Finite generation of cohomology of finite groups

TL;DR

This paper proves that the cohomology ring of a finite p-group over F_p is finitely generated by reducing the problem to elementary abelian groups using Serre's Theorem on Bockstein products.

Contribution

It provides a new proof of finite generation of cohomology rings for finite p-groups, simplifying previous approaches through reduction techniques.

Findings

Cohomology ring of finite p-groups is finitely generated.

Reduction to elementary abelian groups is effective.

Utilizes Serre's Theorem on Bockstein products.

Abstract

We give a proof of the finite generation of the cohomology ring of a finite p-group over F_p by reduction to the case of elementary abelian groups, based on Serre's Theorem on products of Bocksteins.