Finite Groups with Some s-semipermutable subgroups

TL;DR

This paper explores how s-semipermutable subgroups affect the structure of finite groups, generalizing recent results to deepen understanding of subgroup influence in group theory.

Contribution

It introduces the concept of s-semipermutability and extends existing results to analyze their impact on finite group structure.

Findings

s-semipermutable subgroups influence group structure

generalization of recent results in subgroup theory

criteria for subgroup influence on finite groups

Abstract

Suppose that $G$ is a finite group and $H$ is a subgroup of $G$. We say that $H$ is s-semipermutable in $G$ if $HG_p = G_pH$ for any Sylow $p$-subgroup $G_p$ of $G$ with $(p, |H|) = 1$. We investigate the influence of s-semipermutable subgroups on the structure of finite groups. Some recent results are generalized.