Structure of finite groups with some weakly S-semipermutable subgroups

Document Type : Research Paper

Authors

1 Department of Mathematics, payme Noor University, P. O. Box 19395-4697, Tehran, IRAN

2 Faculty of Mathematical Sciences, University of Shahrekord, Shahrekord, Iran.

3 Department of Mathematics, University of Payme Noor, P.O.Box 19395-4697, Tehran, Iran

Abstract

Let G be a finite group. If AG, recall that A is  weakly S-semipermutable  in G provided there is KG such that   KA is S-permutable in G, and  KA is S-semipermutable in G. The purpose of this paper is to demonstrate that weakly S-semipermutability of special types of subgroups in a finite group G can help us to determine  structural properties of G. For example, given a prime p, a p-soluble finite group G and a Sylow p-subgroup Gp of G, we will show that G is p-supersoluble if the maximal subgroups of Gp are weakly S-semipermutable in G. Moreover, we use the concept of weakly S-semipermutability to prove new criteria for p-nilpotency of finite groups.

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