Groups in which some primary subgroups are weakly s-supplemented?

TL;DR

This paper investigates how primary weakly s-supplemented subgroups influence the structure of finite groups, addressing an open question and generalizing known results in group theory.

Contribution

It introduces the concept of weakly s-supplemented subgroups and explores their impact on finite group structure, extending previous findings and addressing an open problem.

Findings

Characterization of finite groups with weakly s-supplemented primary subgroups

Generalization of known results in subgroup structure theory

Insights into the influence of s-permutable subgroups

Abstract

A subgroup $H$ of a group $G$ is called weakly s-supplemented in $G$ if there is a subgroup $T$ such that $G=HT$ and $H\cap T\le H_{sG}$, where $H_{sG}$ is the subgroup of $H$ generated by all those subgroups of $H$ which are s-permutable in $G$. The influence of primary weakly s-supplemented subgroups on the structure of finite groups is investigated. An open question promoted by Skiba is studied and some known results are generalized.