Coprimeness among irreducible character

degrees of finite solvable groups

Author:
Diane Benjamin

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2831-2837

MSC (1991):
Primary 20C15

MathSciNet review:
1443370

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Abstract: Given a finite solvable group , we say that has property if every set of distinct irreducible character degrees of is (setwise) relatively prime. Let be the smallest positive integer such that satisfies property . We derive a bound, which is quadratic in , for the total number of irreducible character degrees of . Three exceptional cases occur; examples are constructed which verify the sharpness of the bound in each of these special cases.

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Additional Information

**Diane Benjamin**

Affiliation:
Department of Mathematics, University of Wisconsin–Platteville, Platteville, Wisconsin 53818

Email:
benjamin@uwplatt.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-97-04269-X

Received by editor(s):
April 4, 1996

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1997
American Mathematical Society