Torsion elements in branch pro-$p$ groups

TL;DR

This paper proves that in certain topological groups with a branch pro-$p$ quotient, the torsion elements are negligible in measure, having Haar measure zero.

Contribution

It establishes a measure-theoretic property of torsion elements in branch pro-$p$ groups, linking group structure with Haar measure.

Findings

Torsion elements have Haar measure zero in these groups

The result applies to groups with a branch pro-$p$ quotient

Provides a measure-theoretic perspective on torsion in topological groups

Abstract

We show that the set of torsion elements of a topological group admitting a branch pro-$p$ quotient has Haar measure zero.