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

Author(s): I. M. Isaacs; M. C. Slattery
Journal: Proc. Amer. Math. Soc. 130 (2002), 2553-2558.
MSC (2000): Primary 20C15
Posted: February 4, 2002
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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 $2 \le n$.

References:

[1]
I. M. Isaacs and D. S. Passman, A characterization of groups in terms of the degrees of their characters. II. Pacific J. Math. 24 (1968) 467-510. MR 39:7001

[2]
I. M. Isaacs, Sets of $p$-powers as irreducible character degrees. Proc. Amer. Math. Soc. 96 (1986) 551-552. MR 87d:20013

[3]
I. M. Isaacs, Character Theory of Finite Groups, Dover, New York, 1994. MR 57:417

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I. M. Isaacs, Characters of groups associated with finite algebras. J. Algebra 177 (1995) 708-730. MR 96k:20011

[5]
I. M. Isaacs and A. Moretó, Character degrees and the nilpotence class of a $p$-group, J. of Algebra 238 (2001) 827-842. CMP 2001:11

[6]
M. C. Slattery, Character degrees and nilpotence class in $p$-groups, J. of Austral. Math. Soc. (Series A) 57 (1994) 76-80. MR 95d:20013

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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: 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
Posted: 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
Copyright of article: Copyright 2002, American Mathematical Society

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