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Proceedings of the American Mathematical Society

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

References [Enhancements On Off] (What's this?)

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Additional Information

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

Received by editor(s): April 4, 1996
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society

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