Simple groups admit Beauville structures

Details Simple groups admit Beauville structures Simple groups admit Beauville structures

2010-09-30

arxiv.org/abs/1009.6183v2

Mathematics

Group Theory

30 pages, in the second version, some results are improved and in particular we prove an irreducibility for a certain variety

Scientific paper

We answer a conjecture of Bauer, Catanese and Grunewald showing that all finite simple groups other than the alternating group of degree 5 admit unmixed Beauville structures. We also consider an analog of the result for simple algebraic groups which depends on some upper bounds for character values of regular semisimple elements in finite groups of Lie type and obtain definitive results about the variety of triples in semisimple regular classes with product 1. Finally, we prove that any finite simple group contains two conjugacy classes C,D such that any pair of elements in C x D generates the group.

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