Generation of finite simple groups with an application to groups acting on Beauville surfaces

Original · EN

We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these theorems to prove that every quasisimple group except Alt(5) and SL₂(5) is a Beauville group. In particular, we settle a conjecture of Bauer, Catanese and Grunewald which asserts that all non-abelian finite simple groups except for the alternating group (5) are Beauville groups.