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

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,*Finite groups with small character degrees and large prime divisors. II*, Pacific J. Math.**29**(1969), 311–324. MR**0245695****[2]**I. M. Isaacs,*Sets of 𝑝-powers as irreducible character degrees*, Proc. Amer. Math. Soc.**96**(1986), no. 4, 551–552. MR**826479**, 10.1090/S0002-9939-1986-0826479-1**[3]**I. Martin Isaacs,*Character theory of finite groups*, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Pure and Applied Mathematics, No. 69. MR**0460423****[4]**I. M. Isaacs,*Characters of groups associated with finite algebras*, J. Algebra**177**(1995), no. 3, 708–730. MR**1358482**, 10.1006/jabr.1995.1325**[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]**Michael C. Slattery,*Character degrees and nilpotence class in 𝑝-groups*, J. Austral. Math. Soc. Ser. A**57**(1994), no. 1, 76–80. MR**1279287**

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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