id	sid	eid	entity	type
ejpam-6859	1	1	european journal	ORG
ejpam-6859	1	2	2025	DATE
ejpam-6859	1	3	18	CARDINAL
ejpam-6859	1	4	4	CARDINAL
ejpam-6859	1	5	6859	CARDINAL
ejpam-6859	1	6	1307-5543	DATE
ejpam-6859	1	7	new york	GPE
ejpam-6859	1	8	abdulaziz mutlaq alotaibi1	PERSON
ejpam-6859	1	9	khalid al-tahat2	PERSON
ejpam-6859	1	10	mustafa al-jamal2,∗ 1	PERSON
ejpam-6859	1	11	al-kharj	GPE
ejpam-6859	1	12	prince sattam bin abdulaziz university	PERSON
ejpam-6859	1	13	al-kharj 11942	ORG
ejpam-6859	1	14	saudi arabia	GPE
ejpam-6859	1	15	2	CARDINAL
ejpam-6859	1	16	arab	NORP
ejpam-6859	1	17	university	GPE
ejpam-6859	1	18	amman	GPE
ejpam-6859	1	19	jordan	GPE
ejpam-6859	2	1	∈	ORG
ejpam-6859	3	1	w	ORG
ejpam-6859	3	2	⊆	CARDINAL
ejpam-6859	3	3	∈	ORG
ejpam-6859	6	1	w ≤	MONEY
ejpam-6859	6	2	∈	ORG
ejpam-6859	8	1	2020	DATE
ejpam-6859	8	2	20d10	CARDINAL
ejpam-6859	8	3	20d15	CARDINAL
ejpam-6859	8	4	1	CARDINAL
ejpam-6859	10	1	1	CARDINAL
ejpam-6859	10	2	2	CARDINAL
ejpam-6859	11	1	3	CARDINAL
ejpam-6859	15	1	g → h may	ORG
ejpam-6859	15	2	two	CARDINAL
ejpam-6859	15	3	intersectingtrivially	ORG
ejpam-6859	16	1	4	CARDINAL
ejpam-6859	17	1	5	CARDINAL
ejpam-6859	17	2	6	CARDINAL
ejpam-6859	19	1	∗corresponding	PERSON
ejpam-6859	20	1	https://doi.org/10.29020/nybg.ejpam.v18i4.6859	DATE
ejpam-6859	20	2	a. m. alotaibi	PERSON
ejpam-6859	20	3	k_tahat@aou.edu.jo	PERSON
ejpam-6859	20	4	k. al-tahat	PERSON
ejpam-6859	20	5	k. m. al-jamal	PERSON
ejpam-6859	21	1	1	CARDINAL
ejpam-6859	21	2	2025	CARDINAL
ejpam-6859	22	1	a. m. alotaibi et al	PERSON
ejpam-6859	23	1	j. pure	PERSON
ejpam-6859	23	2	18	CARDINAL
ejpam-6859	23	3	4	CARDINAL
ejpam-6859	23	4	2025	CARDINAL
ejpam-6859	23	5	6859 2	DATE
ejpam-6859	23	6	6 w ⊆	MONEY
ejpam-6859	24	1	8	CARDINAL
ejpam-6859	25	1	9	CARDINAL
ejpam-6859	26	1	tandem	ORG
ejpam-6859	28	1	1	CARDINAL
ejpam-6859	29	1	9]a	ORG
ejpam-6859	29	2	g. lemma	PERSON
ejpam-6859	30	1	2	CARDINAL
ejpam-6859	31	1	6	CARDINAL
ejpam-6859	32	1	k ≤ g and n	PERSON
ejpam-6859	34	1	k. (ii	PERSON
ejpam-6859	35	1	g/n	FAC
ejpam-6859	36	1	k/n	ORG
ejpam-6859	36	2	g. lemma	PERSON
ejpam-6859	37	1	3	CARDINAL
ejpam-6859	38	1	10	CARDINAL
ejpam-6859	39	1	1	CARDINAL
ejpam-6859	40	1	11	CARDINAL
ejpam-6859	40	2	∈	ORG
ejpam-6859	40	3	w ⊆	ORG
ejpam-6859	41	1	w	ORG
