Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

 
 

 

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
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 https://doi.org/10.1007/BF01203150

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