On permutizers of subgroups of finite groups

TL;DR

This paper investigates the properties of permutizer subgroups in finite groups, providing new characterizations of w-supersoluble and supersoluble groups based on these subgroup systems.

Contribution

It introduces novel characterizations of w-supersoluble and supersoluble groups through the study of permutizer and strongly permutizer subgroups.

Findings

Characterizations of w-supersoluble groups

Characterizations of supersoluble groups

Insights into subgroup permutability properties

Abstract

Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.