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Proceedings of the American Mathematical Society

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

 

 

Two remarks on the group algebra of a finite group


Author: K. L. Fields
Journal: Proc. Amer. Math. Soc. 30 (1971), 247-248
MSC: Primary 20.80
DOI: https://doi.org/10.1090/S0002-9939-1971-0286901-8
MathSciNet review: 0286901
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0286901-8
Keywords: Theorem of Burnside and Blichfeldt, Brauer-Speiser Theorem
Article copyright: © Copyright 1971 American Mathematical Society