id	sid	tid	token	lemma	pos
ejpam-5889	1	1	european	european	PROPN
ejpam-5889	1	2	journal	journal	PROPN
ejpam-5889	1	3	of	of	ADP
ejpam-5889	1	4	pure	pure	ADJ
ejpam-5889	1	5	and	and	CCONJ
ejpam-5889	1	6	applied	applied	ADJ
ejpam-5889	1	7	mathematics	mathematic	NOUN
ejpam-5889	1	8	2025	2025	NUM
ejpam-5889	1	9	,	,	PUNCT
ejpam-5889	1	10	vol	vol	NOUN
ejpam-5889	1	11	.	.	PROPN
ejpam-5889	1	12	18	18	NUM
ejpam-5889	1	13	,	,	PUNCT
ejpam-5889	1	14	issue	issue	NOUN
ejpam-5889	1	15	2	2	NUM
ejpam-5889	1	16	,	,	PUNCT
ejpam-5889	1	17	article	article	NOUN
ejpam-5889	1	18	number	number	NOUN
ejpam-5889	1	19	5889	5889	NUM
ejpam-5889	1	20	issn	issn	PROPN
ejpam-5889	1	21	1307	1307	NUM
ejpam-5889	1	22	-	-	SYM
ejpam-5889	1	23	5543	5543	NUM
ejpam-5889	1	24	–	–	PUNCT
ejpam-5889	1	25	ejpam.com	ejpam.com	X
ejpam-5889	1	26	published	publish	VERB
ejpam-5889	1	27	by	by	ADP
ejpam-5889	1	28	new	new	PROPN
ejpam-5889	1	29	york	york	PROPN
ejpam-5889	1	30	business	business	PROPN
ejpam-5889	1	31	global	global	PROPN
ejpam-5889	1	32	jordan	jordan	PROPN
ejpam-5889	1	33	-	-	PUNCT
ejpam-5889	1	34	hölder	hölder	PROPN
ejpam-5889	1	35	theorem	theorem	NOUN
ejpam-5889	1	36	for	for	ADP
ejpam-5889	1	37	multigroups	multigroup	NOUN
ejpam-5889	1	38	paul	paul	PROPN
ejpam-5889	1	39	augustine	augustine	PROPN
ejpam-5889	1	40	ejegwa1	ejegwa1	PROPN
ejpam-5889	1	41	,	,	PUNCT
ejpam-5889	1	42	nasreen	nasreen	VERB
ejpam-5889	1	43	kausar2	kausar2	PROPN
ejpam-5889	1	44	,	,	PUNCT
ejpam-5889	1	45	musa	musa	PROPN
ejpam-5889	1	46	adeku	adeku	PROPN
ejpam-5889	1	47	ibrahim3	ibrahim3	PROPN
ejpam-5889	1	48	,	,	PUNCT
ejpam-5889	1	49	tonguc	tonguc	PROPN
ejpam-5889	1	50	cagin4,∗	cagin4,∗	PROPN
ejpam-5889	1	51	1	1	NUM
ejpam-5889	1	52	department	department	NOUN
ejpam-5889	1	53	of	of	ADP
ejpam-5889	1	54	mathematics	mathematics	PROPN
ejpam-5889	1	55	,	,	PUNCT
ejpam-5889	1	56	joseph	joseph	PROPN
ejpam-5889	1	57	sarwuan	sarwuan	PROPN
ejpam-5889	1	58	tarka	tarka	PROPN
ejpam-5889	1	59	university	university	PROPN
ejpam-5889	1	60	,	,	PUNCT
ejpam-5889	1	61	p.m.b	p.m.b	NOUN
ejpam-5889	1	62	.	.	PROPN
ejpam-5889	1	63	2373	2373	NUM
ejpam-5889	1	64	,	,	PUNCT
ejpam-5889	1	65	makurdi	makurdi	X
ejpam-5889	1	66	,	,	PUNCT
ejpam-5889	1	67	nigeria	nigeria	PROPN
ejpam-5889	1	68	2	2	NUM
ejpam-5889	1	69	department	department	NOUN
ejpam-5889	1	70	of	of	ADP
ejpam-5889	1	71	mathematics	mathematic	NOUN
ejpam-5889	1	72	,	,	PUNCT
ejpam-5889	1	73	faculty	faculty	NOUN
ejpam-5889	1	74	of	of	ADP
ejpam-5889	1	75	arts	art	NOUN
ejpam-5889	1	76	and	and	CCONJ
ejpam-5889	1	77	sciences	science	NOUN
ejpam-5889	1	78	,	,	PUNCT
ejpam-5889	1	79	balikesir	balikesir	PROPN
ejpam-5889	1	80	university	university	PROPN
ejpam-5889	1	81	,	,	PUNCT
ejpam-5889	1	82	10145	10145	NUM
ejpam-5889	1	83	balikesir	balikesir	NOUN
ejpam-5889	1	84	,	,	PUNCT
ejpam-5889	1	85	türkiye	türkiye	NOUN
ejpam-5889	1	86	3	3	NUM
ejpam-5889	1	87	department	department	NOUN
ejpam-5889	1	88	of	of	ADP
ejpam-5889	1	89	mathematics	mathematics	PROPN
ejpam-5889	1	90	,	,	PUNCT
ejpam-5889	1	91	federal	federal	ADJ
ejpam-5889	1	92	university	university	PROPN
ejpam-5889	1	93	lokoja	lokoja	PROPN
ejpam-5889	1	94	,	,	PUNCT
ejpam-5889	1	95	kogi	kogi	PROPN
ejpam-5889	1	96	state	state	PROPN
ejpam-5889	1	97	,	,	PUNCT
ejpam-5889	1	98	nigeria	nigeria	PROPN
ejpam-5889	1	99	4	4	NUM
ejpam-5889	1	100	college	college	NOUN
ejpam-5889	1	101	of	of	ADP
ejpam-5889	1	102	business	business	PROPN
ejpam-5889	1	103	administration	administration	PROPN
ejpam-5889	1	104	,	,	PUNCT
ejpam-5889	1	105	american	american	PROPN
ejpam-5889	1	106	university	university	PROPN
ejpam-5889	1	107	of	of	ADP
ejpam-5889	1	108	the	the	DET
ejpam-5889	1	109	middle	middle	PROPN
ejpam-5889	1	110	east	east	PROPN
ejpam-5889	1	111	,	,	PUNCT
ejpam-5889	1	112	kuwait	kuwait	PROPN
ejpam-5889	1	113	abstract	abstract	PROPN
ejpam-5889	1	114	.	.	PUNCT
ejpam-5889	2	1	multigroup	multigroup	PROPN
ejpam-5889	2	2	theory	theory	NOUN
ejpam-5889	2	3	is	be	AUX
ejpam-5889	2	4	the	the	DET
ejpam-5889	2	5	application	application	NOUN
ejpam-5889	2	6	of	of	ADP
ejpam-5889	2	7	multisets	multiset	NOUN
ejpam-5889	2	8	to	to	ADP
ejpam-5889	2	9	the	the	DET
ejpam-5889	2	10	theory	theory	NOUN
ejpam-5889	2	11	of	of	ADP
ejpam-5889	2	12	groups	group	NOUN
ejpam-5889	2	13	.	.	PUNCT
ejpam-5889	3	1	many	many	ADJ
ejpam-5889	3	2	group	group	NOUN
ejpam-5889	3	3	’s	’s	PART
ejpam-5889	3	4	theoretic	theoretic	ADJ
ejpam-5889	3	5	notions	notion	NOUN
ejpam-5889	3	6	have	have	AUX
ejpam-5889	3	7	been	be	AUX
ejpam-5889	3	8	studied	study	VERB
ejpam-5889	3	9	in	in	ADP
ejpam-5889	3	10	multigroup	multigroup	PROPN
ejpam-5889	3	11	theory	theory	NOUN
ejpam-5889	3	12	,	,	PUNCT
ejpam-5889	3	13	however	however	ADV
ejpam-5889	3	14	,	,	PUNCT
ejpam-5889	3	15	the	the	DET
ejpam-5889	3	16	ideas	idea	NOUN
ejpam-5889	3	17	of	of	ADP
ejpam-5889	3	18	maximal	maximal	ADJ
ejpam-5889	3	19	normal	normal	ADJ
ejpam-5889	3	20	subgroup	subgroup	NOUN
ejpam-5889	3	21	,	,	PUNCT
ejpam-5889	3	22	simple	simple	ADJ
ejpam-5889	3	23	group	group	NOUN
ejpam-5889	3	24	,	,	PUNCT
ejpam-5889	3	25	normal	normal	ADJ
ejpam-5889	3	26	series	series	NOUN
ejpam-5889	3	27	,	,	PUNCT
ejpam-5889	3	28	composition	composition	NOUN
ejpam-5889	3	29	series	series	NOUN
ejpam-5889	3	30	,	,	PUNCT
ejpam-5889	3	31	and	and	CCONJ
ejpam-5889	3	32	the	the	DET
ejpam-5889	3	33	jordan	jordan	PROPN
ejpam-5889	3	34	-	-	PUNCT
ejpam-5889	3	35	hölder	hölder	PROPN
ejpam-5889	3	36	theorem	theorem	NOUN
ejpam-5889	3	37	are	be	AUX
ejpam-5889	3	38	yet	yet	ADV
ejpam-5889	3	39	to	to	PART
ejpam-5889	3	40	be	be	AUX
ejpam-5889	3	41	investigated	investigate	VERB
ejpam-5889	3	42	in	in	ADP
ejpam-5889	3	43	multiset	multiset	ADJ
ejpam-5889	3	44	context	context	NOUN
ejpam-5889	3	45	.	.	PUNCT
ejpam-5889	4	1	in	in	ADP
ejpam-5889	4	2	this	this	DET
ejpam-5889	4	3	article	article	NOUN
ejpam-5889	4	4	,	,	PUNCT
ejpam-5889	4	5	we	we	PRON
ejpam-5889	4	6	define	define	VERB
ejpam-5889	4	7	simple	simple	ADJ
ejpam-5889	4	8	multigroup	multigroup	NOUN
ejpam-5889	4	9	,	,	PUNCT
ejpam-5889	4	10	maximal	maximal	ADJ
ejpam-5889	4	11	normal	normal	ADJ
ejpam-5889	4	12	submultigroup	submultigroup	NOUN
ejpam-5889	4	13	,	,	PUNCT
ejpam-5889	4	14	normal	normal	ADJ
ejpam-5889	4	15	series	series	NOUN
ejpam-5889	4	16	for	for	ADP
ejpam-5889	4	17	multigroup	multigroup	PROPN
ejpam-5889	4	18	,	,	PUNCT
ejpam-5889	4	19	and	and	CCONJ
ejpam-5889	4	20	composition	composition	NOUN
ejpam-5889	4	21	series	series	NOUN
ejpam-5889	4	22	for	for	ADP
ejpam-5889	4	23	multigroup	multigroup	NOUN
ejpam-5889	4	24	with	with	ADP
ejpam-5889	4	25	examples	example	NOUN
ejpam-5889	4	26	.	.	PUNCT
ejpam-5889	5	1	with	with	ADP
ejpam-5889	5	2	these	these	DET
ejpam-5889	5	3	concepts	concept	NOUN
ejpam-5889	5	4	,	,	PUNCT
ejpam-5889	5	5	we	we	PRON
ejpam-5889	5	6	establish	establish	VERB
ejpam-5889	5	7	the	the	DET
ejpam-5889	5	8	jordan	jordan	PROPN
ejpam-5889	5	9	-	-	PUNCT
ejpam-5889	5	10	hölder	hölder	PROPN
ejpam-5889	5	11	theorem	theorem	NOUN
ejpam-5889	5	12	in	in	ADP
ejpam-5889	5	13	multigroup	multigroup	PROPN
ejpam-5889	5	14	theory	theory	NOUN
ejpam-5889	5	15	.	.	PUNCT
ejpam-5889	6	1	it	it	PRON
ejpam-5889	6	2	is	be	AUX
ejpam-5889	6	3	shown	show	VERB
ejpam-5889	6	4	that	that	SCONJ
ejpam-5889	6	5	every	every	DET
ejpam-5889	6	6	finite	finite	NOUN
ejpam-5889	6	7	multigroup	multigroup	PROPN
ejpam-5889	6	8	defined	define	VERB
ejpam-5889	6	9	over	over	ADP
ejpam-5889	6	10	a	a	DET
ejpam-5889	6	11	finite	finite	ADJ
ejpam-5889	6	12	group	group	NOUN
ejpam-5889	6	13	has	have	VERB
ejpam-5889	6	14	a	a	DET
ejpam-5889	6	15	composition	composition	NOUN
ejpam-5889	6	16	series	series	NOUN
ejpam-5889	6	17	.	.	PUNCT
ejpam-5889	7	1	in	in	ADP
ejpam-5889	7	2	addition	addition	NOUN
ejpam-5889	7	3	,	,	PUNCT
ejpam-5889	7	4	it	it	PRON
ejpam-5889	7	5	is	be	AUX
ejpam-5889	7	6	established	establish	VERB
ejpam-5889	7	7	that	that	SCONJ
ejpam-5889	7	8	every	every	DET
ejpam-5889	7	9	finite	finite	NOUN
ejpam-5889	7	10	multigroup	multigroup	PROPN
ejpam-5889	7	11	defined	define	VERB
ejpam-5889	7	12	over	over	ADP
ejpam-5889	7	13	a	a	DET
ejpam-5889	7	14	finite	finite	ADJ
ejpam-5889	7	15	group	group	NOUN
ejpam-5889	7	16	has	have	VERB
ejpam-5889	7	17	at	at	ADV
ejpam-5889	7	18	least	least	ADV
ejpam-5889	7	19	two	two	NUM
ejpam-5889	7	20	composition	composition	NOUN
ejpam-5889	7	21	series	series	NOUN
ejpam-5889	7	22	which	which	PRON
ejpam-5889	7	23	are	be	AUX
ejpam-5889	7	24	equivalent	equivalent	ADJ
ejpam-5889	7	25	.	.	PUNCT
ejpam-5889	8	1	2020	2020	NUM
ejpam-5889	8	2	mathematics	mathematic	NOUN
ejpam-5889	8	3	subject	subject	NOUN
ejpam-5889	8	4	classifications	classification	NOUN
ejpam-5889	8	5	:	:	PUNCT
ejpam-5889	8	6	03e72	03e72	NUM
ejpam-5889	8	7	,	,	PUNCT
ejpam-5889	8	8	06d72	06d72	NOUN
ejpam-5889	8	9	,	,	PUNCT
ejpam-5889	8	10	11e57	11e57	NUM
ejpam-5889	8	11	,	,	PUNCT
ejpam-5889	8	12	19a22	19a22	NUM
ejpam-5889	8	13	key	key	ADJ
ejpam-5889	8	14	words	word	NOUN
ejpam-5889	8	15	and	and	CCONJ
ejpam-5889	8	16	phrases	phrase	NOUN
ejpam-5889	8	17	:	:	PUNCT
ejpam-5889	8	18	multiset	multiset	PROPN
ejpam-5889	8	19	,	,	PUNCT
ejpam-5889	8	20	multigroup	multigroup	PROPN
ejpam-5889	8	21	,	,	PUNCT
ejpam-5889	8	22	order	order	NOUN
ejpam-5889	8	23	of	of	ADP
ejpam-5889	8	24	multigroup	multigroup	PROPN
ejpam-5889	8	25	,	,	PUNCT
ejpam-5889	8	26	simple	simple	ADJ
ejpam-5889	8	27	multigroup	multigroup	NOUN
ejpam-5889	8	28	,	,	PUNCT
ejpam-5889	8	29	maximal	maximal	ADJ
ejpam-5889	8	30	normal	normal	ADJ
ejpam-5889	8	31	submultigroup	submultigroup	NOUN
ejpam-5889	8	32	,	,	PUNCT
ejpam-5889	8	33	normal	normal	ADJ
ejpam-5889	8	34	series	series	NOUN
ejpam-5889	8	35	,	,	PUNCT
ejpam-5889	8	36	composition	composition	NOUN
ejpam-5889	8	37	series	series	NOUN
ejpam-5889	8	38	one	one	NUM
ejpam-5889	8	39	constraint	constraint	NOUN
ejpam-5889	8	40	of	of	ADP
ejpam-5889	8	41	set	set	NOUN
ejpam-5889	8	42	theory	theory	NOUN
ejpam-5889	8	43	is	be	AUX
ejpam-5889	8	44	the	the	DET
ejpam-5889	8	45	refusal	refusal	NOUN
ejpam-5889	8	46	to	to	PART
ejpam-5889	8	47	allow	allow	VERB
ejpam-5889	8	48	repeated	repeat	VERB
ejpam-5889	8	49	elements	element	NOUN
ejpam-5889	8	50	in	in	ADP
ejpam-5889	8	51	a	a	DET
ejpam-5889	8	52	collection	collection	NOUN
ejpam-5889	8	53	,	,	PUNCT
ejpam-5889	8	54	which	which	PRON
ejpam-5889	8	55	is	be	AUX
ejpam-5889	8	56	admissible	admissible	ADJ
ejpam-5889	8	57	in	in	ADP
ejpam-5889	8	58	real	real	ADJ
ejpam-5889	8	59	-	-	PUNCT
ejpam-5889	8	60	world	world	NOUN
ejpam-5889	8	61	applications	application	NOUN
ejpam-5889	8	62	.	.	PUNCT
ejpam-5889	9	1	the	the	DET
ejpam-5889	9	2	word	word	NOUN
ejpam-5889	9	3	”	"	PUNCT
ejpam-5889	9	4	multiset	multiset	PROPN
ejpam-5889	9	5	”	"	PUNCT
ejpam-5889	9	6	refers	refer	VERB
ejpam-5889	9	7	to	to	ADP
ejpam-5889	9	8	an	an	DET
ejpam-5889	9	9	extensional	extensional	ADJ
ejpam-5889	9	10	set	set	NOUN
ejpam-5889	9	11	where	where	SCONJ
ejpam-5889	9	12	an	an	DET
ejpam-5889	9	13	element	element	NOUN
ejpam-5889	9	14	can	can	AUX
ejpam-5889	9	15	be	be	AUX
ejpam-5889	9	16	repeated	repeat	VERB
ejpam-5889	9	17	in	in	ADP
ejpam-5889	9	18	a	a	DET
ejpam-5889	9	19	collection	collection	NOUN
ejpam-5889	9	20	[	[	X
ejpam-5889	9	21	1	1	NUM
ejpam-5889	9	22	]	]	PUNCT
ejpam-5889	9	23	.	.	PUNCT
ejpam-5889	10	1	according	accord	VERB
ejpam-5889	10	2	to	to	ADP
ejpam-5889	10	3	debruijin	debruijin	NOUN
ejpam-5889	10	4	[	[	X
ejpam-5889	10	5	2	2	NUM
ejpam-5889	10	6	]	]	PUNCT
ejpam-5889	10	7	,	,	PUNCT
ejpam-5889	10	8	the	the	DET
ejpam-5889	10	9	concept	concept	NOUN
ejpam-5889	10	10	of	of	ADP
ejpam-5889	10	11	multiset	multiset	PROPN
ejpam-5889	10	12	was	be	AUX
ejpam-5889	10	13	introduced	introduce	VERB
ejpam-5889	10	14	to	to	ADP
ejpam-5889	10	15	d.	d.	PROPN
ejpam-5889	10	16	e.	e.	PROPN
ejpam-5889	10	17	knuth	knuth	PROPN
ejpam-5889	10	18	by	by	ADP
ejpam-5889	10	19	n.	n.	PROPN
ejpam-5889	10	20	g.	g.	PROPN
ejpam-5889	10	21	de	de	PROPN
ejpam-5889	10	22	bruijn	bruijn	PROPN
ejpam-5889	10	23	in	in	ADP
ejpam-5889	10	24	a	a	DET
ejpam-5889	10	25	private	private	ADJ
ejpam-5889	10	26	message	message	NOUN
ejpam-5889	10	27	,	,	PUNCT
ejpam-5889	10	28	and	and	CCONJ
ejpam-5889	10	29	since	since	SCONJ
ejpam-5889	10	30	then	then	ADV
ejpam-5889	10	31	,	,	PUNCT
ejpam-5889	10	32	the	the	DET
ejpam-5889	10	33	word	word	NOUN
ejpam-5889	10	34	has	have	AUX
ejpam-5889	10	35	been	be	AUX
ejpam-5889	10	36	used	use	VERB
ejpam-5889	10	37	to	to	PART
ejpam-5889	10	38	depict	depict	VERB
ejpam-5889	10	39	a	a	DET
ejpam-5889	10	40	set	set	NOUN
ejpam-5889	10	41	with	with	ADP
ejpam-5889	10	42	repeated	repeat	VERB
ejpam-5889	10	43	elements	element	NOUN
ejpam-5889	10	44	/	/	SYM
ejpam-5889	10	45	members	member	NOUN
ejpam-5889	10	46	.	.	PUNCT
ejpam-5889	11	1	the	the	DET
ejpam-5889	11	2	relevance	relevance	NOUN
ejpam-5889	11	3	of	of	ADP
ejpam-5889	11	4	multiset	multiset	PROPN
ejpam-5889	11	5	has	have	AUX
ejpam-5889	11	6	led	lead	VERB
ejpam-5889	11	7	to	to	ADP
ejpam-5889	11	8	many	many	ADJ
ejpam-5889	11	9	studies	study	NOUN
ejpam-5889	11	10	and	and	CCONJ
ejpam-5889	11	11	applications	application	NOUN
ejpam-5889	11	12	in	in	ADP
ejpam-5889	11	13	a	a	DET
ejpam-5889	11	14	number	number	NOUN
ejpam-5889	11	15	of	of	ADP
ejpam-5889	11	16	fields	field	NOUN
ejpam-5889	11	17	[	[	X
ejpam-5889	11	18	3–9	3–9	NUM
ejpam-5889	11	19	]	]	PUNCT
ejpam-5889	11	20	.	.	PUNCT
ejpam-5889	12	1	by	by	ADP
ejpam-5889	12	2	relaxing	relax	VERB
ejpam-5889	12	3	the	the	DET
ejpam-5889	12	4	condition	condition	NOUN
ejpam-5889	12	5	of	of	ADP
ejpam-5889	12	6	definite	definite	ADJ
ejpam-5889	12	7	collection	collection	NOUN
ejpam-5889	12	8	in	in	ADP
ejpam-5889	12	9	set	set	NOUN
ejpam-5889	12	10	,	,	PUNCT
ejpam-5889	12	11	zadeh	zadeh	PROPN
ejpam-5889	13	1	[	[	X
ejpam-5889	13	2	10	10	NUM
ejpam-5889	13	3	]	]	PUNCT
ejpam-5889	13	4	introduced	introduce	VERB
ejpam-5889	13	5	fuzzy	fuzzy	ADJ
ejpam-5889	13	6	sets	set	NOUN
ejpam-5889	13	7	,	,	PUNCT
ejpam-5889	13	8	which	which	PRON
ejpam-5889	13	9	was	be	AUX
ejpam-5889	13	10	applied	apply	VERB
ejpam-5889	13	11	to	to	ADP
ejpam-5889	13	12	group	group	NOUN
ejpam-5889	13	13	theory	theory	NOUN
ejpam-5889	13	14	by	by	ADP
ejpam-5889	13	15	proposing	propose	VERB
ejpam-5889	13	16	fuzzy	fuzzy	ADJ
ejpam-5889	13	17	group	group	NOUN
ejpam-5889	13	18	theory	theory	NOUN
ejpam-5889	13	19	[	[	X
ejpam-5889	13	20	11	11	NUM
ejpam-5889	13	21	]	]	PUNCT
ejpam-5889	13	22	.	.	PUNCT
ejpam-5889	14	1	some	some	DET
ejpam-5889	14	2	properties	property	NOUN
ejpam-5889	14	3	of	of	ADP
ejpam-5889	14	4	the	the	DET
ejpam-5889	14	5	fuzzy	fuzzy	ADJ
ejpam-5889	14	6	group	group	NOUN
ejpam-5889	14	7	theory	theory	NOUN
ejpam-5889	14	8	were	be	AUX
ejpam-5889	14	9	discussed	discuss	VERB
ejpam-5889	14	10	[	[	X
ejpam-5889	14	11	12–16	12–16	NUM
ejpam-5889	14	12	]	]	X
ejpam-5889	14	13	.	.	PUNCT
ejpam-5889	15	1	nazmul	nazmul	PROPN
ejpam-5889	15	2	et	et	PROPN
ejpam-5889	15	3	al	al	PROPN
ejpam-5889	15	4	.	.	PUNCT
ejpam-5889	16	1	[	[	X
ejpam-5889	16	2	17	17	NUM
ejpam-5889	16	3	]	]	X
ejpam-5889	16	4	utilized	utilize	VERB
ejpam-5889	16	5	multisets	multiset	NOUN
ejpam-5889	16	6	in	in	ADP
ejpam-5889	16	7	group	group	NOUN
ejpam-5889	16	8	theory	theory	NOUN
ejpam-5889	16	9	to	to	PART
ejpam-5889	16	10	introduce	introduce	VERB
ejpam-5889	16	11	the	the	DET
ejpam-5889	16	12	theory	theory	NOUN
ejpam-5889	16	13	of	of	ADP
ejpam-5889	16	14	multigroups	multigroup	NOUN
ejpam-5889	16	15	.	.	PUNCT
ejpam-5889	17	1	∗corresponding	∗corresponde	VERB
ejpam-5889	17	2	author	author	NOUN
ejpam-5889	17	3	.	.	PUNCT
ejpam-5889	18	1	doi	doi	NOUN
ejpam-5889	18	2	:	:	PUNCT
ejpam-5889	18	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5889	https://doi.org/10.29020/nybg.ejpam.v18i2.5889	PROPN
ejpam-5889	18	4	email	email	NOUN
ejpam-5889	18	5	addresses	address	NOUN
ejpam-5889	18	6	:	:	PUNCT
ejpam-5889	18	7	ejegwa.augustine@uam.edu.ng	ejegwa.augustine@uam.edu.ng	NOUN
ejpam-5889	18	8	(	(	PUNCT
ejpam-5889	18	9	p.	p.	NOUN
ejpam-5889	18	10	a.	a.	NOUN
ejpam-5889	18	11	ejegwa	ejegwa	PROPN
ejpam-5889	18	12	)	)	PUNCT
ejpam-5889	18	13	,	,	PUNCT
ejpam-5889	18	14	nasreen.kausar@balikesir.edu.tr	nasreen.kausar@balikesir.edu.tr	PROPN
ejpam-5889	18	15	(	(	PUNCT
ejpam-5889	18	16	n.	n.	PROPN
ejpam-5889	18	17	kausar	kausar	PROPN
ejpam-5889	18	18	)	)	PUNCT
ejpam-5889	18	19	,	,	PUNCT
ejpam-5889	18	20	adekubash@gmail.com	adekubash@gmail.com	X
ejpam-5889	18	21	(	(	PUNCT
ejpam-5889	18	22	m.	m.	NOUN
ejpam-5889	18	23	a.	a.	PROPN
ejpam-5889	18	24	ibrahim	ibrahim	PROPN
ejpam-5889	18	25	)	)	PUNCT
ejpam-5889	18	26	,	,	PUNCT
ejpam-5889	18	27	tonguc.cagin@aum.edu.kw	tonguc.cagin@aum.edu.kw	PROPN
ejpam-5889	18	28	(	(	PUNCT
ejpam-5889	18	29	t.	t.	NOUN
ejpam-5889	18	30	cagin	cagin	NOUN
ejpam-5889	18	31	)	)	PUNCT
ejpam-5889	18	32	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5889	19	1	1	1	NUM
ejpam-5889	19	2	copyright	copyright	NOUN
ejpam-5889	19	3	:	:	PUNCT
ejpam-5889	19	4	©	©	PROPN
ejpam-5889	19	5	2025	2025	NUM
ejpam-5889	19	6	the	the	DET
ejpam-5889	19	7	author(s	author(s	NOUN
ejpam-5889	19	8	)	)	PUNCT
ejpam-5889	19	9	.	.	PUNCT
ejpam-5889	20	1	(	(	PUNCT
ejpam-5889	20	2	cc	cc	NOUN
ejpam-5889	20	3	by	by	ADP
ejpam-5889	20	4	-	-	PUNCT
ejpam-5889	20	5	nc	nc	PROPN
ejpam-5889	20	6	4.0	4.0	NUM
ejpam-5889	20	7	)	)	PUNCT
ejpam-5889	20	8	p.	p.	NOUN
ejpam-5889	20	9	a.	a.	NOUN
ejpam-5889	20	10	ejegwa	ejegwa	PROPN
ejpam-5889	20	11	et	et	PROPN
ejpam-5889	20	12	al	al	PROPN
ejpam-5889	20	13	.	.	PUNCT
ejpam-5889	20	14	/	/	SYM
ejpam-5889	20	15	eur	eur	PROPN
ejpam-5889	20	16	.	.	PUNCT
ejpam-5889	21	1	j.	j.	PROPN
ejpam-5889	21	2	pure	pure	PROPN
ejpam-5889	21	3	appl	appl	PROPN
ejpam-5889	21	4	.	.	PROPN
ejpam-5889	21	5	math	math	PROPN
ejpam-5889	21	6	,	,	PUNCT
ejpam-5889	21	7	18	18	NUM
ejpam-5889	21	8	(	(	PUNCT
ejpam-5889	21	9	2	2	NUM
ejpam-5889	21	10	)	)	PUNCT
ejpam-5889	21	11	(	(	PUNCT
ejpam-5889	21	12	2025	2025	NUM
ejpam-5889	21	13	)	)	PUNCT
ejpam-5889	21	14	,	,	PUNCT
ejpam-5889	21	15	5889	5889	NUM
ejpam-5889	21	16	2	2	NUM
ejpam-5889	21	17	of	of	ADP
ejpam-5889	21	18	13	13	NUM
ejpam-5889	21	19	a	a	DET
ejpam-5889	21	20	comprehensive	comprehensive	ADJ
ejpam-5889	21	21	research	research	NOUN
ejpam-5889	21	22	on	on	ADP
ejpam-5889	21	23	multigroup	multigroup	PROPN
ejpam-5889	21	24	theory	theory	NOUN
ejpam-5889	21	25	was	be	AUX
ejpam-5889	21	26	conducted	conduct	VERB
ejpam-5889	21	27	in	in	ADP
ejpam-5889	21	28	[	[	X
ejpam-5889	21	29	18	18	NUM
ejpam-5889	21	30	]	]	PUNCT
ejpam-5889	21	31	and	and	CCONJ
ejpam-5889	21	32	some	some	DET
ejpam-5889	21	33	results	result	NOUN
ejpam-5889	21	34	in	in	ADP
ejpam-5889	21	35	multigroup	multigroup	ADJ
ejpam-5889	21	36	theory	theory	NOUN
ejpam-5889	21	37	were	be	AUX
ejpam-5889	21	38	discussed	discuss	VERB
ejpam-5889	21	39	[	[	X
ejpam-5889	21	40	19	19	NUM
ejpam-5889	21	41	,	,	PUNCT
ejpam-5889	21	42	20	20	NUM
ejpam-5889	21	43	]	]	PUNCT
ejpam-5889	21	44	.	.	PUNCT
ejpam-5889	22	1	the	the	DET
ejpam-5889	22	2	concepts	concept	NOUN
ejpam-5889	22	3	of	of	ADP
ejpam-5889	22	4	highly	highly	ADV
ejpam-5889	22	5	invariant	invariant	ADJ
ejpam-5889	22	6	submultigroups	submultigroup	NOUN
ejpam-5889	22	7	,	,	PUNCT
ejpam-5889	22	8	characteristic	characteristic	ADJ
ejpam-5889	22	9	submultigroups	submultigroup	NOUN
ejpam-5889	22	10	,	,	PUNCT
ejpam-5889	22	11	normal	normal	ADJ
ejpam-5889	22	12	submultigroups	submultigroup	NOUN
ejpam-5889	22	13	,	,	PUNCT
ejpam-5889	22	14	and	and	CCONJ
ejpam-5889	22	15	frattini	frattini	ADJ
ejpam-5889	22	16	submultigroups	submultigroup	NOUN
ejpam-5889	22	17	were	be	AUX
ejpam-5889	22	18	investigated	investigate	VERB
ejpam-5889	22	19	in	in	ADP
ejpam-5889	22	20	multigroup	multigroup	PROPN
ejpam-5889	22	21	settings	setting	NOUN
ejpam-5889	22	22	,	,	PUNCT
ejpam-5889	22	23	yielding	yield	VERB
ejpam-5889	22	24	some	some	DET
ejpam-5889	22	25	relevant	relevant	ADJ
ejpam-5889	22	26	results	result	NOUN
ejpam-5889	22	27	[	[	X
ejpam-5889	22	28	21	21	NUM
ejpam-5889	22	29	–	–	PUNCT
ejpam-5889	22	30	24	24	NUM
ejpam-5889	22	31	]	]	PUNCT
ejpam-5889	22	32	.	.	PUNCT
ejpam-5889	23	1	in	in	ADP
ejpam-5889	23	2	addition	addition	NOUN
ejpam-5889	23	3	,	,	PUNCT
ejpam-5889	23	4	the	the	DET
ejpam-5889	23	5	order	order	NOUN
ejpam-5889	23	6	of	of	ADP
ejpam-5889	23	7	multigroups	multigroup	NOUN
ejpam-5889	23	8	,	,	PUNCT
ejpam-5889	23	9	cyclic	cyclic	ADJ
ejpam-5889	23	10	multigroups	multigroup	NOUN
ejpam-5889	23	11	,	,	PUNCT
ejpam-5889	23	12	comultisets	comultiset	NOUN
ejpam-5889	23	13	,	,	PUNCT
ejpam-5889	23	14	and	and	CCONJ
ejpam-5889	23	15	factor	factor	NOUN
ejpam-5889	23	16	multigroups	multigroup	NOUN
ejpam-5889	23	17	were	be	AUX
ejpam-5889	23	18	established	establish	VERB
ejpam-5889	23	19	[	[	X
ejpam-5889	23	20	25–28	25–28	NUM
ejpam-5889	23	21	]	]	PUNCT
ejpam-5889	23	22	.	.	PUNCT
ejpam-5889	24	1	the	the	DET
ejpam-5889	24	2	studies	study	NOUN
ejpam-5889	24	3	in	in	ADP
ejpam-5889	24	4	[	[	X
ejpam-5889	24	5	29–34	29–34	NUM
ejpam-5889	24	6	]	]	PUNCT
ejpam-5889	24	7	examined	examine	VERB
ejpam-5889	24	8	various	various	ADJ
ejpam-5889	24	9	notions	notion	NOUN
ejpam-5889	24	10	in	in	ADP
ejpam-5889	24	11	multigroup	multigroup	ADJ
ejpam-5889	24	12	contexts	context	NOUN
ejpam-5889	24	13	,	,	PUNCT
ejpam-5889	24	14	such	such	ADJ
ejpam-5889	24	15	as	as	ADP
ejpam-5889	24	16	direct	direct	ADJ
ejpam-5889	24	17	products	product	NOUN
ejpam-5889	24	18	and	and	CCONJ
ejpam-5889	24	19	actions	action	NOUN
ejpam-5889	24	20	.	.	PUNCT
ejpam-5889	25	1	some	some	DET
ejpam-5889	25	2	algebraic	algebraic	PROPN
ejpam-5889	25	3	systems	system	NOUN
ejpam-5889	25	4	have	have	AUX
ejpam-5889	25	5	been	be	AUX
ejpam-5889	25	6	examined	examine	VERB
ejpam-5889	25	7	using	use	VERB
ejpam-5889	25	8	the	the	DET
ejpam-5889	25	9	idea	idea	NOUN
ejpam-5889	25	10	of	of	ADP
ejpam-5889	25	11	multisets	multiset	NOUN
ejpam-5889	25	12	[	[	X
ejpam-5889	25	13	35–38	35–38	NUM
ejpam-5889	25	14	]	]	X
ejpam-5889	25	15	.	.	PUNCT
ejpam-5889	26	1	finally	finally	ADV
ejpam-5889	26	2	,	,	PUNCT
ejpam-5889	26	3	the	the	DET
ejpam-5889	26	4	idea	idea	NOUN
ejpam-5889	26	5	of	of	ADP
ejpam-5889	26	6	soluble	soluble	ADJ
ejpam-5889	26	7	multigroups	multigroup	NOUN
ejpam-5889	26	8	was	be	AUX
ejpam-5889	26	9	introduced	introduce	VERB
ejpam-5889	26	10	and	and	CCONJ
ejpam-5889	26	11	many	many	ADJ
ejpam-5889	26	12	of	of	ADP
ejpam-5889	26	13	its	its	PRON
ejpam-5889	26	14	properties	property	NOUN
ejpam-5889	26	15	were	be	AUX
ejpam-5889	26	16	studied	study	VERB
ejpam-5889	26	17	in	in	ADP
ejpam-5889	26	18	[	[	X
ejpam-5889	26	19	39	39	NUM
ejpam-5889	26	20	]	]	PUNCT
ejpam-5889	26	21	.	.	PUNCT
ejpam-5889	27	1	although	although	SCONJ
ejpam-5889	27	2	many	many	ADJ
ejpam-5889	27	3	group	group	NOUN
ejpam-5889	27	4	theoretic	theoretic	NOUN
ejpam-5889	27	5	concepts	concept	NOUN
ejpam-5889	27	6	have	have	AUX
ejpam-5889	27	7	been	be	AUX
ejpam-5889	27	8	addressed	address	VERB
ejpam-5889	27	9	under	under	ADP
ejpam-5889	27	10	multiset	multiset	ADJ
ejpam-5889	27	11	context	context	NOUN
ejpam-5889	27	12	,	,	PUNCT
ejpam-5889	27	13	the	the	DET
ejpam-5889	27	14	notions	notion	NOUN
ejpam-5889	27	15	of	of	ADP
ejpam-5889	27	16	maximal	maximal	ADJ
ejpam-5889	27	17	normal	normal	ADJ
ejpam-5889	27	18	subgroup	subgroup	NOUN
ejpam-5889	27	19	,	,	PUNCT
ejpam-5889	27	20	simple	simple	ADJ
ejpam-5889	27	21	group	group	NOUN
ejpam-5889	27	22	,	,	PUNCT
ejpam-5889	27	23	normal	normal	ADJ
ejpam-5889	27	24	series	series	NOUN
ejpam-5889	27	25	,	,	PUNCT
ejpam-5889	27	26	composition	composition	NOUN
ejpam-5889	27	27	series	series	NOUN
ejpam-5889	27	28	,	,	PUNCT
ejpam-5889	27	29	and	and	CCONJ
ejpam-5889	27	30	the	the	DET
ejpam-5889	27	31	jordan	jordan	PROPN
ejpam-5889	27	32	-	-	PUNCT
ejpam-5889	27	33	hölder	hölder	PROPN
ejpam-5889	27	34	theorem	theorem	NOUN
ejpam-5889	27	35	are	be	AUX
ejpam-5889	27	36	yet	yet	ADV
ejpam-5889	27	37	to	to	PART
ejpam-5889	27	38	be	be	AUX
ejpam-5889	27	39	studied	study	VERB
ejpam-5889	27	40	in	in	ADP
ejpam-5889	27	41	multiset	multiset	ADJ
ejpam-5889	27	42	domain	domain	NOUN
ejpam-5889	27	43	.	.	PUNCT
ejpam-5889	28	1	hence	hence	ADV
ejpam-5889	28	2	,	,	PUNCT
ejpam-5889	28	3	it	it	PRON
ejpam-5889	28	4	is	be	AUX
ejpam-5889	28	5	appropriate	appropriate	ADJ
ejpam-5889	28	6	to	to	PART
ejpam-5889	28	7	investigate	investigate	VERB
ejpam-5889	28	8	simple	simple	ADJ
ejpam-5889	28	9	multigroup	multigroup	NOUN
ejpam-5889	28	10	,	,	PUNCT
ejpam-5889	28	11	maximal	maximal	ADJ
ejpam-5889	28	12	normal	normal	ADJ
ejpam-5889	28	13	submultigroup	submultigroup	NOUN
ejpam-5889	28	14	,	,	PUNCT
ejpam-5889	28	15	normal	normal	ADJ
ejpam-5889	28	16	series	series	NOUN
ejpam-5889	28	17	for	for	ADP
ejpam-5889	28	18	multigroup	multigroup	PROPN
ejpam-5889	28	19	,	,	PUNCT
ejpam-5889	28	20	composition	composition	NOUN
ejpam-5889	28	21	series	series	NOUN
ejpam-5889	28	22	for	for	ADP
ejpam-5889	28	23	multigroup	multigroup	PROPN
ejpam-5889	28	24	,	,	PUNCT
ejpam-5889	28	25	and	and	CCONJ
ejpam-5889	28	26	the	the	DET
ejpam-5889	28	27	jordan	jordan	PROPN
ejpam-5889	28	28	-	-	PUNCT
ejpam-5889	28	29	hölder	hölder	PROPN
ejpam-5889	28	30	theorem	theorem	NOUN
ejpam-5889	28	31	for	for	ADP
ejpam-5889	28	32	multigroups	multigroup	NOUN
ejpam-5889	28	33	because	because	SCONJ
ejpam-5889	28	34	the	the	DET
ejpam-5889	28	35	necessary	necessary	ADJ
ejpam-5889	28	36	concepts	concept	NOUN
ejpam-5889	28	37	needed	need	VERB
ejpam-5889	28	38	for	for	ADP
ejpam-5889	28	39	the	the	DET
ejpam-5889	28	40	establishment	establishment	NOUN
ejpam-5889	28	41	of	of	ADP
ejpam-5889	28	42	these	these	DET
ejpam-5889	28	43	concepts	concept	NOUN
ejpam-5889	28	44	have	have	AUX
ejpam-5889	28	45	been	be	AUX
ejpam-5889	28	46	studied	study	VERB
ejpam-5889	28	47	in	in	ADP
ejpam-5889	28	48	multigroup	multigroup	PROPN
ejpam-5889	28	49	theory	theory	NOUN
ejpam-5889	28	50	.	.	PUNCT
ejpam-5889	29	1	thus	thus	ADV
ejpam-5889	29	2	,	,	PUNCT
ejpam-5889	29	3	this	this	DET
ejpam-5889	29	4	article	article	NOUN
ejpam-5889	29	5	establishes	establish	VERB
ejpam-5889	29	6	simple	simple	ADJ
ejpam-5889	29	7	multigroup	multigroup	NOUN
ejpam-5889	29	8	,	,	PUNCT
ejpam-5889	29	9	maximal	maximal	ADJ
ejpam-5889	29	10	normal	normal	ADJ
ejpam-5889	29	11	submultigroup	submultigroup	NOUN
ejpam-5889	29	12	,	,	PUNCT
ejpam-5889	29	13	normal	normal	ADJ
ejpam-5889	29	14	series	series	NOUN
ejpam-5889	29	15	for	for	ADP
ejpam-5889	29	16	multigroup	multigroup	PROPN
ejpam-5889	29	17	,	,	PUNCT
ejpam-5889	29	18	composition	composition	NOUN
ejpam-5889	29	19	series	series	NOUN
ejpam-5889	29	20	for	for	ADP
ejpam-5889	29	21	multigroup	multigroup	PROPN
ejpam-5889	29	22	,	,	PUNCT
ejpam-5889	29	23	and	and	CCONJ
ejpam-5889	29	24	the	the	DET
ejpam-5889	29	25	jordan	jordan	PROPN
ejpam-5889	29	26	-	-	PUNCT
ejpam-5889	29	27	hölder	hölder	PROPN
ejpam-5889	29	28	theorem	theorem	NOUN
ejpam-5889	29	29	for	for	ADP
ejpam-5889	29	30	multigroups	multigroup	NOUN
ejpam-5889	29	31	,	,	PUNCT
ejpam-5889	29	32	respectively	respectively	ADV
ejpam-5889	29	33	.	.	PUNCT
ejpam-5889	30	1	the	the	DET
ejpam-5889	30	2	remainder	remainder	NOUN
ejpam-5889	30	3	of	of	ADP
ejpam-5889	30	4	the	the	DET
ejpam-5889	30	5	article	article	NOUN
ejpam-5889	30	6	is	be	AUX
ejpam-5889	30	7	organized	organize	VERB
ejpam-5889	30	8	as	as	SCONJ
ejpam-5889	30	9	follows	follow	VERB
ejpam-5889	30	10	:	:	PUNCT
ejpam-5889	30	11	section	section	NOUN
ejpam-5889	30	12	2	2	NUM
ejpam-5889	30	13	presents	present	VERB
ejpam-5889	30	14	the	the	DET
ejpam-5889	30	15	preliminaries	preliminary	NOUN
ejpam-5889	30	16	for	for	ADP
ejpam-5889	30	17	the	the	DET
ejpam-5889	30	18	study	study	NOUN
ejpam-5889	30	19	,	,	PUNCT
ejpam-5889	30	20	section	section	NOUN
ejpam-5889	30	21	3	3	NUM
ejpam-5889	30	22	covers	cover	VERB
ejpam-5889	30	23	the	the	DET
ejpam-5889	30	24	main	main	ADJ
ejpam-5889	30	25	results	result	NOUN
ejpam-5889	30	26	of	of	ADP
ejpam-5889	30	27	the	the	DET
ejpam-5889	30	28	articles	article	NOUN
ejpam-5889	30	29	,	,	PUNCT
ejpam-5889	30	30	and	and	CCONJ
ejpam-5889	30	31	section	section	NOUN
ejpam-5889	30	32	4	4	NUM
ejpam-5889	30	33	concludes	conclude	VERB
ejpam-5889	30	34	and	and	CCONJ
ejpam-5889	30	35	makes	make	VERB
ejpam-5889	30	36	suggestions	suggestion	NOUN
ejpam-5889	30	37	for	for	ADP
ejpam-5889	30	38	further	further	ADJ
ejpam-5889	30	39	research	research	NOUN
ejpam-5889	30	40	.	.	PUNCT
ejpam-5889	31	1	1	1	X
ejpam-5889	31	2	.	.	X
ejpam-5889	31	3	preliminaries	preliminary	NOUN
ejpam-5889	31	4	let	let	VERB
ejpam-5889	31	5	s	s	PRON
ejpam-5889	31	6	and	and	CCONJ
ejpam-5889	31	7	g	g	PROPN
ejpam-5889	31	8	represent	represent	VERB
ejpam-5889	31	9	a	a	DET
ejpam-5889	31	10	non	non	ADJ
ejpam-5889	31	11	-	-	ADJ
ejpam-5889	31	12	empty	empty	ADJ
ejpam-5889	31	13	set	set	NOUN
ejpam-5889	31	14	and	and	CCONJ
ejpam-5889	31	15	a	a	DET
ejpam-5889	31	16	group	group	NOUN
ejpam-5889	31	17	,	,	PUNCT
ejpam-5889	31	18	respectively	respectively	ADV
ejpam-5889	31	19	.	.	PUNCT
ejpam-5889	32	1	definition	definition	NOUN
ejpam-5889	32	2	1	1	NUM
ejpam-5889	32	3	(	(	PUNCT
ejpam-5889	32	4	[	[	X
ejpam-5889	32	5	10	10	NUM
ejpam-5889	32	6	]	]	NUM
ejpam-5889	32	7	)	)	PUNCT
ejpam-5889	32	8	.	.	PUNCT
ejpam-5889	33	1	a	a	DET
ejpam-5889	33	2	fuzzy	fuzzy	ADJ
ejpam-5889	33	3	subset	subset	NOUN
ejpam-5889	33	4	f	f	PROPN
ejpam-5889	33	5	of	of	ADP
ejpam-5889	33	6	s	s	PROPN
ejpam-5889	33	7	is	be	AUX
ejpam-5889	33	8	presented	present	VERB
ejpam-5889	33	9	as	as	ADP
ejpam-5889	33	10	:	:	PUNCT
ejpam-5889	33	11	f	f	X
ejpam-5889	33	12	=	=	PRON
ejpam-5889	33	13	{	{	PUNCT
