Constructing free actions of p-groups on products of spheres

TL;DR

This paper proves that any finite p-group of rank 3, where p is an odd prime, can act freely on a space homotopy equivalent to a product of three spheres, expanding understanding of group actions on topological spaces.

Contribution

It establishes that all finite p-groups of rank 3 for odd primes admit free actions on products of three spheres, a new result in the study of group actions on topological spaces.

Findings

Finite p-groups of rank 3 act freely on products of three spheres.

The result applies specifically to odd primes p.

This advances the classification of group actions on topological spaces.

Abstract

We prove that, for p an odd prime, every finite p-group of rank 3 acts freely on a finite complex X homotopy equivalent to a product of three spheres.