The subgroup of the Schur multiplier of a finite group G consisting of all cohomology classes whose restriction to any abelian subgroup of G is zero is called the Bogomolov multiplier of G. We prove that if G is quasisimple or almost simple, its Bogomolov multiplier is trivial except for the case of certain covers of PSL(3, 4).

We classify the sequences 〈Sn | n ∈ N〉 of finite simple nonabelian groups such that ∏ n Sn has uncountable cofinality.

In this paper we construct new Beauville surfaces with group either PSL(2, p), or belonging to some other families of finite simple groups of Lie type of low Lie rank, or an alternating group, or a symmetric group, proving a conjecture of Bauer, Catanese and Grunewald. The proofs rely on probabilistic group theoretical results of Liebeck and Shalev, on classical results of Macbeath and on recen...