ejpam-6859	41	2	⊆	CARDINAL
ejpam-6859	41	3	w.	PERSON
ejpam-6859	41	4	2	CARDINAL
ejpam-6859	42	1	12	CARDINAL
ejpam-6859	43	1	h. lemma 4	PERSON
ejpam-6859	44	1	abelian	NORP
ejpam-6859	44	2	⊆	CARDINAL
ejpam-6859	46	1	abelian	NORP
ejpam-6859	47	1	∈	ORG
ejpam-6859	49	1	g/h	ORG
ejpam-6859	49	2	g/h	ORG
ejpam-6859	49	3	gn ∈ h.	ORG
ejpam-6859	51	1	5	CARDINAL
ejpam-6859	53	1	g/ǵ.	ORG
ejpam-6859	53	2	v(g	PERSON
ejpam-6859	53	3	g. a. m. alotaibi et al	PERSON
ejpam-6859	54	1	j. pure	PERSON
ejpam-6859	54	2	18	CARDINAL
ejpam-6859	54	3	4	CARDINAL
ejpam-6859	54	4	2025	CARDINAL
ejpam-6859	54	5	6859 3	DATE
ejpam-6859	55	1	∈	PRODUCT
ejpam-6859	57	1	g → g/ǵ	ORG
ejpam-6859	57	2	v(g	PERSON
ejpam-6859	60	1	v(g	PERSON
ejpam-6859	60	2	∈	ORG
ejpam-6859	61	1	1	CARDINAL
ejpam-6859	61	2	three	CARDINAL
ejpam-6859	61	3	6	CARDINAL
ejpam-6859	63	1	3	CARDINAL
ejpam-6859	63	2	3	CARDINAL
ejpam-6859	63	3	g/h.	ORG
ejpam-6859	63	4	two	CARDINAL
ejpam-6859	64	1	g/h	ORG
ejpam-6859	64	2	abelian	NORP
ejpam-6859	66	1	12	CARDINAL
ejpam-6859	67	1	12)h	CARDINAL
ejpam-6859	70	1	12	CARDINAL
ejpam-6859	70	2	12)a3	CARDINAL
ejpam-6859	70	3	2	CARDINAL
ejpam-6859	73	1	6	CARDINAL
ejpam-6859	74	1	∈	ORG
ejpam-6859	74	2	∈	ORG
ejpam-6859	83	1	g ∈ ǵ	PERSON
ejpam-6859	84	1	∈	ORG
ejpam-6859	84	2	0	CARDINAL
ejpam-6859	87	1	g /∈	PERSON
ejpam-6859	92	1	∈	ORG
ejpam-6859	96	1	a. m. alotaibi et al	PERSON
ejpam-6859	97	1	j. pure	PERSON
ejpam-6859	97	2	18	CARDINAL
ejpam-6859	97	3	4	CARDINAL
ejpam-6859	97	4	2025	CARDINAL
ejpam-6859	97	5	6859 4	DATE
ejpam-6859	97	6	6	CARDINAL
ejpam-6859	97	7	2	CARDINAL
ejpam-6859	97	8	s5	ORG
ejpam-6859	97	9	5	CARDINAL
ejpam-6859	98	1	2	CARDINAL
ejpam-6859	98	2	2	CARDINAL
ejpam-6859	98	3	s5	GPE
ejpam-6859	99	1	2	CARDINAL
ejpam-6859	99	2	s5	GPE
ejpam-6859	99	3	2	CARDINAL
ejpam-6859	99	4	120	CARDINAL
ejpam-6859	99	5	8	CARDINAL
ejpam-6859	100	1	2	CARDINAL
ejpam-6859	100	2	8	CARDINAL
ejpam-6859	101	1	s5	GPE
ejpam-6859	102	1	60	CARDINAL
ejpam-6859	103	1	12)(34	CARDINAL
ejpam-6859	103	2	1	CARDINAL
ejpam-6859	103	3	2	CARDINAL
ejpam-6859	104	1	2	CARDINAL
ejpam-6859	104	2	2	CARDINAL
ejpam-6859	104	3	12)(34	CARDINAL
ejpam-6859	104	4	14)(23	CARDINAL
ejpam-6859	104	5	〉	CARDINAL
ejpam-6859	104	6	8	CARDINAL
ejpam-6859	106	1	12)(34	CARDINAL
