
ejpam-4755	41	1	there	there	PRON
ejpam-4755	41	2	is	be	VERB
ejpam-4755	41	3	at	at	ADV
ejpam-4755	41	4	least	least	ADJ
ejpam-4755	41	5	one	one	NUM
ejpam-4755	41	6	cyclic	cyclic	ADJ
ejpam-4755	41	7	and	and	CCONJ
ejpam-4755	41	8	nonabelian	nonabelian	PROPN
ejpam-4755	41	9	hgs	hgs	PROPN
ejpam-4755	41	10	for	for	ADP
ejpam-4755	41	11	the	the	DET
ejpam-4755	41	12	pgs	pgs	NOUN
ejpam-4755	41	13	admitted	admit	VERB
ejpam-4755	41	14	by	by	ADP
ejpam-4755	41	15	the	the	DET
ejpam-4755	41	16	corresponding	corresponding	ADJ
ejpam-4755	41	17	field	field	NOUN
ejpam-4755	41	18	extensions	extension	NOUN
ejpam-4755	41	19	l	l	PROPN
ejpam-4755	41	20	/	/	SYM
ejpam-4755	41	21	k.	k.	NOUN
ejpam-4755	41	22	the	the	DET
ejpam-4755	41	23	issue	issue	NOUN
ejpam-4755	41	24	in	in	ADP
ejpam-4755	41	25	[	[	X
ejpam-4755	41	26	6	6	NUM
ejpam-4755	41	27	]	]	PUNCT
ejpam-4755	41	28	then	then	ADV
ejpam-4755	41	29	becomes	become	VERB
ejpam-4755	41	30	whether	whether	SCONJ
ejpam-4755	41	31	the	the	DET
ejpam-4755	41	32	same	same	ADJ
ejpam-4755	41	33	behaviour	behaviour	NOUN
ejpam-4755	41	34	applies	apply	VERB
ejpam-4755	41	35	for	for	ADP
ejpam-4755	41	36	square	square	ADJ
ejpam-4755	41	37	free	free	ADJ
ejpam-4755	41	38	degrees	degree	NOUN
ejpam-4755	41	39	n	n	CCONJ
ejpam-4755	41	40	in	in	ADP
ejpam-4755	41	41	general	general	ADJ
ejpam-4755	41	42	.	.	PUNCT
ejpam-4755	42	1	the	the	DET
ejpam-4755	42	2	primary	primary	ADJ
ejpam-4755	42	3	purpose	purpose	NOUN
ejpam-4755	42	4	of	of	ADP
ejpam-4755	42	5	this	this	DET
ejpam-4755	42	6	research	research	NOUN
ejpam-4755	42	7	is	be	AUX
ejpam-4755	42	8	to	to	PART
ejpam-4755	42	9	answer	answer	VERB
ejpam-4755	42	10	the	the	DET
ejpam-4755	42	11	question	question	NOUN
ejpam-4755	42	12	and	and	CCONJ
ejpam-4755	42	13	extend	extend	VERB
ejpam-4755	42	14	the	the	DET
ejpam-4755	42	15	approach	approach	NOUN
ejpam-4755	42	16	in	in	ADP
ejpam-4755	42	17	[	[	X
ejpam-4755	42	18	6	6	NUM
ejpam-4755	42	19	]	]	PUNCT
ejpam-4755	42	20	for	for	ADP
ejpam-4755	42	21	n	n	NOUN
ejpam-4755	42	22	=	=	SYM
ejpam-4755	42	23	pqw	pqw	PROPN
ejpam-4755	42	24	,	,	PUNCT
ejpam-4755	42	25	where	where	SCONJ
ejpam-4755	42	26	a	a	DET
ejpam-4755	42	27	sophie	sophie	X
ejpam-4755	42	28	germain	germain	PROPN
ejpam-4755	42	29	prime	prime	PROPN
ejpam-4755	42	30	w	w	PROPN
ejpam-4755	42	31	≥	≥	NOUN
ejpam-4755	42	32	3	3	NUM
ejpam-4755	42	33	,	,	PUNCT
ejpam-4755	42	34	a	a	DET
ejpam-4755	42	35	safe	safe	ADJ
ejpam-4755	42	36	prime	prime	NOUN
ejpam-4755	42	37	p	p	NOUN
ejpam-4755	42	38	=	=	PUNCT
ejpam-4755	42	39	2w+1	2w+1	PROPN
ejpam-4755	42	40	,	,	PUNCT
ejpam-4755	42	41	and	and	CCONJ
ejpam-4755	42	42	p	p	X
ejpam-4755	42	43	,	,	PUNCT
ejpam-4755	42	44	q	q	ADJ
ejpam-4755	42	45	,	,	PUNCT
ejpam-4755	42	46	w	w	PROPN
ejpam-4755	42	47	are	be	AUX
ejpam-4755	42	48	square	square	ADJ
ejpam-4755	42	49	free	free	ADJ
ejpam-4755	42	50	primes	prime	NOUN
ejpam-4755	42	51	.	.	PUNCT
ejpam-4755	43	1	we	we	PRON
ejpam-4755	43	2	start	start	VERB
ejpam-4755	43	3	with	with	ADP
ejpam-4755	43	4	the	the	DET
ejpam-4755	43	5	potential	potential	ADJ
ejpam-4755	43	6	group	group	NOUN
ejpam-4755	43	7	jl	jl	NOUN
ejpam-4755	43	8	of	of	ADP
ejpam-4755	43	9	order	order	NOUN
ejpam-4755	43	10	pqw	pqw	NOUN
ejpam-4755	43	11	in	in	ADP
ejpam-4755	43	12	this	this	DET
ejpam-4755	43	13	work	work	NOUN
ejpam-4755	43	14	,	,	PUNCT
ejpam-4755	43	15	and	and	CCONJ
ejpam-4755	43	16	then	then	ADV
ejpam-4755	43	17	look	look	VERB
ejpam-4755	43	18	for	for	ADP
ejpam-4755	43	19	pgs	pgs	NOUN
ejpam-4755	43	20	that	that	PRON
ejpam-4755	43	21	are	be	AUX
ejpam-4755	43	22	released	release	VERB
ejpam-4755	43	23	by	by	ADP
ejpam-4755	43	24	hgss	hgss	NOUN
ejpam-4755	43	25	of	of	ADP
ejpam-4755	43	26	type	type	NOUN
ejpam-4755	43	27	jl	jl	PROPN
ejpam-4755	43	28	.	.	PUNCT
ejpam-4755	43	29	where	where	SCONJ
ejpam-4755	43	30	jl	jl	PROPN
ejpam-4755	43	31	is	be	AUX
ejpam-4755	43	32	the	the	DET
ejpam-4755	43	33	nonabelian	nonabelian	ADJ
ejpam-4755	43	34	group	group	NOUN
ejpam-4755	43	35	.	.	PUNCT
ejpam-4755	44	1	we	we	PRON
ejpam-4755	44	2	then	then	ADV
ejpam-4755	44	3	enumerate	enumerate	VERB
ejpam-4755	44	4	all	all	PRON
ejpam-4755	44	5	hgss	hgss	ADJ
ejpam-4755	44	6	of	of	ADP
ejpam-4755	44	7	cyclic	cyclic	ADJ
ejpam-4755	44	8	type	type	NOUN
ejpam-4755	44	9	on	on	ADP
ejpam-4755	44	10	jl	jl	NOUN
ejpam-4755	44	11	-extension	-extension	NOUN
ejpam-4755	44	12	and	and	CCONJ
ejpam-4755	44	13	identify	identify	VERB
ejpam-4755	44	14	all	all	DET
ejpam-4755	44	15	isomorphism	isomorphism	NOUN
ejpam-4755	44	16	types	type	NOUN
ejpam-4755	44	17	of	of	ADP
ejpam-4755	44	18	pgs	pgs	NOUN
ejpam-4755	44	19	of	of	ADP
ejpam-4755	44	20	degree	degree	NOUN
ejpam-4755	44	21	pqw	pqw	NOUN
ejpam-4755	44	22	.	.	PUNCT
ejpam-4755	45	1	now	now	ADV
ejpam-4755	45	2	we	we	PRON
ejpam-4755	45	3	can	can	AUX
ejpam-4755	45	4	show	show	VERB
ejpam-4755	45	5	the	the	DET
ejpam-4755	45	6	first	first	ADJ
ejpam-4755	45	7	of	of	ADP
ejpam-4755	45	8	our	our	PRON
ejpam-4755	45	9	main	main	ADJ
ejpam-4755	45	10	results	result	NOUN
ejpam-4755	45	11	.	.	PUNCT
ejpam-4755	46	1	theorem	theorem	NOUN
ejpam-4755	46	2	1	1	NUM
ejpam-4755	46	3	.	.	PUNCT
ejpam-4755	47	1	the	the	DET
ejpam-4755	47	2	total	total	ADJ
ejpam-4755	47	3	number	number	NOUN
ejpam-4755	47	4	of	of	ADP
ejpam-4755	47	5	isomorphism	isomorphism	NOUN
ejpam-4755	47	6	types	type	NOUN
ejpam-4755	47	7	admits	admit	VERB
ejpam-4755	47	8	nonabelian	nonabelian	PROPN
ejpam-4755	47	9	hgss	hgss	PROPN
ejpam-4755	47	10	is	be	AUX
ejpam-4755	47	11	2	2	NUM
ejpam-4755	47	12	+	+	CCONJ
ejpam-4755	47	13	(	(	PUNCT
ejpam-4755	47	14	r+	r+	NOUN
ejpam-4755	47	15	1	1	NUM
ejpam-4755	47	16	)	)	PUNCT
ejpam-4755	48	1	+	+	CCONJ
ejpam-4755	48	2	σ0(s	σ0(s	X
ejpam-4755	48	3	)	)	PUNCT
ejpam-4755	48	4	of	of	ADP
ejpam-4755	48	5	pgs	pgs	NOUN
ejpam-4755	48	6	of	of	ADP
ejpam-4755	48	7	degree	degree	NOUN
ejpam-4755	48	8	pqw	pqw	NOUN
ejpam-4755	48	9	.	.	PUNCT
ejpam-4755	49	1	the	the	DET
ejpam-4755	49	2	nonabelain	nonabelain	NOUN
ejpam-4755	49	3	of	of	ADP
ejpam-4755	49	4	order	order	NOUN
ejpam-4755	49	5	pqw	pqw	NOUN
ejpam-4755	49	6	is	be	AUX
ejpam-4755	49	7	the	the	DET
ejpam-4755	49	8	regular	regular	ADJ
ejpam-4755	49	9	group	group	NOUN
ejpam-4755	49	10	.	.	PUNCT
ejpam-4755	50	1	the	the	DET
ejpam-4755	50	2	second	second	NOUN
ejpam-4755	50	3	of	of	ADP
ejpam-4755	50	4	our	our	PRON
ejpam-4755	50	5	main	main	ADJ
ejpam-4755	50	6	results	result	NOUN
ejpam-4755	50	7	shows	show	VERB
ejpam-4755	50	8	the	the	DET
ejpam-4755	50	9	total	total	ADJ
ejpam-4755	50	10	isomorphism	isomorphism	NOUN
ejpam-4755	50	11	types	type	NOUN
ejpam-4755	50	12	that	that	PRON
ejpam-4755	50	13	realise	realise	VERB
ejpam-4755	50	14	by	by	ADP
ejpam-4755	50	15	cyclic	cyclic	ADJ
ejpam-4755	50	16	and	and	CCONJ
ejpam-4755	50	17	nonabelian	nonabelian	ADJ
ejpam-4755	50	18	group	group	NOUN
ejpam-4755	50	19	.	.	PUNCT
ejpam-4755	51	1	theorem	theorem	NOUN
ejpam-4755	51	2	2	2	NUM
ejpam-4755	51	3	.	.	PUNCT
ejpam-4755	51	4	a	a	DET
ejpam-4755	51	5	hgs	hgs	NOUN
ejpam-4755	51	6	of	of	ADP
ejpam-4755	51	7	cyclic	cyclic	ADJ
ejpam-4755	51	8	type	type	NOUN
ejpam-4755	51	9	can	can	AUX
ejpam-4755	51	10	realise	realise	VERB
ejpam-4755	51	11	isomorphism	isomorphism	NOUN
ejpam-4755	51	12	types	type	NOUN
ejpam-4755	51	13	in	in	ADP
ejpam-4755	51	14	total	total	ADJ
ejpam-4755	51	15	12(r	12(r	PROPN
ejpam-4755	52	1	+	+	CCONJ
ejpam-4755	52	2	i	i	PROPN
ejpam-4755	52	3	+	+	X
ejpam-4755	52	4	1)[σ0(s	1)[σ0(s	NUM
ejpam-4755	52	5	)	)	PUNCT
ejpam-4755	52	6	+	+	NUM
ejpam-4755	52	7	σ1(j	σ1(j	X
ejpam-4755	52	8	)	)	PUNCT
ejpam-4755	52	9	+	+	X
ejpam-4755	52	10	σ0(s)σ1(j	σ0(s)σ1(j	NOUN
ejpam-4755	52	11	)	)	PUNCT
ejpam-4755	52	12	]	]	PUNCT
ejpam-4755	53	1	+	+	CCONJ
ejpam-4755	53	2	2	2	NUM
ejpam-4755	53	3	+	+	CCONJ
ejpam-4755	53	4	(	(	PUNCT
ejpam-4755	53	5	r	r	NOUN
ejpam-4755	53	6	+	+	NOUN
ejpam-4755	53	7	1	1	NUM
ejpam-4755	53	8	)	)	PUNCT
ejpam-4755	53	9	+	+	NOUN
ejpam-4755	53	10	σ0(s	σ0(s	X
ejpam-4755	53	11	)	)	PUNCT
ejpam-4755	53	12	of	of	ADP
ejpam-4755	53	13	pgs	pgs	ADJ
ejpam-4755	53	14	g	g	NOUN
ejpam-4755	53	15	of	of	ADP
ejpam-4755	53	16	degree	degree	NOUN
ejpam-4755	53	17	pqw	pqw	NOUN
ejpam-4755	53	18	of	of	ADP
ejpam-4755	53	19	both	both	DET
ejpam-4755	53	20	cases	case	NOUN
ejpam-4755	53	21	regular	regular	ADJ
ejpam-4755	53	22	groups	group	NOUN
ejpam-4755	53	23	(	(	PUNCT
ejpam-4755	53	24	where	where	SCONJ
ejpam-4755	53	25	the	the	DET
ejpam-4755	53	26	galois	galois	PROPN
ejpam-4755	53	27	extensions	extension	NOUN
ejpam-4755	53	28	have	have	VERB
ejpam-4755	53	29	1	1	NUM
ejpam-4755	53	30	hgs	hgs	NOUN
ejpam-4755	53	31	for	for	ADP
ejpam-4755	53	32	the	the	DET
ejpam-4755	53	33	cyclic	cyclic	ADJ
ejpam-4755	53	34	group	group	NOUN
ejpam-4755	53	35	and	and	CCONJ
ejpam-4755	53	36	(	(	PUNCT
ejpam-4755	53	37	p	p	X
ejpam-4755	53	38	−	−	PROPN
ejpam-4755	53	39	1)(q	1)(q	NUM
ejpam-4755	53	40	−	−	NOUN
ejpam-4755	53	41	1	1	NUM
ejpam-4755	53	42	)	)	PUNCT
ejpam-4755	53	43	+	+	CCONJ
ejpam-4755	53	44	1	1	NUM
ejpam-4755	53	45	,	,	PUNCT
ejpam-4755	53	46	1	1	NUM
ejpam-4755	53	47	,	,	PUNCT
ejpam-4755	53	48	r	r	NOUN
ejpam-4755	53	49	+	+	NOUN
ejpam-4755	53	50	1	1	NUM
ejpam-4755	53	51	,	,	PUNCT
ejpam-4755	53	52	and	and	CCONJ
ejpam-4755	53	53	σ0(s	σ0(s	X
ejpam-4755	53	54	)	)	PUNCT
ejpam-4755	53	55	hgss	hgss	ADJ
ejpam-4755	53	56	for	for	ADP
ejpam-4755	53	57	the	the	DET
ejpam-4755	53	58	nonabelian	nonabelian	ADJ
ejpam-4755	53	59	group	group	NOUN
ejpam-4755	53	60	of	of	ADP
ejpam-4755	53	61	the	the	DET
ejpam-4755	53	62	cyclic	cyclic	ADJ
ejpam-4755	53	63	type	type	NOUN
ejpam-4755	53	64	)	)	PUNCT
ejpam-4755	53	65	.	.	PUNCT
ejpam-4755	54	1	b.	b.	PROPN
ejpam-4755	54	2	jamal	jamal	PROPN
ejpam-4755	54	3	,	,	PUNCT
ejpam-4755	54	4	a.	a.	PROPN
ejpam-4755	54	5	alabdali	alabdali	VERB
ejpam-4755	54	6	/	/	SYM
ejpam-4755	54	7	eur	eur	PROPN
ejpam-4755	54	8	.	.	PUNCT
ejpam-4755	55	1	j.	j.	PROPN
ejpam-4755	55	2	pure	pure	PROPN
ejpam-4755	55	3	appl	appl	PROPN
ejpam-4755	55	4	.	.	PROPN
ejpam-4755	55	5	math	math	PROPN
ejpam-4755	55	6	,	,	PUNCT
ejpam-4755	55	7	16	16	NUM
ejpam-4755	55	8	(	(	PUNCT
ejpam-4755	55	9	2	2	NUM
ejpam-4755	55	10	)	)	PUNCT
ejpam-4755	55	11	(	(	PUNCT
ejpam-4755	55	12	2023	2023	NUM
ejpam-4755	55	13	)	)	PUNCT
ejpam-4755	55	14	,	,	PUNCT
ejpam-4755	55	15	1118	1118	NUM
ejpam-4755	55	16	-	-	SYM
ejpam-4755	55	17	1127	1127	NUM
ejpam-4755	55	18	1120	1120	NUM
ejpam-4755	55	19	2	2	NUM
ejpam-4755	55	20	.	.	PUNCT
ejpam-4755	55	21	materials	material	NOUN
ejpam-4755	55	22	and	and	CCONJ
ejpam-4755	55	23	methods	method	NOUN
ejpam-4755	55	24	in	in	ADP
ejpam-4755	55	25	this	this	DET
ejpam-4755	55	26	section	section	NOUN
ejpam-4755	55	27	,	,	PUNCT
ejpam-4755	55	28	we	we	PRON
ejpam-4755	55	29	review	review	VERB
ejpam-4755	55	30	the	the	DET
ejpam-4755	55	31	fundamental	fundamental	ADJ
ejpam-4755	55	32	facts	fact	NOUN
ejpam-4755	55	33	and	and	CCONJ
ejpam-4755	55	34	concepts	concept	NOUN
ejpam-4755	55	35	related	relate	VERB
ejpam-4755	55	36	to	to	ADP
ejpam-4755	55	37	hgss	hgss	ADJ
ejpam-4755	55	38	,	,	PUNCT
ejpam-4755	55	39	as	as	ADV
ejpam-4755	55	40	well	well	ADV
ejpam-4755	55	41	as	as	ADP
ejpam-4755	55	42	the	the	DET
ejpam-4755	55	43	relationship	relationship	NOUN
ejpam-4755	55	44	between	between	ADP
ejpam-4755	55	45	them	they	PRON
ejpam-4755	55	46	and	and	CCONJ
ejpam-4755	55	47	pgs	pgs	ADJ
ejpam-4755	55	48	.	.	PUNCT
ejpam-4755	56	1	using	use	VERB
ejpam-4755	56	2	the	the	DET
ejpam-4755	56	3	method	method	NOUN
ejpam-4755	56	4	provided	provide	VERB
ejpam-4755	56	5	in	in	ADP
ejpam-4755	56	6	[	[	X
ejpam-4755	56	7	3	3	NUM
ejpam-4755	56	8	]	]	PUNCT
ejpam-4755	56	9	,	,	PUNCT
ejpam-4755	56	10	we	we	PRON
ejpam-4755	56	11	demonstrate	demonstrate	VERB
ejpam-4755	56	12	how	how	SCONJ
ejpam-4755	56	13	to	to	PART
ejpam-4755	56	14	count	count	VERB
ejpam-4755	56	15	hgss	hgss	ADJ
ejpam-4755	56	16	.	.	PUNCT
ejpam-4755	57	1	we	we	PRON
ejpam-4755	57	2	recommend	recommend	VERB
ejpam-4755	57	3	[	[	PUNCT
ejpam-4755	57	4	[	[	X
ejpam-4755	57	5	8	8	NUM
ejpam-4755	57	6	]	]	PUNCT
ejpam-4755	57	7	,	,	PUNCT
ejpam-4755	57	8	chapter	chapter	NOUN
ejpam-4755	57	9	2	2	NUM
ejpam-4755	57	10	]	]	PUNCT
ejpam-4755	57	11	to	to	ADP
ejpam-4755	57	12	the	the	DET
ejpam-4755	57	13	reader	reader	NOUN
ejpam-4755	57	14	for	for	ADP
ejpam-4755	57	15	further	further	ADJ
ejpam-4755	57	16	information	information	NOUN
ejpam-4755	57	17	on	on	ADP
ejpam-4755	57	18	counting	count	VERB
ejpam-4755	57	19	hgss	hgss	ADJ
ejpam-4755	57	20	.	.	PUNCT
ejpam-4755	58	1	a	a	DET
ejpam-4755	58	2	pg	pg	NOUN
ejpam-4755	58	3	is	be	AUX
ejpam-4755	58	4	defined	define	VERB
ejpam-4755	58	5	as	as	ADP
ejpam-4755	58	6	a	a	DET
ejpam-4755	58	7	finite	finite	ADJ
ejpam-4755	58	8	group	group	NOUN
ejpam-4755	58	9	g	g	PROPN
ejpam-4755	58	10	with	with	ADP
ejpam-4755	58	11	a	a	DET
ejpam-4755	58	12	one	one	NUM
ejpam-4755	58	13	to	to	ADP
ejpam-4755	58	14	one	one	NUM
ejpam-4755	58	15	homomorphism	homomorphism	NOUN
ejpam-4755	58	16	ρ	ρ	NOUN
ejpam-4755	58	17	from	from	ADP
ejpam-4755	58	18	g	g	PROPN
ejpam-4755	58	19	into	into	ADP
ejpam-4755	58	20	the	the	DET
ejpam-4755	58	21	pg	pg	NOUN
ejpam-4755	58	22	of	of	ADP
ejpam-4755	58	23	a	a	DET
ejpam-4755	58	24	finite	finite	NOUN
ejpam-4755	58	25	set	set	NOUN
ejpam-4755	58	26	x	x	SYM
ejpam-4755	58	27	(	(	PUNCT
ejpam-4755	58	28	ρ	ρ	NOUN
ejpam-4755	58	29	:	:	PUNCT
ejpam-4755	58	30	g→	g→	PROPN
ejpam-4755	58	31	perm(x	perm(x	PROPN
ejpam-4755	58	32	)	)	PUNCT
ejpam-4755	58	33	)	)	PUNCT
ejpam-4755	58	34	.	.	PUNCT
ejpam-4755	59	1	let	let	VERB
ejpam-4755	59	2	y	y	PROPN
ejpam-4755	59	3	∈	∈	PROPN
ejpam-4755	59	4	x	x	PROPN
ejpam-4755	59	5	,	,	PUNCT
ejpam-4755	59	6	h	h	PROPN
ejpam-4755	59	7	∈	∈	PROPN
ejpam-4755	59	8	g	g	NOUN
ejpam-4755	59	9	then	then	ADV
ejpam-4755	59	10	we	we	PRON
ejpam-4755	59	11	express	express	VERB
ejpam-4755	59	12	ρ(h)(x	ρ(h)(x	NOUN
ejpam-4755	59	13	)	)	PUNCT
ejpam-4755	59	14	=	=	SYM
ejpam-4755	59	15	h.y	h.y	PROPN
ejpam-4755	59	16	.	.	PUNCT
ejpam-4755	60	1	the	the	DET
ejpam-4755	60	2	degree	degree	NOUN
ejpam-4755	60	3	of	of	ADP
ejpam-4755	60	4	g	g	PROPN
ejpam-4755	60	5	is	be	AUX
ejpam-4755	60	6	the	the	DET
ejpam-4755	60	7	order	order	NOUN
ejpam-4755	60	8	of	of	ADP
ejpam-4755	60	9	x.	x.	NOUN
ejpam-4755	60	10	if	if	SCONJ
ejpam-4755	60	11	there	there	PRON
ejpam-4755	60	12	is	be	VERB
ejpam-4755	60	13	a	a	DET
ejpam-4755	60	14	unique	unique	ADJ
ejpam-4755	60	15	h	h	NOUN
ejpam-4755	60	16	∈	∈	NOUN
ejpam-4755	60	17	g	g	PROPN
ejpam-4755	60	18	(	(	PUNCT
ejpam-4755	60	19	respectively	respectively	ADV
ejpam-4755	60	20	,	,	PUNCT
ejpam-4755	60	21	some	some	DET
ejpam-4755	60	22	h	h	NOUN
ejpam-4755	60	23	∈	∈	PROPN
ejpam-4755	60	24	g	g	NOUN
ejpam-4755	60	25	)	)	PUNCT
ejpam-4755	60	26	with	with	ADP
ejpam-4755	60	27	h.y	h.y	PROPN
ejpam-4755	60	28	=	=	SYM
ejpam-4755	60	29	x	x	PROPN
ejpam-4755	60	30	for	for	ADP
ejpam-4755	60	31	each	each	DET
ejpam-4755	60	32	x	x	NOUN
ejpam-4755	60	33	,	,	PUNCT
ejpam-4755	60	34	y	y	PROPN
ejpam-4755	60	35	∈	∈	PROPN
ejpam-4755	60	36	x	x	NOUN
ejpam-4755	60	37	,	,	PUNCT
ejpam-4755	60	38	then	then	ADV
ejpam-4755	60	39	g	g	PROPN
ejpam-4755	60	40	is	be	AUX
ejpam-4755	60	41	regular	regular	ADJ
ejpam-4755	60	42	(	(	PUNCT
ejpam-4755	60	43	respectively	respectively	ADV
ejpam-4755	60	44	,	,	PUNCT
ejpam-4755	60	45	transitive	transitive	ADJ
ejpam-4755	60	46	)	)	PUNCT
ejpam-4755	60	47	on	on	ADP
ejpam-4755	60	48	x.	x.	NOUN
ejpam-4755	61	1	we	we	PRON
ejpam-4755	61	2	assume	assume	VERB
ejpam-4755	61	3	all	all	DET
ejpam-4755	61	4	pgs	pgs	NOUN
ejpam-4755	61	5	to	to	PART
ejpam-4755	61	6	be	be	AUX
ejpam-4755	61	7	transitive	transitive	ADJ
ejpam-4755	61	8	groups	group	NOUN
ejpam-4755	61	9	in	in	ADP
ejpam-4755	61	10	our	our	PRON
ejpam-4755	61	11	study	study	NOUN
ejpam-4755	61	12	.	.	PUNCT
ejpam-4755	62	1	we	we	PRON
ejpam-4755	62	2	define	define	VERB
ejpam-4755	62	3	the	the	DET
ejpam-4755	62	4	subgroup	subgroup	NOUN
ejpam-4755	62	5	gy	gy	NOUN
ejpam-4755	62	6	=	=	PRON
ejpam-4755	62	7	{	{	PUNCT
ejpam-4755	62	8	h	h	NOUN
ejpam-4755	62	9	∈	∈	PROPN
ejpam-4755	62	10	g	g	PROPN
ejpam-4755	62	11	:	:	PUNCT
ejpam-4755	62	12	h.y	h.y	PROPN
ejpam-4755	62	13	=	=	SYM
ejpam-4755	62	14	y	y	PROPN
ejpam-4755	62	15	}	}	PUNCT
ejpam-4755	62	16	as	as	ADP
ejpam-4755	62	17	the	the	DET
ejpam-4755	62	18	stabilizer	stabilizer	NOUN
ejpam-4755	62	19	of	of	ADP
ejpam-4755	62	20	y	y	PROPN
ejpam-4755	62	21	∈	∈	PROPN
ejpam-4755	62	22	x	x	NOUN
ejpam-4755	62	23	,	,	PUNCT
ejpam-4755	62	24	so	so	ADV
ejpam-4755	62	25	the	the	DET
ejpam-4755	62	26	stabilizer	stabilizer	NOUN
ejpam-4755	62	27	of	of	ADP
ejpam-4755	62	28	h.y	h.y	PROPN
ejpam-4755	62	29	is	be	AUX
ejpam-4755	62	30	referred	refer	VERB
ejpam-4755	62	31	to	to	PART
ejpam-4755	62	32	be	be	AUX
ejpam-4755	62	33	as	as	ADP
ejpam-4755	62	34	hgyh	hgyh	NOUN
ejpam-4755	62	35	−1	−1	NOUN
ejpam-4755	62	36	.	.	PUNCT
ejpam-4755	63	1	the	the	DET
ejpam-4755	63	2	core	core	NOUN
ejpam-4755	63	3	∩h∈ghgyh	∩h∈ghgyh	PRON
ejpam-4755	63	4	−1	−1	NOUN
ejpam-4755	63	5	of	of	ADP
ejpam-4755	63	6	gy	gy	NOUN
ejpam-4755	63	7	in	in	ADP
ejpam-4755	63	8	g	g	PROPN
ejpam-4755	63	9	is	be	AUX
ejpam-4755	63	10	simple	simple	ADJ
ejpam-4755	63	11	as	as	ADP
ejpam-4755	63	12	a	a	DET
ejpam-4755	63	13	result	result	NOUN
ejpam-4755	63	14	of	of	ADP
ejpam-4755	63	15	the	the	DET
ejpam-4755	63	16	fact	fact	NOUN
ejpam-4755	63	17	that	that	SCONJ
ejpam-4755	63	18	x	x	PRON
ejpam-4755	63	19	affects	affect	VERB
ejpam-4755	63	20	transitively	transitively	NOUN
ejpam-4755	63	21	by	by	ADP
ejpam-4755	63	22	g	g	PROPN
ejpam-4755	63	23	and	and	CCONJ
ejpam-4755	63	24	g	g	PROPN
ejpam-4755	63	25	embedded	embed	VERB
ejpam-4755	63	26	in	in	ADP
ejpam-4755	63	27	perm(x	perm(x	PROPN
ejpam-4755	63	28	)	)	PUNCT
ejpam-4755	63	29	.	.	PUNCT
ejpam-4755	64	1	additionally	additionally	ADV
ejpam-4755	64	2	,	,	PUNCT
ejpam-4755	64	3	by	by	ADP
ejpam-4755	64	4	the	the	DET
ejpam-4755	64	5	left	left	ADJ
ejpam-4755	64	6	multiplication	multiplication	NOUN
ejpam-4755	64	7	action	action	NOUN
ejpam-4755	64	8	µ	µ	NOUN
ejpam-4755	64	9	:	:	PUNCT
ejpam-4755	64	10	g	g	NOUN
ejpam-4755	64	11	→	→	SYM
ejpam-4755	64	12	perm(g	perm(g	NOUN
ejpam-4755	64	13	/	/	SYM
ejpam-4755	64	14	gy	gy	NOUN
ejpam-4755	64	15	)	)	PUNCT
ejpam-4755	64	16	,	,	PUNCT
ejpam-4755	64	17	g	g	PROPN
ejpam-4755	64	18	acts	act	VERB
ejpam-4755	64	19	as	as	ADP
ejpam-4755	64	20	a	a	DET
ejpam-4755	64	21	pg	pg	NOUN
ejpam-4755	64	22	on	on	ADP
ejpam-4755	64	23	g	g	PROPN
ejpam-4755	64	24	/	/	SYM
ejpam-4755	64	25	gy	gy	NOUN
ejpam-4755	64	26	=	=	PUNCT
ejpam-4755	64	27	{	{	PUNCT
ejpam-4755	64	28	hgy	hgy	NOUN
ejpam-4755	64	29	:	:	PUNCT
ejpam-4755	64	30	h	h	PROPN
ejpam-4755	64	31	∈	∈	PROPN
ejpam-4755	65	1	g	g	PROPN
ejpam-4755	65	2	}	}	PUNCT
ejpam-4755	65	3	the	the	DET
ejpam-4755	65	4	set	set	NOUN
ejpam-4755	65	5	of	of	ADP
ejpam-4755	65	6	left	left	ADJ
ejpam-4755	65	7	cosets	coset	NOUN
ejpam-4755	65	8	,	,	PUNCT
ejpam-4755	65	9	where	where	SCONJ
ejpam-4755	65	10	µ(h)(h	µ(h)(h	NUM
ejpam-4755	65	11	′	′	NUM
ejpam-4755	65	12	gy	gy	NOUN
ejpam-4755	65	13	)	)	PUNCT
ejpam-4755	65	14	=	=	SYM
ejpam-4755	65	15	(	(	PUNCT
ejpam-4755	65	16	hh	hh	INTJ
ejpam-4755	65	17	′	′	NUM
ejpam-4755	65	18	)	)	PUNCT
ejpam-4755	65	19	gy	gy	PROPN
ejpam-4755	65	20	.	.	PROPN
ejpam-4755	66	1	as	as	ADP
ejpam-4755	66	2	a	a	DET
ejpam-4755	66	3	result	result	NOUN
ejpam-4755	66	4	,	,	PUNCT
ejpam-4755	66	5	the	the	DET
ejpam-4755	66	6	left	left	ADJ
ejpam-4755	66	7	translation	translation	NOUN
ejpam-4755	66	8	on	on	ADP
ejpam-4755	66	9	g	g	PROPN
ejpam-4755	66	10	/	/	SYM
ejpam-4755	66	11	g	g	NOUN
ejpam-4755	66	12	′	′	NUM
ejpam-4755	66	13	acts	act	VERB
ejpam-4755	66	14	up	up	ADP
ejpam-4755	66	15	to	to	ADP
ejpam-4755	66	16	isomorphism	isomorphism	NOUN
ejpam-4755	66	17	on	on	ADP
ejpam-4755	66	18	the	the	DET
ejpam-4755	66	19	abstract	abstract	ADJ
ejpam-4755	66	20	group	group	NOUN
ejpam-4755	66	21	g	g	PROPN
ejpam-4755	66	22	as	as	ADP
ejpam-4755	66	23	a	a	DET
ejpam-4755	66	24	pg	pg	NOUN
ejpam-4755	66	25	of	of	ADP
ejpam-4755	66	26	degree	degree	NOUN
ejpam-4755	66	27	n	n	CCONJ
ejpam-4755	66	28	,	,	PUNCT
ejpam-4755	66	29	with	with	ADP
ejpam-4755	66	30	the	the	DET
ejpam-4755	66	31	subgroup	subgroup	NOUN
ejpam-4755	66	32	g	g	NOUN
ejpam-4755	66	33	′	′	NUM
ejpam-4755	67	1	having	have	VERB
ejpam-4755	67	2	a	a	DET
ejpam-4755	67	3	trivial	trivial	ADJ
ejpam-4755	67	4	core	core	NOUN
ejpam-4755	67	5	with	with	ADP
ejpam-4755	67	6	index	index	NOUN
