Two remarks on the group algebra of a finite group

Fields, K. L.

doi:10.1090/S0002-9939-1971-0286901-8

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.

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.

Two remarks on the group algebra of a finite group
HTML articles powered by AMS MathViewer

by K. L. Fields PDF

Proc. Amer. Math. Soc. 30 (1971), 247-248 Request permission

Abstract:

If $K \subseteq Q({\zeta _m})$, m least, we find the smallest n such that ${M_n}(K)$ appears in $QG$ for some finite group G when m is either a prime power or not exactly divisible by a prime to the first power. We also show that every group of even order possesses a nontrivial real valued character of Schur index 1 over the rationals.

References

Richard Brauer, Representations of finite groups, Lectures on Modern Mathematics, Vol. I, Wiley, New York, 1963, pp. 133–175. MR 0178056
Richard Brauer, A note on theorems of Burnside and Blichfeldt, Proc. Amer. Math. Soc. 15 (1964), 31–34. MR 158004, DOI 10.1090/S0002-9939-1964-0158004-0