id	sid	tid	token	lemma	pos
ejpam-2822	1	1	european	european	PROPN
ejpam-2822	1	2	journal	journal	PROPN
ejpam-2822	1	3	of	of	ADP
ejpam-2822	1	4	pure	pure	ADJ
ejpam-2822	1	5	and	and	CCONJ
ejpam-2822	1	6	applied	apply	VERB
ejpam-2822	1	7	mathematics	mathematic	NOUN
ejpam-2822	1	8	vol	vol	NOUN
ejpam-2822	1	9	.	.	PROPN
ejpam-2822	2	1	10	10	NUM
ejpam-2822	2	2	,	,	PUNCT
ejpam-2822	2	3	no	no	INTJ
ejpam-2822	2	4	.	.	NOUN
ejpam-2822	2	5	2	2	NUM
ejpam-2822	2	6	,	,	PUNCT
ejpam-2822	2	7	2017	2017	NUM
ejpam-2822	2	8	,	,	PUNCT
ejpam-2822	2	9	255	255	NUM
ejpam-2822	2	10	-	-	SYM
ejpam-2822	2	11	271	271	NUM
ejpam-2822	2	12	issn	issn	PROPN
ejpam-2822	2	13	1307	1307	NUM
ejpam-2822	2	14	-	-	SYM
ejpam-2822	2	15	5543	5543	NUM
ejpam-2822	2	16	–	–	PUNCT
ejpam-2822	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2822	2	18	published	publish	VERB
ejpam-2822	2	19	by	by	ADP
ejpam-2822	2	20	new	new	PROPN
ejpam-2822	2	21	york	york	PROPN
ejpam-2822	2	22	business	business	PROPN
ejpam-2822	2	23	global	global	ADJ
ejpam-2822	2	24	nilpotent	nilpotent	PROPN
ejpam-2822	2	25	l	l	NOUN
ejpam-2822	2	26	-	-	NOUN
ejpam-2822	2	27	subgroups	subgroup	NOUN
ejpam-2822	2	28	and	and	CCONJ
ejpam-2822	2	29	the	the	DET
ejpam-2822	2	30	set	set	ADJ
ejpam-2822	2	31	product	product	NOUN
ejpam-2822	2	32	of	of	ADP
ejpam-2822	2	33	l	l	NOUN
ejpam-2822	2	34	-	-	PUNCT
ejpam-2822	2	35	subsets	subset	NOUN
ejpam-2822	2	36	naseem	naseem	PROPN
ejpam-2822	2	37	ajmal1	ajmal1	PROPN
ejpam-2822	2	38	,	,	PUNCT
ejpam-2822	2	39	iffat	iffat	NOUN
ejpam-2822	2	40	jahan2,∗	jahan2,∗	PROPN
ejpam-2822	2	41	,	,	PUNCT
ejpam-2822	2	42	bijan	bijan	NOUN
ejpam-2822	2	43	davvaz3	davvaz3	ADJ
ejpam-2822	2	44	1	1	NUM
ejpam-2822	2	45	department	department	NOUN
ejpam-2822	2	46	of	of	ADP
ejpam-2822	2	47	mathematics	mathematic	NOUN
ejpam-2822	2	48	,	,	PUNCT
ejpam-2822	2	49	zakir	zakir	PROPN
ejpam-2822	2	50	husain	husain	PROPN
ejpam-2822	2	51	college	college	PROPN
ejpam-2822	2	52	,	,	PUNCT
ejpam-2822	2	53	university	university	NOUN
ejpam-2822	2	54	of	of	ADP
ejpam-2822	2	55	delhi	delhi	PROPN
ejpam-2822	2	56	,	,	PUNCT
ejpam-2822	2	57	delhi	delhi	PROPN
ejpam-2822	2	58	,	,	PUNCT
ejpam-2822	2	59	india	india	PROPN
ejpam-2822	2	60	2	2	NUM
ejpam-2822	2	61	department	department	NOUN
ejpam-2822	2	62	of	of	ADP
ejpam-2822	2	63	mathematics	mathematics	PROPN
ejpam-2822	2	64	,	,	PUNCT
ejpam-2822	2	65	ramjas	ramjas	PROPN
ejpam-2822	2	66	college	college	PROPN
ejpam-2822	2	67	,	,	PUNCT
ejpam-2822	2	68	university	university	NOUN
ejpam-2822	2	69	of	of	ADP
ejpam-2822	2	70	delhi	delhi	PROPN
ejpam-2822	2	71	,	,	PUNCT
ejpam-2822	2	72	delhi	delhi	PROPN
ejpam-2822	2	73	,	,	PUNCT
ejpam-2822	2	74	india	india	PROPN
ejpam-2822	2	75	3	3	NUM
ejpam-2822	2	76	department	department	NOUN
ejpam-2822	2	77	of	of	ADP
ejpam-2822	2	78	mathematics	mathematics	PROPN
ejpam-2822	2	79	,	,	PUNCT
ejpam-2822	2	80	yazd	yazd	PROPN
ejpam-2822	2	81	university	university	PROPN
ejpam-2822	2	82	,	,	PUNCT
ejpam-2822	2	83	iran	iran	PROPN
ejpam-2822	2	84	abstract	abstract	ADJ
ejpam-2822	2	85	.	.	PUNCT
ejpam-2822	3	1	in	in	ADP
ejpam-2822	3	2	this	this	DET
ejpam-2822	3	3	paper	paper	NOUN
ejpam-2822	3	4	,	,	PUNCT
ejpam-2822	3	5	we	we	PRON
ejpam-2822	3	6	study	study	VERB
ejpam-2822	3	7	the	the	DET
ejpam-2822	3	8	set	set	NOUN
ejpam-2822	3	9	product	product	NOUN
ejpam-2822	3	10	of	of	ADP
ejpam-2822	3	11	a	a	DET
ejpam-2822	3	12	pair	pair	NOUN
ejpam-2822	3	13	of	of	ADP
ejpam-2822	3	14	nilpotent	nilpotent	ADJ
ejpam-2822	3	15	normal	normal	ADJ
ejpam-2822	3	16	l	l	NOUN
ejpam-2822	3	17	-	-	NOUN
ejpam-2822	3	18	subgroups	subgroup	NOUN
ejpam-2822	3	19	of	of	ADP
ejpam-2822	3	20	a	a	DET
ejpam-2822	3	21	given	give	VERB
ejpam-2822	3	22	l	l	NOUN
ejpam-2822	3	23	-	-	NOUN
ejpam-2822	3	24	group	group	NOUN
ejpam-2822	3	25	.	.	PUNCT
ejpam-2822	4	1	a	a	DET
ejpam-2822	4	2	necessary	necessary	ADJ
ejpam-2822	4	3	mechanism	mechanism	NOUN
ejpam-2822	4	4	is	be	AUX
ejpam-2822	4	5	developed	develop	VERB
ejpam-2822	4	6	in	in	ADP
ejpam-2822	4	7	order	order	NOUN
ejpam-2822	4	8	to	to	PART
ejpam-2822	4	9	establish	establish	VERB
ejpam-2822	4	10	this	this	DET
ejpam-2822	4	11	result	result	NOUN
ejpam-2822	4	12	.	.	PUNCT
ejpam-2822	5	1	moreover	moreover	ADV
ejpam-2822	5	2	,	,	PUNCT
ejpam-2822	5	3	the	the	DET
ejpam-2822	5	4	tail	tail	NOUN
ejpam-2822	5	5	of	of	ADP
ejpam-2822	5	6	l	l	NOUN
ejpam-2822	5	7	-	-	NOUN
ejpam-2822	5	8	subgroups	subgroup	NOUN
ejpam-2822	5	9	is	be	AUX
ejpam-2822	5	10	used	use	VERB
ejpam-2822	5	11	effectively	effectively	ADV
ejpam-2822	5	12	while	while	SCONJ
ejpam-2822	5	13	developing	develop	VERB
ejpam-2822	5	14	this	this	DET
ejpam-2822	5	15	mechanism	mechanism	NOUN
ejpam-2822	5	16	.	.	PUNCT
ejpam-2822	6	1	2010	2010	NUM
ejpam-2822	6	2	mathematics	mathematic	NOUN
ejpam-2822	6	3	subject	subject	NOUN
ejpam-2822	6	4	classifications	classification	NOUN
ejpam-2822	6	5	:	:	PUNCT
ejpam-2822	6	6	ams	am	NOUN
ejpam-2822	6	7	classification	classification	NOUN
ejpam-2822	6	8	codes	code	VERB
ejpam-2822	6	9	key	key	ADJ
ejpam-2822	6	10	words	word	NOUN
ejpam-2822	6	11	and	and	CCONJ
ejpam-2822	6	12	phrases	phrase	NOUN
ejpam-2822	6	13	:	:	PUNCT
ejpam-2822	6	14	l	l	NOUN
ejpam-2822	6	15	-	-	NOUN
ejpam-2822	6	16	algebra	algebra	NOUN
ejpam-2822	6	17	;	;	PUNCT
ejpam-2822	6	18	l	l	NOUN
ejpam-2822	6	19	-	-	NOUN
ejpam-2822	6	20	subgroup	subgroup	NOUN
ejpam-2822	6	21	;	;	PUNCT
ejpam-2822	6	22	generated	generate	VERB
ejpam-2822	6	23	l	l	PROPN
ejpam-2822	6	24	-	-	NOUN
ejpam-2822	6	25	subgroup	subgroup	NOUN
ejpam-2822	6	26	;	;	PUNCT
ejpam-2822	6	27	normal	normal	ADJ
ejpam-2822	6	28	l	l	NOUN
ejpam-2822	6	29	-	-	NOUN
ejpam-2822	6	30	subgroup	subgroup	NOUN
ejpam-2822	6	31	;	;	PUNCT
ejpam-2822	6	32	nilpotent	nilpotent	ADJ
ejpam-2822	6	33	l	l	PROPN
ejpam-2822	6	34	-	-	NOUN
ejpam-2822	6	35	subgroup	subgroup	NOUN
ejpam-2822	6	36	.	.	PUNCT
ejpam-2822	7	1	1	1	X
ejpam-2822	7	2	.	.	X
ejpam-2822	7	3	introduction	introduction	NOUN
ejpam-2822	7	4	rosenfeld	rosenfeld	PROPN
ejpam-2822	7	5	[	[	X
ejpam-2822	7	6	14	14	NUM
ejpam-2822	7	7	]	]	PUNCT
ejpam-2822	7	8	applied	apply	VERB
ejpam-2822	7	9	the	the	DET
ejpam-2822	7	10	notion	notion	NOUN
ejpam-2822	7	11	of	of	ADP
ejpam-2822	7	12	fuzzy	fuzzy	ADJ
ejpam-2822	7	13	subsets	subset	NOUN
ejpam-2822	7	14	in	in	ADP
ejpam-2822	7	15	algebra	algebra	NOUN
ejpam-2822	7	16	and	and	CCONJ
ejpam-2822	7	17	introduced	introduce	VERB
ejpam-2822	7	18	the	the	DET
ejpam-2822	7	19	concept	concept	NOUN
ejpam-2822	7	20	of	of	ADP
ejpam-2822	7	21	fuzzy	fuzzy	ADJ
ejpam-2822	7	22	subgroups	subgroup	NOUN
ejpam-2822	7	23	in	in	ADP
ejpam-2822	7	24	1971	1971	NUM
ejpam-2822	7	25	.	.	PUNCT
ejpam-2822	8	1	as	as	ADP
ejpam-2822	8	2	a	a	DET
ejpam-2822	8	3	result	result	NOUN
ejpam-2822	8	4	a	a	DET
ejpam-2822	8	5	new	new	ADJ
ejpam-2822	8	6	discipline	discipline	NOUN
ejpam-2822	8	7	of	of	ADP
ejpam-2822	8	8	fuzzy	fuzzy	ADJ
ejpam-2822	8	9	algebraic	algebraic	ADJ
ejpam-2822	8	10	structures	structure	NOUN
ejpam-2822	8	11	emerged	emerge	VERB
ejpam-2822	8	12	which	which	PRON
ejpam-2822	8	13	contains	contain	VERB
ejpam-2822	8	14	the	the	DET
ejpam-2822	8	15	extensions	extension	NOUN
ejpam-2822	8	16	of	of	ADP
ejpam-2822	8	17	various	various	ADJ
ejpam-2822	8	18	concepts	concept	NOUN
ejpam-2822	8	19	and	and	CCONJ
ejpam-2822	8	20	notions	notion	NOUN
ejpam-2822	8	21	of	of	ADP
ejpam-2822	8	22	classical	classical	ADJ
ejpam-2822	8	23	algebra	algebra	NOUN
ejpam-2822	8	24	.	.	PUNCT
ejpam-2822	9	1	however	however	ADV
ejpam-2822	9	2	,	,	PUNCT
ejpam-2822	9	3	the	the	DET
ejpam-2822	9	4	progress	progress	NOUN
ejpam-2822	9	5	of	of	ADP
ejpam-2822	9	6	this	this	DET
ejpam-2822	9	7	discipline	discipline	NOUN
ejpam-2822	9	8	could	could	AUX
ejpam-2822	9	9	not	not	PART
ejpam-2822	9	10	sustain	sustain	VERB
ejpam-2822	9	11	the	the	DET
ejpam-2822	9	12	impact	impact	NOUN
ejpam-2822	9	13	of	of	ADP
ejpam-2822	9	14	metatheorem	metatheorem	ADJ
ejpam-2822	9	15	which	which	PRON
ejpam-2822	9	16	was	be	AUX
ejpam-2822	9	17	developed	develop	VERB
ejpam-2822	9	18	by	by	ADP
ejpam-2822	9	19	tom	tom	PROPN
ejpam-2822	9	20	head	head	PROPN
ejpam-2822	9	21	[	[	X
ejpam-2822	9	22	8	8	NUM
ejpam-2822	9	23	]	]	PUNCT
ejpam-2822	9	24	during	during	ADP
ejpam-2822	9	25	the	the	DET
ejpam-2822	9	26	year	year	NOUN
ejpam-2822	9	27	1995	1995	NUM
ejpam-2822	9	28	.	.	PUNCT
ejpam-2822	10	1	this	this	PRON
ejpam-2822	10	2	is	be	AUX
ejpam-2822	10	3	due	due	ADJ
ejpam-2822	10	4	to	to	ADP
ejpam-2822	10	5	the	the	DET
ejpam-2822	10	6	fact	fact	NOUN
ejpam-2822	10	7	that	that	SCONJ
ejpam-2822	10	8	the	the	DET
ejpam-2822	10	9	various	various	ADJ
ejpam-2822	10	10	notions	notion	NOUN
ejpam-2822	10	11	and	and	CCONJ
ejpam-2822	10	12	concepts	concept	NOUN
ejpam-2822	10	13	formulated	formulate	VERB
ejpam-2822	10	14	in	in	ADP
ejpam-2822	10	15	the	the	DET
ejpam-2822	10	16	areas	area	NOUN
ejpam-2822	10	17	of	of	ADP
ejpam-2822	10	18	fuzzy	fuzzy	ADJ
ejpam-2822	10	19	semigroups	semigroup	NOUN
ejpam-2822	10	20	,	,	PUNCT
ejpam-2822	10	21	fuzzy	fuzzy	ADJ
ejpam-2822	10	22	groups	group	NOUN
ejpam-2822	10	23	and	and	CCONJ
ejpam-2822	10	24	fuzzy	fuzzy	ADJ
ejpam-2822	10	25	rings	ring	NOUN
ejpam-2822	10	26	are	be	AUX
ejpam-2822	10	27	generically	generically	ADV
ejpam-2822	10	28	defined	define	VERB
ejpam-2822	10	29	and	and	CCONJ
ejpam-2822	10	30	hence	hence	ADV
ejpam-2822	10	31	the	the	DET
ejpam-2822	10	32	extension	extension	NOUN
ejpam-2822	10	33	of	of	ADP
ejpam-2822	10	34	results	result	NOUN
ejpam-2822	10	35	from	from	ADP
ejpam-2822	10	36	classical	classical	ADJ
ejpam-2822	10	37	algebra	algebra	NOUN
ejpam-2822	10	38	to	to	ADP
ejpam-2822	10	39	fuzzy	fuzzy	ADJ
ejpam-2822	10	40	algebra	algebra	NOUN
ejpam-2822	10	41	became	become	VERB
ejpam-2822	10	42	just	just	ADV
ejpam-2822	10	43	simple	simple	ADJ
ejpam-2822	10	44	instances	instance	NOUN
ejpam-2822	10	45	of	of	ADP
ejpam-2822	10	46	this	this	DET
ejpam-2822	10	47	indigenous	indigenous	ADJ
ejpam-2822	10	48	result	result	NOUN
ejpam-2822	10	49	.	.	PUNCT
ejpam-2822	11	1	therefore	therefore	ADV
ejpam-2822	11	2	for	for	ADP
ejpam-2822	11	3	further	further	ADJ
ejpam-2822	11	4	growth	growth	NOUN
ejpam-2822	11	5	of	of	ADP
ejpam-2822	11	6	the	the	DET
ejpam-2822	11	7	subject	subject	NOUN
ejpam-2822	11	8	,	,	PUNCT
ejpam-2822	11	9	a	a	DET
ejpam-2822	11	10	need	need	NOUN
ejpam-2822	11	11	was	be	AUX
ejpam-2822	11	12	felt	feel	VERB
ejpam-2822	11	13	to	to	PART
ejpam-2822	11	14	develop	develop	VERB
ejpam-2822	11	15	a	a	DET
ejpam-2822	11	16	framework	framework	NOUN
ejpam-2822	11	17	for	for	ADP
ejpam-2822	11	18	these	these	DET
ejpam-2822	11	19	investigations	investigation	NOUN
ejpam-2822	11	20	which	which	PRON
ejpam-2822	11	21	is	be	AUX
ejpam-2822	11	22	beyond	beyond	ADP
ejpam-2822	11	23	the	the	DET
ejpam-2822	11	24	purview	purview	NOUN
ejpam-2822	11	25	of	of	ADP
ejpam-2822	11	26	the	the	DET
ejpam-2822	11	27	metatheorem	metatheorem	PROPN
ejpam-2822	11	28	.	.	PUNCT
ejpam-2822	12	1	the	the	DET
ejpam-2822	12	2	notion	notion	NOUN
ejpam-2822	12	3	of	of	ADP
ejpam-2822	12	4	lattice	lattice	PROPN
ejpam-2822	12	5	valued	value	VERB
ejpam-2822	12	6	fuzzy	fuzzy	ADJ
ejpam-2822	12	7	subsets	subset	NOUN
ejpam-2822	12	8	was	be	AUX
ejpam-2822	12	9	introduced	introduce	VERB
ejpam-2822	12	10	by	by	ADP
ejpam-2822	12	11	goguen	goguen	PROPN
ejpam-2822	13	1	[	[	X
ejpam-2822	13	2	7	7	X
ejpam-2822	13	3	]	]	PUNCT
ejpam-2822	13	4	in	in	ADP
ejpam-2822	13	5	the	the	DET
ejpam-2822	13	6	year	year	NOUN
ejpam-2822	13	7	1967	1967	NUM
ejpam-2822	13	8	which	which	PRON
ejpam-2822	13	9	was	be	AUX
ejpam-2822	13	10	later	later	ADV
ejpam-2822	13	11	applied	apply	VERB
ejpam-2822	13	12	by	by	ADP
ejpam-2822	13	13	wang	wang	PROPN
ejpam-2822	13	14	jin	jin	PROPN
ejpam-2822	13	15	liu	liu	PROPN
ejpam-2822	14	1	[	[	X
ejpam-2822	14	2	10	10	NUM
ejpam-2822	14	3	]	]	PUNCT
ejpam-2822	14	4	to	to	PART
ejpam-2822	14	5	define	define	VERB
ejpam-2822	14	6	the	the	DET
ejpam-2822	14	7	notions	notion	NOUN
ejpam-2822	14	8	of	of	ADP
ejpam-2822	14	9	lattice	lattice	PROPN
ejpam-2822	14	10	valued	value	VERB
ejpam-2822	14	11	fuzzy	fuzzy	ADJ
ejpam-2822	14	12	subgroup	subgroup	NOUN
ejpam-2822	14	13	of	of	ADP
ejpam-2822	14	14	a	a	DET
ejpam-2822	14	15	group	group	NOUN
ejpam-2822	14	16	and	and	CCONJ
ejpam-2822	14	17	lattice	lattice	NOUN
ejpam-2822	14	18	valued	value	VERB
ejpam-2822	14	19	ideals	ideal	NOUN
ejpam-2822	14	20	of	of	ADP
ejpam-2822	14	21	a	a	DET
ejpam-2822	14	22	ring	ring	NOUN
ejpam-2822	14	23	.	.	PUNCT
ejpam-2822	15	1	it	it	PRON
ejpam-2822	15	2	is	be	AUX
ejpam-2822	15	3	in	in	ADP
ejpam-2822	15	4	this	this	DET
ejpam-2822	15	5	framework	framework	NOUN
ejpam-2822	15	6	that	that	SCONJ
ejpam-2822	15	7	the	the	DET
ejpam-2822	15	8	notions	notion	NOUN
ejpam-2822	15	9	and	and	CCONJ
ejpam-2822	15	10	the	the	DET
ejpam-2822	15	11	concepts	concept	NOUN
ejpam-2822	15	12	extended	extend	VERB
ejpam-2822	15	13	from	from	ADP
ejpam-2822	15	14	classical	classical	ADJ
ejpam-2822	15	15	algebra	algebra	NOUN
ejpam-2822	15	16	do	do	AUX
ejpam-2822	15	17	not	not	PART
ejpam-2822	15	18	remain	remain	VERB
ejpam-2822	15	19	projection	projection	NOUN
ejpam-2822	15	20	closed	close	VERB
ejpam-2822	15	21	which	which	PRON
ejpam-2822	15	22	is	be	AUX
ejpam-2822	15	23	a	a	DET
ejpam-2822	15	24	prerequisite	prerequisite	NOUN
ejpam-2822	15	25	for	for	ADP
ejpam-2822	15	26	an	an	DET
ejpam-2822	15	27	application	application	NOUN
ejpam-2822	15	28	of	of	ADP
ejpam-2822	15	29	tom	tom	PROPN
ejpam-2822	15	30	head	head	NOUN
ejpam-2822	15	31	metatheorem	metatheorem	VERB
ejpam-2822	15	32	.	.	PUNCT
ejpam-2822	16	1	the	the	DET
ejpam-2822	16	2	theory	theory	NOUN
ejpam-2822	16	3	of	of	ADP
ejpam-2822	16	4	l	l	NOUN
ejpam-2822	16	5	-	-	NOUN
ejpam-2822	16	6	subrings	subring	NOUN
ejpam-2822	16	7	is	be	AUX
ejpam-2822	16	8	sufficiently	sufficiently	ADV
ejpam-2822	16	9	developed	develop	VERB
ejpam-2822	16	10	by	by	ADP
ejpam-2822	16	11	mordeson	mordeson	NOUN
ejpam-2822	16	12	and	and	CCONJ
ejpam-2822	16	13	malik	malik	PROPN
ejpam-2822	17	1	[	[	X
ejpam-2822	17	2	13	13	NUM
ejpam-2822	17	3	]	]	PUNCT
ejpam-2822	17	4	along	along	ADP
ejpam-2822	17	5	with	with	ADP
ejpam-2822	17	6	several	several	ADJ
ejpam-2822	17	7	other	other	ADJ
ejpam-2822	17	8	researchers	researcher	NOUN
ejpam-2822	17	9	[	[	X
ejpam-2822	17	10	11	11	NUM
ejpam-2822	17	11	,	,	PUNCT
ejpam-2822	17	12	12	12	NUM
ejpam-2822	17	13	]	]	PUNCT
ejpam-2822	17	14	.	.	PUNCT
ejpam-2822	18	1	however	however	ADV
ejpam-2822	18	2	,	,	PUNCT
ejpam-2822	18	3	in	in	ADP
ejpam-2822	18	4	the	the	DET
ejpam-2822	18	5	area	area	NOUN
ejpam-2822	18	6	of	of	ADP
ejpam-2822	18	7	fuzzy	fuzzy	ADJ
ejpam-2822	18	8	groups	group	NOUN
ejpam-2822	18	9	such	such	DET
ejpam-2822	18	10	an	an	DET
ejpam-2822	18	11	effort	effort	NOUN
ejpam-2822	18	12	is	be	AUX
ejpam-2822	18	13	found	find	VERB
ejpam-2822	18	14	lacking	lack	VERB
ejpam-2822	18	15	.	.	PUNCT
ejpam-2822	19	1	this	this	DET
ejpam-2822	19	2	∗corresponding	∗corresponde	VERB
ejpam-2822	19	3	author	author	NOUN
ejpam-2822	19	4	.	.	PUNCT
ejpam-2822	20	1	email	email	NOUN
ejpam-2822	20	2	addresses	address	NOUN
ejpam-2822	20	3	:	:	PUNCT
ejpam-2822	20	4	nasajmal@yahoo.com	nasajmal@yahoo.com	X
ejpam-2822	20	5	(	(	PUNCT
ejpam-2822	20	6	n.	n.	NOUN
ejpam-2822	20	7	ajmal	ajmal	PROPN
ejpam-2822	20	8	)	)	PUNCT
ejpam-2822	20	9	,	,	PUNCT
ejpam-2822	20	10	ij.umar@yahoo.com	ij.umar@yahoo.com	PROPN
ejpam-2822	20	11	(	(	PUNCT
ejpam-2822	20	12	i.	i.	PROPN
ejpam-2822	20	13	jahan	jahan	PROPN
ejpam-2822	20	14	)	)	PUNCT
ejpam-2822	20	15	,	,	PUNCT
ejpam-2822	20	16	davvaz@yazd.ac.ir	davvaz@yazd.ac.ir	PROPN
ejpam-2822	20	17	(	(	PUNCT
ejpam-2822	20	18	b.	b.	PROPN
ejpam-2822	20	19	davvaz	davvaz	PROPN
ejpam-2822	20	20	)	)	PUNCT
ejpam-2822	20	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2822	21	1	255	255	NUM
ejpam-2822	22	1	c	c	X
ejpam-2822	22	2	©	©	PROPN
ejpam-2822	22	3	2017	2017	NUM
ejpam-2822	22	4	ejpam	ejpam	VERB
ejpam-2822	22	5	all	all	DET
ejpam-2822	22	6	rights	right	NOUN
ejpam-2822	22	7	reserved	reserve	VERB
ejpam-2822	22	8	.	.	PUNCT
ejpam-2822	23	1	i.	i.	PROPN
ejpam-2822	23	2	jahan	jahan	PROPN
ejpam-2822	23	3	,	,	PUNCT
ejpam-2822	23	4	n.	n.	PROPN
ejpam-2822	23	5	ajmal	ajmal	PROPN
ejpam-2822	23	6	,	,	PUNCT
ejpam-2822	23	7	b.	b.	PROPN
ejpam-2822	23	8	davvaz	davvaz	PROPN
ejpam-2822	23	9	/	/	SYM
ejpam-2822	23	10	eur	eur	PROPN
ejpam-2822	23	11	.	.	PUNCT
ejpam-2822	24	1	j.	j.	PROPN
ejpam-2822	24	2	pure	pure	PROPN
ejpam-2822	24	3	appl	appl	PROPN
ejpam-2822	24	4	.	.	PROPN
ejpam-2822	24	5	math	math	PROPN
ejpam-2822	24	6	,	,	PUNCT
ejpam-2822	24	7	10	10	NUM
ejpam-2822	24	8	(	(	PUNCT
ejpam-2822	24	9	2	2	NUM
ejpam-2822	24	10	)	)	PUNCT
ejpam-2822	24	11	(	(	PUNCT
ejpam-2822	24	12	2017	2017	NUM
ejpam-2822	24	13	)	)	PUNCT
ejpam-2822	24	14	,	,	PUNCT
ejpam-2822	24	15	255	255	NUM
ejpam-2822	24	16	-	-	SYM
ejpam-2822	24	17	271	271	NUM
ejpam-2822	24	18	256	256	NUM
ejpam-2822	24	19	motivated	motivate	VERB
ejpam-2822	24	20	us	we	PRON
ejpam-2822	24	21	to	to	PART
ejpam-2822	24	22	formulate	formulate	VERB
ejpam-2822	24	23	several	several	ADJ
ejpam-2822	24	24	concepts	concept	NOUN
ejpam-2822	24	25	in	in	ADP
ejpam-2822	24	26	the	the	DET
ejpam-2822	24	27	studies	study	NOUN
ejpam-2822	24	28	of	of	ADP
ejpam-2822	24	29	lattice	lattice	PROPN
ejpam-2822	24	30	valued	value	VERB
ejpam-2822	24	31	fuzzy	fuzzy	ADJ
ejpam-2822	24	32	subgroups	subgroup	NOUN
ejpam-2822	24	33	(	(	PUNCT
ejpam-2822	24	34	l	l	NOUN
ejpam-2822	24	35	-	-	PUNCT
ejpam-2822	24	36	subgroups	subgroup	NOUN
ejpam-2822	24	37	)	)	PUNCT
ejpam-2822	24	38	which	which	PRON
ejpam-2822	24	39	appeared	appear	VERB
ejpam-2822	24	40	in	in	ADP
ejpam-2822	24	41	a	a	DET
ejpam-2822	24	42	series	series	NOUN
ejpam-2822	24	43	of	of	ADP
ejpam-2822	24	44	papers	paper	NOUN
ejpam-2822	24	45	[	[	X
ejpam-2822	24	46	2	2	NUM
ejpam-2822	24	47	,	,	PUNCT
ejpam-2822	24	48	3	3	NUM
ejpam-2822	24	49	,	,	PUNCT
ejpam-2822	24	50	4	4	NUM
ejpam-2822	24	51	,	,	PUNCT
ejpam-2822	24	52	5	5	NUM
ejpam-2822	24	53	,	,	PUNCT
ejpam-2822	24	54	6	6	NUM
ejpam-2822	24	55	]	]	PUNCT
ejpam-2822	24	56	.	.	PUNCT
ejpam-2822	25	1	in	in	ADP
ejpam-2822	25	2	all	all	DET
ejpam-2822	25	3	the	the	DET
ejpam-2822	25	4	above	above	ADV
ejpam-2822	25	5	mentioned	mention	VERB
ejpam-2822	25	6	papers	paper	NOUN
ejpam-2822	25	7	,	,	PUNCT
ejpam-2822	25	8	we	we	PRON
ejpam-2822	25	9	not	not	PART
ejpam-2822	25	10	only	only	ADV
ejpam-2822	25	11	replaced	replace	VERB
ejpam-2822	25	12	the	the	DET
ejpam-2822	25	13	evaluation	evaluation	NOUN
ejpam-2822	25	14	lattice	lattice	NOUN
ejpam-2822	26	1	[	[	X
ejpam-2822	26	2	0,1	0,1	NUM
ejpam-2822	26	3	]	]	PUNCT
ejpam-2822	26	4	by	by	ADP
ejpam-2822	26	5	a	a	DET
ejpam-2822	26	6	completely	completely	ADV
ejpam-2822	26	7	distributive	distributive	ADJ
ejpam-2822	26	8	lattice	lattice	NOUN
ejpam-2822	26	9	,	,	PUNCT
ejpam-2822	26	10	we	we	PRON
ejpam-2822	26	11	also	also	ADV
ejpam-2822	26	12	replaced	replace	VERB
ejpam-2822	26	13	the	the	DET
ejpam-2822	26	14	parent	parent	NOUN
ejpam-2822	26	15	structure	structure	NOUN
ejpam-2822	26	16	of	of	ADP
ejpam-2822	26	17	an	an	DET
ejpam-2822	26	18	ordinary	ordinary	ADJ
ejpam-2822	26	19	group	group	NOUN
ejpam-2822	26	20	by	by	ADP
ejpam-2822	26	21	an	an	DET
ejpam-2822	26	22	l	l	NOUN
ejpam-2822	26	23	-	-	NOUN
ejpam-2822	26	24	group	group	NOUN
ejpam-2822	26	25	.	.	PUNCT
ejpam-2822	27	1	therefore	therefore	ADV
ejpam-2822	27	2	an	an	DET
ejpam-2822	27	3	application	application	NOUN
ejpam-2822	27	4	of	of	ADP
ejpam-2822	27	5	metatheorem	metatheorem	VERB
ejpam-2822	27	6	in	in	ADP
ejpam-2822	27	7	our	our	PRON
ejpam-2822	27	8	studies	study	NOUN
ejpam-2822	27	9	become	become	VERB
ejpam-2822	27	10	further	far	ADV
ejpam-2822	27	11	remote	remote	ADJ
ejpam-2822	27	12	.	.	PUNCT
ejpam-2822	28	1	consequently	consequently	ADV
ejpam-2822	28	2	,	,	PUNCT
ejpam-2822	28	3	the	the	DET
ejpam-2822	28	4	normality	normality	NOUN
ejpam-2822	28	5	of	of	ADP
ejpam-2822	28	6	an	an	DET
ejpam-2822	28	7	l	l	NOUN
ejpam-2822	28	8	-	-	NOUN
ejpam-2822	28	9	subgroup	subgroup	NOUN
ejpam-2822	28	10	of	of	ADP
ejpam-2822	28	11	an	an	DET
ejpam-2822	28	12	l	l	NOUN
ejpam-2822	28	13	-	-	NOUN
ejpam-2822	28	14	group	group	NOUN
ejpam-2822	28	15	due	due	ADP
ejpam-2822	28	16	to	to	ADP
ejpam-2822	28	17	wu	wu	PROPN
ejpam-2822	28	18	has	have	AUX
ejpam-2822	28	19	been	be	AUX
ejpam-2822	28	20	used	use	VERB
ejpam-2822	28	21	in	in	ADP
ejpam-2822	28	22	these	these	DET
ejpam-2822	28	23	studies	study	NOUN
ejpam-2822	28	24	instead	instead	ADV
ejpam-2822	28	25	of	of	ADP
ejpam-2822	28	26	the	the	DET
ejpam-2822	28	27	concept	concept	NOUN
ejpam-2822	28	28	of	of	ADP
ejpam-2822	28	29	normality	normality	NOUN
ejpam-2822	28	30	due	due	ADP
ejpam-2822	28	31	to	to	ADP
ejpam-2822	28	32	liu	liu	PROPN
ejpam-2822	28	33	.	.	PUNCT
ejpam-2822	29	1	this	this	PRON
ejpam-2822	29	2	allows	allow	VERB
ejpam-2822	29	3	us	we	PRON
ejpam-2822	29	4	to	to	PART
ejpam-2822	29	5	construct	construct	VERB
ejpam-2822	29	6	the	the	DET
ejpam-2822	29	7	chains	chain	NOUN
ejpam-2822	29	8	of	of	ADP
ejpam-2822	29	9	normal	normal	ADJ
ejpam-2822	29	10	l	l	NOUN
ejpam-2822	29	11	-	-	NOUN
ejpam-2822	29	12	subgroups	subgroup	NOUN
ejpam-2822	29	13	in	in	ADP
ejpam-2822	29	14	the	the	DET
ejpam-2822	29	15	same	same	ADJ
ejpam-2822	29	16	fashion	fashion	NOUN
ejpam-2822	29	17	as	as	ADP
ejpam-2822	29	18	that	that	PRON
ejpam-2822	29	19	of	of	ADP
ejpam-2822	29	20	ordinary	ordinary	ADJ
ejpam-2822	29	21	normal	normal	ADJ
ejpam-2822	29	22	subgroups	subgroup	NOUN
ejpam-2822	29	23	in	in	ADP
ejpam-2822	29	24	classical	classical	ADJ
ejpam-2822	29	25	group	group	NOUN
ejpam-2822	29	26	theory	theory	NOUN
ejpam-2822	29	27	.	.	PUNCT
ejpam-2822	30	1	we	we	PRON
ejpam-2822	30	2	have	have	AUX
ejpam-2822	30	3	introduced	introduce	VERB
ejpam-2822	30	4	and	and	CCONJ
ejpam-2822	30	5	studied	study	VERB
ejpam-2822	30	6	the	the	DET
ejpam-2822	30	7	notions	notion	NOUN
ejpam-2822	30	8	of	of	ADP
ejpam-2822	30	9	nilpotent	nilpotent	ADJ
ejpam-2822	30	10	l	l	PROPN
ejpam-2822	30	11	-	-	NOUN
ejpam-2822	30	12	subgroup	subgroup	NOUN
ejpam-2822	30	13	,	,	PUNCT
ejpam-2822	30	14	solvable	solvable	ADJ
ejpam-2822	30	15	l	l	NOUN
ejpam-2822	30	16	-	-	NOUN
ejpam-2822	30	17	subgroup	subgroup	NOUN
ejpam-2822	30	18	,	,	PUNCT
ejpam-2822	30	19	normalizer	normalizer	NOUN
ejpam-2822	30	20	of	of	ADP
ejpam-2822	30	21	an	an	DET
ejpam-2822	30	22	l	l	NOUN
ejpam-2822	30	23	-	-	NOUN
ejpam-2822	30	24	subgroup	subgroup	NOUN
ejpam-2822	30	25	and	and	CCONJ
ejpam-2822	30	26	normal	normal	ADJ
ejpam-2822	30	27	closure	closure	NOUN
ejpam-2822	30	28	of	of	ADP
ejpam-2822	30	29	an	an	DET
ejpam-2822	30	30	l	l	NOUN
ejpam-2822	30	31	-	-	NOUN
ejpam-2822	30	32	group	group	NOUN
ejpam-2822	30	33	having	have	VERB
ejpam-2822	30	34	the	the	DET
ejpam-2822	30	35	parent	parent	NOUN
ejpam-2822	30	36	structure	structure	NOUN
ejpam-2822	30	37	of	of	ADP
ejpam-2822	30	38	an	an	DET
ejpam-2822	30	39	l	l	NOUN
ejpam-2822	30	40	-	-	NOUN
ejpam-2822	30	41	group	group	NOUN
ejpam-2822	30	42	.	.	PUNCT
ejpam-2822	31	1	in	in	ADP
ejpam-2822	31	2	the	the	DET
ejpam-2822	31	3	continuation	continuation	NOUN
ejpam-2822	31	4	of	of	ADP
ejpam-2822	31	5	the	the	DET
ejpam-2822	31	6	development	development	NOUN
ejpam-2822	31	7	of	of	ADP
ejpam-2822	31	8	l	l	NOUN
ejpam-2822	31	9	-	-	NOUN
ejpam-2822	31	10	group	group	NOUN
ejpam-2822	31	11	,	,	PUNCT
ejpam-2822	31	12	the	the	DET
ejpam-2822	31	13	authors	author	NOUN
ejpam-2822	31	14	in	in	ADP
ejpam-2822	31	15	this	this	DET
ejpam-2822	31	16	paper	paper	NOUN
ejpam-2822	31	17	,	,	PUNCT
ejpam-2822	31	18	after	after	ADP
ejpam-2822	31	19	developing	develop	VERB
ejpam-2822	31	20	a	a	DET
ejpam-2822	31	21	necessary	necessary	ADJ
ejpam-2822	31	22	mechanism	mechanism	NOUN
ejpam-2822	31	23	,	,	PUNCT
ejpam-2822	31	24	prove	prove	VERB
ejpam-2822	31	25	that	that	SCONJ
ejpam-2822	31	26	the	the	DET
ejpam-2822	31	27	set	set	NOUN
ejpam-2822	31	28	product	product	NOUN
ejpam-2822	31	29	of	of	ADP
ejpam-2822	31	30	a	a	DET
ejpam-2822	31	31	pair	pair	NOUN
ejpam-2822	31	32	of	of	ADP
ejpam-2822	31	33	nilpotent	nilpotent	ADJ
ejpam-2822	31	34	normal	normal	ADJ
ejpam-2822	31	35	l	l	NOUN
ejpam-2822	31	36	-	-	NOUN
ejpam-2822	31	37	subgroups	subgroup	NOUN
ejpam-2822	31	38	of	of	ADP
ejpam-2822	31	39	an	an	DET
ejpam-2822	31	40	l	l	NOUN
ejpam-2822	31	41	-	-	NOUN
ejpam-2822	31	42	group	group	NOUN
ejpam-2822	31	43	is	be	AUX
ejpam-2822	31	44	again	again	ADV
ejpam-2822	31	45	a	a	DET
ejpam-2822	31	46	nilpotent	nilpotent	ADJ
ejpam-2822	31	47	l	l	NOUN
ejpam-2822	31	48	-	-	NOUN
ejpam-2822	31	49	subgroup	subgroup	NOUN
ejpam-2822	31	50	.	.	PUNCT
ejpam-2822	32	1	2	2	X
ejpam-2822	32	2	.	.	X
ejpam-2822	32	3	preliminaries	preliminary	NOUN
ejpam-2822	32	4	throughout	throughout	ADP
ejpam-2822	32	5	this	this	DET
ejpam-2822	32	6	paper	paper	NOUN
ejpam-2822	32	7	,	,	PUNCT
ejpam-2822	32	8	the	the	DET
ejpam-2822	32	9	system	system	NOUN
ejpam-2822	32	10	〈	〈	PROPN
ejpam-2822	32	11	l,≤,∨,∧	l,≤,∨,∧	PROPN
ejpam-2822	32	12	〉	〉	PROPN
ejpam-2822	32	13	denotes	denote	VERB
ejpam-2822	32	14	a	a	DET
ejpam-2822	32	15	completely	completely	ADV
ejpam-2822	32	16	distributive	distributive	ADJ
ejpam-2822	32	17	lattice	lattice	NOUN
ejpam-2822	32	18	where	where	SCONJ
ejpam-2822	32	19	≤	≤	PROPN
ejpam-2822	32	20	denotes	denote	VERB
ejpam-2822	32	21	the	the	DET
ejpam-2822	32	22	partial	partial	ADJ
ejpam-2822	32	23	ordering	ordering	NOUN
ejpam-2822	32	24	of	of	ADP
ejpam-2822	32	25	l	l	NOUN
ejpam-2822	32	26	,	,	PUNCT
ejpam-2822	32	27	the	the	DET
ejpam-2822	32	28	join	join	NOUN
ejpam-2822	32	29	(	(	PUNCT
ejpam-2822	32	30	sup	sup	NOUN
ejpam-2822	32	31	)	)	PUNCT
ejpam-2822	32	32	and	and	CCONJ
ejpam-2822	32	33	meet	meet	VERB
ejpam-2822	32	34	(	(	PUNCT
ejpam-2822	32	35	inf	inf	NOUN
ejpam-2822	32	36	)	)	PUNCT
ejpam-2822	32	37	of	of	ADP
ejpam-2822	32	38	the	the	DET
ejpam-2822	32	39	elements	element	NOUN
ejpam-2822	32	40	of	of	ADP
ejpam-2822	32	41	l	l	NOUN
ejpam-2822	32	42	are	be	AUX
ejpam-2822	32	43	denoted	denote	VERB
ejpam-2822	32	44	by	by	ADP
ejpam-2822	32	45	∨	∨	NOUN
ejpam-2822	32	46	and	and	CCONJ
ejpam-2822	32	47	∧	∧	PROPN
ejpam-2822	32	48	respectively	respectively	ADV
ejpam-2822	32	49	.	.	PUNCT
ejpam-2822	33	1	also	also	ADV
ejpam-2822	33	2	,	,	PUNCT
ejpam-2822	33	3	we	we	PRON
ejpam-2822	33	4	write	write	VERB
ejpam-2822	33	5	1	1	NUM
ejpam-2822	33	6	and	and	CCONJ
ejpam-2822	33	7	0	0	NUM
ejpam-2822	33	8	for	for	ADP
ejpam-2822	33	9	the	the	DET
ejpam-2822	33	10	maximal	maximal	ADJ
ejpam-2822	33	11	and	and	CCONJ
ejpam-2822	33	12	the	the	DET
ejpam-2822	33	13	minimal	minimal	ADJ
ejpam-2822	33	14	elements	element	NOUN
ejpam-2822	33	15	of	of	ADP
ejpam-2822	33	16	l	l	NOUN
ejpam-2822	33	17	,	,	PUNCT
ejpam-2822	33	18	respectively	respectively	ADV
ejpam-2822	33	19	.	.	PUNCT
ejpam-2822	34	1	moreover	moreover	ADV
ejpam-2822	34	2	,	,	PUNCT
ejpam-2822	34	3	our	our	PRON
ejpam-2822	34	4	work	work	NOUN
ejpam-2822	34	5	is	be	AUX
ejpam-2822	34	6	carried	carry	VERB
ejpam-2822	34	7	out	out	ADP
ejpam-2822	34	8	by	by	ADP
ejpam-2822	34	9	using	use	VERB
ejpam-2822	34	10	the	the	DET
ejpam-2822	34	11	definition	definition	NOUN
ejpam-2822	34	12	of	of	ADP
ejpam-2822	34	13	l	l	NOUN
ejpam-2822	34	14	-	-	NOUN
ejpam-2822	34	15	subset	subset	NOUN
ejpam-2822	34	16	as	as	SCONJ
ejpam-2822	34	17	formulated	formulate	VERB
ejpam-2822	34	18	by	by	ADP
ejpam-2822	34	19	goguen	goguen	PROPN
ejpam-2822	34	20	.	.	PUNCT
ejpam-2822	35	1	the	the	DET
ejpam-2822	35	2	definition	definition	NOUN
ejpam-2822	35	3	of	of	ADP
ejpam-2822	35	4	a	a	DET
ejpam-2822	35	5	completely	completely	ADV
ejpam-2822	35	6	distributive	distributive	ADJ
ejpam-2822	35	7	lattice	lattice	NOUN
ejpam-2822	35	8	is	be	AUX
ejpam-2822	35	9	well	well	ADV
ejpam-2822	35	10	known	know	VERB
ejpam-2822	35	11	in	in	ADP
ejpam-2822	35	12	the	the	DET
ejpam-2822	35	13	literature	literature	NOUN
ejpam-2822	35	14	and	and	CCONJ
ejpam-2822	35	15	can	can	AUX
ejpam-2822	35	16	be	be	AUX
ejpam-2822	35	17	found	find	VERB
ejpam-2822	35	18	in	in	ADP
ejpam-2822	35	19	any	any	DET
ejpam-2822	35	20	standard	standard	ADJ
ejpam-2822	35	21	text	text	NOUN
ejpam-2822	35	22	on	on	ADP
ejpam-2822	35	23	the	the	DET
ejpam-2822	35	24	subject	subject	NOUN
ejpam-2822	35	25	.	.	PUNCT
ejpam-2822	36	1	let	let	VERB
ejpam-2822	36	2	{	{	PUNCT
ejpam-2822	36	3	ji	ji	NOUN
ejpam-2822	36	4	:	:	PUNCT
ejpam-2822	37	1	i	i	PRON
ejpam-2822	37	2	∈	∈	VERB
ejpam-2822	37	3	i	i	PRON
ejpam-2822	37	4	}	}	PUNCT
ejpam-2822	37	5	be	be	VERB
ejpam-2822	37	6	any	any	DET
ejpam-2822	37	7	family	family	NOUN
ejpam-2822	37	8	of	of	ADP
ejpam-2822	37	9	subsets	subset	NOUN
ejpam-2822	37	10	of	of	ADP
ejpam-2822	37	11	a	a	DET
ejpam-2822	37	12	complete	complete	ADJ
ejpam-2822	37	13	lattice	lattice	NOUN
ejpam-2822	37	14	l	l	NOUN
ejpam-2822	37	15	and	and	CCONJ
ejpam-2822	37	16	f	f	PROPN
ejpam-2822	37	17	denotes	denote	VERB
ejpam-2822	37	18	the	the	DET
ejpam-2822	37	19	set	set	NOUN
ejpam-2822	37	20	of	of	ADP
ejpam-2822	37	21	choice	choice	NOUN
ejpam-2822	37	22	functions	function	NOUN
ejpam-2822	37	23	for	for	ADP
ejpam-2822	37	24	ji	ji	PROPN
ejpam-2822	37	25	,	,	PUNCT
ejpam-2822	37	26	i.e.	i.e.	X
ejpam-2822	37	27	,	,	PUNCT
ejpam-2822	37	28	functions	function	NOUN
ejpam-2822	38	1	f	f	NOUN
ejpam-2822	38	2	:	:	PUNCT
ejpam-2822	38	3	i	i	PROPN
ejpam-2822	38	4	→	→	SYM
ejpam-2822	38	5	∏	∏	PROPN
ejpam-2822	38	6	i∈i	i∈i	NOUN
ejpam-2822	38	7	ji	ji	PROPN
ejpam-2822	38	8	such	such	ADJ
ejpam-2822	38	9	that	that	SCONJ
ejpam-2822	38	10	f(i	f(i	PROPN
ejpam-2822	38	11	)	)	PUNCT
ejpam-2822	38	12	∈	∈	PROPN
ejpam-2822	38	13	ji	ji	PROPN
ejpam-2822	38	14	for	for	ADP
ejpam-2822	38	15	each	each	DET
ejpam-2822	38	16	i	i	PRON
ejpam-2822	38	17	∈	∈	PROPN
ejpam-2822	38	18	i.	i.	NOUN
ejpam-2822	38	19	then	then	ADV
ejpam-2822	38	20	,	,	PUNCT
ejpam-2822	38	21	we	we	PRON
ejpam-2822	38	22	say	say	VERB
ejpam-2822	38	23	that	that	SCONJ
ejpam-2822	38	24	l	l	NOUN
ejpam-2822	38	25	is	be	AUX
ejpam-2822	38	26	a	a	DET
ejpam-2822	38	27	completely	completely	ADV
ejpam-2822	38	28	distributive	distributive	ADJ
ejpam-2822	38	29	lattice	lattice	NOUN
ejpam-2822	38	30	,	,	PUNCT
ejpam-2822	38	31	if∧{∨	if∧{∨	PROPN
ejpam-2822	38	32	i∈i	i∈i	ADJ
ejpam-2822	38	33	ji	ji	NOUN
ejpam-2822	38	34	}	}	PUNCT
ejpam-2822	38	35	=	=	PUNCT
ejpam-2822	38	36	∨	∨	NUM
ejpam-2822	38	37	f∈f	f∈f	NOUN
ejpam-2822	38	38	{	{	PUNCT
ejpam-2822	38	39	∧	∧	PROPN
ejpam-2822	38	40	i∈i	i∈i	ADJ
ejpam-2822	38	41	f(i	f(i	PROPN
ejpam-2822	38	42	)	)	PUNCT
ejpam-2822	38	43	}	}	PUNCT
ejpam-2822	38	44	.	.	PUNCT
ejpam-2822	39	1	the	the	DET
ejpam-2822	39	2	above	above	ADJ
ejpam-2822	39	3	law	law	NOUN
ejpam-2822	39	4	is	be	AUX
ejpam-2822	39	5	known	know	VERB
ejpam-2822	39	6	as	as	ADP
ejpam-2822	39	7	the	the	DET
ejpam-2822	39	8	complete	complete	ADJ
ejpam-2822	39	9	distributive	distributive	ADJ
ejpam-2822	39	10	law	law	NOUN
ejpam-2822	39	11	.	.	PUNCT
ejpam-2822	40	1	moreover	moreover	ADV
ejpam-2822	40	2	,	,	PUNCT
ejpam-2822	40	3	a	a	DET
ejpam-2822	40	4	lattice	lattice	NOUN
