On Quasi S-Propermutable Subgroups of Finite Groups

Abstract

A subgroup $H$ of a finite group $G$ is said to be quasi S-propermutable in $G$ if $K\underset{¯}{⊲}G$ such that $HK$ is S-permutable in $G$ and $H\hspace{0.17em}\cap \hspace{0.17em}K\le H_{qsG}$ , where $H_{qsG}$ is the subgroup formed by all those subgroups of $H$ which are $S$ -propermutable in $G$ . In this paper, we give some generalizations of finite group $G$ by using the properties and effects of quasi S-propermutable subgroups.