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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A curiosity concerning the degrees of the characters of a finite group
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by K. L. Fields PDF
Proc. Amer. Math. Soc. 62 (1977), 25-27 Request permission

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.
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Additional 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