ejpam-2822	40	5	l	l	NOUN
ejpam-2822	40	6	is	be	AUX
ejpam-2822	40	7	said	say	VERB
ejpam-2822	40	8	to	to	PART
ejpam-2822	40	9	be	be	AUX
ejpam-2822	40	10	infinitely	infinitely	ADV
ejpam-2822	40	11	meet	meet	VERB
ejpam-2822	40	12	distributive	distributive	ADJ
ejpam-2822	40	13	if	if	SCONJ
ejpam-2822	40	14	for	for	ADP
ejpam-2822	40	15	every	every	DET
ejpam-2822	40	16	subset	subset	NOUN
ejpam-2822	40	17	{	{	PUNCT
ejpam-2822	40	18	bβ	bβ	NOUN
ejpam-2822	40	19	:	:	PUNCT
ejpam-2822	40	20	β	β	X
ejpam-2822	40	21	∈	∈	PROPN
ejpam-2822	40	22	b	b	X
ejpam-2822	40	23	}	}	PUNCT
ejpam-2822	40	24	of	of	ADP
ejpam-2822	40	25	l	l	NOUN
ejpam-2822	40	26	,	,	PUNCT
ejpam-2822	40	27	we	we	PRON
ejpam-2822	40	28	have	have	VERB
ejpam-2822	40	29	a	a	DET
ejpam-2822	40	30	∧	∧	PROPN
ejpam-2822	40	31	{	{	PUNCT
ejpam-2822	40	32	∨	∨	NUM
ejpam-2822	40	33	β∈b	β∈b	NOUN
ejpam-2822	40	34	bβ	bβ	NOUN
ejpam-2822	40	35	}	}	PUNCT
ejpam-2822	40	36	=	=	PUNCT
ejpam-2822	40	37	∨	∨	NUM
ejpam-2822	40	38	β∈b	β∈b	NOUN
ejpam-2822	40	39	{	{	PUNCT
ejpam-2822	40	40	a	a	DET
ejpam-2822	40	41	∧	∧	PROPN
ejpam-2822	40	42	bβ	bβ	NOUN
ejpam-2822	40	43	}	}	PUNCT
ejpam-2822	40	44	,	,	PUNCT
ejpam-2822	40	45	provided	provide	VERB
ejpam-2822	40	46	l	l	NOUN
ejpam-2822	40	47	is	be	AUX
ejpam-2822	40	48	join	join	VERB
ejpam-2822	40	49	complete	complete	ADJ
ejpam-2822	40	50	.	.	PUNCT
ejpam-2822	41	1	the	the	DET
ejpam-2822	41	2	above	above	ADJ
ejpam-2822	41	3	law	law	NOUN
ejpam-2822	41	4	is	be	AUX
ejpam-2822	41	5	known	know	VERB
ejpam-2822	41	6	as	as	ADP
ejpam-2822	41	7	the	the	DET
ejpam-2822	41	8	infinitely	infinitely	ADV
ejpam-2822	41	9	meet	meet	VERB
ejpam-2822	41	10	distributive	distributive	ADJ
ejpam-2822	41	11	law	law	NOUN
ejpam-2822	41	12	.	.	PUNCT
ejpam-2822	42	1	the	the	DET
ejpam-2822	42	2	definition	definition	NOUN
ejpam-2822	42	3	of	of	ADP
ejpam-2822	42	4	infinitely	infinitely	ADV
ejpam-2822	42	5	join	join	VERB
ejpam-2822	42	6	distributive	distributive	ADJ
ejpam-2822	42	7	lattice	lattice	NOUN
ejpam-2822	42	8	is	be	AUX
ejpam-2822	42	9	dual	dual	ADJ
ejpam-2822	42	10	to	to	ADP
ejpam-2822	42	11	the	the	DET
ejpam-2822	42	12	above	above	ADJ
ejpam-2822	42	13	definition	definition	NOUN
ejpam-2822	42	14	i.e.	i.e.	X
ejpam-2822	42	15	a	a	DET
ejpam-2822	42	16	lattice	lattice	NOUN
ejpam-2822	42	17	l	l	NOUN
ejpam-2822	42	18	is	be	AUX
ejpam-2822	42	19	said	say	VERB
ejpam-2822	42	20	to	to	PART
ejpam-2822	42	21	be	be	AUX
ejpam-2822	42	22	infinitely	infinitely	ADV
ejpam-2822	42	23	join	join	VERB
ejpam-2822	42	24	distributive	distributive	ADJ
ejpam-2822	42	25	if	if	SCONJ
ejpam-2822	42	26	for	for	ADP
ejpam-2822	42	27	every	every	DET
ejpam-2822	42	28	subset	subset	NOUN
ejpam-2822	42	29	{	{	PUNCT
ejpam-2822	42	30	bβ	bβ	NOUN
ejpam-2822	42	31	:	:	PUNCT
ejpam-2822	43	1	β	β	X
ejpam-2822	43	2	∈	∈	PROPN
ejpam-2822	43	3	b	b	X
ejpam-2822	43	4	}	}	PUNCT
ejpam-2822	43	5	of	of	ADP
ejpam-2822	43	6	l	l	NOUN
ejpam-2822	43	7	,	,	PUNCT
ejpam-2822	43	8	we	we	PRON
ejpam-2822	43	9	have	have	VERB
ejpam-2822	43	10	a	a	DET
ejpam-2822	43	11	∨	∨	NOUN
ejpam-2822	43	12	{	{	PUNCT
ejpam-2822	43	13	∧	∧	PROPN
ejpam-2822	43	14	β∈b	β∈b	NOUN
ejpam-2822	43	15	bβ	bβ	NOUN
ejpam-2822	43	16	}	}	PUNCT
ejpam-2822	43	17	=	=	SYM
ejpam-2822	43	18	∧	∧	PROPN
ejpam-2822	43	19	β∈b	β∈b	NOUN
ejpam-2822	43	20	{	{	PUNCT
ejpam-2822	43	21	a	a	DET
ejpam-2822	43	22	∨	∨	NUM
ejpam-2822	43	23	bβ	bβ	NOUN
ejpam-2822	43	24	}	}	PUNCT
ejpam-2822	43	25	,	,	PUNCT
ejpam-2822	43	26	provided	provide	VERB
ejpam-2822	43	27	l	l	NOUN
ejpam-2822	43	28	is	be	AUX
ejpam-2822	43	29	meet	meet	VERB
ejpam-2822	43	30	complete	complete	ADJ
ejpam-2822	43	31	.	.	PUNCT
ejpam-2822	44	1	the	the	DET
ejpam-2822	44	2	above	above	ADJ
ejpam-2822	44	3	law	law	NOUN
ejpam-2822	44	4	is	be	AUX
ejpam-2822	44	5	known	know	VERB
ejpam-2822	44	6	as	as	ADP
ejpam-2822	44	7	the	the	DET
ejpam-2822	44	8	infinitely	infinitely	ADV
ejpam-2822	44	9	join	join	VERB
ejpam-2822	44	10	distributive	distributive	ADJ
ejpam-2822	44	11	law	law	NOUN
ejpam-2822	44	12	.	.	PUNCT
ejpam-2822	45	1	clearly	clearly	ADV
ejpam-2822	45	2	,	,	PUNCT
ejpam-2822	45	3	both	both	CCONJ
ejpam-2822	45	4	these	these	DET
ejpam-2822	45	5	laws	law	NOUN
ejpam-2822	45	6	follow	follow	VERB
ejpam-2822	45	7	from	from	ADP
ejpam-2822	45	8	the	the	DET
ejpam-2822	45	9	definition	definition	NOUN
ejpam-2822	45	10	of	of	ADP
ejpam-2822	45	11	a	a	DET
ejpam-2822	45	12	completely	completely	ADV
ejpam-2822	45	13	distributive	distributive	ADJ
ejpam-2822	45	14	lattice	lattice	NOUN
ejpam-2822	45	15	.	.	PUNCT
ejpam-2822	46	1	here	here	ADV
ejpam-2822	46	2	we	we	PRON
ejpam-2822	46	3	also	also	ADV
ejpam-2822	46	4	mention	mention	VERB
ejpam-2822	46	5	that	that	SCONJ
ejpam-2822	46	6	the	the	DET
ejpam-2822	46	7	dual	dual	ADJ
ejpam-2822	46	8	of	of	ADP
ejpam-2822	46	9	completely	completely	ADV
ejpam-2822	46	10	distributive	distributive	ADJ
ejpam-2822	46	11	law	law	NOUN
ejpam-2822	46	12	is	be	AUX
ejpam-2822	46	13	valid	valid	ADJ
ejpam-2822	46	14	in	in	ADP
ejpam-2822	46	15	a	a	DET
ejpam-2822	46	16	completely	completely	ADV
ejpam-2822	46	17	i.	i.	PROPN
ejpam-2822	46	18	jahan	jahan	PROPN
ejpam-2822	46	19	,	,	PUNCT
ejpam-2822	46	20	n.	n.	PROPN
ejpam-2822	46	21	ajmal	ajmal	PROPN
ejpam-2822	46	22	,	,	PUNCT
ejpam-2822	46	23	b.	b.	PROPN
ejpam-2822	46	24	davvaz	davvaz	PROPN
ejpam-2822	46	25	/	/	SYM
ejpam-2822	46	26	eur	eur	PROPN
ejpam-2822	46	27	.	.	PUNCT
ejpam-2822	47	1	j.	j.	PROPN
ejpam-2822	47	2	pure	pure	PROPN
ejpam-2822	47	3	appl	appl	PROPN
ejpam-2822	47	4	.	.	PROPN
ejpam-2822	47	5	math	math	PROPN
ejpam-2822	47	6	,	,	PUNCT
ejpam-2822	47	7	10	10	NUM
ejpam-2822	47	8	(	(	PUNCT
ejpam-2822	47	9	2	2	NUM
ejpam-2822	47	10	)	)	PUNCT
ejpam-2822	47	11	(	(	PUNCT
ejpam-2822	47	12	2017	2017	NUM
ejpam-2822	47	13	)	)	PUNCT
ejpam-2822	47	14	,	,	PUNCT
ejpam-2822	47	15	255	255	NUM
ejpam-2822	47	16	-	-	SYM
ejpam-2822	47	17	271	271	NUM
ejpam-2822	47	18	257	257	NUM
ejpam-2822	47	19	distributive	distributive	ADJ
ejpam-2822	47	20	lattice	lattice	NOUN
ejpam-2822	47	21	whereas	whereas	SCONJ
ejpam-2822	47	22	the	the	DET
ejpam-2822	47	23	infinitely	infinitely	ADV
ejpam-2822	47	24	meet	meet	VERB
ejpam-2822	47	25	and	and	CCONJ
ejpam-2822	47	26	join	join	VERB
ejpam-2822	47	27	distributive	distributive	ADJ
ejpam-2822	47	28	laws	law	NOUN
ejpam-2822	47	29	are	be	AUX
ejpam-2822	47	30	independent	independent	ADJ
ejpam-2822	47	31	from	from	ADP
ejpam-2822	47	32	each	each	DET
ejpam-2822	47	33	other	other	ADJ
ejpam-2822	47	34	.	.	PUNCT
ejpam-2822	48	1	next	next	ADV
ejpam-2822	48	2	we	we	PRON
ejpam-2822	48	3	recall	recall	VERB
ejpam-2822	48	4	the	the	DET
ejpam-2822	48	5	following	following	NOUN
ejpam-2822	48	6	from	from	ADP
ejpam-2822	48	7	[	[	X
ejpam-2822	48	8	1	1	NUM
ejpam-2822	48	9	-	-	SYM
ejpam-2822	48	10	6	6	NUM
ejpam-2822	48	11	,	,	PUNCT
ejpam-2822	48	12	9	9	NUM
ejpam-2822	48	13	,	,	PUNCT
ejpam-2822	48	14	15	15	NUM
ejpam-2822	48	15	]	]	NOUN
ejpam-2822	48	16	:	:	PUNCT
ejpam-2822	48	17	an	an	DET
ejpam-2822	48	18	l	l	NOUN
ejpam-2822	48	19	-	-	NOUN
ejpam-2822	48	20	subset	subset	NOUN
ejpam-2822	48	21	of	of	ADP
ejpam-2822	48	22	x	x	PUNCT
ejpam-2822	48	23	is	be	AUX
ejpam-2822	48	24	a	a	DET
ejpam-2822	48	25	function	function	NOUN
ejpam-2822	48	26	from	from	ADP
ejpam-2822	48	27	x	x	PUNCT
ejpam-2822	48	28	into	into	ADP
ejpam-2822	48	29	l.	l.	NOUN
ejpam-2822	48	30	the	the	DET
ejpam-2822	48	31	set	set	NOUN
ejpam-2822	48	32	of	of	ADP
ejpam-2822	48	33	l	l	NOUN
ejpam-2822	48	34	-subsets	-subset	NOUN
ejpam-2822	48	35	of	of	ADP
ejpam-2822	48	36	x	x	PRON
ejpam-2822	48	37	is	be	AUX
ejpam-2822	48	38	called	call	VERB
ejpam-2822	48	39	the	the	DET
ejpam-2822	48	40	l	l	NOUN
ejpam-2822	48	41	-	-	NOUN
ejpam-2822	48	42	power	power	NOUN
ejpam-2822	48	43	set	set	NOUN
ejpam-2822	48	44	of	of	ADP
ejpam-2822	48	45	x	x	PUNCT
ejpam-2822	48	46	and	and	CCONJ
ejpam-2822	48	47	is	be	AUX
ejpam-2822	48	48	denoted	denote	VERB
ejpam-2822	48	49	by	by	ADP
ejpam-2822	48	50	lx	lx	X
ejpam-2822	48	51	.	.	PUNCT
ejpam-2822	49	1	for	for	ADP
ejpam-2822	49	2	µ	µ	NOUN
ejpam-2822	49	3	∈	∈	NOUN
ejpam-2822	49	4	lx	lx	NOUN
ejpam-2822	49	5	,	,	PUNCT
ejpam-2822	49	6	the	the	DET
ejpam-2822	49	7	set	set	NOUN
ejpam-2822	49	8	{	{	PUNCT
ejpam-2822	49	9	µ(x	µ(x	NUM
ejpam-2822	49	10	)	)	PUNCT
ejpam-2822	49	11	:	:	PUNCT
ejpam-2822	50	1	x	x	X
ejpam-2822	50	2	∈	∈	NOUN
ejpam-2822	50	3	x	x	VERB
ejpam-2822	50	4	}	}	PUNCT
ejpam-2822	50	5	is	be	AUX
ejpam-2822	50	6	called	call	VERB
ejpam-2822	50	7	the	the	DET
ejpam-2822	50	8	image	image	NOUN
ejpam-2822	50	9	of	of	ADP
ejpam-2822	50	10	µ	µ	NUM
ejpam-2822	50	11	and	and	CCONJ
ejpam-2822	50	12	is	be	AUX
ejpam-2822	50	13	denoted	denote	VERB
ejpam-2822	50	14	by	by	ADP
ejpam-2822	50	15	imµ	imµ	NOUN
ejpam-2822	50	16	and	and	CCONJ
ejpam-2822	50	17	the	the	DET
ejpam-2822	50	18	tip	tip	NOUN
ejpam-2822	50	19	of	of	ADP
ejpam-2822	50	20	µ	µ	PROPN
ejpam-2822	50	21	is	be	AUX
ejpam-2822	50	22	defined	define	VERB
ejpam-2822	50	23	as	as	ADP
ejpam-2822	50	24	∨	∨	NUM
ejpam-2822	50	25	x∈x	x∈x	NOUN
ejpam-2822	50	26	µ(x	µ(x	NOUN
ejpam-2822	50	27	)	)	PUNCT
ejpam-2822	50	28	.	.	PUNCT
ejpam-2822	51	1	moreover	moreover	ADV
ejpam-2822	51	2	,	,	PUNCT
ejpam-2822	51	3	the	the	DET
ejpam-2822	51	4	tail	tail	NOUN
ejpam-2822	51	5	of	of	ADP
ejpam-2822	51	6	µ	µ	NOUN
ejpam-2822	51	7	is	be	AUX
ejpam-2822	51	8	defined	define	VERB
ejpam-2822	51	9	as	as	ADP
ejpam-2822	51	10	∧	∧	PROPN
ejpam-2822	51	11	x∈x	x∈x	NOUN
ejpam-2822	51	12	µ(x	µ(x	NUM
ejpam-2822	51	13	)	)	PUNCT
ejpam-2822	51	14	.	.	PUNCT
ejpam-2822	52	1	we	we	PRON
ejpam-2822	52	2	say	say	VERB
ejpam-2822	52	3	that	that	SCONJ
ejpam-2822	52	4	an	an	DET
ejpam-2822	52	5	l	l	NOUN
ejpam-2822	52	6	-	-	NOUN
ejpam-2822	52	7	subset	subset	ADJ
ejpam-2822	52	8	µ	µ	NOUN
ejpam-2822	52	9	of	of	ADP
ejpam-2822	52	10	x	x	PUNCT
ejpam-2822	52	11	is	be	AUX
ejpam-2822	52	12	contained	contain	VERB
ejpam-2822	52	13	in	in	ADP
ejpam-2822	52	14	an	an	DET
ejpam-2822	52	15	l	l	NOUN
ejpam-2822	52	16	-	-	PUNCT
ejpam-2822	52	17	subset	subset	VERB
ejpam-2822	52	18	η	η	PROPN
ejpam-2822	52	19	of	of	ADP
ejpam-2822	52	20	x	x	PRON
ejpam-2822	52	21	if	if	SCONJ
ejpam-2822	52	22	µ(x	µ(x	NOUN
ejpam-2822	52	23	)	)	PUNCT
ejpam-2822	52	24	≤	≤	NOUN
ejpam-2822	52	25	η(x	η(x	NOUN
ejpam-2822	52	26	)	)	PUNCT
ejpam-2822	52	27	for	for	ADP
ejpam-2822	52	28	x	x	SYM
ejpam-2822	52	29	∈	∈	PROPN
ejpam-2822	52	30	x	x	PUNCT
ejpam-2822	52	31	and	and	CCONJ
ejpam-2822	52	32	is	be	AUX
ejpam-2822	52	33	denoted	denote	VERB
ejpam-2822	52	34	by	by	ADP
ejpam-2822	52	35	µ	µ	PROPN
ejpam-2822	52	36	⊆	⊆	NUM
ejpam-2822	52	37	η	η	PROPN
ejpam-2822	52	38	.	.	PROPN
ejpam-2822	52	39	for	for	ADP
ejpam-2822	52	40	a	a	DET
ejpam-2822	52	41	family	family	NOUN
ejpam-2822	52	42	{	{	PUNCT
ejpam-2822	52	43	µi	µi	INTJ
ejpam-2822	52	44	:	:	PUNCT
ejpam-2822	52	45	i	i	PRON
ejpam-2822	52	46	∈	∈	VERB
ejpam-2822	52	47	i	i	PRON
ejpam-2822	52	48	}	}	PUNCT
ejpam-2822	52	49	of	of	ADP
ejpam-2822	52	50	l	l	NOUN
ejpam-2822	52	51	-	-	NOUN
ejpam-2822	52	52	subsets	subset	NOUN
ejpam-2822	52	53	in	in	ADP
ejpam-2822	52	54	x	x	NOUN
ejpam-2822	52	55	,	,	PUNCT
ejpam-2822	52	56	where	where	SCONJ
ejpam-2822	52	57	i	i	PRON
ejpam-2822	52	58	is	be	AUX
ejpam-2822	52	59	a	a	DET
ejpam-2822	52	60	nonempty	nonempty	ADJ
ejpam-2822	52	61	index	index	NOUN
ejpam-2822	52	62	set	set	NOUN
ejpam-2822	52	63	,	,	PUNCT
ejpam-2822	52	64	the	the	DET
ejpam-2822	52	65	union	union	NOUN
ejpam-2822	52	66	⋃	⋃	PUNCT
ejpam-2822	52	67	i∈i	i∈i	ADJ
ejpam-2822	52	68	µi	µi	PROPN
ejpam-2822	52	69	and	and	CCONJ
ejpam-2822	52	70	the	the	DET
ejpam-2822	52	71	intersection⋂	intersection⋂	PROPN
ejpam-2822	52	72	i∈i	i∈i	ADV
ejpam-2822	52	73	µi	µi	ADP
ejpam-2822	52	74	of	of	ADP
ejpam-2822	52	75	{	{	PUNCT
ejpam-2822	52	76	µi	µi	INTJ
ejpam-2822	52	77	:	:	PUNCT
ejpam-2822	52	78	i	i	PRON
ejpam-2822	52	79	∈	∈	VERB
ejpam-2822	53	1	i	i	PRON
ejpam-2822	53	2	}	}	PUNCT
ejpam-2822	53	3	are	be	AUX
ejpam-2822	53	4	,	,	PUNCT
ejpam-2822	53	5	respectively	respectively	ADV
ejpam-2822	53	6	,	,	PUNCT
ejpam-2822	53	7	defined	define	VERB
ejpam-2822	53	8	by	by	ADP
ejpam-2822	53	9	:	:	PUNCT
ejpam-2822	53	10	⋃	⋃	VERB
ejpam-2822	53	11	i∈i	i∈i	ADJ
ejpam-2822	53	12	µi(x	µi(x	NOUN
ejpam-2822	53	13	)	)	PUNCT
ejpam-2822	54	1	=	=	PUNCT
ejpam-2822	54	2	∨	∨	NUM
ejpam-2822	54	3	i∈i	i∈i	ADJ
ejpam-2822	54	4	µ(x	µ(x	PROPN
ejpam-2822	54	5	)	)	PUNCT
ejpam-2822	54	6	and	and	CCONJ
ejpam-2822	54	7	⋂	⋂	PROPN
ejpam-2822	54	8	i∈i	i∈i	ADJ
ejpam-2822	54	9	µi(x	µi(x	NUM
ejpam-2822	54	10	)	)	PUNCT
ejpam-2822	55	1	=	=	SYM
ejpam-2822	55	2	∧	∧	PROPN
ejpam-2822	55	3	i∈i	i∈i	ADJ
ejpam-2822	55	4	µ(x	µ(x	PROPN
ejpam-2822	55	5	)	)	PUNCT
ejpam-2822	55	6	,	,	PUNCT
ejpam-2822	55	7	for	for	ADP
ejpam-2822	55	8	each	each	DET
ejpam-2822	55	9	x	x	SYM
ejpam-2822	55	10	∈	∈	PROPN
ejpam-2822	55	11	x.	x.	NOUN
ejpam-2822	55	12	if	if	SCONJ
ejpam-2822	55	13	µ	µ	X
ejpam-2822	55	14	∈	∈	NOUN
ejpam-2822	55	15	lx	lx	NOUN
ejpam-2822	55	16	and	and	CCONJ
ejpam-2822	55	17	a	a	DET
ejpam-2822	55	18	∈	∈	PROPN
ejpam-2822	55	19	l	l	NOUN
ejpam-2822	55	20	,	,	PUNCT
ejpam-2822	55	21	then	then	ADV
ejpam-2822	55	22	the	the	DET
ejpam-2822	55	23	notion	notion	NOUN
ejpam-2822	55	24	of	of	ADP
ejpam-2822	55	25	level	level	NOUN
ejpam-2822	55	26	subset	subset	VERB
ejpam-2822	55	27	µa	µa	NOUN
ejpam-2822	55	28	of	of	ADP
ejpam-2822	55	29	µ	µ	X
ejpam-2822	55	30	is	be	AUX
ejpam-2822	55	31	defined	define	VERB
ejpam-2822	55	32	as	as	ADP
ejpam-2822	55	33	:	:	PUNCT
ejpam-2822	55	34	µa	µa	NOUN
ejpam-2822	55	35	=	=	PUNCT
ejpam-2822	55	36	{	{	PUNCT
ejpam-2822	55	37	x	x	SYM
ejpam-2822	55	38	∈	∈	PROPN
ejpam-2822	55	39	x	x	X
ejpam-2822	55	40	:	:	PUNCT
ejpam-2822	55	41	µ(x	µ(x	NUM
ejpam-2822	55	42	)	)	PUNCT
ejpam-2822	55	43	≥	≥	NOUN
ejpam-2822	55	44	a	a	PRON
ejpam-2822	55	45	}	}	PUNCT
ejpam-2822	55	46	.	.	PUNCT
ejpam-2822	56	1	the	the	DET
ejpam-2822	56	2	set	set	ADJ
ejpam-2822	56	3	product	product	NOUN
ejpam-2822	56	4	µ	µ	PROPN
ejpam-2822	56	5	◦	◦	NOUN
ejpam-2822	56	6	η	η	PROPN
ejpam-2822	56	7	of	of	ADP
ejpam-2822	56	8	µ	µ	NUM
ejpam-2822	56	9	,	,	PUNCT
ejpam-2822	56	10	η	η	PROPN
ejpam-2822	56	11	∈	∈	PROPN
ejpam-2822	56	12	ls	ls	X
ejpam-2822	56	13	,	,	PUNCT
ejpam-2822	56	14	where	where	SCONJ
ejpam-2822	56	15	s	s	NOUN
ejpam-2822	56	16	is	be	AUX
ejpam-2822	56	17	a	a	DET
ejpam-2822	56	18	groupoid	groupoid	NOUN
ejpam-2822	56	19	,	,	PUNCT
ejpam-2822	56	20	is	be	AUX
ejpam-2822	56	21	an	an	DET
ejpam-2822	56	22	l	l	NOUN
ejpam-2822	56	23	-	-	NOUN
ejpam-2822	56	24	subset	subset	NOUN
ejpam-2822	56	25	of	of	ADP
ejpam-2822	56	26	s	s	PRON
ejpam-2822	56	27	defined	define	VERB
ejpam-2822	56	28	by	by	ADP
ejpam-2822	56	29	µ	µ	X
ejpam-2822	56	30	◦	◦	NOUN
ejpam-2822	56	31	η(x	η(x	PUNCT
ejpam-2822	56	32	)	)	PUNCT
ejpam-2822	56	33	=	=	PUNCT
ejpam-2822	56	34	∨	∨	NOUN
ejpam-2822	56	35	x	x	X
ejpam-2822	56	36	=	=	PROPN
ejpam-2822	56	37	yz	yz	X
ejpam-2822	56	38	{	{	PUNCT
ejpam-2822	56	39	µ(y	µ(y	PROPN
ejpam-2822	56	40	)	)	PUNCT
ejpam-2822	56	41	∧	∧	PROPN
ejpam-2822	56	42	η(z	η(z	PROPN
ejpam-2822	56	43	)	)	PUNCT
ejpam-2822	56	44	}	}	PUNCT
ejpam-2822	56	45	.	.	PUNCT
ejpam-2822	57	1	again	again	ADV
ejpam-2822	57	2	recall	recall	VERB
ejpam-2822	57	3	that	that	SCONJ
ejpam-2822	57	4	if	if	SCONJ
ejpam-2822	57	5	x	x	PRON
ejpam-2822	57	6	can	can	AUX
ejpam-2822	57	7	not	not	PART
ejpam-2822	57	8	be	be	AUX
ejpam-2822	57	9	factored	factor	VERB
ejpam-2822	57	10	as	as	ADP
ejpam-2822	57	11	x	x	X
ejpam-2822	57	12	=	=	PUNCT
ejpam-2822	57	13	yz	yz	PROPN
ejpam-2822	57	14	in	in	ADP
ejpam-2822	57	15	s	s	PROPN
ejpam-2822	57	16	,	,	PUNCT
ejpam-2822	57	17	then	then	ADV
ejpam-2822	57	18	µ	µ	VERB
ejpam-2822	57	19	◦	◦	NOUN
ejpam-2822	57	20	η(x	η(x	PUNCT
ejpam-2822	57	21	)	)	PUNCT
ejpam-2822	57	22	being	be	AUX
ejpam-2822	57	23	the	the	DET
ejpam-2822	57	24	least	least	ADJ
ejpam-2822	57	25	upper	upper	ADJ
ejpam-2822	57	26	bound	bind	VERB
ejpam-2822	57	27	of	of	ADP
ejpam-2822	57	28	the	the	DET
ejpam-2822	57	29	empty	empty	ADJ
ejpam-2822	57	30	set	set	NOUN
ejpam-2822	57	31	is	be	AUX
ejpam-2822	57	32	zero.it	zero.it	NOUN
ejpam-2822	57	33	can	can	AUX
ejpam-2822	57	34	be	be	AUX
ejpam-2822	57	35	verified	verify	VERB
ejpam-2822	57	36	easily	easily	ADV
ejpam-2822	57	37	that	that	SCONJ
ejpam-2822	57	38	the	the	DET
ejpam-2822	57	39	set	set	NOUN
ejpam-2822	57	40	product	product	NOUN
ejpam-2822	57	41	is	be	AUX
ejpam-2822	57	42	associative	associative	ADJ
ejpam-2822	57	43	in	in	ADP
ejpam-2822	57	44	ls	ls	PROPN
ejpam-2822	57	45	if	if	SCONJ
ejpam-2822	57	46	s	s	PROPN
ejpam-2822	57	47	is	be	AUX
ejpam-2822	57	48	a	a	DET
ejpam-2822	57	49	semigroup	semigroup	NOUN
ejpam-2822	57	50	.	.	PUNCT
ejpam-2822	58	1	throughout	throughout	ADP
ejpam-2822	58	2	this	this	DET
ejpam-2822	58	3	paper	paper	NOUN
ejpam-2822	58	4	g	g	PROPN
ejpam-2822	58	5	denotes	denote	VERB
ejpam-2822	58	6	an	an	DET
ejpam-2822	58	7	ordinary	ordinary	ADJ
ejpam-2822	58	8	group	group	NOUN
ejpam-2822	58	9	with	with	ADP
ejpam-2822	58	10	the	the	DET
ejpam-2822	58	11	identity	identity	NOUN
ejpam-2822	58	12	element	element	NOUN
ejpam-2822	58	13	‘	'	PUNCT
ejpam-2822	58	14	e	e	NOUN
ejpam-2822	58	15	’	'	PUNCT
ejpam-2822	58	16	,	,	PUNCT
ejpam-2822	58	17	and	and	CCONJ
ejpam-2822	58	18	i	i	PRON
ejpam-2822	58	19	denotes	denote	VERB
ejpam-2822	58	20	a	a	DET
ejpam-2822	58	21	nonempty	nonempty	ADJ
ejpam-2822	58	22	indexing	indexing	NOUN
ejpam-2822	58	23	set	set	NOUN
ejpam-2822	58	24	.	.	PUNCT
ejpam-2822	59	1	definition	definition	NOUN
ejpam-2822	59	2	1	1	NUM
ejpam-2822	59	3	.	.	PUNCT
ejpam-2822	60	1	let	let	VERB
ejpam-2822	60	2	µ	µ	PRON
ejpam-2822	60	3	∈	∈	PROPN
ejpam-2822	60	4	lg	lg	NOUN
ejpam-2822	60	5	.	.	PROPN
ejpam-2822	61	1	then	then	ADV
ejpam-2822	61	2	,	,	PUNCT
ejpam-2822	61	3	µ	µ	X
ejpam-2822	61	4	is	be	AUX
ejpam-2822	61	5	called	call	VERB
ejpam-2822	61	6	an	an	DET
ejpam-2822	61	7	l	l	NOUN
ejpam-2822	61	8	-	-	NOUN
ejpam-2822	61	9	subgroup	subgroup	NOUN
ejpam-2822	61	10	of	of	ADP
ejpam-2822	61	11	g	g	PROPN
ejpam-2822	61	12	if	if	SCONJ
ejpam-2822	61	13	for	for	ADP
ejpam-2822	61	14	each	each	DET
ejpam-2822	61	15	x	x	NOUN
ejpam-2822	61	16	,	,	PUNCT
ejpam-2822	61	17	y	y	PROPN
ejpam-2822	61	18	∈	∈	PROPN
ejpam-2822	61	19	g	g	PROPN
ejpam-2822	61	20	(	(	PUNCT
ejpam-2822	61	21	i	i	PROPN
ejpam-2822	61	22	)	)	PUNCT
ejpam-2822	61	23	µ(xy	µ(xy	PROPN
ejpam-2822	61	24	)	)	PUNCT
ejpam-2822	61	25	≥	≥	NOUN
ejpam-2822	61	26	µ(x	µ(x	VERB
ejpam-2822	61	27	)	)	PUNCT
ejpam-2822	61	28	∧	∧	PROPN
ejpam-2822	61	29	µ(y	µ(y	PROPN
ejpam-2822	61	30	)	)	PUNCT
ejpam-2822	61	31	,	,	PUNCT
ejpam-2822	61	32	(	(	PUNCT
ejpam-2822	61	33	ii	ii	NOUN
ejpam-2822	61	34	)	)	PUNCT
ejpam-2822	61	35	µ(x−1	µ(x−1	NOUN
ejpam-2822	61	36	)	)	PUNCT
ejpam-2822	61	37	=	=	SYM
ejpam-2822	61	38	µ(x	µ(x	NUM
ejpam-2822	61	39	)	)	PUNCT
ejpam-2822	61	40	.	.	PUNCT
ejpam-2822	62	1	the	the	DET
ejpam-2822	62	2	set	set	NOUN
ejpam-2822	62	3	of	of	ADP
ejpam-2822	62	4	l	l	NOUN
ejpam-2822	62	5	-	-	NOUN
ejpam-2822	62	6	subgroups	subgroup	NOUN
ejpam-2822	62	7	of	of	ADP
ejpam-2822	62	8	g	g	PROPN
ejpam-2822	62	9	is	be	AUX
ejpam-2822	62	10	denoted	denote	VERB
ejpam-2822	62	11	by	by	ADP
ejpam-2822	62	12	l(g	l(g	NOUN
ejpam-2822	62	13	)	)	PUNCT
ejpam-2822	62	14	.	.	PUNCT
ejpam-2822	63	1	clearly	clearly	ADV
ejpam-2822	63	2	,	,	PUNCT
ejpam-2822	63	3	the	the	DET
ejpam-2822	63	4	tip	tip	NOUN
ejpam-2822	63	5	of	of	ADP
ejpam-2822	63	6	an	an	DET
ejpam-2822	63	7	l	l	NOUN
ejpam-2822	63	8	-	-	NOUN
ejpam-2822	63	9	subgroup	subgroup	NOUN
ejpam-2822	63	10	is	be	AUX
ejpam-2822	63	11	attained	attain	VERB
ejpam-2822	63	12	at	at	ADP
ejpam-2822	63	13	the	the	DET
ejpam-2822	63	14	identity	identity	NOUN
ejpam-2822	63	15	element	element	NOUN
ejpam-2822	63	16	e	e	PROPN
ejpam-2822	63	17	of	of	ADP
ejpam-2822	63	18	g.	g.	PROPN
ejpam-2822	63	19	definition	definition	NOUN
ejpam-2822	63	20	2	2	NUM
ejpam-2822	63	21	.	.	PUNCT
ejpam-2822	64	1	let	let	VERB
ejpam-2822	64	2	µ	µ	PRON
ejpam-2822	64	3	∈	∈	PROPN
ejpam-2822	64	4	l(g	l(g	NOUN
ejpam-2822	64	5	)	)	PUNCT
ejpam-2822	64	6	.	.	PUNCT
ejpam-2822	65	1	then	then	ADV
ejpam-2822	65	2	,	,	PUNCT
ejpam-2822	65	3	µ	µ	X
ejpam-2822	65	4	is	be	AUX
ejpam-2822	65	5	called	call	VERB
ejpam-2822	65	6	a	a	DET
ejpam-2822	65	7	normal	normal	ADJ
ejpam-2822	65	8	lsubgroup	lsubgroup	NOUN
ejpam-2822	65	9	of	of	ADP
ejpam-2822	65	10	g	g	PROPN
ejpam-2822	65	11	if	if	SCONJ
ejpam-2822	65	12	,	,	PUNCT
ejpam-2822	65	13	µ(xy	µ(xy	PROPN
ejpam-2822	65	14	)	)	PUNCT
ejpam-2822	65	15	=	=	PUNCT
ejpam-2822	65	16	µ(yx	µ(yx	NOUN
ejpam-2822	65	17	)	)	PUNCT
ejpam-2822	65	18	for	for	ADP
ejpam-2822	65	19	all	all	DET
ejpam-2822	65	20	x	x	NOUN
ejpam-2822	65	21	,	,	PUNCT
ejpam-2822	65	22	y	y	PROPN
ejpam-2822	65	23	∈	∈	PROPN
ejpam-2822	65	24	g.	g.	NOUN
ejpam-2822	65	25	it	it	PRON
ejpam-2822	65	26	is	be	AUX
ejpam-2822	65	27	well	well	ADV
ejpam-2822	65	28	known	know	VERB
ejpam-2822	65	29	that	that	SCONJ
ejpam-2822	65	30	the	the	DET
ejpam-2822	65	31	intersection	intersection	NOUN
ejpam-2822	65	32	of	of	ADP
ejpam-2822	65	33	any	any	DET
ejpam-2822	65	34	arbitrary	arbitrary	ADJ
ejpam-2822	65	35	family	family	NOUN
ejpam-2822	65	36	of	of	ADP
ejpam-2822	65	37	l	l	NOUN
ejpam-2822	65	38	-	-	NOUN
ejpam-2822	65	39	subgroups	subgroup	NOUN
ejpam-2822	65	40	of	of	ADP
ejpam-2822	65	41	a	a	DET
ejpam-2822	65	42	group	group	NOUN
ejpam-2822	65	43	is	be	AUX
ejpam-2822	65	44	an	an	DET
ejpam-2822	65	45	l	l	NOUN
ejpam-2822	65	46	-	-	NOUN
ejpam-2822	65	47	subgroup	subgroup	NOUN
ejpam-2822	65	48	of	of	ADP
ejpam-2822	65	49	the	the	DET
ejpam-2822	65	50	given	give	VERB
ejpam-2822	65	51	group	group	NOUN
ejpam-2822	65	52	.	.	PUNCT
ejpam-2822	66	1	i.	i.	PROPN
ejpam-2822	66	2	jahan	jahan	PROPN
ejpam-2822	66	3	,	,	PUNCT
ejpam-2822	66	4	n.	n.	PROPN
ejpam-2822	66	5	ajmal	ajmal	PROPN
ejpam-2822	66	6	,	,	PUNCT
ejpam-2822	66	7	b.	b.	PROPN
ejpam-2822	66	8	davvaz	davvaz	PROPN
ejpam-2822	66	9	/	/	SYM
ejpam-2822	66	10	eur	eur	PROPN
ejpam-2822	66	11	.	.	PUNCT
ejpam-2822	67	1	j.	j.	PROPN
ejpam-2822	67	2	pure	pure	PROPN
ejpam-2822	67	3	appl	appl	PROPN
ejpam-2822	67	4	.	.	PROPN
ejpam-2822	67	5	math	math	PROPN
ejpam-2822	67	6	,	,	PUNCT
ejpam-2822	67	7	10	10	NUM
ejpam-2822	67	8	(	(	PUNCT
ejpam-2822	67	9	2	2	NUM
ejpam-2822	67	10	)	)	PUNCT
ejpam-2822	67	11	(	(	PUNCT
ejpam-2822	67	12	2017	2017	NUM
ejpam-2822	67	13	)	)	PUNCT
ejpam-2822	67	14	,	,	PUNCT
ejpam-2822	67	15	255	255	NUM
ejpam-2822	67	16	-	-	SYM
ejpam-2822	67	17	271	271	NUM
ejpam-2822	67	18	258	258	NUM
ejpam-2822	67	19	definition	definition	NOUN
ejpam-2822	67	20	3	3	NUM
ejpam-2822	67	21	.	.	PUNCT
ejpam-2822	68	1	let	let	VERB
ejpam-2822	68	2	µ	µ	PRON
ejpam-2822	68	3	∈	∈	PROPN
ejpam-2822	68	4	lg	lg	NOUN
ejpam-2822	68	5	.	.	PROPN
ejpam-2822	69	1	then	then	ADV
ejpam-2822	69	2	,	,	PUNCT
ejpam-2822	69	3	the	the	DET
ejpam-2822	69	4	l	l	NOUN
ejpam-2822	69	5	-	-	NOUN
ejpam-2822	69	6	subgroup	subgroup	NOUN
ejpam-2822	69	7	of	of	ADP
ejpam-2822	69	8	g	g	PROPN
ejpam-2822	69	9	generated	generate	VERB
ejpam-2822	69	10	by	by	ADP
ejpam-2822	69	11	µ	µ	PROPN
ejpam-2822	69	12	is	be	AUX
ejpam-2822	69	13	defined	define	VERB
ejpam-2822	69	14	as	as	ADP
ejpam-2822	69	15	the	the	DET
ejpam-2822	69	16	smallest	small	ADJ
ejpam-2822	69	17	l	l	NOUN
ejpam-2822	69	18	-	-	NOUN
ejpam-2822	69	19	subgroup	subgroup	NOUN
ejpam-2822	69	20	of	of	ADP
ejpam-2822	69	21	g	g	PROPN
ejpam-2822	69	22	which	which	PRON
ejpam-2822	69	23	contains	contain	VERB
ejpam-2822	69	24	µ.	µ.	NOUN
ejpam-2822	69	25	it	it	PRON
ejpam-2822	69	26	is	be	AUX
ejpam-2822	69	27	denoted	denote	VERB
ejpam-2822	69	28	by	by	ADP
ejpam-2822	69	29	〈	〈	PROPN
ejpam-2822	69	30	µ	µ	NOUN
ejpam-2822	69	31	〉	〉	PROPN
ejpam-2822	69	32	i.e.	i.e.	X
ejpam-2822	69	33	〈	〈	PROPN
ejpam-2822	69	34	µ	µ	NOUN
ejpam-2822	69	35	〉	〉	NOUN
ejpam-2822	69	36	=	=	SYM
ejpam-2822	69	37	∩{µi	∩{µi	PROPN
ejpam-2822	69	38	∈	∈	NOUN
ejpam-2822	69	39	l(g	l(g	NOUN
ejpam-2822	69	40	)	)	PUNCT
ejpam-2822	69	41	:	:	PUNCT
ejpam-2822	69	42	µ	µ	PROPN
ejpam-2822	69	43	⊆	⊆	NUM
ejpam-2822	69	44	µi	µi	PROPN
ejpam-2822	69	45	}	}	PUNCT
ejpam-2822	69	46	.	.	PUNCT
ejpam-2822	70	1	if	if	SCONJ
ejpam-2822	70	2	µ	µ	NUM
ejpam-2822	70	3	,	,	PUNCT
ejpam-2822	70	4	η	η	PROPN
ejpam-2822	70	5	∈	∈	PROPN
ejpam-2822	70	6	l(g	l(g	PROPN
ejpam-2822	70	7	)	)	PUNCT
ejpam-2822	70	8	and	and	CCONJ
ejpam-2822	70	9	η	η	PROPN
ejpam-2822	70	10	⊆	⊆	PROPN
ejpam-2822	70	11	µ	µ	NUM
ejpam-2822	70	12	,	,	PUNCT
ejpam-2822	70	13	then	then	ADV
ejpam-2822	70	14	we	we	PRON
ejpam-2822	70	15	say	say	VERB
ejpam-2822	70	16	that	that	SCONJ
ejpam-2822	70	17	η	η	PROPN
ejpam-2822	70	18	is	be	AUX
ejpam-2822	70	19	an	an	DET
ejpam-2822	70	20	l	l	NOUN
ejpam-2822	70	21	-	-	NOUN
ejpam-2822	70	22	subgroup	subgroup	NOUN
ejpam-2822	70	23	of	of	ADP
ejpam-2822	70	24	g.	g.	PROPN
ejpam-2822	70	25	further	far	ADV
ejpam-2822	70	26	,	,	PUNCT
ejpam-2822	70	27	if	if	SCONJ
ejpam-2822	70	28	η	η	PROPN
ejpam-2822	70	29	is	be	AUX
ejpam-2822	70	30	non	non	ADJ
ejpam-2822	70	31	-	-	ADJ
ejpam-2822	70	32	constant	constant	ADJ
ejpam-2822	70	33	and	and	CCONJ
ejpam-2822	70	34	µ	µ	PROPN
ejpam-2822	70	35	6=	6=	PROPN
ejpam-2822	70	36	η	η	PROPN
ejpam-2822	70	37	,	,	PUNCT
ejpam-2822	70	38	then	then	ADV
ejpam-2822	70	39	η	η	PROPN
ejpam-2822	70	40	is	be	AUX
ejpam-2822	70	41	said	say	VERB
ejpam-2822	70	42	to	to	PART
ejpam-2822	70	43	be	be	AUX
ejpam-2822	70	44	a	a	DET
ejpam-2822	70	45	proper	proper	ADJ
ejpam-2822	70	46	l	l	NOUN
ejpam-2822	70	47	-	-	NOUN
ejpam-2822	70	48	subgroup	subgroup	NOUN
ejpam-2822	70	49	of	of	ADP
ejpam-2822	70	50	µ.	µ.	PROPN
ejpam-2822	70	51	clearly	clearly	ADV
ejpam-2822	70	52	,	,	PUNCT
ejpam-2822	70	53	η	η	PROPN
ejpam-2822	70	54	is	be	AUX
ejpam-2822	70	55	a	a	DET
ejpam-2822	70	56	proper	proper	ADJ
ejpam-2822	70	57	l	l	NOUN
ejpam-2822	70	58	-	-	NOUN
ejpam-2822	70	59	subgroup	subgroup	NOUN
ejpam-2822	70	60	of	of	ADP
ejpam-2822	70	61	µ	µ	NOUN
ejpam-2822	70	62	if	if	NOUN
ejpam-2822	70	63	and	and	CCONJ
ejpam-2822	70	64	only	only	ADV
ejpam-2822	70	65	if	if	SCONJ
ejpam-2822	70	66	η	η	PROPN
ejpam-2822	70	67	has	have	VERB
ejpam-2822	70	68	distinct	distinct	ADJ
ejpam-2822	70	69	tip	tip	NOUN
ejpam-2822	70	70	and	and	CCONJ
ejpam-2822	70	71	tail	tail	NOUN
ejpam-2822	70	72	and	and	CCONJ
ejpam-2822	70	73	η	η	PROPN
ejpam-2822	70	74	6=	6=	PROPN
ejpam-2822	70	75	µ.	µ.	PROPN
ejpam-2822	70	76	also	also	ADV
ejpam-2822	70	77	,	,	PUNCT
ejpam-2822	70	78	η	η	PROPN
ejpam-2822	70	79	is	be	AUX
ejpam-2822	70	80	said	say	VERB
ejpam-2822	70	81	to	to	PART
ejpam-2822	70	82	be	be	AUX
ejpam-2822	70	83	a	a	DET
ejpam-2822	70	84	trivial	trivial	ADJ
ejpam-2822	70	85	l	l	NOUN
ejpam-2822	70	86	-	-	NOUN
ejpam-2822	70	87	subgroup	subgroup	NOUN
ejpam-2822	70	88	of	of	ADP
ejpam-2822	70	89	µ	µ	PROPN
ejpam-2822	70	90	if	if	SCONJ
ejpam-2822	70	91	its	its	PRON
ejpam-2822	70	92	chain	chain	NOUN
ejpam-2822	70	93	of	of	ADP
ejpam-2822	70	94	level	level	NOUN
ejpam-2822	70	95	subgroups	subgroup	NOUN
ejpam-2822	70	96	contains	contain	VERB
ejpam-2822	70	97	only	only	ADV
ejpam-2822	70	98	e	e	PROPN
ejpam-2822	70	99	and	and	CCONJ
ejpam-2822	70	100	g.	g.	PROPN
ejpam-2822	70	101	thus	thus	ADV
ejpam-2822	70	102	,	,	PUNCT
ejpam-2822	70	103	an	an	PRON
ejpam-2822	70	104	l	l	NOUN
ejpam-2822	70	105	-	-	NOUN
ejpam-2822	70	106	subgroup	subgroup	NOUN
ejpam-2822	70	107	may	may	AUX
ejpam-2822	70	108	contain	contain	VERB
ejpam-2822	70	109	several	several	ADJ
ejpam-2822	70	110	trivial	trivial	ADJ
ejpam-2822	70	111	l	l	NOUN
ejpam-2822	70	112	-	-	PUNCT
ejpam-2822	70	113	subgroups	subgroup	NOUN
ejpam-2822	70	114	.	.	PUNCT
ejpam-2822	71	1	let	let	VERB
ejpam-2822	71	2	η	η	PROPN
ejpam-2822	71	3	be	be	AUX
ejpam-2822	71	4	an	an	DET
ejpam-2822	71	5	l	l	NOUN
ejpam-2822	71	6	-	-	NOUN
ejpam-2822	71	7	subgroup	subgroup	NOUN
ejpam-2822	71	8	of	of	ADP
ejpam-2822	71	9	µ.	µ.	PROPN
ejpam-2822	71	10	then	then	ADV
ejpam-2822	71	11	,	,	PUNCT
ejpam-2822	71	12	we	we	PRON
ejpam-2822	71	13	define	define	VERB
ejpam-2822	71	14	the	the	DET
ejpam-2822	71	15	following	follow	VERB
ejpam-2822	71	16	l	l	NOUN
ejpam-2822	71	17	-	-	NOUN
ejpam-2822	71	18	subgroup	subgroup	NOUN
ejpam-2822	71	19	of	of	ADP
ejpam-2822	71	20	µ	µ	PROPN
ejpam-2822	71	21	contained	contain	VERB
ejpam-2822	71	22	in	in	ADP
ejpam-2822	71	23	η	η	PROPN
ejpam-2822	71	24	,	,	PUNCT
ejpam-2822	71	25	denoted	denote	VERB
ejpam-2822	71	26	by	by	ADP
ejpam-2822	71	27	ηa0t0	ηa0t0	PROPN
ejpam-2822	71	28	,	,	PUNCT
ejpam-2822	71	29	as	as	SCONJ
ejpam-2822	71	30	follows	follow	VERB
ejpam-2822	71	31	:	:	PUNCT
ejpam-2822	71	32	ηa0t0	ηa0t0	PROPN
ejpam-2822	71	33	(	(	PUNCT
ejpam-2822	71	34	y	y	NOUN
ejpam-2822	71	35	)	)	PUNCT
ejpam-2822	71	36	=	=	PRON
ejpam-2822	71	37	{	{	PUNCT
ejpam-2822	71	38	a0	a0	NOUN
ejpam-2822	71	39	,	,	PUNCT
ejpam-2822	71	40	if	if	SCONJ
ejpam-2822	71	41	y	y	PROPN
ejpam-2822	71	42	=	=	SYM
ejpam-2822	71	43	e	e	PROPN
ejpam-2822	71	44	,	,	PUNCT
ejpam-2822	71	45	t0	t0	PROPN
ejpam-2822	71	46	,	,	PUNCT
ejpam-2822	71	47	if	if	SCONJ
ejpam-2822	71	48	y	y	PROPN
ejpam-2822	71	49	6=	6=	PROPN
ejpam-2822	71	50	e	e	PROPN
ejpam-2822	71	51	,	,	PUNCT
ejpam-2822	71	52	where	where	SCONJ
ejpam-2822	71	53	a0	a0	PROPN
ejpam-2822	71	54	=	=	SYM
ejpam-2822	71	55	η(e	η(e	PROPN
ejpam-2822	71	56	)	)	PUNCT
ejpam-2822	71	57	and	and	CCONJ
ejpam-2822	71	58	t0	t0	PROPN
ejpam-2822	71	59	=	=	PROPN
ejpam-2822	71	60	inf	inf	PROPN
ejpam-2822	71	61	η	η	PROPN
ejpam-2822	71	62	.	.	PROPN
ejpam-2822	71	63	here	here	ADV
ejpam-2822	71	64	ηa0t0	ηa0t0	PROPN
ejpam-2822	71	65	,	,	PUNCT
ejpam-2822	71	66	a	a	DET
ejpam-2822	71	67	trivial	trivial	ADJ
ejpam-2822	71	68	l	l	NOUN
ejpam-2822	71	69	-	-	NOUN
ejpam-2822	71	70	subgroup	subgroup	NOUN
ejpam-2822	71	71	of	of	ADP
ejpam-2822	71	72	µ	µ	NUM
ejpam-2822	71	73	,	,	PUNCT
ejpam-2822	71	74	is	be	AUX
ejpam-2822	71	75	called	call	VERB
ejpam-2822	71	76	the	the	DET
ejpam-2822	71	77	trivial	trivial	ADJ
ejpam-2822	71	78	l	l	NOUN
ejpam-2822	71	79	-	-	NOUN
ejpam-2822	71	80	subgroup	subgroup	NOUN
ejpam-2822	71	81	of	of	ADP
ejpam-2822	71	82	η	η	PROPN
ejpam-2822	71	83	.	.	PROPN
ejpam-2822	71	84	henceforth	henceforth	PROPN
ejpam-2822	71	85	µ	µ	PROPN
ejpam-2822	71	86	denotes	denote	VERB
ejpam-2822	71	87	an	an	DET
ejpam-2822	71	88	l	l	NOUN
ejpam-2822	71	89	-	-	NOUN
ejpam-2822	71	90	subgroup	subgroup	NOUN
ejpam-2822	71	91	of	of	ADP
ejpam-2822	71	92	g	g	PROPN
ejpam-2822	72	1	and	and	CCONJ
ejpam-2822	72	2	we	we	PRON
ejpam-2822	72	3	call	call	VERB
ejpam-2822	72	4	the	the	DET
ejpam-2822	72	5	parent	parent	NOUN
ejpam-2822	72	6	l	l	NOUN
ejpam-2822	72	7	-	-	NOUN
ejpam-2822	72	8	subgroup	subgroup	NOUN
ejpam-2822	72	9	simply	simply	ADV
ejpam-2822	72	10	an	an	DET
ejpam-2822	72	11	l	l	NOUN
ejpam-2822	72	12	-	-	NOUN
ejpam-2822	72	13	group	group	NOUN
ejpam-2822	72	14	.	.	PUNCT
ejpam-2822	73	1	the	the	DET
ejpam-2822	73	2	set	set	NOUN
ejpam-2822	73	3	of	of	ADP
ejpam-2822	73	4	l	l	NOUN
ejpam-2822	73	5	-	-	NOUN
ejpam-2822	73	6	subgroups	subgroup	NOUN
ejpam-2822	73	7	of	of	ADP
ejpam-2822	73	8	µ	µ	NOUN
ejpam-2822	73	9	is	be	AUX
ejpam-2822	73	10	denoted	denote	VERB
ejpam-2822	73	11	by	by	ADP
