The mod-p cohomology rings of some p-groups

TL;DR

This paper computes the mod-p cohomology rings for an infinite family of p-groups with cyclic derived subgroups, using embeddings into compact Lie groups, advancing understanding of their algebraic topology.

Contribution

It introduces a novel method of embedding p-groups into compact Lie groups to determine their cohomology rings, specifically for groups with cyclic derived subgroups.

Findings

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

Method involving embedding into compact Lie groups proved effective.

Results extend knowledge of p-group cohomology structures.

Abstract

We determine the mod-p 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.