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

 

Schur indices and sums of squares


Author: Burton Fein
Journal: Proc. Amer. Math. Soc. 51 (1975), 31-34
MSC: Primary 12A80; Secondary 20C15
MathSciNet review: 0374249
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0374249-6
PII: S 0002-9939(1975)0374249-6
Keywords: Schur index, division algebra
Article copyright: © Copyright 1975 American Mathematical Society