ejpam-4755	67	7	n.	n.	NOUN
ejpam-4755	67	8	we	we	PRON
ejpam-4755	67	9	utilize	utilize	VERB
ejpam-4755	67	10	the	the	DET
ejpam-4755	67	11	automorphism	automorphism	NOUN
ejpam-4755	67	12	definition	definition	NOUN
ejpam-4755	67	13	.	.	PUNCT
ejpam-4755	68	1	if	if	SCONJ
ejpam-4755	68	2	aut(g	aut(g	PROPN
ejpam-4755	68	3	,	,	PUNCT
ejpam-4755	68	4	g	g	NOUN
ejpam-4755	68	5	′	′	NUM
ejpam-4755	68	6	)	)	PUNCT
ejpam-4755	68	7	is	be	AUX
ejpam-4755	68	8	defined	define	VERB
ejpam-4755	68	9	as	as	ADP
ejpam-4755	68	10	aut(g	aut(g	PROPN
ejpam-4755	68	11	,	,	PUNCT
ejpam-4755	68	12	g	g	NOUN
ejpam-4755	68	13	′	′	NUM
ejpam-4755	68	14	)	)	PUNCT
ejpam-4755	69	1	=	=	PRON
ejpam-4755	69	2	{	{	PUNCT
ejpam-4755	69	3	ϕ	ϕ	NOUN
ejpam-4755	69	4	∈	∈	PROPN
ejpam-4755	69	5	aut(g	aut(g	PROPN
ejpam-4755	69	6	)	)	PUNCT
ejpam-4755	69	7	:	:	PUNCT
ejpam-4755	70	1	ϕ(g	ϕ(g	PROPN
ejpam-4755	70	2	′	′	NUM
ejpam-4755	70	3	)	)	PUNCT
ejpam-4755	71	1	=	=	SYM
ejpam-4755	71	2	g	g	PROPN
ejpam-4755	71	3	′	′	NUM
ejpam-4755	71	4	}	}	PUNCT
ejpam-4755	71	5	.	.	PUNCT
ejpam-4755	72	1	thus	thus	ADV
ejpam-4755	72	2	it	it	PRON
ejpam-4755	72	3	is	be	AUX
ejpam-4755	72	4	clear	clear	ADJ
ejpam-4755	72	5	that	that	SCONJ
ejpam-4755	72	6	aut(g	aut(g	PROPN
ejpam-4755	72	7	,	,	PUNCT
ejpam-4755	72	8	g	g	NOUN
ejpam-4755	72	9	′	′	NUM
ejpam-4755	72	10	)	)	PUNCT
ejpam-4755	72	11	forms	form	VERB
ejpam-4755	72	12	a	a	DET
ejpam-4755	72	13	pg	pg	NOUN
ejpam-4755	72	14	of	of	ADP
ejpam-4755	72	15	automorphisms	automorphisms	PROPN
ejpam-4755	72	16	ϕ	ϕ	PROPN
ejpam-4755	72	17	of	of	ADP
ejpam-4755	72	18	g	g	PROPN
ejpam-4755	72	19	such	such	ADJ
ejpam-4755	72	20	that	that	SCONJ
ejpam-4755	72	21	ϕ	ϕ	PROPN
ejpam-4755	72	22	fixes	fix	VERB
ejpam-4755	72	23	the	the	DET
ejpam-4755	72	24	left	left	ADJ
ejpam-4755	72	25	coset	coset	NOUN
ejpam-4755	73	1	1gg	1gg	ADJ
ejpam-4755	73	2	′	′	NUM
ejpam-4755	73	3	of	of	ADP
ejpam-4755	73	4	g	g	PROPN
ejpam-4755	73	5	/	/	SYM
ejpam-4755	73	6	g	g	NOUN
ejpam-4755	73	7	′	′	NUM
ejpam-4755	73	8	(	(	PUNCT
ejpam-4755	73	9	1	1	NUM
ejpam-4755	73	10	g	g	NOUN
ejpam-4755	73	11	is	be	AUX
ejpam-4755	73	12	the	the	DET
ejpam-4755	73	13	identity	identity	NOUN
ejpam-4755	73	14	of	of	ADP
ejpam-4755	73	15	g	g	NOUN
ejpam-4755	73	16	)	)	PUNCT
ejpam-4755	73	17	.	.	PUNCT
ejpam-4755	74	1	let	let	VERB
ejpam-4755	74	2	we	we	PRON
ejpam-4755	74	3	have	have	VERB
ejpam-4755	74	4	a	a	DET
ejpam-4755	74	5	finite	finite	NOUN
ejpam-4755	74	6	sfe	sfe	PROPN
ejpam-4755	74	7	l	l	PROPN
ejpam-4755	74	8	/	/	SYM
ejpam-4755	74	9	k	k	X
ejpam-4755	74	10	of	of	ADP
ejpam-4755	74	11	degree	degree	NOUN
ejpam-4755	74	12	n	n	NOUN
ejpam-4755	74	13	with	with	ADP
ejpam-4755	74	14	a	a	DET
ejpam-4755	74	15	fixed	fix	VERB
ejpam-4755	74	16	algebraic	algebraic	ADJ
ejpam-4755	74	17	closure	closure	NOUN
ejpam-4755	74	18	f	f	PROPN
ejpam-4755	74	19	as	as	ADP
ejpam-4755	74	20	normal	normal	ADJ
ejpam-4755	74	21	closure	closure	NOUN
ejpam-4755	74	22	in	in	ADP
ejpam-4755	74	23	kc	kc	PROPN
ejpam-4755	74	24	of	of	ADP
ejpam-4755	74	25	k.	k.	PROPN
ejpam-4755	74	26	if	if	SCONJ
ejpam-4755	74	27	the	the	DET
ejpam-4755	74	28	group	group	NOUN
ejpam-4755	74	29	g	g	PROPN
ejpam-4755	74	30	=	=	PROPN
ejpam-4755	74	31	gal(f	gal(f	PROPN
ejpam-4755	74	32	/	/	SYM
ejpam-4755	74	33	k	k	NOUN
ejpam-4755	74	34	)	)	PUNCT
ejpam-4755	74	35	and	and	CCONJ
ejpam-4755	74	36	the	the	DET
ejpam-4755	74	37	group	group	NOUN
ejpam-4755	74	38	g	g	NOUN
ejpam-4755	74	39	′	′	NUM
ejpam-4755	74	40	=	=	PUNCT
ejpam-4755	74	41	gal(f	gal(f	PROPN
ejpam-4755	74	42	/	/	SYM
ejpam-4755	74	43	l	l	NOUN
ejpam-4755	74	44	)	)	PUNCT
ejpam-4755	74	45	,	,	PUNCT
ejpam-4755	74	46	then	then	ADV
ejpam-4755	74	47	the	the	DET
ejpam-4755	74	48	map	map	NOUN
ejpam-4755	74	49	µ	µ	X
ejpam-4755	74	50	:	:	PUNCT
ejpam-4755	74	51	g	g	PROPN
ejpam-4755	74	52	→	→	SYM
ejpam-4755	74	53	perm(x	perm(x	NOUN
ejpam-4755	74	54	)	)	PUNCT
ejpam-4755	74	55	is	be	AUX
ejpam-4755	74	56	an	an	DET
ejpam-4755	74	57	embedding	embedding	NOUN
ejpam-4755	74	58	.	.	PUNCT
ejpam-4755	75	1	g	g	NOUN
ejpam-4755	75	2	′	′	NUM
ejpam-4755	75	3	acts	act	NOUN
ejpam-4755	75	4	as	as	ADP
ejpam-4755	75	5	a	a	DET
ejpam-4755	75	6	stabilizer	stabilizer	NOUN
ejpam-4755	75	7	for	for	ADP
ejpam-4755	75	8	the	the	DET
ejpam-4755	75	9	inclusion	inclusion	NOUN
ejpam-4755	75	10	l	l	NOUN
ejpam-4755	75	11	↪	↪	PROPN
ejpam-4755	75	12	→	→	SYM
ejpam-4755	75	13	f	f	PROPN
ejpam-4755	75	14	,	,	PUNCT
ejpam-4755	75	15	and	and	CCONJ
ejpam-4755	75	16	the	the	DET
ejpam-4755	75	17	embeddings	embedding	NOUN
ejpam-4755	75	18	of	of	ADP
ejpam-4755	75	19	k	k	PROPN
ejpam-4755	75	20	linear	linear	PROPN
ejpam-4755	75	21	of	of	ADP
ejpam-4755	75	22	l	l	NOUN
ejpam-4755	75	23	into	into	ADP
ejpam-4755	75	24	kc	kc	PROPN
ejpam-4755	75	25	or	or	CCONJ
ejpam-4755	75	26	f	f	PROPN
ejpam-4755	75	27	is	be	AUX
ejpam-4755	75	28	acted	act	VERB
ejpam-4755	75	29	transitively	transitively	PROPN
ejpam-4755	75	30	by	by	ADP
ejpam-4755	75	31	g.	g.	PROPN
ejpam-4755	75	32	consider	consider	VERB
ejpam-4755	75	33	the	the	DET
ejpam-4755	75	34	cocommutative	cocommutative	ADJ
ejpam-4755	75	35	k	k	PROPN
ejpam-4755	75	36	hopf	hopf	PROPN
ejpam-4755	75	37	algebra	algebra	NOUN
ejpam-4755	75	38	h.	h.	PROPN
ejpam-4755	75	39	let	let	VERB
ejpam-4755	75	40	ϵ	ϵ	X
ejpam-4755	75	41	:	:	PUNCT
ejpam-4755	75	42	h	h	NOUN
ejpam-4755	75	43	→	→	PUNCT
ejpam-4755	75	44	k	k	X
ejpam-4755	75	45	be	be	AUX
ejpam-4755	75	46	the	the	DET
ejpam-4755	75	47	counit	counit	VERB
ejpam-4755	75	48	map	map	NOUN
ejpam-4755	75	49	for	for	ADP
ejpam-4755	75	50	k	k	PROPN
ejpam-4755	75	51	and	and	CCONJ
ejpam-4755	75	52	ν	ν	NOUN
ejpam-4755	75	53	:	:	PUNCT
ejpam-4755	75	54	h	h	NOUN
ejpam-4755	75	55	→	→	SYM
ejpam-4755	75	56	h	h	NOUN
ejpam-4755	75	57	⊗k	⊗k	ADJ
ejpam-4755	75	58	h	h	NOUN
ejpam-4755	75	59	be	be	VERB
ejpam-4755	75	60	the	the	DET
ejpam-4755	75	61	comultiplication	comultiplication	NOUN
ejpam-4755	75	62	map	map	NOUN
ejpam-4755	75	63	for	for	ADP
ejpam-4755	75	64	ν(ξ	ν(ξ	PROPN
ejpam-4755	75	65	)	)	PUNCT
ejpam-4755	76	1	=	=	PUNCT
ejpam-4755	76	2	∑	∑	PUNCT
ejpam-4755	76	3	(	(	PUNCT
ejpam-4755	76	4	ξ	ξ	NOUN
ejpam-4755	76	5	)	)	PUNCT
ejpam-4755	76	6	ξ(1	ξ(1	PROPN
ejpam-4755	76	7	)	)	PUNCT
ejpam-4755	76	8	⊗	⊗	PROPN
ejpam-4755	76	9	ξ(2	ξ(2	PROPN
ejpam-4755	76	10	)	)	PUNCT
ejpam-4755	76	11	.	.	PUNCT
ejpam-4755	77	1	if	if	SCONJ
ejpam-4755	77	2	we	we	PRON
ejpam-4755	77	3	have	have	VERB
ejpam-4755	77	4	ξ(ab	ξ(ab	NOUN
ejpam-4755	77	5	)	)	PUNCT
ejpam-4755	77	6	=	=	PUNCT
ejpam-4755	77	7	∑	∑	PUNCT
ejpam-4755	77	8	(	(	PUNCT
ejpam-4755	77	9	ξ	ξ	NOUN
ejpam-4755	77	10	)	)	PUNCT
ejpam-4755	77	11	ξ(1)(a)ξ(2)(b	ξ(1)(a)ξ(2)(b	NUM
ejpam-4755	77	12	)	)	PUNCT
ejpam-4755	77	13	for	for	ADP
ejpam-4755	77	14	ξ	ξ	PROPN
ejpam-4755	77	15	∈	∈	PROPN
ejpam-4755	77	16	h	h	NOUN
ejpam-4755	77	17	and	and	CCONJ
ejpam-4755	77	18	a	a	DET
ejpam-4755	77	19	,	,	PUNCT
ejpam-4755	77	20	b	b	PROPN
ejpam-4755	77	21	∈	∈	PROPN
ejpam-4755	77	22	l	l	NOUN
ejpam-4755	77	23	,	,	PUNCT
ejpam-4755	77	24	and	and	CCONJ
ejpam-4755	77	25	ξ(k	ξ(k	PROPN
ejpam-4755	77	26	)	)	PUNCT
ejpam-4755	78	1	=	=	SYM
ejpam-4755	78	2	ϵ(ξ)k	ϵ(ξ)k	NOUN
ejpam-4755	78	3	for	for	ADP
ejpam-4755	78	4	all	all	DET
ejpam-4755	78	5	ξ	ξ	PROPN
ejpam-4755	78	6	∈	∈	PROPN
ejpam-4755	78	7	h	h	NOUN
ejpam-4755	78	8	and	and	CCONJ
ejpam-4755	78	9	k	k	PROPN
ejpam-4755	78	10	∈	∈	PROPN
ejpam-4755	78	11	k	k	PROPN
ejpam-4755	78	12	,	,	PUNCT
ejpam-4755	78	13	l	l	PROPN
ejpam-4755	78	14	is	be	AUX
ejpam-4755	78	15	said	say	VERB
ejpam-4755	78	16	to	to	PART
ejpam-4755	78	17	have	have	VERB
ejpam-4755	78	18	h	h	NOUN
ejpam-4755	78	19	module	module	NOUN
ejpam-4755	78	20	algebra	algebra	NOUN
ejpam-4755	78	21	.	.	PUNCT
ejpam-4755	79	1	in	in	ADP
ejpam-4755	79	2	addition	addition	NOUN
ejpam-4755	79	3	,	,	PUNCT
ejpam-4755	79	4	if	if	SCONJ
ejpam-4755	79	5	ϕ	ϕ	X
ejpam-4755	79	6	:	:	PUNCT
ejpam-4755	79	7	l	l	NOUN
ejpam-4755	79	8	⊗k	⊗k	ADJ
ejpam-4755	79	9	h	h	NOUN
ejpam-4755	79	10	→	→	SYM
ejpam-4755	79	11	endk(l	endk(l	PROPN
ejpam-4755	79	12	)	)	PUNCT
ejpam-4755	79	13	described	describe	VERB
ejpam-4755	79	14	as	as	ADP
ejpam-4755	79	15	the	the	DET
ejpam-4755	79	16	k	k	PROPN
ejpam-4755	79	17	module	module	NOUN
ejpam-4755	79	18	homomorphism	homomorphism	NOUN
ejpam-4755	79	19	by	by	ADP
ejpam-4755	79	20	ϕ(a	ϕ(a	NOUN
ejpam-4755	79	21	⊗	⊗	PROPN
ejpam-4755	79	22	ξ)(b	ξ)(b	PROPN
ejpam-4755	79	23	)	)	PUNCT
ejpam-4755	79	24	=	=	PUNCT
ejpam-4755	79	25	aξ(b	aξ(b	NOUN
ejpam-4755	79	26	)	)	PUNCT
ejpam-4755	79	27	is	be	AUX
ejpam-4755	79	28	an	an	DET
ejpam-4755	79	29	isomorphism	isomorphism	NOUN
ejpam-4755	79	30	,	,	PUNCT
ejpam-4755	79	31	we	we	PRON
ejpam-4755	79	32	say	say	VERB
ejpam-4755	79	33	that	that	SCONJ
ejpam-4755	79	34	l	l	PROPN
ejpam-4755	79	35	/	/	SYM
ejpam-4755	79	36	k	k	PROPN
ejpam-4755	79	37	is	be	AUX
ejpam-4755	79	38	a	a	DET
ejpam-4755	79	39	h	h	NOUN
ejpam-4755	79	40	galois	galois	NOUN
ejpam-4755	79	41	extension	extension	NOUN
ejpam-4755	79	42	or	or	CCONJ
ejpam-4755	79	43	that	that	SCONJ
ejpam-4755	79	44	h	h	NOUN
ejpam-4755	79	45	yields	yield	VERB
ejpam-4755	79	46	an	an	DET
ejpam-4755	79	47	hgs	hgs	PROPN
ejpam-4755	79	48	on	on	ADP
ejpam-4755	79	49	l	l	PROPN
ejpam-4755	79	50	/	/	SYM
ejpam-4755	79	51	k.	k.	PROPN
ejpam-4755	79	52	the	the	DET
ejpam-4755	79	53	pg	pg	PROPN
ejpam-4755	79	54	g	g	PROPN
ejpam-4755	79	55	is	be	AUX
ejpam-4755	79	56	necessary	necessary	ADJ
ejpam-4755	79	57	to	to	PART
ejpam-4755	79	58	obtain	obtain	VERB
ejpam-4755	79	59	the	the	DET
ejpam-4755	79	60	hgss	hgss	ADJ
ejpam-4755	79	61	on	on	ADP
ejpam-4755	79	62	l	l	PROPN
ejpam-4755	79	63	/	/	SYM
ejpam-4755	79	64	k.	k.	PROPN
ejpam-4755	79	65	greither	greither	PROPN
ejpam-4755	79	66	and	and	CCONJ
ejpam-4755	79	67	pareigis	pareigis	ADJ
ejpam-4755	79	68	’	'	PUNCT
ejpam-4755	79	69	discovery	discovery	NOUN
ejpam-4755	79	70	is	be	AUX
ejpam-4755	79	71	that	that	SCONJ
ejpam-4755	79	72	the	the	DET
ejpam-4755	79	73	left	left	ADJ
ejpam-4755	79	74	translation	translation	NOUN
ejpam-4755	79	75	group	group	PROPN
ejpam-4755	79	76	µ(g	µ(g	PROPN
ejpam-4755	79	77	)	)	PUNCT
ejpam-4755	79	78	normalizes	normalize	VERB
ejpam-4755	79	79	the	the	DET
ejpam-4755	79	80	regular	regular	ADJ
ejpam-4755	79	81	subgroups	subgroup	NOUN
ejpam-4755	79	82	n	n	CCONJ
ejpam-4755	79	83	of	of	ADP
ejpam-4755	79	84	perm(x	perm(x	PROPN
ejpam-4755	79	85	)	)	PUNCT
ejpam-4755	79	86	that	that	PRON
ejpam-4755	79	87	are	be	AUX
ejpam-4755	79	88	isomorphic	isomorphic	ADJ
ejpam-4755	79	89	to	to	ADP
ejpam-4755	79	90	the	the	DET
ejpam-4755	79	91	hgss	hgss	ADJ
ejpam-4755	79	92	on	on	ADP
ejpam-4755	79	93	l	l	PROPN
ejpam-4755	79	94	/	/	SYM
ejpam-4755	79	95	k.	k.	PROPN
ejpam-4755	79	96	the	the	DET
ejpam-4755	79	97	hopf	hopf	ADJ
ejpam-4755	79	98	algebra	algebra	NOUN
ejpam-4755	79	99	of	of	ADP
ejpam-4755	79	100	k	k	PROPN
ejpam-4755	79	101	for	for	ADP
ejpam-4755	79	102	each	each	DET
ejpam-4755	79	103	such	such	ADJ
ejpam-4755	79	104	group	group	NOUN
ejpam-4755	79	105	n	n	NOUN
ejpam-4755	79	106	,	,	PUNCT
ejpam-4755	80	1	h	h	NOUN
ejpam-4755	80	2	=	=	SYM
ejpam-4755	81	1	f	f	PROPN
ejpam-4755	82	1	[	[	X
ejpam-4755	82	2	n	n	X
ejpam-4755	82	3	]	]	X
ejpam-4755	82	4	g	g	NOUN
ejpam-4755	82	5	acts	act	VERB
ejpam-4755	82	6	on	on	ADP
ejpam-4755	82	7	l	l	NOUN
ejpam-4755	82	8	via	via	ADP
ejpam-4755	82	9	galois	galois	PROPN
ejpam-4755	82	10	descent	descent	NOUN
ejpam-4755	82	11	,	,	PUNCT
ejpam-4755	82	12	where	where	SCONJ
ejpam-4755	82	13	f	f	PROPN
ejpam-4755	82	14	[	[	X
ejpam-4755	82	15	g	g	X
ejpam-4755	82	16	]	]	PUNCT
ejpam-4755	82	17	is	be	AUX
ejpam-4755	82	18	acted	act	VERB
ejpam-4755	82	19	by	by	ADP
ejpam-4755	82	20	g	g	PROPN
ejpam-4755	82	21	as	as	ADP
ejpam-4755	82	22	an	an	DET
ejpam-4755	82	23	automorphisms	automorphisms	PROPN
ejpam-4755	82	24	field	field	NOUN
ejpam-4755	82	25	of	of	ADP
ejpam-4755	82	26	f	f	PROPN
ejpam-4755	82	27	and	and	CCONJ
ejpam-4755	82	28	conjugates	conjugate	NOUN
ejpam-4755	82	29	on	on	ADP
ejpam-4755	82	30	n	n	CCONJ
ejpam-4755	82	31	via	via	ADP
ejpam-4755	82	32	µ.	µ.	PROPN
ejpam-4755	82	33	the	the	DET
ejpam-4755	82	34	hgs	hgs	PROPN
ejpam-4755	82	35	type	type	NOUN
ejpam-4755	82	36	is	be	AUX
ejpam-4755	82	37	also	also	ADV
ejpam-4755	82	38	known	know	VERB
ejpam-4755	82	39	as	as	ADP
ejpam-4755	82	40	the	the	DET
ejpam-4755	82	41	n	n	NUM
ejpam-4755	82	42	isomorphism	isomorphism	NOUN
ejpam-4755	82	43	type	type	NOUN
ejpam-4755	82	44	.	.	PUNCT
ejpam-4755	83	1	if	if	SCONJ
ejpam-4755	83	2	n	n	NUM
ejpam-4755	83	3	=	=	SYM
ejpam-4755	83	4	c	c	NOUN
ejpam-4755	83	5	,	,	PUNCT
ejpam-4755	83	6	where	where	SCONJ
ejpam-4755	83	7	c	c	PROPN
ejpam-4755	83	8	is	be	AUX
ejpam-4755	83	9	the	the	DET
ejpam-4755	83	10	normal	normal	ADJ
ejpam-4755	83	11	complement	complement	NOUN
ejpam-4755	83	12	of	of	ADP
ejpam-4755	83	13	the	the	DET
ejpam-4755	83	14	subgroup	subgroup	NOUN
ejpam-4755	83	15	g	g	PROPN
ejpam-4755	83	16	′	′	NUM
ejpam-4755	83	17	of	of	ADP
ejpam-4755	83	18	g	g	PROPN
ejpam-4755	83	19	,	,	PUNCT
ejpam-4755	83	20	we	we	PRON
ejpam-4755	83	21	get	get	VERB
ejpam-4755	83	22	an	an	DET
ejpam-4755	83	23	hgs	hgs	NOUN
ejpam-4755	83	24	.	.	PUNCT
ejpam-4755	84	1	the	the	DET
ejpam-4755	84	2	classical	classical	ADJ
ejpam-4755	84	3	hgss	hgss	NOUN
ejpam-4755	84	4	on	on	ADP
ejpam-4755	84	5	l	l	PROPN
ejpam-4755	84	6	/	/	SYM
ejpam-4755	84	7	k	k	PROPN
ejpam-4755	84	8	is	be	AUX
ejpam-4755	84	9	then	then	ADV
ejpam-4755	84	10	admitted	admit	VERB
ejpam-4755	84	11	by	by	ADP
ejpam-4755	84	12	f	f	PROPN
ejpam-4755	84	13	[	[	X
ejpam-4755	84	14	n	n	X
ejpam-4755	84	15	]	]	X
ejpam-4755	84	16	g.	g.	PROPN
ejpam-4755	84	17	b.	b.	PROPN
ejpam-4755	84	18	jamal	jamal	PROPN
ejpam-4755	84	19	,	,	PUNCT
ejpam-4755	84	20	a.	a.	PROPN
ejpam-4755	84	21	alabdali	alabdali	VERB
ejpam-4755	84	22	/	/	SYM
ejpam-4755	84	23	eur	eur	PROPN
ejpam-4755	84	24	.	.	PUNCT
ejpam-4755	85	1	j.	j.	PROPN
ejpam-4755	85	2	pure	pure	PROPN
ejpam-4755	85	3	appl	appl	PROPN
ejpam-4755	85	4	.	.	PROPN
ejpam-4755	85	5	math	math	PROPN
ejpam-4755	85	6	,	,	PUNCT
ejpam-4755	85	7	16	16	NUM
ejpam-4755	85	8	(	(	PUNCT
ejpam-4755	85	9	2	2	NUM
ejpam-4755	85	10	)	)	PUNCT
ejpam-4755	85	11	(	(	PUNCT
ejpam-4755	85	12	2023	2023	NUM
ejpam-4755	85	13	)	)	PUNCT
ejpam-4755	85	14	,	,	PUNCT
ejpam-4755	85	15	1118	1118	NUM
ejpam-4755	85	16	-	-	SYM
ejpam-4755	85	17	1127	1127	NUM
ejpam-4755	85	18	1121	1121	NUM
ejpam-4755	85	19	if	if	SCONJ
ejpam-4755	85	20	the	the	DET
ejpam-4755	85	21	isomorphism	isomorphism	NOUN
ejpam-4755	85	22	ϕ	ϕ	X
ejpam-4755	85	23	:	:	PUNCT
ejpam-4755	85	24	g	g	PROPN
ejpam-4755	85	25	→	→	SYM
ejpam-4755	85	26	gal(f	gal(f	PROPN
ejpam-4755	85	27	/	/	SYM
ejpam-4755	85	28	k	k	NOUN
ejpam-4755	85	29	)	)	PUNCT
ejpam-4755	85	30	with	with	ADP
ejpam-4755	85	31	ϕ(g	ϕ(g	PROPN
ejpam-4755	85	32	′	′	NUM
ejpam-4755	85	33	)	)	PUNCT
ejpam-4755	86	1	=	=	PUNCT
ejpam-4755	86	2	gal(f	gal(f	PROPN
ejpam-4755	86	3	/	/	SYM
ejpam-4755	86	4	l	l	NOUN
ejpam-4755	86	5	)	)	PUNCT
ejpam-4755	86	6	exists	exist	VERB
ejpam-4755	86	7	,	,	PUNCT
ejpam-4755	86	8	we	we	PRON
ejpam-4755	86	9	have	have	VERB
ejpam-4755	86	10	g	g	PROPN
ejpam-4755	86	11	is	be	AUX
ejpam-4755	86	12	realised	realise	VERB
ejpam-4755	86	13	by	by	ADP
ejpam-4755	86	14	an	an	DET
ejpam-4755	86	15	sfe	sfe	PROPN
ejpam-4755	86	16	l	l	PROPN
ejpam-4755	86	17	/	/	SYM
ejpam-4755	86	18	k.	k.	PROPN
ejpam-4755	87	1	the	the	DET
ejpam-4755	87	2	point	point	NOUN
ejpam-4755	87	3	stabilizer	stabilizer	NOUN
ejpam-4755	87	4	is	be	AUX
ejpam-4755	87	5	g	g	NOUN
ejpam-4755	87	6	′	′	NOUN
ejpam-4755	87	7	,	,	PUNCT
ejpam-4755	87	8	and	and	CCONJ
ejpam-4755	87	9	the	the	DET
ejpam-4755	87	10	pg	pg	NOUN
ejpam-4755	87	11	is	be	AUX
ejpam-4755	87	12	g.	g.	NOUN
ejpam-4755	87	13	in	in	ADP
ejpam-4755	87	14	addition	addition	NOUN
ejpam-4755	87	15	,	,	PUNCT
ejpam-4755	87	16	we	we	PRON
ejpam-4755	87	17	state	state	VERB
ejpam-4755	87	18	that	that	DET
ejpam-4755	87	19	type	type	NOUN
ejpam-4755	87	20	n	n	PROPN
ejpam-4755	87	21	of	of	ADP
ejpam-4755	87	22	an	an	DET
ejpam-4755	87	23	hgs	hgs	PROPN
ejpam-4755	87	24	realises	realise	VERB
ejpam-4755	87	25	g	g	PROPN
ejpam-4755	87	26	if	if	SCONJ
ejpam-4755	87	27	it	it	PRON
ejpam-4755	87	28	is	be	AUX
ejpam-4755	87	29	admitted	admit	VERB
ejpam-4755	87	30	by	by	ADP
ejpam-4755	87	31	l	l	PROPN
ejpam-4755	87	32	/	/	SYM
ejpam-4755	87	33	k.	k.	NOUN
ejpam-4755	87	34	we	we	PRON
ejpam-4755	87	35	count	count	VERB
ejpam-4755	87	36	the	the	DET
ejpam-4755	87	37	type	type	NOUN
ejpam-4755	87	38	n	n	NOUN
ejpam-4755	87	39	of	of	ADP
ejpam-4755	87	40	the	the	DET
ejpam-4755	87	41	number	number	NOUN
ejpam-4755	87	42	of	of	ADP
ejpam-4755	87	43	hgss	hgss	ADJ
ejpam-4755	87	44	as	as	ADP
ejpam-4755	87	45	a	a	DET
ejpam-4755	87	46	group	group	NOUN
ejpam-4755	87	47	of	of	ADP
ejpam-4755	87	48	order	order	NOUN
ejpam-4755	87	49	n	n	PRON
ejpam-4755	87	50	such	such	ADJ
ejpam-4755	87	51	that	that	SCONJ
ejpam-4755	87	52	g	g	PROPN
ejpam-4755	87	53	is	be	AUX
ejpam-4755	87	54	realised	realise	VERB
ejpam-4755	87	55	by	by	ADP
ejpam-4755	87	56	a	a	DET
ejpam-4755	87	57	sfe	sfe	PROPN
ejpam-4755	87	58	l	l	PROPN
ejpam-4755	87	59	/	/	SYM
ejpam-4755	87	60	k	k	NOUN
ejpam-4755	87	61	,	,	PUNCT
ejpam-4755	87	62	which	which	PRON
ejpam-4755	87	63	corresponds	correspond	VERB
ejpam-4755	87	64	to	to	ADP
ejpam-4755	87	65	the	the	DET
ejpam-4755	87	66	number	number	NOUN
ejpam-4755	87	67	of	of	ADP
ejpam-4755	87	68	regular	regular	ADJ
ejpam-4755	87	69	subgroups	subgroup	NOUN
ejpam-4755	87	70	n∗	n∗	NOUN
ejpam-4755	87	71	normalised	normalise	VERB
ejpam-4755	87	72	by	by	ADP
ejpam-4755	87	73	µ(g	µ(g	NOUN
ejpam-4755	87	74	)	)	PUNCT
ejpam-4755	87	75	and	and	CCONJ
ejpam-4755	87	76	isomorphic	isomorphic	ADJ
ejpam-4755	87	77	to	to	ADP
ejpam-4755	87	78	n	n	PROPN
ejpam-4755	87	79	of	of	ADP
ejpam-4755	87	80	perm(x	perm(x	PROPN
ejpam-4755	87	81	)	)	PUNCT
ejpam-4755	87	82	,	,	PUNCT
ejpam-4755	87	83	according	accord	VERB
ejpam-4755	87	84	to	to	ADP
ejpam-4755	87	85	greither	greither	NOUN
ejpam-4755	87	86	and	and	CCONJ
ejpam-4755	87	87	pareigis	pareigis	ADJ
ejpam-4755	87	88	conclusions	conclusion	NOUN
ejpam-4755	87	89	.	.	PUNCT
ejpam-4755	88	1	let	let	VERB
ejpam-4755	88	2	hol(n	hol(n	NOUN
ejpam-4755	88	3	)	)	PUNCT
ejpam-4755	88	4	=	=	SYM
ejpam-4755	89	1	n	n	CCONJ
ejpam-4755	89	2	⋊aut(n	⋊aut(n	NOUN
ejpam-4755	89	3	)	)	PUNCT
ejpam-4755	89	4	be	be	VERB
ejpam-4755	89	5	the	the	DET
ejpam-4755	89	6	holomorph	holomorph	ADJ
ejpam-4755	89	7	of	of	ADP
ejpam-4755	89	8	n	n	PROPN
ejpam-4755	89	9	.	.	PUNCT
ejpam-4755	90	1	as	as	ADP
ejpam-4755	90	2	a	a	DET
ejpam-4755	90	3	result	result	NOUN
ejpam-4755	90	4	,	,	PUNCT
ejpam-4755	90	5	the	the	DET
ejpam-4755	90	6	number	number	NOUN
ejpam-4755	90	7	of	of	ADP
ejpam-4755	90	8	hgss	hgss	ADJ
ejpam-4755	90	9	on	on	ADP
ejpam-4755	90	10	l	l	PROPN
ejpam-4755	90	11	/	/	SYM
ejpam-4755	90	12	k	k	PROPN
ejpam-4755	90	13	can	can	AUX
ejpam-4755	90	14	be	be	AUX
ejpam-4755	90	15	determined	determine	VERB
ejpam-4755	90	16	using	use	VERB
ejpam-4755	90	17	byott	byott	PROPN
ejpam-4755	90	18	’s	’s	PART
ejpam-4755	90	19	result	result	NOUN
ejpam-4755	90	20	in	in	ADP
ejpam-4755	90	21	[	[	X
ejpam-4755	90	22	3	3	NUM
ejpam-4755	90	23	]	]	PUNCT
ejpam-4755	90	24	and	and	CCONJ
ejpam-4755	90	25	the	the	DET
ejpam-4755	90	26	formula	formula	NOUN
ejpam-4755	90	27	f(g	f(g	NOUN
ejpam-4755	90	28	,	,	PUNCT
ejpam-4755	90	29	n	n	CCONJ
ejpam-4755	90	30	)	)	PUNCT
ejpam-4755	90	31	=	=	SYM
ejpam-4755	90	32	|aut(g	|aut(g	PROPN
ejpam-4755	90	33	,	,	PUNCT
ejpam-4755	90	34	g′	g′	NOUN
ejpam-4755	90	35	)	)	PUNCT
ejpam-4755	91	1	|	|	ADV
ejpam-4755	91	2	|aut(n)|	|aut(n)|	PUNCT
ejpam-4755	91	3	f	f	PROPN
ejpam-4755	91	4	′	′	NUM
ejpam-4755	91	5	(	(	PUNCT
ejpam-4755	91	6	g	g	NOUN
ejpam-4755	91	7	,	,	PUNCT
ejpam-4755	91	8	n	n	CCONJ
ejpam-4755	91	9	)	)	PUNCT
ejpam-4755	91	10	,	,	PUNCT
ejpam-4755	91	11	(	(	PUNCT
ejpam-4755	91	12	1	1	X
ejpam-4755	91	13	)	)	PUNCT
ejpam-4755	91	14	we	we	PRON
ejpam-4755	91	15	denote	denote	VERB
ejpam-4755	91	16	f	f	PROPN
ejpam-4755	91	17	′	′	NUM
ejpam-4755	91	18	(	(	PUNCT
ejpam-4755	91	19	g	g	NOUN
ejpam-4755	91	20	,	,	PUNCT
ejpam-4755	91	21	n	n	CCONJ
ejpam-4755	91	22	)	)	PUNCT
ejpam-4755	91	23	as	as	ADP
ejpam-4755	91	24	the	the	DET
ejpam-4755	91	25	number	number	NOUN
ejpam-4755	91	26	of	of	ADP
ejpam-4755	91	27	regular	regular	ADJ
ejpam-4755	91	28	subgroups	subgroup	NOUN
ejpam-4755	91	29	b	b	NOUN
ejpam-4755	91	30	with	with	ADP
ejpam-4755	91	31	transitive	transitive	NOUN
ejpam-4755	91	32	on	on	ADP
