Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20.80

Retrieve articles in all journals with MSC: 20.80

Additional Information

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