ejpam-2822	73	12	l(µ	l(µ	PROPN
ejpam-2822	73	13	)	)	PUNCT
ejpam-2822	73	14	.	.	PUNCT
ejpam-2822	74	1	remark	remark	PROPN
ejpam-2822	74	2	1	1	NUM
ejpam-2822	74	3	.	.	PUNCT
ejpam-2822	75	1	if	if	SCONJ
ejpam-2822	75	2	η	η	PROPN
ejpam-2822	75	3	∈	∈	PROPN
ejpam-2822	75	4	lµ	lµ	PROPN
ejpam-2822	75	5	,	,	PUNCT
ejpam-2822	75	6	then	then	ADV
ejpam-2822	75	7	it	it	PRON
ejpam-2822	75	8	can	can	AUX
ejpam-2822	75	9	be	be	AUX
ejpam-2822	75	10	easily	easily	ADV
ejpam-2822	75	11	verified	verify	VERB
ejpam-2822	75	12	that	that	SCONJ
ejpam-2822	75	13	〈	〈	PROPN
ejpam-2822	75	14	η〉µ	η〉µ	PROPN
ejpam-2822	75	15	=	=	PUNCT
ejpam-2822	75	16	〈	〈	PROPN
ejpam-2822	75	17	η	η	PROPN
ejpam-2822	75	18	〉	〉	PROPN
ejpam-2822	75	19	,	,	PUNCT
ejpam-2822	75	20	where	where	SCONJ
ejpam-2822	75	21	〈	〈	PROPN
ejpam-2822	75	22	η〉µ	η〉µ	PROPN
ejpam-2822	75	23	denotes	denote	VERB
ejpam-2822	75	24	the	the	DET
ejpam-2822	75	25	l	l	NOUN
ejpam-2822	75	26	-	-	NOUN
ejpam-2822	75	27	subgroup	subgroup	NOUN
ejpam-2822	75	28	of	of	ADP
ejpam-2822	75	29	µ	µ	PROPN
ejpam-2822	75	30	generated	generate	VERB
ejpam-2822	75	31	by	by	ADP
ejpam-2822	75	32	η	η	PROPN
ejpam-2822	75	33	.	.	PROPN
ejpam-2822	75	34	we	we	PRON
ejpam-2822	75	35	recall	recall	VERB
ejpam-2822	75	36	the	the	DET
ejpam-2822	75	37	definition	definition	NOUN
ejpam-2822	75	38	of	of	ADP
ejpam-2822	75	39	a	a	DET
ejpam-2822	75	40	normal	normal	ADJ
ejpam-2822	75	41	l	l	NOUN
ejpam-2822	75	42	-	-	NOUN
ejpam-2822	75	43	subgroup	subgroup	NOUN
ejpam-2822	75	44	of	of	ADP
ejpam-2822	75	45	an	an	DET
ejpam-2822	75	46	l	l	NOUN
ejpam-2822	75	47	-	-	NOUN
ejpam-2822	75	48	group	group	NOUN
ejpam-2822	75	49	.	.	PUNCT
ejpam-2822	76	1	definition	definition	NOUN
ejpam-2822	76	2	4	4	NUM
ejpam-2822	76	3	.	.	PUNCT
ejpam-2822	76	4	let	let	VERB
ejpam-2822	76	5	η	η	PROPN
ejpam-2822	76	6	∈	∈	PROPN
ejpam-2822	76	7	l(µ	l(µ	PROPN
ejpam-2822	76	8	)	)	PUNCT
ejpam-2822	76	9	.	.	PUNCT
ejpam-2822	77	1	then	then	ADV
ejpam-2822	77	2	,	,	PUNCT
ejpam-2822	77	3	we	we	PRON
ejpam-2822	77	4	say	say	VERB
ejpam-2822	77	5	that	that	SCONJ
ejpam-2822	77	6	η	η	PROPN
ejpam-2822	77	7	is	be	AUX
ejpam-2822	77	8	a	a	DET
ejpam-2822	77	9	normal	normal	ADJ
ejpam-2822	77	10	l	l	NOUN
ejpam-2822	77	11	-	-	NOUN
ejpam-2822	77	12	subgroup	subgroup	NOUN
ejpam-2822	77	13	of	of	ADP
ejpam-2822	77	14	µ	µ	NOUN
ejpam-2822	77	15	if	if	SCONJ
ejpam-2822	77	16	η(yxy−1	η(yxy−1	NOUN
ejpam-2822	77	17	)	)	PUNCT
ejpam-2822	77	18	≥	≥	NOUN
ejpam-2822	77	19	η(x	η(x	NOUN
ejpam-2822	77	20	)	)	PUNCT
ejpam-2822	77	21	∧	∧	PROPN
ejpam-2822	77	22	µ(y	µ(y	PROPN
ejpam-2822	77	23	)	)	PUNCT
ejpam-2822	77	24	for	for	ADP
ejpam-2822	77	25	all	all	DET
ejpam-2822	77	26	x	x	NOUN
ejpam-2822	77	27	,	,	PUNCT
ejpam-2822	77	28	y	y	PROPN
ejpam-2822	77	29	∈	∈	PROPN
ejpam-2822	77	30	g.	g.	NOUN
ejpam-2822	77	31	the	the	DET
ejpam-2822	77	32	set	set	NOUN
ejpam-2822	77	33	of	of	ADP
ejpam-2822	77	34	normal	normal	ADJ
ejpam-2822	77	35	l	l	NOUN
ejpam-2822	77	36	-	-	NOUN
ejpam-2822	77	37	subgroups	subgroup	NOUN
ejpam-2822	77	38	of	of	ADP
ejpam-2822	77	39	µ	µ	NOUN
ejpam-2822	77	40	is	be	AUX
ejpam-2822	77	41	denoted	denote	VERB
ejpam-2822	77	42	by	by	ADP
ejpam-2822	77	43	nl(µ	nl(µ	NOUN
ejpam-2822	77	44	)	)	PUNCT
ejpam-2822	77	45	.	.	PUNCT
ejpam-2822	78	1	proposition	proposition	NOUN
ejpam-2822	78	2	1	1	NUM
ejpam-2822	78	3	.	.	PUNCT
ejpam-2822	78	4	let	let	VERB
ejpam-2822	78	5	η	η	PROPN
ejpam-2822	78	6	∈	∈	PROPN
ejpam-2822	78	7	l(µ	l(µ	PROPN
ejpam-2822	78	8	)	)	PUNCT
ejpam-2822	78	9	and	and	CCONJ
ejpam-2822	78	10	θ	θ	PROPN
ejpam-2822	78	11	∈	∈	PROPN
ejpam-2822	78	12	nl(µ	nl(µ	NOUN
ejpam-2822	78	13	)	)	PUNCT
ejpam-2822	78	14	.	.	PUNCT
ejpam-2822	79	1	then	then	ADV
ejpam-2822	79	2	,	,	PUNCT
ejpam-2822	79	3	(	(	PUNCT
ejpam-2822	79	4	i	i	NOUN
ejpam-2822	79	5	)	)	PUNCT
ejpam-2822	79	6	η	η	PROPN
ejpam-2822	79	7	◦	◦	NOUN
ejpam-2822	79	8	θ	θ	X
ejpam-2822	79	9	∈	∈	PROPN
ejpam-2822	79	10	l(µ	l(µ	PROPN
ejpam-2822	79	11	)	)	PUNCT
ejpam-2822	79	12	.	.	PUNCT
ejpam-2822	80	1	(	(	PUNCT
ejpam-2822	80	2	ii)η	ii)η	NOUN
ejpam-2822	80	3	◦	◦	NOUN
ejpam-2822	80	4	θ	θ	X
ejpam-2822	80	5	∈	∈	NOUN
ejpam-2822	80	6	nl(µ	nl(µ	NOUN
ejpam-2822	80	7	)	)	PUNCT
ejpam-2822	80	8	if	if	SCONJ
ejpam-2822	80	9	η	η	PROPN
ejpam-2822	80	10	∈	∈	PROPN
ejpam-2822	80	11	nl(µ	nl(µ	NOUN
ejpam-2822	80	12	)	)	PUNCT
ejpam-2822	80	13	.	.	PUNCT
ejpam-2822	81	1	proposition	proposition	NOUN
ejpam-2822	81	2	2	2	NUM
ejpam-2822	81	3	.	.	PUNCT
ejpam-2822	81	4	let	let	VERB
ejpam-2822	81	5	η	η	PROPN
ejpam-2822	81	6	,	,	PUNCT
ejpam-2822	81	7	θ	θ	PROPN
ejpam-2822	81	8	∈	∈	PROPN
ejpam-2822	81	9	l(µ	l(µ	PROPN
ejpam-2822	81	10	)	)	PUNCT
ejpam-2822	81	11	.	.	PUNCT
ejpam-2822	82	1	then	then	ADV
ejpam-2822	82	2	,	,	PUNCT
ejpam-2822	82	3	η	η	PROPN
ejpam-2822	82	4	⊆	⊆	X
ejpam-2822	82	5	η	η	PROPN
ejpam-2822	82	6	◦	◦	NOUN
ejpam-2822	82	7	θ	θ	PROPN
ejpam-2822	82	8	and	and	CCONJ
ejpam-2822	82	9	θ	θ	PROPN
ejpam-2822	83	1	⊆	⊆	NUM
ejpam-2822	83	2	η	η	PROPN
ejpam-2822	83	3	◦	◦	NOUN
ejpam-2822	83	4	θ	θ	PROPN
ejpam-2822	83	5	if	if	SCONJ
ejpam-2822	83	6	and	and	CCONJ
ejpam-2822	83	7	only	only	ADV
ejpam-2822	83	8	if	if	SCONJ
ejpam-2822	83	9	η(e	η(e	NOUN
ejpam-2822	83	10	)	)	PUNCT
ejpam-2822	83	11	=	=	SYM
ejpam-2822	83	12	θ(e	θ(e	NUM
ejpam-2822	83	13	)	)	PUNCT
ejpam-2822	83	14	.	.	PUNCT
ejpam-2822	84	1	now	now	ADV
ejpam-2822	84	2	,	,	PUNCT
ejpam-2822	84	3	recall	recall	VERB
ejpam-2822	84	4	the	the	DET
ejpam-2822	84	5	following	following	NOUN
ejpam-2822	84	6	from	from	ADP
ejpam-2822	84	7	[	[	X
ejpam-2822	84	8	3	3	NUM
ejpam-2822	84	9	]	]	PUNCT
ejpam-2822	84	10	:	:	PUNCT
ejpam-2822	84	11	definition	definition	NOUN
ejpam-2822	84	12	5	5	NUM
ejpam-2822	84	13	.	.	PUNCT
ejpam-2822	85	1	let	let	VERB
ejpam-2822	85	2	η	η	PROPN
ejpam-2822	85	3	,	,	PUNCT
ejpam-2822	85	4	θ	θ	PROPN
ejpam-2822	85	5	∈	∈	PROPN
ejpam-2822	85	6	lµ.	lµ.	NOUN
ejpam-2822	85	7	then	then	ADV
ejpam-2822	85	8	,	,	PUNCT
ejpam-2822	85	9	the	the	DET
ejpam-2822	85	10	commutator	commutator	NOUN
ejpam-2822	85	11	of	of	ADP
ejpam-2822	85	12	η	η	PROPN
ejpam-2822	85	13	and	and	CCONJ
ejpam-2822	85	14	θ	θ	PROPN
ejpam-2822	85	15	is	be	AUX
ejpam-2822	85	16	an	an	DET
ejpam-2822	85	17	l	l	NOUN
ejpam-2822	85	18	-	-	NOUN
ejpam-2822	85	19	subset	subset	NOUN
ejpam-2822	85	20	(	(	PUNCT
ejpam-2822	85	21	η	η	PROPN
ejpam-2822	85	22	,	,	PUNCT
ejpam-2822	85	23	θ	θ	NOUN
ejpam-2822	85	24	)	)	PUNCT
ejpam-2822	85	25	of	of	ADP
ejpam-2822	85	26	g	g	PROPN
ejpam-2822	85	27	defined	define	VERB
ejpam-2822	85	28	as	as	SCONJ
ejpam-2822	85	29	follows	follow	VERB
ejpam-2822	85	30	:	:	PUNCT
ejpam-2822	85	31	(	(	PUNCT
ejpam-2822	85	32	η	η	PROPN
ejpam-2822	85	33	,	,	PUNCT
ejpam-2822	85	34	θ)(x	θ)(x	PROPN
ejpam-2822	85	35	)	)	PUNCT
ejpam-2822	86	1	=	=	PRON
ejpam-2822	86	2	{	{	PUNCT
ejpam-2822	86	3	∨{η(y	∨{η(y	NOUN
ejpam-2822	86	4	)	)	PUNCT
ejpam-2822	86	5	∧	∧	PROPN
ejpam-2822	86	6	θ(z	θ(z	NOUN
ejpam-2822	86	7	)	)	PUNCT
ejpam-2822	86	8	}	}	PUNCT
ejpam-2822	86	9	,	,	PUNCT
ejpam-2822	86	10	if	if	SCONJ
ejpam-2822	86	11	x	x	X
ejpam-2822	86	12	=	=	PUNCT
ejpam-2822	87	1	[	[	X
ejpam-2822	87	2	y	y	PROPN
ejpam-2822	87	3	,	,	PUNCT
ejpam-2822	87	4	z	z	X
ejpam-2822	87	5	]	]	X
ejpam-2822	87	6	for	for	ADP
ejpam-2822	87	7	some	some	DET
ejpam-2822	87	8	y	y	PROPN
ejpam-2822	87	9	,	,	PUNCT
ejpam-2822	87	10	z	z	PROPN
ejpam-2822	87	11	∈	∈	PROPN
ejpam-2822	87	12	g	g	PROPN
ejpam-2822	87	13	,	,	PUNCT
ejpam-2822	87	14	inf	inf	PROPN
ejpam-2822	87	15	η	η	PROPN
ejpam-2822	87	16	∧	∧	PROPN
ejpam-2822	87	17	inf	inf	PROPN
ejpam-2822	87	18	θ	θ	NOUN
ejpam-2822	87	19	,	,	PUNCT
ejpam-2822	87	20	if	if	SCONJ
ejpam-2822	87	21	x	x	SYM
ejpam-2822	87	22	6=	6=	PROPN
ejpam-2822	88	1	[	[	X
ejpam-2822	88	2	y	y	PROPN
ejpam-2822	88	3	,	,	PUNCT
ejpam-2822	88	4	z	z	X
ejpam-2822	88	5	]	]	X
ejpam-2822	88	6	for	for	ADP
ejpam-2822	88	7	any	any	DET
ejpam-2822	88	8	y	y	NOUN
ejpam-2822	88	9	,	,	PUNCT
ejpam-2822	88	10	z	z	PROPN
ejpam-2822	88	11	∈	∈	PROPN
ejpam-2822	88	12	g.	g.	NOUN
ejpam-2822	88	13	the	the	DET
ejpam-2822	88	14	commutator	commutator	PROPN
ejpam-2822	88	15	l	l	PROPN
ejpam-2822	88	16	-	-	PROPN
ejpam-2822	88	17	subgroup	subgroup	NOUN
ejpam-2822	88	18	of	of	ADP
ejpam-2822	88	19	η	η	PROPN
ejpam-2822	88	20	,	,	PUNCT
ejpam-2822	88	21	θ	θ	PROPN
ejpam-2822	88	22	∈	∈	PROPN
ejpam-2822	89	1	lµ	lµ	PRON
ejpam-2822	89	2	is	be	AUX
ejpam-2822	89	3	defined	define	VERB
ejpam-2822	89	4	as	as	ADP
ejpam-2822	89	5	the	the	DET
ejpam-2822	89	6	l	l	NOUN
ejpam-2822	89	7	-	-	NOUN
ejpam-2822	89	8	subgroup	subgroup	NOUN
ejpam-2822	89	9	of	of	ADP
ejpam-2822	89	10	g	g	PROPN
ejpam-2822	89	11	generated	generate	VERB
ejpam-2822	89	12	by	by	ADP
ejpam-2822	89	13	(	(	PUNCT
ejpam-2822	89	14	η	η	PROPN
ejpam-2822	89	15	,	,	PUNCT
ejpam-2822	89	16	θ	θ	NOUN
ejpam-2822	89	17	)	)	PUNCT
ejpam-2822	89	18	.	.	PUNCT
ejpam-2822	90	1	it	it	PRON
ejpam-2822	90	2	is	be	AUX
ejpam-2822	90	3	denoted	denote	VERB
ejpam-2822	90	4	by	by	ADP
ejpam-2822	90	5	[	[	X
ejpam-2822	90	6	η	η	PROPN
ejpam-2822	90	7	,	,	PUNCT
ejpam-2822	90	8	θ	θ	PROPN
ejpam-2822	90	9	]	]	PUNCT
ejpam-2822	90	10	.	.	PUNCT
ejpam-2822	91	1	clearly	clearly	ADV
ejpam-2822	91	2	,	,	PUNCT
ejpam-2822	91	3	inf(η	inf(η	PROPN
ejpam-2822	91	4	,	,	PUNCT
ejpam-2822	91	5	θ	θ	NOUN
ejpam-2822	91	6	)	)	PUNCT
ejpam-2822	91	7	=	=	SYM
ejpam-2822	91	8	inf	inf	PROPN
ejpam-2822	91	9	η	η	PROPN
ejpam-2822	91	10	∧	∧	PROPN
ejpam-2822	91	11	inf	inf	PROPN
ejpam-2822	91	12	θ	θ	PROPN
ejpam-2822	91	13	and	and	CCONJ
ejpam-2822	91	14	[	[	X
ejpam-2822	91	15	η	η	PROPN
ejpam-2822	91	16	,	,	PUNCT
ejpam-2822	91	17	θ	θ	X
ejpam-2822	91	18	]	]	X
ejpam-2822	91	19	∈	∈	PROPN
ejpam-2822	91	20	l(µ	l(µ	PROPN
ejpam-2822	91	21	)	)	PUNCT
ejpam-2822	91	22	.	.	PUNCT
ejpam-2822	92	1	i.	i.	PROPN
ejpam-2822	92	2	jahan	jahan	PROPN
ejpam-2822	92	3	,	,	PUNCT
ejpam-2822	92	4	n.	n.	PROPN
ejpam-2822	92	5	ajmal	ajmal	PROPN
ejpam-2822	92	6	,	,	PUNCT
ejpam-2822	92	7	b.	b.	PROPN
ejpam-2822	92	8	davvaz	davvaz	PROPN
ejpam-2822	92	9	/	/	SYM
ejpam-2822	92	10	eur	eur	PROPN
ejpam-2822	92	11	.	.	PUNCT
ejpam-2822	93	1	j.	j.	PROPN
ejpam-2822	93	2	pure	pure	PROPN
ejpam-2822	93	3	appl	appl	PROPN
ejpam-2822	93	4	.	.	PROPN
ejpam-2822	93	5	math	math	PROPN
ejpam-2822	93	6	,	,	PUNCT
ejpam-2822	93	7	10	10	NUM
ejpam-2822	93	8	(	(	PUNCT
ejpam-2822	93	9	2	2	NUM
ejpam-2822	93	10	)	)	PUNCT
ejpam-2822	93	11	(	(	PUNCT
ejpam-2822	93	12	2017	2017	NUM
ejpam-2822	93	13	)	)	PUNCT
ejpam-2822	93	14	,	,	PUNCT
ejpam-2822	93	15	255	255	NUM
ejpam-2822	93	16	-	-	SYM
ejpam-2822	93	17	271	271	NUM
ejpam-2822	93	18	259	259	NUM
ejpam-2822	93	19	3	3	NUM
ejpam-2822	93	20	.	.	PUNCT
ejpam-2822	94	1	nilpotent	nilpotent	ADJ
ejpam-2822	94	2	l	l	NOUN
ejpam-2822	94	3	-	-	NOUN
ejpam-2822	94	4	subgroup	subgroup	NOUN
ejpam-2822	94	5	in	in	ADP
ejpam-2822	94	6	[	[	X
ejpam-2822	94	7	6	6	NUM
ejpam-2822	94	8	]	]	PUNCT
ejpam-2822	94	9	,	,	PUNCT
ejpam-2822	94	10	ajmal	ajmal	PROPN
ejpam-2822	94	11	and	and	CCONJ
ejpam-2822	94	12	jahan	jahan	PROPN
ejpam-2822	94	13	extended	extend	VERB
ejpam-2822	94	14	the	the	DET
ejpam-2822	94	15	construction	construction	NOUN
ejpam-2822	94	16	of	of	ADP
ejpam-2822	94	17	a	a	DET
ejpam-2822	94	18	fuzzy	fuzzy	ADJ
ejpam-2822	94	19	subgroup	subgroup	NOUN
ejpam-2822	94	20	generated	generate	VERB
ejpam-2822	94	21	by	by	ADP
ejpam-2822	94	22	a	a	DET
ejpam-2822	94	23	fuzzy	fuzzy	ADJ
ejpam-2822	94	24	subset	subset	NOUN
ejpam-2822	94	25	to	to	ADP
ejpam-2822	94	26	l	l	NOUN
ejpam-2822	94	27	-	-	VERB
ejpam-2822	94	28	setting	setting	NOUN
ejpam-2822	94	29	.	.	PUNCT
ejpam-2822	95	1	they	they	PRON
ejpam-2822	95	2	proved	prove	VERB
ejpam-2822	95	3	for	for	ADP
ejpam-2822	95	4	an	an	DET
ejpam-2822	95	5	l	l	NOUN
ejpam-2822	95	6	-	-	NOUN
ejpam-2822	95	7	subset	subset	NOUN
ejpam-2822	95	8	of	of	ADP
ejpam-2822	95	9	a	a	DET
ejpam-2822	95	10	group	group	NOUN
ejpam-2822	95	11	,	,	PUNCT
ejpam-2822	95	12	the	the	DET
ejpam-2822	95	13	subgroup	subgroup	NOUN
ejpam-2822	95	14	generated	generate	VERB
ejpam-2822	95	15	by	by	ADP
ejpam-2822	95	16	its	its	PRON
ejpam-2822	95	17	level	level	NOUN
ejpam-2822	95	18	subset	subset	NOUN
ejpam-2822	95	19	is	be	AUX
ejpam-2822	95	20	the	the	DET
ejpam-2822	95	21	level	level	NOUN
ejpam-2822	95	22	subset	subset	NOUN
ejpam-2822	95	23	of	of	ADP
ejpam-2822	95	24	the	the	DET
ejpam-2822	95	25	subgroup	subgroup	NOUN
ejpam-2822	95	26	generated	generate	VERB
ejpam-2822	95	27	by	by	ADP
ejpam-2822	95	28	that	that	DET
ejpam-2822	95	29	l	l	NOUN
ejpam-2822	95	30	-	-	NOUN
ejpam-2822	95	31	subset	subset	NOUN
ejpam-2822	95	32	provided	provide	VERB
ejpam-2822	95	33	the	the	DET
ejpam-2822	95	34	given	give	VERB
ejpam-2822	95	35	l	l	NOUN
ejpam-2822	95	36	-	-	ADJ
ejpam-2822	95	37	subset	subset	VERB
ejpam-2822	95	38	possesses	possesse	NOUN
ejpam-2822	95	39	sup	sup	NOUN
ejpam-2822	95	40	-	-	PUNCT
ejpam-2822	95	41	property	property	NOUN
ejpam-2822	95	42	.	.	PUNCT
ejpam-2822	96	1	firstly	firstly	ADV
ejpam-2822	96	2	,	,	PUNCT
ejpam-2822	96	3	we	we	PRON
ejpam-2822	96	4	recall	recall	VERB
ejpam-2822	96	5	from	from	ADP
ejpam-2822	96	6	[	[	X
ejpam-2822	96	7	6	6	NUM
ejpam-2822	96	8	]	]	PUNCT
ejpam-2822	96	9	a	a	DET
ejpam-2822	96	10	construction	construction	NOUN
ejpam-2822	96	11	for	for	ADP
ejpam-2822	96	12	generating	generate	VERB
ejpam-2822	96	13	an	an	DET
ejpam-2822	96	14	l	l	NOUN
ejpam-2822	96	15	-	-	NOUN
ejpam-2822	96	16	subgroup	subgroup	NOUN
ejpam-2822	96	17	by	by	ADP
ejpam-2822	96	18	a	a	DET
ejpam-2822	96	19	given	give	VERB
ejpam-2822	96	20	l	l	NOUN
ejpam-2822	96	21	-	-	NOUN
ejpam-2822	96	22	subset	subset	NOUN
ejpam-2822	96	23	of	of	ADP
ejpam-2822	96	24	an	an	DET
ejpam-2822	96	25	l	l	NOUN
ejpam-2822	96	26	-	-	NOUN
ejpam-2822	96	27	group	group	NOUN
ejpam-2822	96	28	.	.	PUNCT
ejpam-2822	97	1	theorem	theorem	NOUN
ejpam-2822	97	2	1	1	NUM
ejpam-2822	97	3	.	.	PUNCT
ejpam-2822	98	1	let	let	VERB
ejpam-2822	98	2	η	η	PROPN
ejpam-2822	98	3	∈	∈	PROPN
ejpam-2822	98	4	lµ	lµ	PROPN
ejpam-2822	98	5	and	and	CCONJ
ejpam-2822	98	6	a0	a0	PROPN
ejpam-2822	98	7	=	=	SYM
ejpam-2822	98	8	∨	∨	PROPN
ejpam-2822	98	9	x∈g	x∈g	PROPN
ejpam-2822	98	10	{	{	PUNCT
ejpam-2822	98	11	η(x)}.define	η(x)}.define	VERB
ejpam-2822	98	12	an	an	DET
ejpam-2822	98	13	l	l	NOUN
ejpam-2822	98	14	-	-	NOUN
ejpam-2822	98	15	subset	subset	NOUN
ejpam-2822	98	16	η̂	η̂	PUNCT
ejpam-2822	98	17	of	of	ADP
ejpam-2822	98	18	g	g	NOUN
ejpam-2822	98	19	by	by	ADP
ejpam-2822	98	20	:	:	PUNCT
ejpam-2822	98	21	η̂(x	η̂(x	NUM
ejpam-2822	98	22	)	)	PUNCT
ejpam-2822	98	23	=	=	PUNCT
ejpam-2822	98	24	∨	∨	X
ejpam-2822	98	25	a≤a0	a≤a0	X
ejpam-2822	98	26	{	{	PUNCT
ejpam-2822	98	27	a	a	PRON
ejpam-2822	98	28	:	:	PUNCT
ejpam-2822	98	29	x	x	SYM
ejpam-2822	98	30	∈	∈	PROPN
ejpam-2822	98	31	〈	〈	PROPN
ejpam-2822	98	32	ηa	ηa	PROPN
ejpam-2822	98	33	〉	〉	NUM
ejpam-2822	98	34	}	}	PUNCT
ejpam-2822	98	35	.	.	PUNCT
ejpam-2822	99	1	then	then	ADV
ejpam-2822	99	2	,	,	PUNCT
ejpam-2822	99	3	η̂	η̂	PROPN
ejpam-2822	99	4	∈	∈	PROPN
ejpam-2822	99	5	l(µ	l(µ	PROPN
ejpam-2822	99	6	)	)	PUNCT
ejpam-2822	99	7	and	and	CCONJ
ejpam-2822	99	8	η̂	η̂	PROPN
ejpam-2822	99	9	=	=	SYM
ejpam-2822	99	10	〈	〈	PROPN
ejpam-2822	99	11	η	η	PROPN
ejpam-2822	99	12	〉	〉	PROPN
ejpam-2822	99	13	.	.	PUNCT
ejpam-2822	100	1	proposition	proposition	NOUN
ejpam-2822	100	2	3	3	NUM
ejpam-2822	100	3	.	.	PUNCT
ejpam-2822	101	1	let	let	VERB
ejpam-2822	101	2	η	η	PROPN
ejpam-2822	101	3	,	,	PUNCT
ejpam-2822	101	4	θ	θ	PROPN
ejpam-2822	101	5	∈	∈	PROPN
ejpam-2822	101	6	l(µ	l(µ	PROPN
ejpam-2822	101	7	)	)	PUNCT
ejpam-2822	101	8	.	.	PUNCT
ejpam-2822	102	1	then	then	ADV
ejpam-2822	102	2	[	[	X
ejpam-2822	102	3	η	η	X
ejpam-2822	102	4	,	,	PUNCT
ejpam-2822	102	5	θ	θ	PROPN
ejpam-2822	102	6	]	]	X
ejpam-2822	102	7	(	(	PUNCT
ejpam-2822	102	8	e	e	NOUN
ejpam-2822	102	9	)	)	PUNCT
ejpam-2822	102	10	=	=	SYM
ejpam-2822	102	11	η(e	η(e	X
ejpam-2822	102	12	)	)	PUNCT
ejpam-2822	102	13	∧	∧	PROPN
ejpam-2822	102	14	θ(e	θ(e	PROPN
ejpam-2822	102	15	)	)	PUNCT
ejpam-2822	102	16	.	.	PUNCT
ejpam-2822	103	1	proposition	proposition	NOUN
ejpam-2822	103	2	4	4	NUM
ejpam-2822	103	3	.	.	PUNCT
ejpam-2822	103	4	let	let	VERB
ejpam-2822	103	5	η	η	PROPN
ejpam-2822	103	6	,	,	PUNCT
ejpam-2822	103	7	θ	θ	PROPN
ejpam-2822	103	8	∈	∈	PROPN
ejpam-2822	103	9	l(µ	l(µ	PROPN
ejpam-2822	103	10	)	)	PUNCT
ejpam-2822	103	11	and	and	CCONJ
ejpam-2822	103	12	η	η	PROPN
ejpam-2822	103	13	⊆	⊆	NUM
ejpam-2822	103	14	θ	θ	PROPN
ejpam-2822	103	15	.	.	PUNCT
ejpam-2822	104	1	then	then	ADV
ejpam-2822	104	2	,	,	PUNCT
ejpam-2822	104	3	[	[	X
ejpam-2822	104	4	η	η	X
ejpam-2822	104	5	,	,	PUNCT
ejpam-2822	104	6	σ	σ	PROPN
ejpam-2822	104	7	]	]	PUNCT
ejpam-2822	104	8	⊆	⊆	NUM
ejpam-2822	104	9	[	[	X
ejpam-2822	104	10	θ	θ	PROPN
ejpam-2822	104	11	,	,	PUNCT
ejpam-2822	104	12	σ	σ	PROPN
ejpam-2822	104	13	]	]	PUNCT
ejpam-2822	104	14	for	for	ADP
ejpam-2822	104	15	each	each	DET
ejpam-2822	104	16	σ	σ	PROPN
ejpam-2822	104	17	∈	∈	PROPN
ejpam-2822	104	18	lµ.	lµ.	NOUN
ejpam-2822	104	19	proposition	proposition	NOUN
ejpam-2822	104	20	5	5	NUM
ejpam-2822	104	21	.	.	PUNCT
ejpam-2822	104	22	let	let	VERB
ejpam-2822	104	23	η	η	PROPN
ejpam-2822	104	24	,	,	PUNCT
ejpam-2822	104	25	θ	θ	PROPN
ejpam-2822	104	26	∈	∈	PROPN
ejpam-2822	104	27	nl(µ	nl(µ	NOUN
ejpam-2822	104	28	)	)	PUNCT
ejpam-2822	104	29	.	.	PUNCT
ejpam-2822	105	1	then	then	ADV
ejpam-2822	105	2	,	,	PUNCT
ejpam-2822	105	3	[	[	X
ejpam-2822	105	4	η	η	X
ejpam-2822	105	5	,	,	PUNCT
ejpam-2822	105	6	θ	θ	X
ejpam-2822	105	7	]	]	X
ejpam-2822	105	8	∈	∈	PROPN
ejpam-2822	105	9	nl(µ	nl(µ	NOUN
ejpam-2822	105	10	)	)	PUNCT
ejpam-2822	105	11	.	.	PUNCT
ejpam-2822	106	1	next	next	ADV
ejpam-2822	106	2	we	we	PRON
ejpam-2822	106	3	recall	recall	VERB
ejpam-2822	106	4	the	the	DET
ejpam-2822	106	5	notion	notion	NOUN
ejpam-2822	106	6	of	of	ADP
ejpam-2822	106	7	nilpotent	nilpotent	ADJ
ejpam-2822	106	8	l	l	PROPN
ejpam-2822	106	9	-	-	NOUN
ejpam-2822	106	10	subgroup	subgroup	NOUN
ejpam-2822	106	11	[	[	X
ejpam-2822	106	12	3	3	NUM
ejpam-2822	106	13	]	]	PUNCT
ejpam-2822	106	14	:	:	PUNCT
ejpam-2822	106	15	let	let	VERB
ejpam-2822	106	16	η	η	PROPN
ejpam-2822	106	17	∈	∈	PROPN
ejpam-2822	106	18	l(µ	l(µ	PROPN
ejpam-2822	106	19	)	)	PUNCT
ejpam-2822	106	20	and	and	CCONJ
ejpam-2822	106	21	define	define	VERB
ejpam-2822	106	22	z0(η	z0(η	NUM
ejpam-2822	106	23	)	)	PUNCT
ejpam-2822	106	24	=	=	SYM
ejpam-2822	106	25	η	η	PROPN
ejpam-2822	106	26	,	,	PUNCT
ejpam-2822	106	27	z1(η	z1(η	PROPN
ejpam-2822	106	28	)	)	PUNCT
ejpam-2822	106	29	=	=	PUNCT
ejpam-2822	107	1	[	[	X
ejpam-2822	107	2	z0(η	z0(η	NUM
ejpam-2822	107	3	)	)	PUNCT
ejpam-2822	107	4	,	,	PUNCT
ejpam-2822	107	5	η	η	PROPN
ejpam-2822	107	6	]	]	X
ejpam-2822	107	7	.	.	PUNCT
ejpam-2822	108	1	and	and	CCONJ
ejpam-2822	108	2	in	in	ADP
ejpam-2822	108	3	general	general	ADJ
ejpam-2822	108	4	,	,	PUNCT
ejpam-2822	108	5	for	for	ADP
ejpam-2822	108	6	each	each	DET
ejpam-2822	108	7	i	i	PRON
ejpam-2822	108	8	,	,	PUNCT
ejpam-2822	108	9	we	we	PRON
ejpam-2822	108	10	define	define	VERB
ejpam-2822	108	11	zi(η	zi(η	NOUN
ejpam-2822	108	12	)	)	PUNCT
ejpam-2822	108	13	=	=	PUNCT
ejpam-2822	109	1	[	[	X
ejpam-2822	109	2	zi−1(η	zi−1(η	PROPN
ejpam-2822	109	3	)	)	PUNCT
ejpam-2822	109	4	,	,	PUNCT
ejpam-2822	109	5	η].it	η].it	PROPN
ejpam-2822	109	6	is	be	AUX
ejpam-2822	109	7	easy	easy	ADJ
ejpam-2822	109	8	to	to	PART
ejpam-2822	109	9	verify	verify	VERB
ejpam-2822	109	10	that	that	DET
ejpam-2822	109	11	zi(η	zi(η	NOUN
ejpam-2822	109	12	)	)	PUNCT
ejpam-2822	109	13	⊆	⊆	NUM
ejpam-2822	109	14	zi−1(η	zi−1(η	NOUN
ejpam-2822	109	15	)	)	PUNCT
ejpam-2822	109	16	.	.	PUNCT
ejpam-2822	110	1	moreover	moreover	ADV
ejpam-2822	110	2	,	,	PUNCT
ejpam-2822	110	3	zi(η	zi(η	X
ejpam-2822	110	4	)	)	PUNCT
ejpam-2822	110	5	and	and	CCONJ
ejpam-2822	110	6	η	η	PROPN
ejpam-2822	110	7	have	have	VERB
ejpam-2822	110	8	identical	identical	ADJ
ejpam-2822	110	9	tips	tip	NOUN
ejpam-2822	110	10	and	and	CCONJ
ejpam-2822	110	11	identical	identical	ADJ
ejpam-2822	110	12	tails	tail	NOUN
ejpam-2822	110	13	.	.	PUNCT
ejpam-2822	111	1	definition	definition	NOUN
ejpam-2822	111	2	6	6	NUM
ejpam-2822	111	3	.	.	PUNCT
ejpam-2822	111	4	let	let	VERB
ejpam-2822	111	5	η	η	PROPN
ejpam-2822	111	6	∈	∈	PROPN
ejpam-2822	111	7	l(µ	l(µ	PROPN
ejpam-2822	111	8	)	)	PUNCT
ejpam-2822	111	9	with	with	ADP
ejpam-2822	111	10	tip	tip	NOUN
ejpam-2822	111	11	a0	a0	PROPN
ejpam-2822	111	12	and	and	CCONJ
ejpam-2822	111	13	tail	tail	NOUN
ejpam-2822	111	14	t0	t0	PROPN
ejpam-2822	111	15	and	and	CCONJ
ejpam-2822	111	16	a0	a0	PROPN
ejpam-2822	111	17	6=	6=	PROPN
ejpam-2822	111	18	t0	t0	PROPN
ejpam-2822	111	19	.	.	PUNCT
ejpam-2822	112	1	if	if	SCONJ
ejpam-2822	112	2	the	the	DET
ejpam-2822	112	3	descending	descend	VERB
ejpam-2822	112	4	central	central	ADJ
ejpam-2822	112	5	chain	chain	NOUN
ejpam-2822	112	6	η	η	PROPN
ejpam-2822	112	7	=	=	PROPN
ejpam-2822	112	8	z0(η	z0(η	PROPN
ejpam-2822	112	9	)	)	PUNCT
ejpam-2822	112	10	⊇	⊇	PROPN
ejpam-2822	112	11	z1(η	z1(η	PROPN
ejpam-2822	112	12	)	)	PUNCT
ejpam-2822	112	13	⊇	⊇	NOUN
ejpam-2822	112	14	·	·	PUNCT
ejpam-2822	112	15	·	·	PUNCT
ejpam-2822	112	16	·	·	PUNCT
ejpam-2822	112	17	⊇	⊇	ADJ
ejpam-2822	112	18	zi(η	zi(η	NOUN
ejpam-2822	112	19	)	)	PUNCT
ejpam-2822	112	20	⊇	⊇	X
ejpam-2822	112	21	·	·	PUNCT
ejpam-2822	112	22	·	·	PUNCT
ejpam-2822	112	23	·	·	PUNCT
ejpam-2822	112	24	terminates	terminate	VERB
ejpam-2822	112	25	finitely	finitely	ADV
ejpam-2822	112	26	to	to	ADP
ejpam-2822	112	27	the	the	DET
ejpam-2822	112	28	trivial	trivial	ADJ
ejpam-2822	112	29	l	l	NOUN
ejpam-2822	112	30	-	-	NOUN
ejpam-2822	112	31	subgroup	subgroup	NOUN
ejpam-2822	112	32	ηa0t0	ηa0t0	PROPN
ejpam-2822	112	33	,	,	PUNCT
ejpam-2822	112	34	then	then	ADV
ejpam-2822	112	35	η	η	PROPN
ejpam-2822	112	36	is	be	AUX
ejpam-2822	112	37	known	know	VERB
ejpam-2822	112	38	as	as	ADP
ejpam-2822	112	39	a	a	DET
ejpam-2822	112	40	nilpotent	nilpotent	ADJ
ejpam-2822	112	41	l	l	NOUN
ejpam-2822	112	42	-	-	NOUN
ejpam-2822	112	43	subgroup	subgroup	NOUN
ejpam-2822	112	44	of	of	ADP
ejpam-2822	112	45	µ.	µ.	PROPN
ejpam-2822	112	46	more	more	ADV
ejpam-2822	112	47	precisely	precisely	ADV
ejpam-2822	112	48	,	,	PUNCT
ejpam-2822	112	49	η	η	PROPN
ejpam-2822	112	50	is	be	AUX
ejpam-2822	112	51	said	say	VERB
ejpam-2822	112	52	to	to	PART
ejpam-2822	112	53	be	be	AUX
ejpam-2822	112	54	nilpotent	nilpotent	ADJ
ejpam-2822	112	55	of	of	ADP
ejpam-2822	112	56	class	class	NOUN
ejpam-2822	112	57	c	c	NOUN
ejpam-2822	112	58	if	if	SCONJ
ejpam-2822	112	59	c	c	PROPN
ejpam-2822	112	60	is	be	AUX
ejpam-2822	112	61	the	the	DET
ejpam-2822	112	62	least	least	ADJ
ejpam-2822	112	63	non	non	ADJ
ejpam-2822	112	64	-	-	ADJ
ejpam-2822	112	65	negative	negative	ADJ
ejpam-2822	112	66	integer	integer	NOUN
ejpam-2822	112	67	such	such	DET
ejpam-2822	112	68	that	that	PRON
ejpam-2822	112	69	zc(η	zc(η	NUM
ejpam-2822	112	70	)	)	PUNCT
ejpam-2822	112	71	=	=	SYM
ejpam-2822	113	1	ηa0t0	ηa0t0	PROPN
ejpam-2822	113	2	.	.	PUNCT
ejpam-2822	114	1	in	in	ADP
ejpam-2822	114	2	this	this	DET
ejpam-2822	114	3	case	case	NOUN
ejpam-2822	114	4	,	,	PUNCT
ejpam-2822	114	5	the	the	DET
ejpam-2822	114	6	series	series	PROPN
ejpam-2822	114	7	η	η	PROPN
ejpam-2822	114	8	=	=	PROPN
ejpam-2822	114	9	z0(η	z0(η	PROPN
ejpam-2822	114	10	)	)	PUNCT
ejpam-2822	114	11	⊇	⊇	PROPN
ejpam-2822	114	12	z1(η	z1(η	PROPN
ejpam-2822	114	13	)	)	PUNCT
ejpam-2822	114	14	⊇	⊇	NOUN
ejpam-2822	114	15	·	·	PUNCT
ejpam-2822	114	16	·	·	PUNCT
ejpam-2822	114	17	·	·	PUNCT
ejpam-2822	114	18	⊇	⊇	NOUN
ejpam-2822	114	19	zc(η	zc(η	NUM
ejpam-2822	114	20	)	)	PUNCT
ejpam-2822	114	21	=	=	PUNCT
ejpam-2822	114	22	ηa0t0	ηa0t0	PROPN
ejpam-2822	114	23	is	be	AUX
ejpam-2822	114	24	called	call	VERB
ejpam-2822	114	25	the	the	DET
ejpam-2822	114	26	descending	descend	VERB
ejpam-2822	114	27	central	central	ADJ
ejpam-2822	114	28	series	series	NOUN
ejpam-2822	114	29	of	of	ADP
ejpam-2822	114	30	η	η	PROPN
ejpam-2822	114	31	.	.	PROPN
ejpam-2822	114	32	if	if	SCONJ
ejpam-2822	114	33	it	it	PRON
ejpam-2822	114	34	is	be	AUX
ejpam-2822	114	35	a	a	DET
ejpam-2822	114	36	nilpotent	nilpotent	ADJ
ejpam-2822	114	37	l	l	NOUN
ejpam-2822	114	38	-	-	NOUN
ejpam-2822	114	39	subgroup	subgroup	NOUN
ejpam-2822	114	40	of	of	ADP
ejpam-2822	114	41	µ	µ	NUM
ejpam-2822	114	42	,	,	PUNCT
ejpam-2822	114	43	then	then	ADV
ejpam-2822	114	44	we	we	PRON
ejpam-2822	114	45	simply	simply	ADV
ejpam-2822	114	46	write	write	VERB
ejpam-2822	114	47	η	η	PROPN
ejpam-2822	114	48	is	be	AUX
ejpam-2822	114	49	nilpotent	nilpotent	ADJ
ejpam-2822	114	50	.	.	PUNCT
ejpam-2822	115	1	proposition	proposition	NOUN
ejpam-2822	115	2	6	6	NUM
ejpam-2822	115	3	.	.	PUNCT
ejpam-2822	116	1	let	let	VERB
ejpam-2822	116	2	η	η	PROPN
ejpam-2822	116	3	∈	∈	PROPN
ejpam-2822	116	4	nl(µ	nl(µ	NOUN
ejpam-2822	116	5	)	)	PUNCT
ejpam-2822	116	6	.	.	PUNCT
ejpam-2822	117	1	then	then	ADV
ejpam-2822	117	2	,	,	PUNCT
ejpam-2822	117	3	zi(η	zi(η	X
ejpam-2822	117	4	)	)	PUNCT
ejpam-2822	117	5	∈	∈	NOUN
ejpam-2822	117	6	nl(µ	nl(µ	NOUN
ejpam-2822	117	7	)	)	PUNCT
ejpam-2822	117	8	.	.	PUNCT
ejpam-2822	118	1	here	here	ADV
ejpam-2822	118	2	we	we	PRON
ejpam-2822	118	3	give	give	VERB
ejpam-2822	118	4	an	an	DET
ejpam-2822	118	5	example	example	NOUN
ejpam-2822	118	6	of	of	ADP
ejpam-2822	118	7	an	an	DET
ejpam-2822	118	8	l	l	NOUN
ejpam-2822	118	9	-	-	NOUN
ejpam-2822	118	10	subgroup	subgroup	NOUN
ejpam-2822	118	11	of	of	ADP
ejpam-2822	118	12	an	an	DET
ejpam-2822	118	13	l	l	NOUN
ejpam-2822	118	14	-	-	NOUN
ejpam-2822	118	15	group	group	NOUN
ejpam-2822	118	16	:	:	PUNCT
ejpam-2822	118	17	example	example	NOUN
ejpam-2822	119	1	1	1	X
ejpam-2822	119	2	.	.	PUNCT
ejpam-2822	120	1	let	let	VERB
ejpam-2822	120	2	g	g	NOUN
ejpam-2822	120	3	be	be	AUX
ejpam-2822	120	4	the	the	DET
ejpam-2822	120	5	quaternian	quaternian	ADJ
ejpam-2822	120	6	group	group	NOUN
ejpam-2822	120	7	q8	q8	PROPN
ejpam-2822	120	8	given	give	VERB
ejpam-2822	120	9	by	by	ADP
ejpam-2822	120	10	:	:	PUNCT
ejpam-2822	120	11	q8	q8	PROPN
ejpam-2822	120	12	=	=	SYM
ejpam-2822	120	13	{	{	PUNCT
ejpam-2822	120	14	±1,±i,±j,±k	±1,±i,±j,±k	PROPN
ejpam-2822	120	15	}	}	PUNCT
ejpam-2822	120	16	i.	i.	PROPN
ejpam-2822	120	17	jahan	jahan	PROPN
ejpam-2822	120	18	,	,	PUNCT
ejpam-2822	120	19	n.	n.	PROPN
ejpam-2822	120	20	ajmal	ajmal	PROPN
ejpam-2822	120	21	,	,	PUNCT
ejpam-2822	120	22	b.	b.	PROPN
ejpam-2822	120	23	davvaz	davvaz	PROPN
ejpam-2822	120	24	/	/	SYM
ejpam-2822	120	25	eur	eur	PROPN
ejpam-2822	120	26	.	.	PUNCT
ejpam-2822	121	1	j.	j.	PROPN
ejpam-2822	121	2	pure	pure	PROPN
ejpam-2822	121	3	appl	appl	PROPN
ejpam-2822	121	4	.	.	PROPN
ejpam-2822	121	5	math	math	PROPN
ejpam-2822	121	6	,	,	PUNCT
ejpam-2822	121	7	10	10	NUM
ejpam-2822	121	8	(	(	PUNCT
ejpam-2822	121	9	2	2	NUM
ejpam-2822	121	10	)	)	PUNCT
ejpam-2822	121	11	(	(	PUNCT
ejpam-2822	121	12	2017	2017	NUM
ejpam-2822	121	13	)	)	PUNCT
ejpam-2822	121	14	,	,	PUNCT
ejpam-2822	121	15	255	255	NUM
ejpam-2822	121	16	-	-	SYM
ejpam-2822	121	17	271	271	NUM
ejpam-2822	121	18	260	260	NUM
ejpam-2822	121	19	where	where	SCONJ
ejpam-2822	121	20	i2	i2	PROPN
ejpam-2822	121	21	=	=	PROPN
ejpam-2822	121	22	j2	j2	PROPN
ejpam-2822	121	23	=	=	SYM
ejpam-2822	121	24	k2	k2	PROPN
ejpam-2822	121	25	=	=	SYM
ejpam-2822	121	26	−1	−1	NOUN
ejpam-2822	121	27	,	,	PUNCT
ejpam-2822	121	28	ij	ij	NOUN
ejpam-2822	121	29	=	=	SYM
ejpam-2822	121	30	k	k	PROPN
ejpam-2822	121	31	,	,	PUNCT
ejpam-2822	121	32	jk	jk	X
ejpam-2822	121	33	=	=	PUNCT
ejpam-2822	122	1	i	i	PROPN
ejpam-2822	122	2	,	,	PUNCT
ejpam-2822	122	3	kj	kj	PROPN
ejpam-2822	122	4	=	=	PUNCT
ejpam-2822	122	5	i	i	PROPN
ejpam-2822	122	6	.	.	PUNCT
ejpam-2822	123	1	let	let	VERB
ejpam-2822	123	2	c	c	NOUN
ejpam-2822	123	3	=	=	SYM
ejpam-2822	123	4	{	{	PUNCT
ejpam-2822	123	5	1,−1	1,−1	PROPN
ejpam-2822	123	6	}	}	PUNCT
ejpam-2822	123	7	be	be	VERB
ejpam-2822	123	8	the	the	DET
ejpam-2822	123	9	center	center	NOUN
ejpam-2822	123	10	of	of	ADP
ejpam-2822	123	11	g	g	PROPN
ejpam-2822	123	12	and	and	CCONJ
ejpam-2822	123	13	h	h	NOUN
ejpam-2822	123	14	=	=	PUNCT
ejpam-2822	123	15	{	{	PUNCT
ejpam-2822	123	16	±1,±i	±1,±i	ADV
ejpam-2822	123	17	}	}	PUNCT
ejpam-2822	123	18	.	.	PUNCT
ejpam-2822	124	1	let	let	VERB
ejpam-2822	124	2	the	the	DET
ejpam-2822	124	3	evaluation	evaluation	NOUN
ejpam-2822	124	4	lattice	lattice	PROPN
ejpam-2822	124	5	l	l	PROPN
ejpam-2822	124	6	be	be	VERB
ejpam-2822	124	7	the	the	DET
ejpam-2822	124	8	chain	chain	NOUN
ejpam-2822	124	9	given	give	VERB
ejpam-2822	124	10	by	by	ADP
ejpam-2822	124	11	:	:	PUNCT
ejpam-2822	124	12	l	l	NOUN
ejpam-2822	124	13	:	:	PUNCT
ejpam-2822	124	14	f	f	X
ejpam-2822	124	15	≤	≤	VERB
ejpam-2822	124	16	a	a	DET
ejpam-2822	124	17	≤	≤	NUM
ejpam-2822	124	18	b	b	NOUN
ejpam-2822	124	19	≤	≤	NUM
ejpam-2822	124	20	d	d	AUX
ejpam-2822	124	21	define	define	VERB
ejpam-2822	124	22	l	l	NOUN
ejpam-2822	124	23	-	-	PUNCT
ejpam-2822	124	24	subsets	subset	NOUN
ejpam-2822	124	25	µ	µ	NOUN
ejpam-2822	124	26	and	and	CCONJ
ejpam-2822	124	27	η	η	PROPN
ejpam-2822	124	28	of	of	ADP
ejpam-2822	124	29	g	g	PROPN
ejpam-2822	124	30	as	as	SCONJ
ejpam-2822	124	31	follows	follow	VERB
ejpam-2822	124	32	:	:	PUNCT
ejpam-2822	124	33	µ(x	µ(x	NUM
ejpam-2822	124	34	)	)	PUNCT
ejpam-2822	124	35	=	=	PUNCT
ejpam-2822	125	1			PUNCT
ejpam-2822	125	2	d	d	NOUN
ejpam-2822	125	3	if	if	SCONJ
ejpam-2822	125	4	x	x	PROPN
ejpam-2822	125	5	∈	∈	PROPN
ejpam-2822	125	6	c	c	NOUN
ejpam-2822	125	7	b	b	NOUN
ejpam-2822	125	8	if	if	SCONJ
ejpam-2822	125	9	x	x	SYM
ejpam-2822	125	10	∈	∈	NOUN
ejpam-2822	125	11	h	h	NOUN
ejpam-2822	125	12	\	\	PUNCT
ejpam-2822	125	13	c	c	PROPN
ejpam-2822	125	14	a	a	DET
ejpam-2822	125	15	if	if	NOUN
ejpam-2822	125	16	x	x	PROPN
ejpam-2822	125	17	∈	∈	PROPN
ejpam-2822	125	18	q8	q8	PROPN
ejpam-2822	125	19	\h	\h	PROPN
ejpam-2822	125	20	.	.	PUNCT
ejpam-2822	126	1	and	and	CCONJ
ejpam-2822	126	2	η(x	η(x	PROPN
ejpam-2822	126	3	)	)	PUNCT
ejpam-2822	126	4	=	=	SYM
ejpam-2822	127	1			PUNCT
ejpam-2822	128	1	d	d	NOUN
ejpam-2822	128	2	if	if	SCONJ
ejpam-2822	128	3	x	x	PROPN
ejpam-2822	128	4	=	=	SYM
ejpam-2822	128	5	1	1	NUM
ejpam-2822	128	6	b	b	NOUN
ejpam-2822	128	7	if	if	SCONJ
ejpam-2822	128	8	x	x	SYM
ejpam-2822	128	9	∈	∈	PROPN
ejpam-2822	128	10	c	c	NOUN
ejpam-2822	128	11	\	\	X
ejpam-2822	128	12	{	{	PUNCT
ejpam-2822	128	13	1	1	NUM
ejpam-2822	128	14	}	}	PUNCT
ejpam-2822	128	15	a	a	PRON
ejpam-2822	128	16	if	if	NOUN
ejpam-2822	129	1	x	x	SYM
ejpam-2822	129	2	∈	∈	NOUN
ejpam-2822	129	3	h	h	NOUN
ejpam-2822	129	4	\	\	PUNCT
ejpam-2822	130	1	c	c	PROPN
ejpam-2822	130	2	f	f	PROPN
ejpam-2822	131	1	if	if	SCONJ
ejpam-2822	131	2	x	x	PROPN
ejpam-2822	131	3	∈	∈	PROPN
ejpam-2822	131	4	q8	q8	PROPN
ejpam-2822	131	5	\h	\h	PROPN
ejpam-2822	132	1	since	since	SCONJ
ejpam-2822	132	2	the	the	DET
ejpam-2822	132	3	level	level	NOUN
ejpam-2822	132	4	subsets	subset	NOUN
ejpam-2822	132	5	of	of	ADP
ejpam-2822	132	6	η	η	PROPN
ejpam-2822	132	7	and	and	CCONJ
ejpam-2822	132	8	µ	µ	PROPN
ejpam-2822	132	9	are	be	AUX
ejpam-2822	132	10	subgroups	subgroup	NOUN
ejpam-2822	132	11	of	of	ADP
ejpam-2822	132	12	g	g	PROPN
ejpam-2822	132	13	,	,	PUNCT
ejpam-2822	132	14	η	η	PROPN
ejpam-2822	132	15	and	and	CCONJ