ejpam-4755	91	33	n	n	PROPN
ejpam-4755	91	34	of	of	ADP
ejpam-4755	91	35	hol(n	hol(n	NOUN
ejpam-4755	91	36	)	)	PUNCT
ejpam-4755	91	37	and	and	CCONJ
ejpam-4755	91	38	b	b	X
ejpam-4755	91	39	∼=	∼=	NOUN
ejpam-4755	91	40	g	g	NOUN
ejpam-4755	91	41	by	by	ADP
ejpam-4755	91	42	an	an	DET
ejpam-4755	91	43	isomorphism	isomorphism	NOUN
ejpam-4755	91	44	with	with	ADP
ejpam-4755	91	45	the	the	DET
ejpam-4755	91	46	stabilizer	stabilizer	NOUN
ejpam-4755	91	47	b	b	NOUN
ejpam-4755	91	48	′	′	NUM
ejpam-4755	91	49	of	of	ADP
ejpam-4755	91	50	1n	1n	NUM
ejpam-4755	91	51	in	in	ADP
ejpam-4755	91	52	b	b	NOUN
ejpam-4755	91	53	to	to	ADP
ejpam-4755	91	54	g	g	PROPN
ejpam-4755	91	55	′	′	NUM
ejpam-4755	91	56	.	.	PUNCT
ejpam-4755	92	1	if	if	SCONJ
ejpam-4755	92	2	hgs	hgs	PROPN
ejpam-4755	92	3	of	of	ADP
ejpam-4755	92	4	type	type	NOUN
ejpam-4755	92	5	n	n	PROPN
ejpam-4755	92	6	realises	realise	VERB
ejpam-4755	92	7	g	g	NOUN
ejpam-4755	92	8	,	,	PUNCT
ejpam-4755	92	9	then	then	ADV
ejpam-4755	92	10	g	g	PROPN
ejpam-4755	92	11	∼=	∼=	PROPN
ejpam-4755	92	12	b	b	PROPN
ejpam-4755	92	13	of	of	ADP
ejpam-4755	92	14	hol(n	hol(n	PROPN
ejpam-4755	92	15	)	)	PUNCT
ejpam-4755	92	16	.	.	PUNCT
ejpam-4755	93	1	because	because	SCONJ
ejpam-4755	93	2	the	the	DET
ejpam-4755	93	3	preceding	precede	VERB
ejpam-4755	93	4	approach	approach	NOUN
ejpam-4755	93	5	deals	deal	NOUN
ejpam-4755	93	6	with	with	ADP
ejpam-4755	93	7	hol(n	hol(n	NOUN
ejpam-4755	93	8	)	)	PUNCT
ejpam-4755	93	9	instead	instead	ADV
ejpam-4755	93	10	of	of	ADP
ejpam-4755	93	11	the	the	DET
ejpam-4755	93	12	perm(x	perm(x	PROPN
ejpam-4755	93	13	)	)	PUNCT
ejpam-4755	93	14	group	group	NOUN
ejpam-4755	93	15	,	,	PUNCT
ejpam-4755	93	16	counting	count	VERB
ejpam-4755	93	17	hgss	hgss	ADJ
ejpam-4755	93	18	is	be	AUX
ejpam-4755	93	19	made	make	VERB
ejpam-4755	93	20	easy	easy	ADJ
ejpam-4755	93	21	.	.	PUNCT
ejpam-4755	94	1	we	we	PRON
ejpam-4755	94	2	write	write	VERB
ejpam-4755	94	3	the	the	DET
ejpam-4755	94	4	elements	element	NOUN
ejpam-4755	94	5	of	of	ADP
ejpam-4755	94	6	hol(n	hol(n	NOUN
ejpam-4755	94	7	)	)	PUNCT
ejpam-4755	94	8	by	by	ADP
ejpam-4755	94	9	[	[	X
ejpam-4755	94	10	x	x	X
ejpam-4755	94	11	,	,	PUNCT
ejpam-4755	94	12	α	α	NOUN
ejpam-4755	94	13	]	]	PUNCT
ejpam-4755	94	14	where	where	SCONJ
ejpam-4755	94	15	x	x	SYM
ejpam-4755	94	16	∈	∈	PROPN
ejpam-4755	94	17	n	n	NOUN
ejpam-4755	94	18	and	and	CCONJ
ejpam-4755	94	19	α	α	PRON
ejpam-4755	94	20	∈	∈	PROPN
ejpam-4755	94	21	aut(n	aut(n	PROPN
ejpam-4755	94	22	)	)	PUNCT
ejpam-4755	94	23	.	.	PUNCT
ejpam-4755	95	1	thus	thus	ADV
ejpam-4755	95	2	hol(n	hol(n	VERB
ejpam-4755	95	3	)	)	PUNCT
ejpam-4755	95	4	acts	act	VERB
ejpam-4755	95	5	on	on	ADP
ejpam-4755	95	6	n	n	PRON
ejpam-4755	95	7	as	as	ADP
ejpam-4755	95	8	permutations	permutation	NOUN
ejpam-4755	95	9	by	by	ADP
ejpam-4755	95	10	[	[	X
ejpam-4755	95	11	x	x	X
ejpam-4755	95	12	,	,	PUNCT
ejpam-4755	95	13	α].y	α].y	NUM
ejpam-4755	95	14	=	=	SYM
ejpam-4755	95	15	xα(y	xα(y	NOUN
ejpam-4755	95	16	)	)	PUNCT
ejpam-4755	95	17	.	.	PUNCT
ejpam-4755	96	1	then	then	ADV
ejpam-4755	96	2	,	,	PUNCT
ejpam-4755	96	3	in	in	ADP
ejpam-4755	96	4	hol(n	hol(n	PROPN
ejpam-4755	96	5	)	)	PUNCT
ejpam-4755	96	6	the	the	DET
ejpam-4755	96	7	normal	normal	ADJ
ejpam-4755	96	8	subgroup	subgroup	NOUN
ejpam-4755	96	9	n	n	PROPN
ejpam-4755	96	10	specifies	specifie	NOUN
ejpam-4755	96	11	µ(n	µ(n	VERB
ejpam-4755	96	12	)	)	PUNCT
ejpam-4755	96	13	of	of	ADP
ejpam-4755	96	14	the	the	DET
ejpam-4755	96	15	left	left	ADJ
ejpam-4755	96	16	translations	translation	NOUN
ejpam-4755	96	17	,	,	PUNCT
ejpam-4755	96	18	and	and	CCONJ
ejpam-4755	96	19	the	the	DET
ejpam-4755	96	20	stabilizer	stabilizer	NOUN
ejpam-4755	96	21	of	of	ADP
ejpam-4755	96	22	1n	1n	PROPN
ejpam-4755	96	23	creates	create	VERB
ejpam-4755	96	24	the	the	DET
ejpam-4755	96	25	subgroup	subgroup	NOUN
ejpam-4755	96	26	aut(n	aut(n	PROPN
ejpam-4755	96	27	)	)	PUNCT
ejpam-4755	96	28	.	.	PUNCT
ejpam-4755	97	1	in	in	ADP
ejpam-4755	97	2	hol(n	hol(n	PROPN
ejpam-4755	97	3	)	)	PUNCT
ejpam-4755	97	4	,	,	PUNCT
ejpam-4755	97	5	the	the	DET
ejpam-4755	97	6	multiplication	multiplication	NOUN
ejpam-4755	97	7	is	be	AUX
ejpam-4755	97	8	defined	define	VERB
ejpam-4755	97	9	as	as	SCONJ
ejpam-4755	97	10	follows	follow	VERB
ejpam-4755	97	11	[	[	X
ejpam-4755	97	12	x	x	NOUN
ejpam-4755	97	13	,	,	PUNCT
ejpam-4755	97	14	α][y	α][y	ADJ
ejpam-4755	97	15	,	,	PUNCT
ejpam-4755	97	16	β	β	X
ejpam-4755	97	17	]	]	X
ejpam-4755	97	18	=	=	PUNCT
ejpam-4755	98	1	[	[	X
ejpam-4755	98	2	xα(y	xα(y	NOUN
ejpam-4755	98	3	)	)	PUNCT
ejpam-4755	98	4	,	,	PUNCT
ejpam-4755	98	5	αβ	αβ	X
ejpam-4755	98	6	]	]	X
ejpam-4755	98	7	.	.	PUNCT
ejpam-4755	99	1	we	we	PRON
ejpam-4755	99	2	commonly	commonly	ADV
ejpam-4755	99	3	refer	refer	VERB
ejpam-4755	99	4	to	to	ADP
ejpam-4755	99	5	x	x	PUNCT
ejpam-4755	99	6	and	and	CCONJ
ejpam-4755	99	7	α	α	NOUN
ejpam-4755	99	8	instead	instead	ADV
ejpam-4755	99	9	of	of	ADP
ejpam-4755	99	10	[	[	X
ejpam-4755	99	11	x	x	X
ejpam-4755	99	12	,	,	PUNCT
ejpam-4755	99	13	in	in	ADP
ejpam-4755	99	14	]	]	PUNCT
ejpam-4755	99	15	and	and	CCONJ
ejpam-4755	99	16	[	[	X
ejpam-4755	99	17	1n	1n	NUM
ejpam-4755	99	18	,	,	PUNCT
ejpam-4755	99	19	α	α	X
ejpam-4755	99	20	]	]	X
ejpam-4755	99	21	the	the	DET
ejpam-4755	99	22	elements	element	NOUN
ejpam-4755	99	23	of	of	ADP
ejpam-4755	99	24	hol(n	hol(n	PROPN
ejpam-4755	99	25	)	)	PUNCT
ejpam-4755	99	26	,	,	PUNCT
ejpam-4755	99	27	respectively	respectively	ADV
ejpam-4755	99	28	.	.	PUNCT
ejpam-4755	100	1	for	for	ADP
ejpam-4755	100	2	example	example	NOUN
ejpam-4755	100	3	,	,	PUNCT
ejpam-4755	100	4	we	we	PRON
ejpam-4755	100	5	have	have	VERB
ejpam-4755	100	6	the	the	DET
ejpam-4755	100	7	identification	identification	NOUN
ejpam-4755	100	8	αx	αx	NOUN
ejpam-4755	100	9	=	=	SYM
ejpam-4755	100	10	α(x)α	α(x)α	PROPN
ejpam-4755	100	11	.	.	PUNCT
ejpam-4755	101	1	now	now	ADV
ejpam-4755	101	2	we	we	PRON
ejpam-4755	101	3	have	have	VERB
ejpam-4755	101	4	some	some	DET
ejpam-4755	101	5	general	general	ADJ
ejpam-4755	101	6	results	result	NOUN
ejpam-4755	101	7	from	from	ADP
ejpam-4755	101	8	[	[	X
ejpam-4755	101	9	6	6	NUM
ejpam-4755	101	10	]	]	PUNCT
ejpam-4755	101	11	about	about	ADP
ejpam-4755	101	12	holomorphs	holomorph	NOUN
ejpam-4755	101	13	,	,	PUNCT
ejpam-4755	101	14	the	the	DET
ejpam-4755	101	15	group	group	NOUN
ejpam-4755	101	16	n	n	NOUN
ejpam-4755	101	17	and	and	CCONJ
ejpam-4755	101	18	aut(n	aut(n	PROPN
ejpam-4755	101	19	)	)	PUNCT
ejpam-4755	101	20	.	.	PUNCT
ejpam-4755	102	1	proposition	proposition	NOUN
ejpam-4755	102	2	1	1	NUM
ejpam-4755	102	3	.	.	PUNCT
ejpam-4755	102	4	assume	assume	VERB
ejpam-4755	102	5	that	that	SCONJ
ejpam-4755	102	6	n	n	PROPN
ejpam-4755	102	7	and	and	CCONJ
ejpam-4755	102	8	aut(n	aut(n	NOUN
ejpam-4755	102	9	)	)	PUNCT
ejpam-4755	102	10	are	be	AUX
ejpam-4755	102	11	abelian	abelian	ADJ
ejpam-4755	102	12	group	group	NOUN
ejpam-4755	102	13	and	and	CCONJ
ejpam-4755	102	14	abelian	abelian	ADJ
ejpam-4755	102	15	automorphism	automorphism	NOUN
ejpam-4755	102	16	respectively	respectively	ADV
ejpam-4755	102	17	.	.	PUNCT
ejpam-4755	103	1	suppose	suppose	VERB
ejpam-4755	103	2	the	the	DET
ejpam-4755	103	3	two	two	NUM
ejpam-4755	103	4	subgroups	subgroup	NOUN
ejpam-4755	103	5	of	of	ADP
ejpam-4755	103	6	hol(n	hol(n	PROPN
ejpam-4755	103	7	)	)	PUNCT
ejpam-4755	103	8	,	,	PUNCT
ejpam-4755	103	9	b	b	X
ejpam-4755	103	10	=	=	PUNCT
ejpam-4755	103	11	n⋊a	n⋊a	NOUN
ejpam-4755	103	12	and	and	CCONJ
ejpam-4755	103	13	b	b	NOUN
ejpam-4755	103	14	′	′	NUM
ejpam-4755	103	15	=	=	PUNCT
ejpam-4755	104	1	n⋊a′	n⋊a′	ADP
ejpam-4755	104	2	such	such	ADJ
ejpam-4755	104	3	that	that	SCONJ
ejpam-4755	104	4	a	a	PRON
ejpam-4755	104	5	,	,	PUNCT
ejpam-4755	104	6	a	a	DET
ejpam-4755	104	7	′	′	NUM
ejpam-4755	104	8	two	two	NUM
ejpam-4755	104	9	subgroups	subgroup	NOUN
ejpam-4755	104	10	of	of	ADP
ejpam-4755	104	11	aut(n	aut(n	PROPN
ejpam-4755	104	12	)	)	PUNCT
ejpam-4755	104	13	.	.	PUNCT
ejpam-4755	105	1	let	let	VERB
ejpam-4755	105	2	ψ	ψ	X
ejpam-4755	105	3	:	:	PUNCT
ejpam-4755	105	4	b	b	X
ejpam-4755	105	5	→	→	SYM
ejpam-4755	105	6	b	b	NOUN
ejpam-4755	105	7	′	′	NOUN
ejpam-4755	105	8	be	be	AUX
ejpam-4755	105	9	an	an	DET
ejpam-4755	105	10	isomorphism	isomorphism	NOUN
ejpam-4755	105	11	such	such	ADJ
ejpam-4755	105	12	that	that	SCONJ
ejpam-4755	105	13	ψ(n	ψ(n	PROPN
ejpam-4755	105	14	)	)	PUNCT
ejpam-4755	106	1	=	=	SYM
ejpam-4755	106	2	n	n	X
ejpam-4755	106	3	,	,	PUNCT
ejpam-4755	106	4	therefore	therefore	ADV
ejpam-4755	106	5	b	b	X
ejpam-4755	106	6	=	=	SYM
ejpam-4755	106	7	b	b	PROPN
ejpam-4755	106	8	′	′	NOUN
ejpam-4755	106	9	.	.	PUNCT
ejpam-4755	107	1	proposition	proposition	NOUN
ejpam-4755	107	2	2	2	NUM
ejpam-4755	107	3	.	.	PUNCT
ejpam-4755	107	4	suppose	suppose	VERB
ejpam-4755	107	5	that	that	SCONJ
ejpam-4755	107	6	n	n	PRON
ejpam-4755	107	7	is	be	AUX
ejpam-4755	107	8	a	a	DET
ejpam-4755	107	9	group	group	NOUN
ejpam-4755	107	10	such	such	ADJ
ejpam-4755	107	11	that	that	SCONJ
ejpam-4755	107	12	a	a	PRON
ejpam-4755	107	13	is	be	AUX
ejpam-4755	107	14	a	a	DET
ejpam-4755	107	15	subgroup	subgroup	NOUN
ejpam-4755	107	16	of	of	ADP
ejpam-4755	107	17	aut(n	aut(n	PROPN
ejpam-4755	107	18	)	)	PUNCT
ejpam-4755	107	19	.	.	PUNCT
ejpam-4755	108	1	suppose	suppose	VERB
ejpam-4755	108	2	that	that	SCONJ
ejpam-4755	108	3	the	the	DET
ejpam-4755	108	4	subgroup	subgroup	NOUN
ejpam-4755	108	5	of	of	ADP
ejpam-4755	108	6	hol(n	hol(n	PROPN
ejpam-4755	108	7	)	)	PUNCT
ejpam-4755	108	8	is	be	AUX
ejpam-4755	108	9	b	b	NOUN
ejpam-4755	108	10	=	=	PUNCT
ejpam-4755	108	11	n	n	PRON
ejpam-4755	108	12	⋊	⋊	NOUN
ejpam-4755	108	13	a	a	DET
ejpam-4755	108	14	such	such	ADJ
ejpam-4755	108	15	that	that	SCONJ
ejpam-4755	108	16	n	n	PRON
ejpam-4755	108	17	is	be	AUX
ejpam-4755	108	18	characteristic	characteristic	ADJ
ejpam-4755	108	19	in	in	ADP
ejpam-4755	108	20	b.	b.	PROPN
ejpam-4755	108	21	then	then	ADV
ejpam-4755	108	22	the	the	DET
ejpam-4755	108	23	normalizer	normalizer	NOUN
ejpam-4755	108	24	of	of	ADP
ejpam-4755	108	25	a	a	PRON
ejpam-4755	108	26	in	in	ADP
ejpam-4755	108	27	automorphism	automorphism	NOUN
ejpam-4755	108	28	of	of	ADP
ejpam-4755	108	29	n	n	PRON
ejpam-4755	108	30	is	be	AUX
ejpam-4755	108	31	isomorphic	isomorphic	ADJ
ejpam-4755	108	32	to	to	ADP
ejpam-4755	108	33	the	the	DET
ejpam-4755	108	34	group	group	NOUN
ejpam-4755	108	35	aut(b	aut(b	PROPN
ejpam-4755	108	36	,	,	PUNCT
ejpam-4755	108	37	a	a	PRON
ejpam-4755	108	38	)	)	PUNCT
ejpam-4755	108	39	:	:	PUNCT
ejpam-4755	108	40	=	=	SYM
ejpam-4755	108	41	{	{	PUNCT
ejpam-4755	108	42	ϕ	ϕ	NOUN
ejpam-4755	108	43	∈	∈	PROPN
ejpam-4755	108	44	aut(b	aut(b	PROPN
ejpam-4755	108	45	)	)	PUNCT
ejpam-4755	108	46	:	:	PUNCT
ejpam-4755	109	1	ϕ(a	ϕ(a	NOUN
ejpam-4755	109	2	)	)	PUNCT
ejpam-4755	109	3	=	=	SYM
ejpam-4755	109	4	a	a	PRON
ejpam-4755	109	5	}	}	PUNCT
ejpam-4755	109	6	.	.	PUNCT
ejpam-4755	110	1	in	in	ADP
ejpam-4755	110	2	particular	particular	ADJ
ejpam-4755	110	3	,	,	PUNCT
ejpam-4755	110	4	the	the	DET
ejpam-4755	110	5	group	group	NOUN
ejpam-4755	110	6	aut(b	aut(b	PROPN
ejpam-4755	110	7	,	,	PUNCT
ejpam-4755	110	8	a	a	PRON
ejpam-4755	110	9	)	)	PUNCT
ejpam-4755	110	10	is	be	AUX
ejpam-4755	110	11	isomorphic	isomorphic	ADJ
ejpam-4755	110	12	to	to	ADP
ejpam-4755	110	13	aut(n	aut(n	PROPN
ejpam-4755	110	14	)	)	PUNCT
ejpam-4755	110	15	if	if	SCONJ
ejpam-4755	110	16	the	the	DET
ejpam-4755	110	17	group	group	NOUN
ejpam-4755	110	18	aut(n	aut(n	PROPN
ejpam-4755	110	19	)	)	PUNCT
ejpam-4755	110	20	is	be	AUX
ejpam-4755	110	21	abelian	abelian	ADJ
ejpam-4755	110	22	.	.	PUNCT
ejpam-4755	111	1	the	the	DET
ejpam-4755	111	2	next	next	ADJ
ejpam-4755	111	3	result	result	NOUN
ejpam-4755	111	4	from	from	ADP
ejpam-4755	111	5	[	[	X
ejpam-4755	111	6	15	15	NUM
ejpam-4755	111	7	]	]	PUNCT
ejpam-4755	111	8	shows	show	VERB
ejpam-4755	111	9	the	the	DET
ejpam-4755	111	10	total	total	ADJ
ejpam-4755	111	11	number	number	NOUN
ejpam-4755	111	12	of	of	ADP
ejpam-4755	111	13	pgs	pgs	NOUN
ejpam-4755	111	14	which	which	PRON
ejpam-4755	111	15	admit	admit	VERB
ejpam-4755	111	16	hgs	hgs	PROPN
ejpam-4755	111	17	of	of	ADP
ejpam-4755	111	18	cyclic	cyclic	ADJ
ejpam-4755	111	19	case	case	NOUN
ejpam-4755	111	20	of	of	ADP
ejpam-4755	111	21	degree	degree	NOUN
ejpam-4755	111	22	pqw	pqw	PROPN
ejpam-4755	111	23	.	.	PUNCT
ejpam-4755	112	1	theorem	theorem	NOUN
ejpam-4755	112	2	3	3	NUM
ejpam-4755	112	3	.	.	PUNCT
ejpam-4755	113	1	the	the	DET
ejpam-4755	113	2	total	total	ADJ
ejpam-4755	113	3	number	number	NOUN
ejpam-4755	113	4	of	of	ADP
ejpam-4755	113	5	pgs	pgs	NOUN
ejpam-4755	113	6	g	g	NOUN
ejpam-4755	113	7	which	which	PRON
ejpam-4755	113	8	admits	admit	VERB
ejpam-4755	113	9	hgs	hgs	PROPN
ejpam-4755	113	10	of	of	ADP
ejpam-4755	113	11	cyclic	cyclic	ADJ
ejpam-4755	113	12	case	case	NOUN
ejpam-4755	113	13	is	be	AUX
ejpam-4755	113	14	12(r	12(r	PROPN
ejpam-4755	113	15	+	+	CCONJ
ejpam-4755	113	16	i+	i+	NUM
ejpam-4755	113	17	1)[σ0(s	1)[σ0(s	NUM
ejpam-4755	113	18	)	)	PUNCT
ejpam-4755	114	1	+	+	PUNCT
ejpam-4755	114	2	σ1(j	σ1(j	X
ejpam-4755	114	3	)	)	PUNCT
ejpam-4755	114	4	+	+	X
ejpam-4755	114	5	σ0(s)σ1(j	σ0(s)σ1(j	NOUN
ejpam-4755	114	6	)	)	PUNCT
ejpam-4755	114	7	]	]	PUNCT
ejpam-4755	114	8	of	of	ADP
ejpam-4755	114	9	isomorphism	isomorphism	NOUN
ejpam-4755	114	10	types	type	NOUN
ejpam-4755	114	11	of	of	ADP
ejpam-4755	114	12	degree	degree	NOUN
ejpam-4755	114	13	pqw	pqw	NOUN
ejpam-4755	114	14	.	.	PUNCT
ejpam-4755	115	1	the	the	DET
ejpam-4755	115	2	regular	regular	ADJ
ejpam-4755	115	3	group	group	NOUN
ejpam-4755	115	4	is	be	AUX
ejpam-4755	115	5	the	the	DET
ejpam-4755	115	6	cyclic	cyclic	NOUN
ejpam-4755	115	7	of	of	ADP
ejpam-4755	115	8	order	order	NOUN
ejpam-4755	115	9	pqw	pqw	ADJ
ejpam-4755	115	10	.	.	PUNCT
ejpam-4755	116	1	any	any	DET
ejpam-4755	116	2	field	field	NOUN
ejpam-4755	116	3	extension	extension	NOUN
ejpam-4755	116	4	l	l	PROPN
ejpam-4755	116	5	/	/	SYM
ejpam-4755	116	6	k	k	PROPN
ejpam-4755	116	7	admits	admit	VERB
ejpam-4755	116	8	a	a	DET
ejpam-4755	116	9	unique	unique	ADJ
ejpam-4755	116	10	hgs	hgs	NOUN
ejpam-4755	116	11	of	of	ADP
ejpam-4755	116	12	cyclic	cyclic	ADJ
ejpam-4755	116	13	case	case	NOUN
ejpam-4755	116	14	g	g	NOUN
ejpam-4755	116	15	and	and	CCONJ
ejpam-4755	116	16	is	be	AUX
ejpam-4755	116	17	essentially	essentially	ADV
ejpam-4755	116	18	classically	classically	ADV
ejpam-4755	116	19	galois	galois	PROPN
ejpam-4755	116	20	and	and	CCONJ
ejpam-4755	116	21	for	for	ADP
ejpam-4755	116	22	all	all	DET
ejpam-4755	116	23	groups	group	NOUN
ejpam-4755	116	24	g.	g.	VERB
ejpam-4755	116	25	more	more	ADV
ejpam-4755	116	26	general	general	ADJ
ejpam-4755	116	27	,	,	PUNCT
ejpam-4755	116	28	since	since	SCONJ
ejpam-4755	116	29	any	any	DET
ejpam-4755	116	30	sylow	sylow	NOUN
ejpam-4755	116	31	subgroup	subgroup	NOUN
ejpam-4755	116	32	is	be	AUX
ejpam-4755	116	33	cyclic	cyclic	ADJ
ejpam-4755	116	34	.	.	PUNCT
ejpam-4755	117	1	hence	hence	ADV
ejpam-4755	117	2	,	,	PUNCT
ejpam-4755	117	3	the	the	DET
ejpam-4755	117	4	square	square	ADJ
ejpam-4755	117	5	free	free	ADJ
ejpam-4755	117	6	groups	group	NOUN
ejpam-4755	117	7	of	of	ADP
ejpam-4755	117	8	order	order	NOUN
ejpam-4755	117	9	n	n	PRON
ejpam-4755	117	10	can	can	AUX
ejpam-4755	117	11	exist	exist	VERB
ejpam-4755	117	12	and	and	CCONJ
ejpam-4755	117	13	classify	classify	VERB
ejpam-4755	117	14	.	.	PUNCT
ejpam-4755	118	1	b.	b.	PROPN
ejpam-4755	118	2	jamal	jamal	PROPN
ejpam-4755	118	3	,	,	PUNCT
ejpam-4755	118	4	a.	a.	PROPN
ejpam-4755	118	5	alabdali	alabdali	VERB
ejpam-4755	118	6	/	/	SYM
ejpam-4755	118	7	eur	eur	PROPN
ejpam-4755	118	8	.	.	PUNCT
ejpam-4755	119	1	j.	j.	PROPN
ejpam-4755	119	2	pure	pure	PROPN
ejpam-4755	119	3	appl	appl	PROPN
ejpam-4755	119	4	.	.	PROPN
ejpam-4755	119	5	math	math	PROPN
ejpam-4755	119	6	,	,	PUNCT
ejpam-4755	119	7	16	16	NUM
ejpam-4755	119	8	(	(	PUNCT
ejpam-4755	119	9	2	2	NUM
ejpam-4755	119	10	)	)	PUNCT
ejpam-4755	119	11	(	(	PUNCT
ejpam-4755	119	12	2023	2023	NUM
ejpam-4755	119	13	)	)	PUNCT
ejpam-4755	119	14	,	,	PUNCT
ejpam-4755	119	15	1118	1118	NUM
ejpam-4755	119	16	-	-	SYM
ejpam-4755	119	17	1127	1127	NUM
ejpam-4755	119	18	1122	1122	NUM
ejpam-4755	119	19	3	3	NUM
ejpam-4755	119	20	.	.	PUNCT
ejpam-4755	119	21	results	result	NOUN
ejpam-4755	119	22	we	we	PRON
ejpam-4755	119	23	will	will	AUX
ejpam-4755	119	24	concentrate	concentrate	VERB
ejpam-4755	119	25	the	the	DET
ejpam-4755	119	26	rest	rest	NOUN
ejpam-4755	119	27	of	of	ADP
ejpam-4755	119	28	the	the	DET
ejpam-4755	119	29	work	work	NOUN
ejpam-4755	119	30	on	on	ADP
ejpam-4755	119	31	hgss	hgss	ADJ
ejpam-4755	119	32	on	on	ADP
ejpam-4755	119	33	sfes	sfe	NOUN
ejpam-4755	119	34	of	of	ADP
ejpam-4755	119	35	degree	degree	NOUN
ejpam-4755	119	36	pqw	pqw	NOUN
ejpam-4755	119	37	with	with	ADP
ejpam-4755	119	38	p	p	NOUN
ejpam-4755	119	39	=	=	PUNCT
ejpam-4755	119	40	2w	2w	NUM
ejpam-4755	119	41	+	+	CCONJ
ejpam-4755	119	42	1	1	NUM
ejpam-4755	119	43	,	,	PUNCT
ejpam-4755	119	44	q	q	PUNCT
ejpam-4755	119	45	and	and	CCONJ
ejpam-4755	119	46	w	w	PROPN
ejpam-4755	119	47	are	be	AUX
ejpam-4755	119	48	odd	odd	ADJ
ejpam-4755	119	49	primes	prime	NOUN
ejpam-4755	119	50	of	of	ADP
ejpam-4755	119	51	square	square	ADJ
ejpam-4755	119	52	free	free	ADJ
ejpam-4755	119	53	.	.	PUNCT
ejpam-4755	120	1	as	as	ADP
ejpam-4755	120	2	a	a	DET
ejpam-4755	120	3	result	result	NOUN
ejpam-4755	120	4	,	,	PUNCT
ejpam-4755	120	5	w	w	NOUN
ejpam-4755	120	6	and	and	CCONJ
ejpam-4755	120	7	p	p	NOUN
ejpam-4755	120	8	are	be	AUX
ejpam-4755	120	9	sophie	sophie	PROPN
ejpam-4755	120	10	germain	germain	PROPN
ejpam-4755	120	11	prime	prime	ADJ
ejpam-4755	120	12	and	and	CCONJ
ejpam-4755	120	13	safe	safe	ADJ
ejpam-4755	120	14	prime	prime	NOUN
ejpam-4755	120	15	,	,	PUNCT
ejpam-4755	120	16	respectively	respectively	ADV
ejpam-4755	120	17	.	.	PUNCT
ejpam-4755	121	1	we	we	PRON
ejpam-4755	121	2	have	have	VERB
ejpam-4755	121	3	w−	w−	NOUN
ejpam-4755	121	4	1	1	NUM
ejpam-4755	121	5	=	=	SYM
ejpam-4755	121	6	2ij	2ij	NOUN
ejpam-4755	121	7	,	,	PUNCT
ejpam-4755	121	8	q−	q−	PROPN
ejpam-4755	121	9	1	1	NUM
ejpam-4755	122	1	=	=	NOUN
ejpam-4755	122	2	2rs	2rs	ADJ
ejpam-4755	122	3	with	with	ADP
ejpam-4755	122	4	i	i	PRON
ejpam-4755	122	5	,	,	PUNCT
ejpam-4755	122	6	r	r	NOUN
ejpam-4755	122	7	≥	≥	NOUN
ejpam-4755	122	8	1	1	NUM
ejpam-4755	122	9	and	and	CCONJ
ejpam-4755	122	10	s	s	PROPN
ejpam-4755	122	11	,	,	PUNCT
ejpam-4755	122	12	j	j	PROPN
ejpam-4755	122	13	are	be	AUX
ejpam-4755	122	14	odd	odd	ADJ
ejpam-4755	122	15	numbers	number	NOUN
ejpam-4755	122	16	.	.	PUNCT
ejpam-4755	123	1	we	we	PRON
ejpam-4755	123	2	write	write	VERB
ejpam-4755	123	3	gcd(j	gcd(j	PRON
ejpam-4755	123	4	,	,	PUNCT
ejpam-4755	123	5	2pw	2pw	NOUN
ejpam-4755	123	6	)	)	PUNCT
ejpam-4755	123	7	=	=	SYM
ejpam-4755	123	8	1	1	NUM
ejpam-4755	123	9	and	and	CCONJ
ejpam-4755	123	10	gcd(s	gcd(s	PROPN
ejpam-4755	123	11	,	,	PUNCT
ejpam-4755	123	12	2pq	2pq	NOUN
ejpam-4755	123	13	)	)	PUNCT
ejpam-4755	124	1	=	=	SYM
ejpam-4755	124	2	1	1	X
ejpam-4755	124	3	.	.	PUNCT
ejpam-4755	125	1	however	however	ADV
ejpam-4755	125	2	,	,	PUNCT
ejpam-4755	125	3	we	we	PRON
ejpam-4755	125	4	have	have	VERB
ejpam-4755	125	5	no	no	DET
ejpam-4755	125	6	more	more	ADJ
ejpam-4755	125	7	presumptions	presumption	NOUN
ejpam-4755	125	8	regarding	regard	VERB
ejpam-4755	125	9	the	the	DET
ejpam-4755	125	10	prime	prime	ADJ
ejpam-4755	125	11	factors	factor	NOUN
ejpam-4755	125	12	of	of	ADP
ejpam-4755	125	13	j	j	PROPN
ejpam-4755	125	14	and	and	CCONJ
ejpam-4755	125	15	s.	s.	PROPN
ejpam-4755	125	16	there	there	PRON
ejpam-4755	125	17	are	be	VERB
ejpam-4755	125	18	six	six	NUM
ejpam-4755	125	19	groups	group	NOUN
ejpam-4755	125	20	n	n	ADP
ejpam-4755	125	21	of	of	ADP
ejpam-4755	125	22	order	order	NOUN
ejpam-4755	125	23	pqw	pqw	VERB
ejpam-4755	125	24	up	up	ADP
ejpam-4755	125	25	to	to	ADP
ejpam-4755	125	26	isomorphism	isomorphism	NOUN
ejpam-4755	125	27	,	,	PUNCT
ejpam-4755	125	28	but	but	CCONJ
ejpam-4755	125	29	in	in	ADP
ejpam-4755	125	30	this	this	DET
ejpam-4755	125	31	work	work	NOUN
ejpam-4755	125	32	we	we	PRON
ejpam-4755	125	33	deal	deal	VERB
ejpam-4755	125	34	with	with	ADP
ejpam-4755	125	35	the	the	DET
ejpam-4755	125	36	cg	cg	NOUN
ejpam-4755	125	37	cpqw	cpqw	NOUN
ejpam-4755	125	38	and	and	CCONJ
ejpam-4755	125	39	precisely	precisely	ADV
ejpam-4755	125	40	the	the	DET
ejpam-4755	125	41	nonabelian	nonabelian	ADJ
ejpam-4755	125	42	case	case	NOUN
ejpam-4755	125	43	.	.	PUNCT
ejpam-4755	126	1	as	as	ADP
ejpam-4755	126	2	a	a	DET
ejpam-4755	126	3	result	result	NOUN
