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

2010/10/18 by Ben Fairbairn, Fairbairn, Ben, Kay Magaard +3
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR

paper · pdf · doi:10.48550/arxiv.1010.3500

arxiv created 2010/10/18 · arxiv updated 2010/10/19

Abstract

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 \Alt(5) are Beauville groups.

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• Characteristically simple Beauville groups, I: cartesian powers of alternating groups
• New Beauville surfaces and finite simple groups
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• Characteristically simple Beauville groups, II: low rank and sporadic groups
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