ejpam-2822	132	16	µ	µ	PROPN
ejpam-2822	132	17	are	be	AUX
ejpam-2822	132	18	l	l	NOUN
ejpam-2822	132	19	-	-	NOUN
ejpam-2822	132	20	subgroups	subgroup	NOUN
ejpam-2822	132	21	of	of	ADP
ejpam-2822	132	22	g.	g.	PROPN
ejpam-2822	132	23	as	as	ADP
ejpam-2822	132	24	η	η	PROPN
ejpam-2822	132	25	⊆	⊆	PROPN
ejpam-2822	132	26	µ	µ	NUM
ejpam-2822	132	27	,	,	PUNCT
ejpam-2822	132	28	η	η	PROPN
ejpam-2822	132	29	is	be	AUX
ejpam-2822	132	30	an	an	DET
ejpam-2822	132	31	l	l	NOUN
ejpam-2822	132	32	-	-	NOUN
ejpam-2822	132	33	subgroup	subgroup	NOUN
ejpam-2822	132	34	of	of	ADP
ejpam-2822	132	35	µ.	µ.	PROPN
ejpam-2822	132	36	now	now	ADV
ejpam-2822	132	37	in	in	ADP
ejpam-2822	132	38	view	view	NOUN
ejpam-2822	132	39	of	of	ADP
ejpam-2822	132	40	the	the	DET
ejpam-2822	132	41	fact	fact	NOUN
ejpam-2822	132	42	that	that	SCONJ
ejpam-2822	132	43	every	every	DET
ejpam-2822	132	44	subgroup	subgroup	NOUN
ejpam-2822	132	45	of	of	ADP
ejpam-2822	132	46	a	a	DET
ejpam-2822	132	47	nilpotent	nilpotent	ADJ
ejpam-2822	132	48	group	group	NOUN
ejpam-2822	132	49	is	be	AUX
ejpam-2822	132	50	nilpotent	nilpotent	ADJ
ejpam-2822	132	51	,	,	PUNCT
ejpam-2822	132	52	it	it	PRON
ejpam-2822	132	53	follows	follow	VERB
ejpam-2822	132	54	that	that	SCONJ
ejpam-2822	132	55	all	all	DET
ejpam-2822	132	56	the	the	DET
ejpam-2822	132	57	level	level	NOUN
ejpam-2822	132	58	subsets	subset	NOUN
ejpam-2822	132	59	of	of	ADP
ejpam-2822	132	60	η	η	PROPN
ejpam-2822	132	61	are	be	AUX
ejpam-2822	132	62	nilpotent	nilpotent	ADJ
ejpam-2822	132	63	subgroups	subgroup	NOUN
ejpam-2822	132	64	of	of	ADP
ejpam-2822	132	65	the	the	DET
ejpam-2822	132	66	corresponding	corresponding	ADJ
ejpam-2822	132	67	level	level	NOUN
ejpam-2822	132	68	subsets	subset	NOUN
ejpam-2822	132	69	of	of	ADP
ejpam-2822	132	70	µ.	µ.	NOUN
ejpam-2822	132	71	therefore	therefore	ADV
ejpam-2822	132	72	the	the	DET
ejpam-2822	132	73	converse	converse	NOUN
ejpam-2822	132	74	of	of	ADP
ejpam-2822	132	75	theorem	theorem	NOUN
ejpam-2822	132	76	4.1[3	4.1[3	NUM
ejpam-2822	132	77	]	]	PUNCT
ejpam-2822	132	78	,	,	PUNCT
ejpam-2822	132	79	implies	imply	VERB
ejpam-2822	132	80	that	that	SCONJ
ejpam-2822	132	81	η	η	PROPN
ejpam-2822	132	82	is	be	AUX
ejpam-2822	132	83	a	a	DET
ejpam-2822	132	84	nilpotent	nilpotent	ADJ
ejpam-2822	132	85	l	l	NOUN
ejpam-2822	132	86	-	-	NOUN
ejpam-2822	132	87	subgroup	subgroup	NOUN
ejpam-2822	132	88	of	of	ADP
ejpam-2822	132	89	µ.	µ.	PROPN
ejpam-2822	132	90	next	next	ADV
ejpam-2822	132	91	we	we	PRON
ejpam-2822	132	92	show	show	VERB
ejpam-2822	132	93	that	that	SCONJ
ejpam-2822	132	94	just	just	ADV
ejpam-2822	132	95	by	by	ADP
ejpam-2822	132	96	changing	change	VERB
ejpam-2822	132	97	the	the	DET
ejpam-2822	132	98	evaluation	evaluation	NOUN
ejpam-2822	132	99	lattice	lattice	NOUN
ejpam-2822	132	100	l	l	PROPN
ejpam-2822	132	101	and	and	CCONJ
ejpam-2822	132	102	keeping	keep	VERB
ejpam-2822	132	103	the	the	DET
ejpam-2822	132	104	parent	parent	NOUN
ejpam-2822	132	105	group	group	NOUN
ejpam-2822	132	106	as	as	ADP
ejpam-2822	132	107	q8	q8	PROPN
ejpam-2822	132	108	,	,	PUNCT
ejpam-2822	132	109	we	we	PRON
ejpam-2822	132	110	obtain	obtain	VERB
ejpam-2822	132	111	various	various	ADJ
ejpam-2822	132	112	types	type	NOUN
ejpam-2822	132	113	of	of	ADP
ejpam-2822	132	114	l	l	NOUN
ejpam-2822	132	115	-	-	PUNCT
ejpam-2822	132	116	subgroups	subgroup	NOUN
ejpam-2822	132	117	.	.	PUNCT
ejpam-2822	133	1	example	example	NOUN
ejpam-2822	134	1	2	2	NUM
ejpam-2822	134	2	.	.	PUNCT
ejpam-2822	134	3	let	let	VERB
ejpam-2822	134	4	g	g	PROPN
ejpam-2822	134	5	=	=	PROPN
ejpam-2822	134	6	q8	q8	PROPN
ejpam-2822	134	7	and	and	CCONJ
ejpam-2822	134	8	the	the	DET
ejpam-2822	134	9	evaluation	evaluation	NOUN
ejpam-2822	134	10	lattice	lattice	NOUN
ejpam-2822	134	11	be	be	AUX
ejpam-2822	134	12	given	give	VERB
ejpam-2822	134	13	by	by	ADP
ejpam-2822	134	14	the	the	DET
ejpam-2822	134	15	diagram	diagram	NOUN
ejpam-2822	134	16	:	:	PUNCT
ejpam-2822	134	17	consider	consider	VERB
ejpam-2822	134	18	the	the	DET
ejpam-2822	134	19	parent	parent	NOUN
ejpam-2822	134	20	l	l	NOUN
ejpam-2822	134	21	-	-	NOUN
ejpam-2822	134	22	subgroup	subgroup	NOUN
ejpam-2822	134	23	of	of	ADP
ejpam-2822	134	24	g	g	NOUN
ejpam-2822	134	25	given	give	VERB
ejpam-2822	134	26	by	by	ADP
ejpam-2822	134	27	:	:	PUNCT
ejpam-2822	134	28	µ(x	µ(x	X
ejpam-2822	134	29	)	)	PUNCT
ejpam-2822	134	30	=	=	PRON
ejpam-2822	134	31	{	{	PUNCT
ejpam-2822	134	32	u	u	NOUN
ejpam-2822	134	33	if	if	SCONJ
ejpam-2822	134	34	x	x	PROPN
ejpam-2822	134	35	∈	∈	PROPN
ejpam-2822	134	36	c	c	NOUN
ejpam-2822	134	37	,	,	PUNCT
ejpam-2822	134	38	d	d	X
ejpam-2822	134	39	if	if	SCONJ
ejpam-2822	134	40	x	x	PROPN
ejpam-2822	134	41	∈	∈	PROPN
ejpam-2822	134	42	g	g	NOUN
ejpam-2822	134	43	\	\	PROPN
ejpam-2822	134	44	c.	c.	NOUN
ejpam-2822	134	45	now	now	ADV
ejpam-2822	134	46	define	define	VERB
ejpam-2822	134	47	l	l	NOUN
ejpam-2822	134	48	-	-	PUNCT
ejpam-2822	134	49	subset	subset	VERB
ejpam-2822	134	50	η	η	PROPN
ejpam-2822	134	51	of	of	ADP
ejpam-2822	134	52	µ	µ	NOUN
ejpam-2822	134	53	as	as	SCONJ
ejpam-2822	134	54	given	give	VERB
ejpam-2822	134	55	below	below	ADV
ejpam-2822	134	56	:	:	PUNCT
ejpam-2822	134	57	η(x	η(x	X
ejpam-2822	134	58	)	)	PUNCT
ejpam-2822	134	59	=	=	SYM
ejpam-2822	134	60			PUNCT
ejpam-2822	134	61	u	u	NOUN
ejpam-2822	134	62	if	if	SCONJ
ejpam-2822	134	63	x	x	PROPN
ejpam-2822	134	64	∈	∈	PROPN
ejpam-2822	134	65	c	c	NOUN
ejpam-2822	134	66	,	,	PUNCT
ejpam-2822	135	1	d	d	X
ejpam-2822	135	2	if	if	SCONJ
ejpam-2822	135	3	x	x	X
ejpam-2822	135	4	∈	∈	PROPN
ejpam-2822	135	5	h1	h1	PROPN
ejpam-2822	135	6	\	\	PROPN
ejpam-2822	135	7	c	c	PROPN
ejpam-2822	135	8	,	,	PUNCT
ejpam-2822	135	9	a	a	DET
ejpam-2822	135	10	if	if	SCONJ
ejpam-2822	135	11	x	x	SYM
ejpam-2822	135	12	∈	∈	PROPN
ejpam-2822	135	13	h2	h2	NOUN
ejpam-2822	135	14	\	\	PROPN
ejpam-2822	135	15	c	c	PROPN
ejpam-2822	135	16	,	,	PUNCT
ejpam-2822	135	17	b	b	NOUN
ejpam-2822	135	18	if	if	SCONJ
ejpam-2822	135	19	x	x	PROPN
ejpam-2822	135	20	∈	∈	NOUN
ejpam-2822	135	21	h3	h3	NOUN
ejpam-2822	135	22	\	\	PROPN
ejpam-2822	135	23	c	c	PROPN
ejpam-2822	135	24	;	;	PUNCT
ejpam-2822	135	25	i.	i.	PROPN
ejpam-2822	135	26	jahan	jahan	PROPN
ejpam-2822	135	27	,	,	PUNCT
ejpam-2822	135	28	n.	n.	PROPN
ejpam-2822	135	29	ajmal	ajmal	PROPN
ejpam-2822	135	30	,	,	PUNCT
ejpam-2822	135	31	b.	b.	PROPN
ejpam-2822	135	32	davvaz	davvaz	PROPN
ejpam-2822	135	33	/	/	SYM
ejpam-2822	135	34	eur	eur	PROPN
ejpam-2822	135	35	.	.	PUNCT
ejpam-2822	136	1	j.	j.	PROPN
ejpam-2822	136	2	pure	pure	PROPN
ejpam-2822	136	3	appl	appl	PROPN
ejpam-2822	136	4	.	.	PROPN
ejpam-2822	136	5	math	math	PROPN
ejpam-2822	136	6	,	,	PUNCT
ejpam-2822	136	7	10	10	NUM
ejpam-2822	136	8	(	(	PUNCT
ejpam-2822	136	9	2	2	NUM
ejpam-2822	136	10	)	)	PUNCT
ejpam-2822	136	11	(	(	PUNCT
ejpam-2822	136	12	2017	2017	NUM
ejpam-2822	136	13	)	)	PUNCT
ejpam-2822	136	14	,	,	PUNCT
ejpam-2822	136	15	255	255	NUM
ejpam-2822	136	16	-	-	SYM
ejpam-2822	136	17	271	271	NUM
ejpam-2822	136	18	261	261	NUM
ejpam-2822	136	19	where	where	SCONJ
ejpam-2822	136	20	c	c	NOUN
ejpam-2822	136	21	=	=	SYM
ejpam-2822	136	22	{	{	PUNCT
ejpam-2822	136	23	±1	±1	NOUN
ejpam-2822	136	24	}	}	PUNCT
ejpam-2822	136	25	,	,	PUNCT
ejpam-2822	136	26	h1	h1	PROPN
ejpam-2822	136	27	=	=	SYM
ejpam-2822	136	28	{	{	PUNCT
ejpam-2822	136	29	±1,±i	±1,±i	ADV
ejpam-2822	136	30	}	}	PUNCT
ejpam-2822	136	31	,	,	PUNCT
ejpam-2822	136	32	h2	h2	NOUN
ejpam-2822	136	33	=	=	PUNCT
ejpam-2822	136	34	{	{	PUNCT
ejpam-2822	136	35	±1,±j	±1,±j	PROPN
ejpam-2822	136	36	}	}	PUNCT
ejpam-2822	136	37	,	,	PUNCT
ejpam-2822	136	38	h3	h3	NOUN
ejpam-2822	136	39	=	=	SYM
ejpam-2822	136	40	{	{	PUNCT
ejpam-2822	136	41	±1,±k	±1,±k	NOUN
ejpam-2822	136	42	}	}	PUNCT
ejpam-2822	136	43	.	.	PUNCT
ejpam-2822	137	1	since	since	SCONJ
ejpam-2822	137	2	the	the	DET
ejpam-2822	137	3	level	level	NOUN
ejpam-2822	137	4	subsets	subset	NOUN
ejpam-2822	137	5	of	of	ADP
ejpam-2822	137	6	η	η	PROPN
ejpam-2822	137	7	are	be	AUX
ejpam-2822	137	8	normal	normal	ADJ
ejpam-2822	137	9	subgroups	subgroup	NOUN
ejpam-2822	137	10	of	of	ADP
ejpam-2822	137	11	g	g	PROPN
ejpam-2822	137	12	,	,	PUNCT
ejpam-2822	137	13	η	η	PROPN
ejpam-2822	137	14	is	be	AUX
ejpam-2822	137	15	a	a	DET
ejpam-2822	137	16	normal	normal	ADJ
ejpam-2822	137	17	l	l	NOUN
ejpam-2822	137	18	-	-	NOUN
ejpam-2822	137	19	subgroup	subgroup	NOUN
ejpam-2822	137	20	of	of	ADP
ejpam-2822	137	21	g	g	PROPN
ejpam-2822	137	22	and	and	CCONJ
ejpam-2822	137	23	hence	hence	ADV
ejpam-2822	137	24	of	of	ADP
ejpam-2822	137	25	µ.	µ.	NOUN
ejpam-2822	137	26	now	now	ADV
ejpam-2822	137	27	that	that	SCONJ
ejpam-2822	137	28	η	η	PROPN
ejpam-2822	137	29	is	be	AUX
ejpam-2822	137	30	a	a	DET
ejpam-2822	137	31	nilpotent	nilpotent	ADJ
ejpam-2822	137	32	l	l	NOUN
ejpam-2822	137	33	-	-	NOUN
ejpam-2822	137	34	subgroup	subgroup	NOUN
ejpam-2822	137	35	of	of	ADP
ejpam-2822	137	36	µ	µ	NOUN
ejpam-2822	137	37	in	in	ADP
ejpam-2822	137	38	view	view	NOUN
ejpam-2822	137	39	of	of	ADP
ejpam-2822	137	40	definition	definition	NOUN
ejpam-2822	137	41	3.5.we	3.5.we	PRON
ejpam-2822	137	42	demonstrate	demonstrate	VERB
ejpam-2822	137	43	this	this	PRON
ejpam-2822	137	44	as	as	SCONJ
ejpam-2822	137	45	follows	follow	VERB
ejpam-2822	137	46	:	:	PUNCT
ejpam-2822	137	47	note	note	VERB
ejpam-2822	137	48	that	that	SCONJ
ejpam-2822	137	49	g′	g′	NOUN
ejpam-2822	137	50	=	=	PUNCT
ejpam-2822	137	51	{	{	PUNCT
ejpam-2822	137	52	1,−1	1,−1	NUM
ejpam-2822	137	53	}	}	PUNCT
ejpam-2822	137	54	.	.	PUNCT
ejpam-2822	138	1	in	in	ADP
ejpam-2822	138	2	order	order	NOUN
ejpam-2822	138	3	to	to	PART
ejpam-2822	138	4	obtain	obtain	VERB
ejpam-2822	138	5	the	the	DET
ejpam-2822	138	6	members	member	NOUN
ejpam-2822	138	7	of	of	ADP
ejpam-2822	138	8	descending	descend	VERB
ejpam-2822	138	9	central	central	ADJ
ejpam-2822	138	10	series	series	NOUN
ejpam-2822	138	11	of	of	ADP
ejpam-2822	138	12	η	η	PROPN
ejpam-2822	138	13	,	,	PUNCT
ejpam-2822	138	14	we	we	PRON
ejpam-2822	138	15	set	set	VERB
ejpam-2822	138	16	z0(η	z0(η	PRON
ejpam-2822	138	17	)	)	PUNCT
ejpam-2822	138	18	=	=	SYM
ejpam-2822	138	19	η	η	PROPN
ejpam-2822	138	20	and	and	CCONJ
ejpam-2822	138	21	consider	consider	VERB
ejpam-2822	138	22	the	the	DET
ejpam-2822	138	23	commutator	commutator	NOUN
ejpam-2822	138	24	(	(	PUNCT
ejpam-2822	138	25	η	η	PROPN
ejpam-2822	138	26	,	,	PUNCT
ejpam-2822	138	27	η	η	PROPN
ejpam-2822	138	28	)	)	PUNCT
ejpam-2822	138	29	(	(	PUNCT
ejpam-2822	138	30	η	η	PROPN
ejpam-2822	138	31	,	,	PUNCT
ejpam-2822	138	32	η	η	NOUN
ejpam-2822	138	33	)	)	PUNCT
ejpam-2822	138	34	(	(	PUNCT
ejpam-2822	138	35	x	x	X
ejpam-2822	138	36	)	)	PUNCT
ejpam-2822	138	37	=	=	PUNCT
ejpam-2822	139	1			PUNCT
ejpam-2822	139	2	u	u	NOUN
ejpam-2822	139	3	if	if	SCONJ
ejpam-2822	139	4	x	x	SYM
ejpam-2822	139	5	=	=	SYM
ejpam-2822	139	6	1	1	NUM
ejpam-2822	139	7	,	,	PUNCT
ejpam-2822	139	8	d	d	NOUN
ejpam-2822	139	9	if	if	SCONJ
ejpam-2822	139	10	x	x	SYM
ejpam-2822	139	11	∈	∈	PROPN
ejpam-2822	139	12	c	c	NOUN
ejpam-2822	139	13	\	\	X
ejpam-2822	139	14	{	{	PUNCT
ejpam-2822	139	15	1	1	NUM
ejpam-2822	139	16	}	}	PUNCT
ejpam-2822	139	17	,	,	PUNCT
ejpam-2822	139	18	f	f	PROPN
ejpam-2822	139	19	if	if	SCONJ
ejpam-2822	139	20	x	x	PROPN
ejpam-2822	139	21	∈	∈	PROPN
ejpam-2822	139	22	g	g	NOUN
ejpam-2822	139	23	\	\	PROPN
ejpam-2822	139	24	c.	c.	NOUN
ejpam-2822	139	25	as	as	ADP
ejpam-2822	139	26	the	the	DET
ejpam-2822	139	27	level	level	NOUN
ejpam-2822	139	28	subsets	subset	NOUN
ejpam-2822	139	29	of	of	ADP
ejpam-2822	139	30	(	(	PUNCT
ejpam-2822	139	31	η	η	PROPN
ejpam-2822	139	32	,	,	PUNCT
ejpam-2822	139	33	η	η	NOUN
ejpam-2822	139	34	)	)	PUNCT
ejpam-2822	139	35	are	be	AUX
ejpam-2822	139	36	subgroups	subgroup	NOUN
ejpam-2822	139	37	of	of	ADP
ejpam-2822	139	38	g	g	NOUN
ejpam-2822	139	39	,	,	PUNCT
ejpam-2822	139	40	z1(η	z1(η	PROPN
ejpam-2822	139	41	)	)	PUNCT
ejpam-2822	139	42	=	=	PUNCT
ejpam-2822	140	1	[	[	X
ejpam-2822	140	2	η	η	PROPN
ejpam-2822	140	3	,	,	PUNCT
ejpam-2822	140	4	η	η	PROPN
ejpam-2822	140	5	]	]	X
ejpam-2822	140	6	=	=	SYM
ejpam-2822	140	7	(	(	PUNCT
ejpam-2822	140	8	η	η	PROPN
ejpam-2822	140	9	,	,	PUNCT
ejpam-2822	140	10	η	η	NOUN
ejpam-2822	140	11	)	)	PUNCT
ejpam-2822	140	12	.	.	PUNCT
ejpam-2822	141	1	next	next	ADV
ejpam-2822	141	2	,	,	PUNCT
ejpam-2822	141	3	we	we	PRON
ejpam-2822	141	4	calculate	calculate	VERB
ejpam-2822	141	5	the	the	DET
ejpam-2822	141	6	commutator	commutator	NOUN
ejpam-2822	141	7	:	:	PUNCT
ejpam-2822	141	8	(	(	PUNCT
ejpam-2822	141	9	(	(	PUNCT
ejpam-2822	141	10	η	η	PROPN
ejpam-2822	141	11	,	,	PUNCT
ejpam-2822	141	12	η	η	NOUN
ejpam-2822	141	13	)	)	PUNCT
ejpam-2822	141	14	,	,	PUNCT
ejpam-2822	141	15	η	η	PROPN
ejpam-2822	141	16	)	)	PUNCT
ejpam-2822	141	17	(	(	PUNCT
ejpam-2822	141	18	x	x	X
ejpam-2822	141	19	)	)	PUNCT
ejpam-2822	141	20	=	=	SYM
ejpam-2822	141	21	{	{	PUNCT
ejpam-2822	141	22	u	u	NOUN
ejpam-2822	141	23	if	if	SCONJ
ejpam-2822	141	24	x	x	PROPN
ejpam-2822	141	25	=	=	SYM
ejpam-2822	141	26	1	1	NUM
ejpam-2822	141	27	,	,	PUNCT
ejpam-2822	141	28	f	f	PROPN
ejpam-2822	142	1	if	if	SCONJ
ejpam-2822	142	2	x	x	PROPN
ejpam-2822	142	3	∈	∈	PROPN
ejpam-2822	142	4	g	g	NOUN
ejpam-2822	142	5	\	\	PROPN
ejpam-2822	142	6	{	{	PUNCT
ejpam-2822	142	7	1	1	NUM
ejpam-2822	142	8	}	}	PUNCT
ejpam-2822	142	9	.	.	PUNCT
ejpam-2822	143	1	again	again	ADV
ejpam-2822	143	2	by	by	ADP
ejpam-2822	143	3	the	the	DET
ejpam-2822	143	4	reasons	reason	NOUN
ejpam-2822	143	5	as	as	SCONJ
ejpam-2822	143	6	given	give	VERB
ejpam-2822	143	7	above	above	ADP
ejpam-2822	143	8	z2(η	z2(η	NUM
ejpam-2822	143	9	)	)	PUNCT
ejpam-2822	144	1	=	=	PUNCT
ejpam-2822	145	1	[	[	X
ejpam-2822	145	2	[	[	X
ejpam-2822	145	3	η	η	PROPN
ejpam-2822	145	4	,	,	PUNCT
ejpam-2822	145	5	η	η	PROPN
ejpam-2822	145	6	]	]	X
ejpam-2822	145	7	,	,	PUNCT
ejpam-2822	145	8	η	η	PROPN
ejpam-2822	145	9	]	]	X
ejpam-2822	145	10	=	=	SYM
ejpam-2822	145	11	(	(	PUNCT
ejpam-2822	145	12	(	(	PUNCT
ejpam-2822	145	13	η	η	PROPN
ejpam-2822	145	14	,	,	PUNCT
ejpam-2822	145	15	η	η	NOUN
ejpam-2822	145	16	)	)	PUNCT
ejpam-2822	145	17	,	,	PUNCT
ejpam-2822	145	18	η	η	PROPN
ejpam-2822	145	19	)	)	PUNCT
ejpam-2822	145	20	.	.	PUNCT
ejpam-2822	146	1	observe	observe	VERB
ejpam-2822	146	2	that	that	SCONJ
ejpam-2822	146	3	z2(η	z2(η	NOUN
ejpam-2822	146	4	)	)	PUNCT
ejpam-2822	146	5	is	be	AUX
ejpam-2822	146	6	not	not	PART
ejpam-2822	146	7	only	only	ADV
ejpam-2822	146	8	an	an	DET
ejpam-2822	146	9	l	l	NOUN
ejpam-2822	146	10	-	-	NOUN
ejpam-2822	146	11	subgroup	subgroup	NOUN
ejpam-2822	146	12	,	,	PUNCT
ejpam-2822	146	13	it	it	PRON
ejpam-2822	146	14	is	be	AUX
ejpam-2822	146	15	the	the	DET
ejpam-2822	146	16	trivial	trivial	ADJ
ejpam-2822	146	17	l	l	NOUN
ejpam-2822	146	18	-	-	NOUN
ejpam-2822	146	19	subgroup	subgroup	NOUN
ejpam-2822	146	20	of	of	ADP
ejpam-2822	146	21	η	η	PROPN
ejpam-2822	146	22	and	and	CCONJ
ejpam-2822	146	23	so	so	ADV
ejpam-2822	146	24	the	the	DET
ejpam-2822	146	25	descending	descend	VERB
ejpam-2822	146	26	central	central	ADJ
ejpam-2822	146	27	series	series	NOUN
ejpam-2822	146	28	terminates	terminate	VERB
ejpam-2822	146	29	at	at	ADP
ejpam-2822	146	30	z2(η	z2(η	NOUN
ejpam-2822	146	31	)	)	PUNCT
ejpam-2822	146	32	,	,	PUNCT
ejpam-2822	147	1	i.	i.	PROPN
ejpam-2822	147	2	e.	e.	PROPN
ejpam-2822	147	3	η	η	PROPN
ejpam-2822	147	4	=	=	PROPN
ejpam-2822	147	5	z0(η	z0(η	PROPN
ejpam-2822	147	6	)	)	PUNCT
ejpam-2822	147	7	⊇	⊇	PROPN
ejpam-2822	147	8	z1(η	z1(η	PROPN
ejpam-2822	147	9	)	)	PUNCT
ejpam-2822	147	10	⊇	⊇	NOUN
ejpam-2822	147	11	z2(η	z2(η	NOUN
ejpam-2822	147	12	)	)	PUNCT
ejpam-2822	147	13	=	=	PUNCT
ejpam-2822	147	14	ηuf	ηuf	PROPN
ejpam-2822	147	15	.	.	PUNCT
ejpam-2822	148	1	consequently	consequently	ADV
ejpam-2822	148	2	η	η	PROPN
ejpam-2822	148	3	is	be	AUX
ejpam-2822	148	4	a	a	DET
ejpam-2822	148	5	nilpotent	nilpotent	ADJ
ejpam-2822	148	6	l−subgroup	l−subgroup	X
ejpam-2822	148	7	of	of	ADP
ejpam-2822	148	8	µ	µ	PRON
ejpam-2822	148	9	having	have	VERB
ejpam-2822	148	10	nilpotent	nilpotent	ADJ
ejpam-2822	148	11	length	length	NOUN
ejpam-2822	148	12	2	2	NUM
ejpam-2822	148	13	.	.	NOUN
ejpam-2822	148	14	example	example	NOUN
ejpam-2822	149	1	3	3	X
ejpam-2822	149	2	.	.	PUNCT
ejpam-2822	149	3	let	let	VERB
ejpam-2822	149	4	g	g	PROPN
ejpam-2822	149	5	=	=	PROPN
ejpam-2822	149	6	q8	q8	PROPN
ejpam-2822	149	7	and	and	CCONJ
ejpam-2822	149	8	the	the	DET
ejpam-2822	149	9	evaluation	evaluation	NOUN
ejpam-2822	149	10	lattice	lattice	NOUN
ejpam-2822	149	11	be	be	AUX
ejpam-2822	149	12	given	give	VERB
ejpam-2822	149	13	by	by	ADP
ejpam-2822	149	14	the	the	DET
ejpam-2822	149	15	diagram	diagram	NOUN
ejpam-2822	149	16	:	:	PUNCT
ejpam-2822	149	17	i.	i.	PROPN
ejpam-2822	149	18	jahan	jahan	PROPN
ejpam-2822	149	19	,	,	PUNCT
ejpam-2822	149	20	n.	n.	PROPN
ejpam-2822	149	21	ajmal	ajmal	PROPN
ejpam-2822	149	22	,	,	PUNCT
ejpam-2822	149	23	b.	b.	PROPN
ejpam-2822	149	24	davvaz	davvaz	PROPN
ejpam-2822	149	25	/	/	SYM
ejpam-2822	149	26	eur	eur	PROPN
ejpam-2822	149	27	.	.	PUNCT
ejpam-2822	150	1	j.	j.	PROPN
ejpam-2822	150	2	pure	pure	PROPN
ejpam-2822	150	3	appl	appl	PROPN
ejpam-2822	150	4	.	.	PROPN
ejpam-2822	150	5	math	math	PROPN
ejpam-2822	150	6	,	,	PUNCT
ejpam-2822	150	7	10	10	NUM
ejpam-2822	150	8	(	(	PUNCT
ejpam-2822	150	9	2	2	NUM
ejpam-2822	150	10	)	)	PUNCT
ejpam-2822	150	11	(	(	PUNCT
ejpam-2822	150	12	2017	2017	NUM
ejpam-2822	150	13	)	)	PUNCT
ejpam-2822	150	14	,	,	PUNCT
ejpam-2822	150	15	255	255	NUM
ejpam-2822	150	16	-	-	SYM
ejpam-2822	150	17	271	271	NUM
ejpam-2822	150	18	262	262	NUM
ejpam-2822	150	19	consider	consider	VERB
ejpam-2822	150	20	the	the	DET
ejpam-2822	150	21	parent	parent	NOUN
ejpam-2822	150	22	l	l	NOUN
ejpam-2822	150	23	-	-	NOUN
ejpam-2822	150	24	subgroup	subgroup	NOUN
ejpam-2822	150	25	of	of	ADP
ejpam-2822	150	26	g	g	NOUN
ejpam-2822	150	27	given	give	VERB
ejpam-2822	150	28	by	by	ADP
ejpam-2822	150	29	:	:	PUNCT
ejpam-2822	150	30	µ(x	µ(x	X
ejpam-2822	150	31	)	)	PUNCT
ejpam-2822	150	32	=	=	PRON
ejpam-2822	150	33	{	{	PUNCT
ejpam-2822	150	34	u	u	NOUN
ejpam-2822	150	35	if	if	SCONJ
ejpam-2822	150	36	x	x	PROPN
ejpam-2822	150	37	∈	∈	PROPN
ejpam-2822	150	38	c	c	NOUN
ejpam-2822	150	39	,	,	PUNCT
ejpam-2822	150	40	d	d	X
ejpam-2822	150	41	if	if	SCONJ
ejpam-2822	150	42	x	x	PROPN
ejpam-2822	150	43	∈	∈	PROPN
ejpam-2822	150	44	g	g	NOUN
ejpam-2822	150	45	\	\	PROPN
ejpam-2822	150	46	c.	c.	NOUN
ejpam-2822	150	47	now	now	ADV
ejpam-2822	150	48	define	define	VERB
ejpam-2822	150	49	l	l	NOUN
ejpam-2822	150	50	-	-	NOUN
ejpam-2822	150	51	subsets	subset	NOUN
ejpam-2822	150	52	of	of	ADP
ejpam-2822	150	53	µ	µ	NUM
ejpam-2822	150	54	,	,	PUNCT
ejpam-2822	150	55	η	η	PROPN
ejpam-2822	150	56	,	,	PUNCT
ejpam-2822	150	57	θ	θ	PROPN
ejpam-2822	150	58	and	and	CCONJ
ejpam-2822	150	59	φ	φ	PROPN
ejpam-2822	150	60	as	as	SCONJ
ejpam-2822	150	61	given	give	VERB
ejpam-2822	150	62	below	below	ADV
ejpam-2822	150	63	:	:	PUNCT
ejpam-2822	150	64	η(x	η(x	X
ejpam-2822	150	65	)	)	PUNCT
ejpam-2822	150	66	=	=	SYM
ejpam-2822	150	67			PUNCT
ejpam-2822	151	1	d	d	NOUN
ejpam-2822	151	2	if	if	SCONJ
ejpam-2822	151	3	x	x	X
ejpam-2822	151	4	∈	∈	PROPN
ejpam-2822	151	5	c	c	NOUN
ejpam-2822	151	6	,	,	PUNCT
ejpam-2822	151	7	a	a	DET
ejpam-2822	151	8	if	if	SCONJ
ejpam-2822	151	9	x	x	X
ejpam-2822	151	10	∈	∈	PROPN
ejpam-2822	151	11	h1	h1	PROPN
ejpam-2822	151	12	\	\	PROPN
ejpam-2822	151	13	c	c	PROPN
ejpam-2822	151	14	,	,	PUNCT
ejpam-2822	151	15	b	b	NOUN
ejpam-2822	152	1	if	if	SCONJ
ejpam-2822	152	2	x	x	PROPN
ejpam-2822	152	3	∈	∈	PROPN
ejpam-2822	152	4	h2	h2	NOUN
ejpam-2822	152	5	\	\	PROPN
ejpam-2822	152	6	c	c	X
ejpam-2822	152	7	,	,	PUNCT
ejpam-2822	152	8	c	c	NOUN
ejpam-2822	152	9	if	if	SCONJ
ejpam-2822	152	10	x	x	X
ejpam-2822	152	11	∈	∈	NOUN
ejpam-2822	152	12	h3	h3	NOUN
ejpam-2822	152	13	\	\	NOUN
ejpam-2822	152	14	c	c	NOUN
ejpam-2822	152	15	;	;	PUNCT
ejpam-2822	152	16	θ(x	θ(x	PROPN
ejpam-2822	152	17	)	)	PUNCT
ejpam-2822	152	18	=	=	PUNCT
ejpam-2822	153	1			PUNCT
ejpam-2822	154	1	d	d	NOUN
ejpam-2822	154	2	if	if	SCONJ
ejpam-2822	154	3	x	x	X
ejpam-2822	154	4	∈	∈	PROPN
ejpam-2822	154	5	c	c	NOUN
ejpam-2822	154	6	,	,	PUNCT
ejpam-2822	154	7	b	b	NOUN
ejpam-2822	154	8	if	if	SCONJ
ejpam-2822	154	9	x	x	PROPN
ejpam-2822	154	10	∈	∈	PROPN
ejpam-2822	154	11	h1	h1	PROPN
ejpam-2822	154	12	\	\	PROPN
ejpam-2822	154	13	c	c	PROPN
ejpam-2822	154	14	,	,	PUNCT
ejpam-2822	154	15	a	a	DET
ejpam-2822	154	16	if	if	SCONJ
ejpam-2822	154	17	x	x	SYM
ejpam-2822	154	18	∈	∈	PROPN
ejpam-2822	154	19	h2	h2	NOUN
ejpam-2822	154	20	\	\	PROPN
ejpam-2822	154	21	c	c	X
ejpam-2822	154	22	,	,	PUNCT
ejpam-2822	154	23	c	c	NOUN
ejpam-2822	154	24	if	if	SCONJ
ejpam-2822	154	25	x	x	X
ejpam-2822	154	26	∈	∈	NOUN
ejpam-2822	154	27	h3	h3	NOUN
ejpam-2822	154	28	\	\	NOUN
ejpam-2822	154	29	c	c	NOUN
ejpam-2822	154	30	;	;	PUNCT
ejpam-2822	154	31	and	and	CCONJ
ejpam-2822	154	32	φ(x	φ(x	NOUN
ejpam-2822	154	33	)	)	PUNCT
ejpam-2822	154	34	=	=	PUNCT
ejpam-2822	155	1			PUNCT
ejpam-2822	156	1	d	d	NOUN
ejpam-2822	156	2	if	if	SCONJ
ejpam-2822	156	3	x	x	X
ejpam-2822	156	4	∈	∈	PROPN
ejpam-2822	156	5	c	c	NOUN
ejpam-2822	156	6	,	,	PUNCT
ejpam-2822	156	7	a	a	DET
ejpam-2822	156	8	if	if	SCONJ
ejpam-2822	156	9	x	x	X
ejpam-2822	156	10	∈	∈	PROPN
ejpam-2822	156	11	h1	h1	PROPN
ejpam-2822	156	12	\	\	PROPN
ejpam-2822	156	13	c	c	PROPN
ejpam-2822	156	14	,	,	PUNCT
ejpam-2822	156	15	c	c	NOUN
ejpam-2822	156	16	if	if	SCONJ
ejpam-2822	156	17	x	x	X
ejpam-2822	156	18	∈	∈	PROPN
ejpam-2822	156	19	h2	h2	NOUN
ejpam-2822	156	20	\	\	PROPN
ejpam-2822	156	21	c	c	PROPN
ejpam-2822	156	22	,	,	PUNCT
ejpam-2822	156	23	b	b	NOUN
ejpam-2822	156	24	if	if	SCONJ
ejpam-2822	156	25	x	x	PROPN
ejpam-2822	156	26	∈	∈	NOUN
ejpam-2822	156	27	h3	h3	NOUN
ejpam-2822	156	28	\	\	NOUN
ejpam-2822	156	29	c	c	NOUN
ejpam-2822	156	30	;	;	PUNCT
ejpam-2822	156	31	where	where	SCONJ
ejpam-2822	156	32	c	c	NOUN
ejpam-2822	156	33	=	=	PRON
ejpam-2822	156	34	{	{	PUNCT
ejpam-2822	156	35	±1	±1	NOUN
ejpam-2822	156	36	}	}	PUNCT
ejpam-2822	156	37	,	,	PUNCT
ejpam-2822	156	38	h1	h1	PROPN
ejpam-2822	156	39	=	=	SYM
ejpam-2822	156	40	{	{	PUNCT
ejpam-2822	156	41	±1,±i	±1,±i	ADV
ejpam-2822	156	42	}	}	PUNCT
ejpam-2822	156	43	,	,	PUNCT
ejpam-2822	156	44	h2	h2	NOUN
ejpam-2822	156	45	=	=	PUNCT
ejpam-2822	156	46	{	{	PUNCT
ejpam-2822	156	47	±1,±j	±1,±j	PROPN
ejpam-2822	156	48	}	}	PUNCT
ejpam-2822	156	49	,	,	PUNCT
ejpam-2822	156	50	h3	h3	NOUN
ejpam-2822	156	51	=	=	SYM
ejpam-2822	156	52	{	{	PUNCT
ejpam-2822	156	53	±1,±k	±1,±k	NOUN
ejpam-2822	156	54	}	}	PUNCT
ejpam-2822	156	55	.	.	PUNCT
ejpam-2822	157	1	here	here	ADV
ejpam-2822	157	2	ηa	ηa	ADV
ejpam-2822	157	3	=	=	SYM
ejpam-2822	157	4	h1	h1	PROPN
ejpam-2822	157	5	,	,	PUNCT
ejpam-2822	157	6	ηb	ηb	PROPN
ejpam-2822	157	7	=	=	SYM
ejpam-2822	157	8	h2	h2	PROPN
ejpam-2822	157	9	and	and	CCONJ
ejpam-2822	157	10	ηc	ηc	PRON
ejpam-2822	157	11	=	=	NOUN
ejpam-2822	157	12	h3	h3	NOUN
ejpam-2822	157	13	.	.	PUNCT
ejpam-2822	158	1	since	since	SCONJ
ejpam-2822	158	2	the	the	DET
ejpam-2822	158	3	level	level	NOUN
ejpam-2822	158	4	subsets	subset	NOUN
ejpam-2822	158	5	of	of	ADP
ejpam-2822	158	6	η	η	PROPN
ejpam-2822	158	7	are	be	AUX
ejpam-2822	158	8	normal	normal	ADJ
ejpam-2822	158	9	subgroups	subgroup	NOUN
ejpam-2822	158	10	of	of	ADP
ejpam-2822	158	11	g	g	PROPN
ejpam-2822	158	12	,	,	PUNCT
ejpam-2822	158	13	η	η	PROPN
ejpam-2822	158	14	is	be	AUX
ejpam-2822	158	15	a	a	DET
ejpam-2822	158	16	normal	normal	ADJ
ejpam-2822	158	17	l	l	NOUN
ejpam-2822	158	18	-	-	NOUN
ejpam-2822	158	19	subgroup	subgroup	NOUN
ejpam-2822	158	20	of	of	ADP
ejpam-2822	158	21	g.	g.	PROPN
ejpam-2822	158	22	similarly	similarly	ADV
ejpam-2822	158	23	,	,	PUNCT
ejpam-2822	158	24	it	it	PRON
ejpam-2822	158	25	can	can	AUX
ejpam-2822	158	26	be	be	AUX
ejpam-2822	158	27	seen	see	VERB
ejpam-2822	158	28	that	that	SCONJ
ejpam-2822	158	29	θ	θ	PROPN
ejpam-2822	158	30	and	and	CCONJ
ejpam-2822	158	31	φ	φ	PROPN
ejpam-2822	158	32	are	be	AUX
ejpam-2822	158	33	also	also	ADV
ejpam-2822	158	34	normal	normal	ADJ
ejpam-2822	158	35	l−subgroups	l−subgroup	NOUN
ejpam-2822	158	36	of	of	ADP
ejpam-2822	158	37	g	g	NOUN
ejpam-2822	158	38	and	and	CCONJ
ejpam-2822	158	39	hence	hence	ADV
ejpam-2822	158	40	of	of	ADP
ejpam-2822	158	41	µ.	µ.	PROPN
ejpam-2822	158	42	now	now	ADV
ejpam-2822	158	43	η	η	PROPN
ejpam-2822	158	44	is	be	AUX
ejpam-2822	158	45	a	a	DET
ejpam-2822	158	46	nilpotent	nilpotent	ADJ
ejpam-2822	158	47	l	l	NOUN
ejpam-2822	158	48	-	-	NOUN
ejpam-2822	158	49	subgroup	subgroup	NOUN
ejpam-2822	158	50	of	of	ADP
ejpam-2822	158	51	µ	µ	NOUN
ejpam-2822	158	52	,	,	PUNCT
ejpam-2822	158	53	in	in	ADP
ejpam-2822	158	54	view	view	NOUN
ejpam-2822	158	55	of	of	ADP
ejpam-2822	158	56	definition	definition	NOUN
ejpam-2822	158	57	3.2	3.2	NUM
ejpam-2822	158	58	,	,	PUNCT
ejpam-2822	158	59	can	can	AUX
ejpam-2822	158	60	be	be	AUX
ejpam-2822	158	61	seen	see	VERB
ejpam-2822	158	62	as	as	SCONJ
ejpam-2822	158	63	follows	follow	VERB
ejpam-2822	158	64	:	:	PUNCT
ejpam-2822	158	65	note	note	VERB
ejpam-2822	158	66	that	that	SCONJ
ejpam-2822	158	67	g′	g′	NOUN
ejpam-2822	158	68	=	=	PUNCT
ejpam-2822	158	69	{	{	PUNCT
ejpam-2822	158	70	1,−1	1,−1	NUM
ejpam-2822	158	71	}	}	PUNCT
ejpam-2822	158	72	.	.	PUNCT
ejpam-2822	159	1	in	in	ADP
ejpam-2822	159	2	order	order	NOUN
ejpam-2822	159	3	to	to	PART
ejpam-2822	159	4	obtain	obtain	VERB
ejpam-2822	159	5	the	the	DET
ejpam-2822	159	6	members	member	NOUN
ejpam-2822	159	7	of	of	ADP
ejpam-2822	159	8	descending	descend	VERB
ejpam-2822	159	9	central	central	ADJ
ejpam-2822	159	10	series	series	NOUN
ejpam-2822	159	11	of	of	ADP
ejpam-2822	159	12	η	η	PROPN
ejpam-2822	159	13	,	,	PUNCT
ejpam-2822	159	14	we	we	PRON
ejpam-2822	159	15	set	set	VERB
ejpam-2822	159	16	z0(η	z0(η	PRON
ejpam-2822	159	17	)	)	PUNCT
ejpam-2822	159	18	=	=	SYM
ejpam-2822	159	19	η	η	PROPN
ejpam-2822	159	20	and	and	CCONJ
ejpam-2822	159	21	consider	consider	VERB
ejpam-2822	159	22	the	the	DET
ejpam-2822	159	23	commutator	commutator	NOUN
ejpam-2822	159	24	(	(	PUNCT
ejpam-2822	159	25	η	η	PROPN
ejpam-2822	159	26	,	,	PUNCT
ejpam-2822	159	27	η	η	PROPN
ejpam-2822	159	28	)	)	PUNCT
ejpam-2822	159	29	(	(	PUNCT
ejpam-2822	159	30	η	η	PROPN
ejpam-2822	159	31	,	,	PUNCT
ejpam-2822	159	32	η	η	NOUN
ejpam-2822	159	33	)	)	PUNCT
ejpam-2822	159	34	(	(	PUNCT
ejpam-2822	159	35	x	x	X
ejpam-2822	159	36	)	)	PUNCT
ejpam-2822	159	37	=	=	PRON
ejpam-2822	160	1	{	{	PUNCT
ejpam-2822	160	2	d	d	X
ejpam-2822	160	3	if	if	SCONJ
ejpam-2822	160	4	x	x	X
ejpam-2822	160	5	=	=	SYM
ejpam-2822	160	6	1	1	NUM
ejpam-2822	160	7	,	,	PUNCT
ejpam-2822	160	8	f	f	PROPN
ejpam-2822	160	9	if	if	SCONJ
ejpam-2822	160	10	x	x	PROPN
ejpam-2822	160	11	∈	∈	PROPN
ejpam-2822	160	12	g	g	NOUN
ejpam-2822	160	13	\	\	PROPN
ejpam-2822	160	14	{	{	PUNCT
ejpam-2822	160	15	1	1	NUM
ejpam-2822	160	16	}	}	PUNCT
ejpam-2822	160	17	.	.	PUNCT
ejpam-2822	161	1	as	as	SCONJ
ejpam-2822	161	2	the	the	DET
ejpam-2822	161	3	level	level	NOUN
ejpam-2822	161	4	subsets	subset	NOUN
ejpam-2822	161	5	of	of	ADP
ejpam-2822	161	6	(	(	PUNCT
ejpam-2822	161	7	η	η	PROPN
ejpam-2822	161	8	,	,	PUNCT
ejpam-2822	161	9	η	η	NOUN
ejpam-2822	161	10	)	)	PUNCT
ejpam-2822	161	11	are	be	AUX
ejpam-2822	161	12	subgroups	subgroup	NOUN
ejpam-2822	161	13	of	of	ADP
ejpam-2822	161	14	g	g	NOUN
ejpam-2822	161	15	,	,	PUNCT
ejpam-2822	161	16	z1(η	z1(η	PROPN
ejpam-2822	161	17	)	)	PUNCT
ejpam-2822	161	18	=	=	PUNCT
ejpam-2822	162	1	[	[	X
ejpam-2822	162	2	η	η	PROPN
ejpam-2822	162	3	,	,	PUNCT
ejpam-2822	162	4	η	η	PROPN
ejpam-2822	162	5	]	]	X
ejpam-2822	162	6	=	=	SYM
ejpam-2822	162	7	(	(	PUNCT
ejpam-2822	162	8	η	η	PROPN
ejpam-2822	162	9	,	,	PUNCT
ejpam-2822	162	10	η	η	NOUN
ejpam-2822	162	11	)	)	PUNCT
ejpam-2822	162	12	.	.	PUNCT
ejpam-2822	163	1	observe	observe	VERB
ejpam-2822	163	2	that	that	SCONJ
ejpam-2822	163	3	z1(η	z1(η	NOUN
ejpam-2822	163	4	)	)	PUNCT
ejpam-2822	163	5	is	be	AUX
ejpam-2822	163	6	not	not	PART
ejpam-2822	163	7	only	only	ADV
ejpam-2822	163	8	an	an	DET
ejpam-2822	163	9	l	l	NOUN
ejpam-2822	163	10	-	-	NOUN
ejpam-2822	163	11	subgroup	subgroup	NOUN
ejpam-2822	163	12	,	,	PUNCT
ejpam-2822	163	13	it	it	PRON
ejpam-2822	163	14	is	be	AUX
ejpam-2822	163	15	the	the	DET
ejpam-2822	163	16	trivial	trivial	ADJ
ejpam-2822	163	17	l	l	NOUN
ejpam-2822	163	18	-	-	NOUN
ejpam-2822	163	19	subgroup	subgroup	NOUN
ejpam-2822	163	20	of	of	ADP
ejpam-2822	163	21	η	η	PROPN
ejpam-2822	163	22	and	and	CCONJ
ejpam-2822	163	23	so	so	ADV
ejpam-2822	163	24	the	the	DET
ejpam-2822	163	25	descending	descend	VERB
ejpam-2822	163	26	central	central	ADJ
ejpam-2822	163	27	series	series	NOUN
ejpam-2822	163	28	terminates	terminate	VERB
ejpam-2822	163	29	at	at	ADP
ejpam-2822	163	30	z1(η	z1(η	PROPN
ejpam-2822	163	31	)	)	PUNCT
ejpam-2822	163	32	,	,	PUNCT
ejpam-2822	163	33	i.	i.	PROPN
ejpam-2822	163	34	e.	e.	PROPN
ejpam-2822	163	35	i.	i.	PROPN
ejpam-2822	163	36	jahan	jahan	PROPN
ejpam-2822	163	37	,	,	PUNCT
ejpam-2822	163	38	n.	n.	PROPN
ejpam-2822	163	39	ajmal	ajmal	PROPN
ejpam-2822	163	40	,	,	PUNCT
ejpam-2822	163	41	b.	b.	PROPN
ejpam-2822	163	42	davvaz	davvaz	PROPN
ejpam-2822	163	43	/	/	SYM
ejpam-2822	163	44	eur	eur	PROPN
ejpam-2822	163	45	.	.	PUNCT
ejpam-2822	164	1	j.	j.	PROPN
ejpam-2822	164	2	pure	pure	PROPN
ejpam-2822	164	3	appl	appl	PROPN
ejpam-2822	164	4	.	.	PROPN
ejpam-2822	164	5	math	math	PROPN
ejpam-2822	164	6	,	,	PUNCT
ejpam-2822	164	7	10	10	NUM
ejpam-2822	164	8	(	(	PUNCT
ejpam-2822	164	9	2	2	NUM
ejpam-2822	164	10	)	)	PUNCT
ejpam-2822	164	11	(	(	PUNCT
ejpam-2822	164	12	2017	2017	NUM
ejpam-2822	164	13	)	)	PUNCT
ejpam-2822	164	14	,	,	PUNCT
ejpam-2822	164	15	255	255	NUM
ejpam-2822	164	16	-	-	SYM
ejpam-2822	164	17	271	271	NUM
ejpam-2822	164	18	263	263	NUM
ejpam-2822	164	19	η	η	PROPN
ejpam-2822	164	20	=	=	PROPN
ejpam-2822	164	21	z0(η	z0(η	PROPN
ejpam-2822	164	22	)	)	PUNCT
ejpam-2822	164	23	⊇	⊇	PROPN
ejpam-2822	164	24	z1(η	z1(η	PROPN
ejpam-2822	164	25	)	)	PUNCT
ejpam-2822	164	26	=	=	SYM
ejpam-2822	164	27	ηd0	ηd0	NOUN
ejpam-2822	164	28	.	.	PUNCT
ejpam-2822	165	1	consequently	consequently	ADV
ejpam-2822	165	2	η	η	PROPN
ejpam-2822	165	3	is	be	AUX
ejpam-2822	165	4	a	a	DET
ejpam-2822	165	5	nilpotent	nilpotent	ADJ
ejpam-2822	165	6	l−subgroup	l−subgroup	X
ejpam-2822	165	7	of	of	ADP
ejpam-2822	165	8	µ	µ	PRON
ejpam-2822	165	9	having	have	VERB
ejpam-2822	165	10	nilpotent	nilpotent	ADJ
ejpam-2822	165	11	length	length	NOUN
ejpam-2822	165	12	1	1	NUM
ejpam-2822	165	13	.	.	PUNCT
ejpam-2822	166	1	now	now	ADV
ejpam-2822	166	2	in	in	ADP
ejpam-2822	166	3	order	order	NOUN
ejpam-2822	166	4	to	to	PART
ejpam-2822	166	5	continue	continue	VERB
ejpam-2822	166	6	our	our	PRON
ejpam-2822	166	7	studies	study	NOUN
ejpam-2822	166	8	further	far	ADV
ejpam-2822	166	9	,	,	PUNCT
ejpam-2822	166	10	we	we	PRON
ejpam-2822	166	11	mention	mention	VERB
ejpam-2822	166	12	that	that	SCONJ
ejpam-2822	166	13	the	the	DET
ejpam-2822	166	14	set	set	NOUN
ejpam-2822	166	15	product	product	NOUN
ejpam-2822	166	16	of	of	ADP
ejpam-2822	166	17	l	l	NOUN
ejpam-2822	166	18	-	-	NOUN
ejpam-2822	166	19	subgroups	subgroup	NOUN
ejpam-2822	166	20	of	of	ADP
ejpam-2822	166	21	η	η	PROPN
ejpam-2822	166	22	,	,	PUNCT
ejpam-2822	166	23	θ	θ	PROPN