ejpam-4755	126	4	,	,	PUNCT
ejpam-4755	126	5	the	the	DET
ejpam-4755	126	6	transitive	transitive	ADJ
ejpam-4755	126	7	subgroups	subgroup	NOUN
ejpam-4755	126	8	of	of	ADP
ejpam-4755	126	9	hol(cpqw	hol(cpqw	NOUN
ejpam-4755	126	10	)	)	PUNCT
ejpam-4755	126	11	must	must	AUX
ejpam-4755	126	12	be	be	AUX
ejpam-4755	126	13	determined	determine	VERB
ejpam-4755	126	14	.	.	PUNCT
ejpam-4755	127	1	assume	assume	VERB
ejpam-4755	127	2	that	that	SCONJ
ejpam-4755	127	3	n	n	PRON
ejpam-4755	127	4	is	be	AUX
ejpam-4755	127	5	a	a	DET
ejpam-4755	127	6	cg	cg	NOUN
ejpam-4755	127	7	of	of	ADP
ejpam-4755	127	8	order	order	NOUN
ejpam-4755	127	9	pqw	pqw	ADJ
ejpam-4755	127	10	with	with	ADP
ejpam-4755	127	11	the	the	DET
ejpam-4755	127	12	following	follow	VERB
ejpam-4755	127	13	form	form	NOUN
ejpam-4755	127	14	n	n	NOUN
ejpam-4755	127	15	=	=	SYM
ejpam-4755	127	16	⟨σ	⟨σ	NOUN
ejpam-4755	127	17	,	,	PUNCT
ejpam-4755	127	18	τ	τ	X
ejpam-4755	127	19	:	:	PUNCT
ejpam-4755	127	20	σe	σe	PROPN
ejpam-4755	127	21	=	=	PUNCT
ejpam-4755	127	22	τw	τw	NOUN
ejpam-4755	127	23	=	=	SYM
ejpam-4755	127	24	1	1	NUM
ejpam-4755	127	25	,	,	PUNCT
ejpam-4755	127	26	τσ	τσ	PROPN
ejpam-4755	127	27	=	=	SYM
ejpam-4755	127	28	στ⟩	στ⟩	NOUN
ejpam-4755	127	29	,	,	PUNCT
ejpam-4755	127	30	where	where	SCONJ
ejpam-4755	127	31	e	e	PROPN
ejpam-4755	127	32	=	=	SYM
ejpam-4755	127	33	pq	pq	PROPN
ejpam-4755	127	34	.	.	PUNCT
ejpam-4755	128	1	we	we	PRON
ejpam-4755	128	2	write	write	VERB
ejpam-4755	128	3	aut(n	aut(n	PROPN
ejpam-4755	128	4	)	)	PUNCT
ejpam-4755	129	1	∼=	∼=	VERB
ejpam-4755	129	2	aut(⟨σ⟩)×	aut(⟨σ⟩)×	NUM
ejpam-4755	129	3	aut(⟨τ⟩	aut(⟨τ⟩	NOUN
ejpam-4755	129	4	)	)	PUNCT
ejpam-4755	129	5	,	,	PUNCT
ejpam-4755	129	6	since	since	SCONJ
ejpam-4755	129	7	we	we	PRON
ejpam-4755	129	8	have	have	VERB
ejpam-4755	129	9	the	the	DET
ejpam-4755	129	10	two	two	NUM
ejpam-4755	129	11	characteristic	characteristic	ADJ
ejpam-4755	129	12	subgroups	subgroup	NOUN
ejpam-4755	129	13	⟨σ⟩	⟨σ⟩	PROPN
ejpam-4755	129	14	and	and	CCONJ
ejpam-4755	129	15	⟨τ⟩	⟨τ⟩	PROPN
ejpam-4755	129	16	in	in	ADP
ejpam-4755	129	17	n	n	PROPN
ejpam-4755	129	18	,	,	PUNCT
ejpam-4755	129	19	where	where	SCONJ
ejpam-4755	129	20	aut(⟨σ⟩	aut(⟨σ⟩	PROPN
ejpam-4755	129	21	)	)	PUNCT
ejpam-4755	129	22	of	of	ADP
ejpam-4755	129	23	order	order	NOUN
ejpam-4755	129	24	(	(	PUNCT
ejpam-4755	129	25	p−1)(q−1	p−1)(q−1	X
ejpam-4755	129	26	)	)	PUNCT
ejpam-4755	130	1	=	=	SYM
ejpam-4755	130	2	2w2rs	2w2rs	NUM
ejpam-4755	130	3	and	and	CCONJ
ejpam-4755	130	4	aut(⟨τ⟩	aut(⟨τ⟩	PROPN
ejpam-4755	130	5	)	)	PUNCT
ejpam-4755	130	6	of	of	ADP
ejpam-4755	130	7	order	order	NOUN
ejpam-4755	130	8	w−	w−	NOUN
ejpam-4755	130	9	1	1	NUM
ejpam-4755	130	10	=	=	SYM
ejpam-4755	130	11	2ij	2ij	NOUN
ejpam-4755	130	12	are	be	AUX
ejpam-4755	130	13	cyclic	cyclic	ADJ
ejpam-4755	130	14	.	.	PUNCT
ejpam-4755	131	1	suppose	suppose	VERB
ejpam-4755	131	2	that	that	SCONJ
ejpam-4755	131	3	α	α	X
ejpam-4755	131	4	,	,	PUNCT
ejpam-4755	131	5	β	β	X
ejpam-4755	131	6	,	,	PUNCT
ejpam-4755	131	7	γ	γ	PROPN
ejpam-4755	131	8	,	,	PUNCT
ejpam-4755	131	9	δ	δ	PROPN
ejpam-4755	131	10	are	be	AUX
ejpam-4755	131	11	automorphisms	automorphism	NOUN
ejpam-4755	131	12	of	of	ADP
ejpam-4755	131	13	the	the	DET
ejpam-4755	131	14	group	group	NOUN
ejpam-4755	131	15	n	n	PROPN
ejpam-4755	131	16	of	of	ADP
ejpam-4755	131	17	order	order	NOUN
ejpam-4755	131	18	w	w	NOUN
ejpam-4755	131	19	,	,	PUNCT
ejpam-4755	131	20	2	2	NUM
ejpam-4755	131	21	,	,	PUNCT
ejpam-4755	131	22	2r	2r	NUM
ejpam-4755	131	23	,	,	PUNCT
ejpam-4755	131	24	s	s	VERB
ejpam-4755	131	25	respectively	respectively	ADV
ejpam-4755	131	26	that	that	PRON
ejpam-4755	131	27	make	make	VERB
ejpam-4755	131	28	τ	τ	PRON
ejpam-4755	131	29	fix	fix	VERB
ejpam-4755	131	30	,	,	PUNCT
ejpam-4755	131	31	and	and	CCONJ
ejpam-4755	131	32	assume	assume	VERB
ejpam-4755	131	33	that	that	SCONJ
ejpam-4755	131	34	η	η	PROPN
ejpam-4755	131	35	,	,	PUNCT
ejpam-4755	131	36	θ	θ	PROPN
ejpam-4755	131	37	are	be	AUX
ejpam-4755	131	38	automorphisms	automorphism	NOUN
ejpam-4755	131	39	of	of	ADP
ejpam-4755	131	40	the	the	DET
ejpam-4755	131	41	group	group	NOUN
ejpam-4755	131	42	n	n	CCONJ
ejpam-4755	131	43	of	of	ADP
ejpam-4755	131	44	order	order	NOUN
ejpam-4755	131	45	2i	2i	NUM
ejpam-4755	131	46	,	,	PUNCT
ejpam-4755	131	47	j	j	PROPN
ejpam-4755	131	48	respectively	respectively	ADV
ejpam-4755	131	49	that	that	SCONJ
ejpam-4755	131	50	fix	fix	NOUN
ejpam-4755	131	51	σ	σ	PROPN
ejpam-4755	131	52	.	.	PUNCT
ejpam-4755	132	1	the	the	DET
ejpam-4755	132	2	direct	direct	ADJ
ejpam-4755	132	3	product	product	NOUN
ejpam-4755	132	4	⟨α⟩⟨β	⟨α⟩⟨β	PROPN
ejpam-4755	132	5	,	,	PUNCT
ejpam-4755	132	6	γ	γ	PROPN
ejpam-4755	132	7	,	,	PUNCT
ejpam-4755	132	8	η⟩⟨δ	η⟩⟨δ	PROPN
ejpam-4755	132	9	,	,	PUNCT
ejpam-4755	132	10	θ⟩	θ⟩	NUM
ejpam-4755	132	11	is	be	AUX
ejpam-4755	132	12	decomposed	decompose	VERB
ejpam-4755	132	13	by	by	ADP
ejpam-4755	132	14	aut(n	aut(n	PROPN
ejpam-4755	132	15	)	)	PUNCT
ejpam-4755	132	16	,	,	PUNCT
ejpam-4755	132	17	where	where	SCONJ
ejpam-4755	132	18	the	the	DET
ejpam-4755	132	19	factors	factor	NOUN
ejpam-4755	132	20	have	have	VERB
ejpam-4755	132	21	coprime	coprime	NOUN
ejpam-4755	132	22	orders	order	NOUN
ejpam-4755	132	23	w	w	PROPN
ejpam-4755	132	24	,	,	PUNCT
ejpam-4755	132	25	2(r+i+1	2(r+i+1	NUM
ejpam-4755	132	26	)	)	PUNCT
ejpam-4755	132	27	and	and	CCONJ
ejpam-4755	132	28	sj	sj	VERB
ejpam-4755	132	29	respectively	respectively	ADV
ejpam-4755	132	30	.	.	PUNCT
ejpam-4755	133	1	a	a	DET
ejpam-4755	133	2	subgroup	subgroup	NOUN
ejpam-4755	133	3	of	of	ADP
ejpam-4755	133	4	aut(n	aut(n	PROPN
ejpam-4755	133	5	)	)	PUNCT
ejpam-4755	133	6	decomposes	decompose	VERB
ejpam-4755	133	7	into	into	ADP
ejpam-4755	133	8	one	one	NUM
ejpam-4755	133	9	subgroup	subgroup	NOUN
ejpam-4755	133	10	from	from	ADP
ejpam-4755	133	11	each	each	PRON
ejpam-4755	133	12	of	of	ADP
ejpam-4755	133	13	these	these	DET
ejpam-4755	133	14	factors	factor	NOUN
ejpam-4755	133	15	as	as	ADP
ejpam-4755	133	16	a	a	DET
ejpam-4755	133	17	direct	direct	ADJ
ejpam-4755	133	18	product	product	NOUN
ejpam-4755	133	19	.	.	PUNCT
ejpam-4755	134	1	the	the	DET
ejpam-4755	134	2	number	number	NOUN
ejpam-4755	134	3	of	of	ADP
ejpam-4755	134	4	divisors	divisor	NOUN
ejpam-4755	134	5	in	in	ADP
ejpam-4755	134	6	s	s	PROPN
ejpam-4755	134	7	is	be	AUX
ejpam-4755	134	8	σ0(s	σ0(s	PROPN
ejpam-4755	134	9	)	)	PUNCT
ejpam-4755	134	10	,	,	PUNCT
ejpam-4755	134	11	σ1(j	σ1(j	NOUN
ejpam-4755	134	12	)	)	PUNCT
ejpam-4755	134	13	in	in	ADP
ejpam-4755	134	14	j	j	PROPN
ejpam-4755	134	15	and	and	CCONJ
ejpam-4755	134	16	σ0(s)σ1(j	σ0(s)σ1(j	PROPN
ejpam-4755	134	17	)	)	PUNCT
ejpam-4755	134	18	in	in	ADP
ejpam-4755	134	19	sj	sj	PROPN
ejpam-4755	134	20	.	.	PUNCT
ejpam-4755	134	21	proposition	proposition	NOUN
ejpam-4755	134	22	3	3	NUM
ejpam-4755	134	23	.	.	PUNCT
ejpam-4755	135	1	let	let	VERB
ejpam-4755	135	2	jl	jl	NOUN
ejpam-4755	135	3	=	=	SYM
ejpam-4755	135	4	⟨σ	⟨σ	NOUN
ejpam-4755	135	5	,	,	PUNCT
ejpam-4755	135	6	[	[	X
ejpam-4755	135	7	τ	τ	X
ejpam-4755	135	8	,	,	PUNCT
ejpam-4755	135	9	αl]⟩	αl]⟩	NOUN
ejpam-4755	135	10	with	with	ADP
ejpam-4755	135	11	1	1	NUM
ejpam-4755	135	12	≤	≤	NUM
ejpam-4755	135	13	l	l	NOUN
ejpam-4755	135	14	≤	≤	NUM
ejpam-4755	136	1	w	w	ADP
ejpam-4755	136	2	−	−	NOUN
ejpam-4755	137	1	1	1	NUM
ejpam-4755	137	2	.	.	PUNCT
ejpam-4755	138	1	then	then	ADV
ejpam-4755	138	2	jl	jl	PROPN
ejpam-4755	138	3	is	be	AUX
ejpam-4755	138	4	a	a	DET
ejpam-4755	138	5	nonabelian	nonabelian	ADJ
ejpam-4755	138	6	regular	regular	ADJ
ejpam-4755	138	7	subgroup	subgroup	NOUN
ejpam-4755	138	8	of	of	ADP
ejpam-4755	138	9	hol(n	hol(n	PROPN
ejpam-4755	138	10	)	)	PUNCT
ejpam-4755	138	11	.	.	PUNCT
ejpam-4755	139	1	in	in	ADP
ejpam-4755	139	2	addition	addition	NOUN
ejpam-4755	139	3	,	,	PUNCT
ejpam-4755	139	4	table	table	NOUN
ejpam-4755	139	5	1	1	NUM
ejpam-4755	139	6	shows	show	VERB
ejpam-4755	139	7	the	the	DET
ejpam-4755	139	8	transitive	transitive	ADJ
ejpam-4755	139	9	subgroups	subgroup	NOUN
ejpam-4755	139	10	g	g	NOUN
ejpam-4755	139	11	for	for	ADP
ejpam-4755	139	12	the	the	DET
ejpam-4755	139	13	nonabelian	nonabelian	ADJ
ejpam-4755	139	14	group	group	NOUN
ejpam-4755	139	15	jl	jl	NOUN
ejpam-4755	139	16	of	of	ADP
ejpam-4755	139	17	hol(n	hol(n	PROPN
ejpam-4755	139	18	)	)	PUNCT
ejpam-4755	139	19	.	.	PUNCT
ejpam-4755	140	1	proof	proof	NOUN
ejpam-4755	140	2	.	.	PUNCT
ejpam-4755	141	1	it	it	PRON
ejpam-4755	141	2	is	be	AUX
ejpam-4755	141	3	clear	clear	ADJ
ejpam-4755	141	4	that	that	SCONJ
ejpam-4755	141	5	jl	jl	PROPN
ejpam-4755	141	6	is	be	AUX
ejpam-4755	141	7	nonabelian	nonabelian	ADJ
ejpam-4755	141	8	and	and	CCONJ
ejpam-4755	141	9	regular	regular	ADJ
ejpam-4755	141	10	of	of	ADP
ejpam-4755	141	11	order	order	NOUN
ejpam-4755	141	12	pqw	pqw	NOUN
ejpam-4755	141	13	on	on	ADP
ejpam-4755	141	14	n	n	PROPN
ejpam-4755	141	15	,	,	PUNCT
ejpam-4755	141	16	since	since	SCONJ
ejpam-4755	141	17	we	we	PRON
ejpam-4755	141	18	discover	discover	VERB
ejpam-4755	141	19	that	that	SCONJ
ejpam-4755	141	20	[	[	X
ejpam-4755	141	21	τ	τ	X
ejpam-4755	141	22	,	,	PUNCT
ejpam-4755	141	23	αl	αl	AUX
ejpam-4755	141	24	]	]	PUNCT
ejpam-4755	141	25	has	have	VERB
ejpam-4755	141	26	order	order	NOUN
ejpam-4755	141	27	w	w	NOUN
ejpam-4755	141	28	(	(	PUNCT
ejpam-4755	141	29	since	since	SCONJ
ejpam-4755	141	30	α	α	PROPN
ejpam-4755	141	31	fixes	fix	NOUN
ejpam-4755	141	32	τ	τ	X
ejpam-4755	141	33	)	)	PUNCT
ejpam-4755	141	34	and	and	CCONJ
ejpam-4755	141	35	[	[	X
ejpam-4755	141	36	τ	τ	X
ejpam-4755	141	37	,	,	PUNCT
ejpam-4755	141	38	αl]σ	αl]σ	NOUN
ejpam-4755	141	39	=	=	SYM
ejpam-4755	141	40	αl(σ)[τ	αl(σ)[τ	NOUN
ejpam-4755	141	41	,	,	PUNCT
ejpam-4755	141	42	αl	αl	ADP
ejpam-4755	141	43	]	]	PUNCT
ejpam-4755	141	44	in	in	ADP
ejpam-4755	141	45	jl	jl	PROPN
ejpam-4755	141	46	.	.	PUNCT
ejpam-4755	142	1	given	give	VERB
ejpam-4755	142	2	that	that	PRON
ejpam-4755	142	3	holomorph	holomorph	NOUN
ejpam-4755	142	4	of	of	ADP
ejpam-4755	142	5	the	the	DET
ejpam-4755	142	6	n	n	PROPN
ejpam-4755	142	7	has	have	AUX
ejpam-4755	142	8	a	a	DET
ejpam-4755	142	9	subgroup	subgroup	NOUN
ejpam-4755	142	10	z	z	NOUN
ejpam-4755	142	11	=	=	SYM
ejpam-4755	142	12	⟨σ	⟨σ	NOUN
ejpam-4755	142	13	,	,	PUNCT
ejpam-4755	142	14	τ	τ	PROPN
ejpam-4755	142	15	,	,	PUNCT
ejpam-4755	142	16	α⟩	α⟩	NOUN
ejpam-4755	142	17	of	of	ADP
ejpam-4755	142	18	order	order	NOUN
ejpam-4755	142	19	pqw2	pqw2	NOUN
ejpam-4755	142	20	with	with	ADP
ejpam-4755	142	21	index	index	NOUN
ejpam-4755	142	22	2ij	2ij	ADJ
ejpam-4755	142	23	relatively	relatively	ADV
ejpam-4755	142	24	prime	prime	ADJ
ejpam-4755	142	25	to	to	PART
ejpam-4755	142	26	pqw	pqw	VERB
ejpam-4755	142	27	uniquely	uniquely	ADV
ejpam-4755	142	28	.	.	PUNCT
ejpam-4755	143	1	so	so	ADV
ejpam-4755	143	2	pqw	pqw	PROPN
ejpam-4755	143	3	divides	divide	VERB
ejpam-4755	143	4	the	the	DET
ejpam-4755	143	5	order	order	NOUN
ejpam-4755	143	6	of	of	ADP
ejpam-4755	143	7	any	any	DET
ejpam-4755	143	8	transitive	transitive	ADJ
ejpam-4755	143	9	subgroup	subgroup	NOUN
ejpam-4755	143	10	b	b	NOUN
ejpam-4755	143	11	,	,	PUNCT
ejpam-4755	143	12	hence	hence	ADV
ejpam-4755	143	13	b	b	NOUN
ejpam-4755	143	14	∩	∩	NOUN
ejpam-4755	143	15	z	z	NOUN
ejpam-4755	143	16	must	must	AUX
ejpam-4755	143	17	be	be	AUX
ejpam-4755	143	18	transitive	transitive	ADJ
ejpam-4755	143	19	on	on	ADP
ejpam-4755	143	20	n	n	PROPN
ejpam-4755	143	21	.	.	PUNCT
ejpam-4755	144	1	as	as	ADP
ejpam-4755	144	2	a	a	DET
ejpam-4755	144	3	result	result	NOUN
ejpam-4755	144	4	,	,	PUNCT
ejpam-4755	144	5	either	either	CCONJ
ejpam-4755	144	6	b	b	PROPN
ejpam-4755	144	7	∩	∩	NOUN
ejpam-4755	144	8	z	z	NOUN
ejpam-4755	144	9	is	be	AUX
ejpam-4755	144	10	regular	regular	ADJ
ejpam-4755	144	11	on	on	ADP
ejpam-4755	144	12	n	n	PRON
ejpam-4755	144	13	or	or	CCONJ
ejpam-4755	144	14	b	b	PROPN
ejpam-4755	144	15	⊂	⊂	PROPN
ejpam-4755	144	16	z.	z.	PROPN
ejpam-4755	145	1	now	now	ADV
ejpam-4755	145	2	,	,	PUNCT
ejpam-4755	145	3	there	there	PRON
ejpam-4755	145	4	is	be	VERB
ejpam-4755	145	5	one	one	NUM
ejpam-4755	145	6	nonregular	nonregular	ADJ
ejpam-4755	145	7	subgroup	subgroup	NOUN
ejpam-4755	145	8	⟨σ	⟨σ	NOUN
ejpam-4755	145	9	,	,	PUNCT
ejpam-4755	145	10	α⟩	α⟩	X
ejpam-4755	145	11	in	in	ADP
ejpam-4755	145	12	z	z	PROPN
ejpam-4755	145	13	and	and	CCONJ
ejpam-4755	145	14	the	the	DET
ejpam-4755	145	15	other	other	ADJ
ejpam-4755	145	16	subgroups	subgroup	NOUN
ejpam-4755	145	17	of	of	ADP
ejpam-4755	145	18	order	order	NOUN
ejpam-4755	145	19	pqw	pqw	NOUN
ejpam-4755	145	20	are	be	AUX
ejpam-4755	145	21	n	n	PRON
ejpam-4755	145	22	and	and	CCONJ
ejpam-4755	145	23	jl	jl	PROPN
ejpam-4755	145	24	.	.	PUNCT
ejpam-4755	146	1	for	for	ADP
ejpam-4755	146	2	some	some	DET
ejpam-4755	146	3	l	l	NOUN
ejpam-4755	146	4	,	,	PUNCT
ejpam-4755	146	5	we	we	PRON
ejpam-4755	146	6	have	have	VERB
ejpam-4755	146	7	b	b	NOUN
ejpam-4755	146	8	∩	∩	ADJ
ejpam-4755	146	9	z	z	NOUN
ejpam-4755	146	10	=	=	SYM
ejpam-4755	146	11	z	z	PROPN
ejpam-4755	146	12	or	or	CCONJ
ejpam-4755	146	13	n	n	PROPN
ejpam-4755	146	14	or	or	CCONJ
ejpam-4755	146	15	jl	jl	NOUN
ejpam-4755	146	16	.	.	PUNCT
ejpam-4755	147	1	that	that	PRON
ejpam-4755	147	2	means	mean	VERB
ejpam-4755	147	3	each	each	DET
ejpam-4755	147	4	individual	individual	ADJ
ejpam-4755	147	5	transitive	transitive	ADJ
ejpam-4755	147	6	subgroup	subgroup	PROPN
ejpam-4755	147	7	b	b	PROPN
ejpam-4755	147	8	has	have	VERB
ejpam-4755	147	9	either	either	CCONJ
ejpam-4755	147	10	n	n	CCONJ
ejpam-4755	147	11	or	or	CCONJ
ejpam-4755	147	12	some	some	DET
ejpam-4755	147	13	jl	jl	NOUN
ejpam-4755	147	14	.	.	PUNCT
ejpam-4755	148	1	so	so	ADV
ejpam-4755	148	2	any	any	DET
ejpam-4755	148	3	subgroup	subgroup	NOUN
ejpam-4755	148	4	of	of	ADP
ejpam-4755	148	5	aut(n	aut(n	PROPN
ejpam-4755	148	6	)	)	PUNCT
ejpam-4755	148	7	can	can	AUX
ejpam-4755	148	8	be	be	AUX
ejpam-4755	148	9	used	use	VERB
ejpam-4755	148	10	to	to	PART
ejpam-4755	148	11	create	create	VERB
ejpam-4755	148	12	a	a	DET
ejpam-4755	148	13	transitive	transitive	ADJ
ejpam-4755	148	14	subgroup	subgroup	NOUN
ejpam-4755	148	15	b	b	NOUN
ejpam-4755	148	16	,	,	PUNCT
ejpam-4755	148	17	since	since	SCONJ
ejpam-4755	148	18	in	in	ADP
ejpam-4755	148	19	hol(n	hol(n	PROPN
ejpam-4755	148	20	)	)	PUNCT
ejpam-4755	148	21	the	the	DET
ejpam-4755	148	22	group	group	NOUN
ejpam-4755	148	23	n	n	ADV
ejpam-4755	148	24	is	be	AUX
ejpam-4755	148	25	normal	normal	ADJ
ejpam-4755	148	26	.	.	PUNCT
ejpam-4755	149	1	if	if	SCONJ
ejpam-4755	149	2	ψ	ψ	AUX
ejpam-4755	149	3	∈	∈	PROPN
ejpam-4755	149	4	aut(n	aut(n	PROPN
ejpam-4755	149	5	)	)	PUNCT
ejpam-4755	149	6	and	and	CCONJ
ejpam-4755	149	7	ψ(τ	ψ(τ	NOUN
ejpam-4755	149	8	)	)	PUNCT
ejpam-4755	149	9	̸=	̸=	PROPN
ejpam-4755	149	10	τ	τ	PROPN
ejpam-4755	149	11	,	,	PUNCT
ejpam-4755	149	12	we	we	PRON
ejpam-4755	149	13	obtain	obtain	VERB
ejpam-4755	149	14	ψ[τ	ψ[τ	NOUN
ejpam-4755	149	15	,	,	PUNCT
ejpam-4755	149	16	αl]ψ−1	αl]ψ−1	NOUN
ejpam-4755	149	17	=	=	PUNCT
ejpam-4755	150	1	[	[	X
ejpam-4755	150	2	ψ(τ	ψ(τ	X
ejpam-4755	150	3	)	)	PUNCT
ejpam-4755	150	4	,	,	PUNCT
ejpam-4755	150	5	αl	αl	ADP
ejpam-4755	150	6	]	]	PUNCT
ejpam-4755	150	7	/∈	/∈	PUNCT
ejpam-4755	150	8	jl	jl	PROPN
ejpam-4755	150	9	,	,	PUNCT
ejpam-4755	150	10	so	so	ADV
ejpam-4755	150	11	in	in	ADP
ejpam-4755	150	12	aut(n	aut(n	PROPN
ejpam-4755	150	13	)	)	PUNCT
ejpam-4755	150	14	the	the	DET
ejpam-4755	150	15	group	group	NOUN
ejpam-4755	150	16	⟨α	⟨α	PROPN
ejpam-4755	150	17	,	,	PUNCT
ejpam-4755	150	18	β	β	NOUN
ejpam-4755	150	19	,	,	PUNCT
ejpam-4755	150	20	γ2r−c1	γ2r−c1	NOUN
ejpam-4755	150	21	,	,	PUNCT
ejpam-4755	150	22	δs	δs	VERB
ejpam-4755	150	23	/	/	SYM
ejpam-4755	150	24	d⟩	d⟩	NOUN
ejpam-4755	150	25	is	be	AUX
ejpam-4755	150	26	the	the	DET
ejpam-4755	150	27	normalizer	normalizer	NOUN
ejpam-4755	150	28	of	of	ADP
ejpam-4755	150	29	jl	jl	PROPN
ejpam-4755	150	30	.	.	PUNCT
ejpam-4755	151	1	as	as	ADP
ejpam-4755	151	2	a	a	DET
ejpam-4755	151	3	result	result	NOUN
ejpam-4755	151	4	,	,	PUNCT
ejpam-4755	151	5	any	any	DET
ejpam-4755	151	6	transitive	transitive	ADJ
ejpam-4755	151	7	subgroup	subgroup	NOUN
ejpam-4755	151	8	b	b	PROPN
ejpam-4755	151	9	contains	contain	VERB
ejpam-4755	151	10	jl	jl	PROPN
ejpam-4755	151	11	,	,	PUNCT
ejpam-4755	151	12	has	have	VERB
ejpam-4755	151	13	the	the	DET
ejpam-4755	151	14	forms	form	NOUN
ejpam-4755	151	15	jl	jl	NOUN
ejpam-4755	151	16	,	,	PUNCT
ejpam-4755	151	17	jl	jl	NOUN
ejpam-4755	151	18	⋊	⋊	NUM
ejpam-4755	151	19	⟨β⟩	⟨β⟩	PROPN
ejpam-4755	151	20	,	,	PUNCT
ejpam-4755	151	21	jl	jl	NOUN
ejpam-4755	151	22	⋊	⋊	NUM
ejpam-4755	151	23	⟨γ2r−c1	⟨γ2r−c1	PROPN
ejpam-4755	151	24	⟩	⟩	NOUN
ejpam-4755	151	25	or	or	CCONJ
ejpam-4755	151	26	jl	jl	NOUN
ejpam-4755	151	27	⋊	⋊	PUNCT
ejpam-4755	151	28	⟨δs	⟨δs	PROPN
ejpam-4755	151	29	/	/	SYM
ejpam-4755	151	30	d⟩.	d⟩.	NOUN
ejpam-4755	151	31	therefore	therefore	ADV
ejpam-4755	151	32	,	,	PUNCT
ejpam-4755	151	33	the	the	DET
ejpam-4755	151	34	table	table	NOUN
ejpam-4755	151	35	1	1	NUM
ejpam-4755	151	36	of	of	ADP
ejpam-4755	151	37	transitive	transitive	ADJ
ejpam-4755	151	38	subgroups	subgroup	NOUN
ejpam-4755	151	39	is	be	AUX
ejpam-4755	151	40	derived	derive	VERB
ejpam-4755	151	41	from	from	ADP
ejpam-4755	151	42	aut(n	aut(n	PROPN
ejpam-4755	151	43	)	)	PUNCT
ejpam-4755	151	44	subgroups	subgroup	NOUN
ejpam-4755	151	45	.	.	PUNCT
ejpam-4755	152	1	lemma	lemma	PROPN
ejpam-4755	152	2	1	1	NUM
ejpam-4755	152	3	.	.	PUNCT
ejpam-4755	152	4	table	table	NOUN
ejpam-4755	152	5	1	1	NUM
ejpam-4755	152	6	shows	show	VERB
ejpam-4755	152	7	that	that	SCONJ
ejpam-4755	152	8	there	there	PRON
ejpam-4755	152	9	are	be	VERB
ejpam-4755	152	10	w	w	ADJ
ejpam-4755	152	11	−	−	NUM
ejpam-4755	152	12	1	1	NUM
ejpam-4755	152	13	groups	group	NOUN
ejpam-4755	152	14	in	in	ADP
ejpam-4755	152	15	case	case	NOUN
ejpam-4755	152	16	1	1	NUM
ejpam-4755	152	17	and	and	CCONJ
ejpam-4755	152	18	2	2	NUM
ejpam-4755	152	19	which	which	PRON
ejpam-4755	152	20	are	be	AUX
ejpam-4755	152	21	pgs	pgs	ADJ
ejpam-4755	152	22	and	and	CCONJ
ejpam-4755	152	23	isomorphic	isomorphic	ADJ
ejpam-4755	152	24	.	.	PUNCT
ejpam-4755	153	1	but	but	CCONJ
ejpam-4755	153	2	,	,	PUNCT
ejpam-4755	153	3	in	in	ADP
ejpam-4755	153	4	cases	case	NOUN
ejpam-4755	153	5	3	3	NUM
ejpam-4755	153	6	and	and	CCONJ
ejpam-4755	153	7	4	4	NUM
ejpam-4755	153	8	there	there	PRON
ejpam-4755	153	9	are	be	VERB
ejpam-4755	153	10	(	(	PUNCT
ejpam-4755	153	11	w	w	NOUN
ejpam-4755	153	12	−	−	PROPN
ejpam-4755	153	13	1)(r	1)(r	NUM
ejpam-4755	153	14	+	+	CCONJ
ejpam-4755	153	15	1	1	NUM
ejpam-4755	153	16	)	)	PUNCT
ejpam-4755	153	17	and	and	CCONJ
ejpam-4755	153	18	(	(	PUNCT
ejpam-4755	153	19	w	w	NOUN
ejpam-4755	153	20	−	−	NOUN
ejpam-4755	153	21	1)σ0(s	1)σ0(s	NUM
ejpam-4755	153	22	)	)	PUNCT
ejpam-4755	153	23	groups	group	NOUN
ejpam-4755	153	24	respectively	respectively	ADV
ejpam-4755	153	25	which	which	PRON
ejpam-4755	153	26	are	be	AUX
ejpam-4755	153	27	isomorphic	isomorphic	ADJ
ejpam-4755	153	28	as	as	ADP
ejpam-4755	153	29	pgs	pgs	NUM
ejpam-4755	153	30	.	.	PUNCT
ejpam-4755	154	1	b.	b.	PROPN
ejpam-4755	154	2	jamal	jamal	PROPN
ejpam-4755	154	3	,	,	PUNCT
ejpam-4755	154	4	a.	a.	PROPN
ejpam-4755	154	5	alabdali	alabdali	VERB
ejpam-4755	154	6	/	/	SYM
ejpam-4755	154	7	eur	eur	PROPN
ejpam-4755	154	8	.	.	PUNCT
ejpam-4755	155	1	j.	j.	PROPN
ejpam-4755	155	2	pure	pure	PROPN
ejpam-4755	155	3	appl	appl	PROPN
ejpam-4755	155	4	.	.	PROPN
ejpam-4755	155	5	math	math	PROPN
ejpam-4755	155	6	,	,	PUNCT
ejpam-4755	155	7	16	16	NUM
ejpam-4755	155	8	(	(	PUNCT
ejpam-4755	155	9	2	2	NUM
ejpam-4755	155	10	)	)	PUNCT
ejpam-4755	155	11	(	(	PUNCT
ejpam-4755	155	12	2023	2023	NUM
ejpam-4755	155	13	)	)	PUNCT
ejpam-4755	155	14	,	,	PUNCT
ejpam-4755	155	15	1118	1118	NUM
ejpam-4755	155	16	-	-	SYM
ejpam-4755	155	17	1127	1127	NUM
ejpam-4755	155	18	1123	1123	NUM
ejpam-4755	155	19	proof	proof	NOUN
ejpam-4755	155	20	.	.	PUNCT
ejpam-4755	156	1	let	let	VERB
ejpam-4755	156	2	1	1	NUM
ejpam-4755	156	3	≤	≤	NUM
ejpam-4755	156	4	l	l	NOUN
ejpam-4755	156	5	≤	≤	NUM
ejpam-4755	157	1	w	w	ADP
ejpam-4755	157	2	−	−	PROPN
ejpam-4755	157	3	1	1	NUM
ejpam-4755	157	4	and	and	CCONJ
ejpam-4755	157	5	ψ	ψ	X
ejpam-4755	157	6	∈	∈	PROPN
ejpam-4755	157	7	aut(n	aut(n	PROPN
ejpam-4755	157	8	)	)	PUNCT
ejpam-4755	157	9	with	with	ADP
ejpam-4755	157	10	ψ(τ	ψ(τ	NOUN
ejpam-4755	157	11	)	)	PUNCT
ejpam-4755	157	12	=	=	PUNCT
ejpam-4755	158	1	τ	τ	X
ejpam-4755	158	2	l	l	NOUN
ejpam-4755	158	3	be	be	VERB
ejpam-4755	158	4	the	the	DET
ejpam-4755	158	5	two	two	NUM
ejpam-4755	158	6	variables	variable	NOUN
