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Let $G$ be a finite permutation group on $\Omega$. An ordered sequence$(\omega_1,\ldots,\omega_\ell)$ of elements of $\Omega$ is an irredundant basefor $G$ if the pointwise stabilizer is trivial and no point is fixed by thestabilizer of its predecessors. If all irredundant bases of $G$ have the samecardinality, $G$ is said to be an IBIS group.  Lucchini, Morigi and Moscatiello have proved a theorem reducing the problemof 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 analternating group. Moreover, we propose a conjecture aiming to give aclassification of all almost simple primitive IBIS groups.

A classification of finite primitive IBIS groups with alternating socle