ejpam-5889	33	14	⟨s	⟨s	PROPN
ejpam-5889	33	15	,	,	PUNCT
ejpam-5889	33	16	fm(s)⟩	fm(s)⟩	PROPN
ejpam-5889	33	17	|	|	NOUN
ejpam-5889	33	18	s	s	VERB
ejpam-5889	33	19	∈	∈	NOUN
ejpam-5889	33	20	s	s	PART
ejpam-5889	33	21	}	}	PUNCT
ejpam-5889	33	22	,	,	PUNCT
ejpam-5889	33	23	(	(	PUNCT
ejpam-5889	33	24	1	1	X
ejpam-5889	33	25	)	)	PUNCT
ejpam-5889	33	26	where	where	SCONJ
ejpam-5889	33	27	fm	fm	NOUN
ejpam-5889	33	28	:	:	PUNCT
ejpam-5889	33	29	s	s	X
ejpam-5889	33	30	→	→	SYM
ejpam-5889	33	31	[	[	X
ejpam-5889	33	32	0	0	NUM
ejpam-5889	33	33	,	,	PUNCT
ejpam-5889	33	34	1	1	NUM
ejpam-5889	33	35	]	]	PUNCT
ejpam-5889	33	36	is	be	AUX
ejpam-5889	33	37	the	the	DET
ejpam-5889	33	38	membership	membership	NOUN
ejpam-5889	33	39	degree	degree	NOUN
ejpam-5889	33	40	of	of	ADP
ejpam-5889	33	41	s	s	PROPN
ejpam-5889	33	42	∈	∈	PROPN
ejpam-5889	33	43	s.	s.	PROPN
ejpam-5889	33	44	definition	definition	NOUN
ejpam-5889	33	45	2	2	NUM
ejpam-5889	33	46	(	(	PUNCT
ejpam-5889	33	47	[	[	X
ejpam-5889	33	48	11	11	NUM
ejpam-5889	33	49	]	]	NUM
ejpam-5889	33	50	)	)	PUNCT
ejpam-5889	33	51	.	.	PUNCT
ejpam-5889	34	1	a	a	DET
ejpam-5889	34	2	fuzzy	fuzzy	ADJ
ejpam-5889	34	3	subset	subset	NOUN
ejpam-5889	34	4	f	f	PROPN
ejpam-5889	34	5	of	of	ADP
ejpam-5889	34	6	g	g	PROPN
ejpam-5889	34	7	is	be	AUX
ejpam-5889	34	8	a	a	DET
ejpam-5889	34	9	fuzzy	fuzzy	ADJ
ejpam-5889	34	10	subgroup	subgroup	NOUN
ejpam-5889	34	11	of	of	ADP
ejpam-5889	34	12	g	g	PROPN
ejpam-5889	34	13	if	if	SCONJ
ejpam-5889	34	14	(	(	PUNCT
ejpam-5889	34	15	i	i	NOUN
ejpam-5889	34	16	)	)	PUNCT
ejpam-5889	34	17	fm(xy	fm(xy	PROPN
ejpam-5889	34	18	)	)	PUNCT
ejpam-5889	34	19	≥	≥	PROPN
ejpam-5889	34	20	min	min	PROPN
ejpam-5889	34	21	{	{	PUNCT
ejpam-5889	34	22	fm(x),fm(y	fm(x),fm(y	PROPN
ejpam-5889	34	23	)	)	PUNCT
ejpam-5889	34	24	}	}	PUNCT
ejpam-5889	34	25	∀	∀	PUNCT
ejpam-5889	34	26	x	x	NOUN
ejpam-5889	34	27	,	,	PUNCT
ejpam-5889	34	28	y	y	PROPN
ejpam-5889	34	29	∈	∈	PROPN
ejpam-5889	34	30	g	g	PROPN
ejpam-5889	34	31	,	,	PUNCT
ejpam-5889	34	32	(	(	PUNCT
ejpam-5889	34	33	ii	ii	NOUN
ejpam-5889	34	34	)	)	PUNCT
ejpam-5889	34	35	fm(x−1	fm(x−1	NOUN
ejpam-5889	34	36	)	)	PUNCT
ejpam-5889	34	37	=	=	SYM
ejpam-5889	34	38	fm(x	fm(x	X
ejpam-5889	34	39	)	)	PUNCT
ejpam-5889	34	40	∀	∀	X
ejpam-5889	35	1	x	x	SYM
ejpam-5889	35	2	∈	∈	PROPN
ejpam-5889	35	3	g.	g.	NOUN
ejpam-5889	35	4	in	in	ADP
ejpam-5889	35	5	addition	addition	NOUN
ejpam-5889	35	6	,	,	PUNCT
ejpam-5889	35	7	fm(e	fm(e	PUNCT
ejpam-5889	35	8	)	)	PUNCT
ejpam-5889	35	9	=	=	SYM
ejpam-5889	35	10	fm(xx−1	fm(xx−1	NOUN
ejpam-5889	35	11	)	)	PUNCT
ejpam-5889	35	12	≥	≥	NOUN
ejpam-5889	35	13	min	min	PROPN
ejpam-5889	35	14	{	{	PUNCT
ejpam-5889	35	15	fm(x),fm(x	fm(x),fm(x	NOUN
ejpam-5889	35	16	)	)	PUNCT
ejpam-5889	35	17	}	}	PUNCT
ejpam-5889	35	18	=	=	SYM
ejpam-5889	35	19	fm(x	fm(x	X
ejpam-5889	35	20	)	)	PUNCT
ejpam-5889	35	21	∀	∀	PUNCT
ejpam-5889	36	1	x	x	X
ejpam-5889	36	2	∈	∈	NOUN
ejpam-5889	36	3	g	g	NOUN
ejpam-5889	36	4	,	,	PUNCT
ejpam-5889	36	5	where	where	SCONJ
ejpam-5889	36	6	e	e	NOUN
ejpam-5889	36	7	is	be	AUX
ejpam-5889	36	8	the	the	DET
ejpam-5889	36	9	unit	unit	NOUN
ejpam-5889	36	10	element	element	NOUN
ejpam-5889	36	11	of	of	ADP
ejpam-5889	36	12	g.	g.	PROPN
ejpam-5889	36	13	definition	definition	NOUN
ejpam-5889	36	14	3	3	NUM
ejpam-5889	36	15	(	(	PUNCT
ejpam-5889	36	16	[	[	X
ejpam-5889	36	17	6	6	NUM
ejpam-5889	36	18	]	]	NUM
ejpam-5889	36	19	)	)	PUNCT
ejpam-5889	36	20	.	.	PUNCT
ejpam-5889	37	1	a	a	DET
ejpam-5889	37	2	multiset	multiset	ADJ
ejpam-5889	37	3	d	d	NOUN
ejpam-5889	37	4	of	of	ADP
ejpam-5889	37	5	s	s	PROPN
ejpam-5889	37	6	is	be	AUX
ejpam-5889	37	7	a	a	DET
ejpam-5889	37	8	pair	pair	NOUN
ejpam-5889	37	9	⟨s	⟨s	NOUN
ejpam-5889	37	10	,	,	PUNCT
ejpam-5889	37	11	cd⟩	cd⟩	PROPN
ejpam-5889	37	12	,	,	PUNCT
ejpam-5889	37	13	where	where	SCONJ
ejpam-5889	37	14	cd	cd	PROPN
ejpam-5889	37	15	:	:	PUNCT
ejpam-5889	37	16	s	s	X
ejpam-5889	37	17	→	→	SYM
ejpam-5889	37	18	n	n	NOUN
ejpam-5889	37	19	=	=	SYM
ejpam-5889	37	20	{	{	PUNCT
ejpam-5889	37	21	1	1	NUM
ejpam-5889	37	22	,	,	PUNCT
ejpam-5889	37	23	2	2	NUM
ejpam-5889	37	24	,	,	PUNCT
ejpam-5889	37	25	...	...	PUNCT
ejpam-5889	37	26	}	}	PUNCT
ejpam-5889	37	27	(	(	PUNCT
ejpam-5889	37	28	2	2	X
ejpam-5889	37	29	)	)	PUNCT
ejpam-5889	37	30	is	be	AUX
ejpam-5889	37	31	a	a	DET
ejpam-5889	37	32	function	function	NOUN
ejpam-5889	37	33	,	,	PUNCT
ejpam-5889	37	34	such	such	ADJ
ejpam-5889	37	35	that	that	PRON
ejpam-5889	37	36	for	for	ADP
ejpam-5889	37	37	s	s	PROPN
ejpam-5889	37	38	∈	∈	PROPN
ejpam-5889	37	39	s	s	PART
ejpam-5889	37	40	implies	imply	VERB
ejpam-5889	37	41	d(s	d(s	PROPN
ejpam-5889	37	42	)	)	PUNCT
ejpam-5889	37	43	=	=	SYM
ejpam-5889	37	44	cd(s	cd(s	X
ejpam-5889	37	45	)	)	PUNCT
ejpam-5889	37	46	>	>	X
ejpam-5889	37	47	0	0	PUNCT
ejpam-5889	37	48	and	and	CCONJ
ejpam-5889	37	49	cd(s	cd(s	NUM
ejpam-5889	37	50	)	)	PUNCT
ejpam-5889	38	1	is	be	AUX
ejpam-5889	38	2	the	the	DET
ejpam-5889	38	3	multiplicity	multiplicity	NOUN
ejpam-5889	38	4	of	of	ADP
ejpam-5889	38	5	s	s	PRON
ejpam-5889	38	6	in	in	ADP
ejpam-5889	38	7	d.	d.	PROPN
ejpam-5889	38	8	if	if	SCONJ
ejpam-5889	38	9	cd(s	cd(s	PUNCT
ejpam-5889	38	10	)	)	PUNCT
ejpam-5889	39	1	=	=	SYM
ejpam-5889	39	2	0	0	NUM
ejpam-5889	39	3	,	,	PUNCT
ejpam-5889	39	4	then	then	ADV
ejpam-5889	39	5	s	s	VERB
ejpam-5889	39	6	/∈	/∈	PROPN
ejpam-5889	40	1	s.	s.	PROPN
ejpam-5889	40	2	p.	p.	PROPN
ejpam-5889	40	3	a.	a.	PROPN
ejpam-5889	40	4	ejegwa	ejegwa	PROPN
ejpam-5889	40	5	et	et	PROPN
ejpam-5889	40	6	al	al	PROPN
ejpam-5889	40	7	.	.	PUNCT
ejpam-5889	40	8	/	/	SYM
ejpam-5889	40	9	eur	eur	PROPN
ejpam-5889	40	10	.	.	PUNCT
ejpam-5889	41	1	j.	j.	PROPN
ejpam-5889	41	2	pure	pure	PROPN
ejpam-5889	41	3	appl	appl	PROPN
ejpam-5889	41	4	.	.	PROPN
ejpam-5889	41	5	math	math	PROPN
ejpam-5889	41	6	,	,	PUNCT
ejpam-5889	41	7	18	18	NUM
ejpam-5889	41	8	(	(	PUNCT
ejpam-5889	41	9	2	2	NUM
ejpam-5889	41	10	)	)	PUNCT
ejpam-5889	41	11	(	(	PUNCT
ejpam-5889	41	12	2025	2025	NUM
ejpam-5889	41	13	)	)	PUNCT
ejpam-5889	41	14	,	,	PUNCT
ejpam-5889	41	15	5889	5889	NUM
ejpam-5889	41	16	3	3	NUM
ejpam-5889	41	17	of	of	ADP
ejpam-5889	41	18	13	13	NUM
ejpam-5889	41	19	definition	definition	NOUN
ejpam-5889	41	20	4	4	NUM
ejpam-5889	41	21	(	(	PUNCT
ejpam-5889	41	22	[	[	NOUN
ejpam-5889	41	23	8	8	NUM
ejpam-5889	41	24	]	]	PUNCT
ejpam-5889	41	25	)	)	PUNCT
ejpam-5889	41	26	.	.	PUNCT
ejpam-5889	42	1	suppose	suppose	VERB
ejpam-5889	42	2	d	d	NOUN
ejpam-5889	42	3	and	and	CCONJ
ejpam-5889	42	4	e	e	PROPN
ejpam-5889	42	5	are	be	AUX
ejpam-5889	42	6	multisets	multiset	NOUN
ejpam-5889	42	7	of	of	ADP
ejpam-5889	42	8	s	s	NOUN
ejpam-5889	42	9	,	,	PUNCT
ejpam-5889	42	10	then	then	ADV
ejpam-5889	42	11	(	(	PUNCT
ejpam-5889	42	12	i	i	NOUN
ejpam-5889	42	13	)	)	PUNCT
ejpam-5889	43	1	d	d	X
ejpam-5889	43	2	=	=	SYM
ejpam-5889	44	1	e	e	X
ejpam-5889	44	2	⇐	⇐	ADJ
ejpam-5889	44	3	⇒	⇒	NOUN
ejpam-5889	44	4	cd(s	cd(s	PUNCT
ejpam-5889	44	5	)	)	PUNCT
ejpam-5889	45	1	=	=	SYM
ejpam-5889	45	2	ce(s	ce(s	X
ejpam-5889	45	3	)	)	PUNCT
ejpam-5889	45	4	∀	∀	PUNCT
ejpam-5889	45	5	s	s	PART
ejpam-5889	45	6	∈	∈	PROPN
ejpam-5889	45	7	s	s	PART
ejpam-5889	45	8	,	,	PUNCT
ejpam-5889	45	9	(	(	PUNCT
ejpam-5889	45	10	ii	ii	NOUN
ejpam-5889	45	11	)	)	PUNCT
ejpam-5889	45	12	d	d	NOUN
ejpam-5889	46	1	⊆	⊆	NUM
ejpam-5889	46	2	e	e	X
ejpam-5889	46	3	⇐	⇐	ADJ
ejpam-5889	46	4	⇒	⇒	NOUN
ejpam-5889	46	5	cd(s	cd(s	NUM
ejpam-5889	46	6	)	)	PUNCT
ejpam-5889	46	7	≤	≤	NOUN
ejpam-5889	47	1	ce(s	ce(s	ADJ
ejpam-5889	47	2	)	)	PUNCT
ejpam-5889	48	1	∀	∀	PUNCT
ejpam-5889	48	2	s	s	PART
ejpam-5889	48	3	∈	∈	PROPN
ejpam-5889	48	4	s	s	PART
ejpam-5889	48	5	,	,	PUNCT
ejpam-5889	48	6	(	(	PUNCT
ejpam-5889	48	7	iii	iii	X
ejpam-5889	48	8	)	)	PUNCT
ejpam-5889	48	9	d	d	NOUN
ejpam-5889	48	10	∩	∩	X
ejpam-5889	48	11	e	e	NOUN
ejpam-5889	48	12	=	=	NOUN
ejpam-5889	48	13	⇒	⇒	X
ejpam-5889	48	14	cd∩e(s	cd∩e(s	PROPN
ejpam-5889	48	15	)	)	PUNCT
ejpam-5889	48	16	=	=	PUNCT
ejpam-5889	48	17	min{cd(s	min{cd(s	PROPN
ejpam-5889	48	18	)	)	PUNCT
ejpam-5889	48	19	,	,	PUNCT
ejpam-5889	48	20	ce(s	ce(s	ADJ
ejpam-5889	48	21	)	)	PUNCT
ejpam-5889	48	22	}	}	PUNCT
ejpam-5889	48	23	∀	∀	PUNCT
ejpam-5889	48	24	s	s	PART
ejpam-5889	48	25	∈	∈	PROPN
ejpam-5889	48	26	s	s	NOUN
ejpam-5889	48	27	,	,	PUNCT
ejpam-5889	48	28	(	(	PUNCT
ejpam-5889	48	29	iv	iv	X
ejpam-5889	48	30	)	)	PUNCT
ejpam-5889	48	31	d	d	NOUN
ejpam-5889	48	32	∪	∪	ADP
ejpam-5889	48	33	e	e	NOUN
ejpam-5889	48	34	=	=	NOUN
ejpam-5889	48	35	⇒	⇒	NOUN
ejpam-5889	48	36	cd∪e(s	cd∪e(s	NOUN
ejpam-5889	48	37	)	)	PUNCT
ejpam-5889	48	38	=	=	SYM
ejpam-5889	48	39	max{cd(s	max{cd(s	PROPN
ejpam-5889	48	40	)	)	PUNCT
ejpam-5889	48	41	,	,	PUNCT
ejpam-5889	48	42	ce(s	ce(s	ADJ
ejpam-5889	48	43	)	)	PUNCT
ejpam-5889	48	44	}	}	PUNCT
ejpam-5889	48	45	∀	∀	PUNCT
ejpam-5889	48	46	s	s	PART
ejpam-5889	48	47	∈	∈	PROPN
ejpam-5889	48	48	s	s	NOUN
ejpam-5889	48	49	,	,	PUNCT
ejpam-5889	48	50	(	(	PUNCT
ejpam-5889	48	51	v	v	NOUN
ejpam-5889	48	52	)	)	PUNCT
ejpam-5889	48	53	d⊕	d⊕	PROPN
ejpam-5889	48	54	e	e	NOUN
ejpam-5889	48	55	=	=	NOUN
ejpam-5889	48	56	⇒	⇒	NOUN
ejpam-5889	48	57	cd⊕e(s	cd⊕e(s	NOUN
ejpam-5889	48	58	)	)	PUNCT
ejpam-5889	49	1	=	=	SYM
ejpam-5889	50	1	cd(s)⊕	cd(s)⊕	PRON
ejpam-5889	50	2	ce(s	ce(s	ADJ
ejpam-5889	50	3	)	)	PUNCT
ejpam-5889	50	4	∀	∀	PUNCT
ejpam-5889	51	1	s	s	PART
ejpam-5889	51	2	∈	∈	PROPN
ejpam-5889	51	3	s.	s.	PROPN
ejpam-5889	51	4	definition	definition	NOUN
ejpam-5889	51	5	5	5	NUM
ejpam-5889	51	6	(	(	PUNCT
ejpam-5889	51	7	[	[	X
ejpam-5889	51	8	17	17	NUM
ejpam-5889	51	9	]	]	NUM
ejpam-5889	51	10	)	)	PUNCT
ejpam-5889	51	11	.	.	PUNCT
ejpam-5889	52	1	a	a	DET
ejpam-5889	52	2	multiset	multiset	ADJ
ejpam-5889	52	3	d	d	NOUN
ejpam-5889	52	4	of	of	ADP
ejpam-5889	52	5	g	g	PROPN
ejpam-5889	52	6	is	be	AUX
ejpam-5889	52	7	called	call	VERB
ejpam-5889	52	8	a	a	DET
ejpam-5889	52	9	multigroup	multigroup	NOUN
ejpam-5889	52	10	of	of	ADP
ejpam-5889	52	11	g	g	PROPN
ejpam-5889	52	12	if	if	SCONJ
ejpam-5889	52	13	:	:	PUNCT
ejpam-5889	52	14	(	(	PUNCT
ejpam-5889	52	15	i	i	NOUN
ejpam-5889	52	16	)	)	PUNCT
ejpam-5889	52	17	cd(xy	cd(xy	PROPN
ejpam-5889	52	18	)	)	PUNCT
ejpam-5889	52	19	≥	≥	PROPN
ejpam-5889	52	20	min{cd(x	min{cd(x	PROPN
ejpam-5889	52	21	)	)	PUNCT
ejpam-5889	52	22	,	,	PUNCT
ejpam-5889	52	23	cd(y	cd(y	NOUN
ejpam-5889	52	24	)	)	PUNCT
ejpam-5889	52	25	}	}	PUNCT
ejpam-5889	52	26	∀	∀	PUNCT
ejpam-5889	52	27	x	x	NOUN
ejpam-5889	52	28	,	,	PUNCT
ejpam-5889	52	29	y	y	PROPN
ejpam-5889	52	30	∈	∈	PROPN
ejpam-5889	52	31	g	g	PROPN
ejpam-5889	52	32	,	,	PUNCT
ejpam-5889	52	33	(	(	PUNCT
ejpam-5889	52	34	ii	ii	NOUN
ejpam-5889	52	35	)	)	PUNCT
ejpam-5889	52	36	cd(x	cd(x	PUNCT
ejpam-5889	52	37	−1	−1	NOUN
ejpam-5889	52	38	)	)	PUNCT
ejpam-5889	52	39	=	=	SYM
ejpam-5889	52	40	cd(x	cd(x	X
ejpam-5889	52	41	)	)	PUNCT
ejpam-5889	52	42	∀	∀	X
ejpam-5889	53	1	x	x	SYM
ejpam-5889	53	2	∈	∈	NOUN
ejpam-5889	53	3	g.	g.	NOUN
ejpam-5889	53	4	it	it	PRON
ejpam-5889	53	5	is	be	AUX
ejpam-5889	53	6	worthy	worthy	ADJ
ejpam-5889	53	7	to	to	PART
ejpam-5889	53	8	note	note	VERB
ejpam-5889	53	9	that	that	PRON
ejpam-5889	53	10	,	,	PUNCT
ejpam-5889	53	11	cd(e	cd(e	NUM
ejpam-5889	53	12	)	)	PUNCT
ejpam-5889	53	13	≥	≥	NOUN
ejpam-5889	53	14	cd(x	cd(x	NOUN
ejpam-5889	53	15	)	)	PUNCT
ejpam-5889	53	16	∀	∀	X
ejpam-5889	54	1	x	x	SYM
ejpam-5889	54	2	∈	∈	NOUN
ejpam-5889	54	3	x	x	PUNCT
ejpam-5889	54	4	since	since	SCONJ
ejpam-5889	54	5	cd(e	cd(e	NOUN
ejpam-5889	54	6	)	)	PUNCT
ejpam-5889	54	7	=	=	SYM
ejpam-5889	54	8	cd(xx	cd(xx	PROPN
ejpam-5889	54	9	−1	−1	NOUN
ejpam-5889	54	10	)	)	PUNCT
ejpam-5889	54	11	≥	≥	PROPN
ejpam-5889	54	12	min{cd(x	min{cd(x	PROPN
ejpam-5889	54	13	)	)	PUNCT
ejpam-5889	54	14	,	,	PUNCT
ejpam-5889	54	15	cd(x	cd(x	X
ejpam-5889	54	16	)	)	PUNCT
ejpam-5889	54	17	}	}	PUNCT
ejpam-5889	54	18	=	=	SYM
ejpam-5889	54	19	cd(x	cd(x	X
ejpam-5889	54	20	)	)	PUNCT
ejpam-5889	54	21	∀x	∀x	VERB
ejpam-5889	54	22	∈	∈	PROPN
ejpam-5889	54	23	g.	g.	NOUN
ejpam-5889	54	24	in	in	ADP
ejpam-5889	54	25	addition	addition	NOUN
ejpam-5889	54	26	,	,	PUNCT
ejpam-5889	54	27	d∗	d∗	NOUN
ejpam-5889	54	28	defined	define	VERB
ejpam-5889	54	29	by	by	ADP
ejpam-5889	54	30	d∗	d∗	NOUN
ejpam-5889	54	31	=	=	SYM
ejpam-5889	54	32	{	{	PUNCT
ejpam-5889	54	33	x	x	SYM
ejpam-5889	54	34	∈	∈	PROPN
ejpam-5889	54	35	g	g	NOUN
ejpam-5889	54	36	|	|	ADV
ejpam-5889	54	37	cd(x	cd(x	PUNCT
ejpam-5889	54	38	)	)	PUNCT
ejpam-5889	54	39	>	>	X
ejpam-5889	54	40	0	0	NUM
ejpam-5889	54	41	}	}	PUNCT
ejpam-5889	54	42	is	be	AUX
ejpam-5889	54	43	a	a	DET
ejpam-5889	54	44	subgroup	subgroup	NOUN
ejpam-5889	54	45	of	of	ADP
ejpam-5889	54	46	g.	g.	PROPN
ejpam-5889	54	47	definition	definition	NOUN
ejpam-5889	54	48	6	6	NUM
ejpam-5889	54	49	(	(	PUNCT
ejpam-5889	54	50	[	[	X
ejpam-5889	54	51	26	26	NUM
ejpam-5889	54	52	]	]	PUNCT
ejpam-5889	54	53	)	)	PUNCT
ejpam-5889	54	54	.	.	PUNCT
ejpam-5889	55	1	if	if	SCONJ
ejpam-5889	55	2	d	d	PROPN
ejpam-5889	55	3	is	be	AUX
ejpam-5889	55	4	a	a	DET
ejpam-5889	55	5	multigroup	multigroup	NOUN
ejpam-5889	55	6	of	of	ADP
ejpam-5889	55	7	g	g	NOUN
ejpam-5889	55	8	,	,	PUNCT
ejpam-5889	55	9	then	then	ADV
ejpam-5889	55	10	the	the	DET
ejpam-5889	55	11	order	order	NOUN
ejpam-5889	55	12	of	of	ADP
ejpam-5889	55	13	d	d	PROPN
ejpam-5889	55	14	is	be	AUX
ejpam-5889	55	15	the	the	DET
ejpam-5889	55	16	sum	sum	NOUN
ejpam-5889	55	17	of	of	ADP
ejpam-5889	55	18	the	the	DET
ejpam-5889	55	19	multiplicities	multiplicity	NOUN
ejpam-5889	55	20	for	for	ADP
ejpam-5889	55	21	each	each	PRON
ejpam-5889	55	22	of	of	ADP
ejpam-5889	55	23	the	the	DET
ejpam-5889	55	24	elements	element	NOUN
ejpam-5889	55	25	in	in	ADP
ejpam-5889	55	26	d.	d.	PROPN
ejpam-5889	55	27	it	it	PRON
ejpam-5889	55	28	is	be	AUX
ejpam-5889	55	29	mathematically	mathematically	ADV
ejpam-5889	55	30	presented	present	VERB
ejpam-5889	55	31	as	as	ADP
ejpam-5889	55	32	:	:	PUNCT
ejpam-5889	55	33	|d|	|d|	PROPN
ejpam-5889	55	34	=	=	SYM
ejpam-5889	55	35	n∑	n∑	PROPN
ejpam-5889	55	36	i=1	i=1	PROPN
ejpam-5889	56	1	cd(xi	cd(xi	PROPN
ejpam-5889	56	2	)	)	PUNCT
ejpam-5889	57	1	∀xi	∀xi	PROPN
ejpam-5889	57	2	∈	∈	PROPN
ejpam-5889	57	3	g.	g.	NOUN
ejpam-5889	57	4	(	(	PUNCT
ejpam-5889	57	5	3	3	X
ejpam-5889	57	6	)	)	PUNCT
ejpam-5889	57	7	definition	definition	NOUN
ejpam-5889	57	8	7	7	NUM
ejpam-5889	57	9	(	(	PUNCT
ejpam-5889	57	10	[	[	X
ejpam-5889	57	11	31	31	NUM
ejpam-5889	57	12	]	]	PUNCT
ejpam-5889	57	13	)	)	PUNCT
ejpam-5889	57	14	.	.	PUNCT
ejpam-5889	58	1	a	a	DET
ejpam-5889	58	2	multigroup	multigroup	PROPN
ejpam-5889	58	3	d	d	NOUN
ejpam-5889	58	4	of	of	ADP
ejpam-5889	58	5	g	g	PROPN
ejpam-5889	58	6	is	be	AUX
ejpam-5889	58	7	commutative	commutative	ADJ
ejpam-5889	58	8	if	if	SCONJ
ejpam-5889	58	9	cd(xy	cd(xy	NUM
ejpam-5889	58	10	)	)	PUNCT
ejpam-5889	59	1	=	=	SYM
ejpam-5889	59	2	cd(yx	cd(yx	NOUN
ejpam-5889	59	3	)	)	PUNCT
ejpam-5889	59	4	∀	∀	PUNCT
ejpam-5889	60	1	x	x	X
ejpam-5889	60	2	,	,	PUNCT
ejpam-5889	60	3	y	y	PROPN
ejpam-5889	60	4	∈	∈	PROPN
ejpam-5889	60	5	g.	g.	NOUN
ejpam-5889	60	6	if	if	SCONJ
ejpam-5889	60	7	g	g	PROPN
ejpam-5889	60	8	is	be	AUX
ejpam-5889	60	9	commutative	commutative	ADJ
ejpam-5889	60	10	,	,	PUNCT
ejpam-5889	60	11	then	then	ADV
ejpam-5889	60	12	a	a	DET
ejpam-5889	60	13	multigroup	multigroup	NOUN
ejpam-5889	60	14	d	d	NOUN
ejpam-5889	60	15	of	of	ADP
ejpam-5889	60	16	g	g	PROPN
ejpam-5889	60	17	is	be	AUX
ejpam-5889	60	18	a	a	DET
ejpam-5889	60	19	commutative	commutative	ADJ
ejpam-5889	60	20	multigroup	multigroup	NOUN
ejpam-5889	60	21	.	.	PUNCT
ejpam-5889	61	1	definition	definition	NOUN
ejpam-5889	61	2	8	8	NUM
ejpam-5889	61	3	(	(	PUNCT
ejpam-5889	61	4	[	[	X
ejpam-5889	61	5	31	31	NUM
ejpam-5889	61	6	]	]	PUNCT
ejpam-5889	61	7	)	)	PUNCT
ejpam-5889	61	8	.	.	PUNCT
ejpam-5889	62	1	suppose	suppose	VERB
ejpam-5889	62	2	d	d	NOUN
ejpam-5889	62	3	and	and	CCONJ
ejpam-5889	62	4	e	e	NOUN
ejpam-5889	62	5	are	be	AUX
ejpam-5889	62	6	multigroups	multigroup	NOUN
ejpam-5889	62	7	of	of	ADP
ejpam-5889	62	8	g	g	NOUN
ejpam-5889	62	9	,	,	PUNCT
ejpam-5889	62	10	then	then	ADV
ejpam-5889	62	11	d	d	PROPN
ejpam-5889	62	12	is	be	AUX
ejpam-5889	62	13	a	a	DET
ejpam-5889	62	14	submultigroup	submultigroup	NOUN
ejpam-5889	62	15	of	of	ADP
ejpam-5889	62	16	e	e	PROPN
ejpam-5889	62	17	if	if	SCONJ
ejpam-5889	62	18	d	d	PROPN
ejpam-5889	62	19	⊆	⊆	NUM
ejpam-5889	62	20	e.	e.	PROPN
ejpam-5889	62	21	again	again	ADV
ejpam-5889	62	22	,	,	PUNCT
ejpam-5889	62	23	d	d	PROPN
ejpam-5889	62	24	is	be	AUX
ejpam-5889	62	25	a	a	DET
ejpam-5889	62	26	proper	proper	ADJ
ejpam-5889	62	27	submultigroup	submultigroup	NOUN
ejpam-5889	62	28	of	of	ADP
ejpam-5889	62	29	e	e	PROPN
ejpam-5889	62	30	if	if	SCONJ
ejpam-5889	62	31	d	d	PROPN
ejpam-5889	62	32	⊆	⊆	NUM
ejpam-5889	62	33	e	e	NOUN
ejpam-5889	62	34	and	and	CCONJ
ejpam-5889	62	35	d	d	PROPN
ejpam-5889	62	36	̸=	̸=	PROPN
ejpam-5889	62	37	e.	e.	PROPN
ejpam-5889	62	38	definition	definition	NOUN
ejpam-5889	62	39	9	9	NUM
ejpam-5889	62	40	(	(	PUNCT
ejpam-5889	62	41	[	[	X
ejpam-5889	62	42	22	22	NUM
ejpam-5889	62	43	]	]	PUNCT
ejpam-5889	62	44	)	)	PUNCT
ejpam-5889	62	45	.	.	PUNCT
ejpam-5889	63	1	suppose	suppose	VERB
ejpam-5889	63	2	d	d	X
ejpam-5889	63	3	is	be	AUX
ejpam-5889	63	4	a	a	DET
ejpam-5889	63	5	submultigroup	submultigroup	NOUN
ejpam-5889	63	6	of	of	ADP
ejpam-5889	63	7	a	a	DET
ejpam-5889	63	8	multigroup	multigroup	ADJ
ejpam-5889	63	9	e	e	NOUN
ejpam-5889	63	10	of	of	ADP
ejpam-5889	63	11	g	g	PROPN
ejpam-5889	63	12	,	,	PUNCT
ejpam-5889	63	13	then	then	ADV
ejpam-5889	63	14	d	d	PROPN
ejpam-5889	63	15	is	be	AUX
ejpam-5889	63	16	normal	normal	ADJ
ejpam-5889	63	17	in	in	ADP
ejpam-5889	63	18	e	e	NOUN
ejpam-5889	63	19	denoted	denote	VERB
ejpam-5889	63	20	by	by	ADP
ejpam-5889	63	21	d	d	PROPN
ejpam-5889	63	22	◁	◁	X
ejpam-5889	63	23	e	e	NOUN
ejpam-5889	63	24	if	if	SCONJ
ejpam-5889	63	25	cd(xy	cd(xy	PROPN
ejpam-5889	63	26	)	)	PUNCT
ejpam-5889	64	1	=	=	SYM
ejpam-5889	64	2	cd(yx	cd(yx	NOUN
ejpam-5889	64	3	)	)	PUNCT
ejpam-5889	64	4	⇐	⇐	ADJ
ejpam-5889	64	5	⇒	⇒	NOUN
ejpam-5889	64	6	cd(y	cd(y	PUNCT
ejpam-5889	64	7	)	)	PUNCT
ejpam-5889	64	8	=	=	SYM
ejpam-5889	64	9	cd(x	cd(x	X
ejpam-5889	64	10	−1yx	−1yx	NUM
ejpam-5889	64	11	)	)	PUNCT
ejpam-5889	64	12	∀	∀	X
ejpam-5889	65	1	x	x	NOUN
ejpam-5889	65	2	,	,	PUNCT
ejpam-5889	65	3	y	y	PROPN
ejpam-5889	65	4	∈	∈	PROPN
ejpam-5889	65	5	g.	g.	PROPN
ejpam-5889	65	6	certainly	certainly	ADV
ejpam-5889	65	7	,	,	PUNCT
ejpam-5889	65	8	any	any	DET
ejpam-5889	65	9	normal	normal	ADJ
ejpam-5889	65	10	submultigroup	submultigroup	NOUN
ejpam-5889	65	11	is	be	AUX
ejpam-5889	65	12	commutative	commutative	ADJ
ejpam-5889	65	13	and	and	CCONJ
ejpam-5889	65	14	self	self	NOUN
ejpam-5889	65	15	-	-	PUNCT
ejpam-5889	65	16	normal	normal	ADJ
ejpam-5889	65	17	.	.	PUNCT
ejpam-5889	66	1	definition	definition	NOUN
ejpam-5889	66	2	10	10	NUM
ejpam-5889	66	3	(	(	PUNCT
ejpam-5889	66	4	[	[	X
ejpam-5889	66	5	28	28	NUM
ejpam-5889	66	6	]	]	NUM
ejpam-5889	66	7	)	)	PUNCT
ejpam-5889	66	8	.	.	PUNCT
ejpam-5889	67	1	let	let	VERB
ejpam-5889	67	2	d	d	PRON
ejpam-5889	67	3	be	be	AUX
ejpam-5889	67	4	a	a	DET
ejpam-5889	67	5	submultigroup	submultigroup	NOUN
ejpam-5889	67	6	of	of	ADP
ejpam-5889	67	7	a	a	DET
ejpam-5889	67	8	multigroup	multigroup	ADJ
ejpam-5889	67	9	e	e	NOUN
ejpam-5889	67	10	of	of	ADP
ejpam-5889	67	11	g.	g.	PROPN
ejpam-5889	67	12	then	then	ADV
ejpam-5889	67	13	,	,	PUNCT
ejpam-5889	67	14	the	the	DET
ejpam-5889	67	15	submultiset	submultiset	NOUN
ejpam-5889	67	16	yd	yd	NOUN
ejpam-5889	67	17	of	of	ADP
ejpam-5889	67	18	e	e	PROPN
ejpam-5889	67	19	for	for	ADP
ejpam-5889	67	20	y	y	PROPN
ejpam-5889	67	21	∈	∈	PROPN
ejpam-5889	67	22	g	g	PROPN
ejpam-5889	67	23	defined	define	VERB
ejpam-5889	67	24	by	by	ADP
ejpam-5889	67	25	cyd(x	cyd(x	PROPN
ejpam-5889	67	26	)	)	PUNCT
ejpam-5889	67	27	=	=	SYM
ejpam-5889	67	28	cd(y	cd(y	NUM
ejpam-5889	67	29	−1x	−1x	NOUN
ejpam-5889	67	30	)	)	PUNCT
ejpam-5889	67	31	∀	∀	X
ejpam-5889	68	1	x	x	X
ejpam-5889	68	2	∈	∈	NOUN
ejpam-5889	68	3	g	g	PROPN
ejpam-5889	68	4	is	be	AUX
ejpam-5889	68	5	a	a	DET
ejpam-5889	68	6	left	left	ADJ
ejpam-5889	68	7	comultiset	comultiset	NOUN
ejpam-5889	68	8	of	of	ADP
ejpam-5889	68	9	d.	d.	PROPN
ejpam-5889	68	10	similarly	similarly	ADV
ejpam-5889	68	11	,	,	PUNCT
ejpam-5889	68	12	dy	dy	NOUN
ejpam-5889	68	13	of	of	ADP
ejpam-5889	68	14	e	e	PROPN
ejpam-5889	68	15	such	such	ADJ
ejpam-5889	68	16	that	that	PRON
ejpam-5889	68	17	cdy(x	cdy(x	PROPN
ejpam-5889	68	18	)	)	PUNCT
ejpam-5889	68	19	=	=	SYM
ejpam-5889	68	20	cd(xy	cd(xy	NOUN
ejpam-5889	68	21	−1	−1	NOUN
ejpam-5889	68	22	)	)	PUNCT
ejpam-5889	68	23	∀	∀	X
ejpam-5889	69	1	x	x	X
ejpam-5889	69	2	∈	∈	NOUN
ejpam-5889	69	3	g	g	PROPN
ejpam-5889	69	4	is	be	AUX
ejpam-5889	69	5	a	a	DET
ejpam-5889	69	6	right	right	ADJ
ejpam-5889	69	7	comultiset	comultiset	NOUN
ejpam-5889	69	8	of	of	ADP
ejpam-5889	69	9	d.	d.	PROPN
ejpam-5889	69	10	definition	definition	NOUN
ejpam-5889	69	11	11	11	NUM
ejpam-5889	69	12	(	(	PUNCT
ejpam-5889	69	13	[	[	X
ejpam-5889	69	14	18	18	NUM
ejpam-5889	69	15	]	]	NUM
ejpam-5889	69	16	)	)	PUNCT
ejpam-5889	69	17	.	.	PUNCT
ejpam-5889	70	1	suppose	suppose	VERB
ejpam-5889	70	2	d	d	NOUN
ejpam-5889	70	3	and	and	CCONJ
ejpam-5889	70	4	e	e	NOUN
ejpam-5889	70	5	are	be	AUX
ejpam-5889	70	6	multigroups	multigroup	NOUN
ejpam-5889	70	7	of	of	ADP
ejpam-5889	70	8	g.	g.	PROPN
ejpam-5889	70	9	then	then	ADV
ejpam-5889	70	10	,	,	PUNCT
ejpam-5889	70	11	the	the	DET
ejpam-5889	70	12	product	product	NOUN
ejpam-5889	70	13	d	d	X
ejpam-5889	70	14	◦	◦	NOUN
ejpam-5889	70	15	e	e	NOUN
ejpam-5889	70	16	is	be	AUX
ejpam-5889	70	17	a	a	DET
ejpam-5889	70	18	multiset	multiset	NOUN
ejpam-5889	70	19	of	of	ADP
ejpam-5889	70	20	g	g	PROPN
ejpam-5889	70	21	defined	define	VERB
ejpam-5889	70	22	as	as	ADP
ejpam-5889	70	23	follows	follow	VERB
ejpam-5889	70	24	:	:	PUNCT
ejpam-5889	70	25	cd	cd	PROPN
ejpam-5889	70	26	◦	◦	NOUN
ejpam-5889	70	27	e(x	e(x	NUM
ejpam-5889	70	28	)	)	PUNCT
ejpam-5889	70	29	=	=	PRON
ejpam-5889	70	30	{	{	PUNCT
ejpam-5889	70	31	∨	∨	NOUN
ejpam-5889	70	32	x	x	NOUN
ejpam-5889	70	33	=	=	PROPN
ejpam-5889	70	34	yz	yz	PROPN
ejpam-5889	70	35	min{cd(y	min{cd(y	PROPN
ejpam-5889	70	36	)	)	PUNCT
ejpam-5889	70	37	,	,	PUNCT
ejpam-5889	70	38	ce(z	ce(z	NOUN
ejpam-5889	70	39	)	)	PUNCT
ejpam-5889	70	40	}	}	PUNCT
ejpam-5889	70	41	,	,	PUNCT
ejpam-5889	70	42	if	if	SCONJ
ejpam-5889	70	43	∃	∃	PROPN
ejpam-5889	70	44	y	y	PROPN
ejpam-5889	70	45	,	,	PUNCT
ejpam-5889	70	46	z	z	PROPN
ejpam-5889	70	47	∈	∈	PROPN
ejpam-5889	70	48	g	g	NOUN
ejpam-5889	70	49	where	where	SCONJ
ejpam-5889	70	50	x	x	ADP
ejpam-5889	70	51	=	=	PUNCT
ejpam-5889	70	52	yz	yz	PROPN
ejpam-5889	70	53	0	0	PROPN
ejpam-5889	70	54	,	,	PUNCT
ejpam-5889	70	55	otherwise	otherwise	ADV
ejpam-5889	70	56	.	.	PUNCT
ejpam-5889	71	1	(	(	PUNCT
ejpam-5889	71	2	4	4	X
ejpam-5889	71	3	)	)	PUNCT
ejpam-5889	71	4	definition	definition	NOUN
ejpam-5889	71	5	12	12	NUM
ejpam-5889	71	6	(	(	PUNCT
ejpam-5889	71	7	[	[	X
ejpam-5889	71	8	28	28	NUM
ejpam-5889	71	9	]	]	NUM
ejpam-5889	71	10	)	)	PUNCT
ejpam-5889	71	11	.	.	PUNCT
ejpam-5889	72	1	suppose	suppose	VERB
ejpam-5889	72	2	e	e	NOUN
ejpam-5889	72	3	is	be	AUX
ejpam-5889	72	4	a	a	DET
ejpam-5889	72	5	multigroup	multigroup	NOUN
ejpam-5889	72	6	of	of	ADP
ejpam-5889	72	7	g	g	PROPN
ejpam-5889	72	8	and	and	CCONJ
ejpam-5889	72	9	d	d	PROPN
ejpam-5889	72	10	a	a	DET
ejpam-5889	72	11	normal	normal	ADJ
ejpam-5889	72	12	submultigroup	submultigroup	NOUN
ejpam-5889	72	13	in	in	ADP
ejpam-5889	72	14	e.	e.	PROPN
ejpam-5889	72	15	then	then	ADV
ejpam-5889	72	16	,	,	PUNCT
ejpam-5889	72	17	the	the	DET
ejpam-5889	72	18	set	set	NOUN
ejpam-5889	72	19	of	of	ADP
ejpam-5889	72	20	right	right	ADJ
ejpam-5889	72	21	/	/	SYM
ejpam-5889	72	22	left	left	ADJ
ejpam-5889	72	23	comultisets	comultiset	NOUN
ejpam-5889	72	24	of	of	ADP
ejpam-5889	72	25	d	d	PROPN
ejpam-5889	72	26	such	such	ADJ
ejpam-5889	72	27	that	that	DET
ejpam-5889	72	28	cxd	cxd	NOUN
ejpam-5889	72	29	◦	◦	NOUN
ejpam-5889	72	30	yd(z	yd(z	NOUN
ejpam-5889	72	31	)	)	PUNCT
ejpam-5889	72	32	=	=	SYM
ejpam-5889	72	33	cxyd(z	cxyd(z	PROPN
ejpam-5889	72	34	)	)	PUNCT
ejpam-5889	72	35	∀	∀	X
ejpam-5889	73	1	x	x	NOUN
ejpam-5889	73	2	,	,	PUNCT
ejpam-5889	73	3	y	y	PROPN
ejpam-5889	73	4	,	,	PUNCT
ejpam-5889	73	5	z	z	PROPN
ejpam-5889	73	6	∈	∈	PROPN
ejpam-5889	73	7	g	g	PROPN
ejpam-5889	73	8	is	be	AUX
ejpam-5889	73	9	a	a	DET
ejpam-5889	73	10	factor	factor	NOUN
ejpam-5889	73	11	/	/	SYM
ejpam-5889	73	12	quotient	quotient	NOUN
ejpam-5889	73	13	multigroup	multigroup	NOUN
ejpam-5889	73	14	of	of	ADP
ejpam-5889	73	15	e	e	PROPN
ejpam-5889	73	16	by	by	ADP
ejpam-5889	73	17	d	d	PROPN
ejpam-5889	73	18	,	,	PUNCT
ejpam-5889	73	19	represented	represent	VERB
ejpam-5889	73	20	as	as	ADP
ejpam-5889	73	21	e	e	PROPN
ejpam-5889	73	22	/	/	SYM
ejpam-5889	73	23	d.	d.	PROPN
ejpam-5889	73	24	p.	p.	PROPN
ejpam-5889	73	25	a.	a.	PROPN
ejpam-5889	73	26	ejegwa	ejegwa	PROPN
ejpam-5889	73	27	et	et	PROPN
ejpam-5889	73	28	al	al	PROPN
ejpam-5889	73	29	.	.	PUNCT
ejpam-5889	73	30	/	/	SYM
ejpam-5889	73	31	eur	eur	PROPN
ejpam-5889	73	32	.	.	PUNCT
ejpam-5889	74	1	j.	j.	PROPN
ejpam-5889	74	2	pure	pure	PROPN
ejpam-5889	74	3	appl	appl	PROPN
ejpam-5889	74	4	.	.	PROPN
ejpam-5889	74	5	math	math	PROPN
ejpam-5889	74	6	,	,	PUNCT
ejpam-5889	74	7	18	18	NUM
ejpam-5889	74	8	(	(	PUNCT
ejpam-5889	74	9	2	2	NUM
ejpam-5889	74	10	)	)	PUNCT
ejpam-5889	74	11	(	(	PUNCT
ejpam-5889	74	12	2025	2025	NUM
ejpam-5889	74	13	)	)	PUNCT
ejpam-5889	74	14	,	,	PUNCT
ejpam-5889	74	15	5889	5889	NUM
ejpam-5889	74	16	4	4	NUM
ejpam-5889	74	17	of	of	ADP
ejpam-5889	74	18	13	13	NUM
ejpam-5889	74	19	2	2	NUM
ejpam-5889	74	20	.	.	PUNCT
ejpam-5889	74	21	main	main	ADJ
ejpam-5889	74	22	results	result	NOUN
ejpam-5889	74	23	before	before	ADP
ejpam-5889	74	24	the	the	DET
ejpam-5889	74	25	introduction	introduction	NOUN
ejpam-5889	74	26	of	of	ADP
ejpam-5889	74	27	normal	normal	ADJ
ejpam-5889	74	28	series	series	NOUN
ejpam-5889	74	29	,	,	PUNCT
ejpam-5889	74	30	composition	composition	NOUN
ejpam-5889	74	31	series	series	NOUN
ejpam-5889	74	32	,	,	PUNCT
ejpam-5889	74	33	and	and	CCONJ
ejpam-5889	74	34	jordan	jordan	PROPN
ejpam-5889	74	35	-	-	PUNCT
ejpam-5889	74	36	hölder	hölder	PROPN
ejpam-5889	74	37	therorem	therorem	VERB
ejpam-5889	74	38	under	under	ADP
ejpam-5889	74	39	multigroups	multigroup	NOUN
ejpam-5889	74	40	,	,	PUNCT
ejpam-5889	74	41	we	we	PRON
ejpam-5889	74	42	first	first	ADV
ejpam-5889	74	43	reiterate	reiterate	VERB
ejpam-5889	74	44	solvable	solvable	ADJ
ejpam-5889	74	45	multigroups	multigroup	NOUN
ejpam-5889	74	46	as	as	SCONJ
ejpam-5889	74	47	established	establish	VERB
ejpam-5889	74	48	in	in	ADP
ejpam-5889	74	49	[	[	X
ejpam-5889	74	50	39	39	NUM
ejpam-5889	74	51	]	]	PUNCT
ejpam-5889	74	52	as	as	SCONJ
ejpam-5889	74	53	follows	follow	VERB
ejpam-5889	74	54	:	:	PUNCT
ejpam-5889	74	55	definition	definition	NOUN
ejpam-5889	74	56	13	13	NUM
ejpam-5889	74	57	.	.	PUNCT
ejpam-5889	75	1	for	for	ADP
ejpam-5889	75	2	every	every	DET
ejpam-5889	75	3	finite	finite	NOUN
ejpam-5889	75	4	multigroup	multigroup	PROPN
ejpam-5889	75	5	d	d	PROPN
ejpam-5889	75	6	of	of	ADP
ejpam-5889	75	7	a	a	DET
ejpam-5889	75	8	finite	finite	NOUN
ejpam-5889	75	9	g	g	NOUN
ejpam-5889	75	10	,	,	PUNCT
ejpam-5889	75	11	there	there	PRON
ejpam-5889	75	12	is	be	VERB
ejpam-5889	75	13	a	a	DET
ejpam-5889	75	14	chain	chain	NOUN
ejpam-5889	75	15	of	of	ADP
ejpam-5889	75	16	consecutive	consecutive	ADJ
ejpam-5889	75	17	submultigroups	submultigroup	NOUN
ejpam-5889	75	18	of	of	ADP
ejpam-5889	75	19	d	d	NOUN
ejpam-5889	75	20	:	:	PUNCT
ejpam-5889	75	21	d0	d0	NOUN
ejpam-5889	75	22	⊆	⊆	NUM
ejpam-5889	75	23	d1	d1	NOUN
ejpam-5889	75	24	⊆	⊆	NUM
ejpam-5889	75	25	·	·	PUNCT
ejpam-5889	75	26	·	·	PUNCT
ejpam-5889	75	27	·	·	PUNCT
ejpam-5889	76	1	⊆	⊆	NUM
ejpam-5889	76	2	dn	dn	NOUN
ejpam-5889	76	3	=	=	SYM
ejpam-5889	76	4	d	d	PROPN
ejpam-5889	76	5	,	,	PUNCT
ejpam-5889	76	6	(	(	PUNCT
ejpam-5889	76	7	5	5	NUM
ejpam-5889	76	8	)	)	PUNCT
ejpam-5889	76	9	where	where	SCONJ
ejpam-5889	76	10	(	(	PUNCT
ejpam-5889	76	11	d0)∗	d0)∗	NOUN
ejpam-5889	76	12	=	=	SYM
ejpam-5889	76	13	(	(	PUNCT
ejpam-5889	76	14	d1)∗	d1)∗	ADJ
ejpam-5889	76	15	=	=	SYM
ejpam-5889	76	16	·	·	PUNCT
ejpam-5889	76	17	·	·	PUNCT
ejpam-5889	76	18	·	·	PUNCT
ejpam-5889	77	1	=	=	PUNCT
ejpam-5889	77	2	(	(	PUNCT
ejpam-5889	77	3	dn)∗	dn)∗	NUM
ejpam-5889	77	4	=	=	NOUN
ejpam-5889	77	5	d∗.	d∗.	ADP
ejpam-5889	77	6	the	the	DET
ejpam-5889	77	7	chain	chain	NOUN
ejpam-5889	77	8	of	of	ADP
ejpam-5889	77	9	the	the	DET
ejpam-5889	77	10	consecutive	consecutive	ADJ
ejpam-5889	77	11	submultigroups	submultigroup	NOUN
ejpam-5889	77	12	is	be	AUX
ejpam-5889	77	13	also	also	ADV
ejpam-5889	77	14	presented	present	VERB
ejpam-5889	77	15	as	as	ADP
ejpam-5889	77	16	:	:	PUNCT
ejpam-5889	77	17	cd0(x	cd0(x	NOUN
ejpam-5889	77	18	)	)	PUNCT
ejpam-5889	77	19	≤	≤	NUM
ejpam-5889	77	20	cd1(x	cd1(x	NOUN
ejpam-5889	77	21	)	)	PUNCT
ejpam-5889	77	22	≤	≤	NOUN
ejpam-5889	77	23	·	·	PUNCT
ejpam-5889	77	24	·	·	PUNCT
ejpam-5889	78	1	·	·	PUNCT
ejpam-5889	78	2	≤	≤	NUM
ejpam-5889	78	3	cdn(x	cdn(x	PROPN
ejpam-5889	78	4	)	)	PUNCT
ejpam-5889	78	5	=	=	SYM
ejpam-5889	78	6	cd(x	cd(x	X
ejpam-5889	78	7	)	)	PUNCT
ejpam-5889	78	8	,	,	PUNCT
ejpam-5889	78	9	∀x	∀x	VERB
ejpam-5889	78	10	∈	∈	PROPN
ejpam-5889	78	11	g	g	NOUN
ejpam-5889	78	12	(	(	PUNCT
ejpam-5889	78	13	6	6	NUM
ejpam-5889	78	14	)	)	PUNCT
ejpam-5889	78	15	such	such	ADJ
ejpam-5889	78	16	that	that	SCONJ
ejpam-5889	78	17	(	(	PUNCT
ejpam-5889	78	18	d0)∗	d0)∗	NOUN
ejpam-5889	78	19	=	=	SYM
ejpam-5889	78	20	(	(	PUNCT
ejpam-5889	78	21	d1)∗	d1)∗	ADJ
ejpam-5889	78	22	=	=	SYM
ejpam-5889	78	23	·	·	PUNCT