ejpam-4755	158	7	.	.	PUNCT
ejpam-4755	159	1	consequently	consequently	ADV
ejpam-4755	159	2	,	,	PUNCT
ejpam-4755	159	3	ψ[τ	ψ[τ	PROPN
ejpam-4755	159	4	,	,	PUNCT
ejpam-4755	159	5	αl]ψ−1	αl]ψ−1	NOUN
ejpam-4755	159	6	=	=	PUNCT
ejpam-4755	160	1	[	[	X
ejpam-4755	160	2	ψ(τ	ψ(τ	X
ejpam-4755	160	3	)	)	PUNCT
ejpam-4755	160	4	,	,	PUNCT
ejpam-4755	160	5	αl	αl	ADP
ejpam-4755	160	6	]	]	PUNCT
ejpam-4755	160	7	=	=	PUNCT
ejpam-4755	161	1	[	[	X
ejpam-4755	161	2	τ	τ	X
ejpam-4755	161	3	,	,	PUNCT
ejpam-4755	161	4	α]l	α]l	NOUN
ejpam-4755	161	5	.	.	PUNCT
ejpam-4755	162	1	in	in	ADP
ejpam-4755	162	2	addition	addition	NOUN
ejpam-4755	162	3	,	,	PUNCT
ejpam-4755	162	4	ψβψ−1	ψβψ−1	PROPN
ejpam-4755	162	5	=	=	SYM
ejpam-4755	162	6	β	β	X
ejpam-4755	162	7	.	.	PUNCT
ejpam-4755	163	1	as	as	ADP
ejpam-4755	163	2	a	a	DET
ejpam-4755	163	3	result	result	NOUN
ejpam-4755	163	4	,	,	PUNCT
ejpam-4755	163	5	conjugating	conjugate	VERB
ejpam-4755	163	6	by	by	ADP
ejpam-4755	163	7	ψ	ψ	SYM
ejpam-4755	163	8	yields	yield	NOUN
ejpam-4755	163	9	the	the	DET
ejpam-4755	163	10	isomorphism	isomorphism	NOUN
ejpam-4755	163	11	jl	jl	NOUN
ejpam-4755	163	12	⋊	⋊	NUM
ejpam-4755	163	13	⟨β⟩	⟨β⟩	PROPN
ejpam-4755	163	14	→	→	SYM
ejpam-4755	163	15	j1	j1	PROPN
ejpam-4755	163	16	⋊	⋊	NUM
ejpam-4755	163	17	β	β	NOUN
ejpam-4755	163	18	,	,	PUNCT
ejpam-4755	163	19	which	which	PRON
ejpam-4755	163	20	is	be	AUX
ejpam-4755	163	21	a	a	DET
ejpam-4755	163	22	pg	pg	NOUN
ejpam-4755	163	23	isomorphism	isomorphism	NOUN
ejpam-4755	163	24	because	because	SCONJ
ejpam-4755	163	25	the	the	DET
ejpam-4755	163	26	stabilizer	stabilizer	NOUN
ejpam-4755	163	27	⟨β⟩	⟨β⟩	PROPN
ejpam-4755	163	28	of	of	ADP
ejpam-4755	163	29	1n	1n	NUM
ejpam-4755	163	30	is	be	AUX
ejpam-4755	163	31	fixed	fix	VERB
ejpam-4755	163	32	.	.	PUNCT
ejpam-4755	164	1	it	it	PRON
ejpam-4755	164	2	also	also	ADV
ejpam-4755	164	3	determines	determine	VERB
ejpam-4755	164	4	to	to	ADP
ejpam-4755	164	5	jl	jl	PROPN
ejpam-4755	164	6	→	→	SYM
ejpam-4755	164	7	j1	j1	PROPN
ejpam-4755	164	8	isomorphism	isomorphism	NOUN
ejpam-4755	164	9	.	.	PUNCT
ejpam-4755	165	1	as	as	ADP
ejpam-4755	165	2	a	a	DET
ejpam-4755	165	3	result	result	NOUN
ejpam-4755	165	4	,	,	PUNCT
ejpam-4755	165	5	in	in	ADP
ejpam-4755	165	6	case	case	NOUN
ejpam-4755	165	7	(	(	PUNCT
ejpam-4755	165	8	2	2	X
ejpam-4755	165	9	)	)	PUNCT
ejpam-4755	165	10	all	all	DET
ejpam-4755	165	11	the	the	DET
ejpam-4755	165	12	groups	group	NOUN
ejpam-4755	165	13	are	be	AUX
ejpam-4755	165	14	pgs	pgs	ADJ
ejpam-4755	165	15	as	as	ADP
ejpam-4755	165	16	are	be	AUX
ejpam-4755	165	17	isomorphic	isomorphic	ADJ
ejpam-4755	165	18	,	,	PUNCT
ejpam-4755	165	19	and	and	CCONJ
ejpam-4755	165	20	simultaneously	simultaneously	ADV
ejpam-4755	165	21	(	(	PUNCT
ejpam-4755	165	22	1	1	NUM
ejpam-4755	165	23	)	)	PUNCT
ejpam-4755	165	24	.	.	PUNCT
ejpam-4755	166	1	let	let	VERB
ejpam-4755	166	2	1	1	NUM
ejpam-4755	166	3	≤	≤	NUM
ejpam-4755	166	4	l	l	NOUN
ejpam-4755	166	5	≤	≤	NUM
ejpam-4755	167	1	w	w	ADP
ejpam-4755	167	2	−	−	PROPN
ejpam-4755	167	3	1	1	NUM
ejpam-4755	167	4	,	,	PUNCT
ejpam-4755	167	5	0	0	NUM
ejpam-4755	167	6	≤	≤	NUM
ejpam-4755	167	7	c1	c1	NOUN
ejpam-4755	167	8	≤	≤	NOUN
ejpam-4755	167	9	r	r	NOUN
ejpam-4755	167	10	so	so	ADV
ejpam-4755	167	11	ψγ2	ψγ2	NOUN
ejpam-4755	167	12	r−c1ψ−1	r−c1ψ−1	NOUN
ejpam-4755	167	13	=	=	SYM
ejpam-4755	167	14	γ2	γ2	PROPN
ejpam-4755	167	15	r−c1	r−c1	PROPN
ejpam-4755	167	16	and	and	CCONJ
ejpam-4755	167	17	then	then	ADV
ejpam-4755	167	18	conjugating	conjugate	VERB
ejpam-4755	167	19	by	by	ADP
ejpam-4755	167	20	ψ	ψ	SYM
ejpam-4755	167	21	obtains	obtain	VERB
ejpam-4755	167	22	the	the	DET
ejpam-4755	167	23	isomorphism	isomorphism	NOUN
ejpam-4755	167	24	jl⋊⟨γ2r−c1	jl⋊⟨γ2r−c1	PROPN
ejpam-4755	167	25	⟩	⟩	PROPN
ejpam-4755	167	26	→	→	SYM
ejpam-4755	167	27	j1⋊γ2	j1⋊γ2	PROPN
ejpam-4755	167	28	r−c1	r−c1	NOUN
ejpam-4755	167	29	.	.	PUNCT
ejpam-4755	168	1	finally	finally	ADV
ejpam-4755	168	2	,	,	PUNCT
ejpam-4755	168	3	let	let	VERB
ejpam-4755	168	4	1	1	NUM
ejpam-4755	168	5	≤	≤	NUM
ejpam-4755	168	6	l	l	NOUN
ejpam-4755	169	1	≤	≤	NUM
ejpam-4755	169	2	w−1	w−1	PROPN
ejpam-4755	169	3	,	,	PUNCT
ejpam-4755	170	1	d	d	PROPN
ejpam-4755	170	2	|	|	NOUN
ejpam-4755	170	3	s	s	AUX
ejpam-4755	170	4	so	so	ADV
ejpam-4755	170	5	ψδs	ψδs	PROPN
ejpam-4755	170	6	/	/	SYM
ejpam-4755	170	7	dψ−1	dψ−1	PROPN
ejpam-4755	170	8	=	=	SYM
ejpam-4755	170	9	δs	δs	NOUN
ejpam-4755	170	10	/	/	SYM
ejpam-4755	170	11	d	d	NOUN
ejpam-4755	170	12	and	and	CCONJ
ejpam-4755	170	13	then	then	ADV
ejpam-4755	170	14	conjugating	conjugate	VERB
ejpam-4755	170	15	by	by	ADP
ejpam-4755	170	16	ψ	ψ	SYM
ejpam-4755	170	17	obtains	obtain	VERB
ejpam-4755	170	18	the	the	DET
ejpam-4755	170	19	isomorphism	isomorphism	NOUN
ejpam-4755	170	20	jl	jl	NOUN
ejpam-4755	170	21	⋊	⋊	PUNCT
ejpam-4755	170	22	⟨δs	⟨δs	PROPN
ejpam-4755	170	23	/	/	SYM
ejpam-4755	170	24	d⟩	d⟩	NOUN
ejpam-4755	170	25	→	→	SYM
ejpam-4755	170	26	j1	j1	PROPN
ejpam-4755	170	27	⋊	⋊	NUM
ejpam-4755	170	28	δs	δs	NOUN
ejpam-4755	170	29	/	/	SYM
ejpam-4755	170	30	d.	d.	PROPN
ejpam-4755	170	31	as	as	ADP
ejpam-4755	170	32	a	a	DET
ejpam-4755	170	33	result	result	NOUN
ejpam-4755	170	34	,	,	PUNCT
ejpam-4755	170	35	all	all	DET
ejpam-4755	170	36	the	the	DET
ejpam-4755	170	37	groups	group	NOUN
ejpam-4755	170	38	in	in	ADP
ejpam-4755	170	39	case	case	NOUN
ejpam-4755	170	40	(	(	PUNCT
ejpam-4755	170	41	3	3	NUM
ejpam-4755	170	42	)	)	PUNCT
ejpam-4755	170	43	and	and	CCONJ
ejpam-4755	170	44	case	case	NOUN
ejpam-4755	170	45	(	(	PUNCT
ejpam-4755	170	46	4	4	X
ejpam-4755	170	47	)	)	PUNCT
ejpam-4755	170	48	are	be	AUX
ejpam-4755	170	49	pgs	pgs	ADJ
ejpam-4755	170	50	as	as	SCONJ
ejpam-4755	170	51	are	be	AUX
ejpam-4755	170	52	isomorphic	isomorphic	ADJ
ejpam-4755	170	53	.	.	PUNCT
ejpam-4755	171	1	table	table	NOUN
ejpam-4755	171	2	1	1	NUM
ejpam-4755	171	3	:	:	PUNCT
ejpam-4755	171	4	the	the	DET
ejpam-4755	171	5	transitive	transitive	ADJ
ejpam-4755	171	6	subgroups	subgroup	NOUN
ejpam-4755	171	7	for	for	ADP
ejpam-4755	171	8	the	the	DET
ejpam-4755	171	9	nonabelian	nonabelian	ADJ
ejpam-4755	171	10	group	group	PROPN
ejpam-4755	171	11	jl	jl	PROPN
ejpam-4755	171	12	.	.	PUNCT
ejpam-4755	172	1	key	key	ADJ
ejpam-4755	172	2	order	order	NOUN
ejpam-4755	172	3	parameters	parameter	NOUN
ejpam-4755	172	4	#	#	NOUN
ejpam-4755	172	5	groups	group	NOUN
ejpam-4755	172	6	groups	group	NOUN
ejpam-4755	172	7	1	1	NUM
ejpam-4755	172	8	pqw	pqw	NOUN
ejpam-4755	172	9	1	1	NUM
ejpam-4755	172	10	≤	≤	NUM
ejpam-4755	172	11	l	l	NOUN
ejpam-4755	172	12	≤	≤	NUM
ejpam-4755	173	1	w	w	ADP
ejpam-4755	173	2	−	−	PROPN
ejpam-4755	173	3	1	1	NUM
ejpam-4755	173	4	w	w	NOUN
ejpam-4755	173	5	−	−	PROPN
ejpam-4755	173	6	1	1	NUM
ejpam-4755	173	7	jl	jl	NOUN
ejpam-4755	173	8	2	2	NUM
ejpam-4755	173	9	2pqw	2pqw	NUM
ejpam-4755	173	10	1	1	NUM
ejpam-4755	173	11	≤	≤	NUM
ejpam-4755	173	12	l	l	NOUN
ejpam-4755	173	13	≤	≤	NUM
ejpam-4755	173	14	w	w	ADP
ejpam-4755	173	15	−	−	PROPN
ejpam-4755	173	16	1	1	NUM
ejpam-4755	174	1	w	w	NOUN
ejpam-4755	174	2	−	−	NUM
ejpam-4755	174	3	1	1	NUM
ejpam-4755	174	4	jl	jl	PROPN
ejpam-4755	174	5	⋊	⋊	NUM
ejpam-4755	174	6	⟨β⟩	⟨β⟩	PROPN
ejpam-4755	174	7	3	3	NUM
ejpam-4755	174	8	2c1pqw	2c1pqw	NUM
ejpam-4755	174	9	1	1	NUM
ejpam-4755	174	10	≤	≤	NUM
ejpam-4755	174	11	l	l	NOUN
ejpam-4755	174	12	≤	≤	NUM
ejpam-4755	174	13	w	w	ADP
ejpam-4755	174	14	−	−	PROPN
ejpam-4755	174	15	1	1	NUM
ejpam-4755	174	16	,	,	PUNCT
ejpam-4755	174	17	0	0	NUM
ejpam-4755	174	18	≤	≤	NUM
ejpam-4755	174	19	c1	c1	NOUN
ejpam-4755	174	20	≤	≤	PROPN
ejpam-4755	174	21	r	r	NOUN
ejpam-4755	174	22	(	(	PUNCT
ejpam-4755	174	23	w	w	NOUN
ejpam-4755	174	24	−	−	PROPN
ejpam-4755	174	25	1)(r	1)(r	NUM
ejpam-4755	174	26	+	+	CCONJ
ejpam-4755	174	27	1	1	X
ejpam-4755	174	28	)	)	PUNCT
ejpam-4755	174	29	jl	jl	NOUN
ejpam-4755	174	30	⋊	⋊	NUM
ejpam-4755	174	31	⟨γ2r−c1	⟨γ2r−c1	PROPN
ejpam-4755	174	32	⟩	⟩	NOUN
ejpam-4755	174	33	4	4	NUM
ejpam-4755	174	34	pqwd	pqwd	ADJ
ejpam-4755	174	35	1	1	NUM
ejpam-4755	174	36	≤	≤	NUM
ejpam-4755	174	37	l	l	NOUN
ejpam-4755	174	38	≤	≤	NUM
ejpam-4755	174	39	w	w	ADP
ejpam-4755	174	40	−	−	PROPN
ejpam-4755	174	41	1	1	NUM
ejpam-4755	174	42	,	,	PUNCT
ejpam-4755	174	43	d	d	PROPN
ejpam-4755	174	44	|	|	NOUN
ejpam-4755	174	45	s	s	X
ejpam-4755	174	46	(	(	PUNCT
ejpam-4755	174	47	w	w	NOUN
ejpam-4755	174	48	−	−	NOUN
ejpam-4755	174	49	1)σ0(s	1)σ0(s	NUM
ejpam-4755	174	50	)	)	PUNCT
ejpam-4755	174	51	jl	jl	NOUN
ejpam-4755	174	52	⋊	⋊	PUNCT
ejpam-4755	174	53	⟨δs	⟨δs	PROPN
ejpam-4755	174	54	/	/	SYM
ejpam-4755	174	55	d⟩	d⟩	NOUN
ejpam-4755	174	56	lemma	lemma	PROPN
ejpam-4755	174	57	2	2	NUM
ejpam-4755	174	58	.	.	PUNCT
ejpam-4755	175	1	the	the	DET
ejpam-4755	175	2	number	number	NOUN
ejpam-4755	175	3	of	of	ADP
ejpam-4755	175	4	hgss	hgss	ADJ
ejpam-4755	175	5	for	for	ADP
ejpam-4755	175	6	the	the	DET
ejpam-4755	175	7	nonabelian	nonabelian	ADJ
ejpam-4755	175	8	group	group	NOUN
ejpam-4755	175	9	jl	jl	NOUN
ejpam-4755	175	10	is	be	AUX
ejpam-4755	175	11	as	as	ADP
ejpam-4755	175	12	in	in	ADP
ejpam-4755	175	13	table	table	NOUN
ejpam-4755	175	14	3	3	NUM
ejpam-4755	175	15	.	.	PUNCT
ejpam-4755	176	1	proof	proof	NOUN
ejpam-4755	176	2	.	.	PUNCT
ejpam-4755	177	1	in	in	ADP
ejpam-4755	177	2	the	the	DET
ejpam-4755	177	3	cases	case	NOUN
ejpam-4755	177	4	are	be	AUX
ejpam-4755	177	5	shown	show	VERB
ejpam-4755	177	6	in	in	ADP
ejpam-4755	177	7	table	table	NOUN
ejpam-4755	177	8	3	3	NUM
ejpam-4755	177	9	,	,	PUNCT
ejpam-4755	177	10	the	the	DET
ejpam-4755	177	11	stabilizer	stabilizer	NOUN
ejpam-4755	177	12	of	of	ADP
ejpam-4755	177	13	1n	1n	NUM
ejpam-4755	177	14	in	in	ADP
ejpam-4755	177	15	b	b	PROPN
ejpam-4755	177	16	is	be	AUX
ejpam-4755	177	17	b	b	NOUN
ejpam-4755	177	18	′	′	NUM
ejpam-4755	177	19	=	=	PUNCT
ejpam-4755	177	20	b∩aut(n	b∩aut(n	PROPN
ejpam-4755	177	21	)	)	PUNCT
ejpam-4755	177	22	.	.	PUNCT
ejpam-4755	178	1	we	we	PRON
ejpam-4755	178	2	start	start	VERB
ejpam-4755	178	3	with	with	ADP
ejpam-4755	178	4	case	case	NOUN
ejpam-4755	178	5	1	1	NUM
ejpam-4755	178	6	,	,	PUNCT
ejpam-4755	178	7	a	a	DET
ejpam-4755	178	8	single	single	ADJ
ejpam-4755	178	9	isomorphism	isomorphism	NOUN
ejpam-4755	178	10	class	class	NOUN
ejpam-4755	178	11	is	be	AUX
ejpam-4755	178	12	formed	form	VERB
ejpam-4755	178	13	by	by	ADP
ejpam-4755	178	14	the	the	DET
ejpam-4755	178	15	w	w	PROPN
ejpam-4755	178	16	−	−	PROPN
ejpam-4755	178	17	1	1	NUM
ejpam-4755	178	18	regular	regular	ADJ
ejpam-4755	178	19	groups	group	NOUN
ejpam-4755	178	20	jl	jl	PROPN
ejpam-4755	178	21	.	.	PUNCT
ejpam-4755	179	1	the	the	DET
ejpam-4755	179	2	automorphism	automorphism	NOUN
ejpam-4755	179	3	ψ	ψ	NOUN
ejpam-4755	179	4	of	of	ADP
ejpam-4755	179	5	jl	jl	NOUN
ejpam-4755	179	6	must	must	AUX
ejpam-4755	179	7	induce	induce	VERB
ejpam-4755	179	8	an	an	DET
ejpam-4755	179	9	automorphism	automorphism	NOUN
ejpam-4755	179	10	of	of	ADP
ejpam-4755	179	11	the	the	DET
ejpam-4755	179	12	characteristic	characteristic	ADJ
ejpam-4755	179	13	subgroup	subgroup	NOUN
ejpam-4755	179	14	cpqw	cpqw	NOUN
ejpam-4755	179	15	in	in	ADP
ejpam-4755	179	16	order	order	NOUN
ejpam-4755	179	17	for	for	SCONJ
ejpam-4755	179	18	ψ	ψ	NOUN
ejpam-4755	179	19	to	to	PART
ejpam-4755	179	20	be	be	AUX
ejpam-4755	179	21	compatible	compatible	ADJ
ejpam-4755	179	22	with	with	ADP
ejpam-4755	179	23	the	the	DET
ejpam-4755	179	24	relation	relation	NOUN
ejpam-4755	179	25	τσ	τσ	PROPN
ejpam-4755	179	26	=	=	SYM
ejpam-4755	179	27	σuτ	σuτ	PROPN
ejpam-4755	179	28	,	,	PUNCT
ejpam-4755	179	29	u	u	NOUN
ejpam-4755	179	30	>	>	X
ejpam-4755	179	31	1	1	NUM
ejpam-4755	179	32	,	,	PUNCT
ejpam-4755	179	33	therefore	therefore	ADV
ejpam-4755	179	34	ψ(σ	ψ(σ	VERB
ejpam-4755	179	35	)	)	PUNCT
ejpam-4755	179	36	=	=	SYM
ejpam-4755	179	37	σa	σa	X
ejpam-4755	179	38	and	and	CCONJ
ejpam-4755	179	39	ψ(τ	ψ(τ	PROPN
ejpam-4755	179	40	)	)	PUNCT
ejpam-4755	179	41	=	=	PUNCT
ejpam-4755	179	42	σbτ	σbτ	X
ejpam-4755	179	43	c	c	NOUN
ejpam-4755	179	44	with	with	ADP
ejpam-4755	179	45	1	1	NUM
ejpam-4755	179	46	≤	≤	NOUN
ejpam-4755	179	47	a	a	DET
ejpam-4755	179	48	≤	≤	NOUN
ejpam-4755	179	49	(	(	PUNCT
ejpam-4755	179	50	q	q	NOUN
ejpam-4755	179	51	−	−	PROPN
ejpam-4755	179	52	1)(p−	1)(p−	NUM
ejpam-4755	179	53	1	1	NUM
ejpam-4755	179	54	)	)	PUNCT
ejpam-4755	179	55	,	,	PUNCT
ejpam-4755	180	1	0	0	NUM
ejpam-4755	180	2	≤	≤	NUM
ejpam-4755	180	3	b	b	X
ejpam-4755	180	4	≤	≤	NOUN
ejpam-4755	180	5	(	(	PUNCT
ejpam-4755	180	6	q	q	NOUN
ejpam-4755	180	7	−	−	PROPN
ejpam-4755	180	8	1)(p−	1)(p−	NUM
ejpam-4755	180	9	1	1	NUM
ejpam-4755	180	10	)	)	PUNCT
ejpam-4755	180	11	,	,	PUNCT
ejpam-4755	180	12	and	and	CCONJ
ejpam-4755	180	13	1	1	NUM
ejpam-4755	180	14	≤	≤	NOUN
ejpam-4755	180	15	c	c	NOUN
ejpam-4755	180	16	≤	≤	NUM
ejpam-4755	180	17	(	(	PUNCT
ejpam-4755	180	18	w	w	NOUN
ejpam-4755	180	19	−	−	NOUN
ejpam-4755	180	20	1	1	NUM
ejpam-4755	180	21	)	)	PUNCT
ejpam-4755	180	22	are	be	AUX
ejpam-4755	180	23	required	require	VERB
ejpam-4755	180	24	c	c	PROPN
ejpam-4755	180	25	=	=	SYM
ejpam-4755	180	26	1	1	X
ejpam-4755	180	27	.	.	PUNCT
ejpam-4755	180	28	thus	thus	ADV
ejpam-4755	180	29	|	|	ADV
ejpam-4755	180	30	aut(jl	aut(jl	NOUN
ejpam-4755	180	31	)	)	PUNCT
ejpam-4755	180	32	|=	|=	PUNCT
ejpam-4755	180	33	(	(	PUNCT
ejpam-4755	180	34	p	p	NOUN
ejpam-4755	180	35	−	−	PROPN
ejpam-4755	181	1	1)(q	1)(q	NUM
ejpam-4755	181	2	−	−	PROPN
ejpam-4755	181	3	1)[(p	1)[(p	NUM
ejpam-4755	181	4	−	−	PROPN
ejpam-4755	181	5	1)(q	1)(q	NUM
ejpam-4755	181	6	−	−	NOUN
ejpam-4755	181	7	1	1	NUM
ejpam-4755	181	8	)	)	PUNCT
ejpam-4755	181	9	+	+	CCONJ
ejpam-4755	181	10	1	1	NUM
ejpam-4755	181	11	]	]	PUNCT
ejpam-4755	181	12	,	,	PUNCT
ejpam-4755	181	13	and	and	CCONJ
ejpam-4755	181	14	we	we	PRON
ejpam-4755	181	15	have	have	VERB
ejpam-4755	181	16	|	|	ADV
ejpam-4755	181	17	b′	b′	NUM
ejpam-4755	181	18	|=	|=	NOUN
ejpam-4755	181	19	1	1	NUM
ejpam-4755	181	20	for	for	ADP
ejpam-4755	181	21	b	b	NOUN
ejpam-4755	181	22	=	=	SYM
ejpam-4755	181	23	jl	jl	PROPN
ejpam-4755	181	24	.	.	PUNCT
ejpam-4755	182	1	as	as	ADP
ejpam-4755	182	2	a	a	DET
ejpam-4755	182	3	result	result	NOUN
ejpam-4755	182	4	,	,	PUNCT
ejpam-4755	182	5	the	the	DET
ejpam-4755	182	6	number	number	NOUN
ejpam-4755	182	7	of	of	ADP
ejpam-4755	182	8	cyclic	cyclic	ADJ
ejpam-4755	182	9	hgss	hgss	ADJ
ejpam-4755	182	10	on	on	ADP
ejpam-4755	182	11	a	a	DET
ejpam-4755	182	12	jl	jl	NOUN
ejpam-4755	182	13	-	-	PUNCT
ejpam-4755	182	14	extension	extension	NOUN
ejpam-4755	182	15	by	by	ADP
ejpam-4755	182	16	using	use	VERB
ejpam-4755	182	17	byott	byott	PROPN
ejpam-4755	182	18	’s	’s	PART
ejpam-4755	182	19	formula	formula	NOUN
ejpam-4755	182	20	(	(	PUNCT
ejpam-4755	182	21	1	1	X
ejpam-4755	182	22	)	)	PUNCT
ejpam-4755	182	23	is	be	AUX
ejpam-4755	182	24	(	(	PUNCT
ejpam-4755	182	25	p−	p−	NOUN
ejpam-4755	182	26	1)(q	1)(q	NUM
ejpam-4755	182	27	−	−	NOUN
ejpam-4755	182	28	1	1	NUM
ejpam-4755	182	29	)	)	PUNCT
ejpam-4755	182	30	+	+	NOUN
ejpam-4755	182	31	1	1	X
ejpam-4755	182	32	.	.	X
ejpam-4755	182	33	we	we	PRON
ejpam-4755	182	34	assume	assume	VERB
ejpam-4755	182	35	in	in	ADP
ejpam-4755	182	36	case	case	NOUN
ejpam-4755	182	37	2	2	NUM
ejpam-4755	182	38	that	that	PRON
ejpam-4755	182	39	b	b	X
ejpam-4755	182	40	=	=	SYM
ejpam-4755	182	41	jl	jl	PROPN
ejpam-4755	182	42	⋊	⋊	NUM
ejpam-4755	182	43	⟨β⟩	⟨β⟩	PROPN
ejpam-4755	182	44	with	with	ADP
ejpam-4755	182	45	jl	jl	PROPN
ejpam-4755	182	46	instead	instead	ADV
ejpam-4755	182	47	of	of	ADP
ejpam-4755	182	48	n	n	PRON
ejpam-4755	182	49	and	and	CCONJ
ejpam-4755	182	50	b	b	X
ejpam-4755	183	1	′	′	NOUN
ejpam-4755	184	1	=	=	SYM
ejpam-4755	185	1	⟨β⟩	⟨β⟩	NOUN
ejpam-4755	185	2	,	,	PUNCT
ejpam-4755	185	3	we	we	PRON
ejpam-4755	185	4	use	use	VERB
ejpam-4755	185	5	proposition	proposition	NOUN
ejpam-4755	185	6	2	2	NUM
ejpam-4755	185	7	.	.	PUNCT
ejpam-4755	185	8	conjugating	conjugate	VERB
ejpam-4755	185	9	by	by	ADP
ejpam-4755	185	10	β	β	PROPN
ejpam-4755	185	11	fixes	fix	NOUN
ejpam-4755	185	12	the	the	DET
ejpam-4755	185	13	generator	generator	NOUN
ejpam-4755	185	14	f	f	PROPN
ejpam-4755	186	1	=	=	PROPN
ejpam-4755	187	1	[	[	X
ejpam-4755	187	2	τ	τ	X
ejpam-4755	187	3	,	,	PUNCT
ejpam-4755	187	4	αl	αl	ADP
ejpam-4755	187	5	]	]	PUNCT
ejpam-4755	187	6	of	of	ADP
ejpam-4755	187	7	order	order	NOUN
ejpam-4755	187	8	w	w	VERB
ejpam-4755	187	9	by	by	ADP
ejpam-4755	187	10	inverting	invert	VERB
ejpam-4755	187	11	σ	σ	PROPN
ejpam-4755	187	12	.	.	PUNCT
ejpam-4755	188	1	if	if	SCONJ
ejpam-4755	188	2	ψ	ψ	PRON
ejpam-4755	188	3	∈	∈	PROPN
ejpam-4755	188	4	aut(jl	aut(jl	NOUN
ejpam-4755	188	5	)	)	PUNCT
ejpam-4755	188	6	,	,	PUNCT
ejpam-4755	188	7	we	we	PRON
ejpam-4755	188	8	have	have	AUX
ejpam-4755	188	9	ψ(σ	ψ(σ	VERB
ejpam-4755	188	10	)	)	PUNCT
ejpam-4755	188	11	=	=	SYM
ejpam-4755	188	12	σa	σa	NOUN
ejpam-4755	188	13	and	and	CCONJ
ejpam-4755	188	14	ψ(f	ψ(f	NOUN
ejpam-4755	188	15	)	)	PUNCT
ejpam-4755	189	1	=	=	SYM
ejpam-4755	189	2	σbf	σbf	ADJ
ejpam-4755	189	3	for	for	ADP
ejpam-4755	189	4	1	1	NUM
ejpam-4755	189	5	≤	≤	NOUN
ejpam-4755	189	6	a	a	DET
ejpam-4755	189	7	≤	≤	NOUN
ejpam-4755	189	8	(	(	PUNCT
ejpam-4755	189	9	q	q	NOUN
ejpam-4755	189	10	−	−	PROPN
ejpam-4755	189	11	1)(p−	1)(p−	NUM
ejpam-4755	189	12	1	1	NUM
ejpam-4755	189	13	)	)	PUNCT
ejpam-4755	189	14	≤	≤	NOUN
ejpam-4755	189	15	and	and	CCONJ
ejpam-4755	189	16	0	0	NUM
ejpam-4755	189	17	≤	≤	NUM
ejpam-4755	189	18	b	b	X
ejpam-4755	189	19	≤	≤	NOUN
ejpam-4755	189	20	(	(	PUNCT
ejpam-4755	189	21	q	q	NOUN
ejpam-4755	189	22	−	−	PROPN
ejpam-4755	190	1	1)(p−	1)(p−	NUM
ejpam-4755	190	2	1	1	NUM
ejpam-4755	190	3	)	)	PUNCT
ejpam-4755	190	4	respectively	respectively	ADV
ejpam-4755	190	5	.	.	PUNCT
ejpam-4755	191	1	then	then	ADV
ejpam-4755	191	2	,	,	PUNCT
ejpam-4755	191	3	b	b	X
ejpam-4755	191	4	=	=	SYM
ejpam-4755	191	5	0	0	PUNCT
ejpam-4755	191	6	if	if	SCONJ
ejpam-4755	191	7	and	and	CCONJ
ejpam-4755	191	8	only	only	ADV
ejpam-4755	191	9	if	if	SCONJ
ejpam-4755	191	10	ψ	ψ	PRON
ejpam-4755	191	11	normalizes	normalize	VERB
ejpam-4755	191	12	b	b	NOUN
ejpam-4755	191	13	′	′	NOUN
ejpam-4755	191	14	in	in	ADP
ejpam-4755	191	15	aut(jl	aut(jl	NOUN
ejpam-4755	191	16	)	)	PUNCT
ejpam-4755	191	17	.	.	PUNCT
ejpam-4755	192	1	as	as	ADP
ejpam-4755	192	2	a	a	DET
ejpam-4755	192	3	result	result	NOUN
ejpam-4755	192	4	,	,	PUNCT
ejpam-4755	192	5	|	|	ADV
ejpam-4755	192	6	aut(b	aut(b	NOUN
ejpam-4755	192	7	,	,	PUNCT
ejpam-4755	192	8	b′	b′	NUM
ejpam-4755	192	9	)	)	PUNCT
ejpam-4755	192	10	|=	|=	NOUN
ejpam-4755	192	11	(	(	PUNCT
ejpam-4755	192	12	p−	p−	NOUN
ejpam-4755	192	13	1)(q	1)(q	NUM
ejpam-4755	192	14	−	−	NOUN
ejpam-4755	192	15	1	1	NUM
ejpam-4755	192	16	)	)	PUNCT
ejpam-4755	192	17	,	,	PUNCT
ejpam-4755	192	18	and	and	CCONJ
ejpam-4755	192	19	the	the	DET
ejpam-4755	192	20	w	w	NOUN
ejpam-4755	192	21	−	−	PROPN
ejpam-4755	192	22	1	1	NUM
ejpam-4755	192	23	conjugate	conjugate	ADJ
ejpam-4755	192	24	subgroups	subgroup	NOUN
ejpam-4755	192	25	yield	yield	VERB
ejpam-4755	192	26	that	that	SCONJ
ejpam-4755	192	27	the	the	DET
ejpam-4755	192	28	number	number	NOUN
ejpam-4755	192	29	of	of	ADP
ejpam-4755	192	30	hgs	hgs	PROPN
ejpam-4755	192	31	is	be	AUX
ejpam-4755	192	32	1	1	NUM
ejpam-4755	192	33	.	.	PUNCT
ejpam-4755	192	34	table	table	NOUN
ejpam-4755	192	35	2	2	NUM
ejpam-4755	192	36	:	:	PUNCT
ejpam-4755	192	37	the	the	DET
ejpam-4755	192	38	structures	structure	NOUN
ejpam-4755	192	39	of	of	ADP
ejpam-4755	192	40	transitive	transitive	ADJ
ejpam-4755	192	41	subgroups	subgroup	NOUN
ejpam-4755	192	42	for	for	ADP
ejpam-4755	192	43	jl	jl	PROPN
ejpam-4755	192	44	.	.	PUNCT
ejpam-4755	193	1	key	key	ADJ
ejpam-4755	193	2	restrictions	restriction	NOUN
ejpam-4755	193	3	order	order	NOUN
ejpam-4755	193	4	structure	structure	NOUN
ejpam-4755	193	5	1	1	NUM
ejpam-4755	193	6	pqw	pqw	NOUN
ejpam-4755	193	7	cpq	cpq	PROPN
ejpam-4755	193	8	⋊	⋊	PROPN
ejpam-4755	193	9	cw	cw	PROPN
ejpam-4755	193	10	2	2	NUM
ejpam-4755	193	11	2pqw	2pqw	PROPN
ejpam-4755	193	12	cpq	cpq	NOUN
ejpam-4755	193	13	⋊	⋊	NUM
ejpam-4755	193	14	c2w	c2w	NOUN
ejpam-4755	193	15	3	3	NUM
ejpam-4755	193	16	c1	c1	NOUN
ejpam-4755	193	17	̸=	̸=	PROPN
ejpam-4755	193	18	(	(	PUNCT
ejpam-4755	193	19	0	0	NUM
ejpam-4755	193	20	,	,	PUNCT
ejpam-4755	193	21	1	1	NUM
ejpam-4755	193	22	)	)	PUNCT
ejpam-4755	193	23	,	,	PUNCT
ejpam-4755	193	24	c1	c1	PROPN
ejpam-4755	193	25	=	=	PUNCT
ejpam-4755	193	26	0	0	PROPN
ejpam-4755	193	27	,	,	PUNCT
ejpam-4755	193	28	c1	c1	NOUN
ejpam-4755	193	29	=	=	NOUN
ejpam-4755	193	30	1	1	NUM
ejpam-4755	193	31	2c1pqw	2c1pqw	NUM
ejpam-4755	193	32	,	,	PUNCT
