Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-18T16:51:53.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Automorphisms of Iterated Wreath Product p-Groups

Published online by Cambridge University Press:  20 November 2018

Jeffrey M. Riedl
Jeffrey M. Riedl*
Affiliation:
Department of Theoretical and Applied Mathematics, University of Akron, Akron, OH 44325-4002, USAe-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We determine the order of the automorphism group Aut$(W)$ for each member $W$ of an important family of finite $p$-groups that may be constructed as iterated regular wreath products of cyclic groups. We use a method based on representation theory.

Keywords

20D4520D1520E22
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 2 , 01 June 2012 , pp. 390 - 399
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Alperin, J. L. and Fong, P., Weights for symmetric and general linear groups. J. Algebra 131(1990), no. 1, 2–22. http://dx.doi.org/10.1016/0021-8693(90)90163-I Google Scholar
[2] Huppert, B., Endliche Gruppen. I. Die Grundlehren der MathematischenWissenschaften 134. Springer-Verlag, Berlin, 1967.Google Scholar
[3] Isaacs, I. M., Character Theory of Finite Groups. Dover, New York, 1994.Google Scholar
[4] Lentoudis, P., Détermination du groupe des automorphismes du p-groupe de Sylow du groupe symétrique de degré pm: l’idée de la méthode. C. R. Math. Rep. Acad. Sci. Canada 7(1985), no. 1, 67–71.Google Scholar
[5] Lentoudis, P., Le groupe des automorphismes du p-groupe de Sylow du groupe symétrique de degré pm: résultats. C. R. Math. Rep. Acad. Sci. Canada 7(1985), no. 2, 133–136.Google Scholar
[6] Riedl, J. M., The number of automorphisms of a monolithic finite group. J. Algebra 322(2009), no. 12, 4483–4497. http://dx.doi.org/10.1016/j.jalgebra.2009.07.034 Google Scholar