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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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.


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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: http://dx.doi.org/10.1090/S0002-9939-99-05138-2
PII: S 0002-9939(99)05138-2
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