ejpam-5889	78	24	·	·	PUNCT
ejpam-5889	78	25	·	·	PUNCT
ejpam-5889	78	26	=	=	PUNCT
ejpam-5889	78	27	(	(	PUNCT
ejpam-5889	78	28	dn)∗	dn)∗	NUM
ejpam-5889	78	29	=	=	NOUN
ejpam-5889	78	30	d∗.	d∗.	PROPN
ejpam-5889	78	31	definition	definition	NOUN
ejpam-5889	78	32	14	14	NUM
ejpam-5889	78	33	.	.	PUNCT
ejpam-5889	79	1	if	if	SCONJ
ejpam-5889	79	2	d	d	PROPN
ejpam-5889	79	3	is	be	AUX
ejpam-5889	79	4	a	a	DET
ejpam-5889	79	5	multigroup	multigroup	NOUN
ejpam-5889	79	6	of	of	ADP
ejpam-5889	79	7	g	g	NOUN
ejpam-5889	79	8	,	,	PUNCT
ejpam-5889	79	9	then	then	ADV
ejpam-5889	79	10	d	d	PROPN
ejpam-5889	79	11	is	be	AUX
ejpam-5889	79	12	solvable	solvable	ADJ
ejpam-5889	79	13	if	if	SCONJ
ejpam-5889	79	14	it	it	PRON
ejpam-5889	79	15	has	have	VERB
ejpam-5889	79	16	a	a	DET
ejpam-5889	79	17	chain	chain	NOUN
ejpam-5889	79	18	of	of	ADP
ejpam-5889	79	19	consecutive	consecutive	ADJ
ejpam-5889	79	20	submultigroups	submultigroup	NOUN
ejpam-5889	79	21	:	:	PUNCT
ejpam-5889	79	22	d0	d0	NOUN
ejpam-5889	79	23	⊆	⊆	NUM
ejpam-5889	79	24	d1	d1	NOUN
ejpam-5889	79	25	⊆	⊆	NUM
ejpam-5889	79	26	·	·	PUNCT
ejpam-5889	79	27	·	·	PUNCT
ejpam-5889	79	28	·	·	PUNCT
ejpam-5889	80	1	⊆	⊆	NUM
ejpam-5889	80	2	dn	dn	NOUN
ejpam-5889	80	3	=	=	SYM
ejpam-5889	80	4	d	d	PROPN
ejpam-5889	80	5	(	(	PUNCT
ejpam-5889	80	6	7	7	NUM
ejpam-5889	80	7	)	)	PUNCT
ejpam-5889	80	8	such	such	ADJ
ejpam-5889	80	9	that	that	SCONJ
ejpam-5889	80	10	(	(	PUNCT
ejpam-5889	80	11	d0)∗	d0)∗	NOUN
ejpam-5889	80	12	=	=	SYM
ejpam-5889	80	13	(	(	PUNCT
ejpam-5889	80	14	d1)∗	d1)∗	ADJ
ejpam-5889	80	15	=	=	SYM
ejpam-5889	80	16	·	·	PUNCT
ejpam-5889	80	17	·	·	PUNCT
ejpam-5889	80	18	·	·	PUNCT
ejpam-5889	80	19	=	=	PUNCT
ejpam-5889	80	20	(	(	PUNCT
ejpam-5889	80	21	dn)∗	dn)∗	NUM
ejpam-5889	80	22	=	=	SYM
ejpam-5889	80	23	d∗	d∗	PROPN
ejpam-5889	80	24	,	,	PUNCT
ejpam-5889	80	25	where	where	SCONJ
ejpam-5889	80	26	di−1	di−1	PROPN
ejpam-5889	80	27	◁di	◁di	ADJ
ejpam-5889	80	28	and	and	CCONJ
ejpam-5889	80	29	di	di	PROPN
ejpam-5889	80	30	/	/	SYM
ejpam-5889	80	31	di−1	di−1	PROPN
ejpam-5889	80	32	is	be	AUX
ejpam-5889	80	33	commutative	commutative	ADJ
ejpam-5889	80	34	∀	∀	X
ejpam-5889	80	35	1	1	NUM
ejpam-5889	80	36	≤	≤	NUM
ejpam-5889	80	37	i	i	PRON
ejpam-5889	80	38	≤	≤	PROPN
ejpam-5889	80	39	n.	n.	VERB
ejpam-5889	80	40	the	the	DET
ejpam-5889	80	41	finite	finite	PROPN
ejpam-5889	80	42	chain	chain	NOUN
ejpam-5889	80	43	of	of	ADP
ejpam-5889	80	44	consecutive	consecutive	ADJ
ejpam-5889	80	45	submultigroups	submultigroup	NOUN
ejpam-5889	80	46	of	of	ADP
ejpam-5889	80	47	d	d	PROPN
ejpam-5889	80	48	is	be	AUX
ejpam-5889	80	49	a	a	DET
ejpam-5889	80	50	solvable	solvable	ADJ
ejpam-5889	80	51	series	series	NOUN
ejpam-5889	80	52	for	for	ADP
ejpam-5889	80	53	d	d	PROPN
ejpam-5889	80	54	denoted	denote	VERB
ejpam-5889	80	55	by	by	ADP
ejpam-5889	80	56	di	di	NOUN
ejpam-5889	80	57	.	.	PUNCT
ejpam-5889	81	1	in	in	ADP
ejpam-5889	81	2	fact	fact	NOUN
ejpam-5889	81	3	,	,	PUNCT
ejpam-5889	81	4	the	the	DET
ejpam-5889	81	5	solvable	solvable	ADJ
ejpam-5889	81	6	series	series	NOUN
ejpam-5889	81	7	for	for	ADP
ejpam-5889	81	8	d	d	PROPN
ejpam-5889	81	9	is	be	AUX
ejpam-5889	81	10	presented	present	VERB
ejpam-5889	81	11	as	as	ADP
ejpam-5889	81	12	:	:	PUNCT
ejpam-5889	81	13	d0	d0	PROPN
ejpam-5889	81	14	◁d1	◁d1	VERB
ejpam-5889	81	15	◁	◁	X
ejpam-5889	81	16	·	·	PUNCT
ejpam-5889	81	17	·	·	PUNCT
ejpam-5889	81	18	·	·	PUNCT
ejpam-5889	81	19	◁dn	◁dn	NOUN
ejpam-5889	81	20	=	=	SYM
ejpam-5889	81	21	d.	d.	PROPN
ejpam-5889	81	22	(	(	PUNCT
ejpam-5889	81	23	8)	8)	NUM
ejpam-5889	81	24	next	next	ADV
ejpam-5889	81	25	,	,	PUNCT
ejpam-5889	81	26	we	we	PRON
ejpam-5889	81	27	shall	shall	AUX
ejpam-5889	81	28	define	define	VERB
ejpam-5889	81	29	the	the	DET
ejpam-5889	81	30	concepts	concept	NOUN
ejpam-5889	81	31	of	of	ADP
ejpam-5889	81	32	maximal	maximal	ADJ
ejpam-5889	81	33	normal	normal	ADJ
ejpam-5889	81	34	submultigroup	submultigroup	NOUN
ejpam-5889	81	35	of	of	ADP
ejpam-5889	81	36	a	a	DET
ejpam-5889	81	37	multigroup	multigroup	ADJ
ejpam-5889	81	38	and	and	CCONJ
ejpam-5889	81	39	simple	simple	ADJ
ejpam-5889	81	40	multigroup	multigroup	NOUN
ejpam-5889	81	41	.	.	PUNCT
ejpam-5889	82	1	from	from	ADP
ejpam-5889	82	2	the	the	DET
ejpam-5889	82	3	concept	concept	NOUN
ejpam-5889	82	4	of	of	ADP
ejpam-5889	82	5	normal	normal	ADJ
ejpam-5889	82	6	submultigroup	submultigroup	NOUN
ejpam-5889	82	7	in	in	ADP
ejpam-5889	82	8	definition	definition	NOUN
ejpam-5889	82	9	9	9	NUM
ejpam-5889	82	10	,	,	PUNCT
ejpam-5889	82	11	we	we	PRON
ejpam-5889	82	12	define	define	VERB
ejpam-5889	82	13	a	a	DET
ejpam-5889	82	14	maximal	maximal	ADJ
ejpam-5889	82	15	normal	normal	ADJ
ejpam-5889	82	16	submultigroup	submultigroup	NOUN
ejpam-5889	82	17	of	of	ADP
ejpam-5889	82	18	a	a	DET
ejpam-5889	82	19	multigroup	multigroup	NOUN
ejpam-5889	82	20	as	as	SCONJ
ejpam-5889	82	21	follows	follow	VERB
ejpam-5889	82	22	:	:	PUNCT
ejpam-5889	82	23	definition	definition	NOUN
ejpam-5889	82	24	15	15	NUM
ejpam-5889	82	25	.	.	PUNCT
ejpam-5889	83	1	let	let	VERB
ejpam-5889	83	2	c	c	NOUN
ejpam-5889	83	3	and	and	CCONJ
ejpam-5889	83	4	d	d	NOUN
ejpam-5889	83	5	be	be	AUX
ejpam-5889	83	6	multigroups	multigroup	NOUN
ejpam-5889	83	7	of	of	ADP
ejpam-5889	83	8	g	g	NOUN
ejpam-5889	83	9	such	such	ADJ
ejpam-5889	83	10	that	that	SCONJ
ejpam-5889	83	11	c	c	PROPN
ejpam-5889	83	12	◁d	◁d	PROPN
ejpam-5889	83	13	.	.	PUNCT
ejpam-5889	84	1	then	then	ADV
ejpam-5889	84	2	(	(	PUNCT
ejpam-5889	84	3	i	i	NOUN
ejpam-5889	84	4	)	)	PUNCT
ejpam-5889	84	5	c	c	PROPN
ejpam-5889	84	6	is	be	AUX
ejpam-5889	84	7	a	a	DET
ejpam-5889	84	8	maximal	maximal	ADJ
ejpam-5889	84	9	non	non	ADJ
ejpam-5889	84	10	-	-	ADJ
ejpam-5889	84	11	trivial	trivial	ADJ
ejpam-5889	84	12	normal	normal	ADJ
ejpam-5889	84	13	submultigroup	submultigroup	NOUN
ejpam-5889	84	14	if	if	SCONJ
ejpam-5889	84	15	it	it	PRON
ejpam-5889	84	16	is	be	AUX
ejpam-5889	84	17	the	the	DET
ejpam-5889	84	18	largest	large	ADJ
ejpam-5889	84	19	proper	proper	ADJ
ejpam-5889	84	20	non	non	ADJ
ejpam-5889	84	21	-	-	ADJ
ejpam-5889	84	22	trivial	trivial	ADJ
ejpam-5889	84	23	normal	normal	ADJ
ejpam-5889	84	24	submultigroup	submultigroup	NOUN
ejpam-5889	84	25	of	of	ADP
ejpam-5889	84	26	d.	d.	PROPN
ejpam-5889	84	27	(	(	PUNCT
ejpam-5889	84	28	ii	ii	PROPN
ejpam-5889	84	29	)	)	PUNCT
ejpam-5889	84	30	d	d	NOUN
ejpam-5889	84	31	is	be	AUX
ejpam-5889	84	32	simple	simple	ADJ
ejpam-5889	84	33	if	if	SCONJ
ejpam-5889	84	34	it	it	PRON
ejpam-5889	84	35	has	have	VERB
ejpam-5889	84	36	no	no	DET
ejpam-5889	84	37	proper	proper	ADJ
ejpam-5889	84	38	non	non	ADJ
ejpam-5889	84	39	-	-	ADJ
ejpam-5889	84	40	trivial	trivial	ADJ
ejpam-5889	84	41	normal	normal	ADJ
ejpam-5889	84	42	submultigroup	submultigroup	NOUN
ejpam-5889	84	43	.	.	PUNCT
ejpam-5889	85	1	remark	remark	PROPN
ejpam-5889	85	2	1	1	NUM
ejpam-5889	85	3	.	.	PUNCT
ejpam-5889	86	1	a	a	DET
ejpam-5889	86	2	submultigroup	submultigroup	NOUN
ejpam-5889	86	3	b	b	PROPN
ejpam-5889	86	4	of	of	ADP
ejpam-5889	86	5	a	a	DET
ejpam-5889	86	6	multigroup	multigroup	NOUN
ejpam-5889	86	7	d	d	NOUN
ejpam-5889	86	8	of	of	ADP
ejpam-5889	86	9	g	g	PROPN
ejpam-5889	86	10	is	be	AUX
ejpam-5889	86	11	trivial	trivial	ADJ
ejpam-5889	86	12	if	if	SCONJ
ejpam-5889	86	13	:	:	PUNCT
ejpam-5889	86	14	(	(	PUNCT
ejpam-5889	86	15	i	i	NOUN
ejpam-5889	86	16	)	)	PUNCT
ejpam-5889	86	17	b	b	PROPN
ejpam-5889	86	18	is	be	AUX
ejpam-5889	86	19	the	the	DET
ejpam-5889	86	20	identity	identity	NOUN
ejpam-5889	86	21	element	element	NOUN
ejpam-5889	86	22	or	or	CCONJ
ejpam-5889	86	23	the	the	DET
ejpam-5889	86	24	identity	identity	NOUN
ejpam-5889	86	25	element	element	NOUN
ejpam-5889	86	26	with	with	ADP
ejpam-5889	86	27	multiplicity	multiplicity	NOUN
ejpam-5889	86	28	,	,	PUNCT
ejpam-5889	86	29	(	(	PUNCT
ejpam-5889	86	30	ii	ii	NOUN
ejpam-5889	86	31	)	)	PUNCT
ejpam-5889	86	32	b	b	PROPN
ejpam-5889	86	33	is	be	AUX
ejpam-5889	86	34	a	a	DET
ejpam-5889	86	35	subgroup	subgroup	NOUN
ejpam-5889	86	36	of	of	ADP
ejpam-5889	86	37	g	g	PROPN
ejpam-5889	86	38	or	or	CCONJ
ejpam-5889	86	39	g	g	PROPN
ejpam-5889	86	40	itself	itself	PRON
ejpam-5889	86	41	,	,	PUNCT
ejpam-5889	86	42	(	(	PUNCT
ejpam-5889	86	43	iii	iii	X
ejpam-5889	86	44	)	)	PUNCT
ejpam-5889	86	45	b	b	NOUN
ejpam-5889	86	46	is	be	AUX
ejpam-5889	86	47	the	the	DET
ejpam-5889	86	48	same	same	ADJ
ejpam-5889	86	49	as	as	ADP
ejpam-5889	86	50	d.	d.	PROPN
ejpam-5889	86	51	p.	p.	PROPN
ejpam-5889	86	52	a.	a.	PROPN
ejpam-5889	86	53	ejegwa	ejegwa	PROPN
ejpam-5889	86	54	et	et	PROPN
ejpam-5889	86	55	al	al	PROPN
ejpam-5889	86	56	.	.	PUNCT
ejpam-5889	86	57	/	/	SYM
ejpam-5889	86	58	eur	eur	PROPN
ejpam-5889	86	59	.	.	PUNCT
ejpam-5889	87	1	j.	j.	PROPN
ejpam-5889	87	2	pure	pure	PROPN
ejpam-5889	87	3	appl	appl	PROPN
ejpam-5889	87	4	.	.	PROPN
ejpam-5889	87	5	math	math	PROPN
ejpam-5889	87	6	,	,	PUNCT
ejpam-5889	87	7	18	18	NUM
ejpam-5889	87	8	(	(	PUNCT
ejpam-5889	87	9	2	2	NUM
ejpam-5889	87	10	)	)	PUNCT
ejpam-5889	87	11	(	(	PUNCT
ejpam-5889	87	12	2025	2025	NUM
ejpam-5889	87	13	)	)	PUNCT
ejpam-5889	87	14	,	,	PUNCT
ejpam-5889	87	15	5889	5889	NUM
ejpam-5889	87	16	5	5	NUM
ejpam-5889	87	17	of	of	ADP
ejpam-5889	87	18	13	13	NUM
ejpam-5889	87	19	example	example	NOUN
ejpam-5889	87	20	1	1	NUM
ejpam-5889	87	21	.	.	PUNCT
ejpam-5889	87	22	suppose	suppose	VERB
ejpam-5889	87	23	g	g	PROPN
ejpam-5889	87	24	=	=	SYM
ejpam-5889	87	25	{	{	PUNCT
ejpam-5889	87	26	1	1	NUM
ejpam-5889	87	27	,	,	PUNCT
ejpam-5889	87	28	d	d	PROPN
ejpam-5889	87	29	,	,	PUNCT
ejpam-5889	87	30	d2	d2	PROPN
ejpam-5889	87	31	,	,	PUNCT
ejpam-5889	87	32	d3	d3	PROPN
ejpam-5889	87	33	}	}	PUNCT
ejpam-5889	87	34	where	where	SCONJ
ejpam-5889	87	35	d4	d4	PROPN
ejpam-5889	87	36	=	=	SYM
ejpam-5889	87	37	1	1	NUM
ejpam-5889	87	38	,	,	PUNCT
ejpam-5889	87	39	d−1	d−1	PROPN
ejpam-5889	87	40	=	=	PUNCT
ejpam-5889	87	41	d3	d3	PROPN
ejpam-5889	87	42	,	,	PUNCT
ejpam-5889	87	43	(	(	PUNCT
ejpam-5889	87	44	d2)−1	d2)−1	PROPN
ejpam-5889	87	45	=	=	SYM
ejpam-5889	87	46	d2	d2	PROPN
ejpam-5889	87	47	,	,	PUNCT
ejpam-5889	87	48	and	and	CCONJ
ejpam-5889	87	49	(	(	PUNCT
ejpam-5889	87	50	d3)−1	d3)−1	NOUN
ejpam-5889	87	51	=	=	PUNCT
ejpam-5889	87	52	d.	d.	NOUN
ejpam-5889	87	53	then	then	ADV
ejpam-5889	87	54	,	,	PUNCT
ejpam-5889	87	55	a	a	DET
ejpam-5889	87	56	multigroup	multigroup	NOUN
ejpam-5889	87	57	of	of	ADP
ejpam-5889	87	58	g	g	PROPN
ejpam-5889	87	59	is	be	AUX
ejpam-5889	87	60	:	:	PUNCT
ejpam-5889	88	1	d	d	X
ejpam-5889	88	2	=	=	SYM
ejpam-5889	88	3	{	{	PUNCT
ejpam-5889	88	4	1	1	NUM
ejpam-5889	88	5	,	,	PUNCT
ejpam-5889	88	6	1	1	NUM
ejpam-5889	88	7	,	,	PUNCT
ejpam-5889	88	8	1	1	NUM
ejpam-5889	88	9	,	,	PUNCT
ejpam-5889	88	10	1	1	NUM
ejpam-5889	88	11	,	,	PUNCT
ejpam-5889	88	12	d	d	NOUN
ejpam-5889	88	13	,	,	PUNCT
ejpam-5889	88	14	d	d	PROPN
ejpam-5889	88	15	,	,	PUNCT
ejpam-5889	88	16	d2	d2	PROPN
ejpam-5889	88	17	,	,	PUNCT
ejpam-5889	88	18	d2	d2	PROPN
ejpam-5889	88	19	,	,	PUNCT
ejpam-5889	88	20	d2	d2	PROPN
ejpam-5889	88	21	,	,	PUNCT
ejpam-5889	88	22	d3	d3	PROPN
ejpam-5889	88	23	,	,	PUNCT
ejpam-5889	88	24	d3	d3	PROPN
ejpam-5889	88	25	}	}	PUNCT
ejpam-5889	88	26	.	.	PUNCT
ejpam-5889	89	1	certainly	certainly	ADV
ejpam-5889	89	2	,	,	PUNCT
ejpam-5889	89	3	d	d	PROPN
ejpam-5889	89	4	is	be	AUX
ejpam-5889	89	5	commutative	commutative	ADJ
ejpam-5889	89	6	.	.	PUNCT
ejpam-5889	90	1	the	the	DET
ejpam-5889	90	2	submultigroups	submultigroup	NOUN
ejpam-5889	90	3	of	of	ADP
ejpam-5889	90	4	d	d	NOUN
ejpam-5889	90	5	can	can	AUX
ejpam-5889	90	6	be	be	AUX
ejpam-5889	90	7	presented	present	VERB
ejpam-5889	90	8	in	in	ADP
ejpam-5889	90	9	terms	term	NOUN
ejpam-5889	90	10	of	of	ADP
ejpam-5889	90	11	:	:	PUNCT
ejpam-5889	90	12	(	(	PUNCT
ejpam-5889	90	13	i	i	NOUN
ejpam-5889	90	14	)	)	PUNCT
ejpam-5889	90	15	the	the	DET
ejpam-5889	90	16	properties	property	NOUN
ejpam-5889	90	17	of	of	ADP
ejpam-5889	90	18	g	g	NOUN
ejpam-5889	90	19	without	without	ADP
ejpam-5889	90	20	multiplicity	multiplicity	NOUN
ejpam-5889	90	21	(	(	PUNCT
ejpam-5889	90	22	since	since	SCONJ
ejpam-5889	90	23	every	every	DET
ejpam-5889	90	24	subgroup	subgroup	NOUN
ejpam-5889	90	25	is	be	AUX
ejpam-5889	90	26	a	a	DET
ejpam-5889	90	27	submultigroup	submultigroup	NOUN
ejpam-5889	90	28	of	of	ADP
ejpam-5889	90	29	trivial	trivial	ADJ
ejpam-5889	90	30	multiplicity	multiplicity	NOUN
ejpam-5889	90	31	)	)	PUNCT
ejpam-5889	90	32	,	,	PUNCT
ejpam-5889	90	33	(	(	PUNCT
ejpam-5889	90	34	ii	ii	NOUN
ejpam-5889	90	35	)	)	PUNCT
ejpam-5889	90	36	d∗	d∗	PROPN
ejpam-5889	90	37	with	with	ADP
ejpam-5889	90	38	multiplicity	multiplicity	NOUN
ejpam-5889	90	39	,	,	PUNCT
ejpam-5889	90	40	(	(	PUNCT
ejpam-5889	90	41	iii	iii	X
ejpam-5889	90	42	)	)	PUNCT
ejpam-5889	90	43	the	the	DET
ejpam-5889	90	44	properties	property	NOUN
ejpam-5889	90	45	of	of	ADP
ejpam-5889	90	46	g	g	NOUN
ejpam-5889	90	47	and	and	CCONJ
ejpam-5889	90	48	multiplicity	multiplicity	NOUN
ejpam-5889	90	49	.	.	PUNCT
ejpam-5889	91	1	by	by	ADP
ejpam-5889	91	2	case	case	NOUN
ejpam-5889	91	3	(	(	PUNCT
ejpam-5889	91	4	i	i	NOUN
ejpam-5889	91	5	)	)	PUNCT
ejpam-5889	91	6	,	,	PUNCT
ejpam-5889	91	7	the	the	DET
ejpam-5889	91	8	submultigroups	submultigroup	NOUN
ejpam-5889	91	9	of	of	ADP
ejpam-5889	91	10	d	d	NOUN
ejpam-5889	91	11	are	be	AUX
ejpam-5889	91	12	as	as	SCONJ
ejpam-5889	91	13	follows	follow	VERB
ejpam-5889	91	14	:	:	PUNCT
ejpam-5889	91	15	d0	d0	PROPN
ejpam-5889	91	16	=	=	PUNCT
ejpam-5889	91	17	{	{	PUNCT
ejpam-5889	91	18	1},d1	1},d1	NUM
ejpam-5889	91	19	=	=	SYM
ejpam-5889	91	20	{	{	PUNCT
ejpam-5889	91	21	1	1	NUM
ejpam-5889	91	22	,	,	PUNCT
ejpam-5889	91	23	d2},d2	d2},d2	PROPN
ejpam-5889	91	24	=	=	PUNCT
ejpam-5889	91	25	d∗	d∗	PROPN
ejpam-5889	91	26	=	=	SYM
ejpam-5889	91	27	{	{	PUNCT
ejpam-5889	91	28	1	1	NUM
ejpam-5889	91	29	,	,	PUNCT
ejpam-5889	91	30	d	d	PROPN
ejpam-5889	91	31	,	,	PUNCT
ejpam-5889	91	32	d2	d2	PROPN
ejpam-5889	91	33	,	,	PUNCT
ejpam-5889	91	34	d3	d3	PROPN
ejpam-5889	91	35	}	}	PUNCT
ejpam-5889	91	36	.	.	PUNCT
ejpam-5889	92	1	in	in	ADP
ejpam-5889	92	2	this	this	DET
ejpam-5889	92	3	case	case	NOUN
ejpam-5889	92	4	,	,	PUNCT
ejpam-5889	92	5	d	d	NOUN
ejpam-5889	92	6	is	be	AUX
ejpam-5889	92	7	not	not	PART
ejpam-5889	92	8	included	include	VERB
ejpam-5889	92	9	as	as	ADP
ejpam-5889	92	10	a	a	DET
ejpam-5889	92	11	submultigroup	submultigroup	NOUN
ejpam-5889	92	12	of	of	ADP
ejpam-5889	92	13	itself	itself	PRON
ejpam-5889	92	14	because	because	SCONJ
ejpam-5889	92	15	it	it	PRON
ejpam-5889	92	16	contains	contain	VERB
ejpam-5889	92	17	multiplicity	multiplicity	NOUN
ejpam-5889	92	18	.	.	PUNCT
ejpam-5889	93	1	clearly	clearly	ADV
ejpam-5889	93	2	,	,	PUNCT
ejpam-5889	93	3	{	{	PUNCT
ejpam-5889	93	4	1	1	NUM
ejpam-5889	93	5	,	,	PUNCT
ejpam-5889	93	6	d	d	PROPN
ejpam-5889	93	7	,	,	PUNCT
ejpam-5889	93	8	d3	d3	PROPN
ejpam-5889	93	9	}	}	PUNCT
ejpam-5889	93	10	is	be	AUX
ejpam-5889	93	11	not	not	PART
ejpam-5889	93	12	a	a	DET
ejpam-5889	93	13	submultigroup	submultigroup	NOUN
ejpam-5889	93	14	of	of	ADP
ejpam-5889	93	15	d	d	PROPN
ejpam-5889	93	16	because	because	SCONJ
ejpam-5889	93	17	d.d	d.d	PROPN
ejpam-5889	93	18	,	,	PUNCT
ejpam-5889	93	19	d3.d3	d3.d3	NOUN
ejpam-5889	93	20	/∈	/∈	PUNCT
ejpam-5889	93	21	{	{	PUNCT
ejpam-5889	93	22	1	1	NUM
ejpam-5889	93	23	,	,	PUNCT
ejpam-5889	93	24	d	d	PROPN
ejpam-5889	93	25	,	,	PUNCT
ejpam-5889	93	26	d3	d3	PROPN
ejpam-5889	93	27	}	}	PUNCT
ejpam-5889	93	28	.	.	PUNCT
ejpam-5889	94	1	since	since	SCONJ
ejpam-5889	94	2	d0	d0	NOUN
ejpam-5889	94	3	,	,	PUNCT
ejpam-5889	94	4	d1	d1	NOUN
ejpam-5889	94	5	,	,	PUNCT
ejpam-5889	94	6	and	and	CCONJ
ejpam-5889	94	7	d2	d2	PROPN
ejpam-5889	94	8	are	be	AUX
ejpam-5889	94	9	trivial	trivial	ADJ
ejpam-5889	94	10	submultigroups	submultigroup	NOUN
ejpam-5889	94	11	of	of	ADP
ejpam-5889	94	12	d	d	PROPN
ejpam-5889	94	13	(	(	PUNCT
ejpam-5889	94	14	because	because	SCONJ
ejpam-5889	94	15	their	their	PRON
ejpam-5889	94	16	multiplicity	multiplicity	NOUN
ejpam-5889	94	17	is	be	AUX
ejpam-5889	94	18	1	1	NUM
ejpam-5889	94	19	)	)	PUNCT
ejpam-5889	94	20	,	,	PUNCT
ejpam-5889	94	21	d	d	PROPN
ejpam-5889	94	22	has	have	VERB
ejpam-5889	94	23	neither	neither	CCONJ
ejpam-5889	94	24	proper	proper	ADJ
ejpam-5889	94	25	non	non	ADJ
ejpam-5889	94	26	-	-	ADJ
ejpam-5889	94	27	trivial	trivial	ADJ
ejpam-5889	94	28	normal	normal	ADJ
ejpam-5889	94	29	submultigroup	submultigroup	NOUN
ejpam-5889	94	30	nor	nor	CCONJ
ejpam-5889	94	31	a	a	DET
ejpam-5889	94	32	maximal	maximal	ADJ
ejpam-5889	94	33	non	non	ADJ
ejpam-5889	94	34	-	-	ADJ
ejpam-5889	94	35	trivial	trivial	ADJ
ejpam-5889	94	36	normal	normal	ADJ
ejpam-5889	94	37	submultigroup	submultigroup	NOUN
ejpam-5889	94	38	and	and	CCONJ
ejpam-5889	94	39	hence	hence	ADV
ejpam-5889	94	40	,	,	PUNCT
ejpam-5889	94	41	d	d	PRON
ejpam-5889	94	42	is	be	AUX
ejpam-5889	94	43	a	a	DET
ejpam-5889	94	44	simple	simple	ADJ
ejpam-5889	94	45	multigroup	multigroup	NOUN
ejpam-5889	94	46	.	.	PUNCT
ejpam-5889	95	1	using	use	VERB
ejpam-5889	95	2	case	case	NOUN
ejpam-5889	95	3	(	(	PUNCT
ejpam-5889	95	4	ii	ii	NOUN
ejpam-5889	95	5	)	)	PUNCT
ejpam-5889	95	6	,	,	PUNCT
ejpam-5889	95	7	the	the	DET
ejpam-5889	95	8	submultigroups	submultigroup	NOUN
ejpam-5889	95	9	of	of	ADP
ejpam-5889	95	10	d	d	NOUN
ejpam-5889	95	11	are	be	AUX
ejpam-5889	95	12	in	in	ADP
ejpam-5889	95	13	table	table	NOUN
ejpam-5889	95	14	1	1	NUM
ejpam-5889	95	15	:	:	PUNCT
ejpam-5889	95	16	table	table	NOUN
ejpam-5889	95	17	1	1	NUM
ejpam-5889	95	18	:	:	PUNCT
ejpam-5889	95	19	submultigroups	submultigroup	NOUN
ejpam-5889	95	20	of	of	ADP
ejpam-5889	95	21	d	d	PROPN
ejpam-5889	95	22	based	base	VERB
ejpam-5889	95	23	on	on	ADP
ejpam-5889	95	24	case	case	NOUN
ejpam-5889	95	25	(	(	PUNCT
ejpam-5889	95	26	ii	ii	NOUN
ejpam-5889	95	27	)	)	PUNCT
ejpam-5889	95	28	submultigroups	submultigroup	NOUN
ejpam-5889	95	29	and	and	CCONJ
ejpam-5889	95	30	their	their	PRON
ejpam-5889	95	31	structures	structure	NOUN
ejpam-5889	95	32	d̂1	d̂1	NOUN
ejpam-5889	95	33	=	=	SYM
ejpam-5889	95	34	d2	d2	PROPN
ejpam-5889	95	35	=	=	SYM
ejpam-5889	95	36	{	{	PUNCT
ejpam-5889	95	37	1	1	NUM
ejpam-5889	95	38	,	,	PUNCT
ejpam-5889	95	39	d	d	PROPN
ejpam-5889	95	40	,	,	PUNCT
ejpam-5889	95	41	d2	d2	PROPN
ejpam-5889	95	42	,	,	PUNCT
ejpam-5889	95	43	d3	d3	PROPN
ejpam-5889	95	44	}	}	PUNCT
ejpam-5889	95	45	,	,	PUNCT
ejpam-5889	95	46	d̂2	d̂2	NOUN
ejpam-5889	95	47	=	=	PRON
ejpam-5889	95	48	{	{	PUNCT
ejpam-5889	95	49	1	1	NUM
ejpam-5889	95	50	,	,	PUNCT
ejpam-5889	95	51	1	1	NUM
ejpam-5889	95	52	,	,	PUNCT
ejpam-5889	95	53	d	d	PROPN
ejpam-5889	95	54	,	,	PUNCT
ejpam-5889	95	55	d2	d2	PROPN
ejpam-5889	95	56	,	,	PUNCT
ejpam-5889	95	57	d3	d3	PROPN
ejpam-5889	95	58	}	}	PUNCT
ejpam-5889	95	59	,	,	PUNCT
ejpam-5889	95	60	d̂3	d̂3	PROPN
ejpam-5889	95	61	=	=	SYM
ejpam-5889	95	62	{	{	PUNCT
ejpam-5889	95	63	1	1	NUM
ejpam-5889	95	64	,	,	PUNCT
ejpam-5889	95	65	1	1	NUM
ejpam-5889	95	66	,	,	PUNCT
ejpam-5889	95	67	d	d	NOUN
ejpam-5889	95	68	,	,	PUNCT
ejpam-5889	95	69	d	d	PROPN
ejpam-5889	95	70	,	,	PUNCT
ejpam-5889	95	71	d2	d2	PROPN
ejpam-5889	95	72	,	,	PUNCT
ejpam-5889	95	73	d2	d2	PROPN
ejpam-5889	95	74	,	,	PUNCT
ejpam-5889	95	75	d3	d3	PROPN
ejpam-5889	95	76	,	,	PUNCT
ejpam-5889	95	77	d3	d3	PROPN
ejpam-5889	95	78	}	}	PUNCT
ejpam-5889	95	79	,	,	PUNCT
ejpam-5889	95	80	d̂4	d̂4	PROPN
ejpam-5889	95	81	=	=	PUNCT
ejpam-5889	95	82	{	{	PUNCT
ejpam-5889	95	83	1	1	NUM
ejpam-5889	95	84	,	,	PUNCT
ejpam-5889	95	85	1	1	NUM
ejpam-5889	95	86	,	,	PUNCT
ejpam-5889	95	87	1	1	NUM
ejpam-5889	95	88	,	,	PUNCT
ejpam-5889	95	89	d	d	PROPN
ejpam-5889	95	90	,	,	PUNCT
ejpam-5889	95	91	d2	d2	PROPN
ejpam-5889	95	92	,	,	PUNCT
ejpam-5889	95	93	d3	d3	PROPN
ejpam-5889	95	94	}	}	PUNCT
ejpam-5889	95	95	d̂5	d̂5	NOUN
ejpam-5889	95	96	=	=	SYM
ejpam-5889	95	97	{	{	PUNCT
ejpam-5889	95	98	1	1	NUM
ejpam-5889	95	99	,	,	PUNCT
ejpam-5889	95	100	1	1	NUM
ejpam-5889	95	101	,	,	PUNCT
ejpam-5889	95	102	1	1	NUM
ejpam-5889	95	103	,	,	PUNCT
ejpam-5889	95	104	d	d	NOUN
ejpam-5889	95	105	,	,	PUNCT
ejpam-5889	95	106	d	d	PROPN
ejpam-5889	95	107	,	,	PUNCT
ejpam-5889	95	108	d2	d2	PROPN
ejpam-5889	95	109	,	,	PUNCT
ejpam-5889	95	110	d2	d2	PROPN
ejpam-5889	95	111	,	,	PUNCT
ejpam-5889	95	112	d3	d3	PROPN
ejpam-5889	95	113	,	,	PUNCT
ejpam-5889	95	114	d3	d3	PROPN
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ejpam-5889	95	116	,	,	PUNCT
ejpam-5889	96	1	d̂6	d̂6	PROPN
ejpam-5889	96	2	=	=	PUNCT
ejpam-5889	96	3	{	{	PUNCT
ejpam-5889	96	4	1	1	NUM
ejpam-5889	96	5	,	,	PUNCT
ejpam-5889	96	6	1	1	NUM
ejpam-5889	96	7	,	,	PUNCT
ejpam-5889	96	8	1	1	NUM
ejpam-5889	96	9	,	,	PUNCT
ejpam-5889	96	10	d	d	NOUN
ejpam-5889	96	11	,	,	PUNCT
ejpam-5889	96	12	d	d	PROPN
ejpam-5889	96	13	,	,	PUNCT
ejpam-5889	96	14	d2	d2	PROPN
ejpam-5889	96	15	,	,	PUNCT
ejpam-5889	96	16	d2	d2	PROPN
ejpam-5889	96	17	,	,	PUNCT
ejpam-5889	96	18	d2	d2	PROPN
ejpam-5889	96	19	,	,	PUNCT
ejpam-5889	96	20	d3	d3	PROPN
ejpam-5889	96	21	,	,	PUNCT
ejpam-5889	96	22	d3	d3	PROPN
ejpam-5889	96	23	}	}	PUNCT
ejpam-5889	96	24	,	,	PUNCT
ejpam-5889	96	25	d̂7	d̂7	NOUN
ejpam-5889	96	26	=	=	SYM
ejpam-5889	96	27	{	{	PUNCT
ejpam-5889	96	28	1	1	NUM
ejpam-5889	96	29	,	,	PUNCT
ejpam-5889	96	30	1	1	NUM
ejpam-5889	96	31	,	,	PUNCT
ejpam-5889	96	32	1	1	NUM
ejpam-5889	96	33	,	,	PUNCT
ejpam-5889	96	34	1	1	NUM
ejpam-5889	96	35	,	,	PUNCT
ejpam-5889	96	36	d	d	PROPN
ejpam-5889	96	37	,	,	PUNCT
ejpam-5889	96	38	d2	d2	PROPN
ejpam-5889	96	39	,	,	PUNCT
ejpam-5889	96	40	d3	d3	PROPN
ejpam-5889	96	41	}	}	PUNCT
ejpam-5889	96	42	,	,	PUNCT
ejpam-5889	96	43	d̂8	d̂8	ADP
ejpam-5889	96	44	=	=	X
ejpam-5889	96	45	{	{	PUNCT
ejpam-5889	96	46	1	1	NUM
ejpam-5889	96	47	,	,	PUNCT
ejpam-5889	96	48	1	1	NUM
ejpam-5889	96	49	,	,	PUNCT
ejpam-5889	96	50	1	1	NUM
ejpam-5889	96	51	,	,	PUNCT
ejpam-5889	96	52	1	1	NUM
ejpam-5889	96	53	,	,	PUNCT
ejpam-5889	96	54	d	d	NOUN
ejpam-5889	96	55	,	,	PUNCT
ejpam-5889	96	56	d	d	PROPN
ejpam-5889	96	57	,	,	PUNCT
ejpam-5889	96	58	d2	d2	PROPN
ejpam-5889	96	59	,	,	PUNCT
ejpam-5889	96	60	d2	d2	PROPN
ejpam-5889	96	61	,	,	PUNCT
ejpam-5889	96	62	d3	d3	PROPN
ejpam-5889	96	63	,	,	PUNCT
ejpam-5889	96	64	d3	d3	PROPN
ejpam-5889	96	65	}	}	PUNCT
ejpam-5889	96	66	,	,	PUNCT
ejpam-5889	96	67	d̂9	d̂9	PROPN
ejpam-5889	96	68	=	=	PUNCT
ejpam-5889	97	1	d	d	X
ejpam-5889	97	2	=	=	SYM
ejpam-5889	97	3	{	{	PUNCT
ejpam-5889	97	4	1	1	NUM
ejpam-5889	97	5	,	,	PUNCT
ejpam-5889	97	6	1	1	NUM
ejpam-5889	97	7	,	,	PUNCT
ejpam-5889	97	8	1	1	NUM
ejpam-5889	97	9	,	,	PUNCT
ejpam-5889	97	10	1	1	NUM
ejpam-5889	97	11	,	,	PUNCT
ejpam-5889	97	12	d	d	NOUN
ejpam-5889	97	13	,	,	PUNCT
ejpam-5889	97	14	d	d	PROPN
ejpam-5889	97	15	,	,	PUNCT
ejpam-5889	97	16	d2	d2	PROPN
ejpam-5889	97	17	,	,	PUNCT
ejpam-5889	97	18	d2	d2	PROPN
ejpam-5889	97	19	,	,	PUNCT
ejpam-5889	97	20	d2	d2	PROPN
ejpam-5889	97	21	,	,	PUNCT
ejpam-5889	97	22	d3	d3	PROPN
ejpam-5889	97	23	,	,	PUNCT
ejpam-5889	97	24	d3	d3	PROPN
ejpam-5889	97	25	}	}	PUNCT
ejpam-5889	97	26	among	among	ADP
ejpam-5889	97	27	the	the	DET
ejpam-5889	97	28	list	list	NOUN
ejpam-5889	97	29	,	,	PUNCT
ejpam-5889	97	30	d̂1	d̂1	ADJ
ejpam-5889	97	31	and	and	CCONJ
ejpam-5889	97	32	d̂9	d̂9	PROPN
ejpam-5889	97	33	are	be	AUX
ejpam-5889	97	34	trivial	trivial	ADJ
ejpam-5889	97	35	submultigroups	submultigroup	NOUN
ejpam-5889	97	36	because	because	SCONJ
ejpam-5889	97	37	d̂1	d̂1	NOUN
ejpam-5889	97	38	=	=	SYM
ejpam-5889	97	39	d∗	d∗	NOUN
ejpam-5889	97	40	and	and	CCONJ
ejpam-5889	97	41	d̂9	d̂9	PROPN
ejpam-5889	97	42	is	be	AUX
ejpam-5889	97	43	a	a	DET
ejpam-5889	97	44	submultigroup	submultigroup	NOUN
ejpam-5889	97	45	of	of	ADP
ejpam-5889	97	46	itself	itself	PRON
ejpam-5889	97	47	,	,	PUNCT
ejpam-5889	97	48	d̂2	d̂2	PROPN
ejpam-5889	97	49	–	–	PUNCT
ejpam-5889	97	50	d̂8	d̂8	NOUN
ejpam-5889	97	51	are	be	AUX
ejpam-5889	97	52	proper	proper	ADJ
ejpam-5889	97	53	non	non	ADJ
ejpam-5889	97	54	-	-	ADJ
ejpam-5889	97	55	trivial	trivial	ADJ
ejpam-5889	97	56	normal	normal	ADJ
ejpam-5889	97	57	submultigroups	submultigroup	NOUN
ejpam-5889	97	58	of	of	ADP
ejpam-5889	97	59	d	d	NOUN
ejpam-5889	97	60	,	,	PUNCT
ejpam-5889	97	61	and	and	CCONJ
ejpam-5889	97	62	d̂8	d̂8	NOUN
ejpam-5889	97	63	is	be	AUX
ejpam-5889	97	64	the	the	DET
ejpam-5889	97	65	maximal	maximal	ADJ
ejpam-5889	97	66	non	non	ADJ
ejpam-5889	97	67	-	-	ADJ
ejpam-5889	97	68	trivial	trivial	ADJ
ejpam-5889	97	69	normal	normal	ADJ
ejpam-5889	97	70	submultigroup	submultigroup	NOUN
ejpam-5889	97	71	of	of	ADP
ejpam-5889	97	72	d.	d.	PROPN
ejpam-5889	97	73	hence	hence	ADV
ejpam-5889	97	74	,	,	PUNCT
ejpam-5889	97	75	d	d	PROPN
ejpam-5889	97	76	is	be	AUX
ejpam-5889	97	77	not	not	PART
ejpam-5889	97	78	simple	simple	ADJ
ejpam-5889	97	79	.	.	PUNCT
ejpam-5889	98	1	by	by	ADP
ejpam-5889	98	2	case	case	NOUN
ejpam-5889	98	3	(	(	PUNCT
ejpam-5889	98	4	iii	iii	NOUN
ejpam-5889	98	5	)	)	PUNCT
ejpam-5889	98	6	,	,	PUNCT
ejpam-5889	98	7	the	the	DET
ejpam-5889	98	8	submultigroups	submultigroup	NOUN
ejpam-5889	98	9	of	of	ADP
ejpam-5889	98	10	d	d	NOUN
ejpam-5889	98	11	are	be	AUX
ejpam-5889	98	12	in	in	ADP
ejpam-5889	98	13	table	table	NOUN
ejpam-5889	98	14	2	2	NUM
ejpam-5889	98	15	:	:	PUNCT
ejpam-5889	98	16	p.	p.	NOUN
ejpam-5889	98	17	a.	a.	PROPN
ejpam-5889	98	18	ejegwa	ejegwa	PROPN
ejpam-5889	98	19	et	et	PROPN
ejpam-5889	98	20	al	al	PROPN
ejpam-5889	98	21	.	.	PUNCT
ejpam-5889	98	22	/	/	SYM
ejpam-5889	98	23	eur	eur	PROPN
ejpam-5889	98	24	.	.	PUNCT
ejpam-5889	99	1	j.	j.	PROPN
ejpam-5889	99	2	pure	pure	PROPN
ejpam-5889	99	3	appl	appl	PROPN
ejpam-5889	99	4	.	.	PROPN
ejpam-5889	99	5	math	math	PROPN
ejpam-5889	99	6	,	,	PUNCT
ejpam-5889	99	7	18	18	NUM
ejpam-5889	99	8	(	(	PUNCT
ejpam-5889	99	9	2	2	NUM
ejpam-5889	99	10	)	)	PUNCT
ejpam-5889	99	11	(	(	PUNCT
ejpam-5889	99	12	2025	2025	NUM
ejpam-5889	99	13	)	)	PUNCT
ejpam-5889	99	14	,	,	PUNCT
ejpam-5889	99	15	5889	5889	NUM
ejpam-5889	99	16	6	6	NUM
ejpam-5889	99	17	of	of	ADP
ejpam-5889	99	18	13	13	NUM
ejpam-5889	99	19	table	table	NOUN
ejpam-5889	99	20	2	2	NUM
ejpam-5889	99	21	:	:	PUNCT
ejpam-5889	99	22	submultigroups	submultigroup	NOUN
ejpam-5889	99	23	of	of	ADP
ejpam-5889	99	24	d	d	PROPN
ejpam-5889	99	25	based	base	VERB
ejpam-5889	99	26	on	on	ADP
ejpam-5889	99	27	case	case	NOUN
ejpam-5889	99	28	(	(	PUNCT
ejpam-5889	99	29	iii	iii	NOUN
ejpam-5889	99	30	)	)	PUNCT
ejpam-5889	99	31	submultigroups	submultigroup	NOUN
ejpam-5889	99	32	and	and	CCONJ
ejpam-5889	99	33	their	their	PRON
ejpam-5889	99	34	structures	structure	NOUN
ejpam-5889	99	35	d0	d0	NOUN
ejpam-5889	99	36	=	=	PUNCT
ejpam-5889	99	37	{	{	PUNCT
ejpam-5889	99	38	1	1	NUM
ejpam-5889	99	39	}	}	PUNCT
ejpam-5889	99	40	,	,	PUNCT
ejpam-5889	99	41	d1	d1	PROPN
ejpam-5889	99	42	=	=	PUNCT
ejpam-5889	99	43	{	{	PUNCT
ejpam-5889	99	44	1	1	NUM
ejpam-5889	99	45	,	,	PUNCT
ejpam-5889	99	46	d2	d2	PROPN
ejpam-5889	99	47	}	}	PUNCT
ejpam-5889	99	48	,	,	PUNCT
ejpam-5889	99	49	d2	d2	PROPN
ejpam-5889	99	50	=	=	SYM
ejpam-5889	99	51	d̂1	d̂1	PROPN
ejpam-5889	99	52	=	=	PUNCT
ejpam-5889	99	53	{	{	PUNCT
ejpam-5889	99	54	1	1	NUM
ejpam-5889	99	55	,	,	PUNCT
ejpam-5889	99	56	d	d	PROPN
ejpam-5889	99	57	,	,	PUNCT
ejpam-5889	99	58	d2	d2	PROPN
ejpam-5889	99	59	,	,	PUNCT
ejpam-5889	99	60	d3	d3	PROPN
ejpam-5889	99	61	}	}	PUNCT
ejpam-5889	99	62	,	,	PUNCT
ejpam-5889	99	63	d̂2	d̂2	NOUN
ejpam-5889	99	64	=	=	PRON
ejpam-5889	99	65	{	{	PUNCT
ejpam-5889	99	66	1	1	NUM
ejpam-5889	99	67	,	,	PUNCT
ejpam-5889	99	68	1	1	NUM
ejpam-5889	99	69	,	,	PUNCT
ejpam-5889	99	70	d	d	PROPN
ejpam-5889	99	71	,	,	PUNCT
ejpam-5889	99	72	d2	d2	PROPN
ejpam-5889	99	73	,	,	PUNCT
ejpam-5889	99	74	d3	d3	PROPN
ejpam-5889	99	75	}	}	PUNCT
ejpam-5889	99	76	,	,	PUNCT
ejpam-5889	99	77	d̂3	d̂3	PROPN
ejpam-5889	99	78	=	=	SYM
ejpam-5889	99	79	{	{	PUNCT
ejpam-5889	99	80	1	1	NUM
ejpam-5889	99	81	,	,	PUNCT
ejpam-5889	99	82	1	1	NUM
ejpam-5889	99	83	,	,	PUNCT
ejpam-5889	99	84	d	d	NOUN
ejpam-5889	99	85	,	,	PUNCT
ejpam-5889	99	86	d	d	PROPN
ejpam-5889	99	87	,	,	PUNCT
ejpam-5889	99	88	d2	d2	PROPN
ejpam-5889	99	89	,	,	PUNCT
ejpam-5889	99	90	d2	d2	PROPN
ejpam-5889	99	91	,	,	PUNCT
ejpam-5889	99	92	d3	d3	PROPN
ejpam-5889	99	93	,	,	PUNCT
ejpam-5889	99	94	d3	d3	PROPN
ejpam-5889	99	95	}	}	PUNCT
ejpam-5889	99	96	,	,	PUNCT
ejpam-5889	99	97	d̂4	d̂4	PROPN
ejpam-5889	99	98	=	=	PUNCT
ejpam-5889	99	99	{	{	PUNCT
ejpam-5889	99	100	1	1	NUM
ejpam-5889	99	101	,	,	PUNCT
ejpam-5889	99	102	1	1	NUM
ejpam-5889	99	103	,	,	PUNCT
ejpam-5889	99	104	1	1	NUM
ejpam-5889	99	105	,	,	PUNCT
ejpam-5889	99	106	d	d	PROPN
ejpam-5889	99	107	,	,	PUNCT
ejpam-5889	99	108	d2	d2	PROPN
ejpam-5889	99	109	,	,	PUNCT
ejpam-5889	99	110	d3	d3	PROPN
ejpam-5889	99	111	}	}	PUNCT
ejpam-5889	99	112	,	,	PUNCT
ejpam-5889	99	113	d̂5	d̂5	PROPN
ejpam-5889	99	114	=	=	SYM
ejpam-5889	99	115	{	{	PUNCT
ejpam-5889	99	116	1	1	NUM
ejpam-5889	99	117	,	,	PUNCT
ejpam-5889	99	118	1	1	NUM
ejpam-5889	99	119	,	,	PUNCT
ejpam-5889	99	120	1	1	NUM
ejpam-5889	99	121	,	,	PUNCT
ejpam-5889	99	122	d	d	NOUN
ejpam-5889	99	123	,	,	PUNCT
ejpam-5889	99	124	d	d	PROPN
ejpam-5889	99	125	,	,	PUNCT
ejpam-5889	99	126	d2	d2	PROPN
ejpam-5889	99	127	,	,	PUNCT
ejpam-5889	99	128	d2	d2	PROPN
ejpam-5889	99	129	,	,	PUNCT
ejpam-5889	99	130	d3	d3	PROPN
ejpam-5889	99	131	,	,	PUNCT
ejpam-5889	99	132	d3	d3	PROPN
ejpam-5889	99	133	}	}	PUNCT
ejpam-5889	99	134	,	,	PUNCT
ejpam-5889	99	135	d̂6	d̂6	PROPN
ejpam-5889	99	136	=	=	PUNCT
ejpam-5889	99	137	{	{	PUNCT
ejpam-5889	99	138	1	1	NUM
ejpam-5889	99	139	,	,	PUNCT
ejpam-5889	99	140	1	1	NUM
ejpam-5889	99	141	,	,	PUNCT
ejpam-5889	99	142	1	1	NUM
ejpam-5889	99	143	,	,	PUNCT
ejpam-5889	99	144	d	d	NOUN
ejpam-5889	99	145	,	,	PUNCT
ejpam-5889	99	146	d	d	PROPN
ejpam-5889	99	147	,	,	PUNCT
ejpam-5889	99	148	d2	d2	PROPN
ejpam-5889	99	149	,	,	PUNCT