ejpam-2822	166	24	and	and	CCONJ
ejpam-2822	166	25	φ	φ	PROPN
ejpam-2822	166	26	are	be	AUX
ejpam-2822	166	27	given	give	VERB
ejpam-2822	166	28	by	by	ADP
ejpam-2822	166	29	η	η	PROPN
ejpam-2822	166	30	◦	◦	NOUN
ejpam-2822	166	31	θ	θ	NOUN
ejpam-2822	166	32	=	=	SYM
ejpam-2822	166	33	θ	θ	PROPN
ejpam-2822	166	34	◦	◦	NOUN
ejpam-2822	166	35	φ	φ	PROPN
ejpam-2822	166	36	=	=	SYM
ejpam-2822	166	37	η	η	PROPN
ejpam-2822	166	38	◦	◦	PROPN
ejpam-2822	166	39	φ	φ	NUM
ejpam-2822	166	40	=	=	SYM
ejpam-2822	166	41	ψ	ψ	X
ejpam-2822	166	42	where	where	SCONJ
ejpam-2822	166	43	ψ	ψ	NOUN
ejpam-2822	166	44	is	be	AUX
ejpam-2822	166	45	the	the	DET
ejpam-2822	166	46	constant	constant	ADJ
ejpam-2822	166	47	function	function	NOUN
ejpam-2822	166	48	taking	take	VERB
ejpam-2822	166	49	whole	whole	NOUN
ejpam-2822	166	50	of	of	ADP
ejpam-2822	166	51	q8	q8	PROPN
ejpam-2822	166	52	to	to	ADP
ejpam-2822	166	53	d.	d.	PROPN
ejpam-2822	166	54	obviously	obviously	ADV
ejpam-2822	166	55	η	η	PROPN
ejpam-2822	166	56	,	,	PUNCT
ejpam-2822	166	57	θ	θ	PROPN
ejpam-2822	166	58	⊆	⊆	NUM
ejpam-2822	166	59	ψ	ψ	ADP
ejpam-2822	166	60	⊆	⊆	NUM
ejpam-2822	166	61	µ	µ	NOUN
ejpam-2822	166	62	but	but	CCONJ
ejpam-2822	166	63	ψ	ψ	ADP
ejpam-2822	166	64	being	be	AUX
ejpam-2822	166	65	a	a	DET
ejpam-2822	166	66	constant	constant	ADJ
ejpam-2822	166	67	function	function	NOUN
ejpam-2822	166	68	is	be	AUX
ejpam-2822	166	69	not	not	PART
ejpam-2822	166	70	a	a	DET
ejpam-2822	166	71	nilpotent	nilpotent	ADJ
ejpam-2822	166	72	l	l	NOUN
ejpam-2822	166	73	-	-	NOUN
ejpam-2822	166	74	subgroup	subgroup	NOUN
ejpam-2822	166	75	of	of	ADP
ejpam-2822	166	76	µ.	µ.	PROPN
ejpam-2822	166	77	now	now	ADV
ejpam-2822	166	78	,	,	PUNCT
ejpam-2822	166	79	we	we	PRON
ejpam-2822	166	80	ascertain	ascertain	VERB
ejpam-2822	166	81	the	the	DET
ejpam-2822	166	82	tail	tail	NOUN
ejpam-2822	166	83	of	of	ADP
ejpam-2822	166	84	the	the	DET
ejpam-2822	166	85	set	set	NOUN
ejpam-2822	166	86	product	product	NOUN
ejpam-2822	166	87	of	of	ADP
ejpam-2822	166	88	l	l	NOUN
ejpam-2822	166	89	-	-	NOUN
ejpam-2822	166	90	subgroups	subgroup	NOUN
ejpam-2822	166	91	:	:	PUNCT
ejpam-2822	166	92	proposition	proposition	NOUN
ejpam-2822	166	93	7	7	NUM
ejpam-2822	166	94	.	.	PUNCT
ejpam-2822	167	1	let	let	VERB
ejpam-2822	167	2	η	η	PROPN
ejpam-2822	167	3	,	,	PUNCT
ejpam-2822	167	4	θ	θ	PROPN
ejpam-2822	167	5	∈	∈	PROPN
ejpam-2822	167	6	l(µ	l(µ	PROPN
ejpam-2822	167	7	)	)	PUNCT
ejpam-2822	167	8	.	.	PUNCT
ejpam-2822	168	1	if	if	SCONJ
ejpam-2822	168	2	η(e	η(e	PROPN
ejpam-2822	168	3	)	)	PUNCT
ejpam-2822	168	4	=	=	SYM
ejpam-2822	168	5	θ(e	θ(e	NUM
ejpam-2822	168	6	)	)	PUNCT
ejpam-2822	168	7	,	,	PUNCT
ejpam-2822	168	8	then	then	ADV
ejpam-2822	168	9	infη	infη	ADJ
ejpam-2822	168	10	◦	◦	NOUN
ejpam-2822	168	11	θ	θ	PROPN
ejpam-2822	168	12	≥	≥	X
ejpam-2822	168	13	infη	infη	PROPN
ejpam-2822	168	14	∨	∨	NUM
ejpam-2822	168	15	infθ	infθ	NOUN
ejpam-2822	168	16	.	.	PUNCT
ejpam-2822	169	1	the	the	DET
ejpam-2822	169	2	following	follow	VERB
ejpam-2822	169	3	theorem	theorem	VERB
ejpam-2822	169	4	sufficiently	sufficiently	ADV
ejpam-2822	169	5	exhibits	exhibit	VERB
ejpam-2822	169	6	the	the	DET
ejpam-2822	169	7	application	application	NOUN
ejpam-2822	169	8	of	of	ADP
ejpam-2822	169	9	the	the	DET
ejpam-2822	169	10	notion	notion	NOUN
ejpam-2822	169	11	of	of	ADP
ejpam-2822	169	12	infimums	infimums	PROPN
ejpam-2822	169	13	:	:	PUNCT
ejpam-2822	169	14	theorem	theorem	NOUN
ejpam-2822	169	15	2	2	NUM
ejpam-2822	169	16	.	.	PUNCT
ejpam-2822	170	1	let	let	VERB
ejpam-2822	170	2	η	η	PROPN
ejpam-2822	170	3	,	,	PUNCT
ejpam-2822	170	4	θ	θ	PROPN
ejpam-2822	170	5	∈	∈	PROPN
ejpam-2822	170	6	nl(µ	nl(µ	NOUN
ejpam-2822	170	7	)	)	PUNCT
ejpam-2822	170	8	and	and	CCONJ
ejpam-2822	170	9	σ	σ	NUM
ejpam-2822	170	10	∈	∈	PROPN
ejpam-2822	170	11	l(µ	l(µ	PROPN
ejpam-2822	170	12	)	)	PUNCT
ejpam-2822	170	13	.	.	PUNCT
ejpam-2822	171	1	if	if	SCONJ
ejpam-2822	171	2	either	either	CCONJ
ejpam-2822	171	3	η	η	PROPN
ejpam-2822	171	4	and	and	CCONJ
ejpam-2822	171	5	θ	θ	PROPN
ejpam-2822	171	6	or	or	CCONJ
ejpam-2822	171	7	θ	θ	PROPN
ejpam-2822	171	8	and	and	CCONJ
ejpam-2822	171	9	σ	σ	PROPN
ejpam-2822	171	10	have	have	VERB
ejpam-2822	171	11	the	the	DET
ejpam-2822	171	12	same	same	ADJ
ejpam-2822	171	13	tails	tail	NOUN
ejpam-2822	171	14	,	,	PUNCT
ejpam-2822	171	15	then	then	ADV
ejpam-2822	171	16	[	[	X
ejpam-2822	171	17	η	η	PROPN
ejpam-2822	171	18	◦	◦	PROPN
ejpam-2822	171	19	σ	σ	PROPN
ejpam-2822	171	20	,	,	PUNCT
ejpam-2822	171	21	θ	θ	X
ejpam-2822	171	22	]	]	PUNCT
ejpam-2822	171	23	⊆	⊆	NUM
ejpam-2822	171	24	[	[	X
ejpam-2822	171	25	η	η	PROPN
ejpam-2822	171	26	,	,	PUNCT
ejpam-2822	171	27	θ	θ	NOUN
ejpam-2822	171	28	]	]	X
ejpam-2822	171	29	◦	◦	NOUN
ejpam-2822	171	30	[	[	X
ejpam-2822	171	31	θ	θ	X
ejpam-2822	171	32	,	,	PUNCT
ejpam-2822	171	33	σ	σ	PROPN
ejpam-2822	171	34	]	]	PUNCT
ejpam-2822	171	35	.	.	PUNCT
ejpam-2822	172	1	moreover	moreover	ADV
ejpam-2822	172	2	if	if	SCONJ
ejpam-2822	172	3	η(e	η(e	NOUN
ejpam-2822	172	4	)	)	PUNCT
ejpam-2822	172	5	=	=	SYM
ejpam-2822	172	6	θ(e	θ(e	NUM
ejpam-2822	172	7	)	)	PUNCT
ejpam-2822	172	8	,	,	PUNCT
ejpam-2822	172	9	then	then	ADV
ejpam-2822	172	10	the	the	DET
ejpam-2822	172	11	equality	equality	NOUN
ejpam-2822	172	12	holds	hold	VERB
ejpam-2822	172	13	.	.	PUNCT
ejpam-2822	173	1	proof	proof	NOUN
ejpam-2822	173	2	.	.	PUNCT
ejpam-2822	174	1	let	let	VERB
ejpam-2822	174	2	x	x	SYM
ejpam-2822	174	3	∈	∈	PROPN
ejpam-2822	174	4	g.	g.	NOUN
ejpam-2822	174	5	if	if	SCONJ
ejpam-2822	174	6	x	x	PRON
ejpam-2822	174	7	is	be	AUX
ejpam-2822	174	8	not	not	PART
ejpam-2822	174	9	a	a	DET
ejpam-2822	174	10	commutator	commutator	NOUN
ejpam-2822	174	11	and	and	CCONJ
ejpam-2822	174	12	η	η	PROPN
ejpam-2822	174	13	and	and	CCONJ
ejpam-2822	174	14	θ	θ	PROPN
ejpam-2822	174	15	have	have	VERB
ejpam-2822	174	16	the	the	DET
ejpam-2822	174	17	same	same	ADJ
ejpam-2822	174	18	tails	tail	NOUN
ejpam-2822	174	19	,	,	PUNCT
ejpam-2822	174	20	then	then	ADV
ejpam-2822	174	21	[	[	X
ejpam-2822	174	22	η	η	X
ejpam-2822	174	23	,	,	PUNCT
ejpam-2822	174	24	θ	θ	NOUN
ejpam-2822	174	25	]	]	X
ejpam-2822	174	26	◦	◦	NOUN
ejpam-2822	174	27	[	[	X
ejpam-2822	174	28	θ	θ	X
ejpam-2822	174	29	,	,	PUNCT
ejpam-2822	174	30	σ	σ	PROPN
ejpam-2822	174	31	]	]	X
ejpam-2822	174	32	(	(	PUNCT
ejpam-2822	174	33	x	x	X
ejpam-2822	174	34	)	)	PUNCT
ejpam-2822	174	35	≥	≥	NOUN
ejpam-2822	175	1	[	[	X
ejpam-2822	175	2	η	η	X
ejpam-2822	175	3	,	,	PUNCT
ejpam-2822	175	4	θ	θ	PROPN
ejpam-2822	175	5	]	]	X
ejpam-2822	175	6	(	(	PUNCT
ejpam-2822	175	7	x	x	X
ejpam-2822	175	8	)	)	PUNCT
ejpam-2822	175	9	∧	∧	PROPN
ejpam-2822	175	10	[	[	X
ejpam-2822	175	11	θ	θ	PROPN
ejpam-2822	175	12	,	,	PUNCT
ejpam-2822	175	13	σ	σ	PROPN
ejpam-2822	175	14	]	]	X
ejpam-2822	175	15	(	(	PUNCT
ejpam-2822	175	16	e	e	NOUN
ejpam-2822	175	17	)	)	PUNCT
ejpam-2822	175	18	≥	≥	NOUN
ejpam-2822	175	19	infη	infη	ADJ
ejpam-2822	175	20	∧	∧	PROPN
ejpam-2822	175	21	infθ	infθ	NOUN
ejpam-2822	175	22	∧	∧	PROPN
ejpam-2822	175	23	θ(e	θ(e	PROPN
ejpam-2822	175	24	)	)	PUNCT
ejpam-2822	175	25	∧	∧	PROPN
ejpam-2822	175	26	σ(e	σ(e	PROPN
ejpam-2822	175	27	)	)	PUNCT
ejpam-2822	176	1	=	=	SYM
ejpam-2822	176	2	infθ	infθ	NOUN
ejpam-2822	176	3	∧	∧	PROPN
ejpam-2822	176	4	σ(e	σ(e	PROPN
ejpam-2822	176	5	)	)	PUNCT
ejpam-2822	176	6	(	(	PUNCT
ejpam-2822	176	7	as	as	ADP
ejpam-2822	176	8	infθ	infθ	NOUN
ejpam-2822	176	9	=	=	SYM
ejpam-2822	176	10	infη	infη	ADJ
ejpam-2822	176	11	and	and	CCONJ
ejpam-2822	176	12	infθ	infθ	PROPN
ejpam-2822	176	13	∧	∧	PROPN
ejpam-2822	176	14	θ(e	θ(e	PROPN
ejpam-2822	176	15	)	)	PUNCT
ejpam-2822	176	16	=	=	SYM
ejpam-2822	176	17	infθ	infθ	NOUN
ejpam-2822	176	18	)	)	PUNCT
ejpam-2822	176	19	=	=	NOUN
ejpam-2822	176	20	infθ	infθ	PROPN
ejpam-2822	176	21	∧	∧	PROPN
ejpam-2822	176	22	η(e	η(e	PROPN
ejpam-2822	176	23	)	)	PUNCT
ejpam-2822	176	24	∧	∧	PROPN
ejpam-2822	176	25	σ(e	σ(e	PROPN
ejpam-2822	176	26	)	)	PUNCT
ejpam-2822	176	27	(	(	PUNCT
ejpam-2822	176	28	as	as	SCONJ
ejpam-2822	176	29	infθ	infθ	PROPN
ejpam-2822	176	30	∧	∧	PROPN
ejpam-2822	176	31	η(e	η(e	PROPN
ejpam-2822	176	32	)	)	PUNCT
ejpam-2822	177	1	=	=	SYM
ejpam-2822	177	2	infη	infη	PROPN
ejpam-2822	177	3	∧	∧	PROPN
ejpam-2822	177	4	η(e	η(e	PROPN
ejpam-2822	177	5	)	)	PUNCT
ejpam-2822	177	6	=	=	SYM
ejpam-2822	177	7	infη	infη	X
ejpam-2822	177	8	)	)	PUNCT
ejpam-2822	177	9	=	=	SYM
ejpam-2822	178	1	infθ	infθ	PROPN
ejpam-2822	178	2	∧	∧	PROPN
ejpam-2822	178	3	η	η	PROPN
ejpam-2822	178	4	◦	◦	PROPN
ejpam-2822	178	5	σ(e	σ(e	PROPN
ejpam-2822	178	6	)	)	PUNCT
ejpam-2822	178	7	≥	≥	NOUN
ejpam-2822	178	8	infθ	infθ	NOUN
ejpam-2822	178	9	∧	∧	PROPN
ejpam-2822	178	10	infη	infη	PROPN
ejpam-2822	178	11	◦	◦	NOUN
ejpam-2822	178	12	σ	σ	X
ejpam-2822	178	13	=	=	SYM
ejpam-2822	178	14	(	(	PUNCT
ejpam-2822	178	15	η	η	PROPN
ejpam-2822	178	16	◦	◦	PROPN
ejpam-2822	178	17	σ	σ	PROPN
ejpam-2822	178	18	,	,	PUNCT
ejpam-2822	178	19	θ	θ	NOUN
ejpam-2822	178	20	)	)	PUNCT
ejpam-2822	178	21	(	(	PUNCT
ejpam-2822	178	22	x	x	NOUN
ejpam-2822	178	23	)	)	PUNCT
ejpam-2822	178	24	.	.	PUNCT
ejpam-2822	179	1	if	if	SCONJ
ejpam-2822	179	2	θ	θ	PROPN
ejpam-2822	179	3	and	and	CCONJ
ejpam-2822	179	4	σ	σ	PROPN
ejpam-2822	179	5	have	have	VERB
ejpam-2822	179	6	the	the	DET
ejpam-2822	179	7	same	same	ADJ
ejpam-2822	179	8	tails	tail	NOUN
ejpam-2822	179	9	,	,	PUNCT
ejpam-2822	179	10	then	then	ADV
ejpam-2822	179	11	also	also	ADV
ejpam-2822	179	12	(	(	PUNCT
ejpam-2822	179	13	η	η	PROPN
ejpam-2822	179	14	◦	◦	PROPN
ejpam-2822	179	15	σ	σ	PROPN
ejpam-2822	179	16	,	,	PUNCT
ejpam-2822	179	17	θ	θ	NOUN
ejpam-2822	179	18	)	)	PUNCT
ejpam-2822	179	19	(	(	PUNCT
ejpam-2822	179	20	x	x	X
ejpam-2822	179	21	)	)	PUNCT
ejpam-2822	179	22	≤	≤	NOUN
ejpam-2822	180	1	[	[	X
ejpam-2822	180	2	η	η	X
ejpam-2822	180	3	,	,	PUNCT
ejpam-2822	180	4	θ	θ	NOUN
ejpam-2822	180	5	]	]	X
ejpam-2822	180	6	◦	◦	NOUN
ejpam-2822	180	7	[	[	X
ejpam-2822	180	8	θ	θ	X
ejpam-2822	180	9	,	,	PUNCT
ejpam-2822	180	10	σ	σ	PROPN
ejpam-2822	180	11	]	]	X
ejpam-2822	180	12	(	(	PUNCT
ejpam-2822	180	13	x	x	NOUN
ejpam-2822	180	14	)	)	PUNCT
ejpam-2822	180	15	.	.	PUNCT
ejpam-2822	181	1	(	(	PUNCT
ejpam-2822	181	2	1	1	X
ejpam-2822	181	3	)	)	PUNCT
ejpam-2822	181	4	suppose	suppose	VERB
ejpam-2822	181	5	that	that	SCONJ
ejpam-2822	181	6	x	x	PRON
ejpam-2822	181	7	is	be	AUX
ejpam-2822	181	8	a	a	DET
ejpam-2822	181	9	commutator	commutator	NOUN
ejpam-2822	181	10	in	in	ADP
ejpam-2822	181	11	g.	g.	PROPN
ejpam-2822	181	12	now	now	ADV
ejpam-2822	181	13	,	,	PUNCT
ejpam-2822	181	14	for	for	ADP
ejpam-2822	181	15	any	any	DET
ejpam-2822	181	16	u	u	PROPN
ejpam-2822	181	17	∈	∈	PROPN
ejpam-2822	181	18	g	g	NOUN
ejpam-2822	181	19	,	,	PUNCT
ejpam-2822	181	20	define	define	VERB
ejpam-2822	181	21	the	the	DET
ejpam-2822	181	22	following	follow	VERB
ejpam-2822	181	23	subsets	subset	NOUN
ejpam-2822	181	24	of	of	ADP
ejpam-2822	181	25	g×g	g×g	PROPN
ejpam-2822	181	26	by	by	ADP
ejpam-2822	181	27	:	:	PUNCT
ejpam-2822	181	28	c(u	c(u	PROPN
ejpam-2822	181	29	)	)	PUNCT
ejpam-2822	182	1	=	=	PRON
ejpam-2822	182	2	{	{	PUNCT
ejpam-2822	182	3	(	(	PUNCT
ejpam-2822	182	4	y	y	PROPN
ejpam-2822	182	5	,	,	PUNCT
ejpam-2822	182	6	z	z	NOUN
ejpam-2822	182	7	)	)	PUNCT
ejpam-2822	182	8	∈	∈	PROPN
ejpam-2822	182	9	g×g	g×g	PROPN
ejpam-2822	182	10	:	:	PUNCT
ejpam-2822	182	11	u	u	NOUN
ejpam-2822	182	12	=	=	PUNCT
ejpam-2822	183	1	[	[	X
ejpam-2822	183	2	y	y	PROPN
ejpam-2822	183	3	,	,	PUNCT
ejpam-2822	183	4	z	z	NOUN
ejpam-2822	183	5	]	]	X
ejpam-2822	183	6	}	}	PUNCT
ejpam-2822	183	7	and	and	CCONJ
ejpam-2822	183	8	p	p	X
ejpam-2822	183	9	(	(	PUNCT
ejpam-2822	183	10	u	u	NOUN
ejpam-2822	183	11	)	)	PUNCT
ejpam-2822	183	12	=	=	SYM
ejpam-2822	183	13	{	{	PUNCT
ejpam-2822	183	14	(	(	PUNCT
ejpam-2822	183	15	y	y	PROPN
ejpam-2822	183	16	,	,	PUNCT
ejpam-2822	183	17	z	z	NOUN
ejpam-2822	183	18	)	)	PUNCT
ejpam-2822	183	19	∈	∈	PROPN
ejpam-2822	183	20	g×g	g×g	PROPN
ejpam-2822	183	21	:	:	PUNCT
ejpam-2822	183	22	u	u	NOUN
ejpam-2822	183	23	=	=	PROPN
ejpam-2822	183	24	yz	yz	PROPN
ejpam-2822	183	25	}	}	PUNCT
ejpam-2822	183	26	.	.	PUNCT
ejpam-2822	184	1	i.	i.	PROPN
ejpam-2822	184	2	jahan	jahan	PROPN
ejpam-2822	184	3	,	,	PUNCT
ejpam-2822	184	4	n.	n.	PROPN
ejpam-2822	184	5	ajmal	ajmal	PROPN
ejpam-2822	184	6	,	,	PUNCT
ejpam-2822	184	7	b.	b.	PROPN
ejpam-2822	184	8	davvaz	davvaz	PROPN
ejpam-2822	184	9	/	/	SYM
ejpam-2822	184	10	eur	eur	PROPN
ejpam-2822	184	11	.	.	PUNCT
ejpam-2822	185	1	j.	j.	PROPN
ejpam-2822	185	2	pure	pure	PROPN
ejpam-2822	185	3	appl	appl	PROPN
ejpam-2822	185	4	.	.	PROPN
ejpam-2822	185	5	math	math	PROPN
ejpam-2822	185	6	,	,	PUNCT
ejpam-2822	185	7	10	10	NUM
ejpam-2822	185	8	(	(	PUNCT
ejpam-2822	185	9	2	2	NUM
ejpam-2822	185	10	)	)	PUNCT
ejpam-2822	185	11	(	(	PUNCT
ejpam-2822	185	12	2017	2017	NUM
ejpam-2822	185	13	)	)	PUNCT
ejpam-2822	185	14	,	,	PUNCT
ejpam-2822	185	15	255	255	NUM
ejpam-2822	185	16	-	-	SYM
ejpam-2822	185	17	271	271	NUM
ejpam-2822	185	18	264	264	NUM
ejpam-2822	185	19	now	now	ADV
ejpam-2822	185	20	consider	consider	VERB
ejpam-2822	185	21	(	(	PUNCT
ejpam-2822	185	22	σ	σ	PROPN
ejpam-2822	185	23	◦	◦	PROPN
ejpam-2822	185	24	η	η	PROPN
ejpam-2822	185	25	,	,	PUNCT
ejpam-2822	185	26	θ	θ	NOUN
ejpam-2822	185	27	)	)	PUNCT
ejpam-2822	185	28	(	(	PUNCT
ejpam-2822	185	29	x	x	X
ejpam-2822	185	30	)	)	PUNCT
ejpam-2822	185	31	=	=	SYM
ejpam-2822	186	1	∨	∨	X
ejpam-2822	186	2	(	(	PUNCT
ejpam-2822	186	3	y	y	NOUN
ejpam-2822	186	4	,	,	PUNCT
ejpam-2822	186	5	z)∈c(x	z)∈c(x	NUM
ejpam-2822	186	6	)	)	PUNCT
ejpam-2822	186	7	{	{	PUNCT
ejpam-2822	186	8	σ	σ	PROPN
ejpam-2822	186	9	◦	◦	PROPN
ejpam-2822	186	10	η(y	η(y	NOUN
ejpam-2822	186	11	)	)	PUNCT
ejpam-2822	186	12	∧	∧	PROPN
ejpam-2822	186	13	θ(z	θ(z	NOUN
ejpam-2822	186	14	)	)	PUNCT
ejpam-2822	186	15	}	}	PUNCT
ejpam-2822	186	16	=	=	SYM
ejpam-2822	186	17	∨	∨	X
ejpam-2822	186	18	(	(	PUNCT
ejpam-2822	186	19	y	y	NOUN
ejpam-2822	186	20	,	,	PUNCT
ejpam-2822	186	21	z)∈c(x	z)∈c(x	NUM
ejpam-2822	186	22	)	)	PUNCT
ejpam-2822	186	23	{	{	PUNCT
ejpam-2822	186	24	∨	∨	X
ejpam-2822	186	25	(	(	PUNCT
ejpam-2822	186	26	u	u	NOUN
ejpam-2822	186	27	,	,	PUNCT
ejpam-2822	186	28	v)∈p	v)∈p	X
ejpam-2822	186	29	(	(	PUNCT
ejpam-2822	186	30	y	y	NOUN
ejpam-2822	186	31	)	)	PUNCT
ejpam-2822	186	32	{	{	PUNCT
ejpam-2822	186	33	σ(u	σ(u	NOUN
ejpam-2822	186	34	)	)	PUNCT
ejpam-2822	186	35	∧	∧	PROPN
ejpam-2822	186	36	η(v	η(v	NOUN
ejpam-2822	186	37	)	)	PUNCT
ejpam-2822	186	38	}	}	PUNCT
ejpam-2822	186	39	∧	∧	PROPN
ejpam-2822	186	40	θ(z	θ(z	NOUN
ejpam-2822	186	41	)	)	PUNCT
ejpam-2822	186	42	}	}	PUNCT
ejpam-2822	186	43	=	=	SYM
ejpam-2822	186	44	∨	∨	X
ejpam-2822	186	45	(	(	PUNCT
ejpam-2822	186	46	y	y	NOUN
ejpam-2822	186	47	,	,	PUNCT
ejpam-2822	186	48	z)∈c(x	z)∈c(x	NUM
ejpam-2822	186	49	)	)	PUNCT
ejpam-2822	186	50	{	{	PUNCT
ejpam-2822	186	51	∨	∨	X
ejpam-2822	186	52	(	(	PUNCT
ejpam-2822	186	53	u	u	NOUN
ejpam-2822	186	54	,	,	PUNCT
ejpam-2822	186	55	v)∈p	v)∈p	X
ejpam-2822	186	56	(	(	PUNCT
ejpam-2822	186	57	y	y	NOUN
ejpam-2822	186	58	)	)	PUNCT
ejpam-2822	186	59	{	{	PUNCT
ejpam-2822	186	60	σ(u	σ(u	NOUN
ejpam-2822	186	61	)	)	PUNCT
ejpam-2822	186	62	∧	∧	PROPN
ejpam-2822	186	63	η(v	η(v	NOUN
ejpam-2822	186	64	)	)	PUNCT
ejpam-2822	186	65	∧	∧	PROPN
ejpam-2822	186	66	θ(z	θ(z	NOUN
ejpam-2822	186	67	)	)	PUNCT
ejpam-2822	186	68	}	}	PUNCT
ejpam-2822	186	69	}	}	PUNCT
ejpam-2822	186	70	=	=	SYM
ejpam-2822	186	71	∨	∨	X
ejpam-2822	186	72	(	(	PUNCT
ejpam-2822	186	73	y	y	NOUN
ejpam-2822	186	74	,	,	PUNCT
ejpam-2822	186	75	z)∈c(x	z)∈c(x	NUM
ejpam-2822	186	76	)	)	PUNCT
ejpam-2822	186	77	(	(	PUNCT
ejpam-2822	186	78	u	u	NOUN
ejpam-2822	186	79	,	,	PUNCT
ejpam-2822	186	80	v)∈p	v)∈p	X
ejpam-2822	186	81	(	(	PUNCT
ejpam-2822	186	82	y	y	NOUN
ejpam-2822	186	83	)	)	PUNCT
ejpam-2822	186	84	{	{	PUNCT
ejpam-2822	186	85	{	{	PUNCT
ejpam-2822	186	86	σ(u	σ(u	NOUN
ejpam-2822	186	87	)	)	PUNCT
ejpam-2822	186	88	∧	∧	PROPN
ejpam-2822	186	89	θ(z	θ(z	NOUN
ejpam-2822	186	90	)	)	PUNCT
ejpam-2822	186	91	}	}	PUNCT
ejpam-2822	186	92	∧	∧	PROPN
ejpam-2822	186	93	{	{	PUNCT
ejpam-2822	186	94	η(v	η(v	NOUN
ejpam-2822	186	95	)	)	PUNCT
ejpam-2822	186	96	∧	∧	PROPN
ejpam-2822	186	97	θ(z	θ(z	NOUN
ejpam-2822	186	98	)	)	PUNCT
ejpam-2822	186	99	}	}	PUNCT
ejpam-2822	186	100	}	}	PUNCT
ejpam-2822	186	101	.	.	PUNCT
ejpam-2822	187	1	as	as	ADP
ejpam-2822	187	2	σ	σ	PROPN
ejpam-2822	187	3	⊆	⊆	NUM
ejpam-2822	187	4	µ	µ	NUM
ejpam-2822	187	5	,	,	PUNCT
ejpam-2822	187	6	we	we	PRON
ejpam-2822	187	7	have	have	VERB
ejpam-2822	187	8	σ(u	σ(u	NOUN
ejpam-2822	187	9	)	)	PUNCT
ejpam-2822	187	10	∧	∧	NOUN
ejpam-2822	187	11	µ(v	µ(v	NOUN
ejpam-2822	187	12	)	)	PUNCT
ejpam-2822	187	13	=	=	SYM
ejpam-2822	187	14	σ(u	σ(u	NOUN
ejpam-2822	187	15	)	)	PUNCT
ejpam-2822	187	16	.	.	PUNCT
ejpam-2822	188	1	this	this	PRON
ejpam-2822	188	2	implies	imply	VERB
ejpam-2822	188	3	that	that	SCONJ
ejpam-2822	188	4	(	(	PUNCT
ejpam-2822	188	5	σ	σ	PROPN
ejpam-2822	188	6	◦	◦	PROPN
ejpam-2822	188	7	η	η	PROPN
ejpam-2822	188	8	,	,	PUNCT
ejpam-2822	188	9	θ	θ	NOUN
ejpam-2822	188	10	)	)	PUNCT
ejpam-2822	188	11	(	(	PUNCT
ejpam-2822	188	12	x	x	X
ejpam-2822	188	13	)	)	PUNCT
ejpam-2822	188	14	≤	≤	NOUN
ejpam-2822	188	15	∨	∨	NUM
ejpam-2822	188	16	(	(	PUNCT
ejpam-2822	188	17	[	[	X
ejpam-2822	188	18	v	v	NOUN
ejpam-2822	188	19	,	,	PUNCT
ejpam-2822	188	20	z]u,[u	z]u,[u	NOUN
ejpam-2822	188	21	,	,	PUNCT
ejpam-2822	188	22	z)∈p	z)∈p	NUM
ejpam-2822	188	23	(	(	PUNCT
ejpam-2822	188	24	x	x	X
ejpam-2822	188	25	)	)	PUNCT
ejpam-2822	188	26	(	(	PUNCT
ejpam-2822	188	27	uv	uv	INTJ
ejpam-2822	188	28	,	,	PUNCT
ejpam-2822	188	29	z)∈c(x	z)∈c(x	NOUN
ejpam-2822	188	30	)	)	PUNCT
ejpam-2822	188	31	{	{	PUNCT
ejpam-2822	188	32	{	{	PUNCT
ejpam-2822	188	33	σ(u	σ(u	NOUN
ejpam-2822	188	34	)	)	PUNCT
ejpam-2822	188	35	∧	∧	PROPN
ejpam-2822	188	36	µ(u	µ(u	NOUN
ejpam-2822	188	37	)	)	PUNCT
ejpam-2822	188	38	∧	∧	PROPN
ejpam-2822	188	39	θ(z	θ(z	NOUN
ejpam-2822	188	40	)	)	PUNCT
ejpam-2822	188	41	}	}	PUNCT
ejpam-2822	188	42	∧	∧	PROPN
ejpam-2822	188	43	{	{	PUNCT
ejpam-2822	188	44	η(v	η(v	NOUN
ejpam-2822	188	45	)	)	PUNCT
ejpam-2822	188	46	∧	∧	PROPN
ejpam-2822	188	47	θ(z	θ(z	NOUN
ejpam-2822	188	48	)	)	PUNCT
ejpam-2822	188	49	}	}	PUNCT
ejpam-2822	188	50	}	}	PUNCT
ejpam-2822	188	51	=	=	SYM
ejpam-2822	188	52	∨	∨	NOUN
ejpam-2822	188	53	(	(	PUNCT
ejpam-2822	188	54	[	[	X
ejpam-2822	188	55	v	v	NOUN
ejpam-2822	188	56	,	,	PUNCT
ejpam-2822	188	57	z]u,[u	z]u,[u	NOUN
ejpam-2822	188	58	,	,	PUNCT
ejpam-2822	188	59	z])∈p	z])∈p	PROPN
ejpam-2822	188	60	(	(	PUNCT
ejpam-2822	188	61	x	x	X
ejpam-2822	188	62	)	)	PUNCT
ejpam-2822	188	63	(	(	PUNCT
ejpam-2822	188	64	uv	uv	INTJ
ejpam-2822	188	65	,	,	PUNCT
ejpam-2822	188	66	z)∈c(x	z)∈c(x	NOUN
ejpam-2822	188	67	)	)	PUNCT
ejpam-2822	188	68	{	{	PUNCT
ejpam-2822	188	69	{	{	PUNCT
ejpam-2822	188	70	σ(u	σ(u	NOUN
ejpam-2822	188	71	)	)	PUNCT
ejpam-2822	188	72	∧	∧	PROPN
ejpam-2822	188	73	θ(z	θ(z	NOUN
ejpam-2822	188	74	)	)	PUNCT
ejpam-2822	188	75	}	}	PUNCT
ejpam-2822	188	76	∧	∧	PROPN
ejpam-2822	188	77	{	{	PUNCT
ejpam-2822	188	78	η(v	η(v	NOUN
ejpam-2822	188	79	)	)	PUNCT
ejpam-2822	188	80	∧	∧	PROPN
ejpam-2822	188	81	θ(z	θ(z	NOUN
ejpam-2822	188	82	)	)	PUNCT
ejpam-2822	188	83	∧	∧	PROPN
ejpam-2822	188	84	µ(u	µ(u	NOUN
ejpam-2822	188	85	)	)	PUNCT
ejpam-2822	188	86	}	}	PUNCT
ejpam-2822	188	87	}	}	PUNCT
ejpam-2822	188	88	.	.	PUNCT
ejpam-2822	189	1	now	now	ADV
ejpam-2822	189	2	,	,	PUNCT
ejpam-2822	189	3	we	we	PRON
ejpam-2822	189	4	have	have	VERB
ejpam-2822	189	5	[	[	X
ejpam-2822	189	6	σ	σ	PROPN
ejpam-2822	189	7	,	,	PUNCT
ejpam-2822	189	8	θ	θ	PROPN
ejpam-2822	189	9	]	]	X
ejpam-2822	189	10	(	(	PUNCT
ejpam-2822	189	11	[	[	X
ejpam-2822	189	12	u	u	NOUN
ejpam-2822	189	13	,	,	PUNCT
ejpam-2822	189	14	z	z	NOUN
ejpam-2822	189	15	]	]	X
ejpam-2822	189	16	)	)	PUNCT
ejpam-2822	189	17	≥	≥	NOUN
ejpam-2822	189	18	σ(u	σ(u	NOUN
ejpam-2822	189	19	)	)	PUNCT
ejpam-2822	189	20	∧	∧	PROPN
ejpam-2822	189	21	θ(z	θ(z	NOUN
ejpam-2822	189	22	)	)	PUNCT
ejpam-2822	189	23	,	,	PUNCT
ejpam-2822	189	24	and	and	CCONJ
ejpam-2822	189	25	since	since	SCONJ
ejpam-2822	189	26	η	η	PROPN
ejpam-2822	189	27	,	,	PUNCT
ejpam-2822	189	28	θ	θ	PROPN
ejpam-2822	189	29	∈	∈	PROPN
ejpam-2822	189	30	nl(µ	nl(µ	NOUN
ejpam-2822	189	31	)	)	PUNCT
ejpam-2822	189	32	,	,	PUNCT
ejpam-2822	189	33	by	by	ADP
ejpam-2822	189	34	proposition	proposition	NOUN
ejpam-2822	189	35	5	5	NUM
ejpam-2822	189	36	,	,	PUNCT
ejpam-2822	189	37	[	[	X
ejpam-2822	189	38	η	η	X
ejpam-2822	189	39	,	,	PUNCT
ejpam-2822	189	40	θ	θ	X
ejpam-2822	189	41	]	]	X
ejpam-2822	189	42	∈	∈	PROPN
ejpam-2822	189	43	nl(µ	nl(µ	NOUN
ejpam-2822	189	44	)	)	PUNCT
ejpam-2822	189	45	.	.	PUNCT
ejpam-2822	190	1	therefore	therefore	ADV
ejpam-2822	190	2	,	,	PUNCT
ejpam-2822	190	3	[	[	X
ejpam-2822	190	4	η	η	X
ejpam-2822	190	5	,	,	PUNCT
ejpam-2822	190	6	θ	θ	PROPN
ejpam-2822	190	7	]	]	X
ejpam-2822	190	8	(	(	PUNCT
ejpam-2822	190	9	[	[	X
ejpam-2822	190	10	v	v	NOUN
ejpam-2822	190	11	,	,	PUNCT
ejpam-2822	190	12	z]u	z]u	NOUN
ejpam-2822	190	13	)	)	PUNCT
ejpam-2822	190	14	≥	≥	NOUN
ejpam-2822	191	1	[	[	X
ejpam-2822	191	2	η	η	X
ejpam-2822	191	3	,	,	PUNCT
ejpam-2822	191	4	θ	θ	PROPN
ejpam-2822	191	5	]	]	X
ejpam-2822	191	6	(	(	PUNCT
ejpam-2822	191	7	[	[	X
ejpam-2822	191	8	v	v	NOUN
ejpam-2822	191	9	,	,	PUNCT
ejpam-2822	191	10	z	z	NOUN
ejpam-2822	191	11	]	]	X
ejpam-2822	191	12	)	)	PUNCT
ejpam-2822	191	13	∧	∧	PROPN
ejpam-2822	191	14	µ(u	µ(u	NOUN
ejpam-2822	191	15	)	)	PUNCT
ejpam-2822	191	16	≥	≥	NOUN
ejpam-2822	191	17	η(v	η(v	NOUN
ejpam-2822	191	18	)	)	PUNCT
ejpam-2822	191	19	∧	∧	PROPN
ejpam-2822	191	20	θ(z	θ(z	NOUN
ejpam-2822	191	21	)	)	PUNCT
ejpam-2822	191	22	∧	∧	PROPN
ejpam-2822	191	23	µ(u	µ(u	NOUN
ejpam-2822	191	24	)	)	PUNCT
ejpam-2822	191	25	.	.	PUNCT
ejpam-2822	192	1	consequently	consequently	ADV
ejpam-2822	192	2	,	,	PUNCT
ejpam-2822	192	3	we	we	PRON
ejpam-2822	192	4	have	have	VERB
ejpam-2822	192	5	(	(	PUNCT
ejpam-2822	192	6	σ	σ	PROPN
ejpam-2822	192	7	◦	◦	PROPN
ejpam-2822	192	8	η	η	PROPN
ejpam-2822	192	9	,	,	PUNCT
ejpam-2822	192	10	θ	θ	NOUN
ejpam-2822	192	11	)	)	PUNCT
ejpam-2822	192	12	(	(	PUNCT
ejpam-2822	192	13	x	x	X
ejpam-2822	192	14	)	)	PUNCT
ejpam-2822	192	15	≤	≤	NOUN
ejpam-2822	192	16	∨	∨	NUM
ejpam-2822	192	17	(	(	PUNCT
ejpam-2822	192	18	[	[	X
ejpam-2822	192	19	v	v	NOUN
ejpam-2822	192	20	,	,	PUNCT
ejpam-2822	192	21	z]u,[u	z]u,[u	NOUN
ejpam-2822	192	22	,	,	PUNCT
ejpam-2822	192	23	z])∈p	z])∈p	PROPN
ejpam-2822	192	24	(	(	PUNCT
ejpam-2822	192	25	x	x	X
ejpam-2822	192	26	)	)	PUNCT
ejpam-2822	192	27	(	(	PUNCT
ejpam-2822	192	28	uv	uv	INTJ
ejpam-2822	192	29	,	,	PUNCT
ejpam-2822	192	30	z)∈c(x	z)∈c(x	NOUN
ejpam-2822	192	31	)	)	PUNCT
ejpam-2822	192	32	{	{	PUNCT
ejpam-2822	193	1	[	[	X
ejpam-2822	193	2	σ	σ	PROPN
ejpam-2822	193	3	,	,	PUNCT
ejpam-2822	193	4	θ	θ	PROPN
ejpam-2822	193	5	]	]	X
ejpam-2822	193	6	(	(	PUNCT
ejpam-2822	193	7	[	[	X
ejpam-2822	193	8	u	u	NOUN
ejpam-2822	193	9	,	,	PUNCT
ejpam-2822	193	10	z	z	NOUN
ejpam-2822	193	11	]	]	X
ejpam-2822	193	12	)	)	PUNCT
ejpam-2822	193	13	∧	∧	PROPN
ejpam-2822	193	14	[	[	X
ejpam-2822	193	15	η	η	PROPN
ejpam-2822	193	16	,	,	PUNCT
ejpam-2822	193	17	θ	θ	X
ejpam-2822	193	18	]	]	X
ejpam-2822	193	19	(	(	PUNCT
ejpam-2822	193	20	[	[	X
ejpam-2822	193	21	v	v	NOUN
ejpam-2822	193	22	,	,	PUNCT
ejpam-2822	193	23	z]u	z]u	NOUN
ejpam-2822	193	24	)	)	PUNCT
ejpam-2822	193	25	}	}	PUNCT
ejpam-2822	193	26	≤	≤	NOUN
ejpam-2822	194	1	[	[	X
ejpam-2822	194	2	η	η	X
ejpam-2822	194	3	,	,	PUNCT
ejpam-2822	194	4	θ	θ	NOUN
ejpam-2822	194	5	]	]	X
ejpam-2822	194	6	◦	◦	NOUN
ejpam-2822	194	7	[	[	X
ejpam-2822	194	8	σ	σ	NOUN
ejpam-2822	194	9	,	,	PUNCT
ejpam-2822	194	10	θ](x	θ](x	ADJ
ejpam-2822	194	11	)	)	PUNCT
ejpam-2822	194	12	.	.	PUNCT
ejpam-2822	195	1	(	(	PUNCT
ejpam-2822	195	2	2	2	X
ejpam-2822	195	3	)	)	PUNCT
ejpam-2822	195	4	thus	thus	ADV
ejpam-2822	195	5	,	,	PUNCT
ejpam-2822	195	6	by	by	ADP
ejpam-2822	195	7	(	(	PUNCT
ejpam-2822	195	8	1	1	NUM
ejpam-2822	195	9	)	)	PUNCT
ejpam-2822	195	10	and	and	CCONJ
ejpam-2822	195	11	(	(	PUNCT
ejpam-2822	195	12	2	2	X
ejpam-2822	195	13	)	)	PUNCT
ejpam-2822	195	14	(	(	PUNCT
ejpam-2822	195	15	σ	σ	PROPN
ejpam-2822	195	16	◦	◦	PROPN
ejpam-2822	195	17	η	η	PROPN
ejpam-2822	195	18	,	,	PUNCT
ejpam-2822	195	19	θ	θ	NOUN
ejpam-2822	195	20	)	)	PUNCT
ejpam-2822	195	21	≤	≤	NOUN
ejpam-2822	196	1	[	[	X
ejpam-2822	196	2	η	η	X
ejpam-2822	196	3	,	,	PUNCT
ejpam-2822	196	4	θ	θ	NOUN
ejpam-2822	196	5	]	]	X
ejpam-2822	196	6	◦	◦	NOUN
ejpam-2822	196	7	[	[	X
ejpam-2822	196	8	θ	θ	X
ejpam-2822	196	9	,	,	PUNCT
ejpam-2822	196	10	σ	σ	PROPN
ejpam-2822	196	11	]	]	PUNCT
ejpam-2822	196	12	.	.	PUNCT
ejpam-2822	197	1	also	also	ADV
ejpam-2822	197	2	,	,	PUNCT
ejpam-2822	197	3	as	as	ADP
ejpam-2822	197	4	[	[	X
ejpam-2822	197	5	η	η	X
ejpam-2822	197	6	,	,	PUNCT
ejpam-2822	197	7	θ	θ	X
ejpam-2822	197	8	]	]	X
ejpam-2822	197	9	∈	∈	NOUN
ejpam-2822	197	10	nl(µ	nl(µ	NOUN
ejpam-2822	197	11	)	)	PUNCT
ejpam-2822	197	12	and	and	CCONJ
ejpam-2822	197	13	[	[	X
ejpam-2822	197	14	σ	σ	PROPN
ejpam-2822	197	15	,	,	PUNCT
ejpam-2822	197	16	θ	θ	X
ejpam-2822	197	17	]	]	X
ejpam-2822	197	18	∈	∈	PROPN
ejpam-2822	197	19	l(µ	l(µ	PROPN
ejpam-2822	197	20	)	)	PUNCT
ejpam-2822	197	21	,	,	PUNCT
ejpam-2822	197	22	by	by	ADP
ejpam-2822	197	23	proposition	proposition	NOUN
ejpam-2822	197	24	2.6	2.6	NUM
ejpam-2822	197	25	[	[	X
ejpam-2822	197	26	η	η	PROPN
ejpam-2822	197	27	,	,	PUNCT
ejpam-2822	197	28	θ	θ	NOUN
ejpam-2822	197	29	]	]	X
ejpam-2822	197	30	◦	◦	NOUN
ejpam-2822	197	31	[	[	X
ejpam-2822	197	32	σ	σ	X
ejpam-2822	197	33	,	,	PUNCT
ejpam-2822	197	34	θ	θ	PROPN
ejpam-2822	197	35	]	]	X
ejpam-2822	197	36	is	be	AUX
ejpam-2822	197	37	an	an	DET
ejpam-2822	197	38	l−subgroup	l−subgroup	NOUN
ejpam-2822	197	39	of	of	ADP
ejpam-2822	197	40	µ.	µ.	NOUN
ejpam-2822	197	41	again	again	ADV
ejpam-2822	197	42	,	,	PUNCT
ejpam-2822	197	43	by	by	ADP
ejpam-2822	197	44	proposition	proposition	NOUN
ejpam-2822	197	45	2.6	2.6	NUM
ejpam-2822	197	46	,	,	PUNCT
ejpam-2822	197	47	η	η	PROPN
ejpam-2822	197	48	◦	◦	NOUN
ejpam-2822	197	49	σ	σ	X
ejpam-2822	197	50	∈	∈	PROPN
ejpam-2822	197	51	l(µ	l(µ	PROPN
ejpam-2822	197	52	)	)	PUNCT
ejpam-2822	197	53	so	so	SCONJ
ejpam-2822	197	54	that	that	SCONJ
ejpam-2822	197	55	η	η	PROPN
ejpam-2822	197	56	◦	◦	PROPN
ejpam-2822	197	57	σ	σ	X
ejpam-2822	197	58	=	=	PUNCT
ejpam-2822	197	59	σ	σ	PROPN
ejpam-2822	197	60	◦	◦	PROPN
ejpam-2822	197	61	η	η	PROPN
ejpam-2822	197	62	.	.	PROPN
ejpam-2822	198	1	hence	hence	ADV
ejpam-2822	198	2	[	[	X
ejpam-2822	198	3	η	η	PROPN
ejpam-2822	198	4	◦	◦	PROPN
ejpam-2822	198	5	σ	σ	PROPN
ejpam-2822	198	6	,	,	PUNCT
ejpam-2822	198	7	θ	θ	X
ejpam-2822	198	8	]	]	PUNCT
ejpam-2822	198	9	=	=	PUNCT
ejpam-2822	199	1	[	[	X
ejpam-2822	199	2	σ	σ	PROPN
ejpam-2822	199	3	◦	◦	PROPN
ejpam-2822	199	4	η	η	PROPN
ejpam-2822	199	5	,	,	PUNCT
ejpam-2822	199	6	θ	θ	NOUN
ejpam-2822	199	7	]	]	PUNCT
ejpam-2822	199	8	≤	≤	X
ejpam-2822	200	1	[	[	X
ejpam-2822	200	2	η	η	X
ejpam-2822	200	3	,	,	PUNCT
ejpam-2822	200	4	θ	θ	NOUN
ejpam-2822	200	5	]	]	X
ejpam-2822	200	6	◦	◦	NOUN
ejpam-2822	200	7	[	[	X
ejpam-2822	200	8	θ	θ	X
ejpam-2822	200	9	,	,	PUNCT
ejpam-2822	200	10	σ	σ	PROPN
ejpam-2822	200	11	]	]	PUNCT
ejpam-2822	200	12	.	.	PUNCT
ejpam-2822	201	1	lastly	lastly	ADV
ejpam-2822	201	2	,	,	PUNCT
ejpam-2822	201	3	let	let	VERB
ejpam-2822	201	4	η(e	η(e	NOUN
ejpam-2822	201	5	)	)	PUNCT
ejpam-2822	201	6	=	=	SYM
ejpam-2822	201	7	σ(e	σ(e	PROPN
ejpam-2822	201	8	)	)	PUNCT
ejpam-2822	201	9	.	.	PUNCT
ejpam-2822	202	1	we	we	PRON
ejpam-2822	202	2	show	show	VERB
ejpam-2822	202	3	that	that	SCONJ
ejpam-2822	202	4	[	[	X
ejpam-2822	202	5	η	η	X
ejpam-2822	202	6	,	,	PUNCT
ejpam-2822	202	7	θ	θ	NOUN
ejpam-2822	202	8	]	]	X
ejpam-2822	202	9	◦	◦	NOUN
ejpam-2822	202	10	[	[	X
ejpam-2822	202	11	θ	θ	X
ejpam-2822	202	12	,	,	PUNCT
ejpam-2822	202	13	σ	σ	PROPN
ejpam-2822	202	14	]	]	PUNCT
ejpam-2822	202	15	⊆	⊆	NUM
ejpam-2822	202	16	[	[	X
ejpam-2822	202	17	σ	σ	PROPN
ejpam-2822	202	18	◦	◦	PROPN
ejpam-2822	202	19	η	η	PROPN
ejpam-2822	202	20	,	,	PUNCT
ejpam-2822	202	21	θ	θ	NOUN
ejpam-2822	202	22	]	]	PUNCT
ejpam-2822	202	23	.	.	PUNCT
ejpam-2822	203	1	by	by	ADP
ejpam-2822	203	2	proposition	proposition	NOUN
ejpam-2822	203	3	2	2	NUM
ejpam-2822	203	4	,	,	PUNCT
ejpam-2822	203	5	η	η	PROPN
ejpam-2822	203	6	⊆	⊆	NUM
ejpam-2822	203	7	η	η	PROPN
ejpam-2822	203	8	◦	◦	NOUN
ejpam-2822	203	9	θ	θ	PROPN
ejpam-2822	203	10	and	and	CCONJ
ejpam-2822	203	11	σ	σ	PROPN
ejpam-2822	203	12	⊆	⊆	NUM
ejpam-2822	203	13	η	η	PROPN
ejpam-2822	203	14	◦	◦	PROPN
ejpam-2822	203	15	θ	θ	PROPN
ejpam-2822	203	16	.	.	PUNCT
ejpam-2822	203	17	by	by	ADP
ejpam-2822	203	18	lemma	lemma	PROPN
ejpam-2822	203	19	5	5	NUM
ejpam-2822	203	20	i.	i.	PROPN
ejpam-2822	203	21	jahan	jahan	PROPN
ejpam-2822	203	22	,	,	PUNCT
ejpam-2822	203	23	n.	n.	PROPN
ejpam-2822	203	24	ajmal	ajmal	PROPN
ejpam-2822	203	25	,	,	PUNCT
ejpam-2822	203	26	b.	b.	PROPN
ejpam-2822	203	27	davvaz	davvaz	PROPN
ejpam-2822	203	28	/	/	SYM
ejpam-2822	203	29	eur	eur	PROPN
ejpam-2822	203	30	.	.	PUNCT
ejpam-2822	204	1	j.	j.	PROPN
ejpam-2822	204	2	pure	pure	PROPN
ejpam-2822	204	3	appl	appl	PROPN
ejpam-2822	204	4	.	.	PROPN
ejpam-2822	204	5	math	math	PROPN
ejpam-2822	204	6	,	,	PUNCT
ejpam-2822	204	7	10	10	NUM
ejpam-2822	204	8	(	(	PUNCT
ejpam-2822	204	9	2	2	NUM
ejpam-2822	204	10	)	)	PUNCT
ejpam-2822	204	11	(	(	PUNCT
ejpam-2822	204	12	2017	2017	NUM
ejpam-2822	204	13	)	)	PUNCT
ejpam-2822	204	14	,	,	PUNCT
ejpam-2822	204	15	255	255	NUM
ejpam-2822	204	16	-	-	SYM
ejpam-2822	204	17	271	271	NUM
ejpam-2822	205	1	265	265	NUM
ejpam-2822	205	2	[	[	X
ejpam-2822	205	3	η	η	X
ejpam-2822	205	4	,	,	PUNCT
ejpam-2822	205	5	θ	θ	X
ejpam-2822	205	6	]	]	PUNCT
ejpam-2822	205	7	⊆	⊆	NUM
ejpam-2822	205	8	[	[	X
ejpam-2822	205	9	η	η	PROPN
ejpam-2822	205	10	◦	◦	PROPN
ejpam-2822	205	11	σ	σ	PROPN
ejpam-2822	205	12	,	,	PUNCT
ejpam-2822	205	13	θ	θ	X
ejpam-2822	205	14	]	]	PUNCT
ejpam-2822	205	15	and	and	CCONJ
ejpam-2822	205	16	[	[	X
ejpam-2822	205	17	σ	σ	PROPN
ejpam-2822	205	18	,	,	PUNCT
ejpam-2822	205	19	θ	θ	X
ejpam-2822	205	20	]	]	PUNCT
ejpam-2822	205	21	⊆	⊆	NUM
ejpam-2822	205	22	[	[	X
ejpam-2822	205	23	η	η	PROPN
ejpam-2822	205	24	◦	◦	PROPN
ejpam-2822	205	25	σ	σ	PROPN
ejpam-2822	205	26	,	,	PUNCT
ejpam-2822	205	27	θ	θ	PROPN
ejpam-2822	205	28	]	]	PUNCT
ejpam-2822	205	29	.	.	PUNCT
ejpam-2822	206	1	therefore	therefore	ADV
ejpam-2822	206	2	,	,	PUNCT
ejpam-2822	206	3	[	[	X
ejpam-2822	206	4	η	η	X
ejpam-2822	206	5	,	,	PUNCT
ejpam-2822	206	6	θ	θ	NOUN
ejpam-2822	206	7	]	]	X
ejpam-2822	206	8	◦	◦	NOUN
ejpam-2822	206	9	[	[	X
ejpam-2822	206	10	θ	θ	X
ejpam-2822	206	11	,	,	PUNCT
ejpam-2822	206	12	σ	σ	PROPN
ejpam-2822	206	13	]	]	PUNCT
ejpam-2822	206	14	⊆	⊆	NUM
ejpam-2822	206	15	[	[	X
ejpam-2822	206	16	η	η	PROPN
ejpam-2822	206	17	◦	◦	PROPN
ejpam-2822	206	18	σ	σ	PROPN
ejpam-2822	206	19	,	,	PUNCT
ejpam-2822	206	20	θ	θ	PROPN
ejpam-2822	206	21	]	]	PUNCT
ejpam-2822	206	22	.	.	PUNCT
ejpam-2822	207	1	the	the	DET
ejpam-2822	207	2	proof	proof	NOUN
ejpam-2822	207	3	of	of	ADP
ejpam-2822	207	4	the	the	DET
ejpam-2822	207	5	following	following	ADJ
ejpam-2822	207	6	result	result	NOUN
ejpam-2822	207	7	can	can	AUX
