## Coprimeness among irreducible character degrees of finite solvable groups

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- by Diane Benjamin
- Proc. Amer. Math. Soc.
**125**(1997), 2831-2837 - DOI: https://doi.org/10.1090/S0002-9939-97-04269-X
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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

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## Bibliographic Information

**Diane Benjamin**- Affiliation: Department of Mathematics, University of Wisconsin–Platteville, Platteville, Wisconsin 53818
- Email: benjamin@uwplatt.edu
- Received by editor(s): April 4, 1996
- Communicated by: Ronald M. Solomon
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**125**(1997), 2831-2837 - MSC (1991): Primary 20C15
- DOI: https://doi.org/10.1090/S0002-9939-97-04269-X
- MathSciNet review: 1443370