Gasch\"utz Lemma for Compact Groups

TL;DR

This paper proves that the Gaschutz Lemma, a fundamental result in group theory, applies to all metrisable compact groups, extending its validity beyond previously known classes.

Contribution

The paper establishes the Gaschutz Lemma for all metrisable compact groups, broadening its applicability in the study of topological groups.

Findings

Gaschutz Lemma holds for all metrisable compact groups

Extension of the lemma from discrete to topological groups

Implications for the structure theory of compact groups

Abstract

We prove the Gasch\"utz Lemma holds for all metrisable compact groups.