On just-infiniteness of locally finite groups and their C*-algebras

TL;DR

This paper constructs a family of locally finite residually finite groups with just-infinite C*-algebras, answering an open question, and proves that residually finite groups of finite exponent are not just-infinite.

Contribution

It introduces a new family of groups with specific C*-algebra properties and clarifies the limitations of residually finite groups of finite exponent.

Findings

Constructed locally finite residually finite groups with just-infinite C*-algebras

Proved residually finite groups of finite exponent are not just-infinite

Answered an open question from prior research

Abstract

We give a construction of a family of locally finite residually finite groups with just-infinite C*-algebra. This answers a question from [2]. Additionally, we show that residually finite groups of finite exponent are never just-infinite.