Finite groups in which SS-permutability is a transitive relation

TL;DR

This paper investigates the structure of finite groups where SS-permutability among subgroups is transitive, defining SST-groups and exploring their properties.

Contribution

It introduces the concept of SST-groups, characterizes their structure, and analyzes the conditions under which SS-permutability is transitive in finite groups.

Findings

SST-groups are characterized by specific subgroup permutability properties.

The paper establishes criteria for SS-permutability transitivity.

Structural theorems for SST-groups are provided.

Abstract

A subgroup $H$ of a finite group $G$ is said to be SS-permutable in $G$ if $H$ has a supplement $K$ in $G$ such that $H$ permutes with every Sylow subgroup of $K$. A finite group $G$ is called an SST-group if SS-permutability is a transitive relation on the set of all subgroups of $G$. The structure of SST-groups is investigated in this paper.