Beauville surfaces and finite groups
Abstract
Extending results of Bauer, Catanese and Grunewald, and of Fuertes and Gonz\'alez-Diez, we show that Beauville surfaces of unmixed type can be obtained from the groups L2(q) and SL2(q) for all prime powers q>5, and the Suzuki groups Sz(2e) and the Ree groups R(3e) for all odd e>1. We also show that L2(q) and SL2(q) admit strongly real Beauville structures, yielding real Beauville surfaces, if and only if q>5.
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