ejpam-6859	107	1	6	CARDINAL
ejpam-6859	109	1	∈	ORG
ejpam-6859	114	1	12)(34	CARDINAL
ejpam-6859	115	1	∈	ORG
ejpam-6859	117	1	g → g/ǵthat	ORG
ejpam-6859	117	2	v(g	PERSON
ejpam-6859	117	3	v(g	PERSON
ejpam-6859	120	1	g → g/ǵ	ORG
ejpam-6859	122	1	v(g	PERSON
ejpam-6859	122	2	−1	DATE
ejpam-6859	123	1	abelian	NORP
ejpam-6859	124	1	v(g	PERSON
ejpam-6859	125	1	1	CARDINAL
ejpam-6859	126	1	abelian	NORP
ejpam-6859	126	2	2	CARDINAL
ejpam-6859	126	3	25	CARDINAL
ejpam-6859	127	1	abelian	NORP
ejpam-6859	129	1	abelian	NORP
ejpam-6859	129	2	25	CARDINAL
ejpam-6859	129	3	z/25z	PRODUCT
ejpam-6859	129	4	z/25z	PRODUCT
ejpam-6859	129	5	25	CARDINAL
ejpam-6859	129	6	z/5z × z/5z	NORP
ejpam-6859	130	1	z/5z × z/5z	GPE
ejpam-6859	130	2	abelian	NORP
ejpam-6859	130	3	2	CARDINAL
ejpam-6859	131	1	abelian	NORP
ejpam-6859	132	1	abelian	NORP
ejpam-6859	133	1	2	CARDINAL
ejpam-6859	134	1	∈	ORG
ejpam-6859	135	1	k. a. m. alotaibi et al	PERSON
ejpam-6859	136	1	j. pure	PERSON
ejpam-6859	136	2	18	CARDINAL
ejpam-6859	136	3	4	CARDINAL
ejpam-6859	136	4	2025	CARDINAL
ejpam-6859	136	5	6859 5	DATE
ejpam-6859	139	1	php−1 = h	ORG
ejpam-6859	139	2	k = ghg−1	PERSON
ejpam-6859	139	3	∈	ORG
ejpam-6859	140	1	∈	ORG
ejpam-6859	142	1	2	CARDINAL
ejpam-6859	144	1	⊆	CARDINAL
ejpam-6859	144	2	w	ORG
ejpam-6859	144	3	⊆	CARDINAL
ejpam-6859	145	1	w	GPE
ejpam-6859	146	1	∈	ORG
ejpam-6859	147	1	w ⊆	ORG
ejpam-6859	147	2	q. proof	PERSON
ejpam-6859	148	1	w	ORG
ejpam-6859	149	1	∈	ORG
ejpam-6859	151	1	w	GPE
ejpam-6859	151	2	w	PERSON
ejpam-6859	152	1	∈	ORG
ejpam-6859	152	2	w ≤ q.	ORG
ejpam-6859	155	1	−1	DATE
ejpam-6859	157	1	w	ORG
ejpam-6859	158	1	w	ORG
ejpam-6859	158	2	q. ⇐=)	ORG
ejpam-6859	158	3	w	PERSON
ejpam-6859	158	4	∈	ORG
ejpam-6859	160	1	gx−1 ∈	PERSON
ejpam-6859	161	1	gx−1 ∈	PERSON
ejpam-6859	163	1	w x)h	EVENT
ejpam-6859	165	1	w	ORG
ejpam-6859	168	1	⊆	CARDINAL
ejpam-6859	168	2	w	ORG
ejpam-6859	169	1	⊆	CARDINAL
ejpam-6859	170	1	g. corollary 1	PERSON
ejpam-6859	171	1	∈	ORG
ejpam-6859	171	2	w	GPE
ejpam-6859	172	1	3	CARDINAL
ejpam-6859	172	2	∈	ORG
ejpam-6859	172	3	ng	ORG
ejpam-6859	172	4	w	ORG
ejpam-6859	172	5	∈	ORG
ejpam-6859	172	6	a. m. alotaibi et al	PERSON
ejpam-6859	173	1	j. pure	PERSON
ejpam-6859	173	2	18	CARDINAL
ejpam-6859	173	3	4	CARDINAL
