A curiosity concerning the degrees of the characters of a finite group
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- by K. L. Fields
- Proc. Amer. Math. Soc. 62 (1977), 25-27
- DOI: https://doi.org/10.1090/S0002-9939-1977-0424921-6
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Abstract:
Let G be a finite group with irreducible characters $\{ \ldots ,\chi , \ldots \}$ and $K = {\mathbf {Q}}( \ldots ,\chi , \ldots )$ the field generated over the rationals by their values. We will prove: If $K = \mathbf {Q}$ (or if $[K:{\mathbf {Q}}]$ is odd) then $\prod \limits _{\chi (1)\;odd} {\chi (1)}$ is a perfect square.References
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 25-27
- MSC: Primary 20C15
- DOI: https://doi.org/10.1090/S0002-9939-1977-0424921-6
- MathSciNet review: 0424921