Hassan Jafarian Dehkordi - Department of Mathematics, payme Noor University, P. O. Box ۱۹۳۹۵-۴۶۹۷, Tehran, IRAN
Gholamreza Rezaeezadeh - Faculty of Mathematical Sciences, University of Shahrekord, Shahrekord, Iran.
Masoumeh Bibak - Department of Mathematics, University of Payme Noor, P.O.Box ۱۹۳۹۵-۴۶۹۷, Tehran, Iran

Let G be a finite group. If A\leq G , recall that A is  weakly S-semipermutable  in G provided there is K\unlhd G such that   KA is S-permutable in G, and  K\cap A 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 G_{p} of G, we will show that G is p-supersoluble if the maximal subgroups of G_{p} 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.

p-nilpotent, p-supersoluble, weakly S-semipermutable