A new infinite family of non-abelian strongly real Beauville $p$-groups for every odd prime $p$

TL;DR

This paper proves the existence of infinitely many non-abelian strongly real Beauville p-groups for every odd prime p, extending previous results limited to p=2.

Contribution

It establishes the first infinite family of such groups for all odd primes, advancing the understanding of Beauville p-groups.

Findings

Existence of infinitely many non-abelian strongly real Beauville p-groups for all odd primes p.

Extension of known finite cases for p=2 to all odd primes.

New constructions that demonstrate the richness of these groups.

Abstract

We prove that there exist infinitely many a non-abelian strongly real Beauville $p$-group for every prime $p$. Previously only finitely many in the case $p=2$ have been constructed.