Sets of $p$-powers as conjugacy class sizes
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- by John Cossey and Trevor Hawkes PDF
- Proc. Amer. Math. Soc. 128 (2000), 49-51 Request permission
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
- I. M. Isaacs, Sets of $p$-powers as irreducible character degrees, Proc. Amer. Math. Soc. 96 (1986), no. 4, 551–552. MR 826479, DOI 10.1090/S0002-9939-1986-0826479-1
- Hanna Neumann, Varieties of groups, Springer-Verlag New York, Inc., New York, 1967. MR 0215899
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
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 49-51
- MSC (1991): Primary 20D60
- DOI: https://doi.org/10.1090/S0002-9939-99-05138-2
- MathSciNet review: 1641677