On weakly ${\mathfrak{F}}_s$-quasinormal subgroups of finite groups

Abstract

Let $\mathfrak{F}$ be a formation and $G$ a finite group. A subgroup $H$ of $G$ is said to be weakly ${\mathfrak{F}}_s$-quasinormal in $G$ if $G$ has an $S$-quasinormal subgroup $T$ such that $HT$ is $S$-quasinormal in $G$ and $(H\cap T)H_G/H_G\le Z_{\mathfrak{F}}(G/H_G)$, where $Z_{\mathfrak{F}}(G/H_G)$ denotes the $\mathfrak{F}$-hypercenter of $G/H_G$. In this paper, we study the structure of finite groups by using the concept of weakly ${\mathfrak{F}}_s$-quasinormal subgroups.