ejpam-4755	193	33	pqw	pqw	PROPN
ejpam-4755	193	34	,	,	PUNCT
ejpam-4755	193	35	2pqw	2pqw	PROPN
ejpam-4755	193	36	cpq	cpq	PROPN
ejpam-4755	193	37	⋊	⋊	X
ejpam-4755	193	38	c2c1w	c2c1w	NUM
ejpam-4755	193	39	,	,	PUNCT
ejpam-4755	193	40	cpq	cpq	PROPN
ejpam-4755	193	41	⋊	⋊	PROPN
ejpam-4755	193	42	cw	cw	PROPN
ejpam-4755	193	43	,	,	PUNCT
ejpam-4755	193	44	cpq	cpq	PROPN
ejpam-4755	193	45	⋊	⋊	NUM
ejpam-4755	193	46	c2w	c2w	NOUN
ejpam-4755	193	47	4	4	NUM
ejpam-4755	193	48	d	d	NOUN
ejpam-4755	193	49	̸=	̸=	PROPN
ejpam-4755	193	50	1	1	NUM
ejpam-4755	193	51	,	,	PUNCT
ejpam-4755	193	52	d	d	NOUN
ejpam-4755	193	53	=	=	SYM
ejpam-4755	193	54	1	1	NUM
ejpam-4755	193	55	pqwd	pqwd	NOUN
ejpam-4755	193	56	,	,	PUNCT
ejpam-4755	193	57	pqw	pqw	PROPN
ejpam-4755	193	58	cpq	cpq	PROPN
ejpam-4755	193	59	⋊	⋊	PROPN
ejpam-4755	193	60	cwd	cwd	PROPN
ejpam-4755	193	61	,	,	PUNCT
ejpam-4755	193	62	cpq	cpq	PROPN
ejpam-4755	193	63	⋊	⋊	PROPN
ejpam-4755	193	64	cw	cw	PROPN
ejpam-4755	193	65	b.	b.	PROPN
ejpam-4755	193	66	jamal	jamal	PROPN
ejpam-4755	193	67	,	,	PUNCT
ejpam-4755	193	68	a.	a.	PROPN
ejpam-4755	193	69	alabdali	alabdali	VERB
ejpam-4755	193	70	/	/	SYM
ejpam-4755	193	71	eur	eur	PROPN
ejpam-4755	193	72	.	.	PUNCT
ejpam-4755	194	1	j.	j.	PROPN
ejpam-4755	194	2	pure	pure	PROPN
ejpam-4755	194	3	appl	appl	PROPN
ejpam-4755	194	4	.	.	PROPN
ejpam-4755	194	5	math	math	PROPN
ejpam-4755	194	6	,	,	PUNCT
ejpam-4755	194	7	16	16	NUM
ejpam-4755	194	8	(	(	PUNCT
ejpam-4755	194	9	2	2	NUM
ejpam-4755	194	10	)	)	PUNCT
ejpam-4755	194	11	(	(	PUNCT
ejpam-4755	194	12	2023	2023	NUM
ejpam-4755	194	13	)	)	PUNCT
ejpam-4755	194	14	,	,	PUNCT
ejpam-4755	194	15	1118	1118	NUM
ejpam-4755	194	16	-	-	SYM
ejpam-4755	194	17	1127	1127	NUM
ejpam-4755	194	18	1124	1124	NUM
ejpam-4755	194	19	table	table	NOUN
ejpam-4755	194	20	3	3	NUM
ejpam-4755	194	21	:	:	PUNCT
ejpam-4755	194	22	the	the	DET
ejpam-4755	194	23	number	number	NOUN
ejpam-4755	194	24	of	of	ADP
ejpam-4755	194	25	hgss	hgss	ADJ
ejpam-4755	194	26	for	for	ADP
ejpam-4755	194	27	the	the	DET
ejpam-4755	194	28	nonabelian	nonabelian	ADJ
ejpam-4755	194	29	group	group	PROPN
ejpam-4755	194	30	jl	jl	PROPN
ejpam-4755	194	31	.	.	PUNCT
ejpam-4755	195	1	key	key	ADJ
ejpam-4755	195	2	order	order	NOUN
ejpam-4755	195	3	|	|	CCONJ
ejpam-4755	195	4	aut(b	aut(b	NOUN
ejpam-4755	195	5	,	,	PUNCT
ejpam-4755	195	6	b′	b′	NUM
ejpam-4755	195	7	)	)	PUNCT
ejpam-4755	195	8	|	|	ADV
ejpam-4755	195	9	#	#	NOUN
ejpam-4755	195	10	iso	iso	NOUN
ejpam-4755	195	11	.	.	PUNCT
ejpam-4755	196	1	class	class	NOUN
ejpam-4755	196	2	#	#	NOUN
ejpam-4755	196	3	hgs	hgs	NOUN
ejpam-4755	196	4	per	per	ADP
ejpam-4755	196	5	iso	iso	NOUN
ejpam-4755	196	6	.	.	PUNCT
ejpam-4755	197	1	class	class	NOUN
ejpam-4755	197	2	1	1	NUM
ejpam-4755	197	3	pqw	pqw	NOUN
ejpam-4755	197	4	(	(	PUNCT
ejpam-4755	197	5	p−	p−	NOUN
ejpam-4755	197	6	1)(q	1)(q	NUM
ejpam-4755	197	7	−	−	NUM
ejpam-4755	197	8	1)[(p−	1)[(p−	NUM
ejpam-4755	197	9	1)(q	1)(q	NUM
ejpam-4755	197	10	−	−	NOUN
ejpam-4755	197	11	1	1	NUM
ejpam-4755	197	12	)	)	PUNCT
ejpam-4755	197	13	+	+	CCONJ
ejpam-4755	197	14	1	1	NUM
ejpam-4755	197	15	]	]	SYM
ejpam-4755	197	16	1	1	NUM
ejpam-4755	197	17	(	(	PUNCT
ejpam-4755	197	18	p−	p−	NOUN
ejpam-4755	197	19	1)(q	1)(q	NUM
ejpam-4755	197	20	−	−	NOUN
ejpam-4755	197	21	1	1	NUM
ejpam-4755	197	22	)	)	PUNCT
ejpam-4755	197	23	+	+	CCONJ
ejpam-4755	197	24	1	1	NUM
ejpam-4755	197	25	2	2	NUM
ejpam-4755	197	26	2pqw	2pqw	NUM
ejpam-4755	197	27	(	(	PUNCT
ejpam-4755	197	28	p−	p−	NOUN
ejpam-4755	197	29	1)(q	1)(q	NUM
ejpam-4755	197	30	−	−	NOUN
ejpam-4755	197	31	1	1	NUM
ejpam-4755	197	32	)	)	SYM
ejpam-4755	197	33	1	1	NUM
ejpam-4755	197	34	1	1	NUM
ejpam-4755	197	35	3	3	NUM
ejpam-4755	197	36	2c1pqw	2c1pqw	PROPN
ejpam-4755	197	37	(	(	PUNCT
ejpam-4755	197	38	p−	p−	NOUN
ejpam-4755	197	39	1)(q	1)(q	NUM
ejpam-4755	197	40	−	−	NOUN
ejpam-4755	197	41	1	1	NUM
ejpam-4755	197	42	)	)	PUNCT
ejpam-4755	197	43	r	r	NOUN
ejpam-4755	197	44	+	+	NOUN
ejpam-4755	197	45	1	1	NUM
ejpam-4755	197	46	r	r	NOUN
ejpam-4755	197	47	+	+	NUM
ejpam-4755	197	48	1	1	NUM
ejpam-4755	197	49	4	4	NUM
ejpam-4755	197	50	pqwd	pqwd	NOUN
ejpam-4755	197	51	(	(	PUNCT
ejpam-4755	197	52	p−	p−	NOUN
ejpam-4755	197	53	1)(q	1)(q	NUM
ejpam-4755	197	54	−	−	NOUN
ejpam-4755	197	55	1	1	NUM
ejpam-4755	197	56	)	)	PUNCT
ejpam-4755	197	57	σ0(s	σ0(s	PROPN
ejpam-4755	197	58	)	)	PUNCT
ejpam-4755	197	59	σ0(s	σ0(s	PROPN
ejpam-4755	197	60	)	)	PUNCT
ejpam-4755	197	61	we	we	PRON
ejpam-4755	197	62	assume	assume	VERB
ejpam-4755	197	63	in	in	ADP
ejpam-4755	197	64	cases	case	NOUN
ejpam-4755	197	65	3	3	NUM
ejpam-4755	197	66	and	and	CCONJ
ejpam-4755	197	67	4	4	NUM
ejpam-4755	198	1	that	that	DET
ejpam-4755	198	2	b	b	X
ejpam-4755	198	3	=	=	SYM
ejpam-4755	198	4	jl⋊⟨γ2r−c1	jl⋊⟨γ2r−c1	PROPN
ejpam-4755	198	5	⟩	⟩	PROPN
ejpam-4755	198	6	and	and	CCONJ
ejpam-4755	198	7	b	b	NOUN
ejpam-4755	198	8	=	=	SYM
ejpam-4755	198	9	jl⋊⟨δs	jl⋊⟨δs	PROPN
ejpam-4755	198	10	/	/	SYM
ejpam-4755	198	11	d⟩	d⟩	NOUN
ejpam-4755	198	12	respectively	respectively	ADV
ejpam-4755	198	13	with	with	ADP
ejpam-4755	198	14	jl	jl	NOUN
ejpam-4755	198	15	instead	instead	ADV
ejpam-4755	198	16	of	of	ADP
ejpam-4755	198	17	n	n	CCONJ
ejpam-4755	198	18	,	,	PUNCT
ejpam-4755	198	19	b	b	NOUN
ejpam-4755	198	20	′	′	NOUN
ejpam-4755	198	21	=	=	SYM
ejpam-4755	199	1	⟨γ2r−c1	⟨γ2r−c1	PROPN
ejpam-4755	199	2	⟩	⟩	NOUN
ejpam-4755	199	3	and	and	CCONJ
ejpam-4755	199	4	b′	b′	NUM
ejpam-4755	199	5	=	=	PUNCT
ejpam-4755	199	6	⟨δs	⟨δs	NUM
ejpam-4755	199	7	/	/	SYM
ejpam-4755	199	8	d⟩	d⟩	NOUN
ejpam-4755	199	9	respectively	respectively	ADV
ejpam-4755	199	10	,	,	PUNCT
ejpam-4755	199	11	we	we	PRON
ejpam-4755	199	12	also	also	ADV
ejpam-4755	199	13	use	use	VERB
ejpam-4755	199	14	proposition	proposition	NOUN
ejpam-4755	199	15	2	2	NUM
ejpam-4755	199	16	.	.	PUNCT
ejpam-4755	199	17	conjugating	conjugate	VERB
ejpam-4755	199	18	by	by	ADP
ejpam-4755	199	19	⟨γ2r−c1	⟨γ2r−c1	PROPN
ejpam-4755	199	20	⟩	⟩	PROPN
ejpam-4755	199	21	in	in	ADP
ejpam-4755	199	22	case	case	NOUN
ejpam-4755	199	23	3	3	NUM
ejpam-4755	199	24	and	and	CCONJ
ejpam-4755	199	25	⟨δs	⟨δs	PROPN
ejpam-4755	199	26	/	/	SYM
ejpam-4755	199	27	d⟩	d⟩	NOUN
ejpam-4755	199	28	in	in	ADP
ejpam-4755	199	29	case	case	NOUN
ejpam-4755	199	30	4	4	NUM
ejpam-4755	199	31	fixes	fix	NOUN
ejpam-4755	199	32	the	the	DET
ejpam-4755	199	33	generator	generator	NOUN
ejpam-4755	200	1	f	f	PROPN
ejpam-4755	200	2	=	=	PROPN
ejpam-4755	201	1	[	[	X
ejpam-4755	201	2	τ	τ	X
ejpam-4755	201	3	,	,	PUNCT
ejpam-4755	201	4	αl	αl	ADP
ejpam-4755	201	5	]	]	PUNCT
ejpam-4755	201	6	of	of	ADP
ejpam-4755	201	7	order	order	NOUN
ejpam-4755	201	8	w	w	VERB
ejpam-4755	201	9	by	by	ADP
ejpam-4755	201	10	reversing	reverse	VERB
ejpam-4755	201	11	σ	σ	PROPN
ejpam-4755	201	12	.	.	PUNCT
ejpam-4755	202	1	if	if	SCONJ
ejpam-4755	202	2	ψ	ψ	PRON
ejpam-4755	202	3	∈	∈	PROPN
ejpam-4755	202	4	aut(jl	aut(jl	NOUN
ejpam-4755	202	5	)	)	PUNCT
ejpam-4755	202	6	,	,	PUNCT
ejpam-4755	202	7	we	we	PRON
ejpam-4755	202	8	have	have	AUX
ejpam-4755	202	9	ψ(σ	ψ(σ	VERB
ejpam-4755	202	10	)	)	PUNCT
ejpam-4755	202	11	=	=	SYM
ejpam-4755	202	12	σa	σa	NOUN
ejpam-4755	202	13	and	and	CCONJ
ejpam-4755	202	14	ψ(f	ψ(f	NOUN
ejpam-4755	202	15	)	)	PUNCT
ejpam-4755	203	1	=	=	SYM
ejpam-4755	203	2	σbf	σbf	ADJ
ejpam-4755	203	3	for	for	ADP
ejpam-4755	203	4	1	1	NUM
ejpam-4755	203	5	≤	≤	NOUN
ejpam-4755	203	6	a	a	DET
ejpam-4755	203	7	≤	≤	ADJ
ejpam-4755	203	8	(	(	PUNCT
ejpam-4755	203	9	q−1)(p−1	q−1)(p−1	PROPN
ejpam-4755	203	10	)	)	PUNCT
ejpam-4755	203	11	and	and	CCONJ
ejpam-4755	203	12	0	0	NUM
ejpam-4755	203	13	≤	≤	NUM
ejpam-4755	203	14	b	b	X
ejpam-4755	203	15	≤	≤	X
ejpam-4755	203	16	(	(	PUNCT
ejpam-4755	203	17	q−1)(p−1	q−1)(p−1	PROPN
ejpam-4755	203	18	)	)	PUNCT
ejpam-4755	203	19	respectively	respectively	ADV
ejpam-4755	203	20	.	.	PUNCT
ejpam-4755	204	1	then	then	ADV
ejpam-4755	204	2	,	,	PUNCT
ejpam-4755	204	3	b	b	X
ejpam-4755	204	4	=	=	SYM
ejpam-4755	204	5	0	0	PUNCT
ejpam-4755	204	6	if	if	SCONJ
ejpam-4755	204	7	and	and	CCONJ
ejpam-4755	204	8	only	only	ADV
ejpam-4755	204	9	if	if	SCONJ
ejpam-4755	204	10	ψ	ψ	PRON
ejpam-4755	204	11	normalize	normalize	VERB
ejpam-4755	204	12	b	b	NUM
ejpam-4755	204	13	′	′	NOUN
ejpam-4755	204	14	in	in	ADP
ejpam-4755	204	15	aut(jl	aut(jl	NOUN
ejpam-4755	204	16	)	)	PUNCT
ejpam-4755	204	17	.	.	PUNCT
ejpam-4755	205	1	as	as	ADP
ejpam-4755	205	2	a	a	DET
ejpam-4755	205	3	result	result	NOUN
ejpam-4755	205	4	,	,	PUNCT
ejpam-4755	205	5	in	in	ADP
ejpam-4755	205	6	case	case	NOUN
ejpam-4755	205	7	3	3	NUM
ejpam-4755	205	8	and	and	CCONJ
ejpam-4755	205	9	case	case	NOUN
ejpam-4755	205	10	4	4	NUM
ejpam-4755	205	11	|	|	ADV
ejpam-4755	205	12	aut(b	aut(b	NOUN
ejpam-4755	205	13	,	,	PUNCT
ejpam-4755	205	14	b′	b′	NUM
ejpam-4755	205	15	)	)	PUNCT
ejpam-4755	205	16	|=	|=	NOUN
ejpam-4755	205	17	(	(	PUNCT
ejpam-4755	205	18	p−	p−	NOUN
ejpam-4755	205	19	1)(q	1)(q	NUM
ejpam-4755	205	20	−	−	NOUN
ejpam-4755	205	21	1	1	NUM
ejpam-4755	205	22	)	)	PUNCT
ejpam-4755	205	23	.	.	PUNCT
ejpam-4755	206	1	(	(	PUNCT
ejpam-4755	206	2	w	w	NOUN
ejpam-4755	206	3	−	−	PROPN
ejpam-4755	206	4	1)(r	1)(r	NUM
ejpam-4755	206	5	+	+	CCONJ
ejpam-4755	206	6	1	1	X
ejpam-4755	206	7	)	)	PUNCT
ejpam-4755	206	8	in	in	ADP
ejpam-4755	206	9	case	case	NOUN
ejpam-4755	206	10	3	3	NUM
ejpam-4755	206	11	and	and	CCONJ
ejpam-4755	206	12	(	(	PUNCT
ejpam-4755	206	13	w	w	NOUN
ejpam-4755	206	14	−	−	NOUN
ejpam-4755	206	15	1)σ0(s	1)σ0(s	NUM
ejpam-4755	206	16	)	)	PUNCT
ejpam-4755	206	17	in	in	ADP
ejpam-4755	206	18	case	case	NOUN
ejpam-4755	206	19	4	4	NUM
ejpam-4755	206	20	conjugate	conjugate	ADJ
ejpam-4755	206	21	subgroups	subgroup	NOUN
ejpam-4755	206	22	yield	yield	VERB
ejpam-4755	206	23	that	that	SCONJ
ejpam-4755	206	24	the	the	DET
ejpam-4755	206	25	number	number	NOUN
ejpam-4755	206	26	of	of	ADP
ejpam-4755	206	27	hgs	hgs	PROPN
ejpam-4755	206	28	in	in	ADP
ejpam-4755	206	29	case	case	NOUN
ejpam-4755	206	30	3	3	NUM
ejpam-4755	206	31	is	be	AUX
ejpam-4755	206	32	(	(	PUNCT
ejpam-4755	206	33	r	r	NOUN
ejpam-4755	206	34	+	+	NOUN
ejpam-4755	206	35	1	1	NUM
ejpam-4755	206	36	)	)	PUNCT
ejpam-4755	206	37	and	and	CCONJ
ejpam-4755	206	38	in	in	ADP
ejpam-4755	206	39	case	case	NOUN
ejpam-4755	206	40	4	4	NUM
ejpam-4755	206	41	is	be	AUX
ejpam-4755	206	42	σ0(s	σ0(s	PROPN
ejpam-4755	206	43	)	)	PUNCT
ejpam-4755	206	44	.	.	PUNCT
ejpam-4755	207	1	the	the	DET
ejpam-4755	207	2	conclusions	conclusion	NOUN
ejpam-4755	207	3	of	of	ADP
ejpam-4755	207	4	the	the	DET
ejpam-4755	207	5	nonabelian	nonabelian	ADJ
ejpam-4755	207	6	group	group	NOUN
ejpam-4755	207	7	are	be	AUX
ejpam-4755	207	8	summed	sum	VERB
ejpam-4755	207	9	up	up	ADP
ejpam-4755	207	10	in	in	ADP
ejpam-4755	207	11	the	the	DET
ejpam-4755	207	12	theorem	theorem	NOUN
ejpam-4755	207	13	below	below	ADV
ejpam-4755	207	14	.	.	PUNCT
ejpam-4755	208	1	theorem	theorem	VERB
ejpam-4755	208	2	4	4	NUM
ejpam-4755	208	3	.	.	PUNCT
ejpam-4755	209	1	the	the	DET
ejpam-4755	209	2	total	total	ADJ
ejpam-4755	209	3	number	number	NOUN
ejpam-4755	209	4	of	of	ADP
ejpam-4755	209	5	isomorphism	isomorphism	NOUN
ejpam-4755	209	6	types	type	NOUN
ejpam-4755	209	7	admits	admit	VERB
ejpam-4755	209	8	nonabelian	nonabelian	PROPN
ejpam-4755	209	9	hgss	hgss	PROPN
ejpam-4755	209	10	is	be	AUX
ejpam-4755	209	11	2	2	NUM
ejpam-4755	209	12	+	+	CCONJ
ejpam-4755	209	13	(	(	PUNCT
ejpam-4755	209	14	r+	r+	NOUN
ejpam-4755	209	15	1	1	NUM
ejpam-4755	209	16	)	)	PUNCT
ejpam-4755	210	1	+	+	CCONJ
ejpam-4755	210	2	σ0(s	σ0(s	X
ejpam-4755	210	3	)	)	PUNCT
ejpam-4755	210	4	of	of	ADP
ejpam-4755	210	5	pgs	pgs	NOUN
ejpam-4755	210	6	of	of	ADP
ejpam-4755	210	7	degree	degree	NOUN
ejpam-4755	210	8	pqw	pqw	NOUN
ejpam-4755	210	9	.	.	PUNCT
ejpam-4755	211	1	the	the	DET
ejpam-4755	211	2	nonabelain	nonabelain	NOUN
ejpam-4755	211	3	of	of	ADP
ejpam-4755	211	4	order	order	NOUN
ejpam-4755	211	5	pqw	pqw	NOUN
ejpam-4755	211	6	is	be	AUX
ejpam-4755	211	7	the	the	DET
ejpam-4755	211	8	regular	regular	ADJ
ejpam-4755	211	9	group	group	NOUN
ejpam-4755	211	10	.	.	PUNCT
ejpam-4755	212	1	proof	proof	NOUN
ejpam-4755	212	2	.	.	PUNCT
ejpam-4755	213	1	it	it	PRON
ejpam-4755	213	2	is	be	AUX
ejpam-4755	213	3	clear	clear	ADJ
ejpam-4755	213	4	from	from	ADP
ejpam-4755	213	5	summing	sum	VERB
ejpam-4755	213	6	the	the	DET
ejpam-4755	213	7	numbers	number	NOUN
ejpam-4755	213	8	of	of	ADP
ejpam-4755	213	9	permutation	permutation	NOUN
ejpam-4755	213	10	groups	group	NOUN
ejpam-4755	213	11	g	g	ADP
ejpam-4755	213	12	of	of	ADP
ejpam-4755	213	13	degree	degree	NOUN
ejpam-4755	213	14	pqw	pqw	NOUN
ejpam-4755	213	15	of	of	ADP
ejpam-4755	213	16	isomorphism	isomorphism	NOUN
ejpam-4755	213	17	types	type	NOUN
ejpam-4755	213	18	in	in	ADP
ejpam-4755	213	19	column	column	NOUN
ejpam-4755	213	20	four	four	NUM
ejpam-4755	213	21	from	from	ADP
ejpam-4755	213	22	table	table	NOUN
ejpam-4755	213	23	3	3	NUM
ejpam-4755	213	24	that	that	PRON
ejpam-4755	213	25	the	the	DET
ejpam-4755	213	26	total	total	ADJ
ejpam-4755	213	27	number	number	NOUN
ejpam-4755	213	28	is	be	AUX
ejpam-4755	213	29	2+(r+1)+σ0(s	2+(r+1)+σ0(s	NUM
ejpam-4755	213	30	)	)	PUNCT
ejpam-4755	213	31	which	which	PRON
ejpam-4755	213	32	admits	admit	VERB
ejpam-4755	213	33	hgs	hgs	PROPN
ejpam-4755	213	34	of	of	ADP
ejpam-4755	213	35	nonabelain	nonabelain	NOUN
ejpam-4755	213	36	case	case	NOUN
ejpam-4755	213	37	.	.	PUNCT
ejpam-4755	214	1	the	the	DET
ejpam-4755	214	2	following	follow	VERB
ejpam-4755	214	3	theorem	theorem	ADJ
ejpam-4755	214	4	summarizes	summarize	NOUN
ejpam-4755	214	5	the	the	DET
ejpam-4755	214	6	results	result	NOUN
ejpam-4755	214	7	of	of	ADP
ejpam-4755	214	8	the	the	DET
ejpam-4755	214	9	cyclic	cyclic	ADJ
ejpam-4755	214	10	case	case	NOUN
ejpam-4755	214	11	in	in	ADP
ejpam-4755	214	12	theorem	theorem	NOUN
ejpam-4755	214	13	3	3	NUM
ejpam-4755	214	14	and	and	CCONJ
ejpam-4755	214	15	the	the	DET
ejpam-4755	214	16	nonabelain	nonabelain	ADJ
ejpam-4755	214	17	case	case	NOUN
ejpam-4755	214	18	in	in	ADP
ejpam-4755	214	19	theorem	theorem	NOUN
ejpam-4755	214	20	4	4	NUM
ejpam-4755	214	21	.	.	PUNCT
ejpam-4755	214	22	theorem	theorem	NOUN
ejpam-4755	214	23	5	5	NUM
ejpam-4755	214	24	.	.	PUNCT
ejpam-4755	214	25	a	a	DET
ejpam-4755	214	26	hgs	hgs	PROPN
ejpam-4755	214	27	of	of	ADP
ejpam-4755	214	28	cyclic	cyclic	ADJ
ejpam-4755	214	29	type	type	NOUN
ejpam-4755	214	30	can	can	AUX
ejpam-4755	214	31	realise	realise	VERB
ejpam-4755	214	32	isomorphism	isomorphism	NOUN
ejpam-4755	214	33	types	type	NOUN
ejpam-4755	214	34	in	in	ADP
ejpam-4755	214	35	total	total	ADJ
ejpam-4755	214	36	12(r	12(r	PROPN
ejpam-4755	215	1	+	+	CCONJ
ejpam-4755	215	2	i	i	PROPN
ejpam-4755	215	3	+	+	X
ejpam-4755	215	4	1)[σ0(s	1)[σ0(s	NUM
ejpam-4755	215	5	)	)	PUNCT
ejpam-4755	215	6	+	+	NUM
ejpam-4755	215	7	σ1(j	σ1(j	X
ejpam-4755	215	8	)	)	PUNCT
ejpam-4755	215	9	+	+	X
ejpam-4755	215	10	σ0(s)σ1(j	σ0(s)σ1(j	NOUN
ejpam-4755	215	11	)	)	PUNCT
ejpam-4755	215	12	]	]	PUNCT
ejpam-4755	216	1	+	+	CCONJ
ejpam-4755	216	2	2	2	NUM
ejpam-4755	216	3	+	+	CCONJ
ejpam-4755	216	4	(	(	PUNCT
ejpam-4755	216	5	r	r	NOUN
ejpam-4755	216	6	+	+	NOUN
ejpam-4755	216	7	1	1	NUM
ejpam-4755	216	8	)	)	PUNCT
ejpam-4755	216	9	+	+	NOUN
ejpam-4755	216	10	σ0(s	σ0(s	X
ejpam-4755	216	11	)	)	PUNCT
ejpam-4755	216	12	of	of	ADP
ejpam-4755	216	13	pgs	pgs	ADJ
ejpam-4755	216	14	g	g	NOUN
ejpam-4755	216	15	of	of	ADP
ejpam-4755	216	16	degree	degree	NOUN
ejpam-4755	216	17	pqw	pqw	NOUN
ejpam-4755	216	18	of	of	ADP
ejpam-4755	216	19	both	both	DET
ejpam-4755	216	20	cases	case	NOUN
ejpam-4755	216	21	regular	regular	ADJ
ejpam-4755	216	22	groups	group	NOUN
ejpam-4755	216	23	(	(	PUNCT
ejpam-4755	216	24	where	where	SCONJ
ejpam-4755	216	25	the	the	DET
ejpam-4755	216	26	galois	galois	PROPN
ejpam-4755	216	27	extensions	extension	NOUN
ejpam-4755	216	28	have	have	VERB
ejpam-4755	216	29	1	1	NUM
ejpam-4755	216	30	hgs	hgs	NOUN
ejpam-4755	216	31	for	for	ADP
ejpam-4755	216	32	the	the	DET
ejpam-4755	216	33	cyclic	cyclic	ADJ
ejpam-4755	216	34	group	group	NOUN
ejpam-4755	216	35	and	and	CCONJ
ejpam-4755	216	36	(	(	PUNCT
ejpam-4755	216	37	p	p	X
ejpam-4755	216	38	−	−	PROPN
ejpam-4755	216	39	1)(q	1)(q	NUM
ejpam-4755	216	40	−	−	NOUN
ejpam-4755	216	41	1	1	NUM
ejpam-4755	216	42	)	)	PUNCT
ejpam-4755	216	43	+	+	CCONJ
ejpam-4755	216	44	1	1	NUM
ejpam-4755	216	45	,	,	PUNCT
ejpam-4755	216	46	1	1	NUM
ejpam-4755	216	47	,	,	PUNCT
ejpam-4755	216	48	r	r	NOUN
ejpam-4755	216	49	+	+	NOUN
ejpam-4755	216	50	1	1	NUM
ejpam-4755	216	51	,	,	PUNCT
ejpam-4755	216	52	and	and	CCONJ
ejpam-4755	216	53	σ0(s	σ0(s	X
ejpam-4755	216	54	)	)	PUNCT
ejpam-4755	216	55	hgss	hgss	ADJ
ejpam-4755	216	56	for	for	ADP
ejpam-4755	216	57	the	the	DET
ejpam-4755	216	58	nonabelian	nonabelian	ADJ
ejpam-4755	216	59	group	group	NOUN
ejpam-4755	216	60	of	of	ADP
ejpam-4755	216	61	the	the	DET
ejpam-4755	216	62	cyclic	cyclic	ADJ
ejpam-4755	216	63	type	type	NOUN
ejpam-4755	216	64	)	)	PUNCT
ejpam-4755	216	65	.	.	PUNCT
ejpam-4755	217	1	proof	proof	NOUN
ejpam-4755	217	2	.	.	PUNCT
ejpam-4755	218	1	it	it	PRON
ejpam-4755	218	2	is	be	AUX
ejpam-4755	218	3	clear	clear	ADJ
ejpam-4755	218	4	from	from	ADP
ejpam-4755	218	5	summing	sum	VERB
ejpam-4755	218	6	the	the	DET
ejpam-4755	218	7	numbers	number	NOUN
ejpam-4755	218	8	of	of	ADP
ejpam-4755	218	9	pgs	pgs	ADJ
ejpam-4755	218	10	g	g	NOUN
ejpam-4755	218	11	of	of	ADP
ejpam-4755	218	12	degree	degree	NOUN
ejpam-4755	218	13	pqw	pqw	NOUN
ejpam-4755	218	14	of	of	ADP
ejpam-4755	218	15	isomorphism	isomorphism	NOUN
ejpam-4755	218	16	types	type	NOUN
ejpam-4755	218	17	in	in	ADP
ejpam-4755	218	18	column	column	NOUN
ejpam-4755	218	19	four	four	NUM
ejpam-4755	218	20	from	from	ADP
ejpam-4755	218	21	table	table	NOUN
ejpam-4755	218	22	3	3	NUM
ejpam-4755	218	23	and	and	CCONJ
ejpam-4755	218	24	theorem	theorem	VERB
ejpam-4755	218	25	3	3	NUM
ejpam-4755	218	26	that	that	SCONJ
ejpam-4755	218	27	the	the	DET
ejpam-4755	218	28	total	total	ADJ
ejpam-4755	218	29	number	number	NOUN
ejpam-4755	218	30	is	be	AUX
ejpam-4755	218	31	12(r	12(r	NUM
ejpam-4755	219	1	+	+	CCONJ
ejpam-4755	219	2	i	i	PRON
ejpam-4755	219	3	+	+	SYM
ejpam-4755	219	4	1)[σ0(s)+σ1(j)+σ0(s)σ1(j)]+2+(r+1)+σ0(s	1)[σ0(s)+σ1(j)+σ0(s)σ1(j)]+2+(r+1)+σ0(s	X
ejpam-4755	219	5	)	)	PUNCT
ejpam-4755	219	6	which	which	PRON
ejpam-4755	219	7	admits	admit	VERB
ejpam-4755	219	8	hgs	hgs	PROPN
ejpam-4755	219	9	of	of	ADP
ejpam-4755	219	10	cyclic	cyclic	ADJ
ejpam-4755	219	11	and	and	CCONJ
ejpam-4755	219	12	nonabelain	nonabelain	ADJ
ejpam-4755	219	13	type	type	NOUN
ejpam-4755	219	14	g.	g.	PROPN
ejpam-4755	219	15	example	example	NOUN
ejpam-4755	219	16	1	1	X
ejpam-4755	219	17	.	.	X
ejpam-4755	219	18	assume	assume	VERB
ejpam-4755	219	19	that	that	SCONJ
ejpam-4755	219	20	we	we	PRON
ejpam-4755	219	21	have	have	VERB
ejpam-4755	219	22	q	q	NOUN
ejpam-4755	219	23	=	=	SYM
ejpam-4755	219	24	5	5	NUM
ejpam-4755	219	25	,	,	PUNCT
ejpam-4755	219	26	w	w	NOUN
ejpam-4755	219	27	=	=	SYM
ejpam-4755	219	28	3	3	NUM
ejpam-4755	219	29	,	,	PUNCT
ejpam-4755	219	30	p	p	NOUN
ejpam-4755	219	31	=	=	SYM
ejpam-4755	219	32	2w	2w	NUM
ejpam-4755	219	33	+	+	CCONJ
ejpam-4755	219	34	1	1	NUM
ejpam-4755	219	35	=	=	SYM
ejpam-4755	219	36	7	7	NUM
ejpam-4755	219	37	three	three	NUM
ejpam-4755	219	38	squarefree	squarefree	ADJ
ejpam-4755	219	39	prime	prime	ADJ
ejpam-4755	219	40	numbers	number	NOUN
ejpam-4755	219	41	.	.	PUNCT
ejpam-4755	220	1	so	so	ADV
ejpam-4755	220	2	,	,	PUNCT
ejpam-4755	220	3	we	we	PRON
ejpam-4755	220	4	have	have	VERB
ejpam-4755	220	5	the	the	DET
ejpam-4755	220	6	conditions	condition	NOUN
ejpam-4755	220	7	and	and	CCONJ
ejpam-4755	220	8	notations	notation	NOUN
ejpam-4755	220	9	of	of	ADP
ejpam-4755	220	10	the	the	DET
ejpam-4755	220	11	group	group	NOUN
ejpam-4755	220	12	n	n	CCONJ
ejpam-4755	220	13	as	as	SCONJ
ejpam-4755	220	14	follow	follow	VERB
ejpam-4755	220	15	according	accord	VERB
ejpam-4755	220	16	to	to	ADP
ejpam-4755	220	17	the	the	DET
ejpam-4755	220	18	primes	prime	NOUN
ejpam-4755	220	19	above	above	ADV
ejpam-4755	220	20	.	.	PUNCT
ejpam-4755	221	1	q	q	NOUN
ejpam-4755	222	1	−	−	NOUN
ejpam-4755	222	2	1	1	NUM
ejpam-4755	222	3	=	=	SYM
ejpam-4755	222	4	2r.s	2r.s	NUM
ejpam-4755	222	5	,	,	PUNCT
ejpam-4755	222	6	r	r	NOUN
ejpam-4755	222	7	≥	≥	NOUN
ejpam-4755	222	8	1	1	NUM
ejpam-4755	222	9	,	,	PUNCT
ejpam-4755	222	10	s	s	VERB
ejpam-4755	222	11	odd	odd	ADJ
ejpam-4755	222	12	=	=	NOUN
ejpam-4755	222	13	⇒	⇒	NOUN
ejpam-4755	222	14	q	q	NOUN
ejpam-4755	222	15	−	−	PROPN
ejpam-4755	223	1	1	1	NUM
ejpam-4755	223	2	=	=	SYM
