# Weakly <em class="a-plus-plus">SS</em>-Quasinormal Minimal Subgroups and the Nilpotency of a Finite Group

### Abstract

A subgroup*H*is said to be an

*s*-permutable subgroup of a finite group

*G*provided that the equality

*HP*=

*PH*holds for every Sylow subgroup

*P*of

*G.*Moreover,

*H*is called

*SS*-quasinormal in

*G*if there exists a supplement

*B*of

*H*to

*G*such that

*H*permutes with every Sylow subgroup of

*B.*We show that

*H*is weakly

*SS*-quasinormal in

*G*if there exists a normal subgroup

*T*of

*G*such that

*HT*is

*s*-permutable and

*H \ T*is

*SS*-quasinormal in

*G.*We study the influence of some weakly

*SS*-quasinormal minimal subgroups on the nilpotency of a finite group

*G.*Numerous results known from the literature are unified and generalized.

Published

25.02.2014

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 66, no. 2, Feb. 2014, pp. 187–194, http://umj.imath.kiev.ua/index.php/umj/article/view/2122.

Issue

Section

Research articles