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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.

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
  • R. Brauer, Über Zusammenhange zwischen arithmetischen und invariantentheoretischen Eigenschaften von Gruppen linearer Substitutionen, Sitzber. Preuss. Akad. Wiss. (1926), 410-416. ---, Untersuchungen über die arithmetischen Eigenschaften von Gruppen linearer Substitutionen. II, Math. Z. 31 (1930), 737-747.
  • Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1962. MR 0144979
  • A. Speiser, Zahlentheoretische Sätze aus der Gruppentheorie, Math. Z. 5 (1919), no. 1-2, 1–6 (German). MR 1544369, DOI

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