ejpam-4755	223	3	5	5	NUM
ejpam-4755	223	4	−	−	NOUN
ejpam-4755	223	5	1	1	NUM
ejpam-4755	223	6	=	=	SYM
ejpam-4755	223	7	4	4	NUM
ejpam-4755	223	8	=	=	SYM
ejpam-4755	223	9	22.1	22.1	NUM
ejpam-4755	223	10	=	=	NOUN
ejpam-4755	223	11	⇒	⇒	NOUN
ejpam-4755	223	12	r	r	NOUN
ejpam-4755	223	13	=	=	SYM
ejpam-4755	223	14	2	2	NUM
ejpam-4755	223	15	,	,	PUNCT
ejpam-4755	223	16	s	s	PART
ejpam-4755	223	17	=	=	ADJ
ejpam-4755	223	18	1	1	X
ejpam-4755	223	19	.	.	PUNCT
ejpam-4755	224	1	then	then	ADV
ejpam-4755	224	2	d	d	X
ejpam-4755	224	3	|	|	NOUN
ejpam-4755	224	4	s	s	AUX
ejpam-4755	224	5	has	have	VERB
ejpam-4755	224	6	d	d	NOUN
ejpam-4755	224	7	=	=	SYM
ejpam-4755	224	8	1	1	NUM
ejpam-4755	224	9	=	=	NOUN
ejpam-4755	224	10	⇒	⇒	NOUN
ejpam-4755	224	11	σ0(s	σ0(s	PRON
ejpam-4755	224	12	)	)	PUNCT
ejpam-4755	224	13	=	=	NOUN
ejpam-4755	225	1	1	1	X
ejpam-4755	225	2	.	.	PUNCT
ejpam-4755	226	1	w	w	NOUN
ejpam-4755	226	2	−	−	NOUN
ejpam-4755	226	3	1	1	NUM
ejpam-4755	226	4	=	=	SYM
ejpam-4755	226	5	2i.j	2i.j	NUM
ejpam-4755	226	6	,	,	PUNCT
ejpam-4755	226	7	i	i	PRON
ejpam-4755	226	8	≥	≥	VERB
ejpam-4755	226	9	1	1	NUM
ejpam-4755	226	10	,	,	PUNCT
ejpam-4755	227	1	j	j	PROPN
ejpam-4755	227	2	odd	odd	ADJ
ejpam-4755	227	3	=	=	VERB
ejpam-4755	227	4	⇒	⇒	NOUN
ejpam-4755	227	5	w	w	NOUN
ejpam-4755	227	6	−	−	NOUN
ejpam-4755	227	7	1	1	NUM
ejpam-4755	227	8	=	=	SYM
ejpam-4755	227	9	3−	3−	NUM
ejpam-4755	227	10	1	1	NUM
ejpam-4755	227	11	=	=	SYM
ejpam-4755	227	12	2	2	NUM
ejpam-4755	227	13	=	=	SYM
ejpam-4755	227	14	21.1	21.1	NUM
ejpam-4755	227	15	=	=	NOUN
ejpam-4755	227	16	⇒	⇒	VERB
ejpam-4755	227	17	i	i	NOUN
ejpam-4755	227	18	=	=	NOUN
ejpam-4755	227	19	1	1	NUM
ejpam-4755	227	20	,	,	PUNCT
ejpam-4755	227	21	j	j	NOUN
ejpam-4755	227	22	=	=	SYM
ejpam-4755	227	23	1	1	NUM
ejpam-4755	227	24	.	.	NOUN
ejpam-4755	227	25	0	0	NUM
ejpam-4755	227	26	≤	≤	NUM
ejpam-4755	227	27	c1	c1	NOUN
ejpam-4755	227	28	≤	≤	PROPN
ejpam-4755	227	29	r	r	NOUN
ejpam-4755	227	30	=	=	NOUN
ejpam-4755	227	31	⇒	⇒	NOUN
ejpam-4755	227	32	0	0	NUM
ejpam-4755	227	33	≤	≤	ADJ
ejpam-4755	227	34	c1	c1	PROPN
ejpam-4755	227	35	≤	≤	ADV
ejpam-4755	227	36	2	2	NUM
ejpam-4755	227	37	that	that	PRON
ejpam-4755	227	38	means	mean	VERB
ejpam-4755	227	39	c1	c1	PROPN
ejpam-4755	227	40	=	=	PROPN
ejpam-4755	227	41	0	0	PROPN
ejpam-4755	227	42	,	,	PUNCT
ejpam-4755	227	43	1	1	NUM
ejpam-4755	227	44	,	,	PUNCT
ejpam-4755	227	45	2	2	NUM
ejpam-4755	227	46	.	.	PUNCT
ejpam-4755	227	47	b.	b.	PROPN
ejpam-4755	227	48	jamal	jamal	PROPN
ejpam-4755	227	49	,	,	PUNCT
ejpam-4755	227	50	a.	a.	PROPN
ejpam-4755	227	51	alabdali	alabdali	VERB
ejpam-4755	227	52	/	/	SYM
ejpam-4755	227	53	eur	eur	PROPN
ejpam-4755	227	54	.	.	PUNCT
ejpam-4755	228	1	j.	j.	PROPN
ejpam-4755	228	2	pure	pure	PROPN
ejpam-4755	228	3	appl	appl	PROPN
ejpam-4755	228	4	.	.	PROPN
ejpam-4755	228	5	math	math	PROPN
ejpam-4755	228	6	,	,	PUNCT
ejpam-4755	228	7	16	16	NUM
ejpam-4755	228	8	(	(	PUNCT
ejpam-4755	228	9	2	2	NUM
ejpam-4755	228	10	)	)	PUNCT
ejpam-4755	228	11	(	(	PUNCT
ejpam-4755	228	12	2023	2023	NUM
ejpam-4755	228	13	)	)	PUNCT
ejpam-4755	228	14	,	,	PUNCT
ejpam-4755	228	15	1118	1118	NUM
ejpam-4755	228	16	-	-	SYM
ejpam-4755	228	17	1127	1127	NUM
ejpam-4755	228	18	1125	1125	NUM
ejpam-4755	228	19	1	1	NUM
ejpam-4755	228	20	≤	≤	NUM
ejpam-4755	228	21	l	l	NOUN
ejpam-4755	228	22	≤	≤	NUM
ejpam-4755	229	1	w	w	ADP
ejpam-4755	229	2	−	−	NUM
ejpam-4755	229	3	1	1	NUM
ejpam-4755	229	4	=	=	NOUN
ejpam-4755	229	5	⇒	⇒	ADJ
ejpam-4755	229	6	1	1	NUM
ejpam-4755	229	7	≤	≤	NUM
ejpam-4755	229	8	l	l	NOUN
ejpam-4755	229	9	≤	≤	NUM
ejpam-4755	229	10	2	2	NUM
ejpam-4755	229	11	that	that	PRON
ejpam-4755	229	12	means	mean	VERB
ejpam-4755	229	13	l	l	NOUN
ejpam-4755	229	14	=	=	SYM
ejpam-4755	229	15	1	1	NUM
ejpam-4755	229	16	,	,	PUNCT
ejpam-4755	229	17	2	2	NUM
ejpam-4755	229	18	.	.	PUNCT
ejpam-4755	229	19	as	as	ADP
ejpam-4755	229	20	a	a	DET
ejpam-4755	229	21	result	result	NOUN
ejpam-4755	229	22	of	of	ADP
ejpam-4755	229	23	these	these	DET
ejpam-4755	229	24	conditions	condition	NOUN
ejpam-4755	229	25	,	,	PUNCT
ejpam-4755	229	26	table	table	NOUN
ejpam-4755	229	27	1	1	NUM
ejpam-4755	229	28	and	and	CCONJ
ejpam-4755	229	29	table	table	NOUN
ejpam-4755	229	30	3	3	NUM
ejpam-4755	229	31	have	have	VERB
ejpam-4755	229	32	the	the	DET
ejpam-4755	229	33	following	follow	VERB
ejpam-4755	229	34	shape	shape	NOUN
ejpam-4755	229	35	.	.	PUNCT
ejpam-4755	230	1	table	table	NOUN
ejpam-4755	230	2	4	4	NUM
ejpam-4755	230	3	:	:	PUNCT
ejpam-4755	230	4	the	the	DET
ejpam-4755	230	5	transitive	transitive	ADJ
ejpam-4755	230	6	subgroups	subgroup	NOUN
ejpam-4755	230	7	for	for	ADP
ejpam-4755	230	8	the	the	DET
ejpam-4755	230	9	nonabelian	nonabelian	ADJ
ejpam-4755	230	10	group	group	NOUN
ejpam-4755	230	11	jl	jl	NOUN
ejpam-4755	230	12	when	when	SCONJ
ejpam-4755	230	13	p	p	PROPN
ejpam-4755	230	14	=	=	NOUN
ejpam-4755	230	15	7	7	NUM
ejpam-4755	230	16	,	,	PUNCT
ejpam-4755	230	17	q	q	NOUN
ejpam-4755	230	18	=	=	SYM
ejpam-4755	230	19	5	5	NUM
ejpam-4755	230	20	,	,	PUNCT
ejpam-4755	230	21	w	w	NOUN
ejpam-4755	230	22	=	=	SYM
ejpam-4755	230	23	3	3	X
ejpam-4755	230	24	.	.	PUNCT
ejpam-4755	230	25	key	key	ADJ
ejpam-4755	230	26	order	order	NOUN
ejpam-4755	230	27	parameters	parameter	NOUN
ejpam-4755	230	28	#	#	NOUN
ejpam-4755	230	29	groups	group	NOUN
ejpam-4755	230	30	groups	group	NOUN
ejpam-4755	230	31	1	1	NUM
ejpam-4755	230	32	105	105	NUM
ejpam-4755	230	33	l	l	NOUN
ejpam-4755	230	34	=	=	SYM
ejpam-4755	230	35	1	1	NUM
ejpam-4755	230	36	,	,	PUNCT
ejpam-4755	230	37	2	2	NUM
ejpam-4755	230	38	2	2	NUM
ejpam-4755	230	39	j1	j1	NOUN
ejpam-4755	230	40	,	,	PUNCT
ejpam-4755	230	41	j2	j2	NOUN
ejpam-4755	230	42	2	2	NUM
ejpam-4755	230	43	210	210	NUM
ejpam-4755	230	44	l	l	NOUN
ejpam-4755	230	45	=	=	SYM
ejpam-4755	230	46	1	1	NUM
ejpam-4755	230	47	,	,	PUNCT
ejpam-4755	230	48	2	2	NUM
ejpam-4755	230	49	2	2	NUM
ejpam-4755	230	50	j1	j1	PROPN
ejpam-4755	230	51	⋊	⋊	NUM
ejpam-4755	230	52	⟨β⟩	⟨β⟩	PROPN
ejpam-4755	230	53	,	,	PUNCT
ejpam-4755	231	1	j2	j2	PROPN
ejpam-4755	231	2	⋊	⋊	PROPN
ejpam-4755	231	3	⟨β⟩	⟨β⟩	PROPN
ejpam-4755	231	4	3	3	NUM
ejpam-4755	231	5	105	105	NUM
ejpam-4755	231	6	l	l	NOUN
ejpam-4755	231	7	=	=	SYM
ejpam-4755	231	8	1	1	NUM
ejpam-4755	231	9	,	,	PUNCT
ejpam-4755	231	10	2	2	NUM
ejpam-4755	231	11	,	,	PUNCT
ejpam-4755	231	12	c1	c1	NOUN
ejpam-4755	231	13	=	=	PUNCT
ejpam-4755	231	14	0	0	PROPN
ejpam-4755	231	15	,	,	PUNCT
ejpam-4755	231	16	1	1	NUM
ejpam-4755	231	17	,	,	PUNCT
ejpam-4755	231	18	2	2	NUM
ejpam-4755	231	19	6	6	NUM
ejpam-4755	231	20	j1	j1	PROPN
ejpam-4755	231	21	⋊	⋊	NUM
ejpam-4755	231	22	⟨γ4⟩	⟨γ4⟩	PROPN
ejpam-4755	231	23	,	,	PUNCT
ejpam-4755	231	24	j2	j2	PROPN
ejpam-4755	231	25	⋊	⋊	PROPN
ejpam-4755	231	26	⟨γ4⟩	⟨γ4⟩	PROPN
ejpam-4755	231	27	,	,	PUNCT
ejpam-4755	231	28	210	210	NUM
ejpam-4755	231	29	j1	j1	PROPN
ejpam-4755	231	30	⋊	⋊	NUM
ejpam-4755	231	31	⟨γ2⟩	⟨γ2⟩	PROPN
ejpam-4755	231	32	,	,	PUNCT
ejpam-4755	231	33	j2	j2	PROPN
ejpam-4755	231	34	⋊	⋊	PROPN
ejpam-4755	231	35	⟨γ2⟩	⟨γ2⟩	PROPN
ejpam-4755	231	36	,	,	PUNCT
ejpam-4755	231	37	420	420	NUM
ejpam-4755	231	38	j1	j1	PROPN
ejpam-4755	231	39	⋊	⋊	NUM
ejpam-4755	231	40	⟨γ⟩	⟨γ⟩	PROPN
ejpam-4755	231	41	,	,	PUNCT
ejpam-4755	231	42	j2	j2	PROPN
ejpam-4755	231	43	⋊	⋊	NUM
ejpam-4755	231	44	⟨γ⟩	⟨γ⟩	PROPN
ejpam-4755	231	45	4	4	NUM
ejpam-4755	231	46	105	105	NUM
ejpam-4755	231	47	l	l	NOUN
ejpam-4755	231	48	=	=	SYM
ejpam-4755	231	49	1	1	NUM
ejpam-4755	231	50	,	,	PUNCT
ejpam-4755	231	51	2	2	NUM
ejpam-4755	231	52	,	,	PUNCT
ejpam-4755	231	53	d	d	PROPN
ejpam-4755	231	54	|	|	NOUN
ejpam-4755	231	55	s	s	VERB
ejpam-4755	231	56	=	=	NOUN
ejpam-4755	231	57	1	1	NUM
ejpam-4755	231	58	|	|	NOUN
ejpam-4755	231	59	1	1	NUM
ejpam-4755	231	60	2	2	NUM
ejpam-4755	231	61	j1	j1	PROPN
ejpam-4755	231	62	⋊	⋊	NUM
ejpam-4755	231	63	⟨δ⟩	⟨δ⟩	PROPN
ejpam-4755	231	64	,	,	PUNCT
ejpam-4755	231	65	j2	j2	PROPN
ejpam-4755	231	66	⋊	⋊	PROPN
ejpam-4755	231	67	⟨δ⟩	⟨δ⟩	PROPN
ejpam-4755	231	68	table	table	NOUN
ejpam-4755	231	69	5	5	NUM
ejpam-4755	231	70	:	:	PUNCT
ejpam-4755	231	71	the	the	DET
ejpam-4755	231	72	number	number	NOUN
ejpam-4755	231	73	of	of	ADP
ejpam-4755	231	74	hgss	hgss	ADJ
ejpam-4755	231	75	for	for	ADP
ejpam-4755	231	76	the	the	DET
ejpam-4755	231	77	nonabelian	nonabelian	ADJ
ejpam-4755	231	78	group	group	NOUN
ejpam-4755	231	79	jl	jl	NOUN
ejpam-4755	231	80	when	when	SCONJ
ejpam-4755	231	81	p	p	PROPN
ejpam-4755	231	82	=	=	NOUN
ejpam-4755	231	83	7	7	NUM
ejpam-4755	231	84	,	,	PUNCT
ejpam-4755	231	85	q	q	NOUN
ejpam-4755	231	86	=	=	SYM
ejpam-4755	231	87	5	5	NUM
ejpam-4755	231	88	,	,	PUNCT
ejpam-4755	231	89	w	w	NOUN
ejpam-4755	231	90	=	=	SYM
ejpam-4755	231	91	3	3	X
ejpam-4755	231	92	.	.	PUNCT
ejpam-4755	231	93	key	key	ADJ
ejpam-4755	231	94	order	order	NOUN
ejpam-4755	231	95	|	|	CCONJ
ejpam-4755	231	96	aut(b	aut(b	NOUN
ejpam-4755	231	97	,	,	PUNCT
ejpam-4755	231	98	b′	b′	NUM
ejpam-4755	231	99	)	)	PUNCT
ejpam-4755	231	100	|	|	ADV
ejpam-4755	231	101	#	#	NOUN
ejpam-4755	231	102	iso	iso	NOUN
ejpam-4755	231	103	.	.	PUNCT
ejpam-4755	232	1	class	class	NOUN
ejpam-4755	232	2	#	#	NOUN
ejpam-4755	232	3	hgs	hgs	NOUN
ejpam-4755	232	4	per	per	ADP
ejpam-4755	232	5	iso	iso	NOUN
ejpam-4755	232	6	.	.	PUNCT
ejpam-4755	233	1	class	class	NOUN
ejpam-4755	233	2	1	1	NUM
ejpam-4755	233	3	105	105	NUM
ejpam-4755	233	4	600	600	NUM
ejpam-4755	233	5	1	1	NUM
ejpam-4755	233	6	25	25	NUM
ejpam-4755	233	7	2	2	NUM
ejpam-4755	233	8	210	210	NUM
ejpam-4755	233	9	24	24	NUM
ejpam-4755	233	10	1	1	NUM
ejpam-4755	233	11	1	1	NUM
ejpam-4755	233	12	3	3	NUM
ejpam-4755	233	13	105	105	NUM
ejpam-4755	233	14	,	,	PUNCT
ejpam-4755	233	15	210	210	NUM
ejpam-4755	233	16	,	,	PUNCT
ejpam-4755	233	17	420	420	NUM
ejpam-4755	233	18	24	24	NUM
ejpam-4755	233	19	3	3	NUM
ejpam-4755	233	20	3	3	NUM
ejpam-4755	233	21	4	4	NUM
ejpam-4755	233	22	105	105	NUM
ejpam-4755	233	23	24	24	NUM
ejpam-4755	233	24	1	1	NUM
ejpam-4755	233	25	1	1	NUM
ejpam-4755	233	26	we	we	PRON
ejpam-4755	233	27	can	can	AUX
ejpam-4755	233	28	see	see	VERB
ejpam-4755	233	29	from	from	ADP
ejpam-4755	233	30	theorem	theorem	ADJ
ejpam-4755	233	31	4	4	NUM
ejpam-4755	233	32	that	that	SCONJ
ejpam-4755	233	33	there	there	PRON
ejpam-4755	233	34	is	be	VERB
ejpam-4755	233	35	6	6	NUM
ejpam-4755	233	36	isomorphism	isomorphism	NOUN
ejpam-4755	233	37	types	type	NOUN
ejpam-4755	233	38	admits	admit	VERB
ejpam-4755	233	39	nonabelian	nonabelian	ADJ
ejpam-4755	233	40	hgss	hgss	ADJ
ejpam-4755	233	41	of	of	ADP
ejpam-4755	233	42	pgs	pgs	NOUN
ejpam-4755	233	43	of	of	ADP
ejpam-4755	233	44	degree	degree	NOUN
ejpam-4755	233	45	105	105	NUM
ejpam-4755	233	46	.	.	PUNCT
ejpam-4755	234	1	according	accord	VERB
ejpam-4755	234	2	to	to	ADP
ejpam-4755	234	3	the	the	DET
ejpam-4755	234	4	results	result	NOUN
ejpam-4755	234	5	obtained	obtain	VERB
ejpam-4755	234	6	in	in	ADP
ejpam-4755	234	7	theorem	theorem	NOUN
ejpam-4755	234	8	5	5	NUM
ejpam-4755	234	9	,	,	PUNCT
ejpam-4755	234	10	a	a	DET
ejpam-4755	234	11	hgs	hgs	NOUN
ejpam-4755	234	12	of	of	ADP
ejpam-4755	234	13	cyclic	cyclic	ADJ
ejpam-4755	234	14	type	type	NOUN
ejpam-4755	234	15	can	can	AUX
ejpam-4755	234	16	realise	realise	VERB
ejpam-4755	234	17	150	150	NUM
ejpam-4755	234	18	isomorphism	isomorphism	NOUN
ejpam-4755	234	19	types	type	NOUN
ejpam-4755	234	20	of	of	ADP
ejpam-4755	234	21	pgs	pgs	ADJ
ejpam-4755	234	22	g	g	NOUN
ejpam-4755	234	23	of	of	ADP
ejpam-4755	234	24	degree	degree	NOUN
ejpam-4755	234	25	105	105	NUM
ejpam-4755	234	26	of	of	ADP
ejpam-4755	234	27	both	both	DET
ejpam-4755	234	28	cases	case	NOUN
ejpam-4755	234	29	regular	regular	ADJ
ejpam-4755	234	30	groups	group	NOUN
ejpam-4755	234	31	(	(	PUNCT
ejpam-4755	234	32	cyclic	cyclic	ADJ
ejpam-4755	234	33	and	and	CCONJ
ejpam-4755	234	34	nonabelian	nonabelian	ADJ
ejpam-4755	234	35	)	)	PUNCT
ejpam-4755	234	36	,	,	PUNCT
ejpam-4755	234	37	where	where	SCONJ
ejpam-4755	234	38	the	the	DET
ejpam-4755	234	39	extension	extension	NOUN
ejpam-4755	234	40	has	have	VERB
ejpam-4755	234	41	1	1	NUM
ejpam-4755	234	42	hgs	hgs	NOUN
ejpam-4755	234	43	for	for	ADP
ejpam-4755	234	44	the	the	DET
ejpam-4755	234	45	cyclic	cyclic	ADJ
ejpam-4755	234	46	groups	group	NOUN
ejpam-4755	234	47	and	and	CCONJ
ejpam-4755	234	48	25	25	NUM
ejpam-4755	234	49	,	,	PUNCT
ejpam-4755	234	50	1	1	NUM
ejpam-4755	234	51	,	,	PUNCT
ejpam-4755	234	52	3	3	NUM
ejpam-4755	234	53	,	,	PUNCT
ejpam-4755	234	54	1	1	NUM
ejpam-4755	234	55	hgss	hgss	ADJ
ejpam-4755	234	56	for	for	ADP
ejpam-4755	234	57	the	the	DET
ejpam-4755	234	58	nonabelian	nonabelian	ADJ
ejpam-4755	234	59	groups	group	NOUN
ejpam-4755	234	60	of	of	ADP
ejpam-4755	234	61	the	the	DET
ejpam-4755	234	62	cyclic	cyclic	ADJ
ejpam-4755	234	63	type	type	NOUN
ejpam-4755	234	64	.	.	PUNCT
ejpam-4755	235	1	4	4	X
ejpam-4755	235	2	.	.	X
ejpam-4755	235	3	discussion	discussion	NOUN
ejpam-4755	235	4	comparing	compare	VERB
ejpam-4755	235	5	the	the	DET
ejpam-4755	235	6	work	work	NOUN
ejpam-4755	235	7	to	to	ADP
ejpam-4755	235	8	the	the	DET
ejpam-4755	235	9	results	result	NOUN
ejpam-4755	235	10	of	of	ADP
ejpam-4755	235	11	other	other	ADJ
ejpam-4755	235	12	references	reference	NOUN
ejpam-4755	235	13	,	,	PUNCT
ejpam-4755	235	14	we	we	PRON
ejpam-4755	235	15	can	can	AUX
ejpam-4755	235	16	see	see	VERB
ejpam-4755	235	17	from	from	ADP
ejpam-4755	235	18	the	the	DET
ejpam-4755	235	19	tables	table	NOUN
ejpam-4755	235	20	and	and	CCONJ
ejpam-4755	235	21	results	result	VERB
ejpam-4755	235	22	that	that	SCONJ
ejpam-4755	235	23	similar	similar	ADJ
ejpam-4755	235	24	behaviour	behaviour	NOUN
ejpam-4755	235	25	exists	exist	VERB
ejpam-4755	235	26	for	for	ADP
ejpam-4755	235	27	square	square	ADJ
ejpam-4755	235	28	free	free	ADJ
ejpam-4755	235	29	degree	degree	NOUN
ejpam-4755	235	30	n	n	NOUN
ejpam-4755	235	31	=	=	SYM
ejpam-4755	235	32	pqw	pqw	NOUN
ejpam-4755	235	33	as	as	ADP
ejpam-4755	235	34	the	the	DET
ejpam-4755	235	35	field	field	NOUN
ejpam-4755	235	36	extension	extension	NOUN
ejpam-4755	235	37	of	of	ADP
ejpam-4755	235	38	degree	degree	NOUN
ejpam-4755	235	39	n	n	NOUN
ejpam-4755	235	40	=	=	SYM
ejpam-4755	235	41	pq	pq	NOUN
ejpam-4755	235	42	in	in	ADP
ejpam-4755	235	43	[	[	X
ejpam-4755	235	44	6	6	NUM
ejpam-4755	235	45	]	]	PUNCT
ejpam-4755	235	46	.	.	PUNCT
ejpam-4755	236	1	it	it	PRON
ejpam-4755	236	2	is	be	AUX
ejpam-4755	236	3	clear	clear	ADJ
ejpam-4755	236	4	through	through	ADP
ejpam-4755	236	5	tables	table	NOUN
ejpam-4755	236	6	1	1	NUM
ejpam-4755	236	7	,	,	PUNCT
ejpam-4755	236	8	2	2	NUM
ejpam-4755	236	9	and	and	CCONJ
ejpam-4755	236	10	3	3	NUM
ejpam-4755	236	11	that	that	SCONJ
ejpam-4755	236	12	no	no	DET
ejpam-4755	236	13	similar	similar	ADJ
ejpam-4755	236	14	abstract	abstract	ADJ
ejpam-4755	236	15	group	group	NOUN
ejpam-4755	236	16	can	can	AUX
ejpam-4755	236	17	be	be	AUX
ejpam-4755	236	18	found	find	VERB
ejpam-4755	236	19	for	for	SCONJ
ejpam-4755	236	20	any	any	DET
ejpam-4755	236	21	two	two	NUM
ejpam-4755	236	22	distinct	distinct	ADJ
ejpam-4755	236	23	pgs	pgs	NOUN
ejpam-4755	236	24	admitted	admit	VERB
ejpam-4755	236	25	hgss	hgss	ADV
ejpam-4755	236	26	.	.	PUNCT
ejpam-4755	237	1	thus	thus	ADV
ejpam-4755	237	2	we	we	PRON
ejpam-4755	237	3	partially	partially	ADV
ejpam-4755	237	4	answer	answer	VERB
ejpam-4755	237	5	the	the	DET
ejpam-4755	237	6	question	question	NOUN
ejpam-4755	237	7	in	in	ADP
ejpam-4755	237	8	[	[	X
ejpam-4755	237	9	6	6	NUM
ejpam-4755	237	10	]	]	PUNCT
ejpam-4755	237	11	related	relate	VERB
ejpam-4755	237	12	to	to	ADP
ejpam-4755	237	13	the	the	DET
ejpam-4755	237	14	behaviour	behaviour	NOUN
ejpam-4755	237	15	of	of	ADP
ejpam-4755	237	16	square	square	ADJ
ejpam-4755	237	17	free	free	ADJ
ejpam-4755	237	18	degree	degree	NOUN
ejpam-4755	237	19	in	in	ADP
ejpam-4755	237	20	general	general	ADJ
ejpam-4755	237	21	.	.	PUNCT
ejpam-4755	238	1	5	5	X
ejpam-4755	238	2	.	.	X
ejpam-4755	238	3	conclusion	conclusion	NOUN
ejpam-4755	238	4	we	we	PRON
ejpam-4755	238	5	investigate	investigate	VERB
ejpam-4755	238	6	the	the	DET
ejpam-4755	238	7	group	group	NOUN
ejpam-4755	238	8	permutations	permutation	NOUN
ejpam-4755	238	9	g	g	NOUN
ejpam-4755	238	10	for	for	ADP
ejpam-4755	238	11	the	the	DET
ejpam-4755	238	12	nonabelian	nonabelian	ADJ
ejpam-4755	238	13	case	case	NOUN
ejpam-4755	238	14	of	of	ADP
ejpam-4755	238	15	degree	degree	NOUN
ejpam-4755	238	16	pqw	pqw	NOUN
ejpam-4755	238	17	where	where	SCONJ
ejpam-4755	238	18	q	q	X
ejpam-4755	238	19	,	,	PUNCT
ejpam-4755	238	20	w	w	PROPN
ejpam-4755	238	21	≥	≥	NOUN
ejpam-4755	238	22	3	3	NUM
ejpam-4755	238	23	and	and	CCONJ
ejpam-4755	238	24	p	p	NOUN
ejpam-4755	238	25	=	=	SYM
ejpam-4755	238	26	2w	2w	NUM
ejpam-4755	239	1	+	+	CCONJ
ejpam-4755	239	2	1	1	NUM
ejpam-4755	239	3	are	be	AUX
ejpam-4755	239	4	all	all	PRON
ejpam-4755	239	5	square	square	ADJ
ejpam-4755	239	6	free	free	ADJ
ejpam-4755	239	7	primes	prime	NOUN
ejpam-4755	239	8	then	then	ADV
ejpam-4755	239	9	for	for	ADP
ejpam-4755	239	10	each	each	DET
ejpam-4755	239	11	g	g	NOUN
ejpam-4755	239	12	we	we	PRON
ejpam-4755	239	13	enumerate	enumerate	VERB
ejpam-4755	239	14	the	the	DET
ejpam-4755	239	15	hgss	hgss	ADJ
ejpam-4755	239	16	.	.	PUNCT
ejpam-4755	240	1	there	there	PRON
ejpam-4755	240	2	exists	exist	VERB
ejpam-4755	240	3	four	four	NUM
ejpam-4755	240	4	g	g	NOUN
ejpam-4755	240	5	such	such	ADJ
ejpam-4755	240	6	that	that	SCONJ
ejpam-4755	240	7	the	the	DET
ejpam-4755	240	8	field	field	NOUN
ejpam-4755	240	9	extensions	extension	NOUN
ejpam-4755	240	10	l	l	PROPN
ejpam-4755	240	11	/	/	SYM
ejpam-4755	240	12	k	k	PROPN
ejpam-4755	240	13	admit	admit	VERB
ejpam-4755	240	14	the	the	DET
ejpam-4755	240	15	hgss	hgss	ADJ
ejpam-4755	240	16	in	in	ADP
ejpam-4755	240	17	this	this	DET
ejpam-4755	240	18	case	case	NOUN
ejpam-4755	240	19	.	.	PUNCT
ejpam-4755	241	1	furthermore	furthermore	ADV
ejpam-4755	241	2	,	,	PUNCT
ejpam-4755	241	3	we	we	PRON
ejpam-4755	241	4	have	have	AUX
ejpam-4755	241	5	obtained	obtain	VERB
ejpam-4755	241	6	the	the	DET
ejpam-4755	241	7	total	total	ADJ
ejpam-4755	241	8	number	number	NOUN
ejpam-4755	241	9	of	of	ADP
ejpam-4755	241	10	hgss	hgss	ADJ
ejpam-4755	241	11	of	of	ADP
ejpam-4755	241	12	nonabelian	nonabelian	ADJ
ejpam-4755	241	13	case	case	NOUN
ejpam-4755	241	14	as	as	ADP
ejpam-4755	241	15	2	2	NUM
ejpam-4755	241	16	+	+	CCONJ
ejpam-4755	241	17	(	(	PUNCT
ejpam-4755	241	18	r	r	NOUN
ejpam-4755	241	19	+	+	NOUN
ejpam-4755	241	20	1	1	NUM
ejpam-4755	241	21	)	)	PUNCT
ejpam-4755	242	1	+	+	NOUN
ejpam-4755	242	2	σ0(s	σ0(s	X
ejpam-4755	242	3	)	)	PUNCT
ejpam-4755	242	4	of	of	ADP
ejpam-4755	242	5	pgs	pgs	ADJ
ejpam-4755	242	6	g	g	NOUN
ejpam-4755	242	7	of	of	ADP
ejpam-4755	242	8	types	type	NOUN
ejpam-4755	242	9	of	of	ADP
ejpam-4755	242	10	isomorphism	isomorphism	NOUN
ejpam-4755	242	11	of	of	ADP
ejpam-4755	242	12	degree	degree	NOUN
ejpam-4755	242	13	pqw	pqw	NOUN
ejpam-4755	243	1	and	and	CCONJ
ejpam-4755	243	2	we	we	PRON
ejpam-4755	243	3	have	have	AUX
ejpam-4755	243	4	found	find	VERB
ejpam-4755	243	5	references	reference	NOUN
ejpam-4755	243	6	1126	1126	NUM
ejpam-4755	243	7	the	the	DET
ejpam-4755	243	8	number	number	NOUN
ejpam-4755	243	9	of	of	ADP
ejpam-4755	243	10	both	both	DET
ejpam-4755	243	11	cases	case	NOUN
ejpam-4755	243	12	(	(	PUNCT
ejpam-4755	243	13	nonabelian	nonabelian	ADJ
ejpam-4755	243	14	and	and	CCONJ
ejpam-4755	243	15	cyclic	cyclic	ADJ
ejpam-4755	243	16	)	)	PUNCT
ejpam-4755	243	17	in	in	ADP
ejpam-4755	243	18	total	total	NOUN
ejpam-4755	243	19	as	as	ADP
ejpam-4755	243	20	12(r+	12(r+	NUM
ejpam-4755	243	21	i+	i+	NUM
ejpam-4755	243	22	1)[σ0(s	1)[σ0(s	NUM
ejpam-4755	243	23	)	)	PUNCT
ejpam-4755	244	1	+	+	PUNCT
ejpam-4755	244	2	σ1(j	σ1(j	X
ejpam-4755	244	3	)	)	PUNCT
ejpam-4755	244	4	+	+	X
ejpam-4755	244	5	σ0(s)σ1(j	σ0(s)σ1(j	NOUN
ejpam-4755	244	6	)	)	PUNCT
ejpam-4755	244	7	]	]	PUNCT
ejpam-4755	245	1	+	+	CCONJ
ejpam-4755	245	2	2	2	NUM
ejpam-4755	245	3	+	+	CCONJ
ejpam-4755	245	4	(	(	PUNCT
ejpam-4755	245	5	r	r	NOUN
ejpam-4755	245	6	+	+	NOUN
ejpam-4755	245	7	1	1	NUM
ejpam-4755	245	8	)	)	PUNCT
ejpam-4755	245	9	+	+	NUM
ejpam-4755	245	10	σ0(s	σ0(s	X
ejpam-4755	245	11	)	)	PUNCT
ejpam-4755	245	12	pgs	pgs	NOUN
ejpam-4755	245	13	of	of	ADP
ejpam-4755	245	14	isomorphism	isomorphism	NOUN
ejpam-4755	245	15	types	type	NOUN
ejpam-4755	245	16	which	which	PRON
ejpam-4755	245	17	admit	admit	VERB
ejpam-4755	245	18	hgss	hgss	ADJ
ejpam-4755	245	19	.	.	PUNCT
ejpam-4755	246	1	finally	finally	ADV
ejpam-4755	246	2	,	,	PUNCT
ejpam-4755	246	3	we	we	PRON
ejpam-4755	246	4	have	have	AUX
ejpam-4755	246	5	found	find	VERB