ejpam-5889	99	150	d2	d2	PROPN
ejpam-5889	99	151	,	,	PUNCT
ejpam-5889	99	152	d2	d2	PROPN
ejpam-5889	99	153	,	,	PUNCT
ejpam-5889	99	154	d3	d3	PROPN
ejpam-5889	99	155	,	,	PUNCT
ejpam-5889	99	156	d3	d3	PROPN
ejpam-5889	99	157	}	}	PUNCT
ejpam-5889	99	158	,	,	PUNCT
ejpam-5889	99	159	d̂7	d̂7	NOUN
ejpam-5889	99	160	=	=	SYM
ejpam-5889	99	161	{	{	PUNCT
ejpam-5889	99	162	1	1	NUM
ejpam-5889	99	163	,	,	PUNCT
ejpam-5889	99	164	1	1	NUM
ejpam-5889	99	165	,	,	PUNCT
ejpam-5889	99	166	1	1	NUM
ejpam-5889	99	167	,	,	PUNCT
ejpam-5889	99	168	1	1	NUM
ejpam-5889	99	169	,	,	PUNCT
ejpam-5889	99	170	d	d	PROPN
ejpam-5889	99	171	,	,	PUNCT
ejpam-5889	99	172	d2	d2	PROPN
ejpam-5889	99	173	,	,	PUNCT
ejpam-5889	99	174	d3	d3	PROPN
ejpam-5889	99	175	}	}	PUNCT
ejpam-5889	99	176	,	,	PUNCT
ejpam-5889	99	177	d̂8	d̂8	ADP
ejpam-5889	99	178	=	=	X
ejpam-5889	99	179	{	{	PUNCT
ejpam-5889	99	180	1	1	NUM
ejpam-5889	99	181	,	,	PUNCT
ejpam-5889	99	182	1	1	NUM
ejpam-5889	99	183	,	,	PUNCT
ejpam-5889	99	184	1	1	NUM
ejpam-5889	99	185	,	,	PUNCT
ejpam-5889	99	186	1	1	NUM
ejpam-5889	99	187	,	,	PUNCT
ejpam-5889	99	188	d	d	NOUN
ejpam-5889	99	189	,	,	PUNCT
ejpam-5889	99	190	d	d	PROPN
ejpam-5889	99	191	,	,	PUNCT
ejpam-5889	99	192	d2	d2	PROPN
ejpam-5889	99	193	,	,	PUNCT
ejpam-5889	99	194	d2	d2	PROPN
ejpam-5889	99	195	,	,	PUNCT
ejpam-5889	99	196	d3	d3	PROPN
ejpam-5889	99	197	,	,	PUNCT
ejpam-5889	99	198	d3	d3	PROPN
ejpam-5889	99	199	}	}	PUNCT
ejpam-5889	99	200	,	,	PUNCT
ejpam-5889	99	201	d̂9	d̂9	PROPN
ejpam-5889	99	202	=	=	PUNCT
ejpam-5889	100	1	d	d	X
ejpam-5889	100	2	=	=	SYM
ejpam-5889	100	3	{	{	PUNCT
ejpam-5889	100	4	1	1	NUM
ejpam-5889	100	5	,	,	PUNCT
ejpam-5889	100	6	1	1	NUM
ejpam-5889	100	7	,	,	PUNCT
ejpam-5889	100	8	1	1	NUM
ejpam-5889	100	9	,	,	PUNCT
ejpam-5889	100	10	1	1	NUM
ejpam-5889	100	11	,	,	PUNCT
ejpam-5889	100	12	d	d	NOUN
ejpam-5889	100	13	,	,	PUNCT
ejpam-5889	100	14	d	d	PROPN
ejpam-5889	100	15	,	,	PUNCT
ejpam-5889	100	16	d2	d2	PROPN
ejpam-5889	100	17	,	,	PUNCT
ejpam-5889	100	18	d2	d2	PROPN
ejpam-5889	100	19	,	,	PUNCT
ejpam-5889	100	20	d2	d2	PROPN
ejpam-5889	100	21	,	,	PUNCT
ejpam-5889	100	22	d3	d3	PROPN
ejpam-5889	100	23	,	,	PUNCT
ejpam-5889	100	24	d3	d3	PROPN
ejpam-5889	100	25	}	}	PUNCT
ejpam-5889	100	26	,	,	PUNCT
ejpam-5889	100	27	ḋ1	ḋ1	PROPN
ejpam-5889	100	28	=	=	PUNCT
ejpam-5889	100	29	{	{	PUNCT
ejpam-5889	100	30	1	1	NUM
ejpam-5889	100	31	,	,	PUNCT
ejpam-5889	100	32	1	1	NUM
ejpam-5889	100	33	}	}	PUNCT
ejpam-5889	100	34	,	,	PUNCT
ejpam-5889	100	35	ḋ2	ḋ2	PROPN
ejpam-5889	100	36	=	=	PUNCT
ejpam-5889	100	37	{	{	PUNCT
ejpam-5889	100	38	1	1	NUM
ejpam-5889	100	39	,	,	PUNCT
ejpam-5889	100	40	1	1	NUM
ejpam-5889	100	41	,	,	PUNCT
ejpam-5889	100	42	1	1	NUM
ejpam-5889	100	43	}	}	PUNCT
ejpam-5889	100	44	,	,	PUNCT
ejpam-5889	100	45	ḋ3	ḋ3	PROPN
ejpam-5889	100	46	=	=	PUNCT
ejpam-5889	100	47	{	{	PUNCT
ejpam-5889	100	48	1	1	NUM
ejpam-5889	100	49	,	,	PUNCT
ejpam-5889	100	50	1	1	NUM
ejpam-5889	100	51	,	,	PUNCT
ejpam-5889	100	52	1	1	NUM
ejpam-5889	100	53	,	,	PUNCT
ejpam-5889	100	54	1	1	NUM
ejpam-5889	100	55	}	}	PUNCT
ejpam-5889	100	56	,	,	PUNCT
ejpam-5889	100	57	ḋ4	ḋ4	PROPN
ejpam-5889	100	58	=	=	PUNCT
ejpam-5889	100	59	{	{	PUNCT
ejpam-5889	100	60	1	1	NUM
ejpam-5889	100	61	,	,	PUNCT
ejpam-5889	100	62	1	1	NUM
ejpam-5889	100	63	,	,	PUNCT
ejpam-5889	100	64	d2	d2	PROPN
ejpam-5889	100	65	}	}	PUNCT
ejpam-5889	100	66	,	,	PUNCT
ejpam-5889	100	67	ḋ5	ḋ5	PROPN
ejpam-5889	100	68	=	=	PUNCT
ejpam-5889	100	69	{	{	PUNCT
ejpam-5889	100	70	1	1	NUM
ejpam-5889	100	71	,	,	PUNCT
ejpam-5889	100	72	1	1	NUM
ejpam-5889	100	73	,	,	PUNCT
ejpam-5889	100	74	d2	d2	PROPN
ejpam-5889	100	75	,	,	PUNCT
ejpam-5889	100	76	d2	d2	PROPN
ejpam-5889	100	77	}	}	PUNCT
ejpam-5889	100	78	,	,	PUNCT
ejpam-5889	100	79	ḋ6	ḋ6	PROPN
ejpam-5889	100	80	=	=	SYM
ejpam-5889	100	81	{	{	PUNCT
ejpam-5889	100	82	1	1	NUM
ejpam-5889	100	83	,	,	PUNCT
ejpam-5889	100	84	1	1	NUM
ejpam-5889	100	85	,	,	PUNCT
ejpam-5889	100	86	1	1	NUM
ejpam-5889	100	87	,	,	PUNCT
ejpam-5889	100	88	d2	d2	PROPN
ejpam-5889	100	89	}	}	PUNCT
ejpam-5889	100	90	,	,	PUNCT
ejpam-5889	100	91	ḋ7	ḋ7	PROPN
ejpam-5889	100	92	=	=	SYM
ejpam-5889	100	93	{	{	PUNCT
ejpam-5889	100	94	1	1	NUM
ejpam-5889	100	95	,	,	PUNCT
ejpam-5889	100	96	1	1	NUM
ejpam-5889	100	97	,	,	PUNCT
ejpam-5889	100	98	1	1	NUM
ejpam-5889	100	99	,	,	PUNCT
ejpam-5889	100	100	d2	d2	PROPN
ejpam-5889	100	101	,	,	PUNCT
ejpam-5889	100	102	d2	d2	PROPN
ejpam-5889	100	103	}	}	PUNCT
ejpam-5889	100	104	,	,	PUNCT
ejpam-5889	100	105	ḋ8	ḋ8	PROPN
ejpam-5889	100	106	=	=	PUNCT
ejpam-5889	100	107	{	{	PUNCT
ejpam-5889	100	108	1	1	NUM
ejpam-5889	100	109	,	,	PUNCT
ejpam-5889	100	110	1	1	NUM
ejpam-5889	100	111	,	,	PUNCT
ejpam-5889	100	112	1	1	NUM
ejpam-5889	100	113	,	,	PUNCT
ejpam-5889	100	114	d2	d2	PROPN
ejpam-5889	100	115	,	,	PUNCT
ejpam-5889	100	116	d2	d2	PROPN
ejpam-5889	100	117	,	,	PUNCT
ejpam-5889	100	118	d2	d2	PROPN
ejpam-5889	100	119	}	}	PUNCT
ejpam-5889	100	120	,	,	PUNCT
ejpam-5889	100	121	ḋ9	ḋ9	PROPN
ejpam-5889	100	122	=	=	SYM
ejpam-5889	100	123	{	{	PUNCT
ejpam-5889	100	124	1	1	NUM
ejpam-5889	100	125	,	,	PUNCT
ejpam-5889	100	126	1	1	NUM
ejpam-5889	100	127	,	,	PUNCT
ejpam-5889	100	128	1	1	NUM
ejpam-5889	100	129	,	,	PUNCT
ejpam-5889	100	130	1	1	NUM
ejpam-5889	100	131	,	,	PUNCT
ejpam-5889	100	132	d2	d2	PROPN
ejpam-5889	100	133	}	}	PUNCT
ejpam-5889	100	134	,	,	PUNCT
ejpam-5889	100	135	ḋ10	ḋ10	PROPN
ejpam-5889	100	136	=	=	PUNCT
ejpam-5889	100	137	{	{	PUNCT
ejpam-5889	100	138	1	1	NUM
ejpam-5889	100	139	,	,	PUNCT
ejpam-5889	100	140	1	1	NUM
ejpam-5889	100	141	,	,	PUNCT
ejpam-5889	100	142	1	1	NUM
ejpam-5889	100	143	,	,	PUNCT
ejpam-5889	100	144	1	1	NUM
ejpam-5889	100	145	,	,	PUNCT
ejpam-5889	100	146	d2	d2	PROPN
ejpam-5889	100	147	,	,	PUNCT
ejpam-5889	100	148	d2	d2	PROPN
ejpam-5889	100	149	}	}	PUNCT
ejpam-5889	100	150	,	,	PUNCT
ejpam-5889	100	151	ḋ11	ḋ11	ADJ
ejpam-5889	100	152	=	=	SYM
ejpam-5889	100	153	{	{	PUNCT
ejpam-5889	100	154	1	1	NUM
ejpam-5889	100	155	,	,	PUNCT
ejpam-5889	100	156	1	1	NUM
ejpam-5889	100	157	,	,	PUNCT
ejpam-5889	100	158	1	1	NUM
ejpam-5889	100	159	,	,	PUNCT
ejpam-5889	100	160	1	1	NUM
ejpam-5889	100	161	,	,	PUNCT
ejpam-5889	100	162	d2	d2	PROPN
ejpam-5889	100	163	,	,	PUNCT
ejpam-5889	100	164	d2	d2	PROPN
ejpam-5889	100	165	,	,	PUNCT
ejpam-5889	100	166	d2	d2	PROPN
ejpam-5889	100	167	}	}	PUNCT
ejpam-5889	100	168	among	among	ADP
ejpam-5889	100	169	the	the	DET
ejpam-5889	100	170	list	list	NOUN
ejpam-5889	100	171	,	,	PUNCT
ejpam-5889	100	172	d0	d0	NOUN
ejpam-5889	100	173	–	–	PUNCT
ejpam-5889	100	174	d2	d2	NOUN
ejpam-5889	100	175	,	,	PUNCT
ejpam-5889	100	176	ḋ1	ḋ1	PROPN
ejpam-5889	100	177	–	–	PUNCT
ejpam-5889	100	178	ḋ3	ḋ3	PROPN
ejpam-5889	100	179	,	,	PUNCT
ejpam-5889	100	180	and	and	CCONJ
ejpam-5889	100	181	d̂9	d̂9	PROPN
ejpam-5889	100	182	are	be	AUX
ejpam-5889	100	183	trivial	trivial	ADJ
ejpam-5889	100	184	submultigroups	submultigroup	NOUN
ejpam-5889	100	185	of	of	ADP
ejpam-5889	100	186	d.	d.	PROPN
ejpam-5889	100	187	submultigroups	submultigroups	PROPN
ejpam-5889	100	188	d̂2	d̂2	PROPN
ejpam-5889	100	189	–	–	PUNCT
ejpam-5889	100	190	d̂8	d̂8	PROPN
ejpam-5889	100	191	and	and	CCONJ
ejpam-5889	100	192	ḋ4	ḋ4	PROPN
ejpam-5889	100	193	–	–	PUNCT
ejpam-5889	100	194	ḋ11	ḋ11	ADJ
ejpam-5889	100	195	are	be	AUX
ejpam-5889	100	196	proper	proper	ADJ
ejpam-5889	100	197	non	non	ADJ
ejpam-5889	100	198	-	-	ADJ
ejpam-5889	100	199	trivial	trivial	ADJ
ejpam-5889	100	200	normal	normal	ADJ
ejpam-5889	100	201	submultigroups	submultigroup	NOUN
ejpam-5889	100	202	of	of	ADP
ejpam-5889	100	203	d	d	NOUN
ejpam-5889	100	204	,	,	PUNCT
ejpam-5889	100	205	and	and	CCONJ
ejpam-5889	100	206	d̂8	d̂8	NOUN
ejpam-5889	100	207	is	be	AUX
ejpam-5889	100	208	the	the	DET
ejpam-5889	100	209	maximal	maximal	ADJ
ejpam-5889	100	210	non	non	ADJ
ejpam-5889	100	211	-	-	ADJ
ejpam-5889	100	212	trivial	trivial	ADJ
ejpam-5889	100	213	normal	normal	ADJ
ejpam-5889	100	214	submultigroups	submultigroup	NOUN
ejpam-5889	100	215	ofd	ofd	PROPN
ejpam-5889	100	216	.	.	PUNCT
ejpam-5889	101	1	again	again	ADV
ejpam-5889	101	2	,	,	PUNCT
ejpam-5889	101	3	d	d	PRON
ejpam-5889	101	4	is	be	AUX
ejpam-5889	101	5	not	not	PART
ejpam-5889	101	6	a	a	DET
ejpam-5889	101	7	simple	simple	ADJ
ejpam-5889	101	8	multigroup	multigroup	NOUN
ejpam-5889	101	9	.	.	PUNCT
ejpam-5889	102	1	example	example	NOUN
ejpam-5889	103	1	2	2	NUM
ejpam-5889	103	2	.	.	X
ejpam-5889	103	3	in	in	ADP
ejpam-5889	103	4	a	a	DET
ejpam-5889	103	5	symmetry	symmetry	NOUN
ejpam-5889	103	6	group	group	NOUN
ejpam-5889	103	7	sn	sn	PROPN
ejpam-5889	103	8	for	for	ADP
ejpam-5889	103	9	n	n	NOUN
ejpam-5889	103	10	=	=	SYM
ejpam-5889	103	11	3	3	NUM
ejpam-5889	103	12	(	(	PUNCT
ejpam-5889	103	13	i.e.	i.e.	X
ejpam-5889	103	14	,	,	PUNCT
ejpam-5889	103	15	s	s	X
ejpam-5889	103	16	=	=	PUNCT
ejpam-5889	103	17	{	{	PUNCT
ejpam-5889	103	18	1	1	NUM
ejpam-5889	103	19	,	,	PUNCT
ejpam-5889	103	20	2	2	NUM
ejpam-5889	103	21	,	,	PUNCT
ejpam-5889	103	22	3	3	NUM
ejpam-5889	103	23	}	}	PUNCT
ejpam-5889	103	24	)	)	PUNCT
ejpam-5889	103	25	,	,	PUNCT
ejpam-5889	103	26	a3	a3	NOUN
ejpam-5889	103	27	=	=	SYM
ejpam-5889	103	28	{	{	PUNCT
ejpam-5889	103	29	ρ0	ρ0	PROPN
ejpam-5889	103	30	,	,	PUNCT
ejpam-5889	103	31	ρ1	ρ1	NOUN
ejpam-5889	103	32	,	,	PUNCT
ejpam-5889	103	33	ρ2	ρ2	NOUN
ejpam-5889	103	34	}	}	PUNCT
ejpam-5889	103	35	⊆	⊆	NUM
ejpam-5889	103	36	s3	s3	PROPN
ejpam-5889	103	37	is	be	AUX
ejpam-5889	103	38	a	a	DET
ejpam-5889	103	39	simple	simple	ADJ
ejpam-5889	103	40	group	group	NOUN
ejpam-5889	103	41	(	(	PUNCT
ejpam-5889	103	42	ρ−1	ρ−1	PROPN
ejpam-5889	103	43	1	1	NUM
ejpam-5889	103	44	=	=	SYM
ejpam-5889	103	45	ρ2	ρ2	PROPN
ejpam-5889	103	46	,	,	PUNCT
ejpam-5889	103	47	ρ−1	ρ−1	PROPN
ejpam-5889	103	48	2	2	NUM
ejpam-5889	103	49	=	=	SYM
ejpam-5889	103	50	ρ1	ρ1	NOUN
ejpam-5889	103	51	,	,	PUNCT
ejpam-5889	103	52	and	and	CCONJ
ejpam-5889	103	53	ρ0	ρ0	PROPN
ejpam-5889	103	54	is	be	AUX
ejpam-5889	103	55	the	the	DET
ejpam-5889	103	56	identity	identity	NOUN
ejpam-5889	103	57	element	element	NOUN
ejpam-5889	103	58	)	)	PUNCT
ejpam-5889	103	59	.	.	PUNCT
ejpam-5889	104	1	using	use	VERB
ejpam-5889	104	2	a3	a3	NOUN
ejpam-5889	104	3	,	,	PUNCT
ejpam-5889	104	4	a	a	DET
ejpam-5889	104	5	multigroup	multigroup	ADV
ejpam-5889	104	6	defined	define	VERB
ejpam-5889	104	7	over	over	ADP
ejpam-5889	104	8	a3	a3	NOUN
ejpam-5889	104	9	is	be	AUX
ejpam-5889	104	10	:	:	PUNCT
ejpam-5889	104	11	e	e	X
ejpam-5889	104	12	=	=	PUNCT
ejpam-5889	104	13	{	{	PUNCT
ejpam-5889	104	14	ρ0	ρ0	PROPN
ejpam-5889	104	15	,	,	PUNCT
ejpam-5889	104	16	ρ0	ρ0	PROPN
ejpam-5889	104	17	,	,	PUNCT
ejpam-5889	104	18	ρ0	ρ0	PROPN
ejpam-5889	104	19	,	,	PUNCT
ejpam-5889	104	20	ρ1	ρ1	NOUN
ejpam-5889	104	21	,	,	PUNCT
ejpam-5889	104	22	ρ1	ρ1	NOUN
ejpam-5889	104	23	,	,	PUNCT
ejpam-5889	104	24	ρ2	ρ2	NOUN
ejpam-5889	104	25	,	,	PUNCT
ejpam-5889	104	26	ρ2	ρ2	PROPN
ejpam-5889	104	27	}	}	PUNCT
ejpam-5889	104	28	.	.	PUNCT
ejpam-5889	105	1	certainly	certainly	ADV
ejpam-5889	105	2	,	,	PUNCT
ejpam-5889	105	3	a3	a3	PROPN
ejpam-5889	105	4	is	be	AUX
ejpam-5889	105	5	a	a	DET
ejpam-5889	105	6	trivial	trivial	ADJ
ejpam-5889	105	7	multigroup	multigroup	NOUN
ejpam-5889	105	8	.	.	PUNCT
ejpam-5889	106	1	since	since	SCONJ
ejpam-5889	106	2	ρ1.ρ2	ρ1.ρ2	PROPN
ejpam-5889	106	3	=	=	PUNCT
ejpam-5889	106	4	ρ2.ρ1	ρ2.ρ1	X
ejpam-5889	106	5	=	=	SYM
ejpam-5889	106	6	ρ0	ρ0	PROPN
ejpam-5889	106	7	,	,	PUNCT
ejpam-5889	106	8	e	e	PROPN
ejpam-5889	106	9	is	be	AUX
ejpam-5889	106	10	commutative	commutative	ADJ
ejpam-5889	106	11	.	.	PUNCT
ejpam-5889	107	1	by	by	ADP
ejpam-5889	107	2	case	case	NOUN
ejpam-5889	107	3	(	(	PUNCT
ejpam-5889	107	4	i	i	NOUN
ejpam-5889	107	5	)	)	PUNCT
ejpam-5889	107	6	,	,	PUNCT
ejpam-5889	107	7	the	the	DET
ejpam-5889	107	8	submultigroups	submultigroup	NOUN
ejpam-5889	107	9	of	of	ADP
ejpam-5889	107	10	e	e	NOUN
ejpam-5889	107	11	are	be	AUX
ejpam-5889	107	12	as	as	SCONJ
ejpam-5889	107	13	follows	follow	VERB
ejpam-5889	107	14	:	:	PUNCT
ejpam-5889	107	15	e0	e0	PROPN
ejpam-5889	107	16	=	=	PROPN
ejpam-5889	107	17	{	{	PUNCT
ejpam-5889	107	18	ρ0	ρ0	PROPN
ejpam-5889	107	19	}	}	PUNCT
ejpam-5889	107	20	,	,	PUNCT
ejpam-5889	107	21	e1	e1	NOUN
ejpam-5889	107	22	=	=	SYM
ejpam-5889	107	23	a3	a3	NOUN
ejpam-5889	107	24	=	=	SYM
ejpam-5889	107	25	e∗	e∗	PROPN
ejpam-5889	107	26	=	=	SYM
ejpam-5889	107	27	{	{	PUNCT
ejpam-5889	107	28	ρ0	ρ0	PROPN
ejpam-5889	107	29	,	,	PUNCT
ejpam-5889	107	30	ρ1	ρ1	NOUN
ejpam-5889	107	31	,	,	PUNCT
ejpam-5889	107	32	ρ2	ρ2	NOUN
ejpam-5889	107	33	}	}	PUNCT
ejpam-5889	107	34	.	.	PUNCT
ejpam-5889	108	1	because	because	SCONJ
ejpam-5889	108	2	e0	e0	PROPN
ejpam-5889	108	3	and	and	CCONJ
ejpam-5889	108	4	e1	e1	PROPN
ejpam-5889	108	5	are	be	AUX
ejpam-5889	108	6	trivial	trivial	ADJ
ejpam-5889	108	7	,	,	PUNCT
ejpam-5889	108	8	then	then	ADV
ejpam-5889	108	9	e	e	PROPN
ejpam-5889	108	10	is	be	AUX
ejpam-5889	108	11	a	a	DET
ejpam-5889	108	12	simple	simple	ADJ
ejpam-5889	108	13	multigroup	multigroup	NOUN
ejpam-5889	108	14	(	(	PUNCT
ejpam-5889	108	15	because	because	SCONJ
ejpam-5889	108	16	it	it	PRON
ejpam-5889	108	17	has	have	VERB
ejpam-5889	108	18	no	no	DET
ejpam-5889	108	19	proper	proper	ADJ
ejpam-5889	108	20	nontrivial	nontrivial	ADJ
ejpam-5889	108	21	normal	normal	ADJ
ejpam-5889	108	22	submultigroup	submultigroup	NOUN
ejpam-5889	108	23	and	and	CCONJ
ejpam-5889	108	24	hence	hence	ADV
ejpam-5889	108	25	,	,	PUNCT
ejpam-5889	108	26	no	no	DET
ejpam-5889	108	27	maximal	maximal	ADJ
ejpam-5889	108	28	non	non	ADJ
ejpam-5889	108	29	-	-	ADJ
ejpam-5889	108	30	trivial	trivial	ADJ
ejpam-5889	108	31	normal	normal	ADJ
ejpam-5889	108	32	submultigroup	submultigroup	NOUN
ejpam-5889	108	33	)	)	PUNCT
ejpam-5889	108	34	.	.	PUNCT
ejpam-5889	109	1	by	by	ADP
ejpam-5889	109	2	case	case	NOUN
ejpam-5889	109	3	(	(	PUNCT
ejpam-5889	109	4	ii	ii	NOUN
ejpam-5889	109	5	)	)	PUNCT
ejpam-5889	109	6	,	,	PUNCT
ejpam-5889	109	7	the	the	DET
ejpam-5889	109	8	submultigroups	submultigroup	NOUN
ejpam-5889	109	9	of	of	ADP
ejpam-5889	109	10	e	e	NOUN
ejpam-5889	109	11	are	be	AUX
ejpam-5889	109	12	in	in	ADP
ejpam-5889	109	13	table	table	NOUN
ejpam-5889	109	14	3	3	NUM
ejpam-5889	109	15	:	:	PUNCT
ejpam-5889	109	16	table	table	NOUN
ejpam-5889	109	17	3	3	NUM
ejpam-5889	109	18	:	:	PUNCT
ejpam-5889	109	19	submultigroups	submultigroup	NOUN
ejpam-5889	109	20	of	of	ADP
ejpam-5889	109	21	e	e	PROPN
ejpam-5889	109	22	based	base	VERB
ejpam-5889	109	23	on	on	ADP
ejpam-5889	109	24	case	case	NOUN
ejpam-5889	109	25	(	(	PUNCT
ejpam-5889	109	26	ii	ii	NOUN
ejpam-5889	109	27	)	)	PUNCT
ejpam-5889	109	28	submultigroups	submultigroup	NOUN
ejpam-5889	109	29	and	and	CCONJ
ejpam-5889	109	30	their	their	PRON
ejpam-5889	109	31	structures	structure	NOUN
ejpam-5889	109	32	ê1	ê1	NOUN
ejpam-5889	109	33	=	=	SYM
ejpam-5889	109	34	e1	e1	PROPN
ejpam-5889	109	35	=	=	SYM
ejpam-5889	109	36	{	{	PUNCT
ejpam-5889	109	37	ρ0	ρ0	PROPN
ejpam-5889	109	38	,	,	PUNCT
ejpam-5889	109	39	ρ1	ρ1	NOUN
ejpam-5889	109	40	,	,	PUNCT
ejpam-5889	109	41	ρ2	ρ2	NOUN
ejpam-5889	109	42	}	}	PUNCT
ejpam-5889	109	43	,	,	PUNCT
ejpam-5889	109	44	ê2	ê2	NOUN
ejpam-5889	109	45	=	=	SYM
ejpam-5889	109	46	{	{	PUNCT
ejpam-5889	109	47	ρ0	ρ0	PROPN
ejpam-5889	109	48	,	,	PUNCT
ejpam-5889	109	49	ρ0	ρ0	PROPN
ejpam-5889	109	50	,	,	PUNCT
ejpam-5889	109	51	ρ1	ρ1	NOUN
ejpam-5889	109	52	,	,	PUNCT
ejpam-5889	109	53	ρ2	ρ2	PROPN
ejpam-5889	109	54	}	}	PUNCT
ejpam-5889	109	55	,	,	PUNCT
ejpam-5889	109	56	ê3	ê3	PROPN
ejpam-5889	110	1	=	=	PUNCT
ejpam-5889	110	2	{	{	PUNCT
ejpam-5889	110	3	ρ0	ρ0	PROPN
ejpam-5889	110	4	,	,	PUNCT
ejpam-5889	110	5	ρ0	ρ0	PROPN
ejpam-5889	110	6	,	,	PUNCT
ejpam-5889	110	7	ρ1	ρ1	NOUN
ejpam-5889	110	8	,	,	PUNCT
ejpam-5889	110	9	ρ1	ρ1	NOUN
ejpam-5889	110	10	,	,	PUNCT
ejpam-5889	110	11	ρ2	ρ2	NOUN
ejpam-5889	110	12	,	,	PUNCT
ejpam-5889	110	13	ρ2	ρ2	PROPN
ejpam-5889	110	14	}	}	PUNCT
ejpam-5889	110	15	,	,	PUNCT
ejpam-5889	110	16	ê4	ê4	X
ejpam-5889	110	17	=	=	SYM
ejpam-5889	110	18	{	{	PUNCT
ejpam-5889	110	19	ρ0	ρ0	PROPN
ejpam-5889	110	20	,	,	PUNCT
ejpam-5889	110	21	ρ0	ρ0	PROPN
ejpam-5889	110	22	,	,	PUNCT
ejpam-5889	110	23	ρ0	ρ0	PROPN
ejpam-5889	110	24	,	,	PUNCT
ejpam-5889	110	25	ρ1	ρ1	NOUN
ejpam-5889	110	26	,	,	PUNCT
ejpam-5889	110	27	ρ2	ρ2	NOUN
ejpam-5889	110	28	}	}	PUNCT
ejpam-5889	110	29	,	,	PUNCT
ejpam-5889	110	30	ê5	ê5	NOUN
ejpam-5889	110	31	=	=	PUNCT
ejpam-5889	111	1	e	e	X
ejpam-5889	111	2	=	=	PUNCT
ejpam-5889	111	3	{	{	PUNCT
ejpam-5889	111	4	ρ0	ρ0	PROPN
ejpam-5889	111	5	,	,	PUNCT
ejpam-5889	111	6	ρ0	ρ0	PROPN
ejpam-5889	111	7	,	,	PUNCT
ejpam-5889	111	8	ρ0	ρ0	PROPN
ejpam-5889	111	9	,	,	PUNCT
ejpam-5889	111	10	ρ1	ρ1	NOUN
ejpam-5889	111	11	,	,	PUNCT
ejpam-5889	111	12	ρ1	ρ1	NOUN
ejpam-5889	111	13	,	,	PUNCT
ejpam-5889	111	14	ρ2	ρ2	NOUN
ejpam-5889	111	15	,	,	PUNCT
ejpam-5889	111	16	ρ2	ρ2	NOUN
ejpam-5889	111	17	}	}	PUNCT
ejpam-5889	111	18	here	here	ADV
ejpam-5889	111	19	,	,	PUNCT
ejpam-5889	111	20	it	it	PRON
ejpam-5889	111	21	is	be	AUX
ejpam-5889	111	22	observed	observe	VERB
ejpam-5889	111	23	that	that	SCONJ
ejpam-5889	111	24	ê1	ê1	PROPN
ejpam-5889	111	25	and	and	CCONJ
ejpam-5889	111	26	ê5	ê5	PROPN
ejpam-5889	111	27	are	be	AUX
ejpam-5889	111	28	trivial	trivial	ADJ
ejpam-5889	111	29	,	,	PUNCT
ejpam-5889	111	30	and	and	CCONJ
ejpam-5889	111	31	ê2	ê2	PROPN
ejpam-5889	111	32	–	–	PUNCT
ejpam-5889	111	33	ê4	ê4	X
ejpam-5889	111	34	are	be	AUX
ejpam-5889	111	35	proper	proper	ADJ
ejpam-5889	111	36	non	non	ADJ
ejpam-5889	111	37	-	-	ADJ
ejpam-5889	111	38	trivial	trivial	ADJ
ejpam-5889	111	39	normal	normal	ADJ
ejpam-5889	111	40	submultigroups	submultigroup	NOUN
ejpam-5889	111	41	of	of	ADP
ejpam-5889	111	42	e	e	NOUN
ejpam-5889	111	43	without	without	ADP
ejpam-5889	111	44	a	a	DET
ejpam-5889	111	45	maximal	maximal	ADJ
ejpam-5889	111	46	non	non	ADJ
ejpam-5889	111	47	-	-	ADJ
ejpam-5889	111	48	trivial	trivial	ADJ
ejpam-5889	111	49	normal	normal	ADJ
ejpam-5889	111	50	submultigroup	submultigroup	NOUN
ejpam-5889	111	51	ofd	ofd	PROPN
ejpam-5889	111	52	since	since	SCONJ
ejpam-5889	111	53	either	either	ADV
ejpam-5889	111	54	ê3	ê3	VERB
ejpam-5889	112	1	⊈	⊈	X
ejpam-5889	112	2	ê4	ê4	X
ejpam-5889	112	3	or	or	CCONJ
ejpam-5889	112	4	ê4	ê4	ADJ
ejpam-5889	112	5	⊈	⊈	PROPN
ejpam-5889	112	6	ê3	ê3	PROPN
ejpam-5889	112	7	.	.	PUNCT
ejpam-5889	113	1	hence	hence	ADV
ejpam-5889	113	2	,	,	PUNCT
ejpam-5889	113	3	e	e	PROPN
ejpam-5889	113	4	is	be	AUX
ejpam-5889	113	5	not	not	PART
ejpam-5889	113	6	simple	simple	ADJ
ejpam-5889	113	7	.	.	PUNCT
ejpam-5889	114	1	by	by	ADP
ejpam-5889	114	2	case	case	NOUN
ejpam-5889	114	3	(	(	PUNCT
ejpam-5889	114	4	iii	iii	NOUN
ejpam-5889	114	5	)	)	PUNCT
ejpam-5889	114	6	,	,	PUNCT
ejpam-5889	114	7	the	the	DET
ejpam-5889	114	8	submultigroups	submultigroup	NOUN
ejpam-5889	114	9	of	of	ADP
ejpam-5889	114	10	e	e	NOUN
ejpam-5889	114	11	are	be	AUX
ejpam-5889	114	12	in	in	ADP
ejpam-5889	114	13	table	table	NOUN
ejpam-5889	114	14	4	4	NUM
ejpam-5889	114	15	:	:	PUNCT
ejpam-5889	114	16	p.	p.	NOUN
ejpam-5889	114	17	a.	a.	PROPN
ejpam-5889	114	18	ejegwa	ejegwa	PROPN
ejpam-5889	114	19	et	et	PROPN
ejpam-5889	114	20	al	al	PROPN
ejpam-5889	114	21	.	.	PUNCT
ejpam-5889	114	22	/	/	SYM
ejpam-5889	114	23	eur	eur	PROPN
ejpam-5889	114	24	.	.	PUNCT
ejpam-5889	115	1	j.	j.	PROPN
ejpam-5889	115	2	pure	pure	PROPN
ejpam-5889	115	3	appl	appl	PROPN
ejpam-5889	115	4	.	.	PROPN
ejpam-5889	115	5	math	math	PROPN
ejpam-5889	115	6	,	,	PUNCT
ejpam-5889	115	7	18	18	NUM
ejpam-5889	115	8	(	(	PUNCT
ejpam-5889	115	9	2	2	NUM
ejpam-5889	115	10	)	)	PUNCT
ejpam-5889	115	11	(	(	PUNCT
ejpam-5889	115	12	2025	2025	NUM
ejpam-5889	115	13	)	)	PUNCT
ejpam-5889	115	14	,	,	PUNCT
ejpam-5889	115	15	5889	5889	NUM
ejpam-5889	115	16	7	7	NUM
ejpam-5889	115	17	of	of	ADP
ejpam-5889	115	18	13	13	NUM
ejpam-5889	115	19	table	table	NOUN
ejpam-5889	115	20	4	4	NUM
ejpam-5889	115	21	:	:	PUNCT
ejpam-5889	115	22	submultigroups	submultigroup	NOUN
ejpam-5889	115	23	of	of	ADP
ejpam-5889	115	24	e	e	PROPN
ejpam-5889	115	25	based	base	VERB
ejpam-5889	115	26	on	on	ADP
ejpam-5889	115	27	case	case	NOUN
ejpam-5889	115	28	(	(	PUNCT
ejpam-5889	115	29	iii	iii	NOUN
ejpam-5889	115	30	)	)	PUNCT
ejpam-5889	115	31	submultigroups	submultigroup	NOUN
ejpam-5889	115	32	and	and	CCONJ
ejpam-5889	115	33	their	their	PRON
ejpam-5889	115	34	structures	structure	NOUN
ejpam-5889	115	35	e0	e0	PROPN
ejpam-5889	115	36	=	=	PUNCT
ejpam-5889	115	37	{	{	PUNCT
ejpam-5889	115	38	ρ0	ρ0	PROPN
ejpam-5889	115	39	}	}	PUNCT
ejpam-5889	115	40	,	,	PUNCT
ejpam-5889	115	41	ê1	ê1	PROPN
ejpam-5889	115	42	=	=	SYM
ejpam-5889	115	43	e1	e1	PROPN
ejpam-5889	115	44	=	=	SYM
ejpam-5889	115	45	{	{	PUNCT
ejpam-5889	115	46	ρ0	ρ0	PROPN
ejpam-5889	115	47	,	,	PUNCT
ejpam-5889	115	48	ρ1	ρ1	NOUN
ejpam-5889	115	49	,	,	PUNCT
ejpam-5889	115	50	ρ2	ρ2	NOUN
ejpam-5889	115	51	}	}	PUNCT
ejpam-5889	115	52	,	,	PUNCT
ejpam-5889	115	53	ê2	ê2	NOUN
ejpam-5889	115	54	=	=	SYM
ejpam-5889	115	55	{	{	PUNCT
ejpam-5889	115	56	ρ0	ρ0	PROPN
ejpam-5889	115	57	,	,	PUNCT
ejpam-5889	115	58	ρ0	ρ0	PROPN
ejpam-5889	115	59	,	,	PUNCT
ejpam-5889	115	60	ρ1	ρ1	NOUN
ejpam-5889	115	61	,	,	PUNCT
ejpam-5889	115	62	ρ2	ρ2	PROPN
ejpam-5889	115	63	}	}	PUNCT
ejpam-5889	115	64	,	,	PUNCT
ejpam-5889	115	65	ê3	ê3	PROPN
ejpam-5889	116	1	=	=	PUNCT
ejpam-5889	116	2	{	{	PUNCT
ejpam-5889	116	3	ρ0	ρ0	PROPN
ejpam-5889	116	4	,	,	PUNCT
ejpam-5889	116	5	ρ0	ρ0	PROPN
ejpam-5889	116	6	,	,	PUNCT
ejpam-5889	116	7	ρ1	ρ1	NOUN
ejpam-5889	116	8	,	,	PUNCT
ejpam-5889	116	9	ρ1	ρ1	NOUN
ejpam-5889	116	10	,	,	PUNCT
ejpam-5889	116	11	ρ2	ρ2	NOUN
ejpam-5889	116	12	,	,	PUNCT
ejpam-5889	116	13	ρ2	ρ2	PROPN
ejpam-5889	116	14	}	}	PUNCT
ejpam-5889	116	15	,	,	PUNCT
ejpam-5889	116	16	ê4	ê4	X
ejpam-5889	116	17	=	=	SYM
ejpam-5889	116	18	{	{	PUNCT
ejpam-5889	116	19	ρ0	ρ0	PROPN
ejpam-5889	116	20	,	,	PUNCT
ejpam-5889	116	21	ρ0	ρ0	PROPN
ejpam-5889	116	22	,	,	PUNCT
ejpam-5889	116	23	ρ0	ρ0	PROPN
ejpam-5889	116	24	,	,	PUNCT
ejpam-5889	116	25	ρ1	ρ1	NOUN
ejpam-5889	116	26	,	,	PUNCT
ejpam-5889	116	27	ρ2	ρ2	NOUN
ejpam-5889	116	28	}	}	PUNCT
ejpam-5889	116	29	,	,	PUNCT
ejpam-5889	116	30	ê5	ê5	NOUN
ejpam-5889	116	31	=	=	PUNCT
ejpam-5889	117	1	e	e	X
ejpam-5889	117	2	=	=	PUNCT
ejpam-5889	117	3	{	{	PUNCT
ejpam-5889	117	4	ρ0	ρ0	PROPN
ejpam-5889	117	5	,	,	PUNCT
ejpam-5889	117	6	ρ0	ρ0	PROPN
ejpam-5889	117	7	,	,	PUNCT
ejpam-5889	117	8	ρ0	ρ0	PROPN
ejpam-5889	117	9	,	,	PUNCT
ejpam-5889	117	10	ρ1	ρ1	NOUN
ejpam-5889	117	11	,	,	PUNCT
ejpam-5889	117	12	ρ1	ρ1	NOUN
ejpam-5889	117	13	,	,	PUNCT
ejpam-5889	117	14	ρ2	ρ2	NOUN
ejpam-5889	117	15	,	,	PUNCT
ejpam-5889	117	16	ρ2	ρ2	NOUN
ejpam-5889	117	17	}	}	PUNCT
ejpam-5889	117	18	,	,	PUNCT
ejpam-5889	118	1	ė1	ė1	PROPN
ejpam-5889	118	2	=	=	SYM
ejpam-5889	118	3	{	{	PUNCT
ejpam-5889	118	4	ρ0	ρ0	PROPN
ejpam-5889	118	5	,	,	PUNCT
ejpam-5889	118	6	ρ0	ρ0	PROPN
ejpam-5889	118	7	}	}	PUNCT
ejpam-5889	118	8	,	,	PUNCT
ejpam-5889	118	9	ė2	ė2	PROPN
ejpam-5889	118	10	=	=	SYM
ejpam-5889	118	11	{	{	PUNCT
ejpam-5889	118	12	ρ0	ρ0	PROPN
ejpam-5889	118	13	,	,	PUNCT
ejpam-5889	118	14	ρ0	ρ0	PROPN
ejpam-5889	118	15	,	,	PUNCT
ejpam-5889	118	16	ρ0	ρ0	PROPN
ejpam-5889	118	17	}	}	PUNCT
ejpam-5889	118	18	here	here	ADV
ejpam-5889	118	19	,	,	PUNCT
ejpam-5889	118	20	e0	e0	PROPN
ejpam-5889	118	21	,	,	PUNCT
ejpam-5889	118	22	ê1	ê1	PROPN
ejpam-5889	118	23	,	,	PUNCT
ejpam-5889	118	24	ė1	ė1	PROPN
ejpam-5889	118	25	,	,	PUNCT
ejpam-5889	118	26	ė2	ė2	PROPN
ejpam-5889	118	27	and	and	CCONJ
ejpam-5889	118	28	ê5	ê5	NOUN
ejpam-5889	118	29	are	be	AUX
ejpam-5889	118	30	trivial	trivial	ADJ
ejpam-5889	118	31	,	,	PUNCT
ejpam-5889	118	32	and	and	CCONJ
ejpam-5889	118	33	ê2	ê2	PROPN
ejpam-5889	118	34	–	–	PUNCT
ejpam-5889	118	35	ê4	ê4	X
ejpam-5889	118	36	are	be	AUX
ejpam-5889	118	37	proper	proper	ADJ
ejpam-5889	118	38	non	non	ADJ
ejpam-5889	118	39	-	-	ADJ
ejpam-5889	118	40	trivial	trivial	ADJ
ejpam-5889	118	41	normal	normal	ADJ
ejpam-5889	118	42	submultigroups	submultigroup	NOUN
ejpam-5889	118	43	of	of	ADP
ejpam-5889	118	44	e	e	NOUN
ejpam-5889	118	45	without	without	ADP
ejpam-5889	118	46	a	a	DET
ejpam-5889	118	47	maximal	maximal	ADJ
ejpam-5889	118	48	non	non	ADJ
ejpam-5889	118	49	-	-	ADJ
ejpam-5889	118	50	trivial	trivial	ADJ
ejpam-5889	118	51	normal	normal	ADJ
ejpam-5889	118	52	submultigroup	submultigroup	NOUN
ejpam-5889	118	53	of	of	ADP
ejpam-5889	118	54	e	e	PROPN
ejpam-5889	118	55	since	since	SCONJ
ejpam-5889	118	56	either	either	ADV
ejpam-5889	118	57	ê3	ê3	VERB
ejpam-5889	119	1	⊈	⊈	X
ejpam-5889	119	2	ê4	ê4	X
ejpam-5889	119	3	or	or	CCONJ
ejpam-5889	119	4	ê4	ê4	ADJ
ejpam-5889	119	5	⊈	⊈	PROPN
ejpam-5889	119	6	ê3	ê3	PROPN
ejpam-5889	119	7	.	.	PUNCT
ejpam-5889	120	1	hence	hence	ADV
ejpam-5889	120	2	,	,	PUNCT
ejpam-5889	120	3	e	e	PROPN
ejpam-5889	120	4	is	be	AUX
ejpam-5889	120	5	not	not	PART
ejpam-5889	120	6	a	a	DET
ejpam-5889	120	7	simple	simple	ADJ
ejpam-5889	120	8	multigroup	multigroup	NOUN
ejpam-5889	120	9	.	.	PUNCT
ejpam-5889	120	10	example	example	NOUN
ejpam-5889	121	1	3	3	X
ejpam-5889	121	2	.	.	PUNCT
ejpam-5889	121	3	let	let	VERB
ejpam-5889	121	4	g	g	NOUN
ejpam-5889	121	5	=	=	PUNCT
ejpam-5889	121	6	{	{	PUNCT
ejpam-5889	121	7	1	1	NUM
ejpam-5889	121	8	,	,	PUNCT
ejpam-5889	121	9	a	a	PRON
ejpam-5889	121	10	,	,	PUNCT
ejpam-5889	121	11	a2	a2	PROPN
ejpam-5889	121	12	,	,	PUNCT
ejpam-5889	121	13	a3	a3	NOUN
ejpam-5889	121	14	,	,	PUNCT
ejpam-5889	121	15	b	b	PROPN
ejpam-5889	121	16	,	,	PUNCT
ejpam-5889	121	17	ab	ab	PROPN
ejpam-5889	121	18	,	,	PUNCT
ejpam-5889	121	19	a2b	a2b	PROPN
ejpam-5889	121	20	,	,	PUNCT
ejpam-5889	121	21	a3b	a3b	VERB
ejpam-5889	121	22	}	}	PUNCT
ejpam-5889	121	23	be	be	AUX
ejpam-5889	121	24	a	a	DET
ejpam-5889	121	25	group	group	NOUN
ejpam-5889	121	26	of	of	ADP
ejpam-5889	121	27	order	order	NOUN
ejpam-5889	121	28	8	8	NUM
ejpam-5889	121	29	with	with	ADP
ejpam-5889	121	30	two	two	NUM
ejpam-5889	121	31	generators	generator	NOUN
ejpam-5889	121	32	a	a	PRON
ejpam-5889	121	33	and	and	CCONJ
ejpam-5889	121	34	b	b	NOUN
ejpam-5889	121	35	,	,	PUNCT
ejpam-5889	121	36	which	which	PRON
ejpam-5889	121	37	satisfy	satisfy	VERB
ejpam-5889	121	38	the	the	DET
ejpam-5889	121	39	relations	relation	NOUN
ejpam-5889	121	40	:	:	PUNCT
ejpam-5889	121	41	(	(	PUNCT
ejpam-5889	121	42	i	i	NOUN
ejpam-5889	121	43	)	)	PUNCT
ejpam-5889	121	44	a4	a4	NOUN
ejpam-5889	121	45	=	=	SYM
ejpam-5889	121	46	b2	b2	NOUN
ejpam-5889	121	47	=	=	SYM
ejpam-5889	121	48	1	1	NUM
ejpam-5889	121	49	and	and	CCONJ
ejpam-5889	121	50	ba	ba	PROPN
ejpam-5889	121	51	=	=	PRON
ejpam-5889	121	52	a3b	a3b	PROPN
ejpam-5889	121	53	=	=	SYM
ejpam-5889	121	54	a−1b	a−1b	NOUN
ejpam-5889	121	55	,	,	PUNCT
ejpam-5889	121	56	which	which	PRON
ejpam-5889	121	57	is	be	AUX
ejpam-5889	121	58	a	a	DET
ejpam-5889	121	59	group	group	NOUN
ejpam-5889	121	60	recognize	recognize	VERB
ejpam-5889	121	61	as	as	ADP
ejpam-5889	121	62	d4	d4	PROPN
ejpam-5889	121	63	.	.	PUNCT
ejpam-5889	122	1	(	(	PUNCT
ejpam-5889	122	2	ii	ii	NOUN
ejpam-5889	122	3	)	)	PUNCT
ejpam-5889	122	4	a4	a4	NOUN
ejpam-5889	122	5	=	=	SYM
ejpam-5889	122	6	1	1	NUM
ejpam-5889	122	7	,	,	PUNCT
ejpam-5889	122	8	a2	a2	PROPN
ejpam-5889	122	9	=	=	SYM
ejpam-5889	122	10	b2	b2	PROPN
ejpam-5889	122	11	,	,	PUNCT
ejpam-5889	122	12	and	and	CCONJ
ejpam-5889	122	13	ba	ba	PROPN
ejpam-5889	122	14	=	=	PUNCT
ejpam-5889	122	15	a3b	a3b	PROPN
ejpam-5889	122	16	,	,	PUNCT
ejpam-5889	122	17	which	which	PRON
ejpam-5889	122	18	is	be	AUX
ejpam-5889	122	19	a	a	DET
ejpam-5889	122	20	group	group	NOUN
ejpam-5889	122	21	of	of	ADP
ejpam-5889	122	22	unit	unit	NOUN
ejpam-5889	122	23	quaternions	quaternion	NOUN
ejpam-5889	122	24	.	.	PUNCT
ejpam-5889	123	1	indeed	indeed	ADV
ejpam-5889	123	2	,	,	PUNCT
ejpam-5889	123	3	a−1	a−1	PROPN
ejpam-5889	123	4	=	=	PUNCT
ejpam-5889	123	5	a3	a3	PROPN
ejpam-5889	123	6	,	,	PUNCT
ejpam-5889	123	7	(	(	PUNCT
ejpam-5889	123	8	a3)−1	a3)−1	NOUN
ejpam-5889	123	9	=	=	SYM
ejpam-5889	123	10	a	a	X
ejpam-5889	123	11	,	,	PUNCT
ejpam-5889	123	12	(	(	PUNCT
ejpam-5889	123	13	a2)−1	a2)−1	PROPN
ejpam-5889	123	14	=	=	SYM
ejpam-5889	123	15	a2	a2	PROPN
ejpam-5889	123	16	,	,	PUNCT
ejpam-5889	123	17	b−1	b−1	PROPN
ejpam-5889	123	18	=	=	SYM
ejpam-5889	123	19	b	b	PROPN
ejpam-5889	123	20	,	,	PUNCT
ejpam-5889	123	21	(	(	PUNCT
ejpam-5889	123	22	ab)−1	ab)−1	PROPN
ejpam-5889	123	23	=	=	SYM
ejpam-5889	123	24	a3b	a3b	PROPN
ejpam-5889	123	25	,	,	PUNCT
ejpam-5889	123	26	(	(	PUNCT
ejpam-5889	123	27	a2b)−1	a2b)−1	NOUN
ejpam-5889	123	28	=	=	SYM
ejpam-5889	123	29	a2b	a2b	NOUN
ejpam-5889	123	30	,	,	PUNCT
ejpam-5889	123	31	and	and	CCONJ
ejpam-5889	123	32	(	(	PUNCT
ejpam-5889	123	33	a3b)−1	a3b)−1	NOUN
ejpam-5889	123	34	=	=	SYM
ejpam-5889	123	35	ab	ab	PROPN
ejpam-5889	123	36	.	.	PUNCT
ejpam-5889	124	1	certainly	certainly	ADV
ejpam-5889	124	2	,	,	PUNCT
ejpam-5889	124	3	g	g	PROPN
ejpam-5889	124	4	is	be	AUX
ejpam-5889	124	5	non	non	ADJ
ejpam-5889	124	6	-	-	ADJ
ejpam-5889	124	7	abelian	abelian	ADJ
ejpam-5889	124	8	since	since	SCONJ
ejpam-5889	124	9	b(ab	b(ab	NOUN
ejpam-5889	124	10	)	)	PUNCT
ejpam-5889	124	11	̸=	̸=	PROPN
ejpam-5889	124	12	(	(	PUNCT
ejpam-5889	124	13	ab)b	ab)b	PROPN
ejpam-5889	124	14	because	because	SCONJ
ejpam-5889	124	15	b(ab	b(ab	NOUN
ejpam-5889	124	16	)	)	PUNCT
ejpam-5889	124	17	=	=	PUNCT
ejpam-5889	125	1	(	(	PUNCT
ejpam-5889	125	2	ba)b	ba)b	PROPN
ejpam-5889	125	3	=	=	SYM
ejpam-5889	125	4	a3b2	a3b2	PUNCT
ejpam-5889	125	5	=	=	SYM
ejpam-5889	125	6	a3	a3	NOUN
ejpam-5889	125	7	and	and	CCONJ
ejpam-5889	125	8	(	(	PUNCT
ejpam-5889	125	9	ab)b	ab)b	PROPN
ejpam-5889	125	10	=	=	PUNCT
ejpam-5889	125	11	ab2	ab2	NOUN
ejpam-5889	125	12	=	=	NOUN