ejpam-2822	207	8	be	be	AUX
ejpam-2822	207	9	obtained	obtain	VERB
ejpam-2822	207	10	as	as	ADP
ejpam-2822	207	11	in	in	ADP
ejpam-2822	207	12	classical	classical	ADJ
ejpam-2822	207	13	group	group	NOUN
ejpam-2822	207	14	theory	theory	NOUN
ejpam-2822	207	15	which	which	PRON
ejpam-2822	207	16	exhibits	exhibit	VERB
ejpam-2822	207	17	a	a	DET
ejpam-2822	207	18	routine	routine	ADJ
ejpam-2822	207	19	application	application	NOUN
ejpam-2822	207	20	of	of	ADP
ejpam-2822	207	21	the	the	DET
ejpam-2822	207	22	principle	principle	NOUN
ejpam-2822	207	23	of	of	ADP
ejpam-2822	207	24	mathematical	mathematical	ADJ
ejpam-2822	207	25	induction	induction	NOUN
ejpam-2822	207	26	.	.	PUNCT
ejpam-2822	208	1	lemma	lemma	PROPN
ejpam-2822	208	2	1	1	X
ejpam-2822	208	3	.	.	PUNCT
ejpam-2822	209	1	let	let	VERB
ejpam-2822	209	2	η	η	PROPN
ejpam-2822	209	3	,	,	PUNCT
ejpam-2822	209	4	η1	η1	NOUN
ejpam-2822	209	5	,	,	PUNCT
ejpam-2822	209	6	...	...	PUNCT
ejpam-2822	209	7	,	,	PUNCT
ejpam-2822	209	8	ηn+1	ηn+1	PROPN
ejpam-2822	209	9	∈	∈	PROPN
ejpam-2822	209	10	nl(µ	nl(µ	NOUN
ejpam-2822	209	11	)	)	PUNCT
ejpam-2822	209	12	having	have	VERB
ejpam-2822	209	13	identical	identical	ADJ
ejpam-2822	209	14	tails	tail	NOUN
ejpam-2822	209	15	.	.	PUNCT
ejpam-2822	210	1	if	if	SCONJ
ejpam-2822	210	2	ηi	ηi	PROPN
ejpam-2822	210	3	=	=	SYM
ejpam-2822	210	4	η	η	PROPN
ejpam-2822	210	5	for	for	ADP
ejpam-2822	210	6	k+1	k+1	X
ejpam-2822	210	7	distinct	distinct	ADJ
ejpam-2822	210	8	values	value	NOUN
ejpam-2822	210	9	of	of	ADP
ejpam-2822	210	10	i	i	PRON
ejpam-2822	210	11	where	where	SCONJ
ejpam-2822	210	12	0	0	NUM
ejpam-2822	210	13	≤	≤	NUM
ejpam-2822	210	14	k	k	X
ejpam-2822	210	15	≤	≤	PROPN
ejpam-2822	210	16	n	n	CCONJ
ejpam-2822	210	17	,	,	PUNCT
ejpam-2822	210	18	then	then	ADV
ejpam-2822	210	19	[	[	X
ejpam-2822	210	20	η1	η1	NOUN
ejpam-2822	210	21	,	,	PUNCT
ejpam-2822	210	22	η2	η2	NOUN
ejpam-2822	210	23	,	,	PUNCT
ejpam-2822	210	24	...	...	PUNCT
ejpam-2822	210	25	,	,	PUNCT
ejpam-2822	210	26	ηn+1	ηn+1	X
ejpam-2822	210	27	]	]	PUNCT
ejpam-2822	210	28	⊆	⊆	NUM
ejpam-2822	210	29	zk(η	zk(η	NUM
ejpam-2822	210	30	)	)	PUNCT
ejpam-2822	210	31	.	.	PUNCT
ejpam-2822	211	1	next	next	ADJ
ejpam-2822	211	2	result	result	NOUN
ejpam-2822	211	3	provides	provide	VERB
ejpam-2822	211	4	a	a	DET
ejpam-2822	211	5	necessary	necessary	ADJ
ejpam-2822	211	6	and	and	CCONJ
ejpam-2822	211	7	sufficient	sufficient	ADJ
ejpam-2822	211	8	condition	condition	NOUN
ejpam-2822	211	9	for	for	ADP
ejpam-2822	211	10	the	the	DET
ejpam-2822	211	11	set	set	NOUN
ejpam-2822	211	12	product	product	NOUN
ejpam-2822	211	13	of	of	ADP
ejpam-2822	211	14	two	two	NUM
ejpam-2822	211	15	trivial	trivial	ADJ
ejpam-2822	211	16	l	l	NOUN
ejpam-2822	211	17	-	-	NOUN
ejpam-2822	211	18	subgroups	subgroup	NOUN
ejpam-2822	211	19	of	of	ADP
ejpam-2822	211	20	µ	µ	PRON
ejpam-2822	211	21	to	to	PART
ejpam-2822	211	22	be	be	AUX
ejpam-2822	211	23	a	a	DET
ejpam-2822	211	24	trivial	trivial	ADJ
ejpam-2822	211	25	l	l	NOUN
ejpam-2822	211	26	-	-	NOUN
ejpam-2822	211	27	subgroup	subgroup	NOUN
ejpam-2822	211	28	.	.	PUNCT
ejpam-2822	212	1	lemma	lemma	PROPN
ejpam-2822	212	2	2	2	X
ejpam-2822	212	3	.	.	PUNCT
ejpam-2822	213	1	let	let	VERB
ejpam-2822	213	2	η	η	PROPN
ejpam-2822	213	3	and	and	CCONJ
ejpam-2822	213	4	θ	θ	PROPN
ejpam-2822	213	5	be	be	AUX
ejpam-2822	213	6	trivial	trivial	ADJ
ejpam-2822	213	7	l	l	NOUN
ejpam-2822	213	8	-	-	NOUN
ejpam-2822	213	9	subgroups	subgroup	NOUN
ejpam-2822	213	10	of	of	ADP
ejpam-2822	213	11	µ.	µ.	NOUN
ejpam-2822	213	12	then	then	ADV
ejpam-2822	213	13	,	,	PUNCT
ejpam-2822	213	14	the	the	DET
ejpam-2822	213	15	set	set	NOUN
ejpam-2822	213	16	product	product	NOUN
ejpam-2822	213	17	η	η	PROPN
ejpam-2822	213	18	◦	◦	NOUN
ejpam-2822	213	19	θ	θ	PROPN
ejpam-2822	213	20	is	be	AUX
ejpam-2822	213	21	also	also	ADV
ejpam-2822	213	22	a	a	DET
ejpam-2822	213	23	trivial	trivial	ADJ
ejpam-2822	213	24	l	l	NOUN
ejpam-2822	213	25	-	-	NOUN
ejpam-2822	213	26	subgroup	subgroup	NOUN
ejpam-2822	213	27	of	of	ADP
ejpam-2822	213	28	µ	µ	PROPN
ejpam-2822	213	29	defined	define	VERB
ejpam-2822	213	30	by	by	ADP
ejpam-2822	213	31	η	η	PROPN
ejpam-2822	213	32	◦	◦	PROPN
ejpam-2822	213	33	θ(x	θ(x	PROPN
ejpam-2822	213	34	)	)	PUNCT
ejpam-2822	214	1	=	=	PRON
ejpam-2822	214	2	{	{	PUNCT
ejpam-2822	214	3	η(e	η(e	PROPN
ejpam-2822	214	4	)	)	PUNCT
ejpam-2822	214	5	∧	∧	PROPN
ejpam-2822	214	6	θ(e	θ(e	PROPN
ejpam-2822	214	7	)	)	PUNCT
ejpam-2822	214	8	if	if	SCONJ
ejpam-2822	214	9	x	x	X
ejpam-2822	214	10	=	=	SYM
ejpam-2822	214	11	e	e	NOUN
ejpam-2822	214	12	,	,	PUNCT
ejpam-2822	214	13	infη	infη	PROPN
ejpam-2822	214	14	∨	∨	NUM
ejpam-2822	214	15	infθ	infθ	NOUN
ejpam-2822	214	16	if	if	SCONJ
ejpam-2822	214	17	x	x	PROPN
ejpam-2822	214	18	6=	6=	NUM
ejpam-2822	214	19	e	e	NOUN
ejpam-2822	214	20	,	,	PUNCT
ejpam-2822	214	21	if	if	SCONJ
ejpam-2822	214	22	and	and	CCONJ
ejpam-2822	214	23	only	only	ADV
ejpam-2822	215	1	if	if	SCONJ
ejpam-2822	215	2	infη	infη	PROPN
ejpam-2822	215	3	∨	∨	NUM
ejpam-2822	215	4	infθ	infθ	NOUN
ejpam-2822	215	5	<	<	X
ejpam-2822	215	6	η(e	η(e	PROPN
ejpam-2822	215	7	)	)	PUNCT
ejpam-2822	215	8	∧	∧	PROPN
ejpam-2822	215	9	θ(e	θ(e	PROPN
ejpam-2822	215	10	)	)	PUNCT
ejpam-2822	215	11	.	.	PUNCT
ejpam-2822	216	1	proof	proof	NOUN
ejpam-2822	216	2	.	.	PUNCT
ejpam-2822	217	1	since	since	SCONJ
ejpam-2822	217	2	η	η	PROPN
ejpam-2822	217	3	and	and	CCONJ
ejpam-2822	217	4	θ	θ	PROPN
ejpam-2822	217	5	are	be	AUX
ejpam-2822	217	6	trivial	trivial	ADJ
ejpam-2822	217	7	l	l	NOUN
ejpam-2822	217	8	-	-	NOUN
ejpam-2822	217	9	subgroups	subgroup	NOUN
ejpam-2822	217	10	,	,	PUNCT
ejpam-2822	217	11	it	it	PRON
ejpam-2822	217	12	follows	follow	VERB
ejpam-2822	217	13	that	that	DET
ejpam-2822	217	14	imη	imη	NOUN
ejpam-2822	217	15	=	=	X
ejpam-2822	217	16	{	{	PUNCT
ejpam-2822	217	17	infη	infη	ADV
ejpam-2822	217	18	,	,	PUNCT
ejpam-2822	217	19	η(e	η(e	PROPN
ejpam-2822	217	20	)	)	PUNCT
ejpam-2822	217	21	}	}	PUNCT
ejpam-2822	217	22	and	and	CCONJ
ejpam-2822	217	23	imθ	imθ	NOUN
ejpam-2822	217	24	=	=	SYM
ejpam-2822	217	25	{	{	PUNCT
ejpam-2822	217	26	infθ	infθ	NOUN
ejpam-2822	217	27	,	,	PUNCT
ejpam-2822	217	28	θ(e	θ(e	PROPN
ejpam-2822	217	29	)	)	PUNCT
ejpam-2822	217	30	}	}	PUNCT
ejpam-2822	217	31	.	.	PUNCT
ejpam-2822	218	1	thus	thus	ADV
ejpam-2822	218	2	,	,	PUNCT
ejpam-2822	218	3	if	if	SCONJ
ejpam-2822	218	4	x	x	ADP
ejpam-2822	218	5	=	=	SYM
ejpam-2822	218	6	e	e	X
ejpam-2822	218	7	then	then	ADV
ejpam-2822	218	8	η	η	PROPN
ejpam-2822	218	9	◦	◦	PROPN
ejpam-2822	218	10	θ(x	θ(x	PROPN
ejpam-2822	218	11	)	)	PUNCT
ejpam-2822	218	12	=	=	SYM
ejpam-2822	219	1	η(e	η(e	X
ejpam-2822	219	2	)	)	PUNCT
ejpam-2822	219	3	∧	∧	PROPN
ejpam-2822	219	4	θ(e	θ(e	PROPN
ejpam-2822	219	5	)	)	PUNCT
ejpam-2822	219	6	.	.	PUNCT
ejpam-2822	220	1	suppose	suppose	VERB
ejpam-2822	220	2	that	that	SCONJ
ejpam-2822	220	3	x	x	PROPN
ejpam-2822	220	4	6=	6=	PROPN
ejpam-2822	220	5	e.	e.	PROPN
ejpam-2822	220	6	if	if	SCONJ
ejpam-2822	220	7	η(e	η(e	PROPN
ejpam-2822	220	8	)	)	PUNCT
ejpam-2822	220	9	=	=	SYM
ejpam-2822	220	10	a0,θ(e	a0,θ(e	NOUN
ejpam-2822	220	11	)	)	PUNCT
ejpam-2822	220	12	=	=	VERB
ejpam-2822	220	13	a∗0	a∗0	NOUN
ejpam-2822	220	14	and	and	CCONJ
ejpam-2822	220	15	infη	infη	ADJ
ejpam-2822	220	16	=	=	SYM
ejpam-2822	220	17	t0	t0	PROPN
ejpam-2822	220	18	,	,	PUNCT
ejpam-2822	220	19	infθ	infθ	PROPN
ejpam-2822	220	20	=	=	PROPN
ejpam-2822	220	21	t∗0	t∗0	PROPN
ejpam-2822	220	22	,	,	PUNCT
ejpam-2822	220	23	then	then	ADV
ejpam-2822	220	24	η	η	PROPN
ejpam-2822	220	25	◦	◦	PROPN
ejpam-2822	220	26	θ(x	θ(x	PROPN
ejpam-2822	220	27	)	)	PUNCT
ejpam-2822	220	28	=	=	PUNCT
ejpam-2822	221	1	∨	∨	NUM
ejpam-2822	221	2	x	x	X
ejpam-2822	221	3	=	=	PROPN
ejpam-2822	221	4	yz	yz	X
ejpam-2822	221	5	{	{	PUNCT
ejpam-2822	221	6	η(y	η(y	PROPN
ejpam-2822	221	7	)	)	PUNCT
ejpam-2822	221	8	∧	∧	PROPN
ejpam-2822	221	9	θ(z	θ(z	NOUN
ejpam-2822	221	10	)	)	PUNCT
ejpam-2822	221	11	}	}	PUNCT
ejpam-2822	221	12	=	=	SYM
ejpam-2822	221	13	{	{	PUNCT
ejpam-2822	221	14	η(x	η(x	NOUN
ejpam-2822	221	15	)	)	PUNCT
ejpam-2822	221	16	∧	∧	PROPN
ejpam-2822	221	17	θ(e	θ(e	PROPN
ejpam-2822	221	18	)	)	PUNCT
ejpam-2822	221	19	}	}	PUNCT
ejpam-2822	221	20	∨	∨	X
ejpam-2822	221	21	{	{	PUNCT
ejpam-2822	221	22	η(e	η(e	PROPN
ejpam-2822	221	23	)	)	PUNCT
ejpam-2822	221	24	∧	∧	PROPN
ejpam-2822	221	25	θ(x	θ(x	PROPN
ejpam-2822	221	26	)	)	PUNCT
ejpam-2822	221	27	}	}	PUNCT
ejpam-2822	221	28	∨	∨	X
ejpam-2822	221	29	{	{	PUNCT
ejpam-2822	221	30	∨	∨	NUM
ejpam-2822	221	31	b∈g	b∈g	NOUN
ejpam-2822	221	32	b	b	PROPN
ejpam-2822	221	33	6	6	NUM
ejpam-2822	221	34	=	=	SYM
ejpam-2822	221	35	e	e	NOUN
ejpam-2822	221	36	,	,	PUNCT
ejpam-2822	221	37	b	b	PROPN
ejpam-2822	221	38	6	6	NUM
ejpam-2822	221	39	=	=	NOUN
ejpam-2822	221	40	x	x	NOUN
ejpam-2822	221	41	η(xb−1	η(xb−1	NOUN
ejpam-2822	221	42	)	)	PUNCT
ejpam-2822	221	43	∧	∧	PROPN
ejpam-2822	221	44	θ(b	θ(b	NOUN
ejpam-2822	221	45	)	)	PUNCT
ejpam-2822	221	46	}	}	PUNCT
ejpam-2822	221	47	=	=	SYM
ejpam-2822	221	48	{	{	PUNCT
ejpam-2822	221	49	t0	t0	NUM
ejpam-2822	221	50	∧	∧	PROPN
ejpam-2822	221	51	a∗0	a∗0	NOUN
ejpam-2822	221	52	}	}	PUNCT
ejpam-2822	221	53	∨	∨	X
ejpam-2822	221	54	{	{	PUNCT
ejpam-2822	221	55	a0	a0	PROPN
ejpam-2822	221	56	∧	∧	PROPN
ejpam-2822	221	57	t∗0	t∗0	PROPN
ejpam-2822	221	58	}	}	PUNCT
ejpam-2822	221	59	∨	∨	X
ejpam-2822	221	60	{	{	PUNCT
ejpam-2822	221	61	t0	t0	PROPN
ejpam-2822	221	62	∧	∧	PROPN
ejpam-2822	221	63	t∗0	t∗0	PROPN
ejpam-2822	221	64	}	}	PUNCT
ejpam-2822	221	65	=	=	SYM
ejpam-2822	221	66	{	{	PUNCT
ejpam-2822	221	67	t0	t0	NUM
ejpam-2822	221	68	∧	∧	PROPN
ejpam-2822	221	69	a∗0	a∗0	NOUN
ejpam-2822	221	70	}	}	PUNCT
ejpam-2822	221	71	∨	∨	X
ejpam-2822	221	72	{	{	PUNCT
ejpam-2822	221	73	a0	a0	PROPN
ejpam-2822	221	74	∧	∧	PROPN
ejpam-2822	221	75	t∗0	t∗0	PROPN
ejpam-2822	221	76	}	}	PUNCT
ejpam-2822	221	77	,	,	PUNCT
ejpam-2822	221	78	(	(	PUNCT
ejpam-2822	221	79	as	as	ADP
ejpam-2822	221	80	a0	a0	PROPN
ejpam-2822	221	81	∧	∧	PROPN
ejpam-2822	221	82	t∗0	t∗0	PROPN
ejpam-2822	221	83	≥	≥	PROPN
ejpam-2822	221	84	t0	t0	PROPN
ejpam-2822	221	85	∧	∧	PROPN
ejpam-2822	221	86	t∗0	t∗0	PROPN
ejpam-2822	221	87	)	)	PUNCT
ejpam-2822	221	88	=	=	PRON
ejpam-2822	221	89	{	{	PUNCT
ejpam-2822	221	90	t0	t0	PROPN
ejpam-2822	221	91	∨	∨	PROPN
ejpam-2822	221	92	{	{	PUNCT
ejpam-2822	221	93	a0	a0	PROPN
ejpam-2822	221	94	∧	∧	PROPN
ejpam-2822	221	95	t∗0	t∗0	PROPN
ejpam-2822	221	96	}	}	PUNCT
ejpam-2822	221	97	}	}	PUNCT
ejpam-2822	221	98	∨	∨	NUM
ejpam-2822	221	99	{	{	PUNCT
ejpam-2822	221	100	a∗0	a∗0	NOUN
ejpam-2822	221	101	∨	∨	PROPN
ejpam-2822	221	102	{	{	PUNCT
ejpam-2822	221	103	a0	a0	PROPN
ejpam-2822	221	104	∧	∧	PROPN
ejpam-2822	221	105	t∗0	t∗0	PROPN
ejpam-2822	221	106	}	}	PUNCT
ejpam-2822	221	107	}	}	PUNCT
ejpam-2822	221	108	=	=	SYM
ejpam-2822	221	109	{	{	PUNCT
ejpam-2822	221	110	t0	t0	PROPN
ejpam-2822	221	111	∨	∨	PROPN
ejpam-2822	221	112	{	{	PUNCT
ejpam-2822	221	113	a0	a0	PROPN
ejpam-2822	221	114	∧	∧	PROPN
ejpam-2822	221	115	t∗0	t∗0	PROPN
ejpam-2822	221	116	}	}	PUNCT
ejpam-2822	221	117	}	}	PUNCT
ejpam-2822	221	118	∧	∧	NOUN
ejpam-2822	221	119	a∗0	a∗0	NOUN
ejpam-2822	221	120	(	(	PUNCT
ejpam-2822	221	121	as	as	ADP
ejpam-2822	221	122	a∗0	a∗0	ADJ
ejpam-2822	221	123	≥	≥	NUM
ejpam-2822	221	124	t∗0	t∗0	PROPN
ejpam-2822	221	125	≥	≥	PROPN
ejpam-2822	221	126	a0	a0	PROPN
ejpam-2822	221	127	∧	∧	PROPN
ejpam-2822	221	128	t∗0	t∗0	PROPN
ejpam-2822	221	129	)	)	PUNCT
ejpam-2822	221	130	=	=	PRON
ejpam-2822	221	131	{	{	PUNCT
ejpam-2822	221	132	a0	a0	NOUN
ejpam-2822	221	133	∧	∧	PROPN
ejpam-2822	221	134	{	{	PUNCT
ejpam-2822	221	135	t0	t0	PROPN
ejpam-2822	221	136	∨	∨	PROPN
ejpam-2822	221	137	t∗0	t∗0	PROPN
ejpam-2822	221	138	}	}	PUNCT
ejpam-2822	221	139	}	}	PUNCT
ejpam-2822	221	140	∧	∧	NOUN
ejpam-2822	221	141	a∗0	a∗0	NOUN
ejpam-2822	221	142	(	(	PUNCT
ejpam-2822	221	143	as	as	SCONJ
ejpam-2822	221	144	l	l	NOUN
ejpam-2822	221	145	is	be	AUX
ejpam-2822	221	146	modular	modular	ADJ
ejpam-2822	221	147	)	)	PUNCT
ejpam-2822	221	148	=	=	PRON
ejpam-2822	221	149	{	{	PUNCT
ejpam-2822	221	150	a0	a0	PROPN
ejpam-2822	221	151	∧	∧	PROPN
ejpam-2822	221	152	a∗0	a∗0	NOUN
ejpam-2822	221	153	}	}	PUNCT
ejpam-2822	221	154	∧	∧	PROPN
ejpam-2822	221	155	{	{	PUNCT
ejpam-2822	221	156	t0	t0	PROPN
ejpam-2822	221	157	∨	∨	PROPN
ejpam-2822	221	158	t∗0	t∗0	PROPN
ejpam-2822	221	159	}	}	PUNCT
ejpam-2822	221	160	.	.	PUNCT
ejpam-2822	222	1	thus	thus	ADV
ejpam-2822	222	2	,	,	PUNCT
ejpam-2822	222	3	if	if	SCONJ
ejpam-2822	222	4	infη	infη	PROPN
ejpam-2822	222	5	∨	∨	NUM
ejpam-2822	222	6	infθ	infθ	NOUN
ejpam-2822	222	7	<	<	X
ejpam-2822	222	8	η(e	η(e	PROPN
ejpam-2822	222	9	)	)	PUNCT
ejpam-2822	222	10	∧	∧	PROPN
ejpam-2822	222	11	θ(e	θ(e	PROPN
ejpam-2822	222	12	)	)	PUNCT
ejpam-2822	222	13	,	,	PUNCT
ejpam-2822	222	14	then	then	ADV
ejpam-2822	222	15	η	η	PROPN
ejpam-2822	222	16	◦	◦	PROPN
ejpam-2822	222	17	θ	θ	PROPN
ejpam-2822	222	18	is	be	AUX
ejpam-2822	222	19	the	the	DET
ejpam-2822	222	20	trivial	trivial	ADJ
ejpam-2822	222	21	l	l	NOUN
ejpam-2822	222	22	-	-	NOUN
ejpam-2822	222	23	subgroup	subgroup	NOUN
ejpam-2822	222	24	given	give	VERB
ejpam-2822	222	25	by	by	ADP
ejpam-2822	222	26	η	η	PROPN
ejpam-2822	222	27	◦	◦	PROPN
ejpam-2822	222	28	θ(x	θ(x	PROPN
ejpam-2822	222	29	)	)	PUNCT
ejpam-2822	223	1	=	=	PRON
ejpam-2822	223	2	{	{	PUNCT
ejpam-2822	223	3	η(e	η(e	PROPN
ejpam-2822	223	4	)	)	PUNCT
ejpam-2822	223	5	∧	∧	PROPN
ejpam-2822	223	6	θ(e	θ(e	PROPN
ejpam-2822	223	7	)	)	PUNCT
ejpam-2822	223	8	if	if	SCONJ
ejpam-2822	223	9	x	x	X
ejpam-2822	223	10	=	=	SYM
ejpam-2822	223	11	e	e	NOUN
ejpam-2822	223	12	,	,	PUNCT
ejpam-2822	223	13	infη	infη	PROPN
ejpam-2822	223	14	∨	∨	NUM
ejpam-2822	223	15	infθ	infθ	NOUN
ejpam-2822	223	16	if	if	SCONJ
ejpam-2822	223	17	x	x	PROPN
ejpam-2822	223	18	6=	6=	PROPN
ejpam-2822	223	19	e.	e.	PROPN
ejpam-2822	223	20	on	on	ADP
ejpam-2822	223	21	the	the	DET
ejpam-2822	223	22	other	other	ADJ
ejpam-2822	223	23	hand	hand	NOUN
ejpam-2822	223	24	if	if	SCONJ
ejpam-2822	223	25	η	η	PROPN
ejpam-2822	223	26	◦	◦	NOUN
ejpam-2822	223	27	θ	θ	PROPN
ejpam-2822	223	28	is	be	AUX
ejpam-2822	223	29	a	a	DET
ejpam-2822	223	30	trivial	trivial	ADJ
ejpam-2822	223	31	l	l	NOUN
ejpam-2822	223	32	-	-	NOUN
ejpam-2822	223	33	subgroup	subgroup	NOUN
ejpam-2822	223	34	as	as	SCONJ
ejpam-2822	223	35	given	give	VERB
ejpam-2822	223	36	above	above	ADV
ejpam-2822	223	37	,	,	PUNCT
ejpam-2822	223	38	then	then	ADV
ejpam-2822	223	39	for	for	ADP
ejpam-2822	223	40	any	any	DET
ejpam-2822	223	41	x	x	SYM
ejpam-2822	223	42	6=	6=	PROPN
ejpam-2822	223	43	e	e	PROPN
ejpam-2822	223	44	i.	i.	PROPN
ejpam-2822	223	45	jahan	jahan	PROPN
ejpam-2822	223	46	,	,	PUNCT
ejpam-2822	223	47	n.	n.	PROPN
ejpam-2822	223	48	ajmal	ajmal	PROPN
ejpam-2822	223	49	,	,	PUNCT
ejpam-2822	223	50	b.	b.	PROPN
ejpam-2822	223	51	davvaz	davvaz	PROPN
ejpam-2822	223	52	/	/	SYM
ejpam-2822	223	53	eur	eur	PROPN
ejpam-2822	223	54	.	.	PUNCT
ejpam-2822	224	1	j.	j.	PROPN
ejpam-2822	224	2	pure	pure	PROPN
ejpam-2822	224	3	appl	appl	PROPN
ejpam-2822	224	4	.	.	PROPN
ejpam-2822	224	5	math	math	PROPN
ejpam-2822	224	6	,	,	PUNCT
ejpam-2822	224	7	10	10	NUM
ejpam-2822	224	8	(	(	PUNCT
ejpam-2822	224	9	2	2	NUM
ejpam-2822	224	10	)	)	PUNCT
ejpam-2822	224	11	(	(	PUNCT
ejpam-2822	224	12	2017	2017	NUM
ejpam-2822	224	13	)	)	PUNCT
ejpam-2822	224	14	,	,	PUNCT
ejpam-2822	224	15	255	255	NUM
ejpam-2822	224	16	-	-	SYM
ejpam-2822	224	17	271	271	NUM
ejpam-2822	224	18	266	266	NUM
ejpam-2822	224	19	η	η	PROPN
ejpam-2822	224	20	◦	◦	NOUN
ejpam-2822	224	21	θ(x	θ(x	PROPN
ejpam-2822	224	22	)	)	PUNCT
ejpam-2822	225	1	=	=	SYM
ejpam-2822	225	2	infη	infη	PROPN
ejpam-2822	225	3	∨	∨	NUM
ejpam-2822	225	4	infθ	infθ	NOUN
ejpam-2822	225	5	=	=	SYM
ejpam-2822	225	6	{	{	PUNCT
ejpam-2822	225	7	η(e	η(e	PROPN
ejpam-2822	225	8	)	)	PUNCT
ejpam-2822	225	9	∧	∧	PROPN
ejpam-2822	225	10	θ(e	θ(e	PROPN
ejpam-2822	225	11	)	)	PUNCT
ejpam-2822	225	12	}	}	PUNCT
ejpam-2822	225	13	∧	∧	PROPN
ejpam-2822	225	14	{	{	PUNCT
ejpam-2822	225	15	infη	infη	PROPN
ejpam-2822	225	16	∨	∨	NUM
ejpam-2822	225	17	infθ	infθ	NOUN
ejpam-2822	225	18	}	}	PUNCT
ejpam-2822	225	19	.	.	PUNCT
ejpam-2822	226	1	thus	thus	ADV
ejpam-2822	226	2	,	,	PUNCT
ejpam-2822	226	3	infη	infη	PROPN
ejpam-2822	226	4	∨	∨	NUM
ejpam-2822	226	5	infθ	infθ	PROPN
ejpam-2822	226	6	≤	≤	PROPN
ejpam-2822	226	7	η(e	η(e	PROPN
ejpam-2822	226	8	)	)	PUNCT
ejpam-2822	226	9	∧	∧	PROPN
ejpam-2822	226	10	θ(e	θ(e	PROPN
ejpam-2822	226	11	)	)	PUNCT
ejpam-2822	226	12	.	.	PUNCT
ejpam-2822	227	1	since	since	SCONJ
ejpam-2822	227	2	η	η	PROPN
ejpam-2822	227	3	◦	◦	PROPN
ejpam-2822	227	4	θ	θ	PROPN
ejpam-2822	227	5	is	be	AUX
ejpam-2822	227	6	a	a	DET
ejpam-2822	227	7	trivial	trivial	ADJ
ejpam-2822	227	8	l	l	NOUN
ejpam-2822	227	9	-	-	ADJ
ejpam-2822	227	10	subgroup	subgroup	ADJ
ejpam-2822	227	11	infη	infη	PROPN
ejpam-2822	227	12	∨	∨	NUM
ejpam-2822	227	13	infθ	infθ	PROPN
ejpam-2822	227	14	6=	6=	ADP
ejpam-2822	227	15	η(e	η(e	PROPN
ejpam-2822	227	16	)	)	PUNCT
ejpam-2822	227	17	∧	∧	PROPN
ejpam-2822	227	18	θ(e	θ(e	PROPN
ejpam-2822	227	19	)	)	PUNCT
ejpam-2822	227	20	.	.	PUNCT
ejpam-2822	228	1	therefore	therefore	ADV
ejpam-2822	228	2	,	,	PUNCT
ejpam-2822	228	3	infη	infη	PROPN
ejpam-2822	228	4	∨	∨	NUM
ejpam-2822	228	5	infθ	infθ	NOUN
ejpam-2822	228	6	<	<	X
ejpam-2822	228	7	η(e	η(e	PROPN
ejpam-2822	228	8	)	)	PUNCT
ejpam-2822	228	9	∧	∧	PROPN
ejpam-2822	228	10	θ(e	θ(e	PROPN
ejpam-2822	228	11	)	)	PUNCT
ejpam-2822	228	12	.	.	PUNCT
ejpam-2822	229	1	theorem	theorem	NOUN
ejpam-2822	229	2	3	3	X
ejpam-2822	229	3	.	.	PUNCT
ejpam-2822	230	1	let	let	VERB
ejpam-2822	230	2	η	η	PROPN
ejpam-2822	230	3	,	,	PUNCT
ejpam-2822	230	4	θ	θ	PROPN
ejpam-2822	230	5	∈	∈	PROPN
ejpam-2822	230	6	nl(µ	nl(µ	NOUN
ejpam-2822	230	7	)	)	PUNCT
ejpam-2822	230	8	with	with	ADP
ejpam-2822	230	9	common	common	ADJ
ejpam-2822	230	10	tail	tail	NOUN
ejpam-2822	230	11	t0	t0	PROPN
ejpam-2822	230	12	such	such	ADJ
ejpam-2822	230	13	that	that	SCONJ
ejpam-2822	230	14	t0	t0	PROPN
ejpam-2822	230	15	<	<	X
ejpam-2822	230	16	η(e	η(e	PROPN
ejpam-2822	230	17	)	)	PUNCT
ejpam-2822	230	18	∧	∧	PROPN
ejpam-2822	230	19	θ(e	θ(e	PROPN
ejpam-2822	230	20	)	)	PUNCT
ejpam-2822	230	21	and	and	CCONJ
ejpam-2822	230	22	infη	infη	ADJ
ejpam-2822	230	23	◦	◦	NOUN
ejpam-2822	230	24	θ	θ	X
ejpam-2822	230	25	=	=	SYM
ejpam-2822	230	26	t0	t0	PROPN
ejpam-2822	230	27	.	.	PUNCT
ejpam-2822	231	1	if	if	SCONJ
ejpam-2822	231	2	η	η	PROPN
ejpam-2822	231	3	and	and	CCONJ
ejpam-2822	231	4	θ	θ	PROPN
ejpam-2822	231	5	are	be	AUX
ejpam-2822	231	6	nilpotent	nilpotent	ADJ
ejpam-2822	231	7	of	of	ADP
ejpam-2822	231	8	classes	class	NOUN
ejpam-2822	231	9	c	c	PROPN
ejpam-2822	231	10	and	and	CCONJ
ejpam-2822	231	11	d	d	NOUN
ejpam-2822	231	12	respectively	respectively	ADV
ejpam-2822	231	13	,	,	PUNCT
ejpam-2822	231	14	then	then	ADV
ejpam-2822	231	15	η	η	PROPN
ejpam-2822	231	16	◦	◦	PROPN
ejpam-2822	231	17	θ	θ	PROPN
ejpam-2822	231	18	is	be	AUX
ejpam-2822	231	19	a	a	DET
ejpam-2822	231	20	nilpotent	nilpotent	ADJ
ejpam-2822	231	21	l	l	NOUN
ejpam-2822	231	22	-	-	NOUN
ejpam-2822	231	23	subgroup	subgroup	NOUN
ejpam-2822	231	24	of	of	ADP
ejpam-2822	231	25	µ	µ	NOUN
ejpam-2822	231	26	of	of	ADP
ejpam-2822	231	27	nilpotent	nilpotent	ADJ
ejpam-2822	231	28	class	class	NOUN
ejpam-2822	231	29	at	at	ADP
ejpam-2822	231	30	most	most	ADV
ejpam-2822	231	31	c+	c+	VERB
ejpam-2822	231	32	d.	d.	PROPN
ejpam-2822	231	33	proof	proof	NOUN
ejpam-2822	231	34	.	.	PUNCT
ejpam-2822	232	1	since	since	SCONJ
ejpam-2822	232	2	η	η	PROPN
ejpam-2822	232	3	,	,	PUNCT
ejpam-2822	232	4	θ	θ	PROPN
ejpam-2822	232	5	∈	∈	PROPN
ejpam-2822	232	6	nl(µ	nl(µ	NOUN
ejpam-2822	232	7	)	)	PUNCT
ejpam-2822	232	8	,	,	PUNCT
ejpam-2822	232	9	by	by	ADP
ejpam-2822	232	10	proposition	proposition	NOUN
ejpam-2822	232	11	1	1	NUM
ejpam-2822	232	12	,	,	PUNCT
ejpam-2822	232	13	we	we	PRON
ejpam-2822	232	14	conclude	conclude	VERB
ejpam-2822	232	15	that	that	SCONJ
ejpam-2822	232	16	η	η	PROPN
ejpam-2822	232	17	◦	◦	NOUN
ejpam-2822	232	18	θ	θ	X
ejpam-2822	232	19	∈	∈	NOUN
ejpam-2822	232	20	nl(µ	nl(µ	NOUN
ejpam-2822	232	21	)	)	PUNCT
ejpam-2822	232	22	.	.	PUNCT
ejpam-2822	233	1	in	in	ADP
ejpam-2822	233	2	view	view	NOUN
ejpam-2822	233	3	of	of	ADP
ejpam-2822	233	4	proposition	proposition	NOUN
ejpam-2822	233	5	6	6	NUM
ejpam-2822	233	6	,	,	PUNCT
ejpam-2822	233	7	zi(η	zi(η	X
ejpam-2822	233	8	◦	◦	NOUN
ejpam-2822	233	9	θ	θ	NOUN
ejpam-2822	233	10	)	)	PUNCT
ejpam-2822	233	11	∈	∈	PROPN
ejpam-2822	233	12	nl(µ	nl(µ	NOUN
ejpam-2822	233	13	)	)	PUNCT
ejpam-2822	233	14	.	.	PUNCT
ejpam-2822	234	1	now	now	ADV
ejpam-2822	234	2	,	,	PUNCT
ejpam-2822	234	3	let	let	VERB
ejpam-2822	234	4	η	η	PROPN
ejpam-2822	234	5	and	and	CCONJ
ejpam-2822	234	6	θ	θ	PROPN
ejpam-2822	234	7	be	be	AUX
ejpam-2822	234	8	nilpotent	nilpotent	ADJ
ejpam-2822	234	9	of	of	ADP
ejpam-2822	234	10	classes	class	NOUN
ejpam-2822	234	11	c	c	PROPN
ejpam-2822	234	12	and	and	CCONJ
ejpam-2822	234	13	d	d	NOUN
ejpam-2822	234	14	respectively	respectively	ADV
ejpam-2822	234	15	.	.	PUNCT
ejpam-2822	235	1	in	in	ADP
ejpam-2822	235	2	order	order	NOUN
ejpam-2822	235	3	to	to	PART
ejpam-2822	235	4	show	show	VERB
ejpam-2822	235	5	that	that	SCONJ
ejpam-2822	235	6	the	the	DET
ejpam-2822	235	7	set	set	NOUN
ejpam-2822	235	8	product	product	NOUN
ejpam-2822	235	9	η	η	PROPN
ejpam-2822	235	10	◦	◦	NOUN
ejpam-2822	235	11	θ	θ	PROPN
ejpam-2822	235	12	is	be	AUX
ejpam-2822	235	13	nilpotent	nilpotent	ADJ
ejpam-2822	235	14	,	,	PUNCT
ejpam-2822	235	15	we	we	PRON
ejpam-2822	235	16	show	show	VERB
ejpam-2822	235	17	that	that	SCONJ
ejpam-2822	235	18	the	the	DET
ejpam-2822	235	19	descending	descend	VERB
ejpam-2822	235	20	central	central	ADJ
ejpam-2822	235	21	series	series	NOUN
ejpam-2822	235	22	of	of	ADP
ejpam-2822	235	23	η	η	PROPN
ejpam-2822	235	24	◦	◦	PROPN
ejpam-2822	235	25	θ	θ	PROPN
ejpam-2822	235	26	terminates	terminate	VERB
ejpam-2822	235	27	finitely	finitely	ADV
ejpam-2822	235	28	.	.	PUNCT
ejpam-2822	236	1	set	set	VERB
ejpam-2822	236	2	λ	λ	PROPN
ejpam-2822	236	3	=	=	SYM
ejpam-2822	236	4	η	η	PROPN
ejpam-2822	236	5	◦	◦	NOUN
ejpam-2822	236	6	θ	θ	PROPN
ejpam-2822	237	1	so	so	SCONJ
ejpam-2822	237	2	that	that	SCONJ
ejpam-2822	237	3	infλ	infλ	PROPN
ejpam-2822	237	4	=	=	SYM
ejpam-2822	237	5	t0	t0	PROPN
ejpam-2822	237	6	.	.	PUNCT
ejpam-2822	238	1	(	(	PUNCT
ejpam-2822	238	2	1	1	X
ejpam-2822	238	3	)	)	PUNCT
ejpam-2822	238	4	in	in	ADP
ejpam-2822	238	5	view	view	NOUN
ejpam-2822	238	6	of	of	ADP
ejpam-2822	238	7	lemma	lemma	PROPN
ejpam-2822	238	8	2	2	NUM
ejpam-2822	238	9	,	,	PUNCT
ejpam-2822	238	10	the	the	DET
ejpam-2822	238	11	set	set	ADJ
ejpam-2822	238	12	product	product	NOUN
ejpam-2822	238	13	of	of	ADP
ejpam-2822	238	14	two	two	NUM
ejpam-2822	238	15	trivial	trivial	ADJ
ejpam-2822	238	16	l	l	NOUN
ejpam-2822	238	17	-	-	NOUN
ejpam-2822	238	18	subgroups	subgroup	NOUN
ejpam-2822	238	19	is	be	AUX
ejpam-2822	238	20	a	a	DET
ejpam-2822	238	21	trivial	trivial	ADJ
ejpam-2822	238	22	l	l	NOUN
ejpam-2822	238	23	-	-	NOUN
ejpam-2822	238	24	subgroup	subgroup	NOUN
ejpam-2822	238	25	provided	provide	VERB
ejpam-2822	238	26	the	the	DET
ejpam-2822	238	27	join	join	NOUN
ejpam-2822	238	28	of	of	ADP
ejpam-2822	238	29	their	their	PRON
ejpam-2822	238	30	tails	tail	NOUN
ejpam-2822	238	31	is	be	AUX
ejpam-2822	238	32	different	different	ADJ
ejpam-2822	238	33	from	from	ADP
ejpam-2822	238	34	the	the	DET
ejpam-2822	238	35	meet	meet	NOUN
ejpam-2822	238	36	of	of	ADP
ejpam-2822	238	37	their	their	PRON
ejpam-2822	238	38	tips	tip	NOUN
ejpam-2822	238	39	.	.	PUNCT
ejpam-2822	239	1	thus	thus	ADV
ejpam-2822	239	2	,	,	PUNCT
ejpam-2822	239	3	as	as	SCONJ
ejpam-2822	239	4	t0	t0	PROPN
ejpam-2822	239	5	<	<	X
ejpam-2822	239	6	η(e	η(e	PROPN
ejpam-2822	239	7	)	)	PUNCT
ejpam-2822	239	8	∧	∧	PROPN
ejpam-2822	239	9	θ(e	θ(e	PROPN
ejpam-2822	239	10	)	)	PUNCT
ejpam-2822	239	11	and	and	CCONJ
ejpam-2822	239	12	by	by	ADP
ejpam-2822	239	13	(	(	PUNCT
ejpam-2822	239	14	1	1	NUM
ejpam-2822	239	15	)	)	PUNCT
ejpam-2822	239	16	,	,	PUNCT
ejpam-2822	239	17	we	we	PRON
ejpam-2822	239	18	have	have	VERB
ejpam-2822	239	19	ηaot0	ηaot0	ADJ
ejpam-2822	239	20	◦	◦	NOUN
ejpam-2822	239	21	θ	θ	PROPN
ejpam-2822	239	22	a∗0	a∗0	NOUN
ejpam-2822	239	23	t0	t0	PROPN
ejpam-2822	240	1	=	=	SYM
ejpam-2822	241	1	λ	λ	PROPN
ejpam-2822	241	2	ao∧a∗0	ao∧a∗0	NOUN
ejpam-2822	241	3	t0	t0	NOUN
ejpam-2822	241	4	,	,	PUNCT
ejpam-2822	241	5	where	where	SCONJ
ejpam-2822	241	6	ao	ao	PROPN
ejpam-2822	241	7	and	and	CCONJ
ejpam-2822	241	8	a∗0	a∗0	NOUN
ejpam-2822	241	9	denote	denote	VERB
ejpam-2822	241	10	the	the	DET
ejpam-2822	241	11	tips	tip	NOUN
ejpam-2822	241	12	of	of	ADP
ejpam-2822	241	13	η	η	PROPN
ejpam-2822	241	14	and	and	CCONJ
ejpam-2822	241	15	θ	θ	PROPN
ejpam-2822	241	16	respectively	respectively	ADV
ejpam-2822	241	17	.	.	PUNCT
ejpam-2822	242	1	to	to	PART
ejpam-2822	242	2	achieve	achieve	VERB
ejpam-2822	242	3	our	our	PRON
ejpam-2822	242	4	aim	aim	NOUN
ejpam-2822	242	5	,	,	PUNCT
ejpam-2822	242	6	we	we	PRON
ejpam-2822	242	7	demonstrate	demonstrate	VERB
ejpam-2822	242	8	that	that	SCONJ
ejpam-2822	242	9	zn(η	zn(η	VERB
ejpam-2822	242	10	◦	◦	NOUN
ejpam-2822	242	11	θ	θ	NUM
ejpam-2822	242	12	)	)	PUNCT
ejpam-2822	242	13	=	=	SYM
ejpam-2822	242	14	λ	λ	PROPN
ejpam-2822	242	15	ao∧a∗0	ao∧a∗0	NOUN
ejpam-2822	242	16	t0	t0	NOUN
ejpam-2822	242	17	,	,	PUNCT
ejpam-2822	242	18	for	for	ADP
ejpam-2822	242	19	some	some	DET
ejpam-2822	242	20	integer	integer	NOUN
ejpam-2822	242	21	n	n	PRON
ejpam-2822	242	22	≥	≥	NOUN
ejpam-2822	242	23	0	0	NUM
ejpam-2822	242	24	.	.	PUNCT
ejpam-2822	243	1	as	as	SCONJ
ejpam-2822	243	2	η	η	PROPN
ejpam-2822	243	3	and	and	CCONJ
ejpam-2822	243	4	θ	θ	PROPN
ejpam-2822	243	5	are	be	AUX
ejpam-2822	243	6	nilpotent	nilpotent	ADJ
ejpam-2822	243	7	of	of	ADP
ejpam-2822	243	8	classes	class	NOUN
ejpam-2822	243	9	c	c	PROPN
ejpam-2822	243	10	and	and	CCONJ
ejpam-2822	243	11	d	d	NOUN
ejpam-2822	243	12	respectively	respectively	ADV
ejpam-2822	243	13	,	,	PUNCT
ejpam-2822	243	14	we	we	PRON
ejpam-2822	243	15	get	get	VERB
ejpam-2822	243	16	zc(η	zc(η	NUM
ejpam-2822	243	17	)	)	PUNCT
ejpam-2822	243	18	=	=	SYM
ejpam-2822	243	19	ηaot0	ηaot0	NOUN
ejpam-2822	243	20	and	and	CCONJ
ejpam-2822	243	21	zd(θ	zd(θ	NUM
ejpam-2822	243	22	)	)	PUNCT
ejpam-2822	243	23	=	=	SYM
ejpam-2822	243	24	θ	θ	PROPN
ejpam-2822	243	25	a∗0	a∗0	NOUN
ejpam-2822	243	26	t0	t0	PROPN
ejpam-2822	243	27	.	.	PUNCT
ejpam-2822	244	1	(	(	PUNCT
ejpam-2822	244	2	2	2	X
ejpam-2822	244	3	)	)	PUNCT
ejpam-2822	244	4	to	to	PART
ejpam-2822	244	5	prove	prove	VERB
ejpam-2822	244	6	the	the	DET
ejpam-2822	244	7	result	result	NOUN
ejpam-2822	244	8	,	,	PUNCT
ejpam-2822	244	9	it	it	PRON
ejpam-2822	244	10	is	be	AUX
ejpam-2822	244	11	sufficient	sufficient	ADJ
ejpam-2822	244	12	to	to	PART
ejpam-2822	244	13	show	show	VERB
ejpam-2822	244	14	that	that	SCONJ
ejpam-2822	244	15	for	for	ADP
ejpam-2822	244	16	some	some	DET
ejpam-2822	244	17	positive	positive	ADJ
ejpam-2822	244	18	integer	integer	NOUN
ejpam-2822	244	19	n	n	CCONJ
ejpam-2822	244	20	,	,	PUNCT
ejpam-2822	244	21	zn(η	zn(η	X
ejpam-2822	244	22	◦	◦	NOUN
ejpam-2822	244	23	θ	θ	NOUN
ejpam-2822	244	24	)	)	PUNCT
ejpam-2822	244	25	is	be	AUX
ejpam-2822	244	26	contained	contain	VERB
ejpam-2822	244	27	in	in	ADP
ejpam-2822	244	28	the	the	DET
ejpam-2822	244	29	set	set	NOUN
ejpam-2822	244	30	product	product	NOUN
ejpam-2822	244	31	of	of	ADP
ejpam-2822	244	32	trivial	trivial	ADJ
ejpam-2822	244	33	l	l	NOUN
ejpam-2822	244	34	-	-	PUNCT
ejpam-2822	244	35	subgroups	subgroup	NOUN
ejpam-2822	244	36	ηaot0	ηaot0	ADJ
ejpam-2822	244	37	and	and	CCONJ
ejpam-2822	244	38	θ	θ	PROPN
ejpam-2822	244	39	a∗0	a∗0	NOUN
ejpam-2822	244	40	t0	t0	PROPN
ejpam-2822	244	41	.	.	PUNCT
ejpam-2822	245	1	firstly	firstly	ADV
ejpam-2822	245	2	,	,	PUNCT
ejpam-2822	245	3	we	we	PRON
ejpam-2822	245	4	claim	claim	VERB
ejpam-2822	245	5	that	that	SCONJ
ejpam-2822	245	6	for	for	ADP
ejpam-2822	245	7	any	any	DET
ejpam-2822	245	8	positive	positive	ADJ
ejpam-2822	245	9	integer	integer	NOUN
ejpam-2822	245	10	n	n	CCONJ
ejpam-2822	245	11	,	,	PUNCT
ejpam-2822	245	12	zn(η	zn(η	PUNCT
ejpam-2822	245	13	◦	◦	NOUN
ejpam-2822	245	14	θ	θ	NOUN
ejpam-2822	245	15	)	)	PUNCT
ejpam-2822	245	16	is	be	AUX
ejpam-2822	245	17	contained	contain	VERB
ejpam-2822	245	18	in	in	ADP
ejpam-2822	245	19	the	the	DET
ejpam-2822	245	20	set	set	NOUN
ejpam-2822	245	21	product	product	NOUN
ejpam-2822	245	22	of	of	ADP
ejpam-2822	245	23	l	l	NOUN
ejpam-2822	245	24	-	-	NOUN
ejpam-2822	245	25	subgroups	subgroup	NOUN
ejpam-2822	245	26	of	of	ADP
ejpam-2822	245	27	the	the	DET
ejpam-2822	245	28	form	form	NOUN
ejpam-2822	245	29	[	[	X
ejpam-2822	245	30	λ1	λ1	ADJ
ejpam-2822	245	31	,	,	PUNCT
ejpam-2822	245	32	λ2	λ2	NOUN
ejpam-2822	245	33	,	,	PUNCT
ejpam-2822	245	34	...	...	PUNCT
ejpam-2822	245	35	,	,	PUNCT
ejpam-2822	245	36	λn+1	λn+1	PROPN
ejpam-2822	245	37	]	]	PUNCT
ejpam-2822	245	38	,	,	PUNCT
ejpam-2822	245	39	where	where	SCONJ
ejpam-2822	245	40	λi	λi	ADP
ejpam-2822	245	41	=	=	SYM
ejpam-2822	245	42	η	η	PROPN
ejpam-2822	245	43	or	or	CCONJ
ejpam-2822	245	44	θ	θ	PROPN
ejpam-2822	245	45	.	.	PROPN
ejpam-2822	245	46	as	as	ADP
ejpam-2822	245	47	η	η	PROPN
ejpam-2822	245	48	◦	◦	NOUN
ejpam-2822	245	49	θ	θ	X
ejpam-2822	245	50	∈	∈	NOUN
ejpam-2822	245	51	nl(µ	nl(µ	NOUN
ejpam-2822	245	52	)	)	PUNCT
ejpam-2822	245	53	,	,	PUNCT
ejpam-2822	245	54	in	in	ADP
ejpam-2822	245	55	view	view	NOUN
ejpam-2822	245	56	of	of	ADP
ejpam-2822	245	57	(	(	PUNCT
ejpam-2822	245	58	1	1	NUM
ejpam-2822	245	59	)	)	PUNCT
ejpam-2822	245	60	and	and	CCONJ
ejpam-2822	245	61	theorem	theorem	VERB
ejpam-2822	245	62	2	2	NUM
ejpam-2822	245	63	,	,	PUNCT
ejpam-2822	245	64	it	it	PRON
ejpam-2822	245	65	follows	follow	VERB
ejpam-2822	245	66	that	that	SCONJ
ejpam-2822	245	67	z1(η	z1(η	NUM
ejpam-2822	245	68	◦	◦	NOUN
ejpam-2822	245	69	θ	θ	NOUN
ejpam-2822	245	70	)	)	PUNCT
ejpam-2822	245	71	=	=	PUNCT
ejpam-2822	246	1	[	[	X
ejpam-2822	246	2	η	η	X
ejpam-2822	246	3	◦	◦	PROPN
ejpam-2822	246	4	θ	θ	PROPN
ejpam-2822	246	5	,	,	PUNCT
ejpam-2822	246	6	η	η	PROPN
ejpam-2822	246	7	◦	◦	NOUN
ejpam-2822	246	8	θ	θ	X
ejpam-2822	246	9	]	]	X
ejpam-2822	246	10	⊆	⊆	NUM
ejpam-2822	246	11	[	[	X
ejpam-2822	246	12	η	η	PROPN
ejpam-2822	246	13	,	,	PUNCT
ejpam-2822	246	14	η	η	NOUN
ejpam-2822	246	15	]	]	X
ejpam-2822	246	16	◦	◦	NOUN
ejpam-2822	246	17	[	[	X
ejpam-2822	246	18	η	η	X
ejpam-2822	246	19	,	,	PUNCT
ejpam-2822	246	20	θ	θ	NOUN
ejpam-2822	246	21	]	]	X
ejpam-2822	246	22	◦	◦	NOUN
ejpam-2822	246	23	[	[	X
ejpam-2822	246	24	θ	θ	X
ejpam-2822	246	25	,	,	PUNCT
ejpam-2822	246	26	θ	θ	NOUN
ejpam-2822	246	27	]	]	PUNCT
ejpam-2822	246	28	.	.	PUNCT
ejpam-2822	246	29	suppose	suppose	VERB
ejpam-2822	246	30	that	that	SCONJ
ejpam-2822	246	31	for	for	ADP
ejpam-2822	246	32	some	some	DET
ejpam-2822	246	33	positive	positive	ADJ
ejpam-2822	246	34	integer	integer	NOUN
ejpam-2822	246	35	k	k	PROPN
ejpam-2822	246	36	,	,	PUNCT
ejpam-2822	246	37	zk(η	zk(η	NUM
ejpam-2822	246	38	◦	◦	NOUN
ejpam-2822	246	39	θ	θ	NOUN
ejpam-2822	246	40	)	)	PUNCT
ejpam-2822	246	41	is	be	AUX
ejpam-2822	246	42	contained	contain	VERB
