Vol. 8, No. 2, 2015

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Finite groups with some weakly $s$-permutably embedded and weakly $s$-supplemented subgroups

Guo Zhong, XuanLong Ma, Shixun Lin, Jiayi Xia and Jianxing Jin

Vol. 8 (2015), No. 2, 253–262
Abstract

Let G be a finite group. A subgroup H of G is called weakly s-permutably embedded in G if there is a subnormal subgroup T of G and an s-permutably embedded subgroup Hs e of G contained in H such that G = HT and H T Hs e. The subgroup H is called weakly s-supplemented in G if G has a subgroup K such that HK = G and H K HsG, where HsG is the largest s-permutable subgroup of G contained in H. In this paper, we investigate the influence of weakly s-permutably embedded and weakly s-supplemented subgroups on the structure of finite groups. Some recent results are generalized.

Keywords
weakly $s$-permutably embedded subgroups, weakly $s$-supplemented subgroups, $p$-nilpotent groups
Mathematical Subject Classification 2010
Primary: 20D10
Secondary: 20D20
Milestones
Received: 10 January 2013
Revised: 6 August 2013
Accepted: 7 August 2013
Published: 3 March 2015

Communicated by Joseph A. Gallian
Authors
Guo Zhong
School of Mathematical Sciences
Guangxi Teachers Education University
Nanning, Guangxi 530023
China
XuanLong Ma
School of Mathematical Sciences
Beijing Normal University
Beijing 100875
China
Shixun Lin
College of Mathematics and Statistics
Zhaotong University
Zhaotong, Yunnan 657000
China
Jiayi Xia
School of Mathematical Sciences
Guangxi Teachers Education University
Nanning, Guangxi 530023
China
Jianxing Jin
School of Mathematical Sciences
Guangxi Teachers Education University
Nanning, Guangxi 530023
China