ejpam-5889	125	13	a.	a.	NOUN
ejpam-5889	125	14	using	use	VERB
ejpam-5889	125	15	g	g	PROPN
ejpam-5889	125	16	,	,	PUNCT
ejpam-5889	125	17	a	a	DET
ejpam-5889	125	18	multigroup	multigroup	ADV
ejpam-5889	125	19	defined	define	VERB
ejpam-5889	125	20	over	over	ADP
ejpam-5889	125	21	g	g	PROPN
ejpam-5889	125	22	is	be	AUX
ejpam-5889	125	23	:	:	PUNCT
ejpam-5889	125	24	f	f	X
ejpam-5889	125	25	=	=	PUNCT
ejpam-5889	125	26	{	{	PUNCT
ejpam-5889	125	27	1	1	NUM
ejpam-5889	125	28	,	,	PUNCT
ejpam-5889	125	29	1	1	NUM
ejpam-5889	125	30	,	,	PUNCT
ejpam-5889	125	31	1	1	NUM
ejpam-5889	125	32	,	,	PUNCT
ejpam-5889	125	33	a	a	DET
ejpam-5889	125	34	,	,	PUNCT
ejpam-5889	125	35	a	a	PRON
ejpam-5889	125	36	,	,	PUNCT
ejpam-5889	125	37	a2	a2	PROPN
ejpam-5889	125	38	,	,	PUNCT
ejpam-5889	125	39	a2	a2	PROPN
ejpam-5889	125	40	,	,	PUNCT
ejpam-5889	125	41	a2	a2	PROPN
ejpam-5889	125	42	,	,	PUNCT
ejpam-5889	125	43	a3	a3	NOUN
ejpam-5889	125	44	,	,	PUNCT
ejpam-5889	125	45	a3	a3	NOUN
ejpam-5889	125	46	,	,	PUNCT
ejpam-5889	125	47	b	b	PROPN
ejpam-5889	125	48	,	,	PUNCT
ejpam-5889	125	49	b	b	PROPN
ejpam-5889	125	50	,	,	PUNCT
ejpam-5889	125	51	ab	ab	PROPN
ejpam-5889	125	52	,	,	PUNCT
ejpam-5889	125	53	ab	ab	PROPN
ejpam-5889	125	54	,	,	PUNCT
ejpam-5889	125	55	a2b	a2b	PROPN
ejpam-5889	125	56	,	,	PUNCT
ejpam-5889	125	57	a2b	a2b	PROPN
ejpam-5889	125	58	,	,	PUNCT
ejpam-5889	125	59	a3b	a3b	ADV
ejpam-5889	125	60	,	,	PUNCT
ejpam-5889	125	61	a3b	a3b	ADJ
ejpam-5889	125	62	}	}	PUNCT
ejpam-5889	125	63	,	,	PUNCT
ejpam-5889	125	64	which	which	PRON
ejpam-5889	125	65	is	be	AUX
ejpam-5889	125	66	also	also	ADV
ejpam-5889	125	67	non	non	ADJ
ejpam-5889	125	68	-	-	ADJ
ejpam-5889	125	69	commutative	commutative	ADJ
ejpam-5889	125	70	.	.	PUNCT
ejpam-5889	126	1	the	the	DET
ejpam-5889	126	2	following	follow	VERB
ejpam-5889	126	3	structures	structure	NOUN
ejpam-5889	126	4	in	in	ADP
ejpam-5889	126	5	table	table	NOUN
ejpam-5889	126	6	5	5	NUM
ejpam-5889	126	7	are	be	AUX
ejpam-5889	126	8	the	the	DET
ejpam-5889	126	9	submultigroups	submultigroup	NOUN
ejpam-5889	126	10	of	of	ADP
ejpam-5889	126	11	f	f	NOUN
ejpam-5889	126	12	:	:	PUNCT
ejpam-5889	126	13	table	table	NOUN
ejpam-5889	126	14	5	5	NUM
ejpam-5889	126	15	:	:	PUNCT
ejpam-5889	126	16	submultigroups	submultigroup	NOUN
ejpam-5889	126	17	of	of	ADP
ejpam-5889	126	18	f	f	PROPN
ejpam-5889	126	19	submultigroups	submultigroup	NOUN
ejpam-5889	126	20	and	and	CCONJ
ejpam-5889	126	21	their	their	PRON
ejpam-5889	126	22	structures	structure	NOUN
ejpam-5889	126	23	f0	f0	NOUN
ejpam-5889	126	24	=	=	PUNCT
ejpam-5889	126	25	{	{	PUNCT
ejpam-5889	126	26	1	1	NUM
ejpam-5889	126	27	}	}	PUNCT
ejpam-5889	126	28	,	,	PUNCT
ejpam-5889	126	29	f1	f1	NOUN
ejpam-5889	126	30	=	=	SYM
ejpam-5889	126	31	{	{	PUNCT
ejpam-5889	126	32	1	1	NUM
ejpam-5889	126	33	,	,	PUNCT
ejpam-5889	126	34	1	1	NUM
ejpam-5889	126	35	}	}	PUNCT
ejpam-5889	126	36	,	,	PUNCT
ejpam-5889	126	37	f2	f2	PROPN
ejpam-5889	126	38	=	=	SYM
ejpam-5889	126	39	{	{	PUNCT
ejpam-5889	126	40	1	1	NUM
ejpam-5889	126	41	,	,	PUNCT
ejpam-5889	126	42	1	1	NUM
ejpam-5889	126	43	,	,	PUNCT
ejpam-5889	126	44	1	1	NUM
ejpam-5889	126	45	}	}	PUNCT
ejpam-5889	126	46	,	,	PUNCT
ejpam-5889	126	47	f3	f3	PROPN
ejpam-5889	126	48	=	=	SYM
ejpam-5889	126	49	{	{	PUNCT
ejpam-5889	126	50	1	1	NUM
ejpam-5889	126	51	,	,	PUNCT
ejpam-5889	126	52	a	a	DET
ejpam-5889	126	53	,	,	PUNCT
ejpam-5889	126	54	a2	a2	PROPN
ejpam-5889	126	55	,	,	PUNCT
ejpam-5889	126	56	a3	a3	NOUN
ejpam-5889	126	57	}	}	PUNCT
ejpam-5889	126	58	,	,	PUNCT
ejpam-5889	126	59	f4	f4	NOUN
ejpam-5889	126	60	=	=	SYM
ejpam-5889	126	61	{	{	PUNCT
ejpam-5889	126	62	1	1	NUM
ejpam-5889	126	63	,	,	PUNCT
ejpam-5889	126	64	1	1	NUM
ejpam-5889	126	65	,	,	PUNCT
ejpam-5889	126	66	a	a	PRON
ejpam-5889	126	67	,	,	PUNCT
ejpam-5889	126	68	a2	a2	PROPN
ejpam-5889	126	69	,	,	PUNCT
ejpam-5889	126	70	a3	a3	NOUN
ejpam-5889	126	71	}	}	PUNCT
ejpam-5889	126	72	,	,	PUNCT
ejpam-5889	126	73	f5	f5	PROPN
ejpam-5889	126	74	=	=	SYM
ejpam-5889	126	75	{	{	PUNCT
ejpam-5889	126	76	1	1	NUM
ejpam-5889	126	77	,	,	PUNCT
ejpam-5889	126	78	1	1	NUM
ejpam-5889	126	79	,	,	PUNCT
ejpam-5889	126	80	a	a	DET
ejpam-5889	126	81	,	,	PUNCT
ejpam-5889	126	82	a	a	PRON
ejpam-5889	126	83	,	,	PUNCT
ejpam-5889	126	84	a2	a2	PROPN
ejpam-5889	126	85	,	,	PUNCT
ejpam-5889	126	86	a2	a2	PROPN
ejpam-5889	126	87	,	,	PUNCT
ejpam-5889	126	88	a3	a3	NOUN
ejpam-5889	126	89	,	,	PUNCT
ejpam-5889	126	90	a3	a3	NOUN
ejpam-5889	126	91	}	}	PUNCT
ejpam-5889	126	92	,	,	PUNCT
ejpam-5889	126	93	f6	f6	PROPN
ejpam-5889	126	94	=	=	PUNCT
ejpam-5889	126	95	{	{	PUNCT
ejpam-5889	126	96	1	1	NUM
ejpam-5889	126	97	,	,	PUNCT
ejpam-5889	126	98	1	1	NUM
ejpam-5889	126	99	,	,	PUNCT
ejpam-5889	126	100	1	1	NUM
ejpam-5889	126	101	,	,	PUNCT
ejpam-5889	126	102	a	a	PRON
ejpam-5889	126	103	,	,	PUNCT
ejpam-5889	126	104	a2	a2	PROPN
ejpam-5889	126	105	,	,	PUNCT
ejpam-5889	126	106	a3	a3	NOUN
ejpam-5889	126	107	}	}	PUNCT
ejpam-5889	126	108	,	,	PUNCT
ejpam-5889	126	109	f7	f7	PROPN
ejpam-5889	126	110	=	=	PUNCT
ejpam-5889	126	111	{	{	PUNCT
ejpam-5889	126	112	1	1	NUM
ejpam-5889	126	113	,	,	PUNCT
ejpam-5889	126	114	1	1	NUM
ejpam-5889	126	115	,	,	PUNCT
ejpam-5889	126	116	1	1	NUM
ejpam-5889	126	117	,	,	PUNCT
ejpam-5889	126	118	a	a	PRON
ejpam-5889	126	119	,	,	PUNCT
ejpam-5889	126	120	a	a	PRON
ejpam-5889	126	121	,	,	PUNCT
ejpam-5889	126	122	a2	a2	PROPN
ejpam-5889	126	123	,	,	PUNCT
ejpam-5889	126	124	a2	a2	PROPN
ejpam-5889	126	125	,	,	PUNCT
ejpam-5889	126	126	a3	a3	NOUN
ejpam-5889	126	127	,	,	PUNCT
ejpam-5889	126	128	a3	a3	NOUN
ejpam-5889	126	129	}	}	PUNCT
ejpam-5889	126	130	,	,	PUNCT
ejpam-5889	126	131	f8	f8	PROPN
ejpam-5889	126	132	=	=	PUNCT
ejpam-5889	126	133	{	{	PUNCT
ejpam-5889	126	134	1	1	NUM
ejpam-5889	126	135	,	,	PUNCT
ejpam-5889	126	136	1	1	NUM
ejpam-5889	126	137	,	,	PUNCT
ejpam-5889	126	138	1	1	NUM
ejpam-5889	126	139	,	,	PUNCT
ejpam-5889	126	140	a	a	DET
ejpam-5889	126	141	,	,	PUNCT
ejpam-5889	126	142	a	a	PRON
ejpam-5889	126	143	,	,	PUNCT
ejpam-5889	126	144	a2	a2	PROPN
ejpam-5889	126	145	,	,	PUNCT
ejpam-5889	126	146	a2	a2	PROPN
ejpam-5889	126	147	,	,	PUNCT
ejpam-5889	126	148	a2	a2	PROPN
ejpam-5889	126	149	,	,	PUNCT
ejpam-5889	126	150	a3	a3	NOUN
ejpam-5889	126	151	,	,	PUNCT
ejpam-5889	126	152	a3	a3	NOUN
ejpam-5889	126	153	}	}	PUNCT
ejpam-5889	126	154	,	,	PUNCT
ejpam-5889	126	155	f9	f9	PROPN
ejpam-5889	126	156	=	=	PUNCT
ejpam-5889	126	157	{	{	PUNCT
ejpam-5889	126	158	1	1	NUM
ejpam-5889	126	159	,	,	PUNCT
ejpam-5889	126	160	a2	a2	PROPN
ejpam-5889	126	161	}	}	PUNCT
ejpam-5889	126	162	,	,	PUNCT
ejpam-5889	126	163	f10	f10	NOUN
ejpam-5889	126	164	=	=	SYM
ejpam-5889	126	165	{	{	PUNCT
ejpam-5889	126	166	1	1	NUM
ejpam-5889	126	167	,	,	PUNCT
ejpam-5889	126	168	1	1	NUM
ejpam-5889	126	169	,	,	PUNCT
ejpam-5889	126	170	a2	a2	PROPN
ejpam-5889	126	171	,	,	PUNCT
ejpam-5889	126	172	a2	a2	PROPN
ejpam-5889	126	173	}	}	PUNCT
ejpam-5889	126	174	,	,	PUNCT
ejpam-5889	126	175	f11	f11	PROPN
ejpam-5889	126	176	=	=	SYM
ejpam-5889	126	177	{	{	PUNCT
ejpam-5889	126	178	1	1	NUM
ejpam-5889	126	179	,	,	PUNCT
ejpam-5889	126	180	1	1	NUM
ejpam-5889	126	181	,	,	PUNCT
ejpam-5889	126	182	1	1	NUM
ejpam-5889	126	183	,	,	PUNCT
ejpam-5889	126	184	a2	a2	PROPN
ejpam-5889	126	185	,	,	PUNCT
ejpam-5889	126	186	a2	a2	PROPN
ejpam-5889	126	187	,	,	PUNCT
ejpam-5889	126	188	a2	a2	PROPN
ejpam-5889	126	189	}	}	PUNCT
ejpam-5889	126	190	,	,	PUNCT
ejpam-5889	126	191	f12	f12	NOUN
ejpam-5889	126	192	=	=	SYM
ejpam-5889	126	193	{	{	PUNCT
ejpam-5889	126	194	1	1	NUM
ejpam-5889	126	195	,	,	PUNCT
ejpam-5889	126	196	b	b	NOUN
ejpam-5889	126	197	}	}	PUNCT
ejpam-5889	126	198	,	,	PUNCT
ejpam-5889	126	199	f13	f13	X
ejpam-5889	126	200	=	=	SYM
ejpam-5889	126	201	{	{	PUNCT
ejpam-5889	126	202	1	1	NUM
ejpam-5889	126	203	,	,	PUNCT
ejpam-5889	126	204	1	1	NUM
ejpam-5889	126	205	,	,	PUNCT
ejpam-5889	126	206	b	b	NOUN
ejpam-5889	126	207	}	}	PUNCT
ejpam-5889	126	208	,	,	PUNCT
ejpam-5889	126	209	f14	f14	PROPN
ejpam-5889	126	210	=	=	SYM
ejpam-5889	126	211	{	{	PUNCT
ejpam-5889	126	212	1	1	NUM
ejpam-5889	126	213	,	,	PUNCT
ejpam-5889	126	214	1	1	NUM
ejpam-5889	126	215	,	,	PUNCT
ejpam-5889	126	216	b	b	NOUN
ejpam-5889	126	217	,	,	PUNCT
ejpam-5889	126	218	b	b	NOUN
ejpam-5889	126	219	}	}	PUNCT
ejpam-5889	126	220	,	,	PUNCT
ejpam-5889	126	221	f15	f15	PROPN
ejpam-5889	126	222	=	=	PUNCT
ejpam-5889	126	223	{	{	PUNCT
ejpam-5889	126	224	1	1	NUM
ejpam-5889	126	225	,	,	PUNCT
ejpam-5889	126	226	1	1	NUM
ejpam-5889	126	227	,	,	PUNCT
ejpam-5889	126	228	1	1	NUM
ejpam-5889	126	229	,	,	PUNCT
ejpam-5889	126	230	b	b	NOUN
ejpam-5889	126	231	,	,	PUNCT
ejpam-5889	126	232	b	b	NOUN
ejpam-5889	126	233	}	}	PUNCT
ejpam-5889	126	234	,	,	PUNCT
ejpam-5889	126	235	f16	f16	PROPN
ejpam-5889	126	236	=	=	SYM
ejpam-5889	126	237	{	{	PUNCT
ejpam-5889	126	238	1	1	NUM
ejpam-5889	126	239	,	,	PUNCT
ejpam-5889	126	240	a	a	DET
ejpam-5889	126	241	,	,	PUNCT
ejpam-5889	126	242	a2	a2	PROPN
ejpam-5889	126	243	,	,	PUNCT
ejpam-5889	126	244	a3	a3	NOUN
ejpam-5889	126	245	,	,	PUNCT
ejpam-5889	126	246	b	b	PROPN
ejpam-5889	126	247	,	,	PUNCT
ejpam-5889	126	248	ab	ab	PROPN
ejpam-5889	126	249	,	,	PUNCT
ejpam-5889	126	250	a2b	a2b	PROPN
ejpam-5889	126	251	,	,	PUNCT
ejpam-5889	126	252	a3b	a3b	ADJ
ejpam-5889	126	253	}	}	PUNCT
ejpam-5889	126	254	,	,	PUNCT
ejpam-5889	126	255	f17	f17	NOUN
ejpam-5889	126	256	=	=	SYM
ejpam-5889	126	257	{	{	PUNCT
ejpam-5889	126	258	1	1	NUM
ejpam-5889	126	259	,	,	PUNCT
ejpam-5889	126	260	1	1	NUM
ejpam-5889	126	261	,	,	PUNCT
ejpam-5889	126	262	a	a	DET
ejpam-5889	126	263	,	,	PUNCT
ejpam-5889	126	264	a2	a2	PROPN
ejpam-5889	126	265	,	,	PUNCT
ejpam-5889	126	266	a3	a3	NOUN
ejpam-5889	126	267	,	,	PUNCT
ejpam-5889	126	268	b	b	PROPN
ejpam-5889	126	269	,	,	PUNCT
ejpam-5889	126	270	ab	ab	PROPN
ejpam-5889	126	271	,	,	PUNCT
ejpam-5889	126	272	a2b	a2b	PROPN
ejpam-5889	126	273	,	,	PUNCT
ejpam-5889	126	274	a3b	a3b	ADJ
ejpam-5889	126	275	}	}	PUNCT
ejpam-5889	126	276	,	,	PUNCT
ejpam-5889	126	277	f18	f18	PROPN
ejpam-5889	126	278	=	=	SYM
ejpam-5889	126	279	{	{	PUNCT
ejpam-5889	126	280	1	1	NUM
ejpam-5889	126	281	,	,	PUNCT
ejpam-5889	126	282	1	1	NUM
ejpam-5889	126	283	,	,	PUNCT
ejpam-5889	126	284	a	a	DET
ejpam-5889	126	285	,	,	PUNCT
ejpam-5889	126	286	a	a	PRON
ejpam-5889	126	287	,	,	PUNCT
ejpam-5889	126	288	a2	a2	PROPN
ejpam-5889	126	289	,	,	PUNCT
ejpam-5889	126	290	a2	a2	PROPN
ejpam-5889	126	291	,	,	PUNCT
ejpam-5889	126	292	a3	a3	NOUN
ejpam-5889	126	293	,	,	PUNCT
ejpam-5889	126	294	a3	a3	NOUN
ejpam-5889	126	295	,	,	PUNCT
ejpam-5889	126	296	b	b	PROPN
ejpam-5889	126	297	,	,	PUNCT
ejpam-5889	126	298	b	b	PROPN
ejpam-5889	126	299	,	,	PUNCT
ejpam-5889	126	300	ab	ab	PROPN
ejpam-5889	126	301	,	,	PUNCT
ejpam-5889	126	302	ab	ab	PROPN
ejpam-5889	126	303	,	,	PUNCT
ejpam-5889	126	304	a2b	a2b	PROPN
ejpam-5889	126	305	,	,	PUNCT
ejpam-5889	126	306	a2b	a2b	PROPN
ejpam-5889	126	307	,	,	PUNCT
ejpam-5889	126	308	a3b	a3b	ADV
ejpam-5889	126	309	,	,	PUNCT
ejpam-5889	126	310	a3b	a3b	ADJ
ejpam-5889	126	311	}	}	PUNCT
ejpam-5889	126	312	,	,	PUNCT
ejpam-5889	126	313	f19	f19	NOUN
ejpam-5889	126	314	=	=	PUNCT
ejpam-5889	126	315	{	{	PUNCT
ejpam-5889	126	316	1	1	NUM
ejpam-5889	126	317	,	,	PUNCT
ejpam-5889	126	318	1	1	NUM
ejpam-5889	126	319	,	,	PUNCT
ejpam-5889	126	320	1	1	NUM
ejpam-5889	126	321	,	,	PUNCT
ejpam-5889	126	322	a	a	DET
ejpam-5889	126	323	,	,	PUNCT
ejpam-5889	126	324	a2	a2	PROPN
ejpam-5889	126	325	,	,	PUNCT
ejpam-5889	126	326	a3	a3	NOUN
ejpam-5889	126	327	,	,	PUNCT
ejpam-5889	126	328	b	b	PROPN
ejpam-5889	126	329	,	,	PUNCT
ejpam-5889	126	330	ab	ab	PROPN
ejpam-5889	126	331	,	,	PUNCT
ejpam-5889	126	332	a2b	a2b	PROPN
ejpam-5889	126	333	,	,	PUNCT
ejpam-5889	126	334	a3b	a3b	ADJ
ejpam-5889	126	335	}	}	PUNCT
ejpam-5889	126	336	,	,	PUNCT
ejpam-5889	126	337	f20	f20	NOUN
ejpam-5889	126	338	=	=	SYM
ejpam-5889	126	339	{	{	PUNCT
ejpam-5889	126	340	1	1	NUM
ejpam-5889	126	341	,	,	PUNCT
ejpam-5889	126	342	1	1	NUM
ejpam-5889	126	343	,	,	PUNCT
ejpam-5889	126	344	1	1	NUM
ejpam-5889	126	345	,	,	PUNCT
ejpam-5889	126	346	a	a	PRON
ejpam-5889	126	347	,	,	PUNCT
ejpam-5889	126	348	a	a	PRON
ejpam-5889	126	349	,	,	PUNCT
ejpam-5889	126	350	a2	a2	PROPN
ejpam-5889	126	351	,	,	PUNCT
ejpam-5889	126	352	a2	a2	PROPN
ejpam-5889	126	353	,	,	PUNCT
ejpam-5889	126	354	a3	a3	NOUN
ejpam-5889	126	355	,	,	PUNCT
ejpam-5889	126	356	a3	a3	NOUN
ejpam-5889	126	357	,	,	PUNCT
ejpam-5889	126	358	b	b	PROPN
ejpam-5889	126	359	,	,	PUNCT
ejpam-5889	126	360	b	b	PROPN
ejpam-5889	126	361	,	,	PUNCT
ejpam-5889	126	362	ab	ab	PROPN
ejpam-5889	126	363	,	,	PUNCT
ejpam-5889	126	364	ab	ab	PROPN
ejpam-5889	126	365	,	,	PUNCT
ejpam-5889	126	366	a2b	a2b	PROPN
ejpam-5889	126	367	,	,	PUNCT
ejpam-5889	126	368	a2b	a2b	PROPN
ejpam-5889	126	369	,	,	PUNCT
ejpam-5889	126	370	a3b	a3b	ADV
ejpam-5889	126	371	,	,	PUNCT
ejpam-5889	126	372	a3b	a3b	ADJ
ejpam-5889	126	373	}	}	PUNCT
ejpam-5889	126	374	,	,	PUNCT
ejpam-5889	126	375	f	f	X
ejpam-5889	126	376	=	=	PRON
ejpam-5889	126	377	{	{	PUNCT
ejpam-5889	126	378	1	1	NUM
ejpam-5889	126	379	,	,	PUNCT
ejpam-5889	126	380	1	1	NUM
ejpam-5889	126	381	,	,	PUNCT
ejpam-5889	126	382	1	1	NUM
ejpam-5889	126	383	,	,	PUNCT
ejpam-5889	126	384	a	a	DET
ejpam-5889	126	385	,	,	PUNCT
ejpam-5889	126	386	a	a	PRON
ejpam-5889	126	387	,	,	PUNCT
ejpam-5889	126	388	a2	a2	PROPN
ejpam-5889	126	389	,	,	PUNCT
ejpam-5889	126	390	a2	a2	PROPN
ejpam-5889	126	391	,	,	PUNCT
ejpam-5889	126	392	a2	a2	PROPN
ejpam-5889	126	393	,	,	PUNCT
ejpam-5889	126	394	a3	a3	NOUN
ejpam-5889	126	395	,	,	PUNCT
ejpam-5889	126	396	a3	a3	NOUN
ejpam-5889	126	397	,	,	PUNCT
ejpam-5889	126	398	b	b	PROPN
ejpam-5889	126	399	,	,	PUNCT
ejpam-5889	126	400	b	b	PROPN
ejpam-5889	126	401	,	,	PUNCT
ejpam-5889	126	402	ab	ab	PROPN
ejpam-5889	126	403	,	,	PUNCT
ejpam-5889	126	404	ab	ab	PROPN
ejpam-5889	126	405	,	,	PUNCT
ejpam-5889	126	406	a2b	a2b	PROPN
ejpam-5889	126	407	,	,	PUNCT
ejpam-5889	126	408	a2b	a2b	PROPN
ejpam-5889	126	409	,	,	PUNCT
ejpam-5889	126	410	a3b	a3b	ADV
ejpam-5889	126	411	,	,	PUNCT
ejpam-5889	126	412	a3b	a3b	ADJ
ejpam-5889	126	413	}	}	PUNCT
ejpam-5889	126	414	p.	p.	NOUN
ejpam-5889	126	415	a.	a.	NOUN
ejpam-5889	126	416	ejegwa	ejegwa	PROPN
ejpam-5889	126	417	et	et	PROPN
ejpam-5889	126	418	al	al	PROPN
ejpam-5889	126	419	.	.	PUNCT
ejpam-5889	126	420	/	/	SYM
ejpam-5889	126	421	eur	eur	PROPN
ejpam-5889	126	422	.	.	PUNCT
ejpam-5889	127	1	j.	j.	PROPN
ejpam-5889	127	2	pure	pure	PROPN
ejpam-5889	127	3	appl	appl	PROPN
ejpam-5889	127	4	.	.	PROPN
ejpam-5889	127	5	math	math	PROPN
ejpam-5889	127	6	,	,	PUNCT
ejpam-5889	127	7	18	18	NUM
ejpam-5889	127	8	(	(	PUNCT
ejpam-5889	127	9	2	2	NUM
ejpam-5889	127	10	)	)	PUNCT
ejpam-5889	127	11	(	(	PUNCT
ejpam-5889	127	12	2025	2025	NUM
ejpam-5889	127	13	)	)	PUNCT
ejpam-5889	127	14	,	,	PUNCT
ejpam-5889	127	15	5889	5889	NUM
ejpam-5889	127	16	8	8	NUM
ejpam-5889	127	17	of	of	ADP
ejpam-5889	127	18	13	13	NUM
ejpam-5889	127	19	here	here	ADV
ejpam-5889	127	20	,	,	PUNCT
ejpam-5889	127	21	f0	f0	PROPN
ejpam-5889	127	22	–	–	PUNCT
ejpam-5889	127	23	f3	f3	ADJ
ejpam-5889	127	24	,	,	PUNCT
ejpam-5889	127	25	f9	f9	PROPN
ejpam-5889	127	26	,	,	PUNCT
ejpam-5889	127	27	f12	f12	NOUN
ejpam-5889	127	28	,	,	PUNCT
ejpam-5889	127	29	and	and	CCONJ
ejpam-5889	127	30	f	f	PROPN
ejpam-5889	127	31	are	be	AUX
ejpam-5889	127	32	trivial	trivial	ADJ
ejpam-5889	127	33	.	.	PUNCT
ejpam-5889	128	1	the	the	DET
ejpam-5889	128	2	submultigroups	submultigroup	NOUN
ejpam-5889	128	3	f4	f4	PROPN
ejpam-5889	128	4	–	–	PUNCT
ejpam-5889	128	5	f8	f8	PROPN
ejpam-5889	128	6	,	,	PUNCT
ejpam-5889	128	7	f10	f10	PROPN
ejpam-5889	128	8	,	,	PUNCT
ejpam-5889	128	9	f11	f11	NOUN
ejpam-5889	128	10	,	,	PUNCT
ejpam-5889	128	11	and	and	CCONJ
ejpam-5889	128	12	f13	f13	ADJ
ejpam-5889	128	13	–	–	PUNCT
ejpam-5889	128	14	f20	f20	NOUN
ejpam-5889	128	15	are	be	AUX
ejpam-5889	128	16	proper	proper	ADJ
ejpam-5889	128	17	non	non	ADJ
ejpam-5889	128	18	-	-	ADJ
ejpam-5889	128	19	trivial	trivial	ADJ
ejpam-5889	128	20	normal	normal	ADJ
ejpam-5889	128	21	submultigroups	submultigroup	NOUN
ejpam-5889	128	22	of	of	ADP
ejpam-5889	128	23	f.	f.	PROPN
ejpam-5889	128	24	hence	hence	PROPN
ejpam-5889	128	25	,	,	PUNCT
ejpam-5889	128	26	f	f	PROPN
ejpam-5889	128	27	is	be	AUX
ejpam-5889	128	28	not	not	PART
ejpam-5889	128	29	a	a	DET
ejpam-5889	128	30	simple	simple	ADJ
ejpam-5889	128	31	multigroup	multigroup	NOUN
ejpam-5889	128	32	.	.	PUNCT
ejpam-5889	129	1	again	again	ADV
ejpam-5889	129	2	,	,	PUNCT
ejpam-5889	129	3	the	the	DET
ejpam-5889	129	4	maximal	maximal	ADJ
ejpam-5889	129	5	non	non	ADJ
ejpam-5889	129	6	-	-	ADJ
ejpam-5889	129	7	trivial	trivial	ADJ
ejpam-5889	129	8	normal	normal	ADJ
ejpam-5889	129	9	submultigroup	submultigroup	NOUN
ejpam-5889	129	10	of	of	ADP
ejpam-5889	129	11	f	f	PROPN
ejpam-5889	129	12	is	be	AUX
ejpam-5889	129	13	f20	f20	NOUN
ejpam-5889	129	14	.	.	PUNCT
ejpam-5889	130	1	remark	remark	PROPN
ejpam-5889	130	2	2	2	NUM
ejpam-5889	130	3	.	.	PUNCT
ejpam-5889	131	1	every	every	DET
ejpam-5889	131	2	multigroup	multigroup	NOUN
ejpam-5889	131	3	whose	whose	DET
ejpam-5889	131	4	submultigroups	submultigroup	NOUN
ejpam-5889	131	5	are	be	AUX
ejpam-5889	131	6	trivial	trivial	ADJ
ejpam-5889	131	7	is	be	AUX
ejpam-5889	131	8	a	a	DET
ejpam-5889	131	9	simple	simple	ADJ
ejpam-5889	131	10	multigroup	multigroup	NOUN
ejpam-5889	131	11	.	.	PUNCT
ejpam-5889	132	1	to	to	PART
ejpam-5889	132	2	see	see	VERB
ejpam-5889	132	3	this	this	PRON
ejpam-5889	132	4	,	,	PUNCT
ejpam-5889	132	5	given	give	VERB
ejpam-5889	132	6	a	a	DET
ejpam-5889	132	7	multigroup	multigroup	NOUN
ejpam-5889	132	8	e	e	NOUN
ejpam-5889	132	9	=	=	PUNCT
ejpam-5889	132	10	{	{	PUNCT
ejpam-5889	132	11	ρ0	ρ0	PROPN
ejpam-5889	132	12	,	,	PUNCT
ejpam-5889	132	13	ρ0	ρ0	PROPN
ejpam-5889	132	14	,	,	PUNCT
ejpam-5889	132	15	ρ1	ρ1	NOUN
ejpam-5889	132	16	,	,	PUNCT
ejpam-5889	132	17	ρ2	ρ2	NOUN
ejpam-5889	132	18	}	}	PUNCT
ejpam-5889	132	19	defined	define	VERB
ejpam-5889	132	20	over	over	ADP
ejpam-5889	132	21	a3	a3	NOUN
ejpam-5889	132	22	=	=	SYM
ejpam-5889	132	23	{	{	PUNCT
ejpam-5889	132	24	ρ0	ρ0	PROPN
ejpam-5889	132	25	,	,	PUNCT
ejpam-5889	132	26	ρ1	ρ1	NOUN
ejpam-5889	132	27	,	,	PUNCT
ejpam-5889	132	28	ρ2	ρ2	NOUN
ejpam-5889	132	29	}	}	PUNCT
ejpam-5889	132	30	.	.	PUNCT
ejpam-5889	133	1	then	then	ADV
ejpam-5889	133	2	,	,	PUNCT
ejpam-5889	133	3	the	the	DET
ejpam-5889	133	4	submultigroups	submultigroup	NOUN
ejpam-5889	133	5	of	of	ADP
ejpam-5889	133	6	e	e	NOUN
ejpam-5889	133	7	are	be	AUX
ejpam-5889	133	8	:	:	PUNCT
ejpam-5889	133	9	e0	e0	PROPN
ejpam-5889	133	10	=	=	PUNCT
ejpam-5889	133	11	{	{	PUNCT
ejpam-5889	133	12	ρ0	ρ0	PROPN
ejpam-5889	133	13	}	}	PUNCT
ejpam-5889	133	14	,	,	PUNCT
ejpam-5889	133	15	e1	e1	NOUN
ejpam-5889	133	16	=	=	SYM
ejpam-5889	133	17	{	{	PUNCT
ejpam-5889	133	18	ρ0	ρ0	PROPN
ejpam-5889	133	19	,	,	PUNCT
ejpam-5889	133	20	ρ1	ρ1	NOUN
ejpam-5889	133	21	,	,	PUNCT
ejpam-5889	133	22	ρ2	ρ2	PROPN
ejpam-5889	133	23	}	}	PUNCT
ejpam-5889	133	24	,	,	PUNCT
ejpam-5889	133	25	e2	e2	PROPN
ejpam-5889	133	26	=	=	SYM
ejpam-5889	133	27	{	{	PUNCT
ejpam-5889	133	28	ρ0	ρ0	PROPN
ejpam-5889	133	29	,	,	PUNCT
ejpam-5889	133	30	ρ0	ρ0	PROPN
ejpam-5889	133	31	,	,	PUNCT
ejpam-5889	133	32	ρ1	ρ1	NOUN
ejpam-5889	133	33	,	,	PUNCT
ejpam-5889	133	34	ρ2	ρ2	NOUN
ejpam-5889	133	35	}	}	PUNCT
ejpam-5889	133	36	=	=	SYM
ejpam-5889	133	37	e.	e.	PROPN
ejpam-5889	133	38	among	among	ADP
ejpam-5889	133	39	these	these	DET
ejpam-5889	133	40	submultigroups	submultigroup	NOUN
ejpam-5889	133	41	of	of	ADP
ejpam-5889	133	42	e	e	NOUN
ejpam-5889	133	43	,	,	PUNCT
ejpam-5889	133	44	we	we	PRON
ejpam-5889	133	45	notice	notice	VERB
ejpam-5889	133	46	that	that	SCONJ
ejpam-5889	133	47	all	all	PRON
ejpam-5889	133	48	of	of	ADP
ejpam-5889	133	49	them	they	PRON
ejpam-5889	133	50	are	be	AUX
ejpam-5889	133	51	trivial	trivial	ADJ
ejpam-5889	133	52	.	.	PUNCT
ejpam-5889	134	1	thus	thus	ADV
ejpam-5889	134	2	,	,	PUNCT
ejpam-5889	134	3	e	e	PROPN
ejpam-5889	134	4	is	be	AUX
ejpam-5889	134	5	simple	simple	ADJ
ejpam-5889	134	6	.	.	PUNCT
ejpam-5889	135	1	definition	definition	NOUN
ejpam-5889	135	2	16	16	NUM
ejpam-5889	135	3	.	.	PUNCT
ejpam-5889	136	1	let	let	VERB
ejpam-5889	136	2	g	g	PRON
ejpam-5889	136	3	be	be	AUX
ejpam-5889	136	4	a	a	DET
ejpam-5889	136	5	finite	finite	ADJ
ejpam-5889	136	6	group	group	NOUN
ejpam-5889	136	7	and	and	CCONJ
ejpam-5889	136	8	d	d	NOUN
ejpam-5889	136	9	be	be	AUX
ejpam-5889	136	10	a	a	DET
ejpam-5889	136	11	multigroup	multigroup	NOUN
ejpam-5889	136	12	of	of	ADP
ejpam-5889	136	13	g	g	NOUN
ejpam-5889	136	14	with	with	ADP
ejpam-5889	136	15	a	a	DET
ejpam-5889	136	16	finite	finite	ADJ
ejpam-5889	136	17	multiplicity	multiplicity	NOUN
ejpam-5889	136	18	.	.	PUNCT
ejpam-5889	137	1	then	then	ADV
ejpam-5889	137	2	,	,	PUNCT
ejpam-5889	137	3	d	d	PROPN
ejpam-5889	137	4	has	have	VERB
ejpam-5889	137	5	a	a	DET
ejpam-5889	137	6	normal	normal	ADJ
ejpam-5889	137	7	series	series	NOUN
ejpam-5889	137	8	if	if	SCONJ
ejpam-5889	137	9	there	there	PRON
ejpam-5889	137	10	exist	exist	VERB
ejpam-5889	137	11	:	:	PUNCT
ejpam-5889	137	12	cd0(x	cd0(x	NOUN
ejpam-5889	137	13	)	)	PUNCT
ejpam-5889	137	14	≤	≤	NUM
ejpam-5889	137	15	cd1(x	cd1(x	NOUN
ejpam-5889	137	16	)	)	PUNCT
ejpam-5889	137	17	≤	≤	NOUN
ejpam-5889	137	18	·	·	PUNCT
ejpam-5889	137	19	·	·	PUNCT
ejpam-5889	138	1	·	·	PUNCT
ejpam-5889	138	2	≤	≤	NUM
ejpam-5889	138	3	cdn(x	cdn(x	PROPN
ejpam-5889	138	4	)	)	PUNCT
ejpam-5889	138	5	=	=	SYM
ejpam-5889	138	6	cd(x	cd(x	X
ejpam-5889	138	7	)	)	PUNCT
ejpam-5889	138	8	∀x	∀x	VERB
ejpam-5889	138	9	∈	∈	PROPN
ejpam-5889	138	10	g	g	NOUN
ejpam-5889	138	11	,	,	PUNCT
ejpam-5889	138	12	(	(	PUNCT
ejpam-5889	138	13	9	9	X
ejpam-5889	138	14	)	)	PUNCT
ejpam-5889	138	15	such	such	ADJ
ejpam-5889	138	16	that	that	SCONJ
ejpam-5889	138	17	(	(	PUNCT
ejpam-5889	138	18	d0)∗	d0)∗	NOUN
ejpam-5889	138	19	=	=	SYM
ejpam-5889	138	20	(	(	PUNCT
ejpam-5889	138	21	d1)∗	d1)∗	ADJ
ejpam-5889	138	22	=	=	SYM
ejpam-5889	138	23	·	·	PUNCT
ejpam-5889	138	24	·	·	PUNCT
ejpam-5889	138	25	·	·	PUNCT
ejpam-5889	138	26	=	=	PUNCT
ejpam-5889	138	27	(	(	PUNCT
ejpam-5889	138	28	dn)∗	dn)∗	NUM
ejpam-5889	138	29	=	=	SYM
ejpam-5889	138	30	d∗	d∗	NOUN
ejpam-5889	138	31	and	and	CCONJ
ejpam-5889	138	32	di	di	NOUN
ejpam-5889	138	33	◁di+1	◁di+1	PRON
ejpam-5889	138	34	∀	∀	NOUN
ejpam-5889	138	35	0	0	NUM
ejpam-5889	138	36	≤	≤	NUM
ejpam-5889	139	1	i	i	PRON
ejpam-5889	139	2	≤	≤	ADJ
ejpam-5889	139	3	n−	n−	NOUN
ejpam-5889	139	4	1	1	NUM
ejpam-5889	139	5	.	.	PUNCT
ejpam-5889	139	6	example	example	NOUN
ejpam-5889	139	7	4	4	NUM
ejpam-5889	139	8	.	.	PUNCT
ejpam-5889	139	9	using	use	VERB
ejpam-5889	139	10	the	the	DET
ejpam-5889	139	11	submultigroups	submultigroup	NOUN
ejpam-5889	139	12	of	of	ADP
ejpam-5889	139	13	d	d	PROPN
ejpam-5889	139	14	in	in	ADP
ejpam-5889	139	15	example	example	NOUN
ejpam-5889	139	16	1	1	NUM
ejpam-5889	139	17	,	,	PUNCT
ejpam-5889	139	18	we	we	PRON
ejpam-5889	139	19	observe	observe	VERB
ejpam-5889	139	20	that	that	SCONJ
ejpam-5889	139	21	normal	normal	ADJ
ejpam-5889	139	22	series	series	NOUN
ejpam-5889	139	23	only	only	ADV
ejpam-5889	139	24	exists	exist	VERB
ejpam-5889	139	25	for	for	ADP
ejpam-5889	139	26	case	case	NOUN
ejpam-5889	139	27	(	(	PUNCT
ejpam-5889	139	28	ii	ii	NOUN
ejpam-5889	139	29	)	)	PUNCT
ejpam-5889	139	30	and	and	CCONJ
ejpam-5889	139	31	case	case	NOUN
ejpam-5889	139	32	(	(	PUNCT
ejpam-5889	139	33	iii	iii	NOUN
ejpam-5889	139	34	)	)	PUNCT
ejpam-5889	139	35	.	.	PUNCT
ejpam-5889	140	1	it	it	PRON
ejpam-5889	140	2	does	do	AUX
ejpam-5889	140	3	not	not	PART
ejpam-5889	140	4	exist	exist	VERB
ejpam-5889	140	5	for	for	ADP
ejpam-5889	140	6	case	case	NOUN
ejpam-5889	140	7	(	(	PUNCT
ejpam-5889	140	8	i	i	NOUN
ejpam-5889	140	9	)	)	PUNCT
ejpam-5889	140	10	because	because	SCONJ
ejpam-5889	140	11	(	(	PUNCT
ejpam-5889	140	12	d0)∗	d0)∗	ADJ
ejpam-5889	140	13	̸=	̸=	PROPN
ejpam-5889	140	14	d∗	d∗	PROPN
ejpam-5889	140	15	,	,	PUNCT
ejpam-5889	140	16	(	(	PUNCT
ejpam-5889	140	17	d1)∗	d1)∗	ADJ
ejpam-5889	140	18	̸=	̸=	PROPN
ejpam-5889	140	19	d∗	d∗	PROPN
ejpam-5889	140	20	,	,	PUNCT
ejpam-5889	140	21	and	and	CCONJ
ejpam-5889	140	22	(	(	PUNCT
ejpam-5889	140	23	d2)∗	d2)∗	NOUN
ejpam-5889	140	24	̸=	̸=	PROPN
ejpam-5889	140	25	d∗.	d∗.	ADP
ejpam-5889	140	26	the	the	DET
ejpam-5889	140	27	normal	normal	ADJ
ejpam-5889	140	28	series	series	NOUN
ejpam-5889	140	29	for	for	ADP
ejpam-5889	140	30	case	case	NOUN
ejpam-5889	140	31	(	(	PUNCT
ejpam-5889	140	32	ii	ii	NOUN
ejpam-5889	140	33	)	)	PUNCT
ejpam-5889	140	34	is	be	AUX
ejpam-5889	140	35	identical	identical	ADJ
ejpam-5889	140	36	to	to	PART
ejpam-5889	140	37	case	case	NOUN
ejpam-5889	140	38	(	(	PUNCT
ejpam-5889	140	39	iii	iii	NOUN
ejpam-5889	140	40	)	)	PUNCT
ejpam-5889	140	41	because	because	SCONJ
ejpam-5889	140	42	all	all	DET
ejpam-5889	140	43	the	the	DET
ejpam-5889	140	44	submultigroups	submultigroup	NOUN
ejpam-5889	140	45	in	in	ADP
ejpam-5889	140	46	case	case	NOUN
ejpam-5889	140	47	(	(	PUNCT
ejpam-5889	140	48	ii	ii	NOUN
ejpam-5889	140	49	)	)	PUNCT
ejpam-5889	140	50	are	be	AUX
ejpam-5889	140	51	in	in	ADP
ejpam-5889	140	52	case	case	NOUN
ejpam-5889	140	53	(	(	PUNCT
ejpam-5889	140	54	iii	iii	NOUN
ejpam-5889	140	55	)	)	PUNCT
ejpam-5889	140	56	,	,	PUNCT
ejpam-5889	140	57	and	and	CCONJ
ejpam-5889	140	58	the	the	DET
ejpam-5889	140	59	rest	rest	NOUN
ejpam-5889	140	60	of	of	ADP
ejpam-5889	140	61	the	the	DET
ejpam-5889	140	62	submultigroups	submultigroup	NOUN
ejpam-5889	140	63	in	in	ADP
ejpam-5889	140	64	case	case	NOUN
ejpam-5889	140	65	(	(	PUNCT
ejpam-5889	140	66	iii	iii	X
ejpam-5889	140	67	)	)	PUNCT
ejpam-5889	140	68	do	do	AUX
ejpam-5889	140	69	not	not	PART
ejpam-5889	140	70	share	share	VERB
ejpam-5889	140	71	the	the	DET
ejpam-5889	140	72	same	same	ADJ
ejpam-5889	140	73	elements	element	NOUN
ejpam-5889	140	74	as	as	ADP
ejpam-5889	140	75	g.	g.	PROPN
ejpam-5889	140	76	thus	thus	ADV
ejpam-5889	140	77	,	,	PUNCT
ejpam-5889	140	78	the	the	DET
ejpam-5889	140	79	normal	normal	ADJ
ejpam-5889	140	80	series	series	NOUN
ejpam-5889	140	81	for	for	ADP
ejpam-5889	140	82	d	d	PROPN
ejpam-5889	140	83	are	be	AUX
ejpam-5889	140	84	:	:	PUNCT
ejpam-5889	140	85	d̂1	d̂1	ADJ
ejpam-5889	140	86	⊆	⊆	NUM
ejpam-5889	140	87	d̂2	d̂2	NOUN
ejpam-5889	140	88	⊆	⊆	NUM
ejpam-5889	140	89	d̂4	d̂4	PROPN
ejpam-5889	140	90	⊆	⊆	NUM
ejpam-5889	140	91	d̂7	d̂7	NOUN
ejpam-5889	140	92	⊆	⊆	NUM
ejpam-5889	140	93	d̂8	d̂8	NOUN
ejpam-5889	140	94	⊆	⊆	NUM
ejpam-5889	140	95	d̂9	d̂9	NOUN
ejpam-5889	140	96	=	=	SYM
ejpam-5889	141	1	d	d	NOUN
ejpam-5889	141	2	,	,	PUNCT
ejpam-5889	141	3	d̂1	d̂1	ADJ
ejpam-5889	141	4	⊆	⊆	NUM
ejpam-5889	141	5	d̂2	d̂2	NOUN
ejpam-5889	141	6	⊆	⊆	NUM
ejpam-5889	141	7	d̂3	d̂3	PROPN
ejpam-5889	141	8	⊆	⊆	NUM
ejpam-5889	141	9	d̂5	d̂5	NOUN
ejpam-5889	141	10	⊆	⊆	NUM
ejpam-5889	141	11	d̂6	d̂6	PROPN
ejpam-5889	141	12	⊆	⊆	NUM
ejpam-5889	141	13	d̂8	d̂8	NOUN
ejpam-5889	141	14	⊆	⊆	NUM
ejpam-5889	141	15	d̂9	d̂9	NOUN
ejpam-5889	141	16	=	=	SYM
ejpam-5889	142	1	d	d	NOUN
ejpam-5889	142	2	,	,	PUNCT
ejpam-5889	142	3	d̂1	d̂1	ADJ
ejpam-5889	142	4	⊆	⊆	NUM
ejpam-5889	142	5	d̂2	d̂2	NOUN
ejpam-5889	142	6	⊆	⊆	NUM
ejpam-5889	142	7	d̂4	d̂4	PROPN
ejpam-5889	142	8	⊆	⊆	NUM
ejpam-5889	142	9	d̂5	d̂5	PROPN
ejpam-5889	142	10	⊆	⊆	NUM
ejpam-5889	142	11	d̂6	d̂6	PROPN
ejpam-5889	142	12	⊆	⊆	NUM
ejpam-5889	142	13	d̂8	d̂8	NOUN
ejpam-5889	142	14	⊆	⊆	NUM
ejpam-5889	142	15	d̂9	d̂9	NOUN
ejpam-5889	142	16	=	=	SYM
ejpam-5889	142	17	d.	d.	PROPN
ejpam-5889	142	18	certainly	certainly	ADV
ejpam-5889	142	19	,	,	PUNCT
ejpam-5889	142	20	d̂i	d̂i	VERB
ejpam-5889	142	21	◁	◁	X
ejpam-5889	142	22	d̂i+1	d̂i+1	VERB
ejpam-5889	142	23	∀	∀	NOUN
ejpam-5889	142	24	0	0	X
ejpam-5889	142	25	≤	≤	NUM
ejpam-5889	143	1	i	i	PRON
ejpam-5889	143	2	≤	≤	ADJ
ejpam-5889	143	3	n−	n−	NOUN
ejpam-5889	143	4	1	1	NUM
ejpam-5889	143	5	.	.	PUNCT
ejpam-5889	143	6	example	example	NOUN
ejpam-5889	143	7	5	5	NUM
ejpam-5889	143	8	.	.	PUNCT
ejpam-5889	144	1	using	use	VERB
ejpam-5889	144	2	the	the	DET
ejpam-5889	144	3	submultigroups	submultigroup	NOUN
ejpam-5889	144	4	of	of	ADP
ejpam-5889	144	5	e	e	PROPN
ejpam-5889	144	6	in	in	ADP
ejpam-5889	144	7	example	example	NOUN
ejpam-5889	144	8	2	2	NUM
ejpam-5889	144	9	,	,	PUNCT
ejpam-5889	144	10	we	we	PRON
ejpam-5889	144	11	have	have	VERB
ejpam-5889	144	12	the	the	DET
ejpam-5889	144	13	following	follow	VERB
ejpam-5889	144	14	normal	normal	ADJ
ejpam-5889	144	15	series	series	NOUN
ejpam-5889	144	16	:	:	PUNCT
ejpam-5889	144	17	ê1	ê1	PROPN
ejpam-5889	144	18	⊆	⊆	NUM
ejpam-5889	144	19	ê2	ê2	NOUN
ejpam-5889	144	20	⊆	⊆	NUM
ejpam-5889	144	21	ê3	ê3	SYM
ejpam-5889	144	22	⊆	⊆	NUM
ejpam-5889	144	23	ê5	ê5	NOUN
ejpam-5889	144	24	=	=	SYM
ejpam-5889	144	25	e	e	PROPN
ejpam-5889	144	26	,	,	PUNCT
ejpam-5889	144	27	ê1	ê1	PROPN
ejpam-5889	144	28	⊆	⊆	NUM
ejpam-5889	144	29	ê2	ê2	NOUN
ejpam-5889	144	30	⊆	⊆	NUM
ejpam-5889	144	31	ê4	ê4	X
ejpam-5889	144	32	⊆	⊆	NUM
ejpam-5889	144	33	ê5	ê5	NOUN
ejpam-5889	144	34	=	=	SYM
ejpam-5889	145	1	e	e	NOUN
ejpam-5889	145	2	,	,	PUNCT
ejpam-5889	145	3	where	where	SCONJ
ejpam-5889	145	4	êi	êi	VERB
ejpam-5889	145	5	◁	◁	PROPN
ejpam-5889	145	6	êi+1	êi+1	ADJ
ejpam-5889	145	7	∀	∀	NOUN
ejpam-5889	145	8	0	0	NUM
ejpam-5889	145	9	≤	≤	NUM
ejpam-5889	146	1	i	i	PRON
ejpam-5889	146	2	≤	≤	ADJ
ejpam-5889	146	3	n−	n−	PROPN
ejpam-5889	146	4	1	1	NUM
ejpam-5889	146	5	.	.	PUNCT
ejpam-5889	147	1	closely	closely	ADV
ejpam-5889	147	2	related	relate	VERB
ejpam-5889	147	3	to	to	ADP
ejpam-5889	147	4	normal	normal	ADJ
ejpam-5889	147	5	series	series	NOUN
ejpam-5889	147	6	is	be	AUX
ejpam-5889	147	7	the	the	DET
ejpam-5889	147	8	concept	concept	NOUN
