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

 

Character degree sets that do not bound the class of a $p$-group


Authors: I. M. Isaacs and M. C. Slattery
Journal: Proc. Amer. Math. Soc. 130 (2002), 2553-2558
MSC (2000): Primary 20C15
Published electronically: February 4, 2002
MathSciNet review: 1900861
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Abstract: Suppose that we are given a set $\mathcal{S}$ of powers of a prime $p$ and that $1 \in \mathcal{S}$. A technique is presented that enables the construction of a $p$-group of specified nilpotence class $n$ such that its set of irreducible character degrees is exactly $\mathcal{S}$. If $\vert\mathcal{S}\vert \ge 2$, then this can be done for $2 \le n \le p$ and if $p \in \mathcal{S}$, then the only requirement is $2 \le n$.


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Additional Information

I. M. Isaacs
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706
Email: isaacs@math.wisc.edu

M. C. Slattery
Affiliation: Department of Mathematics, Statistics and Computer Science, Marquette University, P.O. Box 1881, Milwaukee, Wisconsin 53201
Email: mikes@mscs.mu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06364-5
PII: S 0002-9939(02)06364-5
Received by editor(s): February 23, 2001
Received by editor(s) in revised form: April 16, 2001
Published electronically: February 4, 2002
Additional Notes: The research of the first author was partially supported by the U. S. National Security Agency.
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2002 American Mathematical Society