Strongly Real Beauville Groups

TL;DR

This paper explores the existence and construction of strongly real Beauville groups, focusing on finite simple, abelian, nilpotent, characteristically simple, and almost simple groups, and presents new examples and open problems.

Contribution

It provides new examples of infinite families of strongly real Beauville groups and discusses their properties across various group classes.

Findings

Identification of new infinite families of strongly real Beauville groups

Analysis of strongly real Beauville groups in simple, abelian, and nilpotent classes

Open problems and conjectures in the classification of these groups

Abstract

A strongly real Beauville group is a Beauville group that defines a real Beauville surface. Here we discuss efforts to find examples of these groups, emphasising on the one extreme finite simple groups and on the other abelian and nilpotent groups. We will also discuss the case of characteristically simple groups and almost simple groups. \emph{En route} we shall discuss several questions, open problems and conjectures as well as giving several new examples of infinite families of strongly real Beauville groups.