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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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Schur indices and sums of squares
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by Burton Fein PDF
Proc. Amer. Math. Soc. 51 (1975), 31-34 Request permission

Abstract:

Let $G$ be a finite group of exponent $n, F$ a field of characteristic zero, $\varepsilon$ a primitive $n$th root of unity, and suppose that the Sylow $2$-subgroup of the Galois group of $F(\varepsilon )$ over $F$ is cyclic. Let $\chi$ be an absolutely irreducible character of $G$. Strengthening a recent result of Goldschmidt and Isaacs, it is shown that if — 1 is a sum of two squares in $F$, then the Schur index of $\chi$ over $F$ is odd.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 31-34
  • MSC: Primary 12A80; Secondary 20C15
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0374249-6
  • MathSciNet review: 0374249