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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A curiosity concerning the degrees of the characters of a finite group


Author: K. L. Fields
Journal: Proc. Amer. Math. Soc. 62 (1977), 25-27
MSC: Primary 20C15
MathSciNet review: 0424921
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0424921-6
PII: S 0002-9939(1977)0424921-6
Article copyright: © Copyright 1977 American Mathematical Society