# Second Maximal Subgroups of a Sylow <em class="a-plus-plus">p</em>-Subgroup and the <em class="a-plus-plus">p</em>-Nilpotency of Finite Groups

### Abstract

A subgroup*H*of a group

*G*is said to be weakly

*s*-semipermutable in

*G*if

*G*has a subnormal subgroup

*T*such that

*HT*=

*G*and

*H*∩

*T ≤*\( {H}_{\overline{s}G} \) , where \( {H}_{\overline{s}G} \) is the subgroup of

*H*generated by all subgroups of

*H*that are

*s*-semipermutable in

*G*. The main aim of the paper is to study the

*p*-nilpotency of a group for which every second maximal subgroup of its Sylow

*p*-subgroups is weakly

*s*-semipermutable. Some new results are obtained.

Published

25.05.2014

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 66, no. 5, May 2014, pp. 694–698, http://umj.imath.kiev.ua/index.php/umj/article/view/2170.

Issue

Section

Research articles