Arbitrary classes in >2-degree cohomology of a finite group with arbitrary coefficients may be trivialized in a finite extension

TL;DR

This paper provides an exposition of a proof demonstrating that high-degree cohomology classes of finite groups can be trivialized in finite extensions, clarifying a known but not explicitly documented result.

Contribution

It offers a detailed proof of a known fact that high-degree cohomology classes of finite groups become trivial in finite extensions, filling a gap in the literature.

Findings

High-degree cohomology classes can be trivialized in finite extensions.

The proof clarifies a previously known but undocumented result.

Provides a foundation for further research in group cohomology.

Abstract

The purpose of this note is to provide exposition for a proof of the statement in the title. This idea, that arbitrary cohomology classes (of high enough degree) of a finite group $G$ can be trivialized in a finite group extension, has been known to experts for some time.