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Sets of $p$-powers as conjugacy class sizes

Authors: John Cossey and Trevor Hawkes
Journal: Proc. Amer. Math. Soc. 128 (2000), 49-51
MSC (1991): Primary 20D60
Published electronically: May 27, 1999
MathSciNet review: 1641677
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that any finite set of powers of a fixed prime $p$ which includes $1$ can be the set of conjugacy class sizes of a $p$-group of nilpotency class $2$. This corresponds to a result of Isaacs for degrees of irreducible characters.

References [Enhancements On Off] (What's this?)

  • 1. I. M. Isaacs, Sets of $p$-powers as irreducible character degrees, Proceedings of the Amer. Math. Soc. 96 (1986), 551-552. MR 87d:20013
  • 2. Hanna Neumann, Varieties of groups, Springer-Verlag, Berlin, 1967. MR 35:6734

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Additional Information

John Cossey
Affiliation: Department of Mathematics, School of Mathematical Sciences, Australian National University, Canberra, 0200, Australia

Trevor Hawkes
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

Received by editor(s): March 24, 1998
Published electronically: May 27, 1999
Additional Notes: The authors wish to acknowledge the support of the Australian Research Council and the Engineering and Physical Sciences Research Council. They are also grateful to the referee for pointing out a gap in the proof and an elegant way to fill the gap.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1999 American Mathematical Society