The group of automorphisms of an elementary-abelian-over-cyclic regular wreath product p-group

Abstract

Let W denote the regular wreath product finite group where C is a cyclic p-group and is an elementary abelian p-group. Let A denote the subgroup of consisting of those automorphisms that act trivially on , where B is the base group. We determine A by describing where each of its elements map a certain generating set for W. We find that A is as large as possible in a certain sense. We determine some information about the subgroup structure of A, and we prove that every class-preserving automorphism of W is an inner automorphism of W.