ejpam-4755	246	6	that	that	SCONJ
ejpam-4755	246	7	any	any	DET
ejpam-4755	246	8	two	two	NUM
ejpam-4755	246	9	distinct	distinct	ADJ
ejpam-4755	246	10	pgs	pgs	NOUN
ejpam-4755	246	11	admitted	admit	VERB
ejpam-4755	246	12	hgss	hgss	ADJ
ejpam-4755	246	13	can	can	AUX
ejpam-4755	246	14	not	not	PART
ejpam-4755	246	15	have	have	VERB
ejpam-4755	246	16	the	the	DET
ejpam-4755	246	17	same	same	ADJ
ejpam-4755	246	18	abstract	abstract	ADJ
ejpam-4755	246	19	group	group	NOUN
ejpam-4755	246	20	.	.	PUNCT
ejpam-4755	247	1	acknowledgements	acknowledgement	NOUN
ejpam-4755	247	2	we	we	PRON
ejpam-4755	247	3	would	would	AUX
ejpam-4755	247	4	like	like	VERB
ejpam-4755	247	5	to	to	PART
ejpam-4755	247	6	thank	thank	VERB
ejpam-4755	247	7	and	and	CCONJ
ejpam-4755	247	8	appreciate	appreciate	VERB
ejpam-4755	247	9	the	the	DET
ejpam-4755	247	10	supporting	supporting	NOUN
ejpam-4755	247	11	of	of	ADP
ejpam-4755	247	12	university	university	NOUN
ejpam-4755	247	13	of	of	ADP
ejpam-4755	247	14	mosul	mosul	PROPN
ejpam-4755	247	15	and	and	CCONJ
ejpam-4755	247	16	the	the	DET
ejpam-4755	247	17	college	college	NOUN
ejpam-4755	247	18	of	of	ADP
ejpam-4755	247	19	education	education	NOUN
ejpam-4755	247	20	for	for	ADP
ejpam-4755	247	21	pure	pure	ADJ
ejpam-4755	247	22	science	science	NOUN
ejpam-4755	247	23	for	for	ADP
ejpam-4755	247	24	the	the	DET
ejpam-4755	247	25	scientific	scientific	ADJ
ejpam-4755	247	26	research	research	NOUN
ejpam-4755	247	27	and	and	CCONJ
ejpam-4755	247	28	researchers	researcher	NOUN
ejpam-4755	247	29	.	.	PUNCT
ejpam-4755	248	1	references	reference	NOUN
ejpam-4755	248	2	[	[	X
ejpam-4755	248	3	1	1	X
ejpam-4755	248	4	]	]	PUNCT
ejpam-4755	248	5	ali	ali	PROPN
ejpam-4755	248	6	a	a	DET
ejpam-4755	248	7	alabdali	alabdali	ADJ
ejpam-4755	248	8	and	and	CCONJ
ejpam-4755	248	9	nigel	nigel	PROPN
ejpam-4755	248	10	p	p	PROPN
ejpam-4755	248	11	byott	byott	PROPN
ejpam-4755	248	12	.	.	PUNCT
ejpam-4755	249	1	hopf	hopf	ADJ
ejpam-4755	249	2	-	-	PUNCT
ejpam-4755	249	3	galois	galois	NOUN
ejpam-4755	249	4	structures	structure	NOUN
ejpam-4755	249	5	of	of	ADP
ejpam-4755	249	6	squarefree	squarefree	NOUN
ejpam-4755	249	7	degree	degree	NOUN
ejpam-4755	249	8	.	.	PUNCT
ejpam-4755	250	1	journal	journal	NOUN
ejpam-4755	250	2	of	of	ADP
ejpam-4755	250	3	algebra	algebra	PROPN
ejpam-4755	250	4	,	,	PUNCT
ejpam-4755	250	5	559:58–86	559:58–86	NUM
ejpam-4755	250	6	,	,	PUNCT
ejpam-4755	250	7	2020	2020	NUM
ejpam-4755	250	8	.	.	PUNCT
ejpam-4755	251	1	[	[	X
ejpam-4755	251	2	2	2	NUM
ejpam-4755	251	3	]	]	X
ejpam-4755	251	4	david	david	PROPN
ejpam-4755	251	5	bachiller	bachiller	PROPN
ejpam-4755	251	6	.	.	PUNCT
ejpam-4755	251	7	counterexample	counterexample	PROPN
ejpam-4755	251	8	to	to	ADP
ejpam-4755	251	9	a	a	DET
ejpam-4755	251	10	conjecture	conjecture	NOUN
ejpam-4755	251	11	about	about	ADP
ejpam-4755	251	12	braces	brace	NOUN
ejpam-4755	251	13	.	.	PUNCT
ejpam-4755	252	1	journal	journal	NOUN
ejpam-4755	252	2	of	of	ADP
ejpam-4755	252	3	algebra	algebra	PROPN
ejpam-4755	252	4	,	,	PUNCT
ejpam-4755	252	5	453:160–176	453:160–176	NOUN
ejpam-4755	252	6	,	,	PUNCT
ejpam-4755	252	7	2016	2016	NUM
ejpam-4755	252	8	.	.	PUNCT
ejpam-4755	253	1	[	[	X
ejpam-4755	253	2	3	3	X
ejpam-4755	253	3	]	]	PUNCT
ejpam-4755	253	4	n	n	PRON
ejpam-4755	253	5	p	p	PROPN
ejpam-4755	253	6	byott	byott	NOUN
ejpam-4755	253	7	.	.	PUNCT
ejpam-4755	254	1	uniqueness	uniqueness	NOUN
ejpam-4755	254	2	of	of	ADP
ejpam-4755	254	3	hopf	hopf	ADJ
ejpam-4755	254	4	galois	galois	PROPN
ejpam-4755	254	5	structure	structure	NOUN
ejpam-4755	254	6	for	for	ADP
ejpam-4755	254	7	separable	separable	ADJ
ejpam-4755	254	8	field	field	NOUN
ejpam-4755	254	9	extensions	extension	NOUN
ejpam-4755	254	10	.	.	PUNCT
ejpam-4755	255	1	comm	comm	NOUN
ejpam-4755	255	2	.	.	PUNCT
ejpam-4755	256	1	algebra	algebra	PROPN
ejpam-4755	256	2	,	,	PUNCT
ejpam-4755	256	3	24(10):3217–3228	24(10):3217–3228	NUM
ejpam-4755	256	4	,	,	PUNCT
ejpam-4755	256	5	1996	1996	NUM
ejpam-4755	256	6	.	.	PUNCT
ejpam-4755	257	1	[	[	X
ejpam-4755	257	2	4	4	NUM
ejpam-4755	257	3	]	]	PUNCT
ejpam-4755	257	4	nigel	nigel	PROPN
ejpam-4755	257	5	p.	p.	PROPN
ejpam-4755	257	6	byott	byott	PROPN
ejpam-4755	257	7	.	.	PUNCT
ejpam-4755	258	1	hopf	hopf	ADJ
ejpam-4755	258	2	–	–	PUNCT
ejpam-4755	258	3	galois	galois	PROPN
ejpam-4755	258	4	structures	structure	NOUN
ejpam-4755	258	5	on	on	ADP
ejpam-4755	258	6	galois	galois	PROPN
ejpam-4755	258	7	field	field	NOUN
ejpam-4755	258	8	extensions	extension	NOUN
ejpam-4755	258	9	of	of	ADP
ejpam-4755	258	10	degree	degree	NOUN
ejpam-4755	258	11	pq	pq	PROPN
ejpam-4755	258	12	.	.	PROPN
ejpam-4755	258	13	journal	journal	PROPN
ejpam-4755	258	14	of	of	ADP
ejpam-4755	258	15	pure	pure	ADJ
ejpam-4755	258	16	and	and	CCONJ
ejpam-4755	258	17	applied	applied	ADJ
ejpam-4755	258	18	algebra	algebra	NOUN
ejpam-4755	258	19	,	,	PUNCT
ejpam-4755	258	20	188:45–57	188:45–57	NUM
ejpam-4755	258	21	,	,	PUNCT
ejpam-4755	258	22	2004	2004	NUM
ejpam-4755	258	23	.	.	PUNCT
ejpam-4755	259	1	[	[	X
ejpam-4755	259	2	5	5	NUM
ejpam-4755	259	3	]	]	PUNCT
ejpam-4755	259	4	nigel	nigel	PROPN
ejpam-4755	259	5	p	p	PROPN
ejpam-4755	259	6	byott	byott	PROPN
ejpam-4755	259	7	and	and	CCONJ
ejpam-4755	259	8	lindsay	lindsay	PROPN
ejpam-4755	259	9	n	n	PROPN
ejpam-4755	259	10	childs	childs	PROPN
ejpam-4755	259	11	.	.	PUNCT
ejpam-4755	260	1	fixed	fix	VERB
ejpam-4755	260	2	-	-	PUNCT
ejpam-4755	260	3	point	point	NOUN
ejpam-4755	260	4	free	free	ADJ
ejpam-4755	260	5	pairs	pair	NOUN
ejpam-4755	260	6	of	of	ADP
ejpam-4755	260	7	homomorphisms	homomorphism	NOUN
ejpam-4755	260	8	and	and	CCONJ
ejpam-4755	260	9	nonabelian	nonabelian	ADJ
ejpam-4755	260	10	hopf	hopf	ADJ
ejpam-4755	260	11	-	-	PUNCT
ejpam-4755	260	12	galois	galois	NOUN
ejpam-4755	260	13	structure	structure	NOUN
ejpam-4755	260	14	.	.	PUNCT
ejpam-4755	261	1	18:707–731	18:707–731	NUM
ejpam-4755	261	2	,	,	PUNCT
ejpam-4755	261	3	2012	2012	NUM
ejpam-4755	261	4	.	.	PUNCT
ejpam-4755	262	1	[	[	X
ejpam-4755	262	2	6	6	NUM
ejpam-4755	262	3	]	]	PUNCT
ejpam-4755	262	4	nigel	nigel	PROPN
ejpam-4755	262	5	p	p	PROPN
ejpam-4755	262	6	byott	byott	PROPN
ejpam-4755	262	7	and	and	CCONJ
ejpam-4755	262	8	isabel	isabel	PROPN
ejpam-4755	262	9	martin	martin	PROPN
ejpam-4755	262	10	-	-	PUNCT
ejpam-4755	262	11	lyons	lyons	PROPN
ejpam-4755	262	12	.	.	PUNCT
ejpam-4755	263	1	hopf	hopf	ADJ
ejpam-4755	263	2	-	-	PUNCT
ejpam-4755	263	3	galois	galois	NOUN
ejpam-4755	263	4	structures	structure	NOUN
ejpam-4755	263	5	on	on	ADP
ejpam-4755	263	6	non	non	ADJ
ejpam-4755	263	7	-	-	ADJ
ejpam-4755	263	8	normal	normal	ADJ
ejpam-4755	263	9	extensions	extension	NOUN
ejpam-4755	263	10	of	of	ADP
ejpam-4755	263	11	degree	degree	NOUN
ejpam-4755	263	12	related	relate	VERB
ejpam-4755	263	13	to	to	ADP
ejpam-4755	263	14	sophie	sophie	PROPN
ejpam-4755	263	15	germain	germain	PROPN
ejpam-4755	263	16	primes	prime	NOUN
ejpam-4755	263	17	.	.	PUNCT
ejpam-4755	264	1	journal	journal	NOUN
ejpam-4755	264	2	of	of	ADP
ejpam-4755	264	3	pure	pure	ADJ
ejpam-4755	264	4	and	and	CCONJ
ejpam-4755	264	5	applied	applied	ADJ
ejpam-4755	264	6	algebra	algebra	NOUN
ejpam-4755	264	7	,	,	PUNCT
ejpam-4755	264	8	226(3):106869	226(3):106869	PROPN
ejpam-4755	264	9	,	,	PUNCT
ejpam-4755	264	10	2022	2022	NUM
ejpam-4755	264	11	.	.	PUNCT
ejpam-4755	265	1	[	[	X
ejpam-4755	265	2	7	7	X
ejpam-4755	265	3	]	]	X
ejpam-4755	265	4	stephen	stephen	NOUN
ejpam-4755	265	5	u	u	PROPN
ejpam-4755	265	6	chase	chase	NOUN
ejpam-4755	265	7	and	and	CCONJ
ejpam-4755	265	8	moss	moss	NOUN
ejpam-4755	265	9	e	e	PROPN
ejpam-4755	265	10	sweedler	sweedler	NOUN
ejpam-4755	265	11	.	.	PUNCT
ejpam-4755	266	1	hopf	hopf	PROPN
ejpam-4755	266	2	algebras	algebras	PROPN
ejpam-4755	266	3	and	and	CCONJ
ejpam-4755	266	4	galois	galois	PROPN
ejpam-4755	266	5	theory	theory	NOUN
ejpam-4755	266	6	.	.	PUNCT
ejpam-4755	267	1	in	in	ADP
ejpam-4755	267	2	hopf	hopf	ADJ
ejpam-4755	267	3	algebras	algebra	NOUN
ejpam-4755	267	4	and	and	CCONJ
ejpam-4755	267	5	galois	galois	PROPN
ejpam-4755	267	6	theory	theory	NOUN
ejpam-4755	267	7	,	,	PUNCT
ejpam-4755	267	8	volume	volume	NOUN
ejpam-4755	267	9	97	97	NUM
ejpam-4755	267	10	,	,	PUNCT
ejpam-4755	267	11	pages	page	NOUN
ejpam-4755	267	12	52–83	52–83	NUM
ejpam-4755	267	13	.	.	PUNCT
ejpam-4755	267	14	springer	springer	NOUN
ejpam-4755	267	15	-	-	PUNCT
ejpam-4755	267	16	verlag	verlag	PROPN
ejpam-4755	267	17	,	,	PUNCT
ejpam-4755	267	18	berlin	berlin	PROPN
ejpam-4755	267	19	-	-	PUNCT
ejpam-4755	267	20	new	new	PROPN
ejpam-4755	267	21	york	york	PROPN
ejpam-4755	267	22	,	,	PUNCT
ejpam-4755	267	23	1969	1969	NUM
ejpam-4755	267	24	.	.	PUNCT
ejpam-4755	268	1	[	[	X
ejpam-4755	268	2	8	8	NUM
ejpam-4755	268	3	]	]	X
ejpam-4755	268	4	lindsay	lindsay	PROPN
ejpam-4755	268	5	childs	childs	PROPN
ejpam-4755	268	6	.	.	PUNCT
ejpam-4755	269	1	taming	tame	VERB
ejpam-4755	269	2	wild	wild	ADJ
ejpam-4755	269	3	extensions	extension	NOUN
ejpam-4755	269	4	:	:	PUNCT
ejpam-4755	269	5	hopf	hopf	ADJ
ejpam-4755	269	6	algebras	algebra	NOUN
ejpam-4755	269	7	and	and	CCONJ
ejpam-4755	269	8	local	local	ADJ
ejpam-4755	269	9	galois	galois	PROPN
ejpam-4755	269	10	module	module	NOUN
ejpam-4755	269	11	theory	theory	NOUN
ejpam-4755	269	12	.	.	PUNCT
ejpam-4755	270	1	number	number	NOUN
ejpam-4755	270	2	80	80	NUM
ejpam-4755	270	3	.	.	PUNCT
ejpam-4755	271	1	american	american	PROPN
ejpam-4755	271	2	mathematical	mathematical	PROPN
ejpam-4755	271	3	soc	soc	PROPN
ejpam-4755	271	4	.	.	PUNCT
ejpam-4755	271	5	,	,	PUNCT
ejpam-4755	271	6	2000	2000	NUM
ejpam-4755	271	7	.	.	PUNCT
ejpam-4755	272	1	[	[	X
ejpam-4755	272	2	9	9	NUM
ejpam-4755	272	3	]	]	X
ejpam-4755	272	4	lindsay	lindsay	PROPN
ejpam-4755	272	5	n	n	PROPN
ejpam-4755	272	6	childs	childs	PROPN
ejpam-4755	272	7	.	.	PUNCT
ejpam-4755	273	1	on	on	ADP
ejpam-4755	273	2	the	the	DET
ejpam-4755	273	3	hopf	hopf	ADJ
ejpam-4755	273	4	galois	galois	PROPN
ejpam-4755	273	5	theory	theory	NOUN
ejpam-4755	273	6	for	for	ADP
ejpam-4755	273	7	separable	separable	ADJ
ejpam-4755	273	8	field	field	NOUN
ejpam-4755	273	9	extensions	extension	NOUN
ejpam-4755	273	10	.	.	PUNCT
ejpam-4755	274	1	comm	comm	NOUN
ejpam-4755	274	2	.	.	PUNCT
ejpam-4755	275	1	algebra	algebra	PROPN
ejpam-4755	275	2	,	,	PUNCT
ejpam-4755	275	3	17(4):809–825	17(4):809–825	PROPN
ejpam-4755	275	4	,	,	PUNCT
ejpam-4755	275	5	1989	1989	NUM
ejpam-4755	275	6	.	.	PUNCT
ejpam-4755	276	1	[	[	X
ejpam-4755	276	2	10	10	NUM
ejpam-4755	276	3	]	]	X
ejpam-4755	276	4	lindsay	lindsay	PROPN
ejpam-4755	276	5	n	n	PROPN
ejpam-4755	276	6	childs	child	VERB
ejpam-4755	276	7	.	.	PUNCT
ejpam-4755	277	1	on	on	ADP
ejpam-4755	277	2	hopf	hopf	ADJ
ejpam-4755	277	3	galois	galois	PROPN
ejpam-4755	277	4	structures	structure	NOUN
ejpam-4755	277	5	and	and	CCONJ
ejpam-4755	277	6	complete	complete	ADJ
ejpam-4755	277	7	groups	group	NOUN
ejpam-4755	277	8	.	.	PUNCT
ejpam-4755	278	1	new	new	PROPN
ejpam-4755	278	2	york	york	PROPN
ejpam-4755	278	3	journal	journal	PROPN
ejpam-4755	278	4	of	of	ADP
ejpam-4755	278	5	mathematics	mathematic	NOUN
ejpam-4755	278	6	,	,	PUNCT
ejpam-4755	278	7	9:99–115	9:99–115	NUM
ejpam-4755	278	8	,	,	PUNCT
ejpam-4755	278	9	2003	2003	NUM
ejpam-4755	278	10	.	.	PUNCT
ejpam-4755	279	1	[	[	X
ejpam-4755	279	2	11	11	NUM
ejpam-4755	279	3	]	]	X
ejpam-4755	279	4	lindsay	lindsay	PROPN
ejpam-4755	279	5	n	n	PROPN
ejpam-4755	279	6	childs	childs	PROPN
ejpam-4755	279	7	.	.	PUNCT
ejpam-4755	280	1	elementary	elementary	PROPN
ejpam-4755	280	2	abelian	abelian	PROPN
ejpam-4755	280	3	hopf	hopf	PROPN
ejpam-4755	280	4	galois	galois	PROPN
ejpam-4755	280	5	structures	structure	NOUN
ejpam-4755	280	6	and	and	CCONJ
ejpam-4755	280	7	polynomial	polynomial	ADJ
ejpam-4755	280	8	formal	formal	ADJ
ejpam-4755	280	9	groups	group	NOUN
ejpam-4755	280	10	.	.	PUNCT
ejpam-4755	281	1	journal	journal	NOUN
ejpam-4755	281	2	of	of	ADP
ejpam-4755	281	3	algebra	algebra	PROPN
ejpam-4755	281	4	,	,	PUNCT
ejpam-4755	281	5	283(1):292–316	283(1):292–316	NUM
ejpam-4755	281	6	,	,	PUNCT
ejpam-4755	281	7	2005	2005	NUM
ejpam-4755	281	8	.	.	PUNCT
ejpam-4755	282	1	references	reference	NOUN
ejpam-4755	282	2	1127	1127	NUM
ejpam-4755	282	3	[	[	X
ejpam-4755	282	4	12	12	NUM
ejpam-4755	282	5	]	]	X
ejpam-4755	282	6	teresa	teresa	PROPN
ejpam-4755	282	7	crespo	crespo	PROPN
ejpam-4755	282	8	,	,	PUNCT
ejpam-4755	282	9	anna	anna	PROPN
ejpam-4755	282	10	rio	rio	PROPN
ejpam-4755	282	11	,	,	PUNCT
ejpam-4755	282	12	and	and	CCONJ
ejpam-4755	282	13	montserrat	montserrat	PROPN
ejpam-4755	282	14	vela	vela	PROPN
ejpam-4755	282	15	.	.	PUNCT
ejpam-4755	283	1	induced	induce	VERB
ejpam-4755	283	2	hopf	hopf	ADJ
ejpam-4755	283	3	galois	galois	PROPN
ejpam-4755	283	4	structures	structure	NOUN
ejpam-4755	283	5	.	.	PUNCT
ejpam-4755	284	1	journal	journal	NOUN
ejpam-4755	284	2	of	of	ADP
ejpam-4755	284	3	algebra	algebra	PROPN
ejpam-4755	284	4	,	,	PUNCT
ejpam-4755	284	5	457:312–322	457:312–322	NUM
ejpam-4755	284	6	,	,	PUNCT
ejpam-4755	284	7	2016	2016	NUM
ejpam-4755	284	8	.	.	PUNCT
ejpam-4755	285	1	[	[	X
ejpam-4755	285	2	13	13	NUM
ejpam-4755	285	3	]	]	X
ejpam-4755	285	4	teresa	teresa	PROPN
ejpam-4755	285	5	crespo	crespo	PROPN
ejpam-4755	285	6	and	and	CCONJ
ejpam-4755	285	7	marta	marta	PROPN
ejpam-4755	285	8	salguero	salguero	PROPN
ejpam-4755	285	9	.	.	PUNCT
ejpam-4755	286	1	computation	computation	NOUN
ejpam-4755	286	2	of	of	ADP
ejpam-4755	286	3	hopf	hopf	ADJ
ejpam-4755	286	4	galois	galois	PROPN
ejpam-4755	286	5	structures	structure	NOUN
ejpam-4755	286	6	on	on	ADP
ejpam-4755	286	7	low	low	ADJ
ejpam-4755	286	8	degree	degree	NOUN
ejpam-4755	286	9	separable	separable	ADJ
ejpam-4755	286	10	extensions	extension	NOUN
ejpam-4755	286	11	and	and	CCONJ
ejpam-4755	286	12	classification	classification	NOUN
ejpam-4755	286	13	of	of	ADP
ejpam-4755	286	14	those	those	PRON
ejpam-4755	286	15	for	for	ADP
ejpam-4755	286	16	degrees	degree	NOUN
ejpam-4755	286	17	p2	p2	NOUN
ejpam-4755	286	18	and	and	CCONJ
ejpam-4755	286	19	2p	2p	NOUN
ejpam-4755	286	20	.	.	PUNCT
ejpam-4755	287	1	publicacions	publicacion	NOUN
ejpam-4755	287	2	matemàtiques	matemàtique	NOUN
ejpam-4755	287	3	,	,	PUNCT
ejpam-4755	287	4	64(1):121–141	64(1):121–141	NOUN
ejpam-4755	287	5	,	,	PUNCT
ejpam-4755	287	6	2020	2020	NUM
ejpam-4755	287	7	.	.	PUNCT
ejpam-4755	288	1	[	[	X
ejpam-4755	288	2	14	14	NUM
ejpam-4755	288	3	]	]	X
ejpam-4755	288	4	cornelius	cornelius	PROPN
ejpam-4755	288	5	greither	greither	NOUN
ejpam-4755	288	6	and	and	CCONJ
ejpam-4755	288	7	bodo	bodo	PROPN
ejpam-4755	288	8	pareigis	pareigis	PROPN
ejpam-4755	288	9	.	.	PUNCT
ejpam-4755	289	1	hopf	hopf	PROPN
ejpam-4755	289	2	galois	galois	PROPN
ejpam-4755	289	3	theory	theory	NOUN
ejpam-4755	289	4	for	for	ADP
ejpam-4755	289	5	separable	separable	ADJ
ejpam-4755	289	6	field	field	NOUN
ejpam-4755	289	7	extensions	extension	NOUN
ejpam-4755	289	8	.	.	PUNCT
ejpam-4755	290	1	journal	journal	NOUN
ejpam-4755	290	2	of	of	ADP
ejpam-4755	290	3	algebra	algebra	PROPN
ejpam-4755	290	4	,	,	PUNCT
ejpam-4755	290	5	106(1):239–258	106(1):239–258	NUM
ejpam-4755	290	6	,	,	PUNCT
ejpam-4755	290	7	1987	1987	NUM
ejpam-4755	290	8	.	.	PUNCT
ejpam-4755	291	1	[	[	X
ejpam-4755	291	2	15	15	NUM
ejpam-4755	291	3	]	]	X
ejpam-4755	291	4	baraa	baraa	ADJ
ejpam-4755	291	5	m.	m.	NOUN
ejpam-4755	291	6	jamal	jamal	PROPN
ejpam-4755	291	7	and	and	CCONJ
ejpam-4755	291	8	ali	ali	PROPN
ejpam-4755	291	9	a.	a.	PROPN
ejpam-4755	291	10	alabdali	alabdali	VERB
ejpam-4755	291	11	.	.	PUNCT
ejpam-4755	292	1	hopf	hopf	PROPN
ejpam-4755	292	2	galois	galois	PROPN
ejpam-4755	292	3	structures	structure	NOUN
ejpam-4755	292	4	on	on	ADP
ejpam-4755	292	5	nonnormal	nonnormal	ADJ
ejpam-4755	292	6	extensions	extension	NOUN
ejpam-4755	292	7	of	of	ADP
ejpam-4755	292	8	degree	degree	NOUN
ejpam-4755	292	9	pqw	pqw	NOUN
ejpam-4755	292	10	.	.	PUNCT
ejpam-4755	293	1	in	in	ADP
ejpam-4755	293	2	iicesat	iicesat	NOUN
ejpam-4755	293	3	2022	2022	NUM
ejpam-4755	293	4	,	,	PUNCT
ejpam-4755	293	5	pages	page	NOUN
ejpam-4755	293	6	1–14	1–14	PROPN
ejpam-4755	293	7	.	.	PUNCT
ejpam-4755	293	8	prepublish	prepublish	PROPN
ejpam-4755	293	9	,	,	PUNCT
ejpam-4755	293	10	to	to	PART
ejpam-4755	293	11	appear	appear	VERB
ejpam-4755	293	12	in	in	ADP
ejpam-4755	293	13	american	american	PROPN
ejpam-4755	293	14	institute	institute	PROPN
ejpam-4755	293	15	of	of	ADP
ejpam-4755	293	16	physics	physics	PROPN
ejpam-4755	293	17	(	(	PUNCT
ejpam-4755	293	18	aip	aip	PROPN
ejpam-4755	293	19	)	)	PUNCT
ejpam-4755	293	20	.	.	PUNCT
ejpam-4755	294	1	,	,	PUNCT
ejpam-4755	295	1	2022	2022	NUM
ejpam-4755	295	2	.	.	PUNCT
ejpam-4755	296	1	[	[	X
ejpam-4755	296	2	16	16	NUM
ejpam-4755	296	3	]	]	X
ejpam-4755	296	4	timothy	timothy	PROPN
ejpam-4755	296	5	kohl	kohl	NOUN
ejpam-4755	296	6	.	.	PUNCT
ejpam-4755	297	1	classification	classification	NOUN
ejpam-4755	297	2	of	of	ADP
ejpam-4755	297	3	the	the	DET
ejpam-4755	297	4	hopf	hopf	ADJ
ejpam-4755	297	5	galois	galois	PROPN
ejpam-4755	297	6	structures	structure	NOUN
ejpam-4755	297	7	on	on	ADP
ejpam-4755	297	8	prime	prime	ADJ
ejpam-4755	297	9	power	power	NOUN
ejpam-4755	297	10	radical	radical	ADJ
ejpam-4755	297	11	extensions	extension	NOUN
ejpam-4755	297	12	.	.	PUNCT
ejpam-4755	298	1	journal	journal	NOUN
ejpam-4755	298	2	of	of	ADP
ejpam-4755	298	3	algebra	algebra	PROPN
ejpam-4755	298	4	,	,	PUNCT
ejpam-4755	298	5	207(2):525–546	207(2):525–546	NUM
ejpam-4755	298	6	,	,	PUNCT
ejpam-4755	298	7	1998	1998	NUM
ejpam-4755	298	8	.	.	PUNCT
ejpam-4755	299	1	[	[	X
ejpam-4755	299	2	17	17	NUM
ejpam-4755	299	3	]	]	X
ejpam-4755	299	4	timothy	timothy	PROPN
ejpam-4755	299	5	kohl	kohl	PROPN
ejpam-4755	299	6	.	.	PUNCT
ejpam-4755	300	1	regular	regular	ADJ
ejpam-4755	300	2	permutation	permutation	NOUN
ejpam-4755	300	3	groups	group	NOUN
ejpam-4755	300	4	of	of	ADP
ejpam-4755	300	5	order	order	NOUN
ejpam-4755	300	6	mp	mp	NOUN
ejpam-4755	300	7	and	and	CCONJ
ejpam-4755	300	8	hopf	hopf	ADJ
ejpam-4755	300	9	-	-	PUNCT
ejpam-4755	300	10	galois	galois	NOUN
ejpam-4755	300	11	structures	structure	NOUN
ejpam-4755	300	12	.	.	PUNCT
ejpam-4755	301	1	algebra	algebra	NOUN
ejpam-4755	301	2	number	number	NOUN
ejpam-4755	301	3	theory	theory	NOUN
ejpam-4755	301	4	,	,	PUNCT
ejpam-4755	301	5	7(9):2203–2240	7(9):2203–2240	NUM
ejpam-4755	301	6	,	,	PUNCT
ejpam-4755	301	7	2013	2013	NUM
ejpam-4755	301	8	.	.	PUNCT
ejpam-4755	302	1	[	[	X
ejpam-4755	302	2	18	18	NUM
ejpam-4755	302	3	]	]	PUNCT
ejpam-4755	302	4	agata	agata	PROPN
ejpam-4755	302	5	smoktunowicz	smoktunowicz	PROPN
ejpam-4755	302	6	and	and	CCONJ
ejpam-4755	302	7	leandro	leandro	PROPN
ejpam-4755	302	8	vendramin	vendramin	NOUN
ejpam-4755	302	9	.	.	PUNCT
ejpam-4755	303	1	on	on	ADP
ejpam-4755	303	2	skew	skew	ADJ
ejpam-4755	303	3	braces	brace	NOUN
ejpam-4755	303	4	(	(	PUNCT
ejpam-4755	303	5	with	with	ADP
ejpam-4755	303	6	an	an	DET
ejpam-4755	303	7	appendix	appendix	NOUN
ejpam-4755	303	8	by	by	ADP
ejpam-4755	303	9	n.	n.	PROPN
ejpam-4755	303	10	byott	byott	PROPN
ejpam-4755	303	11	and	and	CCONJ
ejpam-4755	303	12	l.	l.	PROPN
ejpam-4755	303	13	vendramin	vendramin	PROPN
ejpam-4755	303	14	)	)	PUNCT
ejpam-4755	303	15	.	.	PUNCT
ejpam-4755	304	1	journal	journal	NOUN
ejpam-4755	304	2	of	of	ADP
ejpam-4755	304	3	combinatorial	combinatorial	ADJ
ejpam-4755	304	4	algebra	algebra	NOUN
ejpam-4755	304	5	,	,	PUNCT
ejpam-4755	304	6	2(1):47–86	2(1):47–86	NUM
ejpam-4755	304	7	,	,	PUNCT
ejpam-4755	304	8	2018	2018	NUM
ejpam-4755	304	9	.	.	PUNCT
ejpam-4755	305	1	[	[	X
ejpam-4755	305	2	19	19	NUM
ejpam-4755	305	3	]	]	X
ejpam-4755	305	4	cindy	cindy	PROPN
ejpam-4755	305	5	(	(	PUNCT
ejpam-4755	305	6	sin	sin	PROPN
ejpam-4755	305	7	yi	yi	PROPN
ejpam-4755	305	8	)	)	PUNCT
ejpam-4755	305	9	tsang	tsang	PROPN
ejpam-4755	305	10	.	.	PUNCT
ejpam-4755	306	1	hopf	hopf	ADJ
ejpam-4755	306	2	-	-	PUNCT
ejpam-4755	306	3	galois	galois	NOUN
ejpam-4755	306	4	structures	structure	NOUN
ejpam-4755	306	5	on	on	ADP
ejpam-4755	306	6	finite	finite	ADJ
ejpam-4755	306	7	extensions	extension	NOUN
ejpam-4755	306	8	with	with	ADP
ejpam-4755	306	9	almost	almost	ADV
ejpam-4755	306	10	simple	simple	ADJ
ejpam-4755	306	11	galois	galois	PROPN
ejpam-4755	306	12	group	group	NOUN
ejpam-4755	306	13	.	.	PUNCT
ejpam-4755	307	1	journal	journal	PROPN
ejpam-4755	307	2	of	of	ADP
ejpam-4755	307	3	number	number	NOUN
ejpam-4755	307	4	theory	theory	NOUN
ejpam-4755	307	5	,	,	PUNCT
ejpam-4755	307	6	214:286–311	214:286–311	NUM
ejpam-4755	307	7	,	,	PUNCT
ejpam-4755	307	8	2020	2020	NUM
ejpam-4755	307	9	.	.	PUNCT