Permutable subgroups in $\GL_n(D)$ and applications to locally finite group algebras

TL;DR

This paper investigates the existence of free non-abelian subgroups within non-central permutable subgroups of general skew linear groups and locally finite group algebras, providing insights into their algebraic structure.

Contribution

It introduces new results on free subgroup existence in permutable subgroups of skew linear groups and applications to locally finite group algebras.

Findings

Existence of free non-abelian subgroups in certain permutable subgroups

Characterization of permutable subgroups in skew linear groups

Applications to the structure of locally finite group algebras

Abstract

In this paper we study the existence of free non-abelian subgroups in non-central permutable subgroups of general skew linear groups and locally finite group algebras.