Automorphisms of Regular Wreath Product 𝑝-Groups

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.