On $W$-$S$-permutable subgroups of finite groups

Abstract

A subgroup $H$ of a finite group $G$ is said to be $W$-$S$-permutable in $G$ if there is a subgroup $K$ of $G$ such that $G=HK$ and $H\cap K$ is a nearly $S$-permutable subgroup of $G$. In this article, we analyse the structure of a finite group $G$ by using the properties of $W$-$S$-permutable subgroups and obtain some new characterizations of finite $p$-nilpotent groups and finite supersolvable groups. Some known results are generalized