On just-infinite periodic locally soluble groups

TL;DR

This paper constructs an uncountable family of periodic, locally soluble groups that are hereditarily just infinite and demonstrates that their associated full C*-algebras are also just infinite.

Contribution

It introduces a new large family of hereditarily just infinite groups and analyzes their C*-algebras, expanding understanding of their structure and properties.

Findings

Uncountable family of periodic locally soluble hereditarily just infinite groups

Full C*-algebras of many groups in this family are just infinite

Provides new examples linking group properties with C*-algebra properties

Abstract

We construct an uncountable family of periodic locally soluble groups which are hereditarily just infinite. We also show that the associated full C*-algebra C*(G) is just infinite for many groups $G$ in this family.