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International Journal of Mathematics and Mathematical Sciences
Volume 2009, Article ID 245617, 12 pages
Research Article

Automorphisms of Regular Wreath Product 𝑝 -Groups

Department of Theoretical and Applied Mathematics, University of Akron, Akron, OH 44325-4002, USA

Received 12 July 2009; Revised 5 November 2009; Accepted 6 November 2009

Academic Editor: Alexander Rosa

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.


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.