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

Authors:
I. M. Isaacs and M. C. Slattery

Journal:
Proc. Amer. Math. Soc. **130** (2002), 2553-2558

MSC (2000):
Primary 20C15

DOI:
https://doi.org/10.1090/S0002-9939-02-06364-5

Published electronically:
February 4, 2002

MathSciNet review:
1900861

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that we are given a set of powers of a prime and that . A technique is presented that enables the construction of a -group of specified nilpotence class such that its set of irreducible character degrees is exactly . If , then this can be done for and if , then the only requirement is .

**[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 -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****[4]**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 -group, J. of Algebra**238**(2001) 827-842. CMP**2001:11****[6]**M. C. Slattery, Character degrees and nilpotence class in -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:
https://doi.org/10.1090/S0002-9939-02-06364-5

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