Abstract.
A Beauville surface of unmixed type is a complex algebraic surface which is the quotient of the product of two curves of genus at least 2 by a finite group G acting freely on the product, where G preserves the two curves and their quotients by G are isomorphic to the projective line, ramified over three points. We show that the automorphism group A of such a surface has an abelian normal subgroup I isomorphic to the centre of G, induced by pairs of elements of G acting compatibly on the curves (a result obtained independently by Fuertes and González-Diez). Results of Singerman on inclusions between triangle groups imply that A/I is isomorphic to a subgroup of the wreath product 
, so A is a finite solvable group. Using constructions based on Lucchini's work on generators of special linear groups, we show that every finite abelian group can arise as I, even if one restricts the index 
to the extreme values 1 or 72.
© 2013 by Walter de Gruyter Berlin Boston
