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)

 
 

 

Schur indices and sums of squares


Author: Burton Fein
Journal: Proc. Amer. Math. Soc. 51 (1975), 31-34
MSC: Primary 12A80; Secondary 20C15
DOI: https://doi.org/10.1090/S0002-9939-1975-0374249-6
MathSciNet review: 0374249
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $G$ be a finite group of exponent $n, F$ a field of characteristic zero, $\varepsilon$ a primitive $n$th root of unity, and suppose that the Sylow $2$-subgroup of the Galois group of $F(\varepsilon )$ over $F$ is cyclic. Let $\chi$ be an absolutely irreducible character of $G$. Strengthening a recent result of Goldschmidt and Isaacs, it is shown that if — 1 is a sum of two squares in $F$, then the Schur index of $\chi$ over $F$ is odd.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 12A80, 20C15

Retrieve articles in all journals with MSC: 12A80, 20C15


Additional Information

Keywords: Schur index, division algebra
Article copyright: © Copyright 1975 American Mathematical Society