ejpam-2822	246	43	in	in	ADP
ejpam-2822	246	44	the	the	DET
ejpam-2822	246	45	set	set	NOUN
ejpam-2822	246	46	product	product	NOUN
ejpam-2822	246	47	of	of	ADP
ejpam-2822	246	48	l	l	NOUN
ejpam-2822	246	49	-	-	NOUN
ejpam-2822	246	50	subgroups	subgroup	NOUN
ejpam-2822	246	51	of	of	ADP
ejpam-2822	246	52	the	the	DET
ejpam-2822	246	53	form	form	NOUN
ejpam-2822	246	54	[	[	X
ejpam-2822	246	55	λ1	λ1	ADJ
ejpam-2822	246	56	,	,	PUNCT
ejpam-2822	246	57	λ2	λ2	NOUN
ejpam-2822	246	58	,	,	PUNCT
ejpam-2822	246	59	...	...	PUNCT
ejpam-2822	246	60	,	,	PUNCT
ejpam-2822	246	61	λk+1	λk+1	X
ejpam-2822	246	62	]	]	PUNCT
ejpam-2822	246	63	,	,	PUNCT
ejpam-2822	246	64	where	where	SCONJ
ejpam-2822	246	65	λi	λi	ADP
ejpam-2822	246	66	=	=	SYM
ejpam-2822	246	67	η	η	PROPN
ejpam-2822	246	68	or	or	CCONJ
ejpam-2822	246	69	θ	θ	PROPN
ejpam-2822	246	70	.	.	PUNCT
ejpam-2822	247	1	also	also	ADV
ejpam-2822	247	2	,	,	PUNCT
ejpam-2822	247	3	infzk(η	infzk(η	ADP
ejpam-2822	247	4	◦	◦	NOUN
ejpam-2822	247	5	θ	θ	NOUN
ejpam-2822	247	6	)	)	PUNCT
ejpam-2822	247	7	=	=	SYM
ejpam-2822	247	8	infη	infη	PROPN
ejpam-2822	248	1	◦	◦	NOUN
ejpam-2822	248	2	θ	θ	PROPN
ejpam-2822	248	3	.	.	PUNCT
ejpam-2822	248	4	i.	i.	PROPN
ejpam-2822	248	5	jahan	jahan	PROPN
ejpam-2822	248	6	,	,	PUNCT
ejpam-2822	248	7	n.	n.	PROPN
ejpam-2822	248	8	ajmal	ajmal	PROPN
ejpam-2822	248	9	,	,	PUNCT
ejpam-2822	248	10	b.	b.	PROPN
ejpam-2822	248	11	davvaz	davvaz	PROPN
ejpam-2822	248	12	/	/	SYM
ejpam-2822	248	13	eur	eur	PROPN
ejpam-2822	248	14	.	.	PUNCT
ejpam-2822	249	1	j.	j.	PROPN
ejpam-2822	249	2	pure	pure	PROPN
ejpam-2822	249	3	appl	appl	PROPN
ejpam-2822	249	4	.	.	PROPN
ejpam-2822	249	5	math	math	PROPN
ejpam-2822	249	6	,	,	PUNCT
ejpam-2822	249	7	10	10	NUM
ejpam-2822	249	8	(	(	PUNCT
ejpam-2822	249	9	2	2	NUM
ejpam-2822	249	10	)	)	PUNCT
ejpam-2822	249	11	(	(	PUNCT
ejpam-2822	249	12	2017	2017	NUM
ejpam-2822	249	13	)	)	PUNCT
ejpam-2822	249	14	,	,	PUNCT
ejpam-2822	249	15	255	255	NUM
ejpam-2822	249	16	-	-	SYM
ejpam-2822	249	17	271	271	NUM
ejpam-2822	249	18	267	267	NUM
ejpam-2822	249	19	(	(	PUNCT
ejpam-2822	249	20	3	3	NUM
ejpam-2822	249	21	)	)	PUNCT
ejpam-2822	249	22	hence	hence	ADV
ejpam-2822	249	23	in	in	ADP
ejpam-2822	249	24	view	view	NOUN
ejpam-2822	249	25	of	of	ADP
ejpam-2822	249	26	(	(	PUNCT
ejpam-2822	249	27	1	1	NUM
ejpam-2822	249	28	)	)	PUNCT
ejpam-2822	249	29	and	and	CCONJ
ejpam-2822	249	30	theorem	theorem	VERB
ejpam-2822	249	31	2	2	NUM
ejpam-2822	249	32	,	,	PUNCT
ejpam-2822	249	33	we	we	PRON
ejpam-2822	249	34	have	have	VERB
ejpam-2822	249	35	zk+1(η	zk+1(η	NUM
ejpam-2822	249	36	◦	◦	NOUN
ejpam-2822	249	37	θ	θ	NOUN
ejpam-2822	249	38	)	)	PUNCT
ejpam-2822	249	39	=	=	NOUN
ejpam-2822	250	1	[	[	X
ejpam-2822	250	2	zk(η	zk(η	NUM
ejpam-2822	250	3	◦	◦	NOUN
ejpam-2822	250	4	θ	θ	PROPN
ejpam-2822	250	5	)	)	PUNCT
ejpam-2822	250	6	,	,	PUNCT
ejpam-2822	250	7	η	η	PROPN
ejpam-2822	250	8	◦	◦	NOUN
ejpam-2822	250	9	θ	θ	X
ejpam-2822	250	10	]	]	X
ejpam-2822	250	11	⊆	⊆	NUM
ejpam-2822	250	12	[	[	SYM
ejpam-2822	250	13	zk(η	zk(η	NUM
ejpam-2822	250	14	◦	◦	NOUN
ejpam-2822	250	15	θ	θ	PROPN
ejpam-2822	250	16	)	)	PUNCT
ejpam-2822	250	17	,	,	PUNCT
ejpam-2822	250	18	η	η	PROPN
ejpam-2822	250	19	]	]	X
ejpam-2822	250	20	◦	◦	NOUN
ejpam-2822	250	21	[	[	X
ejpam-2822	250	22	zk(η	zk(η	NUM
ejpam-2822	250	23	◦	◦	NOUN
ejpam-2822	250	24	θ	θ	NOUN
ejpam-2822	250	25	)	)	PUNCT
ejpam-2822	250	26	,	,	PUNCT
ejpam-2822	250	27	θ	θ	PROPN
ejpam-2822	250	28	]	]	PUNCT
ejpam-2822	250	29	.	.	PUNCT
ejpam-2822	251	1	by	by	ADP
ejpam-2822	251	2	the	the	DET
ejpam-2822	251	3	hypothesis	hypothesis	NOUN
ejpam-2822	251	4	zk(η	zk(η	NUM
ejpam-2822	251	5	◦	◦	NOUN
ejpam-2822	251	6	θ	θ	PROPN
ejpam-2822	251	7	)	)	PUNCT
ejpam-2822	251	8	is	be	AUX
ejpam-2822	251	9	contained	contain	VERB
ejpam-2822	251	10	in	in	ADP
ejpam-2822	251	11	the	the	DET
ejpam-2822	251	12	set	set	NOUN
ejpam-2822	251	13	product	product	NOUN
ejpam-2822	251	14	of	of	ADP
ejpam-2822	251	15	l	l	NOUN
ejpam-2822	251	16	-	-	NOUN
ejpam-2822	251	17	subgroups	subgroup	NOUN
ejpam-2822	251	18	of	of	ADP
ejpam-2822	251	19	the	the	DET
ejpam-2822	251	20	form	form	NOUN
ejpam-2822	251	21	[	[	X
ejpam-2822	251	22	λ1	λ1	ADJ
ejpam-2822	251	23	,	,	PUNCT
ejpam-2822	251	24	λ2	λ2	NOUN
ejpam-2822	251	25	,	,	PUNCT
ejpam-2822	251	26	...	...	PUNCT
ejpam-2822	251	27	,	,	PUNCT
ejpam-2822	251	28	λk+1	λk+1	X
ejpam-2822	251	29	]	]	PUNCT
ejpam-2822	251	30	,	,	PUNCT
ejpam-2822	251	31	where	where	SCONJ
ejpam-2822	251	32	λi	λi	ADP
ejpam-2822	251	33	=	=	SYM
ejpam-2822	251	34	η	η	PROPN
ejpam-2822	251	35	or	or	CCONJ
ejpam-2822	251	36	θ	θ	PROPN
ejpam-2822	251	37	.	.	PUNCT
ejpam-2822	252	1	thus	thus	ADV
ejpam-2822	252	2	,	,	PUNCT
ejpam-2822	252	3	it	it	PRON
ejpam-2822	252	4	follows	follow	VERB
ejpam-2822	252	5	that	that	SCONJ
ejpam-2822	252	6	zk+1(η	zk+1(η	PROPN
ejpam-2822	252	7	◦	◦	NOUN
ejpam-2822	252	8	θ	θ	NOUN
ejpam-2822	252	9	)	)	PUNCT
ejpam-2822	252	10	is	be	AUX
ejpam-2822	252	11	contained	contain	VERB
ejpam-2822	252	12	in	in	ADP
ejpam-2822	252	13	the	the	DET
ejpam-2822	252	14	set	set	NOUN
ejpam-2822	252	15	product	product	NOUN
ejpam-2822	252	16	of	of	ADP
ejpam-2822	252	17	l	l	NOUN
ejpam-2822	252	18	-	-	NOUN
ejpam-2822	252	19	subgroups	subgroup	NOUN
ejpam-2822	252	20	of	of	ADP
ejpam-2822	252	21	the	the	DET
ejpam-2822	252	22	form	form	NOUN
ejpam-2822	252	23	[	[	X
ejpam-2822	252	24	λ1	λ1	ADJ
ejpam-2822	252	25	,	,	PUNCT
ejpam-2822	252	26	λ2	λ2	NOUN
ejpam-2822	252	27	,	,	PUNCT
ejpam-2822	252	28	...	...	PUNCT
ejpam-2822	252	29	,	,	PUNCT
ejpam-2822	252	30	λk+2	λk+2	NOUN
ejpam-2822	252	31	]	]	X
ejpam-2822	252	32	,	,	PUNCT
ejpam-2822	252	33	where	where	SCONJ
ejpam-2822	252	34	λi	λi	ADP
ejpam-2822	252	35	=	=	SYM
ejpam-2822	252	36	η	η	PROPN
ejpam-2822	252	37	or	or	CCONJ
ejpam-2822	252	38	θ	θ	PROPN
ejpam-2822	252	39	.	.	PUNCT
ejpam-2822	253	1	thus	thus	ADV
ejpam-2822	253	2	,	,	PUNCT
ejpam-2822	253	3	by	by	ADP
ejpam-2822	253	4	the	the	DET
ejpam-2822	253	5	principle	principle	NOUN
ejpam-2822	253	6	of	of	ADP
ejpam-2822	253	7	mathematical	mathematical	ADJ
ejpam-2822	253	8	induction	induction	NOUN
ejpam-2822	253	9	our	our	PRON
ejpam-2822	253	10	claim	claim	NOUN
ejpam-2822	253	11	is	be	AUX
ejpam-2822	253	12	established	establish	VERB
ejpam-2822	253	13	for	for	ADP
ejpam-2822	253	14	every	every	DET
ejpam-2822	253	15	positive	positive	ADJ
ejpam-2822	253	16	integer	integer	NOUN
ejpam-2822	253	17	n.	n.	NOUN
ejpam-2822	253	18	now	now	ADV
ejpam-2822	253	19	,	,	PUNCT
ejpam-2822	253	20	let	let	VERB
ejpam-2822	253	21	n	n	PRON
ejpam-2822	253	22	=	=	PRON
ejpam-2822	253	23	c+	c+	X
ejpam-2822	253	24	d.	d.	PROPN
ejpam-2822	253	25	then	then	ADV
ejpam-2822	253	26	,	,	PUNCT
ejpam-2822	253	27	in	in	ADP
ejpam-2822	253	28	any	any	DET
ejpam-2822	253	29	commutator	commutator	NOUN
ejpam-2822	253	30	l	l	PROPN
ejpam-2822	253	31	-	-	NOUN
ejpam-2822	253	32	subgroup	subgroup	NOUN
ejpam-2822	253	33	of	of	ADP
ejpam-2822	253	34	the	the	DET
ejpam-2822	253	35	form	form	NOUN
ejpam-2822	253	36	[	[	X
ejpam-2822	253	37	λ1	λ1	ADJ
ejpam-2822	253	38	,	,	PUNCT
ejpam-2822	253	39	λ2	λ2	NOUN
ejpam-2822	253	40	,	,	PUNCT
ejpam-2822	253	41	...	...	PUNCT
ejpam-2822	253	42	,	,	PUNCT
ejpam-2822	253	43	λn+1	λn+1	PROPN
ejpam-2822	253	44	]	]	X
ejpam-2822	253	45	if	if	SCONJ
ejpam-2822	253	46	the	the	DET
ejpam-2822	253	47	number	number	NOUN
ejpam-2822	253	48	of	of	ADP
ejpam-2822	253	49	occurrences	occurrence	NOUN
ejpam-2822	253	50	of	of	ADP
ejpam-2822	253	51	η	η	PROPN
ejpam-2822	253	52	is	be	AUX
ejpam-2822	253	53	greater	great	ADJ
ejpam-2822	253	54	than	than	ADP
ejpam-2822	253	55	c	c	NOUN
ejpam-2822	253	56	,	,	PUNCT
ejpam-2822	253	57	then	then	ADV
ejpam-2822	253	58	by	by	ADP
ejpam-2822	253	59	lemma	lemma	PROPN
ejpam-2822	253	60	1	1	NUM
ejpam-2822	253	61	and	and	CCONJ
ejpam-2822	253	62	by	by	ADP
ejpam-2822	253	63	(	(	PUNCT
ejpam-2822	253	64	2	2	X
ejpam-2822	253	65	)	)	PUNCT
ejpam-2822	253	66	[	[	X
ejpam-2822	253	67	λ1	λ1	ADJ
ejpam-2822	253	68	,	,	PUNCT
ejpam-2822	253	69	λ2	λ2	NOUN
ejpam-2822	253	70	,	,	PUNCT
ejpam-2822	253	71	...	...	PUNCT
ejpam-2822	253	72	,	,	PUNCT
ejpam-2822	253	73	λn+1	λn+1	ADP
ejpam-2822	253	74	]	]	X
ejpam-2822	253	75	⊆	⊆	NUM
ejpam-2822	253	76	zc(η	zc(η	NUM
ejpam-2822	253	77	)	)	PUNCT
ejpam-2822	253	78	=	=	PUNCT
ejpam-2822	253	79	ηaot0	ηaot0	NOUN
ejpam-2822	253	80	.	.	PUNCT
ejpam-2822	254	1	on	on	ADP
ejpam-2822	254	2	the	the	DET
ejpam-2822	254	3	other	other	ADJ
ejpam-2822	254	4	hand	hand	NOUN
ejpam-2822	254	5	,	,	PUNCT
ejpam-2822	254	6	if	if	SCONJ
ejpam-2822	254	7	the	the	DET
ejpam-2822	254	8	number	number	NOUN
ejpam-2822	254	9	of	of	ADP
ejpam-2822	254	10	occurrences	occurrence	NOUN
ejpam-2822	254	11	of	of	ADP
ejpam-2822	254	12	η	η	PROPN
ejpam-2822	254	13	is	be	AUX
ejpam-2822	254	14	less	less	ADJ
ejpam-2822	254	15	than	than	ADP
ejpam-2822	254	16	or	or	CCONJ
ejpam-2822	254	17	equal	equal	ADJ
ejpam-2822	254	18	to	to	ADP
ejpam-2822	254	19	c	c	NOUN
ejpam-2822	254	20	,	,	PUNCT
ejpam-2822	254	21	then	then	ADV
ejpam-2822	254	22	the	the	DET
ejpam-2822	254	23	number	number	NOUN
ejpam-2822	254	24	of	of	ADP
ejpam-2822	254	25	occurrences	occurrence	NOUN
ejpam-2822	254	26	of	of	ADP
ejpam-2822	254	27	θ	θ	PROPN
ejpam-2822	254	28	is	be	AUX
ejpam-2822	254	29	greater	great	ADJ
ejpam-2822	254	30	than	than	ADP
ejpam-2822	254	31	or	or	CCONJ
ejpam-2822	254	32	equal	equal	ADJ
ejpam-2822	254	33	to	to	ADP
ejpam-2822	254	34	d	d	PROPN
ejpam-2822	254	35	+	+	NOUN
ejpam-2822	254	36	1	1	NUM
ejpam-2822	254	37	.	.	PUNCT
ejpam-2822	255	1	hence	hence	ADV
ejpam-2822	255	2	,	,	PUNCT
ejpam-2822	255	3	again	again	ADV
ejpam-2822	255	4	by	by	ADP
ejpam-2822	255	5	lemma	lemma	PROPN
ejpam-2822	255	6	1	1	NUM
ejpam-2822	255	7	and	and	CCONJ
ejpam-2822	255	8	by	by	ADP
ejpam-2822	255	9	(	(	PUNCT
ejpam-2822	255	10	2	2	X
ejpam-2822	255	11	)	)	PUNCT
ejpam-2822	255	12	[	[	X
ejpam-2822	255	13	λ1	λ1	ADJ
ejpam-2822	255	14	,	,	PUNCT
ejpam-2822	255	15	λ2	λ2	NOUN
ejpam-2822	255	16	,	,	PUNCT
ejpam-2822	255	17	...	...	PUNCT
ejpam-2822	255	18	,	,	PUNCT
ejpam-2822	255	19	λn+1	λn+1	ADP
ejpam-2822	255	20	]	]	X
ejpam-2822	255	21	⊆	⊆	NUM
ejpam-2822	255	22	zd(θ	zd(θ	NUM
ejpam-2822	255	23	)	)	PUNCT
ejpam-2822	255	24	=	=	SYM
ejpam-2822	255	25	θ	θ	PROPN
ejpam-2822	255	26	a∗o	a∗o	X
ejpam-2822	255	27	t0	t0	PROPN
ejpam-2822	255	28	.	.	PUNCT
ejpam-2822	256	1	thus	thus	ADV
ejpam-2822	256	2	,	,	PUNCT
ejpam-2822	256	3	each	each	DET
ejpam-2822	256	4	l	l	NOUN
ejpam-2822	256	5	-	-	NOUN
ejpam-2822	256	6	subgroup	subgroup	NOUN
ejpam-2822	256	7	of	of	ADP
ejpam-2822	256	8	the	the	DET
ejpam-2822	256	9	form	form	NOUN
ejpam-2822	256	10	[	[	X
ejpam-2822	256	11	λ1	λ1	ADJ
ejpam-2822	256	12	,	,	PUNCT
ejpam-2822	256	13	λ2	λ2	NOUN
ejpam-2822	256	14	,	,	PUNCT
ejpam-2822	256	15	...	...	PUNCT
ejpam-2822	256	16	,	,	PUNCT
ejpam-2822	256	17	λn+1	λn+1	PROPN
ejpam-2822	256	18	]	]	PUNCT
ejpam-2822	256	19	,	,	PUNCT
ejpam-2822	256	20	where	where	SCONJ
ejpam-2822	256	21	λi	λi	ADP
ejpam-2822	256	22	=	=	SYM
ejpam-2822	256	23	η	η	PROPN
ejpam-2822	256	24	or	or	CCONJ
ejpam-2822	256	25	θ	θ	PROPN
ejpam-2822	256	26	is	be	AUX
ejpam-2822	256	27	contained	contain	VERB
ejpam-2822	256	28	in	in	ADP
ejpam-2822	256	29	ηaot0	ηaot0	ADJ
ejpam-2822	256	30	or	or	CCONJ
ejpam-2822	256	31	θ	θ	PROPN
ejpam-2822	256	32	a∗o	a∗o	PROPN
ejpam-2822	256	33	t0	t0	PROPN
ejpam-2822	256	34	.	.	PUNCT
ejpam-2822	257	1	therefore	therefore	ADV
ejpam-2822	257	2	,	,	PUNCT
ejpam-2822	257	3	zk(η	zk(η	ADP
ejpam-2822	257	4	◦	◦	NOUN
ejpam-2822	257	5	θ	θ	NOUN
ejpam-2822	257	6	)	)	PUNCT
ejpam-2822	257	7	is	be	AUX
ejpam-2822	257	8	contained	contain	VERB
ejpam-2822	257	9	in	in	ADP
ejpam-2822	257	10	the	the	DET
ejpam-2822	257	11	set	set	NOUN
ejpam-2822	257	12	product	product	NOUN
ejpam-2822	257	13	of	of	ADP
ejpam-2822	257	14	finitely	finitely	ADV
ejpam-2822	257	15	many	many	ADJ
ejpam-2822	257	16	trivial	trivial	ADJ
ejpam-2822	257	17	l	l	NOUN
ejpam-2822	257	18	-	-	PUNCT
ejpam-2822	257	19	subgroups	subgroup	NOUN
ejpam-2822	257	20	ηaot0	ηaot0	ADJ
ejpam-2822	257	21	and	and	CCONJ
ejpam-2822	257	22	θ	θ	PROPN
ejpam-2822	257	23	a∗o	a∗o	PROPN
ejpam-2822	257	24	t0	t0	PROPN
ejpam-2822	257	25	.this	.this	PRON
ejpam-2822	257	26	product	product	NOUN
ejpam-2822	257	27	turns	turn	VERB
ejpam-2822	257	28	out	out	ADP
ejpam-2822	257	29	to	to	PART
ejpam-2822	257	30	be	be	AUX
ejpam-2822	257	31	ηaot0	ηaot0	ADJ
ejpam-2822	257	32	◦	◦	NOUN
ejpam-2822	257	33	θ	θ	NOUN
ejpam-2822	257	34	a∗o	a∗o	X
ejpam-2822	257	35	t0	t0	X
ejpam-2822	257	36	=	=	PUNCT
ejpam-2822	257	37	λ	λ	PROPN
ejpam-2822	257	38	a0∧a∗0	a0∧a∗0	PROPN
ejpam-2822	257	39	t0	t0	PROPN
ejpam-2822	257	40	.on	.on	PUNCT
ejpam-2822	258	1	the	the	DET
ejpam-2822	258	2	other	other	ADJ
ejpam-2822	258	3	hand	hand	NOUN
ejpam-2822	258	4	,	,	PUNCT
ejpam-2822	258	5	zn(η	zn(η	PUNCT
ejpam-2822	258	6	◦	◦	NOUN
ejpam-2822	258	7	θ)(e	θ)(e	NOUN
ejpam-2822	258	8	)	)	PUNCT
ejpam-2822	258	9	=	=	PUNCT
ejpam-2822	258	10	η	η	PROPN
ejpam-2822	258	11	◦	◦	PROPN
ejpam-2822	258	12	θ(e	θ(e	NUM
ejpam-2822	258	13	)	)	PUNCT
ejpam-2822	258	14	.	.	PUNCT
ejpam-2822	259	1	also	also	ADV
ejpam-2822	259	2	,	,	PUNCT
ejpam-2822	259	3	in	in	ADP
ejpam-2822	259	4	view	view	NOUN
ejpam-2822	259	5	of	of	ADP
ejpam-2822	259	6	(	(	PUNCT
ejpam-2822	259	7	1	1	NUM
ejpam-2822	259	8	)	)	PUNCT
ejpam-2822	259	9	and	and	CCONJ
ejpam-2822	259	10	(	(	PUNCT
ejpam-2822	259	11	3	3	X
ejpam-2822	259	12	)	)	PUNCT
ejpam-2822	259	13	infzn(η	infzn(η	NOUN
ejpam-2822	259	14	◦	◦	NOUN
ejpam-2822	259	15	θ	θ	NOUN
ejpam-2822	259	16	)	)	PUNCT
ejpam-2822	259	17	=	=	SYM
ejpam-2822	259	18	t0	t0	PROPN
ejpam-2822	259	19	.	.	PUNCT
ejpam-2822	260	1	this	this	PRON
ejpam-2822	260	2	implies	imply	VERB
ejpam-2822	260	3	λ	λ	PROPN
ejpam-2822	260	4	a0∧a∗0	a0∧a∗0	PROPN
ejpam-2822	260	5	t0	t0	PROPN
ejpam-2822	260	6	⊆	⊆	NUM
ejpam-2822	260	7	zn(η	zn(η	X
ejpam-2822	260	8	◦	◦	NOUN
ejpam-2822	260	9	θ	θ	NOUN
ejpam-2822	260	10	)	)	PUNCT
ejpam-2822	260	11	⊆	⊆	NUM
ejpam-2822	260	12	λa0∧a	λa0∧a	X
ejpam-2822	260	13	∗	∗	NOUN
ejpam-2822	260	14	0	0	NUM
ejpam-2822	260	15	t0	t0	NOUN
ejpam-2822	260	16	.	.	PUNCT
ejpam-2822	261	1	hence	hence	ADV
ejpam-2822	261	2	zn(η	zn(η	VERB
ejpam-2822	261	3	◦	◦	NOUN
ejpam-2822	261	4	θ	θ	NUM
ejpam-2822	261	5	)	)	PUNCT
ejpam-2822	261	6	=	=	SYM
ejpam-2822	261	7	λ	λ	X
ejpam-2822	261	8	a0∧a∗0	a0∧a∗0	PROPN
ejpam-2822	261	9	t0	t0	PROPN
ejpam-2822	261	10	.	.	PUNCT
ejpam-2822	262	1	below	below	ADP
ejpam-2822	262	2	we	we	PRON
ejpam-2822	262	3	illustrate	illustrate	VERB
ejpam-2822	262	4	the	the	DET
ejpam-2822	262	5	above	above	ADJ
ejpam-2822	262	6	theorem	theorem	NOUN
ejpam-2822	262	7	with	with	ADP
ejpam-2822	262	8	the	the	DET
ejpam-2822	262	9	help	help	NOUN
ejpam-2822	262	10	of	of	ADP
ejpam-2822	262	11	an	an	DET
ejpam-2822	262	12	example	example	NOUN
ejpam-2822	262	13	:	:	PUNCT
ejpam-2822	262	14	example	example	NOUN
ejpam-2822	262	15	4	4	X
ejpam-2822	262	16	.	.	PUNCT
ejpam-2822	263	1	let	let	VERB
ejpam-2822	263	2	g	g	PROPN
ejpam-2822	263	3	=	=	PROPN
ejpam-2822	263	4	q8	q8	PROPN
ejpam-2822	263	5	as	as	ADP
ejpam-2822	263	6	in	in	ADP
ejpam-2822	263	7	example	example	NOUN
ejpam-2822	263	8	1.let	1.let	NUM
ejpam-2822	263	9	l	l	NOUN
ejpam-2822	263	10	be	be	VERB
ejpam-2822	263	11	the	the	DET
ejpam-2822	263	12	evaluation	evaluation	NOUN
ejpam-2822	263	13	lattice	lattice	NOUN
ejpam-2822	263	14	given	give	VERB
ejpam-2822	263	15	by	by	ADP
ejpam-2822	263	16	the	the	DET
ejpam-2822	263	17	diagram	diagram	NOUN
ejpam-2822	263	18	:	:	PUNCT
ejpam-2822	263	19	i.	i.	PROPN
ejpam-2822	263	20	jahan	jahan	PROPN
ejpam-2822	263	21	,	,	PUNCT
ejpam-2822	263	22	n.	n.	PROPN
ejpam-2822	263	23	ajmal	ajmal	PROPN
ejpam-2822	263	24	,	,	PUNCT
ejpam-2822	263	25	b.	b.	PROPN
ejpam-2822	263	26	davvaz	davvaz	PROPN
ejpam-2822	263	27	/	/	SYM
ejpam-2822	263	28	eur	eur	PROPN
ejpam-2822	263	29	.	.	PUNCT
ejpam-2822	264	1	j.	j.	PROPN
ejpam-2822	264	2	pure	pure	PROPN
ejpam-2822	264	3	appl	appl	PROPN
ejpam-2822	264	4	.	.	PROPN
ejpam-2822	264	5	math	math	PROPN
ejpam-2822	264	6	,	,	PUNCT
ejpam-2822	264	7	10	10	NUM
ejpam-2822	264	8	(	(	PUNCT
ejpam-2822	264	9	2	2	NUM
ejpam-2822	264	10	)	)	PUNCT
ejpam-2822	264	11	(	(	PUNCT
ejpam-2822	264	12	2017	2017	NUM
ejpam-2822	264	13	)	)	PUNCT
ejpam-2822	264	14	,	,	PUNCT
ejpam-2822	264	15	255	255	NUM
ejpam-2822	264	16	-	-	SYM
ejpam-2822	264	17	271	271	NUM
ejpam-2822	264	18	268	268	NUM
ejpam-2822	264	19	let	let	VERB
ejpam-2822	264	20	c	c	NOUN
ejpam-2822	264	21	,	,	PUNCT
ejpam-2822	264	22	h1	h1	PROPN
ejpam-2822	264	23	,	,	PUNCT
ejpam-2822	264	24	h2	h2	NOUN
ejpam-2822	264	25	and	and	CCONJ
ejpam-2822	264	26	h3	h3	NOUN
ejpam-2822	264	27	be	be	VERB
ejpam-2822	264	28	the	the	DET
ejpam-2822	264	29	following	follow	VERB
ejpam-2822	264	30	subgroups	subgroup	NOUN
ejpam-2822	264	31	of	of	ADP
ejpam-2822	264	32	g	g	NOUN
ejpam-2822	264	33	:	:	PUNCT
ejpam-2822	264	34	c	c	X
ejpam-2822	264	35	=	=	SYM
ejpam-2822	264	36	{	{	PUNCT
ejpam-2822	264	37	±1	±1	NOUN
ejpam-2822	264	38	}	}	PUNCT
ejpam-2822	264	39	,	,	PUNCT
ejpam-2822	264	40	h1	h1	PROPN
ejpam-2822	264	41	=	=	SYM
ejpam-2822	264	42	{	{	PUNCT
ejpam-2822	264	43	±1,±i	±1,±i	ADV
ejpam-2822	264	44	}	}	PUNCT
ejpam-2822	264	45	,	,	PUNCT
ejpam-2822	264	46	h2	h2	NOUN
ejpam-2822	264	47	=	=	PUNCT
ejpam-2822	264	48	{	{	PUNCT
ejpam-2822	264	49	±1,±j	±1,±j	PROPN
ejpam-2822	264	50	}	}	PUNCT
ejpam-2822	264	51	,	,	PUNCT
ejpam-2822	264	52	h3	h3	NOUN
ejpam-2822	264	53	=	=	SYM
ejpam-2822	264	54	{	{	PUNCT
ejpam-2822	264	55	±1,±k	±1,±k	NOUN
ejpam-2822	264	56	}	}	PUNCT
ejpam-2822	264	57	.	.	PUNCT
ejpam-2822	265	1	consider	consider	VERB
ejpam-2822	265	2	the	the	DET
ejpam-2822	265	3	parent	parent	NOUN
ejpam-2822	265	4	l	l	NOUN
ejpam-2822	265	5	-	-	NOUN
ejpam-2822	265	6	subgroup	subgroup	NOUN
ejpam-2822	265	7	of	of	ADP
ejpam-2822	265	8	g	g	NOUN
ejpam-2822	265	9	,	,	PUNCT
ejpam-2822	265	10	defined	define	VERB
ejpam-2822	265	11	as	as	ADP
ejpam-2822	265	12	follows	follow	VERB
ejpam-2822	265	13	:	:	PUNCT
ejpam-2822	265	14	µ(x	µ(x	NUM
ejpam-2822	265	15	)	)	PUNCT
ejpam-2822	265	16	=	=	PRON
ejpam-2822	265	17	{	{	PUNCT
ejpam-2822	265	18	u	u	NOUN
ejpam-2822	265	19	if	if	SCONJ
ejpam-2822	265	20	x	x	SYM
ejpam-2822	265	21	=	=	SYM
ejpam-2822	265	22	1	1	NUM
ejpam-2822	265	23	,	,	PUNCT
ejpam-2822	265	24	d	d	NOUN
ejpam-2822	265	25	if	if	SCONJ
ejpam-2822	265	26	x	x	PROPN
ejpam-2822	265	27	∈	∈	PROPN
ejpam-2822	265	28	g	g	NOUN
ejpam-2822	265	29	\	\	PROPN
ejpam-2822	265	30	{	{	PUNCT
ejpam-2822	265	31	1	1	NUM
ejpam-2822	265	32	}	}	PUNCT
ejpam-2822	265	33	.	.	PUNCT
ejpam-2822	266	1	now	now	ADV
ejpam-2822	266	2	define	define	VERB
ejpam-2822	266	3	l	l	NOUN
ejpam-2822	266	4	-	-	PUNCT
ejpam-2822	266	5	subsets	subset	NOUN
ejpam-2822	266	6	η	η	PROPN
ejpam-2822	266	7	and	and	CCONJ
ejpam-2822	266	8	θ	θ	PROPN
ejpam-2822	266	9	of	of	ADP
ejpam-2822	266	10	g	g	PROPN
ejpam-2822	266	11	,	,	PUNCT
ejpam-2822	266	12	as	as	SCONJ
ejpam-2822	266	13	given	give	VERB
ejpam-2822	266	14	below	below	ADV
ejpam-2822	266	15	:	:	PUNCT
ejpam-2822	266	16	η(x	η(x	X
ejpam-2822	266	17	)	)	PUNCT
ejpam-2822	266	18	=	=	PUNCT
ejpam-2822	267	1			PUNCT
ejpam-2822	267	2	d	d	NOUN
ejpam-2822	267	3	if	if	SCONJ
ejpam-2822	267	4	x	x	PROPN
ejpam-2822	267	5	=	=	SYM
ejpam-2822	267	6	1	1	NUM
ejpam-2822	267	7	,	,	PUNCT
ejpam-2822	267	8	a	a	PRON
ejpam-2822	267	9	if	if	SCONJ
ejpam-2822	267	10	x	x	X
ejpam-2822	267	11	∈	∈	PROPN
ejpam-2822	267	12	h1	h1	PROPN
ejpam-2822	267	13	\	\	PROPN
ejpam-2822	267	14	{	{	PUNCT
ejpam-2822	267	15	1	1	NUM
ejpam-2822	267	16	}	}	PUNCT
ejpam-2822	267	17	,	,	PUNCT
ejpam-2822	267	18	f	f	PROPN
ejpam-2822	267	19	if	if	SCONJ
ejpam-2822	267	20	x	x	PROPN
ejpam-2822	267	21	∈	∈	PROPN
ejpam-2822	267	22	g	g	PROPN
ejpam-2822	267	23	\h1	\h1	PROPN
ejpam-2822	267	24	;	;	PUNCT
ejpam-2822	267	25	and	and	CCONJ
ejpam-2822	267	26	θ(x	θ(x	PROPN
ejpam-2822	267	27	)	)	PUNCT
ejpam-2822	267	28	=	=	PUNCT
ejpam-2822	268	1			PUNCT
ejpam-2822	268	2	u	u	NOUN
ejpam-2822	268	3	if	if	SCONJ
ejpam-2822	268	4	x	x	PROPN
ejpam-2822	268	5	=	=	SYM
ejpam-2822	268	6	1	1	NUM
ejpam-2822	268	7	,	,	PUNCT
ejpam-2822	268	8	b	b	NOUN
ejpam-2822	268	9	if	if	SCONJ
ejpam-2822	268	10	x	x	PROPN
ejpam-2822	268	11	∈	∈	PROPN
ejpam-2822	268	12	h2	h2	NOUN
ejpam-2822	268	13	\	\	PROPN
ejpam-2822	268	14	{	{	PUNCT
ejpam-2822	268	15	1	1	NUM
ejpam-2822	268	16	}	}	PUNCT
ejpam-2822	268	17	,	,	PUNCT
ejpam-2822	268	18	f	f	PROPN
ejpam-2822	268	19	if	if	SCONJ
ejpam-2822	268	20	x	x	PROPN
ejpam-2822	268	21	∈	∈	PROPN
ejpam-2822	268	22	g	g	NOUN
ejpam-2822	268	23	\h2	\h2	VERB
ejpam-2822	268	24	.	.	PUNCT
ejpam-2822	269	1	since	since	SCONJ
ejpam-2822	269	2	the	the	DET
ejpam-2822	269	3	level	level	NOUN
ejpam-2822	269	4	subsets	subset	NOUN
ejpam-2822	269	5	of	of	ADP
ejpam-2822	269	6	η	η	PROPN
ejpam-2822	269	7	are	be	AUX
ejpam-2822	269	8	normal	normal	ADJ
ejpam-2822	269	9	subgroups	subgroup	NOUN
ejpam-2822	269	10	of	of	ADP
ejpam-2822	269	11	g	g	PROPN
ejpam-2822	269	12	,	,	PUNCT
ejpam-2822	269	13	η	η	PROPN
ejpam-2822	269	14	is	be	AUX
ejpam-2822	269	15	a	a	DET
ejpam-2822	269	16	normal	normal	ADJ
ejpam-2822	269	17	l	l	NOUN
ejpam-2822	269	18	-	-	NOUN
ejpam-2822	269	19	subgroup	subgroup	NOUN
ejpam-2822	269	20	of	of	ADP
ejpam-2822	269	21	g.	g.	PROPN
ejpam-2822	269	22	similarly	similarly	ADV
ejpam-2822	269	23	,	,	PUNCT
ejpam-2822	269	24	it	it	PRON
ejpam-2822	269	25	can	can	AUX
ejpam-2822	269	26	be	be	AUX
ejpam-2822	269	27	seen	see	VERB
ejpam-2822	269	28	that	that	SCONJ
ejpam-2822	269	29	θ	θ	PROPN
ejpam-2822	269	30	is	be	AUX
ejpam-2822	269	31	also	also	ADV
ejpam-2822	269	32	a	a	DET
ejpam-2822	269	33	normal	normal	ADJ
ejpam-2822	269	34	l−subgroup	l−subgroup	NOUN
ejpam-2822	269	35	of	of	ADP
ejpam-2822	269	36	g	g	NOUN
ejpam-2822	269	37	and	and	CCONJ
ejpam-2822	269	38	hence	hence	ADV
ejpam-2822	269	39	of	of	ADP
ejpam-2822	269	40	µ.	µ.	PROPN
ejpam-2822	269	41	now	now	ADV
ejpam-2822	269	42	η	η	PROPN
ejpam-2822	269	43	is	be	AUX
ejpam-2822	269	44	a	a	DET
ejpam-2822	269	45	nilpotent	nilpotent	ADJ
ejpam-2822	269	46	l	l	NOUN
ejpam-2822	269	47	-	-	NOUN
ejpam-2822	269	48	subgroup	subgroup	NOUN
ejpam-2822	269	49	of	of	ADP
ejpam-2822	269	50	µ	µ	PROPN
ejpam-2822	269	51	,	,	PUNCT
ejpam-2822	269	52	in	in	ADP
ejpam-2822	269	53	view	view	NOUN
ejpam-2822	269	54	of	of	ADP
ejpam-2822	269	55	the	the	DET
ejpam-2822	269	56	definition	definition	NOUN
ejpam-2822	269	57	3.5	3.5	NUM
ejpam-2822	269	58	follows	follow	VERB
ejpam-2822	269	59	as	as	SCONJ
ejpam-2822	269	60	given	give	VERB
ejpam-2822	269	61	below	below	ADV
ejpam-2822	269	62	:	:	PUNCT
ejpam-2822	269	63	note	note	VERB
ejpam-2822	269	64	that	that	SCONJ
ejpam-2822	269	65	g′	g′	NOUN
ejpam-2822	269	66	=	=	SYM
ejpam-2822	269	67	c.	c.	NOUN
ejpam-2822	270	1	in	in	ADP
ejpam-2822	270	2	order	order	NOUN
ejpam-2822	270	3	to	to	PART
ejpam-2822	270	4	obtain	obtain	VERB
ejpam-2822	270	5	the	the	DET
ejpam-2822	270	6	members	member	NOUN
ejpam-2822	270	7	of	of	ADP
ejpam-2822	270	8	descending	descend	VERB
ejpam-2822	270	9	central	central	ADJ
ejpam-2822	270	10	series	series	NOUN
ejpam-2822	270	11	,	,	PUNCT
ejpam-2822	270	12	we	we	PRON
ejpam-2822	270	13	start	start	VERB
ejpam-2822	270	14	with	with	ADP
ejpam-2822	270	15	z0(η	z0(η	NOUN
ejpam-2822	270	16	)	)	PUNCT
ejpam-2822	270	17	=	=	SYM
ejpam-2822	271	1	η	η	PROPN
ejpam-2822	271	2	.	.	PROPN
ejpam-2822	271	3	next	next	ADV
ejpam-2822	271	4	consider	consider	VERB
ejpam-2822	271	5	the	the	DET
ejpam-2822	271	6	commutator	commutator	NOUN
ejpam-2822	271	7	(	(	PUNCT
ejpam-2822	271	8	η	η	PROPN
ejpam-2822	271	9	,	,	PUNCT
ejpam-2822	271	10	η	η	PROPN
ejpam-2822	271	11	):	):	PUNCT
ejpam-2822	271	12	(	(	PUNCT
ejpam-2822	271	13	η	η	PROPN
ejpam-2822	271	14	,	,	PUNCT
ejpam-2822	271	15	η	η	NOUN
ejpam-2822	271	16	)	)	PUNCT
ejpam-2822	271	17	(	(	PUNCT
ejpam-2822	271	18	x	x	X
ejpam-2822	271	19	)	)	PUNCT
ejpam-2822	271	20	=	=	PRON
ejpam-2822	272	1	{	{	PUNCT
ejpam-2822	272	2	d	d	X
ejpam-2822	272	3	if	if	SCONJ
ejpam-2822	272	4	x	x	X
ejpam-2822	272	5	=	=	SYM
ejpam-2822	272	6	1	1	NUM
ejpam-2822	272	7	,	,	PUNCT
ejpam-2822	272	8	f	f	PROPN
ejpam-2822	272	9	if	if	SCONJ
ejpam-2822	272	10	x	x	PROPN
ejpam-2822	272	11	∈	∈	PROPN
ejpam-2822	272	12	g	g	NOUN
ejpam-2822	272	13	\	\	PROPN
ejpam-2822	272	14	{	{	PUNCT
ejpam-2822	272	15	1	1	NUM
ejpam-2822	272	16	}	}	PUNCT
ejpam-2822	272	17	.	.	PUNCT
ejpam-2822	273	1	as	as	SCONJ
ejpam-2822	273	2	the	the	DET
ejpam-2822	273	3	level	level	NOUN
ejpam-2822	273	4	subsets	subset	NOUN
ejpam-2822	273	5	of	of	ADP
ejpam-2822	273	6	(	(	PUNCT
ejpam-2822	273	7	η	η	PROPN
ejpam-2822	273	8	,	,	PUNCT
ejpam-2822	273	9	η	η	NOUN
ejpam-2822	273	10	)	)	PUNCT
ejpam-2822	273	11	are	be	AUX
ejpam-2822	273	12	subgroups	subgroup	NOUN
ejpam-2822	273	13	,	,	PUNCT
ejpam-2822	273	14	z1(η	z1(η	PROPN
ejpam-2822	273	15	)	)	PUNCT
ejpam-2822	273	16	=	=	PUNCT
ejpam-2822	274	1	[	[	X
ejpam-2822	274	2	η	η	PROPN
ejpam-2822	274	3	,	,	PUNCT
ejpam-2822	274	4	η	η	PROPN
ejpam-2822	274	5	]	]	X
ejpam-2822	274	6	=	=	SYM
ejpam-2822	274	7	(	(	PUNCT
ejpam-2822	274	8	η	η	PROPN
ejpam-2822	274	9	,	,	PUNCT
ejpam-2822	274	10	η	η	NOUN
ejpam-2822	274	11	)	)	PUNCT
ejpam-2822	274	12	.	.	PUNCT
ejpam-2822	275	1	note	note	VERB
ejpam-2822	275	2	that	that	SCONJ
ejpam-2822	275	3	z1(η	z1(η	X
ejpam-2822	275	4	)	)	PUNCT
ejpam-2822	275	5	is	be	AUX
ejpam-2822	275	6	the	the	DET
ejpam-2822	275	7	trivial	trivial	ADJ
ejpam-2822	275	8	l	l	NOUN
ejpam-2822	275	9	-	-	NOUN
ejpam-2822	275	10	subgroup	subgroup	NOUN
ejpam-2822	275	11	ηdf	ηdf	PROPN
ejpam-2822	275	12	of	of	ADP
ejpam-2822	275	13	η	η	PROPN
ejpam-2822	275	14	and	and	CCONJ
ejpam-2822	275	15	so	so	ADV
ejpam-2822	275	16	the	the	DET
ejpam-2822	275	17	descending	descend	VERB
ejpam-2822	275	18	central	central	ADJ
ejpam-2822	275	19	series	series	NOUN
ejpam-2822	275	20	terminates	terminate	VERB
ejpam-2822	275	21	at	at	ADP
ejpam-2822	275	22	z1(η	z1(η	PROPN
ejpam-2822	275	23	)	)	PUNCT
ejpam-2822	275	24	i.e.	i.e.	X
ejpam-2822	275	25	η	η	X
ejpam-2822	275	26	=	=	PROPN
ejpam-2822	275	27	z0(η	z0(η	PROPN
ejpam-2822	275	28	)	)	PUNCT
ejpam-2822	275	29	⊇	⊇	PROPN
ejpam-2822	275	30	z1(η	z1(η	PROPN
ejpam-2822	275	31	)	)	PUNCT
ejpam-2822	276	1	=	=	SYM
ejpam-2822	276	2	ηdf	ηdf	PROPN
ejpam-2822	276	3	.	.	PUNCT
ejpam-2822	277	1	consequently	consequently	ADV
ejpam-2822	277	2	η	η	PROPN
ejpam-2822	277	3	is	be	AUX
ejpam-2822	277	4	a	a	DET
ejpam-2822	277	5	nilpotent	nilpotent	ADJ
ejpam-2822	277	6	l−subgroup	l−subgroup	X
ejpam-2822	277	7	of	of	ADP
ejpam-2822	277	8	µ	µ	PRON
ejpam-2822	277	9	having	have	VERB
ejpam-2822	277	10	nilpotent	nilpotent	ADJ
ejpam-2822	277	11	length	length	NOUN
ejpam-2822	277	12	1	1	NUM
ejpam-2822	277	13	.	.	PUNCT
ejpam-2822	278	1	similarly	similarly	ADV
ejpam-2822	278	2	it	it	PRON
ejpam-2822	278	3	can	can	AUX
ejpam-2822	278	4	be	be	AUX
ejpam-2822	278	5	shown	show	VERB
ejpam-2822	278	6	that	that	SCONJ
ejpam-2822	278	7	θ	θ	PROPN
ejpam-2822	278	8	is	be	AUX
ejpam-2822	278	9	also	also	ADV
ejpam-2822	278	10	a	a	DET
ejpam-2822	278	11	nilpotent	nilpotent	ADJ
ejpam-2822	278	12	l−subgroup	l−subgroup	X
ejpam-2822	278	13	of	of	ADP
ejpam-2822	278	14	µ	µ	PRON
ejpam-2822	278	15	having	have	VERB
ejpam-2822	278	16	nilpotent	nilpotent	ADJ
ejpam-2822	278	17	length	length	NOUN
ejpam-2822	278	18	1	1	NUM
ejpam-2822	278	19	.	.	PUNCT
ejpam-2822	279	1	next	next	ADV
ejpam-2822	279	2	,	,	PUNCT
ejpam-2822	279	3	we	we	PRON
ejpam-2822	279	4	exhibit	exhibit	VERB
ejpam-2822	279	5	the	the	DET
ejpam-2822	279	6	set	set	ADJ
ejpam-2822	279	7	product	product	NOUN
ejpam-2822	279	8	of	of	ADP
ejpam-2822	279	9	l	l	NOUN
ejpam-2822	279	10	-	-	PUNCT
ejpam-2822	279	11	subgroups	subgroup	NOUN
ejpam-2822	279	12	η	η	PROPN
ejpam-2822	279	13	and	and	CCONJ
ejpam-2822	279	14	θ	θ	PROPN
ejpam-2822	279	15	.	.	PUNCT
ejpam-2822	280	1	it	it	PRON
ejpam-2822	280	2	can	can	AUX
ejpam-2822	280	3	be	be	AUX
ejpam-2822	280	4	verified	verify	VERB
ejpam-2822	280	5	that	that	SCONJ
ejpam-2822	280	6	η	η	PROPN
ejpam-2822	280	7	◦	◦	NOUN
ejpam-2822	280	8	θ	θ	X
ejpam-2822	280	9	=	=	SYM
ejpam-2822	280	10	θ	θ	PROPN
ejpam-2822	280	11	◦	◦	NOUN
ejpam-2822	280	12	η	η	PROPN
ejpam-2822	280	13	=	=	SYM
ejpam-2822	280	14	φ	φ	PROPN
ejpam-2822	280	15	,	,	PUNCT
ejpam-2822	280	16	i.	i.	PROPN
ejpam-2822	280	17	jahan	jahan	PROPN
ejpam-2822	280	18	,	,	PUNCT
ejpam-2822	280	19	n.	n.	PROPN
ejpam-2822	280	20	ajmal	ajmal	PROPN
ejpam-2822	280	21	,	,	PUNCT
ejpam-2822	280	22	b.	b.	PROPN
ejpam-2822	280	23	davvaz	davvaz	PROPN
ejpam-2822	280	24	/	/	SYM
ejpam-2822	280	25	eur	eur	PROPN
ejpam-2822	280	26	.	.	PUNCT
ejpam-2822	281	1	j.	j.	PROPN
ejpam-2822	281	2	pure	pure	PROPN
ejpam-2822	281	3	appl	appl	PROPN
ejpam-2822	281	4	.	.	PROPN
ejpam-2822	281	5	math	math	PROPN
ejpam-2822	281	6	,	,	PUNCT
ejpam-2822	281	7	10	10	NUM
ejpam-2822	281	8	(	(	PUNCT
ejpam-2822	281	9	2	2	NUM
ejpam-2822	281	10	)	)	PUNCT
ejpam-2822	281	11	(	(	PUNCT
ejpam-2822	281	12	2017	2017	NUM
ejpam-2822	281	13	)	)	PUNCT
ejpam-2822	281	14	,	,	PUNCT
ejpam-2822	281	15	255	255	NUM
ejpam-2822	281	16	-	-	SYM
ejpam-2822	281	17	271	271	NUM
ejpam-2822	281	18	269	269	NUM
ejpam-2822	281	19	where	where	SCONJ
ejpam-2822	281	20	φ	φ	PROPN
ejpam-2822	281	21	is	be	AUX
ejpam-2822	281	22	the	the	DET
ejpam-2822	281	23	l−subgroup	l−subgroup	PROPN
ejpam-2822	281	24	of	of	ADP
ejpam-2822	281	25	µ	µ	NOUN
ejpam-2822	281	26	given	give	VERB
ejpam-2822	281	27	by	by	ADP
ejpam-2822	281	28	φ(x	φ(x	NOUN
ejpam-2822	281	29	)	)	PUNCT
ejpam-2822	281	30	=	=	PUNCT
ejpam-2822	282	1			PUNCT
ejpam-2822	283	1	d	d	NOUN
ejpam-2822	283	2	if	if	SCONJ
ejpam-2822	283	3	x	x	X
ejpam-2822	283	4	∈	∈	PROPN
ejpam-2822	283	5	c	c	NOUN
ejpam-2822	283	6	,	,	PUNCT
ejpam-2822	283	7	a	a	DET
ejpam-2822	283	8	if	if	SCONJ
ejpam-2822	283	9	x	x	X
ejpam-2822	283	10	∈	∈	PROPN
ejpam-2822	283	11	h1	h1	PROPN
ejpam-2822	283	12	\	\	PROPN
ejpam-2822	283	13	c	c	PROPN
ejpam-2822	283	14	,	,	PUNCT
ejpam-2822	283	15	b	b	NOUN
ejpam-2822	284	1	if	if	SCONJ
ejpam-2822	284	2	x	x	PROPN
ejpam-2822	284	3	∈	∈	PROPN
ejpam-2822	284	4	h2	h2	NOUN
ejpam-2822	284	5	\	\	PROPN
ejpam-2822	284	6	c	c	PROPN
ejpam-2822	284	7	,	,	PUNCT
ejpam-2822	284	8	f	f	PROPN
ejpam-2822	284	9	if	if	SCONJ
ejpam-2822	284	10	x	x	PROPN
ejpam-2822	284	11	∈	∈	PROPN
ejpam-2822	284	12	g	g	PROPN
ejpam-2822	284	13	\	\	PROPN
ejpam-2822	284	14	{	{	PUNCT
ejpam-2822	284	15	h1	h1	NOUN
ejpam-2822	284	16	∪h2	∪h2	NOUN
ejpam-2822	284	17	}	}	PUNCT
ejpam-2822	284	18	.	.	PUNCT
ejpam-2822	285	1	note	note	VERB
ejpam-2822	285	2	that	that	SCONJ
ejpam-2822	285	3	here	here	ADV
ejpam-2822	285	4	infη	infη	PROPN
ejpam-2822	285	5	=	=	SYM
ejpam-2822	285	6	infθ	infθ	NOUN
ejpam-2822	285	7	=	=	PUNCT
ejpam-2822	285	8	infη	infη	ADJ
ejpam-2822	285	9	◦	◦	NOUN
ejpam-2822	285	10	θ	θ	NOUN
ejpam-2822	285	11	.	.	PUNCT
ejpam-2822	285	12	hence	hence	ADV
ejpam-2822	285	13	in	in	ADP
ejpam-2822	285	14	view	view	NOUN
ejpam-2822	285	15	of	of	ADP
ejpam-2822	285	16	the	the	DET
ejpam-2822	285	17	above	above	ADJ
ejpam-2822	285	18	theorem	theorem	ADJ
ejpam-2822	285	19	η	η	PROPN
ejpam-2822	285	20	◦	◦	PROPN
ejpam-2822	285	21	θ	θ	PROPN
