A bound for in terms
of the largest irreducible character degree
of a finite -solvable group
Author:
Diane Benjamin
Journal:
Proc. Amer. Math. Soc. 127 (1999), 371-376
MSC (1991):
Primary 20C15
DOI:
https://doi.org/10.1090/S0002-9939-99-04746-2
MathSciNet review:
1485458
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Abstract | References | Similar Articles | Additional Information
Abstract: Let denote the largest irreducible character degree of a finite group
, and let
be a prime. Two results are obtained. First, we show that, if
is a
-solvable group and if
, then
. Next, we restrict attention to solvable groups and show that, if
and if
is a Sylow
-subgroup of
, then
.
- [1] 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
- [2] I. Martin Isaacs, Algebra, Brooks/Cole Publishing Co., Pacific Grove, CA, 1994. A graduate course. MR 1276273
- [3] D. S. Passman, Groups with normal solvable Hall 𝑝′-subgroups, Trans. Amer. Math. Soc. 123 (1966), 99–111. MR 195947, https://doi.org/10.1090/S0002-9947-1966-0195947-2
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Additional Information
Diane Benjamin
Affiliation:
Department of Mathematics, University of Wisconsin – Platteville, Platteville, Wisconsin, 53818
Email:
benjamin@uwplatt.edu
DOI:
https://doi.org/10.1090/S0002-9939-99-04746-2
Received by editor(s):
May 31, 1997
Communicated by:
Ronald M. Solomon
Article copyright:
© Copyright 1999
American Mathematical Society