A classification of finite primitive IBIS groups with alternating socle

Abstract

Abstract Let 𝐺 be a finite permutation group on Ω. An ordered sequence ( ω 1 , … , ω ℓ ) (\omega_{1},\ldots,\omega_{\ell}) 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.