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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 in finite quaternion-free groups


Author: A. D. Oh
Journal: Proc. Amer. Math. Soc. 85 (1982), 514-516
MSC: Primary 20C15
MathSciNet review: 660593
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Abstract: Let $ G$ be a finite, quaternion-free group with exponent $ e$, let $ F$ be a field of characteristic zero and let $ \chi $ be an absolutely irreducible character of $ G$. Suppose that a Sylow $ 2$-subgroup of the Galois group of $ F{(^e}\sqrt 1 )$ over $ F$ is cyclic. It is shown that if $ \chi $ is not real valued, then the Schur index of $ \chi $ over $ F$ is odd.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660593-5
PII: S 0002-9939(1982)0660593-5
Article copyright: © Copyright 1982 American Mathematical Society