On groups whose subnormal subgroups are inert

TL;DR

This paper classifies soluble-by-finite groups where subnormal subgroups are inert, focusing on cases with no nontrivial torsion normal subgroups or finitely generated groups, providing structural insights into these groups.

Contribution

It offers a classification of soluble-by-finite groups with inert subnormal subgroups under specific torsion and generation conditions, advancing understanding of their subgroup structure.

Findings

Classification of soluble-by-finite groups with inert subnormal subgroups

Results for groups without nontrivial torsion normal subgroups

Analysis of finitely generated groups with inert subnormal subgroups

Abstract

A subgroup H of a group G is called inert if for each $g\in G$ the index of $H\cap H^g$ in $H$ is finite. We give a classification of soluble-by-finite groups $G$ in which subnormal subgroups are inert in the cases where $G$ has no nontrivial torsion normal subgroups or $G$ is finitely generated.