ejpam-5889	147	9	of	of	ADP
ejpam-5889	147	10	composition	composition	NOUN
ejpam-5889	147	11	series	series	NOUN
ejpam-5889	147	12	.	.	PUNCT
ejpam-5889	148	1	p.	p.	NOUN
ejpam-5889	148	2	a.	a.	PROPN
ejpam-5889	148	3	ejegwa	ejegwa	PROPN
ejpam-5889	148	4	et	et	PROPN
ejpam-5889	148	5	al	al	PROPN
ejpam-5889	148	6	.	.	PUNCT
ejpam-5889	148	7	/	/	SYM
ejpam-5889	148	8	eur	eur	PROPN
ejpam-5889	148	9	.	.	PUNCT
ejpam-5889	149	1	j.	j.	PROPN
ejpam-5889	149	2	pure	pure	PROPN
ejpam-5889	149	3	appl	appl	PROPN
ejpam-5889	149	4	.	.	PROPN
ejpam-5889	149	5	math	math	PROPN
ejpam-5889	149	6	,	,	PUNCT
ejpam-5889	149	7	18	18	NUM
ejpam-5889	149	8	(	(	PUNCT
ejpam-5889	149	9	2	2	NUM
ejpam-5889	149	10	)	)	PUNCT
ejpam-5889	149	11	(	(	PUNCT
ejpam-5889	149	12	2025	2025	NUM
ejpam-5889	149	13	)	)	PUNCT
ejpam-5889	149	14	,	,	PUNCT
ejpam-5889	149	15	5889	5889	NUM
ejpam-5889	149	16	9	9	NUM
ejpam-5889	149	17	of	of	ADP
ejpam-5889	149	18	13	13	NUM
ejpam-5889	149	19	definition	definition	NOUN
ejpam-5889	149	20	17	17	NUM
ejpam-5889	149	21	.	.	PUNCT
ejpam-5889	150	1	let	let	VERB
ejpam-5889	150	2	g	g	PRON
ejpam-5889	150	3	be	be	AUX
ejpam-5889	150	4	a	a	DET
ejpam-5889	150	5	finite	finite	ADJ
ejpam-5889	150	6	group	group	NOUN
ejpam-5889	150	7	and	and	CCONJ
ejpam-5889	150	8	d	d	NOUN
ejpam-5889	150	9	be	be	AUX
ejpam-5889	150	10	a	a	DET
ejpam-5889	150	11	multigroup	multigroup	NOUN
ejpam-5889	150	12	of	of	ADP
ejpam-5889	150	13	g	g	NOUN
ejpam-5889	150	14	with	with	ADP
ejpam-5889	150	15	a	a	DET
ejpam-5889	150	16	finite	finite	ADJ
ejpam-5889	150	17	multiplicity	multiplicity	NOUN
ejpam-5889	150	18	.	.	PUNCT
ejpam-5889	151	1	then	then	ADV
ejpam-5889	151	2	,	,	PUNCT
ejpam-5889	151	3	d	d	PROPN
ejpam-5889	151	4	has	have	VERB
ejpam-5889	151	5	a	a	DET
ejpam-5889	151	6	composition	composition	NOUN
ejpam-5889	151	7	series	series	NOUN
ejpam-5889	151	8	if	if	SCONJ
ejpam-5889	151	9	there	there	PRON
ejpam-5889	151	10	exist	exist	VERB
ejpam-5889	151	11	a	a	DET
ejpam-5889	151	12	chain	chain	NOUN
ejpam-5889	151	13	of	of	ADP
ejpam-5889	151	14	consecutive	consecutive	ADJ
ejpam-5889	151	15	submultigroups	submultigroup	NOUN
ejpam-5889	151	16	:	:	PUNCT
ejpam-5889	151	17	cd0(x	cd0(x	NOUN
ejpam-5889	151	18	)	)	PUNCT
ejpam-5889	151	19	≤	≤	NUM
ejpam-5889	151	20	cd1(x	cd1(x	NOUN
ejpam-5889	151	21	)	)	PUNCT
ejpam-5889	151	22	≤	≤	NOUN
ejpam-5889	151	23	·	·	PUNCT
ejpam-5889	151	24	·	·	PUNCT
ejpam-5889	152	1	·	·	PUNCT
ejpam-5889	152	2	≤	≤	NUM
ejpam-5889	152	3	cdn(x	cdn(x	PROPN
ejpam-5889	152	4	)	)	PUNCT
ejpam-5889	152	5	=	=	SYM
ejpam-5889	152	6	cd(x	cd(x	X
ejpam-5889	152	7	)	)	PUNCT
ejpam-5889	152	8	∀x	∀x	VERB
ejpam-5889	152	9	∈	∈	PROPN
ejpam-5889	152	10	g	g	NOUN
ejpam-5889	152	11	,	,	PUNCT
ejpam-5889	152	12	(	(	PUNCT
ejpam-5889	152	13	10	10	NUM
ejpam-5889	152	14	)	)	PUNCT
ejpam-5889	152	15	such	such	ADJ
ejpam-5889	152	16	that	that	SCONJ
ejpam-5889	152	17	(	(	PUNCT
ejpam-5889	152	18	d0)∗	d0)∗	NOUN
ejpam-5889	152	19	=	=	SYM
ejpam-5889	152	20	(	(	PUNCT
ejpam-5889	152	21	d1)∗	d1)∗	ADJ
ejpam-5889	152	22	=	=	SYM
ejpam-5889	152	23	·	·	PUNCT
ejpam-5889	152	24	·	·	PUNCT
ejpam-5889	152	25	·	·	PUNCT
ejpam-5889	152	26	=	=	PUNCT
ejpam-5889	152	27	(	(	PUNCT
ejpam-5889	152	28	dn)∗	dn)∗	NUM
ejpam-5889	152	29	=	=	NOUN
ejpam-5889	152	30	d∗	d∗	NOUN
ejpam-5889	152	31	with	with	ADP
ejpam-5889	152	32	the	the	DET
ejpam-5889	152	33	properties	property	NOUN
ejpam-5889	152	34	(	(	PUNCT
ejpam-5889	152	35	i	i	NOUN
ejpam-5889	152	36	)	)	PUNCT
ejpam-5889	152	37	di	di	NOUN
ejpam-5889	152	38	◁di+1	◁di+1	PRON
ejpam-5889	152	39	∀	∀	NOUN
ejpam-5889	152	40	0	0	NUM
ejpam-5889	152	41	≤	≤	NUM
ejpam-5889	153	1	i	i	PRON
ejpam-5889	153	2	≤	≤	ADJ
ejpam-5889	153	3	n−	n−	NOUN
ejpam-5889	153	4	1	1	NUM
ejpam-5889	153	5	,	,	PUNCT
ejpam-5889	153	6	(	(	PUNCT
ejpam-5889	153	7	ii	ii	NOUN
ejpam-5889	153	8	)	)	PUNCT
ejpam-5889	153	9	di+1	di+1	PROPN
ejpam-5889	153	10	/	/	SYM
ejpam-5889	153	11	di	di	NOUN
ejpam-5889	153	12	is	be	AUX
ejpam-5889	153	13	simple	simple	ADJ
ejpam-5889	153	14	∀	∀	NOUN
ejpam-5889	153	15	0	0	NUM
ejpam-5889	153	16	≤	≤	NUM
ejpam-5889	154	1	i	i	PRON
ejpam-5889	154	2	≤	≤	ADJ
ejpam-5889	154	3	n−	n−	PROPN
ejpam-5889	154	4	1	1	NUM
ejpam-5889	154	5	.	.	PUNCT
ejpam-5889	155	1	for	for	ADP
ejpam-5889	155	2	example	example	NOUN
ejpam-5889	155	3	1	1	NUM
ejpam-5889	155	4	,	,	PUNCT
ejpam-5889	155	5	the	the	DET
ejpam-5889	155	6	composition	composition	NOUN
ejpam-5889	155	7	series	series	NOUN
ejpam-5889	155	8	for	for	ADP
ejpam-5889	155	9	d	d	PROPN
ejpam-5889	155	10	are	be	AUX
ejpam-5889	155	11	:	:	PUNCT
ejpam-5889	155	12	d̂1	d̂1	ADJ
ejpam-5889	155	13	⊆	⊆	NUM
ejpam-5889	155	14	d̂2	d̂2	NOUN
ejpam-5889	155	15	⊆	⊆	NUM
ejpam-5889	155	16	d̂4	d̂4	PROPN
ejpam-5889	155	17	⊆	⊆	NUM
ejpam-5889	155	18	d̂7	d̂7	NOUN
ejpam-5889	155	19	⊆	⊆	NUM
ejpam-5889	155	20	d̂8	d̂8	NOUN
ejpam-5889	155	21	⊆	⊆	NUM
ejpam-5889	155	22	d̂9	d̂9	NOUN
ejpam-5889	155	23	=	=	SYM
ejpam-5889	156	1	d	d	NOUN
ejpam-5889	156	2	,	,	PUNCT
ejpam-5889	156	3	d̂1	d̂1	ADJ
ejpam-5889	156	4	⊆	⊆	NUM
ejpam-5889	156	5	d̂2	d̂2	NOUN
ejpam-5889	156	6	⊆	⊆	NUM
ejpam-5889	156	7	d̂3	d̂3	PROPN
ejpam-5889	156	8	⊆	⊆	NUM
ejpam-5889	156	9	d̂5	d̂5	NOUN
ejpam-5889	156	10	⊆	⊆	NUM
ejpam-5889	156	11	d̂6	d̂6	PROPN
ejpam-5889	156	12	⊆	⊆	NUM
ejpam-5889	156	13	d̂8	d̂8	NOUN
ejpam-5889	156	14	⊆	⊆	NUM
ejpam-5889	156	15	d̂9	d̂9	NOUN
ejpam-5889	156	16	=	=	SYM
ejpam-5889	157	1	d	d	NOUN
ejpam-5889	157	2	,	,	PUNCT
ejpam-5889	157	3	d̂1	d̂1	ADJ
ejpam-5889	157	4	⊆	⊆	NUM
ejpam-5889	157	5	d̂2	d̂2	NOUN
ejpam-5889	157	6	⊆	⊆	NUM
ejpam-5889	157	7	d̂4	d̂4	PROPN
ejpam-5889	157	8	⊆	⊆	NUM
ejpam-5889	157	9	d̂5	d̂5	PROPN
ejpam-5889	157	10	⊆	⊆	NUM
ejpam-5889	157	11	d̂6	d̂6	PROPN
ejpam-5889	157	12	⊆	⊆	NUM
ejpam-5889	157	13	d̂8	d̂8	NOUN
ejpam-5889	157	14	⊆	⊆	NUM
ejpam-5889	157	15	d̂9	d̂9	NOUN
ejpam-5889	157	16	=	=	SYM
ejpam-5889	157	17	d.	d.	PROPN
ejpam-5889	157	18	certainly	certainly	ADV
ejpam-5889	157	19	,	,	PUNCT
ejpam-5889	157	20	d̂i	d̂i	VERB
ejpam-5889	157	21	◁	◁	X
ejpam-5889	157	22	d̂i+1	d̂i+1	VERB
ejpam-5889	157	23	∀	∀	NOUN
ejpam-5889	157	24	0	0	X
ejpam-5889	157	25	≤	≤	NUM
ejpam-5889	158	1	i	i	PRON
ejpam-5889	158	2	≤	≤	ADJ
ejpam-5889	158	3	n−	n−	NOUN
ejpam-5889	158	4	1	1	NUM
ejpam-5889	158	5	and	and	CCONJ
ejpam-5889	158	6	d̂i+1	d̂i+1	ADJ
ejpam-5889	158	7	/	/	SYM
ejpam-5889	158	8	d̂i	d̂i	NOUN
ejpam-5889	158	9	is	be	AUX
ejpam-5889	158	10	simple	simple	ADJ
ejpam-5889	158	11	∀	∀	NOUN
ejpam-5889	158	12	0	0	NUM
ejpam-5889	158	13	≤	≤	NUM
ejpam-5889	159	1	i	i	PRON
ejpam-5889	159	2	≤	≤	ADJ
ejpam-5889	159	3	n−	n−	PROPN
ejpam-5889	159	4	1	1	NUM
ejpam-5889	159	5	.	.	PUNCT
ejpam-5889	160	1	for	for	ADP
ejpam-5889	160	2	example	example	NOUN
ejpam-5889	160	3	2	2	NUM
ejpam-5889	160	4	,	,	PUNCT
ejpam-5889	160	5	we	we	PRON
ejpam-5889	160	6	have	have	VERB
ejpam-5889	160	7	the	the	DET
ejpam-5889	160	8	following	follow	VERB
ejpam-5889	160	9	normal	normal	ADJ
ejpam-5889	160	10	series	series	NOUN
ejpam-5889	160	11	:	:	PUNCT
ejpam-5889	160	12	ê1	ê1	PROPN
ejpam-5889	160	13	⊆	⊆	NUM
ejpam-5889	160	14	ê2	ê2	NOUN
ejpam-5889	160	15	⊆	⊆	NUM
ejpam-5889	160	16	ê3	ê3	SYM
ejpam-5889	160	17	⊆	⊆	NUM
ejpam-5889	160	18	ê5	ê5	NOUN
ejpam-5889	160	19	=	=	SYM
ejpam-5889	160	20	e	e	PROPN
ejpam-5889	160	21	,	,	PUNCT
ejpam-5889	160	22	ê1	ê1	PROPN
ejpam-5889	160	23	⊆	⊆	NUM
ejpam-5889	160	24	ê2	ê2	NOUN
ejpam-5889	160	25	⊆	⊆	NUM
ejpam-5889	160	26	ê4	ê4	X
ejpam-5889	160	27	⊆	⊆	NUM
ejpam-5889	160	28	ê5	ê5	NOUN
ejpam-5889	160	29	=	=	X
ejpam-5889	160	30	e.	e.	PROPN
ejpam-5889	160	31	since	since	SCONJ
ejpam-5889	160	32	êi	êi	NUM
ejpam-5889	160	33	for	for	ADP
ejpam-5889	160	34	i	i	PROPN
ejpam-5889	160	35	=	=	NOUN
ejpam-5889	160	36	1	1	NUM
ejpam-5889	160	37	,	,	PUNCT
ejpam-5889	160	38	2	2	NUM
ejpam-5889	160	39	,	,	PUNCT
ejpam-5889	160	40	3	3	NUM
ejpam-5889	160	41	,	,	PUNCT
ejpam-5889	160	42	4	4	NUM
ejpam-5889	160	43	,	,	PUNCT
ejpam-5889	160	44	5	5	NUM
ejpam-5889	160	45	are	be	AUX
ejpam-5889	160	46	normal	normal	ADJ
ejpam-5889	160	47	,	,	PUNCT
ejpam-5889	160	48	then	then	ADV
ejpam-5889	160	49	êi	êi	VERB
ejpam-5889	160	50	◁	◁	PUNCT
ejpam-5889	160	51	êi+1	êi+1	NUM
ejpam-5889	160	52	∀	∀	NOUN
ejpam-5889	160	53	0	0	NUM
ejpam-5889	160	54	≤	≤	NUM
ejpam-5889	161	1	i	i	PRON
ejpam-5889	161	2	≤	≤	NOUN
ejpam-5889	161	3	n	n	CCONJ
ejpam-5889	161	4	−	−	PROPN
ejpam-5889	161	5	1	1	NUM
ejpam-5889	161	6	and	and	CCONJ
ejpam-5889	161	7	êi+1	êi+1	NUM
ejpam-5889	161	8	/	/	SYM
ejpam-5889	161	9	êi	êi	PROPN
ejpam-5889	161	10	is	be	AUX
ejpam-5889	161	11	simple	simple	ADJ
ejpam-5889	161	12	∀	∀	NOUN
ejpam-5889	161	13	0	0	NUM
ejpam-5889	161	14	≤	≤	NUM
ejpam-5889	162	1	i	i	PRON
ejpam-5889	162	2	≤	≤	ADJ
ejpam-5889	162	3	n−	n−	NOUN
ejpam-5889	162	4	1	1	NUM
ejpam-5889	162	5	.	.	PUNCT
ejpam-5889	162	6	example	example	NOUN
ejpam-5889	162	7	6	6	NUM
ejpam-5889	162	8	.	.	PUNCT
ejpam-5889	162	9	let	let	VERB
ejpam-5889	162	10	c	c	NOUN
ejpam-5889	162	11	=	=	PUNCT
ejpam-5889	162	12	{	{	PUNCT
ejpam-5889	162	13	0	0	NUM
ejpam-5889	162	14	,	,	PUNCT
ejpam-5889	162	15	0	0	NUM
ejpam-5889	162	16	,	,	PUNCT
ejpam-5889	162	17	0	0	NUM
ejpam-5889	162	18	,	,	PUNCT
ejpam-5889	162	19	1	1	NUM
ejpam-5889	162	20	,	,	PUNCT
ejpam-5889	162	21	1	1	NUM
ejpam-5889	162	22	,	,	PUNCT
ejpam-5889	162	23	2	2	NUM
ejpam-5889	162	24	,	,	PUNCT
ejpam-5889	162	25	2	2	NUM
ejpam-5889	162	26	,	,	PUNCT
ejpam-5889	162	27	3	3	NUM
ejpam-5889	162	28	,	,	PUNCT
ejpam-5889	162	29	3	3	NUM
ejpam-5889	162	30	,	,	PUNCT
ejpam-5889	162	31	4	4	NUM
ejpam-5889	162	32	,	,	PUNCT
ejpam-5889	162	33	4	4	NUM
ejpam-5889	162	34	,	,	PUNCT
ejpam-5889	162	35	5	5	NUM
ejpam-5889	162	36	,	,	PUNCT
ejpam-5889	162	37	5	5	NUM
ejpam-5889	162	38	}	}	PUNCT
ejpam-5889	162	39	be	be	AUX
ejpam-5889	162	40	a	a	DET
ejpam-5889	162	41	multigroup	multigroup	NOUN
ejpam-5889	162	42	of	of	ADP
ejpam-5889	162	43	z6	z6	PROPN
ejpam-5889	162	44	.	.	PUNCT
ejpam-5889	163	1	then	then	ADV
ejpam-5889	163	2	,	,	PUNCT
ejpam-5889	163	3	the	the	DET
ejpam-5889	163	4	non	non	ADJ
ejpam-5889	163	5	-	-	ADJ
ejpam-5889	163	6	trivial	trivial	ADJ
ejpam-5889	163	7	submultigroups	submultigroup	NOUN
ejpam-5889	163	8	of	of	ADP
ejpam-5889	163	9	c	c	NOUN
ejpam-5889	163	10	which	which	PRON
ejpam-5889	163	11	share	share	VERB
ejpam-5889	163	12	the	the	DET
ejpam-5889	163	13	same	same	ADJ
ejpam-5889	163	14	elements	element	NOUN
ejpam-5889	163	15	as	as	SCONJ
ejpam-5889	163	16	g	g	PROPN
ejpam-5889	163	17	are	be	AUX
ejpam-5889	163	18	:	:	PUNCT
ejpam-5889	163	19	ĉ1	ĉ1	X
ejpam-5889	163	20	=	=	SYM
ejpam-5889	163	21	{	{	PUNCT
ejpam-5889	163	22	0	0	NUM
ejpam-5889	163	23	,	,	PUNCT
ejpam-5889	163	24	1	1	NUM
ejpam-5889	163	25	,	,	PUNCT
ejpam-5889	163	26	2	2	NUM
ejpam-5889	163	27	,	,	PUNCT
ejpam-5889	163	28	3	3	NUM
ejpam-5889	163	29	,	,	PUNCT
ejpam-5889	163	30	4	4	NUM
ejpam-5889	163	31	,	,	PUNCT
ejpam-5889	163	32	5	5	NUM
ejpam-5889	163	33	}	}	PUNCT
ejpam-5889	163	34	,	,	PUNCT
ejpam-5889	163	35	ĉ2	ĉ2	PROPN
ejpam-5889	163	36	=	=	PUNCT
ejpam-5889	163	37	{	{	PUNCT
ejpam-5889	163	38	0	0	NUM
ejpam-5889	163	39	,	,	PUNCT
ejpam-5889	163	40	0	0	NUM
ejpam-5889	163	41	,	,	PUNCT
ejpam-5889	163	42	1	1	NUM
ejpam-5889	163	43	,	,	PUNCT
ejpam-5889	163	44	2	2	NUM
ejpam-5889	163	45	,	,	PUNCT
ejpam-5889	163	46	3	3	NUM
ejpam-5889	163	47	,	,	PUNCT
ejpam-5889	163	48	4	4	NUM
ejpam-5889	163	49	,	,	PUNCT
ejpam-5889	163	50	5	5	NUM
ejpam-5889	163	51	}	}	PUNCT
ejpam-5889	163	52	,	,	PUNCT
ejpam-5889	163	53	ĉ3	ĉ3	PROPN
ejpam-5889	163	54	=	=	PUNCT
ejpam-5889	163	55	{	{	PUNCT
ejpam-5889	163	56	0	0	NUM
ejpam-5889	163	57	,	,	PUNCT
ejpam-5889	163	58	0	0	NUM
ejpam-5889	163	59	,	,	PUNCT
ejpam-5889	163	60	1	1	NUM
ejpam-5889	163	61	,	,	PUNCT
ejpam-5889	163	62	1	1	NUM
ejpam-5889	163	63	,	,	PUNCT
ejpam-5889	163	64	2	2	NUM
ejpam-5889	163	65	,	,	PUNCT
ejpam-5889	163	66	2	2	NUM
ejpam-5889	163	67	,	,	PUNCT
ejpam-5889	163	68	3	3	NUM
ejpam-5889	163	69	,	,	PUNCT
ejpam-5889	163	70	3	3	NUM
ejpam-5889	163	71	,	,	PUNCT
ejpam-5889	163	72	4	4	NUM
ejpam-5889	163	73	,	,	PUNCT
ejpam-5889	163	74	4	4	NUM
ejpam-5889	163	75	,	,	PUNCT
ejpam-5889	163	76	5	5	NUM
ejpam-5889	163	77	,	,	PUNCT
ejpam-5889	163	78	5	5	NUM
ejpam-5889	163	79	}	}	PUNCT
ejpam-5889	163	80	,	,	PUNCT
ejpam-5889	163	81	ĉ4	ĉ4	VERB
ejpam-5889	163	82	=	=	SYM
ejpam-5889	163	83	{	{	PUNCT
ejpam-5889	163	84	0	0	NUM
ejpam-5889	163	85	,	,	PUNCT
ejpam-5889	163	86	0	0	NUM
ejpam-5889	163	87	,	,	PUNCT
ejpam-5889	163	88	0	0	NUM
ejpam-5889	163	89	,	,	PUNCT
ejpam-5889	163	90	1	1	NUM
ejpam-5889	163	91	,	,	PUNCT
ejpam-5889	163	92	2	2	NUM
ejpam-5889	163	93	,	,	PUNCT
ejpam-5889	163	94	3	3	NUM
ejpam-5889	163	95	,	,	PUNCT
ejpam-5889	163	96	4	4	NUM
ejpam-5889	163	97	,	,	PUNCT
ejpam-5889	163	98	5	5	NUM
ejpam-5889	163	99	}	}	PUNCT
ejpam-5889	163	100	,	,	PUNCT
ejpam-5889	163	101	ĉ5	ĉ5	NOUN
ejpam-5889	163	102	=	=	PUNCT
ejpam-5889	163	103	{	{	PUNCT
ejpam-5889	163	104	0	0	NUM
ejpam-5889	163	105	,	,	PUNCT
ejpam-5889	163	106	0	0	NUM
ejpam-5889	163	107	,	,	PUNCT
ejpam-5889	163	108	0	0	NUM
ejpam-5889	163	109	,	,	PUNCT
ejpam-5889	163	110	1	1	NUM
ejpam-5889	163	111	,	,	PUNCT
ejpam-5889	163	112	1	1	NUM
ejpam-5889	163	113	,	,	PUNCT
ejpam-5889	163	114	2	2	NUM
ejpam-5889	163	115	,	,	PUNCT
ejpam-5889	163	116	2	2	NUM
ejpam-5889	163	117	,	,	PUNCT
ejpam-5889	163	118	3	3	NUM
ejpam-5889	163	119	,	,	PUNCT
ejpam-5889	163	120	3	3	NUM
ejpam-5889	163	121	,	,	PUNCT
ejpam-5889	163	122	4	4	NUM
ejpam-5889	163	123	,	,	PUNCT
ejpam-5889	163	124	4	4	NUM
ejpam-5889	163	125	,	,	PUNCT
ejpam-5889	163	126	5	5	NUM
ejpam-5889	163	127	,	,	PUNCT
ejpam-5889	163	128	5	5	NUM
ejpam-5889	163	129	}	}	PUNCT
ejpam-5889	163	130	=	=	SYM
ejpam-5889	163	131	c.	c.	NOUN
ejpam-5889	163	132	then	then	ADV
ejpam-5889	163	133	,	,	PUNCT
ejpam-5889	163	134	the	the	DET
ejpam-5889	163	135	composition	composition	NOUN
ejpam-5889	163	136	series	series	NOUN
ejpam-5889	163	137	are	be	AUX
ejpam-5889	163	138	:	:	PUNCT
ejpam-5889	163	139	ĉ1	ĉ1	X
ejpam-5889	163	140	⊆	⊆	NUM
ejpam-5889	163	141	ĉ2	ĉ2	PROPN
ejpam-5889	163	142	⊆	⊆	NUM
ejpam-5889	163	143	ĉ3	ĉ3	ADJ
ejpam-5889	163	144	⊆	⊆	NUM
ejpam-5889	163	145	ĉ5	ĉ5	NOUN
ejpam-5889	163	146	=	=	SYM
ejpam-5889	163	147	c	c	NOUN
ejpam-5889	163	148	,	,	PUNCT
ejpam-5889	163	149	ĉ1	ĉ1	X
ejpam-5889	163	150	⊆	⊆	NUM
ejpam-5889	163	151	ĉ2	ĉ2	PROPN
ejpam-5889	163	152	⊆	⊆	NUM
ejpam-5889	163	153	ĉ4	ĉ4	VERB
ejpam-5889	163	154	⊆	⊆	NUM
ejpam-5889	163	155	ĉ5	ĉ5	X
ejpam-5889	163	156	=	=	SYM
ejpam-5889	163	157	c.	c.	NOUN
ejpam-5889	164	1	because	because	SCONJ
ejpam-5889	164	2	ĉi	ĉi	NOUN
ejpam-5889	164	3	◁	◁	PUNCT
ejpam-5889	164	4	c	c	NOUN
ejpam-5889	164	5	for	for	ADP
ejpam-5889	164	6	i	i	PRON
ejpam-5889	164	7	=	=	NOUN
ejpam-5889	164	8	1	1	NUM
ejpam-5889	164	9	,	,	PUNCT
ejpam-5889	164	10	2	2	NUM
ejpam-5889	164	11	,	,	PUNCT
ejpam-5889	164	12	3	3	NUM
ejpam-5889	164	13	,	,	PUNCT
ejpam-5889	164	14	4	4	NUM
ejpam-5889	164	15	,	,	PUNCT
ejpam-5889	164	16	then	then	ADV
ejpam-5889	164	17	ĉi	ĉi	NOUN
ejpam-5889	164	18	◁	◁	X
ejpam-5889	164	19	ĉi+1	ĉi+1	PRON
ejpam-5889	164	20	∀	∀	NOUN
ejpam-5889	164	21	0	0	X
ejpam-5889	164	22	≤	≤	NUM
ejpam-5889	164	23	i	i	PRON
ejpam-5889	164	24	≤	≤	NOUN
ejpam-5889	164	25	n	n	CCONJ
ejpam-5889	164	26	−	−	PROPN
ejpam-5889	164	27	1	1	NUM
ejpam-5889	164	28	and	and	CCONJ
ejpam-5889	164	29	ĉi+1	ĉi+1	ADV
ejpam-5889	164	30	/	/	SYM
ejpam-5889	164	31	ĉi	ĉi	NOUN
ejpam-5889	164	32	is	be	AUX
ejpam-5889	164	33	simple	simple	ADJ
ejpam-5889	164	34	∀	∀	NOUN
ejpam-5889	164	35	0	0	NUM
ejpam-5889	164	36	≤	≤	NUM
ejpam-5889	165	1	i	i	PRON
ejpam-5889	165	2	≤	≤	ADJ
ejpam-5889	165	3	n−	n−	NOUN
ejpam-5889	165	4	1	1	NUM
ejpam-5889	165	5	.	.	PUNCT
ejpam-5889	166	1	theorem	theorem	NOUN
ejpam-5889	166	2	1	1	NUM
ejpam-5889	166	3	.	.	PUNCT
ejpam-5889	167	1	every	every	DET
ejpam-5889	167	2	finite	finite	NOUN
ejpam-5889	167	3	multigroup	multigroup	PROPN
ejpam-5889	167	4	defined	define	VERB
ejpam-5889	167	5	over	over	ADP
ejpam-5889	167	6	a	a	DET
ejpam-5889	167	7	finite	finite	ADJ
ejpam-5889	167	8	group	group	NOUN
ejpam-5889	167	9	has	have	VERB
ejpam-5889	167	10	a	a	DET
ejpam-5889	167	11	composition	composition	NOUN
ejpam-5889	167	12	series	series	NOUN
ejpam-5889	167	13	.	.	PUNCT
ejpam-5889	168	1	p.	p.	NOUN
ejpam-5889	168	2	a.	a.	PROPN
ejpam-5889	168	3	ejegwa	ejegwa	PROPN
ejpam-5889	168	4	et	et	PROPN
ejpam-5889	168	5	al	al	PROPN
ejpam-5889	168	6	.	.	PUNCT
ejpam-5889	168	7	/	/	SYM
ejpam-5889	168	8	eur	eur	PROPN
ejpam-5889	168	9	.	.	PUNCT
ejpam-5889	169	1	j.	j.	PROPN
ejpam-5889	169	2	pure	pure	PROPN
ejpam-5889	169	3	appl	appl	PROPN
ejpam-5889	169	4	.	.	PROPN
ejpam-5889	169	5	math	math	PROPN
ejpam-5889	169	6	,	,	PUNCT
ejpam-5889	169	7	18	18	NUM
ejpam-5889	169	8	(	(	PUNCT
ejpam-5889	169	9	2	2	NUM
ejpam-5889	169	10	)	)	PUNCT
ejpam-5889	169	11	(	(	PUNCT
ejpam-5889	169	12	2025	2025	NUM
ejpam-5889	169	13	)	)	PUNCT
ejpam-5889	169	14	,	,	PUNCT
ejpam-5889	169	15	5889	5889	NUM
ejpam-5889	169	16	10	10	NUM
ejpam-5889	169	17	of	of	ADP
ejpam-5889	169	18	13	13	NUM
ejpam-5889	169	19	proof	proof	NOUN
ejpam-5889	169	20	.	.	PUNCT
ejpam-5889	170	1	let	let	VERB
ejpam-5889	170	2	d	d	PRON
ejpam-5889	170	3	be	be	AUX
ejpam-5889	170	4	a	a	DET
ejpam-5889	170	5	finite	finite	NOUN
ejpam-5889	170	6	multigroup	multigroup	NOUN
ejpam-5889	170	7	over	over	ADP
ejpam-5889	170	8	a	a	DET
ejpam-5889	170	9	finite	finite	ADJ
ejpam-5889	170	10	g.	g.	NOUN
ejpam-5889	170	11	we	we	PRON
ejpam-5889	170	12	establish	establish	VERB
ejpam-5889	170	13	the	the	DET
ejpam-5889	170	14	proof	proof	NOUN
ejpam-5889	170	15	by	by	ADP
ejpam-5889	170	16	the	the	DET
ejpam-5889	170	17	principle	principle	NOUN
ejpam-5889	170	18	of	of	ADP
ejpam-5889	170	19	induction	induction	NOUN
ejpam-5889	170	20	.	.	PUNCT
ejpam-5889	171	1	suppose	suppose	VERB
ejpam-5889	171	2	every	every	DET
ejpam-5889	171	3	finite	finite	NOUN
ejpam-5889	171	4	multigroup	multigroup	NOUN
ejpam-5889	171	5	of	of	ADP
ejpam-5889	171	6	order	order	NOUN
ejpam-5889	171	7	less	less	ADJ
ejpam-5889	171	8	than	than	SCONJ
ejpam-5889	171	9	|d|	|d|	PROPN
ejpam-5889	171	10	has	have	VERB
ejpam-5889	171	11	a	a	DET
ejpam-5889	171	12	composition	composition	NOUN
ejpam-5889	171	13	series	series	NOUN
ejpam-5889	171	14	.	.	PUNCT
ejpam-5889	172	1	now	now	ADV
ejpam-5889	172	2	,	,	PUNCT
ejpam-5889	172	3	if	if	SCONJ
ejpam-5889	172	4	d	d	NOUN
ejpam-5889	172	5	is	be	AUX
ejpam-5889	172	6	simple	simple	ADJ
ejpam-5889	172	7	,	,	PUNCT
ejpam-5889	172	8	then	then	ADV
ejpam-5889	172	9	there	there	PRON
ejpam-5889	172	10	is	be	VERB
ejpam-5889	172	11	no	no	DET
ejpam-5889	172	12	composition	composition	NOUN
ejpam-5889	172	13	series	series	NOUN
ejpam-5889	172	14	since	since	SCONJ
ejpam-5889	172	15	no	no	DET
ejpam-5889	172	16	non	non	ADJ
ejpam-5889	172	17	-	-	ADJ
ejpam-5889	172	18	trivial	trivial	ADJ
ejpam-5889	172	19	proper	proper	ADJ
ejpam-5889	172	20	normal	normal	ADJ
ejpam-5889	172	21	submultigroup	submultigroup	NOUN
ejpam-5889	172	22	exist	exist	VERB
ejpam-5889	172	23	.	.	PUNCT
ejpam-5889	173	1	on	on	ADP
ejpam-5889	173	2	the	the	DET
ejpam-5889	173	3	other	other	ADJ
ejpam-5889	173	4	hand	hand	NOUN
ejpam-5889	173	5	,	,	PUNCT
ejpam-5889	173	6	if	if	SCONJ
ejpam-5889	173	7	d	d	NOUN
ejpam-5889	173	8	is	be	AUX
ejpam-5889	173	9	not	not	PART
ejpam-5889	173	10	simple	simple	ADJ
ejpam-5889	173	11	,	,	PUNCT
ejpam-5889	173	12	then	then	ADV
ejpam-5889	173	13	there	there	PRON
ejpam-5889	173	14	must	must	AUX
ejpam-5889	173	15	be	be	AUX
ejpam-5889	173	16	a	a	DET
ejpam-5889	173	17	non	non	ADJ
ejpam-5889	173	18	-	-	ADJ
ejpam-5889	173	19	trivial	trivial	ADJ
ejpam-5889	173	20	proper	proper	ADJ
ejpam-5889	173	21	normal	normal	ADJ
ejpam-5889	173	22	submultigroup	submultigroup	NOUN
ejpam-5889	173	23	.	.	PUNCT
ejpam-5889	174	1	since	since	SCONJ
ejpam-5889	174	2	d	d	PROPN
ejpam-5889	174	3	is	be	AUX
ejpam-5889	174	4	finite	finite	ADJ
ejpam-5889	174	5	,	,	PUNCT
ejpam-5889	174	6	there	there	PRON
ejpam-5889	174	7	is	be	VERB
ejpam-5889	174	8	a	a	DET
ejpam-5889	174	9	maximal	maximal	ADJ
ejpam-5889	174	10	non	non	ADJ
ejpam-5889	174	11	-	-	ADJ
ejpam-5889	174	12	trivial	trivial	ADJ
ejpam-5889	174	13	normal	normal	ADJ
ejpam-5889	174	14	submultigroup	submultigroup	NOUN
ejpam-5889	174	15	in	in	ADP
ejpam-5889	174	16	d	d	PROPN
ejpam-5889	174	17	,	,	PUNCT
ejpam-5889	174	18	which	which	PRON
ejpam-5889	174	19	we	we	PRON
ejpam-5889	174	20	denote	denote	VERB
ejpam-5889	174	21	as	as	ADP
ejpam-5889	174	22	b.	b.	PROPN
ejpam-5889	174	23	certainly	certainly	ADV
ejpam-5889	174	24	,	,	PUNCT
ejpam-5889	174	25	|b|	|b|	PROPN
ejpam-5889	174	26	<	<	X
ejpam-5889	174	27	|d|	|d|	PROPN
ejpam-5889	174	28	.	.	PUNCT
ejpam-5889	175	1	by	by	ADP
ejpam-5889	175	2	induction	induction	NOUN
ejpam-5889	175	3	,	,	PUNCT
ejpam-5889	175	4	|b|	|b|	PROPN
ejpam-5889	175	5	has	have	VERB
ejpam-5889	175	6	a	a	DET
ejpam-5889	175	7	composition	composition	NOUN
ejpam-5889	175	8	series	series	NOUN
ejpam-5889	175	9	:	:	PUNCT
ejpam-5889	175	10	cb0(x	cb0(x	NOUN
ejpam-5889	175	11	)	)	PUNCT
ejpam-5889	175	12	≤	≤	NUM
ejpam-5889	175	13	cb1(x	cb1(x	PROPN
ejpam-5889	175	14	)	)	PUNCT
ejpam-5889	175	15	≤	≤	NOUN
ejpam-5889	175	16	·	·	PUNCT
ejpam-5889	175	17	·	·	PUNCT
ejpam-5889	175	18	·	·	PUNCT
ejpam-5889	176	1	≤	≤	NUM
ejpam-5889	176	2	cbn(x	cbn(x	X
ejpam-5889	176	3	)	)	PUNCT
ejpam-5889	176	4	=	=	PUNCT
ejpam-5889	176	5	cb(x	cb(x	X
ejpam-5889	176	6	)	)	PUNCT
ejpam-5889	176	7	∀x	∀x	VERB
ejpam-5889	176	8	∈	∈	PROPN
ejpam-5889	176	9	g.	g.	NOUN
ejpam-5889	177	1	but	but	CCONJ
ejpam-5889	177	2	then	then	ADV
ejpam-5889	177	3	,	,	PUNCT
ejpam-5889	177	4	b	b	X
ejpam-5889	177	5	◁d	◁d	NUM
ejpam-5889	177	6	since	since	SCONJ
ejpam-5889	177	7	b	b	NOUN
ejpam-5889	177	8	is	be	AUX
ejpam-5889	177	9	maximal	maximal	ADJ
ejpam-5889	177	10	in	in	ADP
ejpam-5889	177	11	d	d	NOUN
ejpam-5889	177	12	,	,	PUNCT
ejpam-5889	177	13	and	and	CCONJ
ejpam-5889	177	14	so	so	ADV
ejpam-5889	177	15	cb0(x	cb0(x	NOUN
ejpam-5889	177	16	)	)	PUNCT
ejpam-5889	177	17	≤	≤	NUM
ejpam-5889	177	18	cb1(x	cb1(x	PROPN
ejpam-5889	177	19	)	)	PUNCT
ejpam-5889	177	20	≤	≤	NOUN
ejpam-5889	177	21	·	·	PUNCT
ejpam-5889	177	22	·	·	PUNCT
ejpam-5889	177	23	·	·	PUNCT
ejpam-5889	178	1	≤	≤	NUM
ejpam-5889	178	2	cbn(x	cbn(x	X
ejpam-5889	178	3	)	)	PUNCT
ejpam-5889	178	4	=	=	PUNCT
ejpam-5889	178	5	cb(x	cb(x	X
ejpam-5889	178	6	)	)	PUNCT
ejpam-5889	178	7	≤	≤	NOUN
ejpam-5889	178	8	cd(x	cd(x	NOUN
ejpam-5889	178	9	)	)	PUNCT
ejpam-5889	178	10	∀x	∀x	VERB
ejpam-5889	178	11	∈	∈	PROPN
ejpam-5889	178	12	g	g	NOUN
ejpam-5889	178	13	,	,	PUNCT
ejpam-5889	178	14	which	which	PRON
ejpam-5889	178	15	is	be	AUX
ejpam-5889	178	16	the	the	DET
ejpam-5889	178	17	composition	composition	NOUN
ejpam-5889	178	18	series	series	NOUN
ejpam-5889	178	19	for	for	ADP
ejpam-5889	178	20	d.	d.	PROPN
ejpam-5889	178	21	theorem	theorem	VERB
ejpam-5889	178	22	2	2	NUM
ejpam-5889	178	23	(	(	PUNCT
ejpam-5889	178	24	the	the	DET
ejpam-5889	178	25	jordan	jordan	PROPN
ejpam-5889	178	26	-	-	PUNCT
ejpam-5889	178	27	hölder	hölder	NOUN
ejpam-5889	178	28	theorem	theorem	NOUN
ejpam-5889	178	29	)	)	PUNCT
ejpam-5889	178	30	.	.	PUNCT
ejpam-5889	179	1	every	every	DET
ejpam-5889	179	2	finite	finite	PROPN
ejpam-5889	179	3	multigroup	multigroup	PROPN
ejpam-5889	179	4	defined	define	VERB
ejpam-5889	179	5	over	over	ADP
ejpam-5889	179	6	a	a	DET
ejpam-5889	179	7	finite	finite	ADJ
ejpam-5889	179	8	group	group	NOUN
ejpam-5889	179	9	has	have	VERB
ejpam-5889	179	10	at	at	ADV
ejpam-5889	179	11	least	least	ADV
ejpam-5889	179	12	two	two	NUM
ejpam-5889	179	13	composition	composition	NOUN
ejpam-5889	179	14	series	series	NOUN
ejpam-5889	179	15	which	which	PRON
ejpam-5889	179	16	are	be	AUX
ejpam-5889	179	17	equivalent	equivalent	ADJ
ejpam-5889	179	18	.	.	PUNCT
ejpam-5889	180	1	proof	proof	NOUN
ejpam-5889	180	2	.	.	PUNCT
ejpam-5889	181	1	let	let	VERB
ejpam-5889	181	2	d	d	PRON
ejpam-5889	181	3	be	be	AUX
ejpam-5889	181	4	a	a	DET
ejpam-5889	181	5	finite	finite	NOUN
ejpam-5889	181	6	multigroup	multigroup	NOUN
ejpam-5889	181	7	over	over	ADP
ejpam-5889	181	8	a	a	DET
ejpam-5889	181	9	finite	finite	ADJ
ejpam-5889	181	10	group	group	NOUN
ejpam-5889	181	11	g.	g.	PROPN
ejpam-5889	181	12	suppose	suppose	VERB
ejpam-5889	181	13	we	we	PRON
ejpam-5889	181	14	have	have	VERB
ejpam-5889	181	15	two	two	NUM
ejpam-5889	181	16	composition	composition	NOUN
ejpam-5889	181	17	series	series	NOUN
ejpam-5889	181	18	for	for	ADP
ejpam-5889	181	19	d	d	PROPN
ejpam-5889	181	20	:	:	PUNCT
ejpam-5889	181	21	cd0(x	cd0(x	NOUN
ejpam-5889	181	22	)	)	PUNCT
ejpam-5889	181	23	≤	≤	NUM
ejpam-5889	181	24	cd1(x	cd1(x	NOUN
ejpam-5889	181	25	)	)	PUNCT
ejpam-5889	181	26	≤	≤	NOUN
ejpam-5889	181	27	·	·	PUNCT
ejpam-5889	181	28	·	·	PUNCT
ejpam-5889	182	1	·	·	PUNCT
ejpam-5889	182	2	≤	≤	NUM
ejpam-5889	182	3	cdn(x	cdn(x	PROPN
ejpam-5889	182	4	)	)	PUNCT
ejpam-5889	182	5	=	=	SYM
ejpam-5889	182	6	cd(x	cd(x	X
ejpam-5889	182	7	)	)	PUNCT
ejpam-5889	182	8	∀x	∀x	VERB
ejpam-5889	182	9	∈	∈	PROPN
ejpam-5889	182	10	g	g	NOUN
ejpam-5889	182	11	,	,	PUNCT
ejpam-5889	182	12	cb0(x	cb0(x	NOUN
ejpam-5889	182	13	)	)	PUNCT
ejpam-5889	182	14	≤	≤	NUM
ejpam-5889	182	15	cb1(x	cb1(x	PROPN
ejpam-5889	182	16	)	)	PUNCT
ejpam-5889	182	17	≤	≤	NOUN
ejpam-5889	182	18	·	·	PUNCT
ejpam-5889	182	19	·	·	PUNCT
ejpam-5889	182	20	·	·	PUNCT
ejpam-5889	182	21	≤	≤	NUM
ejpam-5889	182	22	cbm(x	cbm(x	PROPN
ejpam-5889	182	23	)	)	PUNCT
ejpam-5889	182	24	=	=	PUNCT
ejpam-5889	182	25	cd(x	cd(x	X
ejpam-5889	182	26	)	)	PUNCT
ejpam-5889	182	27	∀x	∀x	VERB
ejpam-5889	182	28	∈	∈	PROPN
ejpam-5889	182	29	g	g	NOUN
ejpam-5889	182	30	,	,	PUNCT
ejpam-5889	182	31	such	such	ADJ
ejpam-5889	182	32	that	that	DET
ejpam-5889	182	33	di	di	NOUN
ejpam-5889	182	34	◁di+1	◁di+1	NOUN
ejpam-5889	182	35	with	with	ADP
ejpam-5889	182	36	di+1	di+1	NOUN
ejpam-5889	182	37	/	/	SYM
ejpam-5889	182	38	di	di	X
ejpam-5889	182	39	simple	simple	ADJ
ejpam-5889	182	40	∀	∀	NOUN
ejpam-5889	182	41	0	0	NUM
ejpam-5889	182	42	≤	≤	NUM
ejpam-5889	183	1	i	i	PRON
ejpam-5889	183	2	≤	≤	ADJ
ejpam-5889	183	3	n−	n−	NOUN
ejpam-5889	183	4	1	1	NUM
ejpam-5889	183	5	and	and	CCONJ
ejpam-5889	183	6	bj	bj	VERB
ejpam-5889	183	7	◁bj+1	◁bj+1	PUNCT
ejpam-5889	183	8	with	with	ADP
ejpam-5889	183	9	bj+1	bj+1	PROPN
ejpam-5889	183	10	/	/	SYM
ejpam-5889	183	11	bj	bj	NOUN
ejpam-5889	183	12	simple	simple	ADJ
ejpam-5889	183	13	∀	∀	NOUN
ejpam-5889	183	14	0	0	NUM
ejpam-5889	183	15	≤	≤	NUM
ejpam-5889	183	16	j	j	PROPN
ejpam-5889	183	17	≤	≤	PROPN
ejpam-5889	183	18	m−1	m−1	PROPN
ejpam-5889	183	19	.	.	PUNCT
ejpam-5889	184	1	we	we	PRON
ejpam-5889	184	2	need	need	VERB
ejpam-5889	184	3	to	to	PART
ejpam-5889	184	4	prove	prove	VERB
ejpam-5889	184	5	that	that	SCONJ
ejpam-5889	184	6	n	n	NOUN
ejpam-5889	184	7	=	=	SYM
ejpam-5889	184	8	m	m	PROPN
ejpam-5889	184	9	and	and	CCONJ
ejpam-5889	184	10	(	(	PUNCT
ejpam-5889	184	11	d1	d1	PROPN
ejpam-5889	184	12	/	/	SYM
ejpam-5889	184	13	d0,d2	d0,d2	PROPN
ejpam-5889	184	14	/	/	SYM
ejpam-5889	184	15	d1	d1	PROPN
ejpam-5889	184	16	,	,	PUNCT
ejpam-5889	184	17	·	·	PUNCT
ejpam-5889	184	18	·	·	PUNCT
ejpam-5889	184	19	·	·	PUNCT
ejpam-5889	184	20	,	,	PUNCT
ejpam-5889	184	21	dn	dn	PROPN
ejpam-5889	184	22	/	/	SYM
ejpam-5889	184	23	dn−1	dn−1	NOUN
ejpam-5889	184	24	)	)	PUNCT
ejpam-5889	184	25	is	be	AUX
ejpam-5889	184	26	a	a	DET
ejpam-5889	184	27	rearrangement	rearrangement	NOUN
ejpam-5889	184	28	(	(	PUNCT
ejpam-5889	184	29	denoted	denote	VERB
ejpam-5889	184	30	as	as	ADP
ejpam-5889	184	31	∼	∼	NOUN
ejpam-5889	184	32	)	)	PUNCT
ejpam-5889	184	33	of	of	ADP
ejpam-5889	184	34	(	(	PUNCT
ejpam-5889	184	35	b1	b1	NOUN
ejpam-5889	184	36	/	/	SYM
ejpam-5889	184	37	b0,b2	b0,b2	PROPN
ejpam-5889	184	38	/	/	SYM
ejpam-5889	184	39	b1	b1	NOUN
ejpam-5889	184	40	,	,	PUNCT
ejpam-5889	184	41	·	·	PUNCT
ejpam-5889	184	42	·	·	PUNCT
ejpam-5889	184	43	·	·	PUNCT
ejpam-5889	184	44	,	,	PUNCT
ejpam-5889	184	45	bm	bm	PROPN
ejpam-5889	184	46	/	/	SYM
ejpam-5889	184	47	bm−1	bm−1	PROPN
ejpam-5889	184	48	)	)	PUNCT
ejpam-5889	184	49	.	.	PUNCT
ejpam-5889	185	1	we	we	PRON
ejpam-5889	185	2	prove	prove	VERB
ejpam-5889	185	3	by	by	ADP
ejpam-5889	185	4	induction	induction	NOUN
ejpam-5889	185	5	on	on	ADP
ejpam-5889	185	6	|d|	|d|	PROPN
ejpam-5889	185	7	.	.	PUNCT
ejpam-5889	186	1	for	for	ADP
ejpam-5889	186	2	|d|	|d|	PROPN
ejpam-5889	186	3	=	=	SYM
ejpam-5889	186	4	1	1	NUM
ejpam-5889	186	5	,	,	PUNCT
ejpam-5889	186	6	the	the	DET
ejpam-5889	186	7	result	result	NOUN
ejpam-5889	186	8	is	be	AUX
ejpam-5889	186	9	trivial	trivial	ADJ
ejpam-5889	186	10	.	.	PUNCT
ejpam-5889	187	1	assumedn−1	assumedn−1	ADV
ejpam-5889	187	2	=	=	SYM
ejpam-5889	187	3	bm−1	bm−1	PROPN
ejpam-5889	187	4	,	,	PUNCT
ejpam-5889	187	5	the	the	DET
ejpam-5889	187	6	result	result	NOUN
ejpam-5889	187	7	follows	follow	VERB
ejpam-5889	187	8	by	by	ADP
ejpam-5889	187	9	induction	induction	NOUN
ejpam-5889	187	10	.	.	PUNCT
ejpam-5889	188	1	then	then	ADV
ejpam-5889	188	2	,	,	PUNCT
ejpam-5889	188	3	assume	assume	VERB
ejpam-5889	188	4	dn−1	dn−1	PROPN
ejpam-5889	188	5	̸=	̸=	PROPN
ejpam-5889	188	6	bm−1	bm−1	PROPN
ejpam-5889	188	7	.	.	PUNCT
ejpam-5889	189	1	set	set	VERB
ejpam-5889	189	2	φ	φ	PROPN
ejpam-5889	189	3	=	=	SYM
ejpam-5889	189	4	dn−1	dn−1	PROPN
ejpam-5889	189	5	,	,	PUNCT
ejpam-5889	189	6	ψ	ψ	NOUN
ejpam-5889	189	7	=	=	SYM
ejpam-5889	189	8	bm−1	bm−1	PROPN
ejpam-5889	189	9	,	,	PUNCT
ejpam-5889	189	10	and	and	CCONJ
ejpam-5889	189	11	ω	ω	X
ejpam-5889	189	12	=	=	SYM
ejpam-5889	189	13	φ	φ	PROPN
ejpam-5889	189	14	∩ψ	∩ψ	PROPN
ejpam-5889	189	15	,	,	PUNCT
ejpam-5889	189	16	where	where	SCONJ
ejpam-5889	189	17	ω	ω	PROPN
ejpam-5889	189	18	is	be	AUX
ejpam-5889	189	19	a	a	DET
