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A note on the Brauer-Speiser theorem

Author: Burton Fein
Journal: Proc. Amer. Math. Soc. 25 (1970), 620-621
MSC: Primary 20.80
MathSciNet review: 0258982
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Abstract: The Brauer-Speiser theorem asserts that the Schur index of a real-valued complex irreducible character of a finite group is either $ 1$ or $ 2$. In this paper we present a brief proof of this result. From this it follows that the $ K$-central nontrivial division algebra components of group algebras over a real algebraic number field $ K$ are quaternions.

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Keywords: Schur index, Brauer group, exponent
Article copyright: © Copyright 1970 American Mathematical Society

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