ON s-PERMUTABLY EMBEDDED AND WEAKLY c-NORMAL SUBGROUPS OF FINITE GROUPS

Year 2013, Volume: 14 Issue: 14, 44 - 52, 01.12.2013

Guo Zhong Liying Yang Xuanlong Ma Shixun Lin

Abstract

Let G be a finite group, p the smallest prime dividing the order
of G and P a Sylow p-subgroup of G with the smallest generator number d.
We consider such a set Md(P) = {P1, P2, . . . , Pd} of maximal subgroups of P
such that ∩di=1Pi = Φ(P). Groups with certain s-permutably embedded and
weakly c-normal subgroups of prime power order are studied. We present some
sufficient conditions for a group to be p-nilpotent or p-supersolvable.

Keywords

weakly c-normal subgroups, s-permutably embedded subgroups, p-nilpotent groups

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• Guo Zhong and Liying Yang School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, P. R. China e-mails: [e-mail] (Guo Zhong) Xuanlong Ma
• School of Mathematical Sciences Beijing Normal University, Beijing, P. R. China e-mail: [e-mail] [e-mail] (Liying Yang) Shixun Lin
• College of Mathematics and Statistics, Zhaotong University, Zhaotong, P. R. China e-mail: [e-mail]