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Transactions of the American Mathematical Society

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Enumerating classes and characters of $ p$-groups


Authors: E. A. O’Brien and C. Voll
Journal: Trans. Amer. Math. Soc. 367 (2015), 7775-7796
MSC (2010): Primary 20C15, 20D15
DOI: https://doi.org/10.1090/tran/6276
Published electronically: April 3, 2015
MathSciNet review: 3391899
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Abstract: We develop general formulae for the numbers of conjugacy classes and irreducible complex characters of finite $ p$-groups of nilpotency class less than $ p$. This allows us to unify and generalize a number of existing enumerative results, and to obtain new such results for generalizations of relatively free $ p$-groups of exponent $ p$. Our main tools are the Lazard correspondence and the Kirillov orbit method.


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Additional Information

E. A. O’Brien
Affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand
Email: obrien@math.auckland.ac.nz

C. Voll
Affiliation: School of Mathematics, University of Southampton, University Road, Southampton SO17 1BJ, United Kingdom
Address at time of publication: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
Email: C.Voll.98@cantab.net

DOI: https://doi.org/10.1090/tran/6276
Keywords: Finite $p$-groups, character degrees, conjugacy class sizes, Kirillov orbit methods, Lazard correspondence, relatively free $p$-groups
Received by editor(s): November 28, 2012
Received by editor(s) in revised form: August 7, 2013
Published electronically: April 3, 2015
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.