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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
DOI: https://doi.org/10.1090/S0002-9939-1970-0258982-8
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.


References [Enhancements On Off] (What's this?)

  • A. Adrian Albert, Structure of algebras, American Mathematical Society Colloquium Publications, Vol. XXIV, American Mathematical Society, Providence, R.I., 1961. Revised printing. MR 0123587
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Keywords: Schur index, Brauer group, exponent
Article copyright: © Copyright 1970 American Mathematical Society