Topologically simple, totally disconnected, locally compact infinite matrix groups

TL;DR

This paper investigates infinite matrix groups over finite fields, revealing their topologically simple, totally disconnected, locally compact structures and establishing their non-discrete topologies.

Contribution

It demonstrates that certain infinite matrix groups over finite fields are topologically simple and admit nondiscrete locally compact topologies.

Findings

Groups are topologically simple

Groups admit nondiscrete totally disconnected locally compact topology

Applicable to infinite matrices over finite fields

Abstract

Groups of almost upper triangular infinite matrices with entries indexed by integers are studied. It is shown that, when the matrices are over a finite field, these groups admit a nondiscrete totally disconnected, locally compact group topology and are topologically simple.