ejpam-2822	285	22	is	be	AUX
ejpam-2822	285	23	a	a	DET
ejpam-2822	285	24	nilpotent	nilpotent	ADJ
ejpam-2822	285	25	l	l	NOUN
ejpam-2822	285	26	-	-	NOUN
ejpam-2822	285	27	subgroup	subgroup	NOUN
ejpam-2822	285	28	of	of	ADP
ejpam-2822	285	29	µ.	µ.	PROPN
ejpam-2822	285	30	the	the	DET
ejpam-2822	285	31	following	follow	VERB
ejpam-2822	285	32	example	example	NOUN
ejpam-2822	285	33	exhibits	exhibit	VERB
ejpam-2822	285	34	that	that	SCONJ
ejpam-2822	285	35	the	the	DET
ejpam-2822	285	36	condition	condition	NOUN
ejpam-2822	285	37	infη	infη	NOUN
ejpam-2822	285	38	=	=	SYM
ejpam-2822	285	39	infθ	infθ	NOUN
ejpam-2822	285	40	=	=	PUNCT
ejpam-2822	285	41	infη	infη	ADJ
ejpam-2822	285	42	◦	◦	NOUN
ejpam-2822	285	43	θ	θ	PROPN
ejpam-2822	285	44	is	be	AUX
ejpam-2822	285	45	only	only	ADV
ejpam-2822	285	46	sufficient	sufficient	ADJ
ejpam-2822	285	47	:	:	PUNCT
ejpam-2822	285	48	example	example	NOUN
ejpam-2822	285	49	5	5	X
ejpam-2822	285	50	.	.	PUNCT
ejpam-2822	286	1	let	let	VERB
ejpam-2822	286	2	g	g	PROPN
ejpam-2822	286	3	=	=	PROPN
ejpam-2822	286	4	q8	q8	PROPN
ejpam-2822	286	5	as	as	ADP
ejpam-2822	286	6	in	in	ADP
ejpam-2822	286	7	example	example	NOUN
ejpam-2822	286	8	1.let	1.let	NUM
ejpam-2822	286	9	l	l	NOUN
ejpam-2822	286	10	be	be	VERB
ejpam-2822	286	11	the	the	DET
ejpam-2822	286	12	evaluation	evaluation	NOUN
ejpam-2822	286	13	lattice	lattice	NOUN
ejpam-2822	286	14	given	give	VERB
ejpam-2822	286	15	by	by	ADP
ejpam-2822	286	16	the	the	DET
ejpam-2822	286	17	diagram	diagram	NOUN
ejpam-2822	286	18	:	:	PUNCT
ejpam-2822	286	19	let	let	VERB
ejpam-2822	286	20	c	c	X
ejpam-2822	286	21	,	,	PUNCT
ejpam-2822	286	22	h1	h1	PROPN
ejpam-2822	286	23	,	,	PUNCT
ejpam-2822	286	24	h2	h2	NOUN
ejpam-2822	286	25	and	and	CCONJ
ejpam-2822	286	26	h3	h3	NOUN
ejpam-2822	286	27	be	be	VERB
ejpam-2822	286	28	the	the	DET
ejpam-2822	286	29	following	follow	VERB
ejpam-2822	286	30	subgroups	subgroup	NOUN
ejpam-2822	286	31	of	of	ADP
ejpam-2822	286	32	g	g	NOUN
ejpam-2822	286	33	:	:	PUNCT
ejpam-2822	286	34	c	c	X
ejpam-2822	286	35	=	=	SYM
ejpam-2822	286	36	{	{	PUNCT
ejpam-2822	286	37	±1	±1	NOUN
ejpam-2822	286	38	}	}	PUNCT
ejpam-2822	286	39	,	,	PUNCT
ejpam-2822	286	40	h1	h1	PROPN
ejpam-2822	286	41	=	=	SYM
ejpam-2822	286	42	{	{	PUNCT
ejpam-2822	286	43	±1,±i	±1,±i	ADV
ejpam-2822	286	44	}	}	PUNCT
ejpam-2822	286	45	,	,	PUNCT
ejpam-2822	286	46	h2	h2	NOUN
ejpam-2822	286	47	=	=	PUNCT
ejpam-2822	286	48	{	{	PUNCT
ejpam-2822	286	49	±1,±j	±1,±j	PROPN
ejpam-2822	286	50	}	}	PUNCT
ejpam-2822	286	51	,	,	PUNCT
ejpam-2822	286	52	h3	h3	NOUN
ejpam-2822	286	53	=	=	SYM
ejpam-2822	286	54	{	{	PUNCT
ejpam-2822	286	55	±1,±k	±1,±k	NOUN
ejpam-2822	286	56	}	}	PUNCT
ejpam-2822	286	57	.	.	PUNCT
ejpam-2822	287	1	consider	consider	VERB
ejpam-2822	287	2	the	the	DET
ejpam-2822	287	3	parent	parent	NOUN
ejpam-2822	287	4	l	l	NOUN
ejpam-2822	287	5	-	-	NOUN
ejpam-2822	287	6	subgroup	subgroup	NOUN
ejpam-2822	287	7	of	of	ADP
ejpam-2822	287	8	g	g	NOUN
ejpam-2822	287	9	,	,	PUNCT
ejpam-2822	287	10	defined	define	VERB
ejpam-2822	287	11	as	as	ADP
ejpam-2822	287	12	follows	follow	VERB
ejpam-2822	287	13	:	:	PUNCT
ejpam-2822	287	14	µ(x	µ(x	NUM
ejpam-2822	287	15	)	)	PUNCT
ejpam-2822	287	16	=	=	PRON
ejpam-2822	287	17	{	{	PUNCT
ejpam-2822	287	18	u	u	NOUN
ejpam-2822	287	19	if	if	SCONJ
ejpam-2822	287	20	x	x	SYM
ejpam-2822	287	21	=	=	SYM
ejpam-2822	287	22	1	1	NUM
ejpam-2822	287	23	,	,	PUNCT
ejpam-2822	287	24	d	d	NOUN
ejpam-2822	287	25	if	if	SCONJ
ejpam-2822	287	26	x	x	PROPN
ejpam-2822	287	27	∈	∈	PROPN
ejpam-2822	287	28	g	g	NOUN
ejpam-2822	287	29	\	\	PROPN
ejpam-2822	287	30	{	{	PUNCT
ejpam-2822	287	31	1	1	NUM
ejpam-2822	287	32	}	}	PUNCT
ejpam-2822	287	33	.	.	PUNCT
ejpam-2822	288	1	now	now	ADV
ejpam-2822	288	2	define	define	VERB
ejpam-2822	288	3	l	l	NOUN
ejpam-2822	288	4	-	-	PUNCT
ejpam-2822	288	5	subsets	subset	NOUN
ejpam-2822	288	6	η	η	PROPN
ejpam-2822	288	7	,	,	PUNCT
ejpam-2822	288	8	and	and	CCONJ
ejpam-2822	288	9	θ	θ	PROPN
ejpam-2822	288	10	of	of	ADP
ejpam-2822	288	11	g	g	PROPN
ejpam-2822	288	12	,	,	PUNCT
ejpam-2822	288	13	as	as	SCONJ
ejpam-2822	288	14	given	give	VERB
ejpam-2822	288	15	below	below	ADV
ejpam-2822	288	16	:	:	PUNCT
ejpam-2822	288	17	η(x	η(x	X
ejpam-2822	288	18	)	)	PUNCT
ejpam-2822	288	19	=	=	SYM
ejpam-2822	289	1			PUNCT
ejpam-2822	290	1	d	d	NOUN
ejpam-2822	290	2	if	if	SCONJ
ejpam-2822	290	3	x	x	X
ejpam-2822	290	4	∈	∈	PROPN
ejpam-2822	290	5	c	c	NOUN
ejpam-2822	290	6	,	,	PUNCT
ejpam-2822	290	7	a	a	DET
ejpam-2822	290	8	if	if	SCONJ
ejpam-2822	290	9	x	x	X
ejpam-2822	290	10	∈	∈	PROPN
ejpam-2822	290	11	h1	h1	PROPN
ejpam-2822	290	12	\	\	PROPN
ejpam-2822	290	13	c	c	PROPN
ejpam-2822	290	14	,	,	PUNCT
ejpam-2822	290	15	b	b	NOUN
ejpam-2822	291	1	if	if	SCONJ
ejpam-2822	291	2	x	x	PROPN
ejpam-2822	291	3	∈	∈	PROPN
ejpam-2822	291	4	h2	h2	NOUN
ejpam-2822	291	5	\	\	PROPN
ejpam-2822	291	6	c	c	PROPN
ejpam-2822	291	7	,	,	PUNCT
ejpam-2822	291	8	f	f	PROPN
ejpam-2822	291	9	if	if	SCONJ
ejpam-2822	291	10	x	x	PROPN
ejpam-2822	291	11	∈	∈	PROPN
ejpam-2822	291	12	g	g	PROPN
ejpam-2822	291	13	\	\	PROPN
ejpam-2822	291	14	{	{	PUNCT
ejpam-2822	291	15	h1	h1	NOUN
ejpam-2822	291	16	∪h2	∪h2	NOUN
ejpam-2822	291	17	}	}	PUNCT
ejpam-2822	291	18	;	;	PUNCT
ejpam-2822	291	19	and	and	CCONJ
ejpam-2822	291	20	θ(x	θ(x	PROPN
ejpam-2822	291	21	)	)	PUNCT
ejpam-2822	291	22	=	=	PUNCT
ejpam-2822	291	23			PUNCT
ejpam-2822	292	1	d	d	NOUN
ejpam-2822	292	2	if	if	SCONJ
ejpam-2822	292	3	x	x	X
ejpam-2822	292	4	∈	∈	PROPN
ejpam-2822	292	5	c	c	NOUN
ejpam-2822	292	6	,	,	PUNCT
ejpam-2822	292	7	a	a	DET
ejpam-2822	292	8	if	if	SCONJ
ejpam-2822	292	9	x	x	X
ejpam-2822	292	10	∈	∈	PROPN
ejpam-2822	292	11	h1	h1	PROPN
ejpam-2822	292	12	\	\	PROPN
ejpam-2822	292	13	c	c	PROPN
ejpam-2822	292	14	,	,	PUNCT
ejpam-2822	292	15	b	b	NOUN
ejpam-2822	292	16	if	if	SCONJ
ejpam-2822	292	17	x	x	PROPN
ejpam-2822	292	18	∈	∈	NOUN
ejpam-2822	292	19	h3	h3	NOUN
ejpam-2822	292	20	\	\	NOUN
ejpam-2822	292	21	c	c	NOUN
ejpam-2822	292	22	,	,	PUNCT
ejpam-2822	292	23	f	f	PROPN
ejpam-2822	293	1	if	if	SCONJ
ejpam-2822	293	2	x	x	PROPN
ejpam-2822	293	3	∈	∈	PROPN
ejpam-2822	293	4	g	g	PROPN
ejpam-2822	293	5	\	\	PROPN
ejpam-2822	293	6	{	{	PUNCT
ejpam-2822	293	7	h1	h1	VERB
ejpam-2822	293	8	∪h3	∪h3	NOUN
ejpam-2822	293	9	}	}	PUNCT
ejpam-2822	293	10	.	.	PUNCT
ejpam-2822	294	1	references	reference	NOUN
ejpam-2822	294	2	270	270	NUM
ejpam-2822	294	3	since	since	SCONJ
ejpam-2822	294	4	the	the	DET
ejpam-2822	294	5	level	level	NOUN
ejpam-2822	294	6	subsets	subset	NOUN
ejpam-2822	294	7	of	of	ADP
ejpam-2822	294	8	η	η	PROPN
ejpam-2822	294	9	are	be	AUX
ejpam-2822	294	10	normal	normal	ADJ
ejpam-2822	294	11	subgroups	subgroup	NOUN
ejpam-2822	294	12	of	of	ADP
ejpam-2822	294	13	g	g	PROPN
ejpam-2822	294	14	,	,	PUNCT
ejpam-2822	294	15	η	η	PROPN
ejpam-2822	294	16	is	be	AUX
ejpam-2822	294	17	a	a	DET
ejpam-2822	294	18	normal	normal	ADJ
ejpam-2822	294	19	l	l	NOUN
ejpam-2822	294	20	-	-	NOUN
ejpam-2822	294	21	subgroup	subgroup	NOUN
ejpam-2822	294	22	of	of	ADP
ejpam-2822	294	23	g.	g.	PROPN
ejpam-2822	294	24	similarly	similarly	ADV
ejpam-2822	294	25	,	,	PUNCT
ejpam-2822	294	26	it	it	PRON
ejpam-2822	294	27	can	can	AUX
ejpam-2822	294	28	be	be	AUX
ejpam-2822	294	29	seen	see	VERB
ejpam-2822	294	30	that	that	SCONJ
ejpam-2822	294	31	θ	θ	PROPN
ejpam-2822	294	32	is	be	AUX
ejpam-2822	294	33	also	also	ADV
ejpam-2822	294	34	a	a	DET
ejpam-2822	294	35	normal	normal	ADJ
ejpam-2822	294	36	l−subgroup	l−subgroup	NOUN
ejpam-2822	294	37	of	of	ADP
ejpam-2822	294	38	g	g	NOUN
ejpam-2822	294	39	and	and	CCONJ
ejpam-2822	294	40	hence	hence	ADV
ejpam-2822	294	41	of	of	ADP
ejpam-2822	294	42	µ.	µ.	NOUN
ejpam-2822	294	43	now	now	ADV
ejpam-2822	294	44	that	that	SCONJ
ejpam-2822	294	45	η	η	PROPN
ejpam-2822	294	46	is	be	AUX
ejpam-2822	294	47	a	a	DET
ejpam-2822	294	48	nilpotent	nilpotent	ADJ
ejpam-2822	294	49	l	l	NOUN
ejpam-2822	294	50	-	-	NOUN
ejpam-2822	294	51	subgroup	subgroup	NOUN
ejpam-2822	294	52	of	of	ADP
ejpam-2822	294	53	µ	µ	PROPN
ejpam-2822	294	54	,	,	PUNCT
ejpam-2822	294	55	in	in	ADP
ejpam-2822	294	56	view	view	NOUN
ejpam-2822	294	57	of	of	ADP
ejpam-2822	294	58	the	the	DET
ejpam-2822	294	59	definition	definition	NOUN
ejpam-2822	294	60	3.5	3.5	NUM
ejpam-2822	294	61	,	,	PUNCT
ejpam-2822	294	62	can	can	AUX
ejpam-2822	294	63	be	be	AUX
ejpam-2822	294	64	seen	see	VERB
ejpam-2822	294	65	as	as	SCONJ
ejpam-2822	294	66	follows	follow	VERB
ejpam-2822	294	67	:	:	PUNCT
ejpam-2822	294	68	note	note	VERB
ejpam-2822	295	1	that	that	SCONJ
ejpam-2822	295	2	g′	g′	NOUN
ejpam-2822	295	3	=	=	SYM
ejpam-2822	295	4	c.	c.	NOUN
ejpam-2822	295	5	in	in	ADP
ejpam-2822	295	6	order	order	NOUN
ejpam-2822	295	7	to	to	PART
ejpam-2822	295	8	obtain	obtain	VERB
ejpam-2822	295	9	the	the	DET
ejpam-2822	295	10	members	member	NOUN
ejpam-2822	295	11	of	of	ADP
ejpam-2822	295	12	descending	descend	VERB
ejpam-2822	295	13	central	central	ADJ
ejpam-2822	295	14	series	series	NOUN
ejpam-2822	295	15	,	,	PUNCT
ejpam-2822	295	16	we	we	PRON
ejpam-2822	295	17	start	start	VERB
ejpam-2822	295	18	with	with	ADP
ejpam-2822	295	19	z0(η	z0(η	NOUN
ejpam-2822	295	20	)	)	PUNCT
ejpam-2822	295	21	=	=	SYM
ejpam-2822	295	22	η	η	PROPN
ejpam-2822	295	23	.	.	PROPN
ejpam-2822	295	24	next	next	ADV
ejpam-2822	295	25	consider	consider	VERB
ejpam-2822	295	26	the	the	DET
ejpam-2822	295	27	commutator	commutator	NOUN
ejpam-2822	295	28	(	(	PUNCT
ejpam-2822	295	29	η	η	PROPN
ejpam-2822	295	30	,	,	PUNCT
ejpam-2822	295	31	η	η	PROPN
ejpam-2822	295	32	):	):	PUNCT
ejpam-2822	295	33	(	(	PUNCT
ejpam-2822	295	34	η	η	PROPN
ejpam-2822	295	35	,	,	PUNCT
ejpam-2822	295	36	η	η	NOUN
ejpam-2822	295	37	)	)	PUNCT
ejpam-2822	295	38	(	(	PUNCT
ejpam-2822	295	39	x	x	X
ejpam-2822	295	40	)	)	PUNCT
ejpam-2822	295	41	=	=	PRON
ejpam-2822	296	1	{	{	PUNCT
ejpam-2822	296	2	d	d	X
ejpam-2822	296	3	if	if	SCONJ
ejpam-2822	296	4	x	x	X
ejpam-2822	296	5	=	=	SYM
ejpam-2822	296	6	1	1	NUM
ejpam-2822	296	7	,	,	PUNCT
ejpam-2822	296	8	f	f	PROPN
ejpam-2822	296	9	if	if	SCONJ
ejpam-2822	296	10	x	x	PROPN
ejpam-2822	296	11	∈	∈	PROPN
ejpam-2822	296	12	g	g	NOUN
ejpam-2822	296	13	\	\	PROPN
ejpam-2822	296	14	{	{	PUNCT
ejpam-2822	296	15	1	1	NUM
ejpam-2822	296	16	}	}	PUNCT
ejpam-2822	296	17	.	.	PUNCT
ejpam-2822	297	1	as	as	SCONJ
ejpam-2822	297	2	the	the	DET
ejpam-2822	297	3	level	level	NOUN
ejpam-2822	297	4	subsets	subset	NOUN
ejpam-2822	297	5	of	of	ADP
ejpam-2822	297	6	(	(	PUNCT
ejpam-2822	297	7	η	η	PROPN
ejpam-2822	297	8	,	,	PUNCT
ejpam-2822	297	9	η	η	NOUN
ejpam-2822	297	10	)	)	PUNCT
ejpam-2822	297	11	are	be	AUX
ejpam-2822	297	12	subgroups	subgroup	NOUN
ejpam-2822	297	13	,	,	PUNCT
ejpam-2822	297	14	z1(η	z1(η	PROPN
ejpam-2822	297	15	)	)	PUNCT
ejpam-2822	297	16	=	=	PUNCT
ejpam-2822	298	1	[	[	X
ejpam-2822	298	2	η	η	PROPN
ejpam-2822	298	3	,	,	PUNCT
ejpam-2822	298	4	η	η	PROPN
ejpam-2822	298	5	]	]	X
ejpam-2822	298	6	=	=	SYM
ejpam-2822	298	7	(	(	PUNCT
ejpam-2822	298	8	η	η	PROPN
ejpam-2822	298	9	,	,	PUNCT
ejpam-2822	298	10	η	η	NOUN
ejpam-2822	298	11	)	)	PUNCT
ejpam-2822	298	12	.	.	PUNCT
ejpam-2822	299	1	note	note	VERB
ejpam-2822	299	2	that	that	SCONJ
ejpam-2822	299	3	z1(η	z1(η	X
ejpam-2822	299	4	)	)	PUNCT
ejpam-2822	299	5	is	be	AUX
ejpam-2822	299	6	the	the	DET
ejpam-2822	299	7	trivial	trivial	ADJ
ejpam-2822	299	8	l	l	NOUN
ejpam-2822	299	9	-	-	NOUN
ejpam-2822	299	10	subgroup	subgroup	NOUN
ejpam-2822	299	11	ηdf	ηdf	PROPN
ejpam-2822	299	12	of	of	ADP
ejpam-2822	299	13	η	η	PROPN
ejpam-2822	299	14	and	and	CCONJ
ejpam-2822	299	15	so	so	ADV
ejpam-2822	299	16	the	the	DET
ejpam-2822	299	17	descending	descend	VERB
ejpam-2822	299	18	central	central	ADJ
ejpam-2822	299	19	series	series	NOUN
ejpam-2822	299	20	terminates	terminate	VERB
ejpam-2822	299	21	at	at	ADP
ejpam-2822	299	22	z1(η	z1(η	PROPN
ejpam-2822	299	23	)	)	PUNCT
ejpam-2822	299	24	i.e.	i.e.	X
ejpam-2822	299	25	η	η	X
ejpam-2822	299	26	=	=	PROPN
ejpam-2822	299	27	z0(η	z0(η	PROPN
ejpam-2822	299	28	)	)	PUNCT
ejpam-2822	299	29	⊇	⊇	PROPN
ejpam-2822	299	30	z1(η	z1(η	PROPN
ejpam-2822	299	31	)	)	PUNCT
ejpam-2822	300	1	=	=	SYM
ejpam-2822	300	2	ηdf	ηdf	PROPN
ejpam-2822	300	3	.	.	PUNCT
ejpam-2822	301	1	consequently	consequently	ADV
ejpam-2822	301	2	η	η	PROPN
ejpam-2822	301	3	is	be	AUX
ejpam-2822	301	4	a	a	DET
ejpam-2822	301	5	nilpotent	nilpotent	ADJ
ejpam-2822	301	6	l−subgroup	l−subgroup	X
ejpam-2822	301	7	of	of	ADP
ejpam-2822	301	8	µ	µ	PRON
ejpam-2822	301	9	having	have	VERB
ejpam-2822	301	10	nilpotent	nilpotent	ADJ
ejpam-2822	301	11	length	length	NOUN
ejpam-2822	301	12	1	1	NUM
ejpam-2822	301	13	.	.	PUNCT
ejpam-2822	302	1	similarly	similarly	ADV
ejpam-2822	302	2	it	it	PRON
ejpam-2822	302	3	can	can	AUX
ejpam-2822	302	4	be	be	AUX
ejpam-2822	302	5	shown	show	VERB
ejpam-2822	302	6	that	that	SCONJ
ejpam-2822	302	7	θ	θ	PROPN
ejpam-2822	302	8	is	be	AUX
ejpam-2822	302	9	also	also	ADV
ejpam-2822	302	10	a	a	DET
ejpam-2822	302	11	nilpotent	nilpotent	ADJ
ejpam-2822	302	12	l−subgroup	l−subgroup	X
ejpam-2822	302	13	of	of	ADP
ejpam-2822	302	14	µ	µ	PRON
ejpam-2822	302	15	having	have	VERB
ejpam-2822	302	16	nilpotent	nilpotent	ADJ
ejpam-2822	302	17	length	length	NOUN
ejpam-2822	302	18	1	1	NUM
ejpam-2822	302	19	.	.	PUNCT
ejpam-2822	303	1	next	next	ADV
ejpam-2822	303	2	,	,	PUNCT
ejpam-2822	303	3	we	we	PRON
ejpam-2822	303	4	exhibit	exhibit	VERB
ejpam-2822	303	5	the	the	DET
ejpam-2822	303	6	set	set	ADJ
ejpam-2822	303	7	product	product	NOUN
ejpam-2822	303	8	of	of	ADP
ejpam-2822	303	9	l	l	NOUN
ejpam-2822	303	10	-	-	PUNCT
ejpam-2822	303	11	subgroups	subgroup	NOUN
ejpam-2822	303	12	η	η	PROPN
ejpam-2822	303	13	and	and	CCONJ
ejpam-2822	303	14	θ	θ	PROPN
ejpam-2822	303	15	.	.	PUNCT
ejpam-2822	304	1	it	it	PRON
ejpam-2822	304	2	can	can	AUX
ejpam-2822	304	3	be	be	AUX
ejpam-2822	304	4	verified	verify	VERB
ejpam-2822	304	5	that	that	SCONJ
ejpam-2822	304	6	η	η	PROPN
ejpam-2822	304	7	◦	◦	NOUN
ejpam-2822	304	8	θ	θ	X
ejpam-2822	304	9	=	=	SYM
ejpam-2822	304	10	θ	θ	PROPN
ejpam-2822	304	11	◦	◦	NOUN
ejpam-2822	304	12	η	η	PROPN
ejpam-2822	304	13	=	=	SYM
ejpam-2822	304	14	φ	φ	PROPN
ejpam-2822	304	15	,	,	PUNCT
ejpam-2822	304	16	where	where	SCONJ
ejpam-2822	304	17	φ	φ	PROPN
ejpam-2822	304	18	is	be	AUX
ejpam-2822	304	19	the	the	DET
ejpam-2822	304	20	l−subgroup	l−subgroup	PROPN
ejpam-2822	304	21	of	of	ADP
ejpam-2822	304	22	µ	µ	NOUN
ejpam-2822	304	23	given	give	VERB
ejpam-2822	304	24	by	by	ADP
ejpam-2822	304	25	φ(x	φ(x	NOUN
ejpam-2822	304	26	)	)	PUNCT
ejpam-2822	304	27	=	=	PRON
ejpam-2822	305	1	{	{	PUNCT
ejpam-2822	305	2	d	d	X
ejpam-2822	305	3	if	if	SCONJ
ejpam-2822	305	4	x	x	X
ejpam-2822	305	5	∈	∈	PROPN
ejpam-2822	305	6	h1	h1	PROPN
ejpam-2822	305	7	,	,	PUNCT
ejpam-2822	305	8	b	b	NOUN
ejpam-2822	306	1	if	if	SCONJ
ejpam-2822	306	2	x	x	PROPN
ejpam-2822	306	3	∈	∈	PROPN
ejpam-2822	306	4	g	g	PROPN
ejpam-2822	306	5	\h1	\h1	PROPN
ejpam-2822	306	6	.	.	PUNCT
ejpam-2822	307	1	again	again	ADV
ejpam-2822	307	2	in	in	ADP
ejpam-2822	307	3	view	view	NOUN
ejpam-2822	307	4	of	of	ADP
ejpam-2822	307	5	the	the	DET
ejpam-2822	307	6	converse	converse	NOUN
ejpam-2822	307	7	of	of	ADP
ejpam-2822	307	8	theorem	theorem	NOUN
ejpam-2822	307	9	4.1[3	4.1[3	NUM
ejpam-2822	307	10	]	]	PUNCT
ejpam-2822	307	11	,	,	PUNCT
ejpam-2822	307	12	it	it	PRON
ejpam-2822	307	13	follows	follow	VERB
ejpam-2822	307	14	that	that	SCONJ
ejpam-2822	307	15	φ	φ	PROPN
ejpam-2822	307	16	is	be	AUX
ejpam-2822	307	17	a	a	DET
ejpam-2822	307	18	nilpotent	nilpotent	ADJ
ejpam-2822	307	19	l	l	NOUN
ejpam-2822	307	20	-	-	NOUN
ejpam-2822	307	21	subgroup	subgroup	NOUN
ejpam-2822	307	22	but	but	CCONJ
ejpam-2822	307	23	infφ	infφ	VERB
ejpam-2822	307	24	6=	6=	PROPN
ejpam-2822	307	25	infη	infη	ADJ
ejpam-2822	307	26	and	and	CCONJ
ejpam-2822	307	27	infθ	infθ	NOUN
ejpam-2822	307	28	.	.	PUNCT
ejpam-2822	308	1	acknowledgements	acknowledgement	VERB
ejpam-2822	308	2	the	the	DET
ejpam-2822	308	3	first	first	ADJ
ejpam-2822	308	4	author	author	NOUN
ejpam-2822	308	5	was	be	AUX
ejpam-2822	308	6	supported	support	VERB
ejpam-2822	308	7	by	by	ADP
ejpam-2822	308	8	emeritus	emeritus	ADJ
ejpam-2822	308	9	fellowship	fellowship	NOUN
ejpam-2822	308	10	of	of	ADP
ejpam-2822	308	11	ugc	ugc	PROPN
ejpam-2822	308	12	,	,	PUNCT
ejpam-2822	308	13	india	india	PROPN
ejpam-2822	308	14	during	during	ADP
ejpam-2822	308	15	the	the	DET
ejpam-2822	308	16	course	course	NOUN
ejpam-2822	308	17	of	of	ADP
ejpam-2822	308	18	development	development	NOUN
ejpam-2822	308	19	of	of	ADP
ejpam-2822	308	20	this	this	DET
ejpam-2822	308	21	paper	paper	NOUN
ejpam-2822	308	22	.	.	PUNCT
ejpam-2822	309	1	references	reference	NOUN
ejpam-2822	309	2	[	[	X
ejpam-2822	309	3	1	1	NUM
ejpam-2822	309	4	]	]	PUNCT
ejpam-2822	309	5	n.	n.	NOUN
ejpam-2822	309	6	ajmal	ajmal	PROPN
ejpam-2822	309	7	and	and	CCONJ
ejpam-2822	309	8	i.	i.	PROPN
ejpam-2822	309	9	jahan	jahan	PROPN
ejpam-2822	309	10	,	,	PUNCT
ejpam-2822	309	11	a	a	DET
ejpam-2822	309	12	study	study	NOUN
ejpam-2822	309	13	of	of	ADP
ejpam-2822	309	14	normal	normal	ADJ
ejpam-2822	309	15	fuzzy	fuzzy	ADJ
ejpam-2822	309	16	subgroups	subgroup	NOUN
ejpam-2822	309	17	and	and	CCONJ
ejpam-2822	309	18	characteristic	characteristic	ADJ
ejpam-2822	309	19	fuzzy	fuzzy	ADJ
ejpam-2822	309	20	subgroups	subgroup	NOUN
ejpam-2822	309	21	of	of	ADP
ejpam-2822	309	22	a	a	DET
ejpam-2822	309	23	fuzzy	fuzzy	ADJ
ejpam-2822	309	24	group	group	NOUN
ejpam-2822	309	25	,	,	PUNCT
ejpam-2822	309	26	fuzzy	fuzzy	ADJ
ejpam-2822	309	27	information	information	NOUN
ejpam-2822	309	28	and	and	CCONJ
ejpam-2822	309	29	engineering	engineering	NOUN
ejpam-2822	309	30	,	,	PUNCT
ejpam-2822	309	31	2	2	NUM
ejpam-2822	309	32	:	:	SYM
ejpam-2822	309	33	123	123	NUM
ejpam-2822	309	34	-	-	SYM
ejpam-2822	309	35	143	143	NUM
ejpam-2822	309	36	,	,	PUNCT
ejpam-2822	309	37	2012	2012	NUM
ejpam-2822	309	38	.	.	PUNCT
ejpam-2822	310	1	[	[	X
ejpam-2822	310	2	2	2	NUM
ejpam-2822	310	3	]	]	PUNCT
ejpam-2822	310	4	n.	n.	NOUN
ejpam-2822	310	5	ajmal	ajmal	PROPN
ejpam-2822	310	6	and	and	CCONJ
ejpam-2822	310	7	i.	i.	PROPN
ejpam-2822	310	8	jahan	jahan	PROPN
ejpam-2822	310	9	,	,	PUNCT
ejpam-2822	310	10	normal	normal	ADJ
ejpam-2822	310	11	closure	closure	NOUN
ejpam-2822	310	12	of	of	ADP
ejpam-2822	310	13	an	an	DET
ejpam-2822	310	14	l	l	NOUN
ejpam-2822	310	15	-	-	NOUN
ejpam-2822	310	16	subgroup	subgroup	NOUN
ejpam-2822	310	17	of	of	ADP
ejpam-2822	310	18	an	an	DET
ejpam-2822	310	19	l	l	NOUN
ejpam-2822	310	20	-	-	NOUN
ejpam-2822	310	21	group	group	NOUN
ejpam-2822	310	22	,	,	PUNCT
ejpam-2822	310	23	the	the	DET
ejpam-2822	310	24	journal	journal	NOUN
ejpam-2822	310	25	of	of	ADP
ejpam-2822	310	26	fuzzy	fuzzy	ADJ
ejpam-2822	310	27	mathematics	mathematic	NOUN
ejpam-2822	310	28	,	,	PUNCT
ejpam-2822	310	29	22	22	NUM
ejpam-2822	310	30	:	:	SYM
ejpam-2822	310	31	115	115	NUM
ejpam-2822	310	32	-	-	SYM
ejpam-2822	310	33	126	126	NUM
ejpam-2822	310	34	,	,	PUNCT
ejpam-2822	310	35	2014	2014	NUM
ejpam-2822	310	36	.	.	PUNCT
ejpam-2822	311	1	references	reference	NOUN
ejpam-2822	311	2	271	271	NUM
ejpam-2822	311	3	[	[	X
ejpam-2822	311	4	3	3	NUM
ejpam-2822	311	5	]	]	X
ejpam-2822	311	6	n.	n.	NOUN
ejpam-2822	311	7	ajmal	ajmal	PROPN
ejpam-2822	311	8	and	and	CCONJ
ejpam-2822	311	9	i.	i.	PROPN
ejpam-2822	311	10	jahan	jahan	PROPN
ejpam-2822	311	11	,	,	PUNCT
ejpam-2822	311	12	nilpotency	nilpotency	NOUN
ejpam-2822	311	13	and	and	CCONJ
ejpam-2822	311	14	theory	theory	NOUN
ejpam-2822	311	15	of	of	ADP
ejpam-2822	311	16	l	l	NOUN
ejpam-2822	311	17	subgroups	subgroup	NOUN
ejpam-2822	311	18	of	of	ADP
ejpam-2822	311	19	an	an	DET
ejpam-2822	311	20	l	l	NOUN
ejpam-2822	311	21	-	-	NOUN
ejpam-2822	311	22	group	group	NOUN
ejpam-2822	311	23	,	,	PUNCT
ejpam-2822	311	24	fuzzy	fuzzy	ADJ
ejpam-2822	311	25	information	information	NOUN
ejpam-2822	311	26	and	and	CCONJ
ejpam-2822	311	27	engineering	engineering	NOUN
ejpam-2822	311	28	,	,	PUNCT
ejpam-2822	311	29	6	6	NUM
ejpam-2822	311	30	:	:	SYM
ejpam-2822	311	31	2014	2014	NUM
ejpam-2822	311	32	,	,	PUNCT
ejpam-2822	311	33	1	1	NUM
ejpam-2822	311	34	-	-	SYM
ejpam-2822	311	35	17	17	NUM
ejpam-2822	311	36	.	.	PUNCT
ejpam-2822	312	1	[	[	X
ejpam-2822	312	2	4	4	X
ejpam-2822	312	3	]	]	X
ejpam-2822	312	4	n.	n.	NOUN
ejpam-2822	312	5	ajmal	ajmal	PROPN
ejpam-2822	312	6	and	and	CCONJ
ejpam-2822	312	7	i.	i.	PROPN
ejpam-2822	312	8	jahan	jahan	PROPN
ejpam-2822	312	9	,	,	PUNCT
ejpam-2822	312	10	an	an	DET
ejpam-2822	312	11	l	l	NOUN
ejpam-2822	312	12	-	-	PUNCT
ejpam-2822	312	13	point	point	NOUN
ejpam-2822	312	14	characterization	characterization	NOUN
ejpam-2822	312	15	of	of	ADP
ejpam-2822	312	16	normality	normality	NOUN
ejpam-2822	312	17	and	and	CCONJ
ejpam-2822	312	18	normalizer	normalizer	NOUN
ejpam-2822	312	19	of	of	ADP
ejpam-2822	312	20	an	an	DET
ejpam-2822	312	21	l	l	NOUN
ejpam-2822	312	22	-	-	NOUN
ejpam-2822	312	23	subgroup	subgroup	NOUN
ejpam-2822	312	24	of	of	ADP
ejpam-2822	312	25	an	an	DET
ejpam-2822	312	26	l	l	NOUN
ejpam-2822	312	27	-	-	NOUN
ejpam-2822	312	28	group	group	NOUN
ejpam-2822	312	29	,	,	PUNCT
ejpam-2822	312	30	fuzzy	fuzzy	ADJ
ejpam-2822	312	31	information	information	NOUN
ejpam-2822	312	32	and	and	CCONJ
ejpam-2822	312	33	engineering	engineering	NOUN
ejpam-2822	312	34	,	,	PUNCT
ejpam-2822	312	35	6	6	NUM
ejpam-2822	312	36	:	:	SYM
ejpam-2822	312	37	147	147	NUM
ejpam-2822	312	38	-	-	SYM
ejpam-2822	312	39	166	166	NUM
ejpam-2822	312	40	,	,	PUNCT
ejpam-2822	312	41	2014	2014	NUM
ejpam-2822	312	42	.	.	PUNCT
ejpam-2822	313	1	[	[	X
ejpam-2822	313	2	5	5	X
ejpam-2822	313	3	]	]	PUNCT
ejpam-2822	313	4	n.	n.	NOUN
ejpam-2822	313	5	ajmal	ajmal	PROPN
ejpam-2822	313	6	and	and	CCONJ
ejpam-2822	313	7	i.	i.	PROPN
ejpam-2822	313	8	jahan	jahan	PROPN
ejpam-2822	313	9	,	,	PUNCT
ejpam-2822	313	10	solvable	solvable	ADJ
ejpam-2822	313	11	l	l	NOUN
ejpam-2822	313	12	-	-	NOUN
ejpam-2822	313	13	subgroup	subgroup	NOUN
ejpam-2822	313	14	of	of	ADP
ejpam-2822	313	15	an	an	DET
ejpam-2822	313	16	l	l	NOUN
ejpam-2822	313	17	-	-	NOUN
ejpam-2822	313	18	group	group	NOUN
ejpam-2822	313	19	,	,	PUNCT
ejpam-2822	313	20	iranian	iranian	ADJ
ejpam-2822	313	21	journal	journal	PROPN
ejpam-2822	313	22	of	of	ADP
ejpam-2822	313	23	fuzzy	fuzzy	ADJ
ejpam-2822	313	24	systems	system	NOUN
ejpam-2822	313	25	,	,	PUNCT
ejpam-2822	313	26	12	12	NUM
ejpam-2822	313	27	:	:	SYM
ejpam-2822	313	28	151	151	NUM
ejpam-2822	313	29	-	-	SYM
ejpam-2822	313	30	161	161	NUM
ejpam-2822	313	31	,	,	PUNCT
ejpam-2822	313	32	2015	2015	NUM
ejpam-2822	313	33	.	.	PUNCT
ejpam-2822	314	1	[	[	X
ejpam-2822	314	2	6	6	NUM
ejpam-2822	314	3	]	]	PUNCT
ejpam-2822	314	4	n.	n.	NOUN
ejpam-2822	314	5	ajmal	ajmal	PROPN
ejpam-2822	314	6	and	and	CCONJ
ejpam-2822	314	7	i.	i.	PROPN
ejpam-2822	314	8	jahan	jahan	PROPN
ejpam-2822	314	9	,	,	PUNCT
ejpam-2822	314	10	generated	generate	VERB
ejpam-2822	314	11	l	l	NOUN
ejpam-2822	314	12	-	-	NOUN
ejpam-2822	314	13	subgroup	subgroup	NOUN
ejpam-2822	314	14	of	of	ADP
ejpam-2822	314	15	an	an	DET
ejpam-2822	314	16	l	l	NOUN
ejpam-2822	314	17	-	-	NOUN
ejpam-2822	314	18	group	group	NOUN
ejpam-2822	314	19	,	,	PUNCT
ejpam-2822	314	20	iranian	iranian	ADJ
ejpam-2822	314	21	journal	journal	PROPN
ejpam-2822	314	22	of	of	ADP
ejpam-2822	314	23	fuzzy	fuzzy	ADJ
ejpam-2822	314	24	systems	system	NOUN
ejpam-2822	314	25	,	,	PUNCT
ejpam-2822	314	26	12	12	NUM
ejpam-2822	314	27	:	:	SYM
ejpam-2822	314	28	129	129	NUM
ejpam-2822	314	29	-	-	SYM
ejpam-2822	314	30	136	136	NUM
ejpam-2822	314	31	,	,	PUNCT
ejpam-2822	314	32	2015	2015	NUM
ejpam-2822	314	33	.	.	PUNCT
ejpam-2822	315	1	[	[	X
ejpam-2822	315	2	7	7	X
ejpam-2822	315	3	]	]	PUNCT
ejpam-2822	315	4	j.	j.	PROPN
ejpam-2822	315	5	a.	a.	PROPN
ejpam-2822	315	6	goguen	goguen	PROPN
ejpam-2822	315	7	,	,	PUNCT
ejpam-2822	315	8	l	l	ADJ
ejpam-2822	315	9	-	-	ADJ
ejpam-2822	315	10	fuzzy	fuzzy	ADJ
ejpam-2822	315	11	sets	set	NOUN
ejpam-2822	315	12	,	,	PUNCT
ejpam-2822	315	13	j.	j.	PROPN
ejpam-2822	315	14	math	math	PROPN
ejpam-2822	315	15	.	.	PUNCT
ejpam-2822	316	1	anal	anal	PROPN
ejpam-2822	316	2	.	.	PUNCT
ejpam-2822	316	3	appl	appl	PROPN
ejpam-2822	316	4	.	.	PROPN
ejpam-2822	316	5	,	,	PUNCT
ejpam-2822	316	6	18	18	NUM
ejpam-2822	316	7	:	:	SYM
ejpam-2822	316	8	145	145	NUM
ejpam-2822	316	9	-	-	SYM
ejpam-2822	316	10	174	174	NUM
ejpam-2822	316	11	,	,	PUNCT
ejpam-2822	316	12	1967	1967	NUM
ejpam-2822	316	13	.	.	PUNCT
ejpam-2822	317	1	[	[	X
ejpam-2822	317	2	8	8	X
ejpam-2822	317	3	]	]	PUNCT
ejpam-2822	317	4	t.	t.	NOUN
ejpam-2822	317	5	head	head	NOUN
ejpam-2822	317	6	,	,	PUNCT
ejpam-2822	317	7	a	a	DET
ejpam-2822	317	8	metatheorem	metatheorem	NOUN
ejpam-2822	317	9	for	for	ADP
ejpam-2822	317	10	deriving	derive	VERB
ejpam-2822	317	11	fuzzy	fuzzy	ADJ
ejpam-2822	317	12	theorems	theorem	NOUN
ejpam-2822	317	13	from	from	ADP
ejpam-2822	317	14	crisp	crisp	ADJ
ejpam-2822	317	15	versions	version	NOUN
ejpam-2822	317	16	,	,	PUNCT
ejpam-2822	317	17	fuzzy	fuzzy	ADJ
ejpam-2822	317	18	sets	set	NOUN
ejpam-2822	317	19	and	and	CCONJ
ejpam-2822	317	20	systems	system	NOUN
ejpam-2822	317	21	,	,	PUNCT
ejpam-2822	317	22	73	73	NUM
ejpam-2822	317	23	:	:	SYM
ejpam-2822	317	24	349	349	NUM
ejpam-2822	317	25	-	-	SYM
ejpam-2822	317	26	358	358	NUM
ejpam-2822	317	27	,	,	PUNCT
ejpam-2822	317	28	1995	1995	NUM
ejpam-2822	317	29	.	.	PUNCT
ejpam-2822	318	1	[	[	X
ejpam-2822	318	2	9	9	NUM
ejpam-2822	318	3	]	]	X
ejpam-2822	318	4	w.j	w.j	PROPN
ejpam-2822	318	5	.	.	PROPN
ejpam-2822	318	6	liu	liu	PROPN
ejpam-2822	318	7	,	,	PUNCT
ejpam-2822	318	8	fuzzy	fuzzy	ADJ
ejpam-2822	318	9	invariant	invariant	ADJ
ejpam-2822	318	10	subgroups	subgroup	NOUN
ejpam-2822	318	11	and	and	CCONJ
ejpam-2822	318	12	fuzzy	fuzzy	ADJ
ejpam-2822	318	13	ideals	ideal	NOUN
ejpam-2822	318	14	,	,	PUNCT
ejpam-2822	318	15	fuzzy	fuzzy	ADJ
ejpam-2822	318	16	sets	set	NOUN
ejpam-2822	318	17	and	and	CCONJ
ejpam-2822	318	18	systems	system	NOUN
ejpam-2822	318	19	8	8	NUM
ejpam-2822	318	20	:	:	PUNCT
ejpam-2822	318	21	133	133	NUM
ejpam-2822	318	22	-	-	SYM
ejpam-2822	318	23	139	139	NUM
ejpam-2822	318	24	,	,	PUNCT
ejpam-2822	318	25	1982	1982	NUM
ejpam-2822	318	26	.	.	PUNCT
ejpam-2822	319	1	[	[	X
ejpam-2822	319	2	10	10	NUM
ejpam-2822	319	3	]	]	X
ejpam-2822	319	4	w.	w.	PROPN
ejpam-2822	319	5	j.	j.	PROPN
ejpam-2822	319	6	liu	liu	PROPN
ejpam-2822	319	7	,	,	PUNCT
ejpam-2822	319	8	operations	operation	NOUN
ejpam-2822	319	9	on	on	ADP
ejpam-2822	319	10	fuzzy	fuzzy	ADJ
ejpam-2822	319	11	ideals	ideal	NOUN
ejpam-2822	319	12	,	,	PUNCT
ejpam-2822	319	13	fuzzy	fuzzy	ADJ
ejpam-2822	319	14	sets	set	NOUN
ejpam-2822	319	15	and	and	CCONJ
ejpam-2822	319	16	systems	system	NOUN
ejpam-2822	319	17	11	11	NUM
ejpam-2822	319	18	:	:	PUNCT
ejpam-2822	319	19	31	31	NUM
ejpam-2822	319	20	-	-	SYM
ejpam-2822	319	21	34	34	NUM
ejpam-2822	319	22	,	,	PUNCT
ejpam-2822	319	23	1983	1983	NUM
ejpam-2822	319	24	.	.	PUNCT
ejpam-2822	320	1	[	[	X
ejpam-2822	320	2	11	11	NUM
ejpam-2822	320	3	]	]	X
ejpam-2822	320	4	d.	d.	PROPN
ejpam-2822	320	5	s.	s.	PROPN
ejpam-2822	320	6	malik	malik	PROPN
ejpam-2822	320	7	,	,	PUNCT
ejpam-2822	320	8	j.	j.	PROPN
ejpam-2822	320	9	n.	n.	PROPN
ejpam-2822	320	10	mordeson	mordeson	PROPN
ejpam-2822	320	11	and	and	CCONJ
ejpam-2822	320	12	p.s	p.s	PROPN
ejpam-2822	320	13	.	.	PROPN
ejpam-2822	320	14	nair	nair	PROPN
ejpam-2822	320	15	,	,	PUNCT
ejpam-2822	320	16	fuzzy	fuzzy	ADJ
ejpam-2822	320	17	normal	normal	ADJ
ejpam-2822	320	18	subgroups	subgroup	NOUN
ejpam-2822	320	19	in	in	ADP
ejpam-2822	320	20	fuzzy	fuzzy	ADJ
ejpam-2822	320	21	subgroups	subgroup	NOUN
ejpam-2822	320	22	,	,	PUNCT
ejpam-2822	320	23	j.	j.	PROPN
ejpam-2822	320	24	korean	korean	PROPN
ejpam-2822	320	25	math	math	PROPN
ejpam-2822	320	26	.	.	PUNCT
ejpam-2822	321	1	soc	soc	PROPN
ejpam-2822	321	2	.	.	PUNCT
ejpam-2822	321	3	,	,	PUNCT
ejpam-2822	321	4	29	29	NUM
ejpam-2822	321	5	:	:	SYM
ejpam-2822	321	6	1	1	NUM
ejpam-2822	321	7	-	-	SYM
ejpam-2822	321	8	8	8	NUM
ejpam-2822	321	9	,	,	PUNCT
ejpam-2822	321	10	1992	1992	NUM
ejpam-2822	321	11	.	.	PUNCT
ejpam-2822	322	1	[	[	X
ejpam-2822	322	2	12	12	NUM
ejpam-2822	322	3	]	]	PUNCT
ejpam-2822	322	4	l.	l.	PROPN
ejpam-2822	322	5	martinez	martinez	PROPN
ejpam-2822	322	6	,	,	PUNCT
ejpam-2822	322	7	l	l	PROPN
ejpam-2822	322	8	fuzzy	fuzzy	ADJ
ejpam-2822	322	9	subgroups	subgroup	NOUN
ejpam-2822	322	10	of	of	ADP
ejpam-2822	322	11	fuzzy	fuzzy	ADJ
ejpam-2822	322	12	groups	group	NOUN
ejpam-2822	322	13	and	and	CCONJ
ejpam-2822	322	14	fuzzy	fuzzy	ADJ
ejpam-2822	322	15	ideals	ideal	NOUN
ejpam-2822	322	16	of	of	ADP
ejpam-2822	322	17	fuzzy	fuzzy	ADJ
ejpam-2822	322	18	rings	ring	NOUN
ejpam-2822	322	19	,	,	PUNCT
ejpam-2822	322	20	j.	j.	PROPN
ejpam-2822	322	21	fuzzy	fuzzy	PROPN
ejpam-2822	322	22	math	math	PROPN
ejpam-2822	322	23	.	.	PUNCT
ejpam-2822	322	24	,	,	PUNCT
ejpam-2822	322	25	3	3	NUM
ejpam-2822	322	26	:	:	SYM
ejpam-2822	322	27	833	833	NUM
ejpam-2822	322	28	-	-	SYM
ejpam-2822	322	29	849	849	NUM
ejpam-2822	322	30	,	,	PUNCT
ejpam-2822	322	31	1995	1995	NUM
ejpam-2822	322	32	.	.	PUNCT
ejpam-2822	323	1	[	[	X
ejpam-2822	323	2	13	13	NUM
ejpam-2822	323	3	]	]	PUNCT
ejpam-2822	323	4	j.	j.	PROPN
ejpam-2822	323	5	n.	n.	PROPN
ejpam-2822	323	6	mordeson	mordeson	PROPN
ejpam-2822	323	7	and	and	CCONJ
ejpam-2822	323	8	d.	d.	PROPN
ejpam-2822	323	9	s.	s.	PROPN
ejpam-2822	323	10	malik	malik	PROPN
ejpam-2822	323	11	,	,	PUNCT
ejpam-2822	323	12	fuzzy	fuzzy	ADJ
ejpam-2822	323	13	commutative	commutative	ADJ
ejpam-2822	323	14	algebra	algebra	NOUN
ejpam-2822	323	15	,	,	PUNCT
ejpam-2822	323	16	world	world	NOUN
ejpam-2822	323	17	scientific	scientific	NOUN
ejpam-2822	323	18	,	,	PUNCT
ejpam-2822	323	19	(	(	PUNCT
ejpam-2822	323	20	1998	1998	NUM
ejpam-2822	323	21	)	)	PUNCT
ejpam-2822	323	22	.	.	PUNCT
ejpam-2822	324	1	[	[	X
ejpam-2822	324	2	14	14	NUM
ejpam-2822	324	3	]	]	PUNCT
ejpam-2822	324	4	a.	a.	NOUN
ejpam-2822	324	5	rosenfeld	rosenfeld	PROPN
ejpam-2822	324	6	,	,	PUNCT
ejpam-2822	324	7	fuzzy	fuzzy	ADJ
ejpam-2822	324	8	groups	group	NOUN
ejpam-2822	324	9	,	,	PUNCT
ejpam-2822	324	10	j.	j.	PROPN
ejpam-2822	324	11	math	math	PROPN
ejpam-2822	324	12	.	.	PUNCT
ejpam-2822	325	1	anal	anal	PROPN
ejpam-2822	325	2	.	.	PUNCT
ejpam-2822	326	1	appl	appl	PROPN
ejpam-2822	326	2	.	.	PROPN
ejpam-2822	326	3	,	,	PUNCT
ejpam-2822	326	4	35	35	NUM
ejpam-2822	326	5	:	:	SYM
ejpam-2822	326	6	512	512	NUM
ejpam-2822	326	7	-	-	SYM
ejpam-2822	326	8	517	517	NUM
ejpam-2822	326	9	,	,	PUNCT
ejpam-2822	326	10	1971	1971	NUM
ejpam-2822	326	11	.	.	PUNCT
ejpam-2822	327	1	[	[	X
ejpam-2822	327	2	15	15	NUM
ejpam-2822	327	3	]	]	X
ejpam-2822	327	4	w.	w.	PROPN
ejpam-2822	327	5	wu	wu	PROPN
ejpam-2822	327	6	,	,	PUNCT
ejpam-2822	327	7	normal	normal	ADJ
ejpam-2822	327	8	fuzzy	fuzzy	ADJ
ejpam-2822	327	9	subgroups	subgroup	NOUN
ejpam-2822	327	10	,	,	PUNCT
ejpam-2822	327	11	fuzzy	fuzzy	ADJ
ejpam-2822	327	12	math	math	NOUN
ejpam-2822	327	13	.	.	PUNCT
ejpam-2822	327	14	,	,	PUNCT
ejpam-2822	327	15	1	1	NUM
ejpam-2822	327	16	:	:	SYM
ejpam-2822	327	17	21	21	NUM
ejpam-2822	327	18	-	-	SYM
ejpam-2822	327	19	30	30	NUM
ejpam-2822	327	20	,	,	PUNCT
ejpam-2822	327	21	1981	1981	NUM
ejpam-2822	327	22	.	.	PUNCT