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Sets of $p$-powers as conjugacy class sizes

Author(s): John Cossey; Trevor Hawkes
Journal: Proc. Amer. Math. Soc. 128 (2000), 49-51.
MSC (1991): Primary 20D60
Posted: May 27, 1999
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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:

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
Email: John.Cossey@maths.anu.edu.au

Trevor Hawkes
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: toh@maths.warwick.ac.uk

DOI: 10.1090/S0002-9939-99-05138-2
PII: S 0002-9939(99)05138-2
Received by editor(s): March 24, 1998
Posted: 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
Copyright of article: Copyright 1999, American Mathematical Society

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