Generation of iterated wreath products constructed from alternating, symmetric and cyclic groups

Abstract

Let G1, G2, … be a sequence of groups each of which is either an alternating group, a symmetric group or a cyclic group. Let us construct a sequence (Wi) of wreath products via W1 = G1 and, for each i ≥ 1, Wi+1 = Gi+1 wr Wi via the natural permutation action. We determine the minimum number d(Wi) of generators required for each wreath product in this sequence