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A Note on Brauer Character Degrees of Solvable Groups

Published online by Cambridge University Press:  20 November 2018

You-Qiang Wang
You-Qiang Wang*
Affiliation:
Department of Mathematics, Ohio University, P.O.Box 5688, Athens, Ohio, USA 45701
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Abstract

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Let G be a finite solvable group. Fix a prime integer p and let t be the number of distinct degrees of irreducible Brauer characters of G with respect to the prime p. We obtain the bound 3t — 2 for the derived length of a Hall p'-subgroup of G. Furthermore, if |G| is odd, then the derived length of a Hall p'-subgroup of G is bounded by /.

Keywords

20C20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 3 , 01 September 1991 , pp. 423 - 425
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Berger, T. R., Character degrees and derived length in groups of odd order, Journal of Algebra 39 (1976), 199–207.Google Scholar
2. Isaacs, I. M., Character degrees and derived length of a solvable group , Canadian J. Math. 27( 1975), 146– 151.Google Scholar
3. Isaacs, I. M., Character theory of finite groups. Academic Press, New York, 1976.Google Scholar