id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3399	Hijazi, Rola A.; Charaf, Fatme M.	Finite Groups with Certain Permutability Criteria	2019	6	.pdf	application/pdf	3063	212	82	Thus p is the largest prime dividing |G| and since K is cyclic, it follows, by Burnside′s p-Nilpotent Theorem ([10], Satz 2.8, p.420), that P C G. But G/P ∼= K, therefore G/P is cyclic and so abelian, then G′ ≤ P . Thus we may assume that there exists a subgroup H of P of order p such that H is not normal in G. By the hypothesis, H is S-permutable in G and hence by ([13], Lemma A), Op(G) ≤ NG(H)	cache/ejpam-3399.pdf	txt/ejpam-3399.txt