Copyright © 2009 Jeffrey M. Riedl. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a useful new characterization of the automorphisms of the regular wreath product group P of a finite cyclic p-group by a finite cyclic p-group, for any prime p, and we discuss an application. We also present a short new proof, based on representation theory, for determining the order of the automorphism group Aut(P), where P is the regular wreath product of a finite cyclic p-group by an arbitrary finite p-group.