ejpam-5889	189	20	maximal	maximal	ADJ
ejpam-5889	189	21	submultigroup	submultigroup	NOUN
ejpam-5889	189	22	of	of	ADP
ejpam-5889	189	23	dn−1	dn−1	PROPN
ejpam-5889	189	24	and	and	CCONJ
ejpam-5889	189	25	bm−1	bm−1	PROPN
ejpam-5889	189	26	.	.	PUNCT
ejpam-5889	190	1	now	now	ADV
ejpam-5889	190	2	,	,	PUNCT
ejpam-5889	190	3	ω	ω	PROPN
ejpam-5889	190	4	has	have	VERB
ejpam-5889	190	5	a	a	DET
ejpam-5889	190	6	composition	composition	NOUN
ejpam-5889	190	7	series	series	NOUN
ejpam-5889	190	8	,	,	PUNCT
ejpam-5889	190	9	cω0(x	cω0(x	NOUN
ejpam-5889	190	10	)	)	PUNCT
ejpam-5889	190	11	≤	≤	NOUN
ejpam-5889	190	12	cω1(x	cω1(x	PROPN
ejpam-5889	190	13	)	)	PUNCT
ejpam-5889	190	14	≤	≤	NOUN
ejpam-5889	190	15	·	·	PUNCT
ejpam-5889	190	16	·	·	PUNCT
ejpam-5889	190	17	·	·	PUNCT
ejpam-5889	191	1	≤	≤	NUM
ejpam-5889	191	2	cωt(x	cωt(x	NOUN
ejpam-5889	191	3	)	)	PUNCT
ejpam-5889	191	4	=	=	SYM
ejpam-5889	191	5	cω(x	cω(x	X
ejpam-5889	191	6	)	)	PUNCT
ejpam-5889	191	7	∀x	∀x	VERB
ejpam-5889	191	8	∈	∈	PROPN
ejpam-5889	191	9	g.	g.	NOUN
ejpam-5889	191	10	then	then	ADV
ejpam-5889	191	11	,	,	PUNCT
ejpam-5889	191	12	cd0(x	cd0(x	PROPN
ejpam-5889	191	13	)	)	PUNCT
ejpam-5889	191	14	≤	≤	NUM
ejpam-5889	191	15	cd1(x	cd1(x	NOUN
ejpam-5889	191	16	)	)	PUNCT
ejpam-5889	191	17	≤	≤	NOUN
ejpam-5889	191	18	·	·	PUNCT
ejpam-5889	191	19	·	·	PUNCT
ejpam-5889	191	20	·	·	PUNCT
ejpam-5889	191	21	≤	≤	NUM
ejpam-5889	191	22	cdn−1(x	cdn−1(x	NOUN
ejpam-5889	191	23	)	)	PUNCT
ejpam-5889	191	24	=	=	SYM
ejpam-5889	191	25	cφ(x	cφ(x	PRON
ejpam-5889	191	26	)	)	PUNCT
ejpam-5889	191	27	∀x	∀x	VERB
ejpam-5889	191	28	∈	∈	PROPN
ejpam-5889	191	29	g	g	NOUN
ejpam-5889	191	30	and	and	CCONJ
ejpam-5889	191	31	cω0(x	cω0(x	PROPN
ejpam-5889	191	32	)	)	PUNCT
ejpam-5889	191	33	≤	≤	NOUN
ejpam-5889	191	34	cω1(x	cω1(x	PROPN
ejpam-5889	191	35	)	)	PUNCT
ejpam-5889	191	36	≤	≤	NOUN
ejpam-5889	191	37	·	·	PUNCT
ejpam-5889	191	38	·	·	PUNCT
ejpam-5889	191	39	·	·	PUNCT
ejpam-5889	192	1	≤	≤	NUM
ejpam-5889	192	2	cωt(x	cωt(x	NOUN
ejpam-5889	192	3	)	)	PUNCT
ejpam-5889	192	4	=	=	SYM
ejpam-5889	192	5	cω(x	cω(x	X
ejpam-5889	192	6	)	)	PUNCT
ejpam-5889	192	7	≤	≤	NOUN
ejpam-5889	192	8	cφ(x	cφ(x	NUM
ejpam-5889	192	9	)	)	PUNCT
ejpam-5889	192	10	∀x	∀x	VERB
ejpam-5889	192	11	∈	∈	PROPN
ejpam-5889	192	12	g	g	NOUN
ejpam-5889	192	13	are	be	AUX
ejpam-5889	192	14	both	both	PRON
ejpam-5889	192	15	composition	composition	NOUN
ejpam-5889	192	16	series	series	NOUN
ejpam-5889	192	17	for	for	ADP
ejpam-5889	192	18	φ	φ	PROPN
ejpam-5889	192	19	.	.	PUNCT
ejpam-5889	193	1	by	by	ADP
ejpam-5889	193	2	induction	induction	NOUN
ejpam-5889	193	3	,	,	PUNCT
ejpam-5889	193	4	we	we	PRON
ejpam-5889	193	5	have	have	VERB
ejpam-5889	193	6	n−	n−	NOUN
ejpam-5889	193	7	1	1	NUM
ejpam-5889	193	8	=	=	SYM
ejpam-5889	193	9	t+	t+	PUNCT
ejpam-5889	193	10	1	1	NUM
ejpam-5889	193	11	⇒	⇒	NOUN
ejpam-5889	193	12	n−	n−	PROPN
ejpam-5889	193	13	2	2	NUM
ejpam-5889	193	14	=	=	SYM
ejpam-5889	193	15	t	t	PROPN
ejpam-5889	193	16	,	,	PUNCT
ejpam-5889	193	17	and	and	CCONJ
ejpam-5889	193	18	(	(	PUNCT
ejpam-5889	193	19	d1	d1	NOUN
ejpam-5889	193	20	/	/	SYM
ejpam-5889	193	21	d0,d2	d0,d2	PROPN
ejpam-5889	193	22	/	/	SYM
ejpam-5889	193	23	d1	d1	PROPN
ejpam-5889	193	24	,	,	PUNCT
ejpam-5889	193	25	·	·	PUNCT
ejpam-5889	193	26	·	·	PUNCT
ejpam-5889	193	27	·	·	PUNCT
ejpam-5889	193	28	,	,	PUNCT
ejpam-5889	193	29	dn−1	dn−1	PROPN
ejpam-5889	193	30	/	/	SYM
ejpam-5889	193	31	dn−2	dn−2	PROPN
ejpam-5889	193	32	)	)	PUNCT
ejpam-5889	193	33	∼	∼	NOUN
ejpam-5889	193	34	(	(	PUNCT
ejpam-5889	193	35	ω1	ω1	PROPN
ejpam-5889	193	36	/	/	SYM
ejpam-5889	193	37	ω0,ω2	ω0,ω2	PROPN
ejpam-5889	193	38	/	/	SYM
ejpam-5889	193	39	ω1	ω1	PROPN
ejpam-5889	193	40	,	,	PUNCT
ejpam-5889	193	41	·	·	PUNCT
ejpam-5889	193	42	·	·	PUNCT
ejpam-5889	193	43	·	·	PUNCT
ejpam-5889	193	44	,	,	PUNCT
ejpam-5889	193	45	ωt	ωt	PROPN
ejpam-5889	193	46	/	/	SYM
ejpam-5889	193	47	ωt−1,φ	ωt−1,φ	NOUN
ejpam-5889	193	48	/	/	SYM
ejpam-5889	193	49	ω	ω	NOUN
ejpam-5889	193	50	)	)	PUNCT
ejpam-5889	193	51	.	.	PUNCT
ejpam-5889	194	1	(	(	PUNCT
ejpam-5889	194	2	11	11	NUM
ejpam-5889	194	3	)	)	PUNCT
ejpam-5889	194	4	similarly	similarly	ADV
ejpam-5889	194	5	,	,	PUNCT
ejpam-5889	194	6	cb0(x	cb0(x	NOUN
ejpam-5889	194	7	)	)	PUNCT
ejpam-5889	194	8	≤	≤	NUM
ejpam-5889	194	9	cb1(x	cb1(x	PROPN
ejpam-5889	194	10	)	)	PUNCT
ejpam-5889	194	11	≤	≤	NOUN
ejpam-5889	194	12	·	·	PUNCT
ejpam-5889	195	1	·	·	PUNCT
ejpam-5889	195	2	·	·	PUNCT
ejpam-5889	195	3	≤	≤	NUM
ejpam-5889	195	4	cbm−1(x	cbm−1(x	NOUN
ejpam-5889	195	5	)	)	PUNCT
ejpam-5889	195	6	=	=	SYM
ejpam-5889	195	7	cψ(x	cψ(x	X
ejpam-5889	195	8	)	)	PUNCT
ejpam-5889	195	9	∀x	∀x	VERB
ejpam-5889	195	10	∈	∈	PROPN
ejpam-5889	195	11	g	g	NOUN
ejpam-5889	195	12	and	and	CCONJ
ejpam-5889	195	13	cω0(x	cω0(x	PROPN
ejpam-5889	195	14	)	)	PUNCT
ejpam-5889	195	15	≤	≤	NOUN
ejpam-5889	195	16	cω1(x	cω1(x	PROPN
ejpam-5889	195	17	)	)	PUNCT
ejpam-5889	195	18	≤	≤	NOUN
ejpam-5889	195	19	·	·	PUNCT
ejpam-5889	195	20	·	·	PUNCT
ejpam-5889	195	21	·	·	PUNCT
ejpam-5889	196	1	≤	≤	NUM
ejpam-5889	196	2	cωt(x	cωt(x	NOUN
ejpam-5889	196	3	)	)	PUNCT
ejpam-5889	196	4	=	=	SYM
ejpam-5889	196	5	cω(x	cω(x	X
ejpam-5889	196	6	)	)	PUNCT
ejpam-5889	196	7	≤	≤	NOUN
ejpam-5889	196	8	cψ(x	cψ(x	X
ejpam-5889	196	9	)	)	PUNCT
ejpam-5889	196	10	∀x	∀x	VERB
ejpam-5889	196	11	∈	∈	PROPN
ejpam-5889	196	12	g	g	PROPN
ejpam-5889	196	13	p.	p.	PROPN
ejpam-5889	196	14	a.	a.	PROPN
ejpam-5889	196	15	ejegwa	ejegwa	PROPN
ejpam-5889	196	16	et	et	PROPN
ejpam-5889	196	17	al	al	PROPN
ejpam-5889	196	18	.	.	PUNCT
ejpam-5889	196	19	/	/	SYM
ejpam-5889	196	20	eur	eur	PROPN
ejpam-5889	196	21	.	.	PUNCT
ejpam-5889	197	1	j.	j.	PROPN
ejpam-5889	197	2	pure	pure	PROPN
ejpam-5889	197	3	appl	appl	PROPN
ejpam-5889	197	4	.	.	PROPN
ejpam-5889	197	5	math	math	PROPN
ejpam-5889	197	6	,	,	PUNCT
ejpam-5889	197	7	18	18	NUM
ejpam-5889	197	8	(	(	PUNCT
ejpam-5889	197	9	2	2	NUM
ejpam-5889	197	10	)	)	PUNCT
ejpam-5889	197	11	(	(	PUNCT
ejpam-5889	197	12	2025	2025	NUM
ejpam-5889	197	13	)	)	PUNCT
ejpam-5889	197	14	,	,	PUNCT
ejpam-5889	197	15	5889	5889	NUM
ejpam-5889	197	16	11	11	NUM
ejpam-5889	197	17	of	of	ADP
ejpam-5889	197	18	13	13	NUM
ejpam-5889	197	19	are	be	AUX
ejpam-5889	197	20	both	both	DET
ejpam-5889	197	21	composition	composition	NOUN
ejpam-5889	197	22	series	series	NOUN
ejpam-5889	197	23	for	for	ADP
ejpam-5889	197	24	ψ	ψ	X
ejpam-5889	197	25	.	.	PUNCT
ejpam-5889	198	1	thus	thus	ADV
ejpam-5889	198	2	,	,	PUNCT
ejpam-5889	198	3	m−	m−	PROPN
ejpam-5889	198	4	1	1	NUM
ejpam-5889	198	5	=	=	SYM
ejpam-5889	198	6	t+	t+	PUNCT
ejpam-5889	198	7	1	1	NUM
ejpam-5889	198	8	⇒	⇒	NOUN
ejpam-5889	198	9	m−	m−	PROPN
ejpam-5889	198	10	2	2	NUM
ejpam-5889	198	11	=	=	SYM
ejpam-5889	198	12	t	t	PROPN
ejpam-5889	198	13	,	,	PUNCT
ejpam-5889	198	14	and	and	CCONJ
ejpam-5889	198	15	(	(	PUNCT
ejpam-5889	198	16	b1	b1	NOUN
ejpam-5889	198	17	/	/	SYM
ejpam-5889	198	18	b0,b2	b0,b2	PROPN
ejpam-5889	198	19	/	/	SYM
ejpam-5889	198	20	b1	b1	NOUN
ejpam-5889	198	21	,	,	PUNCT
ejpam-5889	198	22	·	·	PUNCT
ejpam-5889	198	23	·	·	PUNCT
ejpam-5889	198	24	·	·	PUNCT
ejpam-5889	198	25	,	,	PUNCT
ejpam-5889	198	26	bm−1	bm−1	PROPN
ejpam-5889	198	27	/	/	SYM
ejpam-5889	198	28	bm−2	bm−2	PROPN
ejpam-5889	198	29	)	)	PUNCT
ejpam-5889	198	30	∼	∼	NOUN
ejpam-5889	198	31	(	(	PUNCT
ejpam-5889	198	32	ω1	ω1	PROPN
ejpam-5889	198	33	/	/	SYM
ejpam-5889	198	34	ω0,ω2	ω0,ω2	PROPN
ejpam-5889	198	35	/	/	SYM
ejpam-5889	198	36	ω1	ω1	PROPN
ejpam-5889	198	37	,	,	PUNCT
ejpam-5889	198	38	·	·	PUNCT
ejpam-5889	198	39	·	·	PUNCT
ejpam-5889	198	40	·	·	PUNCT
ejpam-5889	198	41	,	,	PUNCT
ejpam-5889	198	42	ωt	ωt	PROPN
ejpam-5889	198	43	/	/	SYM
ejpam-5889	198	44	ωt−1,ψ	ωt−1,ψ	PROPN
ejpam-5889	198	45	/	/	SYM
ejpam-5889	198	46	ω	ω	NOUN
ejpam-5889	198	47	)	)	PUNCT
ejpam-5889	198	48	.	.	PUNCT
ejpam-5889	199	1	(	(	PUNCT
ejpam-5889	199	2	12	12	NUM
ejpam-5889	199	3	)	)	PUNCT
ejpam-5889	199	4	from	from	ADP
ejpam-5889	199	5	m	m	PROPN
ejpam-5889	199	6	−	−	PROPN
ejpam-5889	199	7	1	1	NUM
ejpam-5889	199	8	=	=	SYM
ejpam-5889	199	9	t	t	NOUN
ejpam-5889	199	10	+	+	CCONJ
ejpam-5889	199	11	1	1	NUM
ejpam-5889	199	12	and	and	CCONJ
ejpam-5889	199	13	n	n	CCONJ
ejpam-5889	199	14	−	−	PROPN
ejpam-5889	199	15	1	1	NUM
ejpam-5889	199	16	=	=	SYM
ejpam-5889	199	17	t	t	NOUN
ejpam-5889	199	18	+	+	CCONJ
ejpam-5889	199	19	1	1	NUM
ejpam-5889	199	20	,	,	PUNCT
ejpam-5889	199	21	we	we	PRON
ejpam-5889	199	22	have	have	VERB
ejpam-5889	199	23	n	n	NOUN
ejpam-5889	199	24	=	=	X
ejpam-5889	199	25	m.	m.	NOUN
ejpam-5889	199	26	by	by	ADP
ejpam-5889	199	27	appending	append	VERB
ejpam-5889	199	28	d	d	PROPN
ejpam-5889	199	29	/	/	SYM
ejpam-5889	199	30	φ	φ	PROPN
ejpam-5889	199	31	to	to	ADP
ejpam-5889	199	32	both	both	DET
ejpam-5889	199	33	sides	side	NOUN
ejpam-5889	199	34	of	of	ADP
ejpam-5889	199	35	(	(	PUNCT
ejpam-5889	199	36	11	11	NUM
ejpam-5889	199	37	)	)	PUNCT
ejpam-5889	199	38	,	,	PUNCT
ejpam-5889	199	39	we	we	PRON
ejpam-5889	199	40	have	have	VERB
ejpam-5889	199	41	(	(	PUNCT
ejpam-5889	199	42	d1	d1	NOUN
ejpam-5889	199	43	/	/	SYM
ejpam-5889	199	44	d0	d0	NOUN
ejpam-5889	199	45	,	,	PUNCT
ejpam-5889	199	46	·	·	PUNCT
ejpam-5889	199	47	·	·	PUNCT
ejpam-5889	199	48	·	·	PUNCT
ejpam-5889	199	49	,	,	PUNCT
ejpam-5889	199	50	dn−1	dn−1	NOUN
ejpam-5889	199	51	/	/	SYM
ejpam-5889	199	52	dn−2,d	dn−2,d	VERB
ejpam-5889	199	53	/	/	SYM
ejpam-5889	199	54	dn−1	dn−1	ADJ
ejpam-5889	199	55	)	)	PUNCT
ejpam-5889	199	56	∼	∼	NOUN
ejpam-5889	199	57	(	(	PUNCT
ejpam-5889	199	58	ω1	ω1	PROPN
ejpam-5889	199	59	/	/	SYM
ejpam-5889	199	60	ω0	ω0	PROPN
ejpam-5889	199	61	,	,	PUNCT
ejpam-5889	199	62	·	·	PUNCT
ejpam-5889	199	63	·	·	PUNCT
ejpam-5889	199	64	·	·	PUNCT
ejpam-5889	199	65	,	,	PUNCT
ejpam-5889	199	66	ωt	ωt	PROPN
ejpam-5889	199	67	/	/	SYM
ejpam-5889	199	68	ωt−1,φ	ωt−1,φ	NOUN
ejpam-5889	199	69	/	/	SYM
ejpam-5889	199	70	ω	ω	NOUN
ejpam-5889	199	71	,	,	PUNCT
ejpam-5889	199	72	d	d	PROPN
ejpam-5889	199	73	/	/	SYM
ejpam-5889	199	74	φ	φ	NUM
ejpam-5889	199	75	)	)	PUNCT
ejpam-5889	199	76	.	.	PUNCT
ejpam-5889	200	1	(	(	PUNCT
ejpam-5889	200	2	13	13	NUM
ejpam-5889	200	3	)	)	PUNCT
ejpam-5889	200	4	similarly	similarly	ADV
ejpam-5889	200	5	,	,	PUNCT
ejpam-5889	200	6	appending	append	VERB
ejpam-5889	200	7	d	d	X
ejpam-5889	200	8	/	/	SYM
ejpam-5889	200	9	ψ	ψ	NOUN
ejpam-5889	200	10	to	to	ADP
ejpam-5889	200	11	both	both	DET
ejpam-5889	200	12	sides	side	NOUN
ejpam-5889	200	13	of	of	ADP
ejpam-5889	200	14	(	(	PUNCT
ejpam-5889	200	15	12	12	NUM
ejpam-5889	200	16	)	)	PUNCT
ejpam-5889	200	17	,	,	PUNCT
ejpam-5889	200	18	we	we	PRON
ejpam-5889	200	19	have	have	VERB
ejpam-5889	200	20	(	(	PUNCT
ejpam-5889	200	21	b1	b1	NOUN
ejpam-5889	200	22	/	/	SYM
ejpam-5889	200	23	b0	b0	NOUN
ejpam-5889	200	24	,	,	PUNCT
ejpam-5889	200	25	·	·	PUNCT
ejpam-5889	200	26	·	·	PUNCT
ejpam-5889	200	27	·	·	PUNCT
ejpam-5889	200	28	,	,	PUNCT
ejpam-5889	200	29	bm−1	bm−1	NOUN
ejpam-5889	200	30	/	/	SYM
ejpam-5889	200	31	bm−2,d	bm−2,d	NOUN
ejpam-5889	200	32	/	/	SYM
ejpam-5889	200	33	bm−1	bm−1	NOUN
ejpam-5889	200	34	)	)	PUNCT
ejpam-5889	201	1	∼	∼	NOUN
ejpam-5889	201	2	(	(	PUNCT
ejpam-5889	201	3	ω1	ω1	PROPN
ejpam-5889	201	4	/	/	SYM
ejpam-5889	201	5	ω0	ω0	PROPN
ejpam-5889	201	6	,	,	PUNCT
ejpam-5889	201	7	·	·	PUNCT
ejpam-5889	201	8	·	·	PUNCT
ejpam-5889	201	9	·	·	PUNCT
ejpam-5889	201	10	,	,	PUNCT
ejpam-5889	201	11	ωt	ωt	PROPN
ejpam-5889	201	12	/	/	SYM
ejpam-5889	201	13	ωt−1,ψ	ωt−1,ψ	PROPN
ejpam-5889	201	14	/	/	SYM
ejpam-5889	201	15	ω	ω	PROPN
ejpam-5889	201	16	,	,	PUNCT
ejpam-5889	201	17	d	d	PROPN
ejpam-5889	201	18	/	/	SYM
ejpam-5889	201	19	ψ	ψ	NOUN
ejpam-5889	201	20	)	)	PUNCT
ejpam-5889	201	21	.	.	PUNCT
ejpam-5889	202	1	(	(	PUNCT
ejpam-5889	202	2	14	14	NUM
ejpam-5889	202	3	)	)	PUNCT
ejpam-5889	202	4	the	the	DET
ejpam-5889	202	5	right	right	ADJ
ejpam-5889	202	6	hand	hand	NOUN
ejpam-5889	202	7	side	side	NOUN
ejpam-5889	202	8	of	of	ADP
ejpam-5889	202	9	(	(	PUNCT
ejpam-5889	202	10	13	13	NUM
ejpam-5889	202	11	)	)	PUNCT
ejpam-5889	202	12	and	and	CCONJ
ejpam-5889	202	13	(	(	PUNCT
ejpam-5889	202	14	14	14	NUM
ejpam-5889	202	15	)	)	PUNCT
ejpam-5889	202	16	are	be	AUX
ejpam-5889	202	17	identical	identical	ADJ
ejpam-5889	202	18	except	except	SCONJ
ejpam-5889	202	19	(	(	PUNCT
ejpam-5889	202	20	φ	φ	PROPN
ejpam-5889	202	21	/	/	SYM
ejpam-5889	202	22	ω	ω	PROPN
ejpam-5889	202	23	,	,	PUNCT
ejpam-5889	202	24	d	d	PROPN
ejpam-5889	202	25	/	/	SYM
ejpam-5889	202	26	φ	φ	NUM
ejpam-5889	202	27	)	)	PUNCT
ejpam-5889	202	28	and	and	CCONJ
ejpam-5889	202	29	(	(	PUNCT
ejpam-5889	202	30	ψ	ψ	X
ejpam-5889	202	31	/	/	SYM
ejpam-5889	202	32	ω	ω	NUM
ejpam-5889	202	33	,	,	PUNCT
ejpam-5889	202	34	d	d	PROPN
ejpam-5889	202	35	/	/	SYM
ejpam-5889	202	36	ψ	ψ	NOUN
ejpam-5889	202	37	)	)	PUNCT
ejpam-5889	202	38	.	.	PUNCT
ejpam-5889	203	1	hence	hence	ADV
ejpam-5889	203	2	,	,	PUNCT
ejpam-5889	203	3	(	(	PUNCT
ejpam-5889	203	4	φ	φ	PROPN
ejpam-5889	203	5	/	/	SYM
ejpam-5889	203	6	ω	ω	PROPN
ejpam-5889	203	7	,	,	PUNCT
ejpam-5889	203	8	d	d	PROPN
ejpam-5889	203	9	/	/	SYM
ejpam-5889	203	10	φ	φ	NOUN
ejpam-5889	203	11	)	)	PUNCT
ejpam-5889	203	12	∼	∼	NOUN
ejpam-5889	203	13	(	(	PUNCT
ejpam-5889	203	14	ψ	ψ	X
ejpam-5889	203	15	/	/	SYM
ejpam-5889	203	16	ω	ω	NUM
ejpam-5889	203	17	,	,	PUNCT
ejpam-5889	203	18	d	d	PROPN
ejpam-5889	203	19	/	/	SYM
ejpam-5889	203	20	ψ	ψ	NOUN
ejpam-5889	203	21	)	)	PUNCT
ejpam-5889	203	22	and	and	CCONJ
ejpam-5889	203	23	so	so	ADV
ejpam-5889	203	24	(	(	PUNCT
ejpam-5889	203	25	d1	d1	NOUN
ejpam-5889	203	26	/	/	SYM
ejpam-5889	203	27	d0	d0	NOUN
ejpam-5889	203	28	,	,	PUNCT
ejpam-5889	203	29	·	·	PUNCT
ejpam-5889	203	30	·	·	PUNCT
ejpam-5889	203	31	·	·	PUNCT
ejpam-5889	203	32	,	,	PUNCT
ejpam-5889	203	33	dn	dn	PROPN
ejpam-5889	203	34	/	/	SYM
ejpam-5889	203	35	dn−1	dn−1	ADJ
ejpam-5889	203	36	)	)	PUNCT
ejpam-5889	203	37	∼	∼	NOUN
ejpam-5889	203	38	(	(	PUNCT
ejpam-5889	203	39	b1	b1	NOUN
ejpam-5889	203	40	/	/	SYM
ejpam-5889	203	41	b0	b0	NOUN
ejpam-5889	203	42	,	,	PUNCT
ejpam-5889	203	43	·	·	PUNCT
ejpam-5889	203	44	·	·	PUNCT
ejpam-5889	203	45	·	·	PUNCT
ejpam-5889	203	46	,	,	PUNCT
ejpam-5889	203	47	bm	bm	PROPN
ejpam-5889	203	48	/	/	SYM
ejpam-5889	203	49	bm−1	bm−1	PROPN
ejpam-5889	203	50	)	)	PUNCT
ejpam-5889	203	51	.	.	PUNCT
ejpam-5889	204	1	3	3	X
ejpam-5889	204	2	.	.	X
ejpam-5889	204	3	conclusion	conclusion	NOUN
ejpam-5889	204	4	in	in	ADP
ejpam-5889	204	5	this	this	DET
ejpam-5889	204	6	paper	paper	NOUN
ejpam-5889	204	7	,	,	PUNCT
ejpam-5889	204	8	the	the	DET
ejpam-5889	204	9	notions	notion	NOUN
ejpam-5889	204	10	of	of	ADP
ejpam-5889	204	11	simple	simple	ADJ
ejpam-5889	204	12	multigroup	multigroup	PROPN
ejpam-5889	204	13	,	,	PUNCT
ejpam-5889	204	14	maximal	maximal	ADJ
ejpam-5889	204	15	normal	normal	ADJ
ejpam-5889	204	16	submultigroup	submultigroup	NOUN
ejpam-5889	204	17	,	,	PUNCT
ejpam-5889	204	18	normal	normal	ADJ
ejpam-5889	204	19	series	series	NOUN
ejpam-5889	204	20	for	for	ADP
ejpam-5889	204	21	multigroup	multigroup	PROPN
ejpam-5889	204	22	,	,	PUNCT
ejpam-5889	204	23	and	and	CCONJ
ejpam-5889	204	24	composition	composition	NOUN
ejpam-5889	204	25	series	series	NOUN
ejpam-5889	204	26	for	for	ADP
ejpam-5889	204	27	multigroup	multigroup	NOUN
ejpam-5889	204	28	were	be	AUX
ejpam-5889	204	29	defined	define	VERB
ejpam-5889	204	30	as	as	ADP
ejpam-5889	204	31	algebraic	algebraic	ADJ
ejpam-5889	204	32	structures	structure	NOUN
ejpam-5889	204	33	in	in	ADP
ejpam-5889	204	34	multiset	multiset	ADJ
ejpam-5889	204	35	context	context	NOUN
ejpam-5889	204	36	and	and	CCONJ
ejpam-5889	204	37	characterized	characterize	VERB
ejpam-5889	204	38	with	with	ADP
ejpam-5889	204	39	examples	example	NOUN
ejpam-5889	204	40	and	and	CCONJ
ejpam-5889	204	41	some	some	DET
ejpam-5889	204	42	results	result	NOUN
ejpam-5889	204	43	.	.	PUNCT
ejpam-5889	205	1	in	in	ADP
ejpam-5889	205	2	addition	addition	NOUN
ejpam-5889	205	3	,	,	PUNCT
ejpam-5889	205	4	it	it	PRON
ejpam-5889	205	5	was	be	AUX
ejpam-5889	205	6	proven	prove	VERB
ejpam-5889	205	7	that	that	SCONJ
ejpam-5889	205	8	every	every	DET
ejpam-5889	205	9	finite	finite	NOUN
ejpam-5889	205	10	multigroup	multigroup	PROPN
ejpam-5889	205	11	defined	define	VERB
ejpam-5889	205	12	over	over	ADP
ejpam-5889	205	13	a	a	DET
ejpam-5889	205	14	finite	finite	ADJ
ejpam-5889	205	15	group	group	NOUN
ejpam-5889	205	16	has	have	VERB
ejpam-5889	205	17	a	a	DET
ejpam-5889	205	18	composition	composition	NOUN
ejpam-5889	205	19	series	series	NOUN
ejpam-5889	205	20	.	.	PUNCT
ejpam-5889	206	1	finally	finally	ADV
ejpam-5889	206	2	,	,	PUNCT
ejpam-5889	206	3	the	the	DET
ejpam-5889	206	4	jordan	jordan	PROPN
ejpam-5889	206	5	-	-	PUNCT
ejpam-5889	206	6	hölder	hölder	PROPN
ejpam-5889	206	7	theorem	theorem	NOUN
ejpam-5889	206	8	was	be	AUX
ejpam-5889	206	9	presented	present	VERB
ejpam-5889	206	10	in	in	ADP
ejpam-5889	206	11	multiset	multiset	ADJ
ejpam-5889	206	12	context	context	NOUN
ejpam-5889	206	13	,	,	PUNCT
ejpam-5889	206	14	and	and	CCONJ
ejpam-5889	206	15	it	it	PRON
ejpam-5889	206	16	was	be	AUX
ejpam-5889	206	17	established	establish	VERB
ejpam-5889	206	18	that	that	SCONJ
ejpam-5889	206	19	every	every	DET
ejpam-5889	206	20	finite	finite	NOUN
ejpam-5889	206	21	multigroup	multigroup	PROPN
ejpam-5889	206	22	defined	define	VERB
ejpam-5889	206	23	over	over	ADP
ejpam-5889	206	24	a	a	DET
ejpam-5889	206	25	finite	finite	ADJ
ejpam-5889	206	26	group	group	NOUN
ejpam-5889	206	27	has	have	VERB
ejpam-5889	206	28	at	at	ADV
ejpam-5889	206	29	least	least	ADV
ejpam-5889	206	30	two	two	NUM
ejpam-5889	206	31	composition	composition	NOUN
ejpam-5889	206	32	series	series	NOUN
ejpam-5889	206	33	which	which	PRON
ejpam-5889	206	34	are	be	AUX
ejpam-5889	206	35	equivalent	equivalent	ADJ
ejpam-5889	206	36	.	.	PUNCT
ejpam-5889	207	1	the	the	DET
ejpam-5889	207	2	multigroup	multigroup	PROPN
ejpam-5889	207	3	structures	structure	NOUN
ejpam-5889	207	4	can	can	AUX
ejpam-5889	207	5	be	be	AUX
ejpam-5889	207	6	applicable	applicable	ADJ
ejpam-5889	207	7	in	in	ADP
ejpam-5889	207	8	cryptography	cryptography	NOUN
ejpam-5889	207	9	for	for	ADP
ejpam-5889	207	10	the	the	DET
ejpam-5889	207	11	security	security	NOUN
ejpam-5889	207	12	of	of	ADP
ejpam-5889	207	13	data	datum	NOUN
ejpam-5889	207	14	,	,	PUNCT
ejpam-5889	207	15	molecular	molecular	ADJ
ejpam-5889	207	16	symmetry	symmetry	NOUN
ejpam-5889	207	17	and	and	CCONJ
ejpam-5889	207	18	molecular	molecular	ADJ
ejpam-5889	207	19	behavior	behavior	NOUN
ejpam-5889	207	20	during	during	ADP
ejpam-5889	207	21	chemical	chemical	ADJ
ejpam-5889	207	22	reactions	reaction	NOUN
ejpam-5889	207	23	,	,	PUNCT
ejpam-5889	207	24	quantum	quantum	NOUN
ejpam-5889	207	25	mechanics	mechanic	NOUN
ejpam-5889	207	26	and	and	CCONJ
ejpam-5889	207	27	particle	particle	NOUN
ejpam-5889	207	28	physics	physics	PROPN
ejpam-5889	207	29	,	,	PUNCT
ejpam-5889	207	30	algorithms	algorithm	NOUN
ejpam-5889	207	31	in	in	ADP
ejpam-5889	207	32	areas	area	NOUN
ejpam-5889	207	33	related	relate	VERB
ejpam-5889	207	34	to	to	ADP
ejpam-5889	207	35	coding	code	VERB
ejpam-5889	207	36	theory	theory	NOUN
ejpam-5889	207	37	and	and	CCONJ
ejpam-5889	207	38	data	datum	NOUN
ejpam-5889	207	39	structure	structure	NOUN
ejpam-5889	207	40	,	,	PUNCT
ejpam-5889	207	41	robotics	robotic	NOUN
ejpam-5889	207	42	and	and	CCONJ
ejpam-5889	207	43	computer	computer	NOUN
ejpam-5889	207	44	graphics	graphic	NOUN
ejpam-5889	207	45	,	,	PUNCT
ejpam-5889	207	46	etc	etc	X
ejpam-5889	207	47	.	.	X
ejpam-5889	208	1	for	for	ADP
ejpam-5889	208	2	further	further	ADJ
ejpam-5889	208	3	investigation	investigation	NOUN
ejpam-5889	208	4	,	,	PUNCT
ejpam-5889	208	5	the	the	DET
ejpam-5889	208	6	concept	concept	NOUN
ejpam-5889	208	7	of	of	ADP
ejpam-5889	208	8	nilpotency	nilpotency	NOUN
ejpam-5889	208	9	in	in	ADP
ejpam-5889	208	10	multigroup	multigroup	ADJ
ejpam-5889	208	11	setting	setting	NOUN
ejpam-5889	208	12	could	could	AUX
ejpam-5889	208	13	be	be	AUX
ejpam-5889	208	14	considered	consider	VERB
ejpam-5889	208	15	.	.	PUNCT
ejpam-5889	209	1	acknowledgements	acknowledgement	NOUN
ejpam-5889	209	2	we	we	PRON
ejpam-5889	209	3	greatly	greatly	ADV
ejpam-5889	209	4	appreciate	appreciate	VERB
ejpam-5889	209	5	the	the	DET
ejpam-5889	209	6	editor	editor	NOUN
ejpam-5889	209	7	-	-	PUNCT
ejpam-5889	209	8	in	in	ADP
ejpam-5889	209	9	-	-	PUNCT
ejpam-5889	209	10	chiefs	chief	NOUN
ejpam-5889	209	11	and	and	CCONJ
ejpam-5889	209	12	the	the	DET
ejpam-5889	209	13	reviewers	reviewer	NOUN
ejpam-5889	209	14	for	for	ADP
ejpam-5889	209	15	their	their	PRON
ejpam-5889	209	16	valuable	valuable	ADJ
ejpam-5889	209	17	comments	comment	NOUN
ejpam-5889	209	18	,	,	PUNCT
ejpam-5889	209	19	which	which	PRON
ejpam-5889	209	20	have	have	AUX
ejpam-5889	209	21	improved	improve	VERB
ejpam-5889	209	22	the	the	DET
ejpam-5889	209	23	quality	quality	NOUN
ejpam-5889	209	24	of	of	ADP
ejpam-5889	209	25	the	the	DET
ejpam-5889	209	26	work	work	NOUN
ejpam-5889	209	27	.	.	PUNCT
ejpam-5889	210	1	references	reference	NOUN
ejpam-5889	210	2	[	[	X
ejpam-5889	210	3	1	1	NUM
ejpam-5889	210	4	]	]	X
ejpam-5889	210	5	d	d	X
ejpam-5889	210	6	knuth	knuth	PROPN
ejpam-5889	210	7	.	.	PUNCT
ejpam-5889	211	1	the	the	DET
ejpam-5889	211	2	art	art	NOUN
ejpam-5889	211	3	of	of	ADP
ejpam-5889	211	4	computer	computer	NOUN
ejpam-5889	211	5	programming	programming	NOUN
ejpam-5889	211	6	.	.	PUNCT
ejpam-5889	212	1	semi	semi	ADJ
ejpam-5889	212	2	numerical	numerical	ADJ
ejpam-5889	212	3	algorithms	algorithm	NOUN
ejpam-5889	212	4	,	,	PUNCT
ejpam-5889	212	5	second	second	ADJ
ejpam-5889	212	6	edition	edition	NOUN
ejpam-5889	212	7	,	,	PUNCT
ejpam-5889	212	8	volume	volume	NOUN
ejpam-5889	212	9	2	2	NUM
ejpam-5889	212	10	.	.	PUNCT
ejpam-5889	212	11	addison	addison	PROPN
ejpam-5889	212	12	-	-	PUNCT
ejpam-5889	212	13	wesley	wesley	PROPN
ejpam-5889	212	14	,	,	PUNCT
ejpam-5889	212	15	reading	reading	NOUN
ejpam-5889	212	16	,	,	PUNCT
ejpam-5889	212	17	massachusetts	massachusetts	PROPN
ejpam-5889	212	18	,	,	PUNCT
ejpam-5889	212	19	1981	1981	NUM
ejpam-5889	212	20	.	.	PUNCT
ejpam-5889	213	1	[	[	X
ejpam-5889	213	2	2	2	NUM
ejpam-5889	213	3	]	]	PUNCT
ejpam-5889	213	4	n	n	PRON
ejpam-5889	213	5	g	g	NOUN
ejpam-5889	213	6	debruijin	debruijin	NOUN
ejpam-5889	213	7	.	.	PUNCT
ejpam-5889	214	1	denumerations	denumeration	NOUN
ejpam-5889	214	2	of	of	ADP
ejpam-5889	214	3	rooted	rooted	ADJ
ejpam-5889	214	4	trees	tree	NOUN
ejpam-5889	214	5	and	and	CCONJ
ejpam-5889	214	6	multisets	multiset	NOUN
ejpam-5889	214	7	.	.	PUNCT
ejpam-5889	215	1	discrete	discrete	ADJ
ejpam-5889	215	2	appl	appl	PROPN
ejpam-5889	215	3	.	.	PUNCT
ejpam-5889	215	4	math	math	PROPN
ejpam-5889	215	5	.	.	PUNCT
ejpam-5889	215	6	,	,	PUNCT
ejpam-5889	216	1	6:25–33	6:25–33	NOUN
ejpam-5889	216	2	,	,	PUNCT
ejpam-5889	216	3	1983	1983	NUM
ejpam-5889	216	4	.	.	PUNCT
ejpam-5889	217	1	p.	p.	NOUN
ejpam-5889	217	2	a.	a.	PROPN
ejpam-5889	217	3	ejegwa	ejegwa	PROPN
ejpam-5889	217	4	et	et	PROPN
ejpam-5889	217	5	al	al	PROPN
ejpam-5889	217	6	.	.	PUNCT
ejpam-5889	217	7	/	/	SYM
ejpam-5889	217	8	eur	eur	PROPN
ejpam-5889	217	9	.	.	PUNCT
ejpam-5889	218	1	j.	j.	PROPN
ejpam-5889	218	2	pure	pure	PROPN
ejpam-5889	218	3	appl	appl	PROPN
ejpam-5889	218	4	.	.	PROPN
ejpam-5889	218	5	math	math	PROPN
ejpam-5889	218	6	,	,	PUNCT
ejpam-5889	218	7	18	18	NUM
ejpam-5889	218	8	(	(	PUNCT
ejpam-5889	218	9	2	2	NUM
ejpam-5889	218	10	)	)	PUNCT
ejpam-5889	218	11	(	(	PUNCT
ejpam-5889	218	12	2025	2025	NUM
ejpam-5889	218	13	)	)	PUNCT
ejpam-5889	218	14	,	,	PUNCT
ejpam-5889	218	15	5889	5889	NUM
ejpam-5889	218	16	12	12	NUM
ejpam-5889	218	17	of	of	ADP
ejpam-5889	218	18	13	13	NUM
ejpam-5889	218	19	[	[	X
ejpam-5889	218	20	3	3	NUM
ejpam-5889	218	21	]	]	X
ejpam-5889	218	22	w	w	PROPN
ejpam-5889	218	23	d	d	PROPN
ejpam-5889	218	24	blizard	blizard	NOUN
ejpam-5889	218	25	.	.	PUNCT
ejpam-5889	219	1	multiset	multiset	PROPN
ejpam-5889	219	2	theory	theory	NOUN
ejpam-5889	219	3	.	.	PUNCT
ejpam-5889	220	1	notre	notre	PROPN
ejpam-5889	220	2	dame	dame	PROPN
ejpam-5889	220	3	j.	j.	PROPN
ejpam-5889	220	4	logic	logic	PROPN
ejpam-5889	220	5	,	,	PUNCT
ejpam-5889	220	6	31:36–65	31:36–65	NUM
ejpam-5889	220	7	,	,	PUNCT
ejpam-5889	220	8	1989	1989	NUM
ejpam-5889	220	9	.	.	PUNCT
ejpam-5889	221	1	[	[	X
ejpam-5889	221	2	4	4	NUM
ejpam-5889	221	3	]	]	SYM
ejpam-5889	221	4	w	w	PROPN
ejpam-5889	221	5	d	d	PROPN
ejpam-5889	221	6	blizard	blizard	NOUN
ejpam-5889	221	7	.	.	PUNCT
ejpam-5889	222	1	the	the	DET
ejpam-5889	222	2	development	development	NOUN
ejpam-5889	222	3	of	of	ADP
ejpam-5889	222	4	multiset	multiset	ADJ
ejpam-5889	222	5	theory	theory	NOUN
ejpam-5889	222	6	.	.	PUNCT
ejpam-5889	223	1	modern	modern	ADJ
ejpam-5889	223	2	logic	logic	NOUN
ejpam-5889	223	3	,	,	PUNCT
ejpam-5889	223	4	1(4):319–352	1(4):319–352	NUM
ejpam-5889	223	5	,	,	PUNCT
ejpam-5889	223	6	1991	1991	NUM
ejpam-5889	223	7	.	.	PUNCT
ejpam-5889	224	1	[	[	X
ejpam-5889	224	2	5	5	X
ejpam-5889	224	3	]	]	X
ejpam-5889	224	4	k	k	NOUN
ejpam-5889	224	5	p	p	PROPN
ejpam-5889	224	6	girish	girish	PROPN
ejpam-5889	224	7	and	and	CCONJ
ejpam-5889	224	8	s	s	PROPN
ejpam-5889	224	9	j	j	PROPN
ejpam-5889	224	10	john	john	PROPN
ejpam-5889	224	11	.	.	PUNCT
ejpam-5889	225	1	relations	relation	NOUN
ejpam-5889	225	2	and	and	CCONJ
ejpam-5889	225	3	functions	function	NOUN
ejpam-5889	225	4	in	in	ADP
ejpam-5889	225	5	multiset	multiset	ADJ
ejpam-5889	225	6	context	context	NOUN
ejpam-5889	225	7	.	.	PUNCT
ejpam-5889	226	1	inf	inf	PROPN
ejpam-5889	226	2	.	.	PUNCT
ejpam-5889	227	1	sci	sci	PROPN
ejpam-5889	227	2	.	.	PROPN
ejpam-5889	227	3	,	,	PUNCT
ejpam-5889	227	4	179:758–768	179:758–768	NUM
ejpam-5889	227	5	,	,	PUNCT
ejpam-5889	227	6	2009	2009	NUM
ejpam-5889	227	7	.	.	PUNCT
ejpam-5889	228	1	[	[	X
ejpam-5889	228	2	6	6	NUM
ejpam-5889	228	3	]	]	SYM
ejpam-5889	228	4	s	s	X
ejpam-5889	228	5	p	p	X
ejpam-5889	228	6	jena	jena	PROPN
ejpam-5889	228	7	,	,	PUNCT
ejpam-5889	228	8	s	s	PROPN
ejpam-5889	228	9	k	k	PROPN
ejpam-5889	228	10	ghosh	ghosh	PROPN
ejpam-5889	228	11	,	,	PUNCT
ejpam-5889	228	12	and	and	CCONJ
ejpam-5889	228	13	b	b	X
ejpam-5889	228	14	k	k	PROPN
ejpam-5889	228	15	tripathy	tripathy	PROPN
ejpam-5889	228	16	.	.	PUNCT
ejpam-5889	229	1	on	on	ADP
ejpam-5889	229	2	the	the	DET
ejpam-5889	229	3	theory	theory	NOUN
ejpam-5889	229	4	of	of	ADP
ejpam-5889	229	5	bags	bag	NOUN
ejpam-5889	229	6	and	and	CCONJ
ejpam-5889	229	7	lists	list	NOUN
ejpam-5889	229	8	.	.	PUNCT
ejpam-5889	230	1	inf	inf	PROPN
ejpam-5889	230	2	.	.	PUNCT
ejpam-5889	231	1	sci	sci	PROPN
ejpam-5889	231	2	.	.	PROPN
ejpam-5889	231	3	,	,	PUNCT
ejpam-5889	231	4	132:241–254	132:241–254	NUM
ejpam-5889	231	5	,	,	PUNCT
ejpam-5889	231	6	2001	2001	NUM
ejpam-5889	231	7	.	.	PUNCT
ejpam-5889	232	1	[	[	X
ejpam-5889	232	2	7	7	NUM
ejpam-5889	232	3	]	]	X
ejpam-5889	232	4	d	d	X
ejpam-5889	232	5	singh	singh	PROPN
ejpam-5889	232	6	,	,	PUNCT
ejpam-5889	232	7	a	a	PRON
ejpam-5889	232	8	m	m	PROPN
ejpam-5889	232	9	ibrahim	ibrahim	NOUN
ejpam-5889	232	10	,	,	PUNCT
ejpam-5889	232	11	t	t	NOUN
ejpam-5889	232	12	yohanna	yohanna	NOUN
ejpam-5889	232	13	,	,	PUNCT
ejpam-5889	232	14	and	and	CCONJ
ejpam-5889	232	15	j	j	PROPN
ejpam-5889	232	16	n	n	PRON
ejpam-5889	232	17	singh	singh	PROPN
ejpam-5889	232	18	.	.	PUNCT
ejpam-5889	233	1	an	an	DET
ejpam-5889	233	2	overview	overview	NOUN
ejpam-5889	233	3	of	of	ADP
ejpam-5889	233	4	the	the	DET
ejpam-5889	233	5	applications	application	NOUN
ejpam-5889	233	6	of	of	ADP
ejpam-5889	233	7	multisets	multiset	NOUN
ejpam-5889	233	8	.	.	PUNCT
ejpam-5889	234	1	novi	novi	PROPN
ejpam-5889	234	2	sad	sad	PROPN
ejpam-5889	234	3	j.	j.	PROPN
ejpam-5889	234	4	math	math	PROPN
ejpam-5889	234	5	.	.	PUNCT
ejpam-5889	234	6	,	,	PUNCT
ejpam-5889	234	7	37(2):73–92	37(2):73–92	NUM
ejpam-5889	234	8	,	,	PUNCT
ejpam-5889	234	9	2007	2007	NUM
ejpam-5889	234	10	.	.	PUNCT
ejpam-5889	235	1	[	[	X
ejpam-5889	235	2	8	8	X
ejpam-5889	235	3	]	]	PUNCT
ejpam-5889	235	4	a	a	DET
ejpam-5889	235	5	syropoulos	syropoulo	NOUN
ejpam-5889	235	6	.	.	PUNCT
ejpam-5889	236	1	mathematics	mathematic	NOUN
ejpam-5889	236	2	of	of	ADP
ejpam-5889	236	3	multisets	multiset	NOUN
ejpam-5889	236	4	.	.	PUNCT
ejpam-5889	237	1	springer	springer	NOUN
ejpam-5889	237	2	-	-	PUNCT
ejpam-5889	237	3	verlag	verlag	PROPN
ejpam-5889	237	4	,	,	PUNCT
ejpam-5889	237	5	berlin	berlin	PROPN
ejpam-5889	237	6	,	,	PUNCT
ejpam-5889	237	7	heidelberg	heidelberg	PROPN
ejpam-5889	237	8	,	,	PUNCT
ejpam-5889	237	9	347358	347358	NUM
ejpam-5889	237	10	,	,	PUNCT
ejpam-5889	237	11	2001	2001	NUM
ejpam-5889	237	12	.	.	PUNCT
ejpam-5889	238	1	[	[	X
ejpam-5889	238	2	9	9	NUM
ejpam-5889	238	3	]	]	PUNCT
ejpam-5889	238	4	t	t	NOUN
ejpam-5889	238	5	o	o	X
ejpam-5889	238	6	william	william	PROPN
ejpam-5889	238	7	-	-	PUNCT
ejpam-5889	238	8	west	west	PROPN
ejpam-5889	238	9	,	,	PUNCT
ejpam-5889	238	10	p	p	X
ejpam-5889	238	11	a	a	DET
ejpam-5889	238	12	ejegwa	ejegwa	NOUN
ejpam-5889	238	13	,	,	PUNCT
ejpam-5889	238	14	and	and	CCONJ
ejpam-5889	238	15	a	a	DET
ejpam-5889	238	16	u	u	NOUN
ejpam-5889	238	17	amaonyeiro	amaonyeiro	ADV
ejpam-5889	238	18	.	.	PUNCT
ejpam-5889	239	1	on	on	ADP
ejpam-5889	239	2	dynamic	dynamic	ADJ
ejpam-5889	239	3	multisets	multiset	NOUN
ejpam-5889	239	4	and	and	CCONJ
ejpam-5889	239	5	their	their	PRON
ejpam-5889	239	6	operations	operation	NOUN
ejpam-5889	239	7	.	.	PUNCT
ejpam-5889	240	1	ann	ann	AUX
ejpam-5889	240	2	.	.	PUNCT
ejpam-5889	240	3	commun	commun	PROPN
ejpam-5889	240	4	.	.	PUNCT
ejpam-5889	241	1	math	math	PROPN
ejpam-5889	241	2	.	.	PUNCT
ejpam-5889	241	3	,	,	PUNCT
ejpam-5889	241	4	4(3):284–292	4(3):284–292	NUM
ejpam-5889	241	5	,	,	PUNCT
ejpam-5889	241	6	2021	2021	NUM
ejpam-5889	241	7	.	.	PUNCT