ejpam-6859	173	4	2025	CARDINAL
ejpam-6859	173	5	6859 6	DATE
ejpam-6859	175	1	bin abdulaziz university	PERSON
ejpam-6859	176	1	1	CARDINAL
ejpam-6859	176	2	k. m. aljamal	PERSON
ejpam-6859	176	3	a. t. ab ghani	PERSON
ejpam-6859	176	4	r. m. saleh	PERSON
ejpam-6859	178	1	340–343	CARDINAL
ejpam-6859	179	1	2021	CARDINAL
ejpam-6859	180	1	2	CARDINAL
ejpam-6859	180	2	a. m. alotaibi	PERSON
ejpam-6859	180	3	k. m. aljamal	PERSON
ejpam-6859	182	1	european journal	ORG
ejpam-6859	182	2	17(3):2329–2335	DATE
ejpam-6859	182	3	2024	DATE
ejpam-6859	183	1	3	CARDINAL
ejpam-6859	183	2	a. alotaibi	PERSON
ejpam-6859	185	1	mississippi state university	ORG
ejpam-6859	185	2	2023	CARDINAL
ejpam-6859	186	1	4	CARDINAL
ejpam-6859	186	2	a. m. alotaibi	PERSON
ejpam-6859	186	3	k. al-tahat	PERSON
ejpam-6859	186	4	k. m. aljamal	PERSON
ejpam-6859	188	1	european journal	ORG
ejpam-6859	188	2	18(3):6033–6033	CARDINAL
ejpam-6859	188	3	2025	DATE
ejpam-6859	189	1	5	CARDINAL
ejpam-6859	189	2	w. burnside	PERSON
ejpam-6859	191	1	cambridge university press	ORG
ejpam-6859	191	2	2 edition	QUANTITY
ejpam-6859	191	3	1911	DATE
ejpam-6859	192	1	6	CARDINAL
ejpam-6859	192	2	i. m. isaacs	PERSON
ejpam-6859	193	1	92	CARDINAL
ejpam-6859	194	1	american mathematical society	ORG
ejpam-6859	194	2	2008	DATE
ejpam-6859	195	1	7	CARDINAL
ejpam-6859	197	1	harper & row,	ORG
ejpam-6859	197	2	1968	DATE
ejpam-6859	198	1	8	CARDINAL
ejpam-6859	198	2	j. l. alperin	PERSON
ejpam-6859	200	1	cambridge university press	ORG
ejpam-6859	200	2	1986	DATE
ejpam-6859	201	1	9	CARDINAL
ejpam-6859	201	2	m. aschbacher	PERSON
ejpam-6859	201	3	r. kessar	PERSON
ejpam-6859	201	4	b. oliver	PERSON
ejpam-6859	202	1	cambridge university press	ORG
ejpam-6859	202	2	new york	GPE
ejpam-6859	202	3	ny	GPE
ejpam-6859	202	4	2011	DATE
ejpam-6859	203	1	10	CARDINAL
ejpam-6859	203	2	j. tate	PERSON
ejpam-6859	205	1	3:109–111, 1964	DATE
ejpam-6859	206	1	11	CARDINAL
ejpam-6859	206	2	l. puig.	PERSON
ejpam-6859	208	1	3(1):59–120	CARDINAL
ejpam-6859	208	2	2009	DATE
ejpam-6859	209	1	12	CARDINAL
ejpam-6859	209	2	d. s. dummit	PERSON
ejpam-6859	209	3	r. m. foote	PERSON
ejpam-6859	211	1	john wiley & sons	ORG
ejpam-6859	211	2	hoboken	GPE
ejpam-6859	211	3	nj	ORG
ejpam-6859	211	4	3 edition	QUANTITY
ejpam-6859	211	5	2004	DATE