The integral cohomology rings of some p-groups

TL;DR

This paper computes the integral cohomology rings of an infinite family of p-groups with cyclic derived subgroups, using a novel embedding method into compact Lie groups.

Contribution

It introduces a new approach to determine cohomology rings of p-groups by embedding them into compact Lie groups, expanding understanding of their algebraic topology.

Findings

Cohomology rings explicitly computed for the family of p-groups.

Method applicable to groups with cyclic derived subgroups.

Provides insights into the structure of p-groups via Lie group embeddings.

Abstract

We determine the integral cohomology rings of an infinite family of p-groups, for odd primes p, with cyclic derived subgroups. Our method involves embedding the groups in a compact Lie group of dimension one, and was suggested by P H Kropholler and J Huebschmann.