An infinite family of strongly real Beauville p-groups

Abstract

We give an infinite family of non-abelian strongly real Beauville p-groups for every prime p by considering the quotients of triangle groups, and indeed we prove that there are non-abelian strongly real Beauville p-groups of order \(p^n\) for every \(n\ge 3,5\) or 7 according as \(p\ge 5\) or \(p=3\) or \(p=2\). This shows that there are strongly real Beauville p-groups exactly for the same orders for which there exist Beauville p-groups.