Closures of permutation groups with restricted nonabelian composition factors

Given a permutation group G on a finite set [Formula: see text], let [Formula: see text] denote the k-closure of G, that is, the largest permutation group on [Formula: see text] having the same orbits in the induced action on [Formula: see text] as G. Recall that a group is [Formula: see text]-free if it does not contain a section isomorphic to the alternating group of degree d. Motivated by some problems in computational group theory, we prove that the k-closure of an [Formula: see text]-free group is again [Formula: see text]-free for [Formula: see text] and [Formula: see text].