Cohomological uniqueness of some $p$-groups

TL;DR

This paper proves that for certain p-groups, their mod p cohomology with Bockstein spectral sequences uniquely determines their homotopy type among p-completed CW-complexes, with applications to group theory.

Contribution

It establishes cohomological criteria for the homotopy classification of specific p-groups, a novel approach in the field.

Findings

Cohomology with Bockstein spectral sequences determines homotopy type.

Results apply to a class of p-groups.

Applications to group theory are demonstrated.

Abstract

In this paper we consider classifying spaces of a family of $p$-groups and we prove that mod $p$ cohomology enriched with Bockstein spectral sequences determines their homotopy type among $p$-completed CW-complexes. We end with some applications to group theory.