ejpam-5889	242	1	[	[	X
ejpam-5889	242	2	10	10	NUM
ejpam-5889	242	3	]	]	X
ejpam-5889	242	4	l	l	NOUN
ejpam-5889	242	5	a	a	DET
ejpam-5889	242	6	zadeh	zadeh	PROPN
ejpam-5889	242	7	.	.	PUNCT
ejpam-5889	242	8	fuzzy	fuzzy	ADJ
ejpam-5889	242	9	sets	set	NOUN
ejpam-5889	242	10	.	.	PUNCT
ejpam-5889	243	1	inf	inf	PROPN
ejpam-5889	243	2	.	.	PUNCT
ejpam-5889	243	3	contr	contr	PROPN
ejpam-5889	243	4	.	.	PROPN
ejpam-5889	243	5	,	,	PUNCT
ejpam-5889	243	6	8(3):338–353	8(3):338–353	NUM
ejpam-5889	243	7	,	,	PUNCT
ejpam-5889	243	8	1965	1965	NUM
ejpam-5889	243	9	.	.	PUNCT
ejpam-5889	244	1	[	[	X
ejpam-5889	244	2	11	11	NUM
ejpam-5889	244	3	]	]	PUNCT
ejpam-5889	244	4	a	a	DET
ejpam-5889	244	5	rosenfeld	rosenfeld	PROPN
ejpam-5889	244	6	.	.	PUNCT
ejpam-5889	245	1	fuzzy	fuzzy	ADJ
ejpam-5889	245	2	groups	group	NOUN
ejpam-5889	245	3	.	.	PUNCT
ejpam-5889	246	1	j.	j.	PROPN
ejpam-5889	246	2	math	math	PROPN
ejpam-5889	246	3	.	.	PUNCT
ejpam-5889	247	1	anal	anal	PROPN
ejpam-5889	247	2	.	.	PUNCT
ejpam-5889	248	1	appl	appl	PROPN
ejpam-5889	248	2	.	.	PROPN
ejpam-5889	249	1	,	,	PUNCT
ejpam-5889	249	2	35(3):512–517	35(3):512–517	PROPN
ejpam-5889	249	3	,	,	PUNCT
ejpam-5889	249	4	1971	1971	NUM
ejpam-5889	249	5	.	.	PUNCT
ejpam-5889	250	1	[	[	X
ejpam-5889	250	2	12	12	NUM
ejpam-5889	250	3	]	]	X
ejpam-5889	250	4	j	j	PROPN
ejpam-5889	250	5	m	m	PROPN
ejpam-5889	250	6	anthony	anthony	PROPN
ejpam-5889	250	7	and	and	CCONJ
ejpam-5889	250	8	h	h	PROPN
ejpam-5889	250	9	sherwood	sherwood	PROPN
ejpam-5889	250	10	.	.	PUNCT
ejpam-5889	251	1	a	a	DET
ejpam-5889	251	2	characterization	characterization	NOUN
ejpam-5889	251	3	of	of	ADP
ejpam-5889	251	4	fuzzy	fuzzy	ADJ
ejpam-5889	251	5	subgroups	subgroup	NOUN
ejpam-5889	251	6	.	.	PUNCT
ejpam-5889	252	1	fuzzy	fuzzy	ADJ
ejpam-5889	252	2	set	set	VERB
ejpam-5889	252	3	syst	syst	PROPN
ejpam-5889	252	4	.	.	PUNCT
ejpam-5889	252	5	,	,	PUNCT
ejpam-5889	252	6	7:297–305	7:297–305	NOUN
ejpam-5889	252	7	,	,	PUNCT
ejpam-5889	252	8	1982	1982	NUM
ejpam-5889	252	9	.	.	PUNCT
ejpam-5889	253	1	[	[	X
ejpam-5889	253	2	13	13	NUM
ejpam-5889	253	3	]	]	X
ejpam-5889	253	4	p	p	X
ejpam-5889	253	5	a	a	DET
ejpam-5889	253	6	ejegwa	ejegwa	NOUN
ejpam-5889	253	7	and	and	CCONJ
ejpam-5889	253	8	j	j	PROPN
ejpam-5889	253	9	a	a	DET
ejpam-5889	253	10	otuwe	otuwe	NOUN
ejpam-5889	253	11	.	.	PUNCT
ejpam-5889	254	1	frattini	frattini	VERB
ejpam-5889	254	2	fuzzy	fuzzy	ADJ
ejpam-5889	254	3	subgroups	subgroup	NOUN
ejpam-5889	254	4	of	of	ADP
ejpam-5889	254	5	fuzzy	fuzzy	ADJ
ejpam-5889	254	6	groups	group	NOUN
ejpam-5889	254	7	.	.	PUNCT
ejpam-5889	255	1	j.	j.	PROPN
ejpam-5889	255	2	uni	uni	PROPN
ejpam-5889	255	3	.	.	PROPN
ejpam-5889	255	4	math	math	PROPN
ejpam-5889	255	5	.	.	PUNCT
ejpam-5889	255	6	,	,	PUNCT
ejpam-5889	255	7	2(2):175–182	2(2):175–182	NOUN
ejpam-5889	255	8	,	,	PUNCT
ejpam-5889	255	9	2019	2019	NUM
ejpam-5889	255	10	.	.	PUNCT
ejpam-5889	256	1	[	[	X
ejpam-5889	256	2	14	14	NUM
ejpam-5889	256	3	]	]	X
ejpam-5889	256	4	a	a	DET
ejpam-5889	256	5	kumari	kumari	PROPN
ejpam-5889	256	6	,	,	PUNCT
ejpam-5889	256	7	p	p	PROPN
ejpam-5889	256	8	preeti	preeti	PROPN
ejpam-5889	256	9	,	,	PUNCT
ejpam-5889	256	10	a	a	DET
ejpam-5889	256	11	sehgal	sehgal	NOUN
ejpam-5889	256	12	,	,	PUNCT
ejpam-5889	256	13	p	p	PROPN
ejpam-5889	256	14	k	k	PROPN
ejpam-5889	256	15	sharma	sharma	PROPN
ejpam-5889	256	16	,	,	PUNCT
ejpam-5889	256	17	and	and	CCONJ
ejpam-5889	256	18	s	s	VERB
ejpam-5889	256	19	sarita	sarita	PROPN
ejpam-5889	256	20	.	.	PUNCT
ejpam-5889	257	1	fuzzy	fuzzy	ADJ
ejpam-5889	257	2	subgroups	subgroup	NOUN
ejpam-5889	257	3	of	of	ADP
ejpam-5889	257	4	non	non	ADJ
ejpam-5889	257	5	–	–	NOUN
ejpam-5889	257	6	abelian	abelian	ADJ
ejpam-5889	257	7	group	group	NOUN
ejpam-5889	257	8	zpn	zpn	PROPN
ejpam-5889	258	1	⋉	⋉	PROPN
ejpam-5889	258	2	zp	zp	PROPN
ejpam-5889	258	3	for	for	ADP
ejpam-5889	258	4	any	any	DET
ejpam-5889	258	5	prime	prime	ADJ
ejpam-5889	258	6	p.	p.	PROPN
ejpam-5889	258	7	aip	aip	PROPN
ejpam-5889	258	8	conf	conf	PROPN
ejpam-5889	258	9	.	.	PUNCT
ejpam-5889	259	1	proceedings	proceeding	NOUN
ejpam-5889	259	2	,	,	PUNCT
ejpam-5889	259	3	2142:170025	2142:170025	NUM
ejpam-5889	259	4	,	,	PUNCT
ejpam-5889	259	5	2019	2019	NUM
ejpam-5889	259	6	.	.	PUNCT
ejpam-5889	260	1	[	[	X
ejpam-5889	260	2	15	15	NUM
ejpam-5889	260	3	]	]	X
ejpam-5889	260	4	a	a	DET
ejpam-5889	260	5	sehgal	sehgal	PROPN
ejpam-5889	260	6	and	and	CCONJ
ejpam-5889	260	7	j	j	PROPN
ejpam-5889	260	8	manjeet	manjeet	NOUN
ejpam-5889	260	9	.	.	PUNCT
ejpam-5889	261	1	the	the	DET
ejpam-5889	261	2	number	number	NOUN
ejpam-5889	261	3	of	of	ADP
ejpam-5889	261	4	fuzzy	fuzzy	ADJ
ejpam-5889	261	5	subgroups	subgroup	NOUN
ejpam-5889	261	6	for	for	ADP
ejpam-5889	261	7	finite	finite	ADJ
ejpam-5889	261	8	abelian	abelian	PROPN
ejpam-5889	261	9	p	p	PROPN
ejpam-5889	261	10	-	-	PUNCT
ejpam-5889	261	11	group	group	NOUN
ejpam-5889	261	12	of	of	ADP
ejpam-5889	261	13	rank	rank	PROPN
ejpam-5889	261	14	three	three	NUM
ejpam-5889	261	15	.	.	PUNCT
ejpam-5889	262	1	adv	adv	PROPN
ejpam-5889	262	2	.	.	PUNCT
ejpam-5889	262	3	fuzzy	fuzzy	ADJ
ejpam-5889	262	4	math	math	NOUN
ejpam-5889	262	5	.	.	PUNCT
ejpam-5889	262	6	,	,	PUNCT
ejpam-5889	262	7	12(4):1035–1045	12(4):1035–1045	NUM
ejpam-5889	262	8	,	,	PUNCT
ejpam-5889	262	9	2017	2017	NUM
ejpam-5889	262	10	.	.	PUNCT
ejpam-5889	263	1	[	[	X
ejpam-5889	263	2	16	16	NUM
ejpam-5889	263	3	]	]	X
ejpam-5889	263	4	a	a	DET
ejpam-5889	263	5	sehgal	sehgal	PROPN
ejpam-5889	263	6	,	,	PUNCT
ejpam-5889	263	7	s	s	NOUN
ejpam-5889	263	8	sarita	sarita	PROPN
ejpam-5889	263	9	,	,	PUNCT
ejpam-5889	263	10	and	and	CCONJ
ejpam-5889	263	11	p	p	PROPN
ejpam-5889	263	12	k	k	PROPN
ejpam-5889	263	13	sharma	sharma	PROPN
ejpam-5889	263	14	.	.	PUNCT
ejpam-5889	264	1	the	the	DET
ejpam-5889	264	2	number	number	NOUN
ejpam-5889	264	3	of	of	ADP
ejpam-5889	264	4	fuzzy	fuzzy	ADJ
ejpam-5889	264	5	subgroups	subgroup	NOUN
ejpam-5889	264	6	of	of	ADP
ejpam-5889	264	7	a	a	DET
ejpam-5889	264	8	finite	finite	ADJ
ejpam-5889	264	9	dihedral	dihedral	NOUN
ejpam-5889	264	10	.	.	PUNCT
ejpam-5889	265	1	int	int	NOUN
ejpam-5889	265	2	.	.	PUNCT
ejpam-5889	266	1	j.	j.	PROPN
ejpam-5889	266	2	fuzzy	fuzzy	PROPN
ejpam-5889	266	3	math	math	PROPN
ejpam-5889	266	4	.	.	PUNCT
ejpam-5889	267	1	archive	archive	NOUN
ejpam-5889	267	2	,	,	PUNCT
ejpam-5889	267	3	8(1):51–57	8(1):51–57	NUM
ejpam-5889	267	4	,	,	PUNCT
ejpam-5889	267	5	2015	2015	NUM
ejpam-5889	267	6	.	.	PUNCT
ejpam-5889	268	1	[	[	X
ejpam-5889	268	2	17	17	NUM
ejpam-5889	268	3	]	]	PUNCT
ejpam-5889	268	4	sk	sk	X
ejpam-5889	268	5	nazmul	nazmul	ADJ
ejpam-5889	268	6	,	,	PUNCT
ejpam-5889	268	7	p	p	PROPN
ejpam-5889	268	8	majumdar	majumdar	PROPN
ejpam-5889	268	9	,	,	PUNCT
ejpam-5889	268	10	and	and	CCONJ
ejpam-5889	268	11	s	s	PROPN
ejpam-5889	268	12	k	k	PROPN
ejpam-5889	268	13	samanta	samanta	PROPN
ejpam-5889	268	14	.	.	PUNCT
ejpam-5889	269	1	on	on	ADP
ejpam-5889	269	2	multisets	multiset	NOUN
ejpam-5889	269	3	and	and	CCONJ
ejpam-5889	269	4	multigroups	multigroup	NOUN
ejpam-5889	269	5	.	.	PUNCT
ejpam-5889	270	1	ann	ann	PROPN
ejpam-5889	270	2	.	.	PUNCT
ejpam-5889	270	3	fuzzy	fuzzy	ADJ
ejpam-5889	270	4	math	math	NOUN
ejpam-5889	270	5	.	.	PUNCT
ejpam-5889	271	1	inform	inform	NOUN
ejpam-5889	271	2	.	.	PUNCT
ejpam-5889	271	3	,	,	PUNCT
ejpam-5889	271	4	6(3):643–656	6(3):643–656	NOUN
ejpam-5889	271	5	,	,	PUNCT
ejpam-5889	271	6	2013	2013	NUM
ejpam-5889	271	7	.	.	PUNCT
ejpam-5889	272	1	[	[	X
ejpam-5889	272	2	18	18	NUM
ejpam-5889	272	3	]	]	X
ejpam-5889	272	4	p	p	X
ejpam-5889	272	5	a	a	DET
ejpam-5889	272	6	ejegwa	ejegwa	NOUN
ejpam-5889	272	7	.	.	PUNCT
ejpam-5889	273	1	a	a	DET
ejpam-5889	273	2	study	study	NOUN
ejpam-5889	273	3	of	of	ADP
ejpam-5889	273	4	multigroup	multigroup	PROPN
ejpam-5889	273	5	structure	structure	NOUN
ejpam-5889	273	6	and	and	CCONJ
ejpam-5889	273	7	its	its	PRON
ejpam-5889	273	8	acting	act	VERB
ejpam-5889	273	9	principles	principle	NOUN
ejpam-5889	273	10	on	on	ADP
ejpam-5889	273	11	multiset	multiset	PROPN
ejpam-5889	273	12	.	.	PUNCT
ejpam-5889	274	1	phd	phd	NOUN
ejpam-5889	274	2	thesis	thesis	NOUN
ejpam-5889	274	3	,	,	PUNCT
ejpam-5889	274	4	ahmadu	ahmadu	PROPN
ejpam-5889	274	5	bello	bello	PROPN
ejpam-5889	274	6	university	university	PROPN
ejpam-5889	274	7	,	,	PUNCT
ejpam-5889	274	8	zaria	zaria	PROPN
ejpam-5889	274	9	,	,	PUNCT
ejpam-5889	274	10	nigeria	nigeria	PROPN
ejpam-5889	274	11	,	,	PUNCT
ejpam-5889	274	12	2018	2018	NUM
ejpam-5889	274	13	.	.	PUNCT
ejpam-5889	275	1	[	[	X
ejpam-5889	275	2	19	19	NUM
ejpam-5889	275	3	]	]	X
ejpam-5889	275	4	j	j	PROPN
ejpam-5889	275	5	a	a	DET
ejpam-5889	275	6	awolola	awolola	PROPN
ejpam-5889	275	7	and	and	CCONJ
ejpam-5889	275	8	a	a	DET
ejpam-5889	275	9	m	m	NOUN
ejpam-5889	275	10	ibrahim	ibrahim	NOUN
ejpam-5889	275	11	.	.	PUNCT
ejpam-5889	276	1	some	some	DET
ejpam-5889	276	2	results	result	VERB
ejpam-5889	276	3	on	on	ADP
ejpam-5889	276	4	multigroups	multigroup	NOUN
ejpam-5889	276	5	.	.	PUNCT
ejpam-5889	277	1	quasi	quasi	ADJ
ejpam-5889	277	2	.	.	PUNCT
ejpam-5889	277	3	related	related	ADJ
ejpam-5889	277	4	syst	syst	NOUN
ejpam-5889	277	5	.	.	PUNCT
ejpam-5889	277	6	,	,	PUNCT
ejpam-5889	277	7	24(2):169–177	24(2):169–177	NUM
ejpam-5889	277	8	,	,	PUNCT
ejpam-5889	277	9	2016	2016	NUM
ejpam-5889	277	10	.	.	PUNCT
ejpam-5889	278	1	[	[	X
ejpam-5889	278	2	20	20	NUM
ejpam-5889	278	3	]	]	X
ejpam-5889	278	4	p	p	X
ejpam-5889	278	5	a	a	DET
ejpam-5889	278	6	ejegwa	ejegwa	NOUN
ejpam-5889	278	7	and	and	CCONJ
ejpam-5889	278	8	a	a	DET
ejpam-5889	278	9	m	m	NOUN
ejpam-5889	278	10	ibrahim	ibrahim	NOUN
ejpam-5889	278	11	.	.	PUNCT
ejpam-5889	279	1	some	some	DET
ejpam-5889	279	2	homomorphic	homomorphic	ADJ
ejpam-5889	279	3	properties	property	NOUN
ejpam-5889	279	4	of	of	ADP
ejpam-5889	279	5	multigroups	multigroup	NOUN
ejpam-5889	279	6	.	.	PUNCT
ejpam-5889	280	1	bul	bul	PROPN
ejpam-5889	280	2	.	.	PUNCT
ejpam-5889	281	1	acad	acad	PROPN
ejpam-5889	281	2	.	.	PUNCT
ejpam-5889	282	1	stiinte	stiinte	PROPN
ejpam-5889	282	2	repub	repub	PROPN
ejpam-5889	282	3	.	.	PUNCT
ejpam-5889	283	1	mold	mold	NOUN
ejpam-5889	283	2	.	.	PUNCT
ejpam-5889	284	1	mat	mat	NOUN
ejpam-5889	284	2	.	.	PROPN
ejpam-5889	284	3	,	,	PUNCT
ejpam-5889	284	4	83(1):67–76	83(1):67–76	NUM
ejpam-5889	284	5	,	,	PUNCT
ejpam-5889	284	6	2017	2017	NUM
ejpam-5889	284	7	.	.	PUNCT
ejpam-5889	285	1	[	[	X
ejpam-5889	285	2	21	21	NUM
ejpam-5889	285	3	]	]	X
ejpam-5889	285	4	u	u	X
ejpam-5889	285	5	adamu	adamu	PROPN
ejpam-5889	285	6	and	and	CCONJ
ejpam-5889	285	7	m	m	PROPN
ejpam-5889	285	8	a	a	DET
ejpam-5889	285	9	ibrahim	ibrahim	NOUN
ejpam-5889	285	10	.	.	PUNCT
ejpam-5889	286	1	strongly	strongly	ADV
ejpam-5889	286	2	invariant	invariant	ADJ
ejpam-5889	286	3	submultigroups	submultigroup	NOUN
ejpam-5889	286	4	.	.	PUNCT
ejpam-5889	287	1	theory	theory	NOUN
ejpam-5889	287	2	appl	appl	PROPN
ejpam-5889	287	3	.	.	PUNCT
ejpam-5889	287	4	math	math	NOUN
ejpam-5889	287	5	.	.	PUNCT
ejpam-5889	288	1	computer	computer	NOUN
ejpam-5889	288	2	sci	sci	PROPN
ejpam-5889	288	3	.	.	PROPN
ejpam-5889	288	4	,	,	PUNCT
ejpam-5889	288	5	10(2):96–103	10(2):96–103	NUM
ejpam-5889	288	6	,	,	PUNCT
ejpam-5889	288	7	2020	2020	NUM
ejpam-5889	288	8	.	.	PUNCT
ejpam-5889	289	1	[	[	X
ejpam-5889	289	2	22	22	NUM
ejpam-5889	289	3	]	]	X
ejpam-5889	289	4	p	p	X
ejpam-5889	289	5	a	a	DET
ejpam-5889	289	6	ejegwa	ejegwa	NOUN
ejpam-5889	289	7	and	and	CCONJ
ejpam-5889	289	8	a	a	DET
ejpam-5889	289	9	m	m	NOUN
ejpam-5889	289	10	ibrahim	ibrahim	NOUN
ejpam-5889	289	11	.	.	PUNCT
ejpam-5889	290	1	normal	normal	ADJ
ejpam-5889	290	2	submultigroups	submultigroup	NOUN
ejpam-5889	290	3	and	and	CCONJ
ejpam-5889	290	4	comultisets	comultiset	NOUN
ejpam-5889	290	5	of	of	ADP
ejpam-5889	290	6	a	a	DET
ejpam-5889	290	7	multigroup	multigroup	NOUN
ejpam-5889	290	8	.	.	PUNCT
ejpam-5889	291	1	quasi	quasi	PROPN
ejpam-5889	291	2	.	.	PUNCT
ejpam-5889	291	3	related	related	ADJ
ejpam-5889	291	4	syst	syst	NOUN
ejpam-5889	291	5	.	.	PUNCT
ejpam-5889	291	6	,	,	PUNCT
ejpam-5889	291	7	25(2):231–244	25(2):231–244	NOUN
ejpam-5889	291	8	,	,	PUNCT
ejpam-5889	291	9	2017	2017	NUM
ejpam-5889	291	10	.	.	PUNCT
ejpam-5889	292	1	[	[	X
ejpam-5889	292	2	23	23	NUM
ejpam-5889	292	3	]	]	X
ejpam-5889	292	4	a	a	PRON
ejpam-5889	292	5	m	m	VERB
ejpam-5889	292	6	ibrahim	ibrahim	NOUN
ejpam-5889	292	7	and	and	CCONJ
ejpam-5889	292	8	p	p	X
ejpam-5889	292	9	a	a	DET
ejpam-5889	292	10	ejegwa	ejegwa	NOUN
ejpam-5889	292	11	.	.	PUNCT
ejpam-5889	293	1	characteristic	characteristic	ADJ
ejpam-5889	293	2	submultigroups	submultigroup	NOUN
ejpam-5889	293	3	of	of	ADP
ejpam-5889	293	4	a	a	DET
ejpam-5889	293	5	multigroup	multigroup	NOUN
ejpam-5889	293	6	.	.	PUNCT
ejpam-5889	294	1	gulf	gulf	PROPN
ejpam-5889	294	2	j.	j.	PROPN
ejpam-5889	294	3	math	math	PROPN
ejpam-5889	294	4	.	.	PUNCT
ejpam-5889	294	5	,	,	PUNCT
ejpam-5889	294	6	5(4):1–8	5(4):1–8	NUM
ejpam-5889	294	7	,	,	PUNCT
ejpam-5889	294	8	2017	2017	NUM
ejpam-5889	294	9	.	.	PUNCT
ejpam-5889	295	1	[	[	X
ejpam-5889	295	2	24	24	NUM
ejpam-5889	295	3	]	]	X
ejpam-5889	295	4	j	j	PROPN
ejpam-5889	295	5	a	a	DET
ejpam-5889	295	6	otuwe	otuwe	NOUN
ejpam-5889	295	7	and	and	CCONJ
ejpam-5889	295	8	m	m	VERB
ejpam-5889	295	9	a	a	DET
ejpam-5889	295	10	ibrahim	ibrahim	NOUN
ejpam-5889	295	11	.	.	PUNCT
ejpam-5889	296	1	frattini	frattini	ADJ
ejpam-5889	296	2	submultigroups	submultigroup	NOUN
ejpam-5889	296	3	of	of	ADP
ejpam-5889	296	4	multigroups	multigroup	NOUN
ejpam-5889	296	5	.	.	PUNCT
ejpam-5889	297	1	ratio	ratio	PROPN
ejpam-5889	297	2	mathematica	mathematica	PROPN
ejpam-5889	297	3	,	,	PUNCT
ejpam-5889	297	4	39:147–163	39:147–163	NUM
ejpam-5889	297	5	,	,	PUNCT
ejpam-5889	297	6	2020	2020	NUM
ejpam-5889	297	7	.	.	PUNCT
ejpam-5889	298	1	[	[	X
ejpam-5889	298	2	25	25	NUM
ejpam-5889	298	3	]	]	X
ejpam-5889	298	4	j	j	PROPN
ejpam-5889	298	5	a	a	DET
ejpam-5889	298	6	awolola	awolola	PROPN
ejpam-5889	298	7	.	.	PUNCT
ejpam-5889	299	1	on	on	ADP
ejpam-5889	299	2	multiset	multiset	ADJ
ejpam-5889	299	3	relations	relation	NOUN
ejpam-5889	299	4	and	and	CCONJ
ejpam-5889	299	5	factor	factor	NOUN
ejpam-5889	299	6	multigroups	multigroup	NOUN
ejpam-5889	299	7	.	.	PUNCT
ejpam-5889	300	1	south	south	PROPN
ejpam-5889	300	2	east	east	PROPN
ejpam-5889	300	3	asian	asian	PROPN
ejpam-5889	300	4	j.	j.	PROPN
ejpam-5889	300	5	math	math	PROPN
ejpam-5889	300	6	.	.	PUNCT
ejpam-5889	300	7	mathemat	mathemat	PROPN
ejpam-5889	300	8	.	.	PUNCT
ejpam-5889	301	1	sci	sci	PROPN
ejpam-5889	301	2	.	.	PROPN
ejpam-5889	301	3	,	,	PUNCT
ejpam-5889	301	4	15(3):1–10	15(3):1–10	NUM
ejpam-5889	301	5	,	,	PUNCT
ejpam-5889	301	6	2019	2019	NUM
ejpam-5889	301	7	.	.	PUNCT
ejpam-5889	302	1	p.	p.	NOUN
ejpam-5889	302	2	a.	a.	PROPN
ejpam-5889	302	3	ejegwa	ejegwa	PROPN
ejpam-5889	302	4	et	et	PROPN
ejpam-5889	302	5	al	al	PROPN
ejpam-5889	302	6	.	.	PUNCT
ejpam-5889	302	7	/	/	SYM
ejpam-5889	302	8	eur	eur	PROPN
ejpam-5889	302	9	.	.	PUNCT
ejpam-5889	303	1	j.	j.	PROPN
ejpam-5889	303	2	pure	pure	PROPN
ejpam-5889	303	3	appl	appl	PROPN
ejpam-5889	303	4	.	.	PROPN
ejpam-5889	303	5	math	math	PROPN
ejpam-5889	303	6	,	,	PUNCT
ejpam-5889	303	7	18	18	NUM
ejpam-5889	303	8	(	(	PUNCT
ejpam-5889	303	9	2	2	NUM
ejpam-5889	303	10	)	)	PUNCT
ejpam-5889	303	11	(	(	PUNCT
ejpam-5889	303	12	2025	2025	NUM
ejpam-5889	303	13	)	)	PUNCT
ejpam-5889	303	14	,	,	PUNCT
ejpam-5889	303	15	5889	5889	NUM
ejpam-5889	303	16	13	13	NUM
ejpam-5889	303	17	of	of	ADP
ejpam-5889	303	18	13	13	NUM
ejpam-5889	303	19	[	[	SYM
ejpam-5889	303	20	26	26	NUM
ejpam-5889	303	21	]	]	X
ejpam-5889	303	22	j	j	PROPN
ejpam-5889	303	23	a	a	DET
ejpam-5889	303	24	awolola	awolola	PROPN
ejpam-5889	303	25	.	.	PUNCT
ejpam-5889	304	1	on	on	ADP
ejpam-5889	304	2	cyclic	cyclic	PROPN
ejpam-5889	304	3	multigroup	multigroup	PROPN
ejpam-5889	304	4	family	family	NOUN
ejpam-5889	304	5	.	.	PUNCT
ejpam-5889	305	1	ratio	ratio	PROPN
ejpam-5889	305	2	mathematica	mathematica	PROPN
ejpam-5889	305	3	,	,	PUNCT
ejpam-5889	305	4	37:61–68	37:61–68	NUM
ejpam-5889	305	5	,	,	PUNCT
ejpam-5889	305	6	2019	2019	NUM
ejpam-5889	305	7	.	.	PUNCT
ejpam-5889	306	1	[	[	X
ejpam-5889	306	2	27	27	NUM
ejpam-5889	306	3	]	]	X
ejpam-5889	306	4	j	j	PROPN
ejpam-5889	306	5	a	a	DET
ejpam-5889	306	6	awolola	awolola	PROPN
ejpam-5889	306	7	and	and	CCONJ
ejpam-5889	306	8	p	p	X
ejpam-5889	306	9	a	a	DET
ejpam-5889	306	10	ejegwa	ejegwa	NOUN
ejpam-5889	306	11	.	.	PUNCT
ejpam-5889	307	1	on	on	ADP
ejpam-5889	307	2	some	some	DET
ejpam-5889	307	3	algebraic	algebraic	ADJ
ejpam-5889	307	4	properties	property	NOUN
ejpam-5889	307	5	of	of	ADP
ejpam-5889	307	6	order	order	NOUN
ejpam-5889	307	7	of	of	ADP
ejpam-5889	307	8	an	an	DET
ejpam-5889	307	9	element	element	NOUN
ejpam-5889	307	10	of	of	ADP
ejpam-5889	307	11	a	a	DET
ejpam-5889	307	12	multigroup	multigroup	NOUN
ejpam-5889	307	13	.	.	PUNCT
ejpam-5889	308	1	quasi	quasi	PROPN
ejpam-5889	308	2	.	.	PUNCT
ejpam-5889	308	3	related	related	ADJ
ejpam-5889	308	4	syst	syst	NOUN
ejpam-5889	308	5	.	.	PUNCT
ejpam-5889	308	6	,	,	PUNCT
ejpam-5889	308	7	25(1):21–26	25(1):21–26	NUM
ejpam-5889	308	8	,	,	PUNCT
ejpam-5889	308	9	2017	2017	NUM
ejpam-5889	308	10	.	.	PUNCT
ejpam-5889	309	1	[	[	X
ejpam-5889	309	2	28	28	NUM
ejpam-5889	309	3	]	]	X
ejpam-5889	309	4	p	p	X
ejpam-5889	309	5	a	a	DET
ejpam-5889	309	6	ejegwa	ejegwa	NOUN
ejpam-5889	309	7	and	and	CCONJ
ejpam-5889	309	8	a	a	DET
ejpam-5889	309	9	m	m	NOUN
ejpam-5889	309	10	ibrahim	ibrahim	NOUN
ejpam-5889	309	11	.	.	PUNCT
ejpam-5889	310	1	on	on	ADP
ejpam-5889	310	2	comultisets	comultiset	NOUN
ejpam-5889	310	3	and	and	CCONJ
ejpam-5889	310	4	factor	factor	NOUN
ejpam-5889	310	5	multigroups	multigroup	NOUN
ejpam-5889	310	6	.	.	PUNCT
ejpam-5889	311	1	theory	theory	NOUN
ejpam-5889	311	2	appl	appl	PROPN
ejpam-5889	311	3	.	.	PUNCT
ejpam-5889	311	4	math	math	NOUN
ejpam-5889	311	5	.	.	PUNCT
ejpam-5889	312	1	computer	computer	NOUN
ejpam-5889	312	2	sci	sci	PROPN
ejpam-5889	312	3	.	.	PROPN
ejpam-5889	312	4	,	,	PUNCT
ejpam-5889	312	5	7(2):124–140	7(2):124–140	NUM
ejpam-5889	312	6	,	,	PUNCT
ejpam-5889	312	7	2017	2017	NUM
ejpam-5889	312	8	.	.	PUNCT
ejpam-5889	313	1	[	[	X
ejpam-5889	313	2	29	29	NUM
ejpam-5889	313	3	]	]	X
ejpam-5889	313	4	p	p	X
ejpam-5889	313	5	a	a	DET
ejpam-5889	313	6	ejegwa	ejegwa	NOUN
ejpam-5889	313	7	and	and	CCONJ
ejpam-5889	313	8	a	a	DET
ejpam-5889	313	9	m	m	NOUN
ejpam-5889	313	10	ibrahim	ibrahim	NOUN
ejpam-5889	313	11	.	.	PUNCT
ejpam-5889	314	1	direct	direct	ADJ
ejpam-5889	314	2	product	product	NOUN
ejpam-5889	314	3	of	of	ADP
ejpam-5889	314	4	multigroups	multigroup	NOUN
ejpam-5889	314	5	and	and	CCONJ
ejpam-5889	314	6	its	its	PRON
ejpam-5889	314	7	generalization	generalization	NOUN
ejpam-5889	314	8	.	.	PUNCT
ejpam-5889	315	1	int	int	NOUN
ejpam-5889	315	2	.	.	PUNCT
ejpam-5889	316	1	j.	j.	PROPN
ejpam-5889	316	2	math	math	PROPN
ejpam-5889	316	3	.	.	PUNCT
ejpam-5889	317	1	combin	combin	NOUN
ejpam-5889	317	2	.	.	PROPN
ejpam-5889	317	3	,	,	PUNCT
ejpam-5889	317	4	4:1–18	4:1–18	NUM
ejpam-5889	317	5	,	,	PUNCT
ejpam-5889	317	6	2017	2017	NUM
ejpam-5889	317	7	.	.	PUNCT
ejpam-5889	318	1	[	[	X
ejpam-5889	318	2	30	30	NUM
ejpam-5889	318	3	]	]	X
ejpam-5889	318	4	p	p	X
ejpam-5889	318	5	a	a	DET
ejpam-5889	318	6	ejegwa	ejegwa	NOUN
ejpam-5889	318	7	and	and	CCONJ
ejpam-5889	318	8	a	a	DET
ejpam-5889	318	9	m	m	NOUN
ejpam-5889	318	10	ibrahim	ibrahim	NOUN
ejpam-5889	318	11	.	.	PUNCT
ejpam-5889	319	1	some	some	DET
ejpam-5889	319	2	group	group	NOUN
ejpam-5889	319	3	’s	’s	PART
ejpam-5889	319	4	analogous	analogous	ADJ
ejpam-5889	319	5	results	result	NOUN
ejpam-5889	319	6	in	in	ADP
ejpam-5889	319	7	multigroup	multigroup	ADJ
ejpam-5889	319	8	setting	setting	NOUN
ejpam-5889	319	9	.	.	PUNCT
ejpam-5889	320	1	ann	ann	PROPN
ejpam-5889	320	2	.	.	PUNCT
ejpam-5889	320	3	fuzzy	fuzzy	ADJ
ejpam-5889	320	4	math	math	NOUN
ejpam-5889	320	5	.	.	PUNCT
ejpam-5889	321	1	inform	inform	NOUN
ejpam-5889	321	2	.	.	PUNCT
ejpam-5889	321	3	,	,	PUNCT
ejpam-5889	321	4	17(3):231–245	17(3):231–245	PROPN
ejpam-5889	321	5	,	,	PUNCT
ejpam-5889	321	6	2019	2019	NUM
ejpam-5889	321	7	.	.	PUNCT
ejpam-5889	322	1	[	[	X
ejpam-5889	322	2	31	31	NUM
ejpam-5889	322	3	]	]	X
ejpam-5889	322	4	p	p	X
ejpam-5889	322	5	a	a	DET
ejpam-5889	322	6	ejegwa	ejegwa	NOUN
ejpam-5889	322	7	and	and	CCONJ
ejpam-5889	322	8	a	a	DET
ejpam-5889	322	9	m	m	NOUN
ejpam-5889	322	10	ibrahim	ibrahim	NOUN
ejpam-5889	322	11	.	.	PUNCT
ejpam-5889	323	1	some	some	DET
ejpam-5889	323	2	properties	property	NOUN
ejpam-5889	323	3	of	of	ADP
ejpam-5889	323	4	multigroups	multigroup	NOUN
ejpam-5889	323	5	.	.	PUNCT
ejpam-5889	324	1	palestine	palestine	PROPN
ejpam-5889	324	2	j.	j.	PROPN
ejpam-5889	324	3	math	math	PROPN
ejpam-5889	324	4	.	.	PUNCT
ejpam-5889	324	5	,	,	PUNCT
ejpam-5889	324	6	9(1):31–47	9(1):31–47	NUM
ejpam-5889	324	7	,	,	PUNCT
ejpam-5889	324	8	2020	2020	NUM
ejpam-5889	324	9	.	.	PUNCT
ejpam-5889	325	1	[	[	X
ejpam-5889	325	2	32	32	NUM
ejpam-5889	325	3	]	]	PUNCT
ejpam-5889	325	4	a	a	PRON
ejpam-5889	325	5	m	m	VERB
ejpam-5889	325	6	ibrahim	ibrahim	NOUN
ejpam-5889	325	7	and	and	CCONJ
ejpam-5889	325	8	p	p	X
ejpam-5889	325	9	a	a	DET
ejpam-5889	325	10	ejegwa	ejegwa	NOUN
ejpam-5889	325	11	.	.	PUNCT
ejpam-5889	326	1	multigroup	multigroup	PROPN
ejpam-5889	326	2	actions	action	NOUN
ejpam-5889	326	3	on	on	ADP
ejpam-5889	326	4	multiset	multiset	PROPN
ejpam-5889	326	5	.	.	PUNCT
ejpam-5889	327	1	ann	ann	PROPN
ejpam-5889	327	2	.	.	PUNCT
ejpam-5889	327	3	fuzzy	fuzzy	ADJ
ejpam-5889	327	4	math	math	NOUN
ejpam-5889	327	5	.	.	PUNCT
ejpam-5889	328	1	inform	inform	NOUN
ejpam-5889	328	2	.	.	PUNCT
ejpam-5889	328	3	,	,	PUNCT
ejpam-5889	328	4	14(5):515–526	14(5):515–526	PROPN
ejpam-5889	328	5	,	,	PUNCT
ejpam-5889	328	6	2017	2017	NUM
ejpam-5889	328	7	.	.	PUNCT
ejpam-5889	329	1	[	[	X
ejpam-5889	329	2	33	33	NUM
ejpam-5889	329	3	]	]	X
ejpam-5889	329	4	p	p	X
ejpam-5889	329	5	a	a	DET
ejpam-5889	329	6	ejegwa	ejegwa	NOUN
ejpam-5889	329	7	and	and	CCONJ
ejpam-5889	329	8	j	j	PROPN
ejpam-5889	329	9	m	m	NOUN
ejpam-5889	329	10	agbetayo	agbetayo	VERB
ejpam-5889	329	11	.	.	PUNCT
ejpam-5889	330	1	some	some	DET
ejpam-5889	330	2	results	result	VERB
ejpam-5889	330	3	on	on	ADP
ejpam-5889	330	4	commutators	commutator	NOUN
ejpam-5889	330	5	in	in	ADP
ejpam-5889	330	6	multigroup	multigroup	PROPN
ejpam-5889	330	7	framework	framework	NOUN
ejpam-5889	330	8	.	.	PUNCT
ejpam-5889	331	1	ramanujan	ramanujan	PROPN
ejpam-5889	331	2	soc	soc	PROPN
ejpam-5889	331	3	.	.	PUNCT
ejpam-5889	332	1	math	math	PROPN
ejpam-5889	332	2	.	.	PUNCT
ejpam-5889	333	1	mathemat	mathemat	PROPN
ejpam-5889	333	2	.	.	PUNCT
ejpam-5889	334	1	sci	sci	PROPN
ejpam-5889	334	2	.	.	PROPN
ejpam-5889	334	3	,	,	PUNCT
ejpam-5889	334	4	7(2):67–82	7(2):67–82	NUM
ejpam-5889	334	5	,	,	PUNCT
ejpam-5889	334	6	2020	2020	NUM
ejpam-5889	334	7	.	.	PUNCT
ejpam-5889	335	1	[	[	X
ejpam-5889	335	2	34	34	NUM
ejpam-5889	335	3	]	]	X
ejpam-5889	335	4	p	p	X
ejpam-5889	335	5	a	a	DET
ejpam-5889	335	6	ejegwa	ejegwa	NOUN
ejpam-5889	335	7	and	and	CCONJ
ejpam-5889	335	8	a	a	DET
ejpam-5889	335	9	m	m	NOUN
ejpam-5889	335	10	ibrahim	ibrahim	NOUN
ejpam-5889	335	11	.	.	PUNCT
ejpam-5889	336	1	on	on	ADP
ejpam-5889	336	2	divisible	divisible	ADJ
ejpam-5889	336	3	and	and	CCONJ
ejpam-5889	336	4	pure	pure	ADJ
ejpam-5889	336	5	multigroups	multigroup	NOUN
ejpam-5889	336	6	and	and	CCONJ
ejpam-5889	336	7	their	their	PRON
ejpam-5889	336	8	properties	property	NOUN
ejpam-5889	336	9	.	.	PUNCT
ejpam-5889	337	1	open	open	ADJ
ejpam-5889	337	2	j.	j.	PROPN
ejpam-5889	337	3	math	math	PROPN
ejpam-5889	337	4	.	.	PUNCT
ejpam-5889	338	1	sci	sci	PROPN
ejpam-5889	338	2	.	.	PROPN
ejpam-5889	338	3	,	,	PUNCT
ejpam-5889	338	4	4:377–385	4:377–385	PROPN
ejpam-5889	338	5	,	,	PUNCT
ejpam-5889	338	6	2020	2020	NUM
ejpam-5889	338	7	.	.	PUNCT
ejpam-5889	339	1	[	[	X
ejpam-5889	339	2	35	35	NUM
ejpam-5889	339	3	]	]	SYM
ejpam-5889	339	4	s	s	PART
ejpam-5889	339	5	debnath	debnath	NOUN
ejpam-5889	339	6	and	and	CCONJ
ejpam-5889	339	7	a	a	DET
ejpam-5889	339	8	debnath	debnath	NOUN
ejpam-5889	339	9	.	.	PUNCT
ejpam-5889	340	1	study	study	NOUN
ejpam-5889	340	2	of	of	ADP
ejpam-5889	340	3	ring	ring	NOUN
ejpam-5889	340	4	structure	structure	NOUN
ejpam-5889	340	5	from	from	ADP
ejpam-5889	340	6	multiset	multiset	ADJ
ejpam-5889	340	7	context	context	NOUN
ejpam-5889	340	8	.	.	PUNCT
ejpam-5889	341	1	applied	apply	VERB
ejpam-5889	341	2	sci	sci	PROPN
ejpam-5889	341	3	.	.	PROPN
ejpam-5889	341	4	,	,	PUNCT
ejpam-5889	341	5	21:84–90	21:84–90	NUM
ejpam-5889	341	6	,	,	PUNCT
ejpam-5889	341	7	2019	2019	NUM
ejpam-5889	341	8	.	.	PUNCT
ejpam-5889	342	1	[	[	X
ejpam-5889	342	2	36	36	NUM
ejpam-5889	342	3	]	]	X
ejpam-5889	342	4	p	p	X
ejpam-5889	342	5	a	a	DET
ejpam-5889	342	6	ejegwa	ejegwa	NOUN
ejpam-5889	342	7	.	.	PUNCT
ejpam-5889	343	1	concept	concept	NOUN
ejpam-5889	343	2	of	of	ADP
ejpam-5889	343	3	anti	anti	ADJ
ejpam-5889	343	4	multigroups	multigroup	NOUN
ejpam-5889	343	5	and	and	CCONJ
ejpam-5889	343	6	its	its	PRON
ejpam-5889	343	7	properties	property	NOUN
ejpam-5889	343	8	.	.	PUNCT
ejpam-5889	344	1	earthline	earthline	PROPN
ejpam-5889	344	2	j.	j.	PROPN
ejpam-5889	344	3	math	math	PROPN
ejpam-5889	344	4	.	.	PUNCT
ejpam-5889	345	1	sci	sci	PROPN
ejpam-5889	345	2	.	.	PROPN
ejpam-5889	345	3	,	,	PUNCT
ejpam-5889	345	4	4(1):83–97	4(1):83–97	NUM
ejpam-5889	345	5	,	,	PUNCT
ejpam-5889	345	6	2020	2020	NUM
ejpam-5889	345	7	.	.	PUNCT
ejpam-5889	346	1	[	[	X
ejpam-5889	346	2	37	37	NUM
ejpam-5889	346	3	]	]	X
ejpam-5889	346	4	p	p	PROPN
ejpam-5889	346	5	suma	suma	PROPN
ejpam-5889	346	6	and	and	CCONJ
ejpam-5889	346	7	s	s	PROPN
ejpam-5889	346	8	j	j	PROPN
ejpam-5889	346	9	john	john	PROPN
ejpam-5889	346	10	.	.	PUNCT
ejpam-5889	347	1	multiset	multiset	PROPN
ejpam-5889	347	2	approach	approach	NOUN
ejpam-5889	347	3	to	to	ADP
ejpam-5889	347	4	algebraic	algebraic	ADJ
ejpam-5889	347	5	structures	structure	NOUN
ejpam-5889	347	6	,	,	PUNCT
ejpam-5889	347	7	in	in	ADP
ejpam-5889	347	8	:	:	PUNCT
ejpam-5889	347	9	jana	jana	PROPN
ejpam-5889	347	10	,	,	PUNCT
ejpam-5889	347	11	c.	c.	PROPN
ejpam-5889	347	12	,	,	PUNCT
ejpam-5889	347	13	senapati	senapati	NOUN
ejpam-5889	347	14	,	,	PUNCT
ejpam-5889	347	15	t.	t.	NOUN
ejpam-5889	347	16	pal	pal	NOUN
ejpam-5889	347	17	,	,	PUNCT
ejpam-5889	347	18	m.	m.	NOUN
ejpam-5889	347	19	(	(	PUNCT
ejpam-5889	347	20	eds	ed	NOUN
ejpam-5889	347	21	.	.	PUNCT
ejpam-5889	347	22	)	)	PUNCT
ejpam-5889	347	23	;	;	PUNCT
ejpam-5889	347	24	handbook	handbook	NOUN
ejpam-5889	347	25	of	of	ADP
ejpam-5889	347	26	research	research	NOUN
ejpam-5889	347	27	on	on	ADP
ejpam-5889	347	28	emerging	emerge	VERB
ejpam-5889	347	29	applications	application	NOUN
ejpam-5889	347	30	of	of	ADP
ejpam-5889	347	31	fuzzy	fuzzy	ADJ
ejpam-5889	347	32	algebraic	algebraic	ADJ
ejpam-5889	347	33	structures	structure	NOUN
ejpam-5889	347	34	.	.	PUNCT
ejpam-5889	348	1	igi	igi	PROPN
ejpam-5889	348	2	global	global	PROPN
ejpam-5889	348	3	publisher	publisher	PROPN
ejpam-5889	348	4	,	,	PUNCT
ejpam-5889	348	5	hershey	hershey	PROPN
ejpam-5889	348	6	,	,	PUNCT
ejpam-5889	348	7	pennsylvania	pennsylvania	PROPN
ejpam-5889	348	8	17033	17033	NUM
ejpam-5889	348	9	-	-	SYM
ejpam-5889	348	10	1240	1240	NUM
ejpam-5889	348	11	,	,	PUNCT
ejpam-5889	348	12	usa	usa	PROPN
ejpam-5889	348	13	,	,	PUNCT
ejpam-5889	348	14	78	78	NUM
ejpam-5889	348	15	-	-	SYM
ejpam-5889	348	16	90	90	NUM
ejpam-5889	348	17	,	,	PUNCT
ejpam-5889	348	18	2020	2020	NUM
ejpam-5889	348	19	.	.	PUNCT
ejpam-5889	349	1	[	[	X
ejpam-5889	349	2	38	38	NUM
ejpam-5889	349	3	]	]	SYM
ejpam-5889	349	4	b	b	PROPN
ejpam-5889	349	5	c	c	X
ejpam-5889	349	6	tripathy	tripathy	PROPN
ejpam-5889	349	7	,	,	PUNCT
ejpam-5889	349	8	s	s	VERB
ejpam-5889	349	9	debnath	debnath	NOUN
ejpam-5889	349	10	,	,	PUNCT
ejpam-5889	349	11	and	and	CCONJ
ejpam-5889	349	12	d	d	ADP
ejpam-5889	349	13	rakshit	rakshit	NOUN
ejpam-5889	349	14	.	.	PUNCT
ejpam-5889	350	1	on	on	ADP
ejpam-5889	350	2	multiset	multiset	PROPN
ejpam-5889	350	3	group	group	NOUN
ejpam-5889	350	4	.	.	PUNCT
ejpam-5889	351	1	proyecciones	proyecciones	PROPN
ejpam-5889	351	2	j.	j.	PROPN
ejpam-5889	351	3	math	math	PROPN
ejpam-5889	351	4	.	.	PROPN
ejpam-5889	351	5	,	,	PUNCT
ejpam-5889	351	6	37(3):479–489	37(3):479–489	PROPN
ejpam-5889	351	7	,	,	PUNCT
ejpam-5889	351	8	2018	2018	NUM
ejpam-5889	351	9	.	.	PUNCT
ejpam-5889	352	1	[	[	X
ejpam-5889	352	2	39	39	NUM
ejpam-5889	352	3	]	]	PUNCT
ejpam-5889	352	4	p	p	X
ejpam-5889	352	5	a	a	DET
ejpam-5889	352	6	ejegwa	ejegwa	NOUN
ejpam-5889	352	7	,	,	PUNCT
ejpam-5889	352	8	j	j	PROPN
ejpam-5889	352	9	m	m	NOUN
ejpam-5889	352	10	agbetayo	agbetayo	NOUN
ejpam-5889	352	11	,	,	PUNCT
ejpam-5889	352	12	j	j	PROPN
ejpam-5889	352	13	a	a	DET
ejpam-5889	352	14	agba	agba	PROPN
ejpam-5889	352	15	,	,	PUNCT
ejpam-5889	352	16	and	and	CCONJ
ejpam-5889	352	17	i	i	PRON
ejpam-5889	352	18	m	m	PROPN
ejpam-5889	352	19	adamu	adamu	PROPN
ejpam-5889	352	20	.	.	PUNCT
ejpam-5889	353	1	solvable	solvable	PROPN
ejpam-5889	353	2	multigroup	multigroup	PROPN
ejpam-5889	353	3	and	and	CCONJ
ejpam-5889	353	4	its	its	PRON
ejpam-5889	353	5	properties	property	NOUN
ejpam-5889	353	6	.	.	PUNCT
ejpam-5889	354	1	bull	bull	NOUN
ejpam-5889	354	2	.	.	PUNCT
ejpam-5889	355	1	int	int	NOUN
ejpam-5889	355	2	.	.	PUNCT
ejpam-5889	356	1	math	math	NOUN
ejpam-5889	356	2	.	.	PUNCT
ejpam-5889	357	1	virtual	virtual	ADJ
ejpam-5889	357	2	inst	inst	PROPN
ejpam-5889	357	3	.	.	PROPN
ejpam-5889	357	4	,	,	PUNCT
ejpam-5889	357	5	13(2):375–381	13(2):375–381	PROPN
ejpam-5889	357	6	,	,	PUNCT
ejpam-5889	357	7	2023	2023	NUM
ejpam-5889	357	8	.	.	PUNCT