Schur indices in finite quaternion-free groups

Oh, A. D.

doi:10.1090/S0002-9939-1982-0660593-5

Schur indices in finite quaternion-free groups
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by A. D. Oh

Proc. Amer. Math. Soc. 85 (1982), 514-516

DOI: https://doi.org/10.1090/S0002-9939-1982-0660593-5

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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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