A classification of finite primitive IBIS groups with alternating socle

Let G be a finite permutation group on ω. An ordered sequence (ω 1, ⋯, ω ℓ) of elements of ω is an irredundant base for G if the pointwise stabilizer is trivial and no point is fixed by the stabilizer of its predecessors. If all irredundant bases of G have the same cardinality, G is said to be an IBIS group. Lucchini, Morigi and Moscatiello have proved a theorem reducing the problem of classifying finite primitive IBIS groups G to the case that the socle of G is either abelian or non-abelian simple. In this paper, we classify the finite primitive IBIS groups having socle an alternating group. Moreover, we propose a conjecture aiming to give a classification of all almost simple primitive IBIS groups.