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 the Galois group


Author: Eugene Spiegel
Journal: Proc. Amer. Math. Soc. 81 (1981), 189-190
MSC: Primary 20C05; Secondary 12A55
DOI: https://doi.org/10.1090/S0002-9939-1981-0593453-8
MathSciNet review: 593453
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we show that the order of the Schur index of an irreducible representation divides the order of a certain subgroup of the Galois group of a cyclotomic extension of the ground field.


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

  • [1] A. A. Albert, Structure of algebras, Amer. Math. Soc. Colloq. Publ., vol. 24, Amer. Math. Soc., Providence, R. I., 1961. MR 0123587 (23:A912)
  • [2] B. Fein, Schur indices and sums of squares, Proc. Amer. Math. Soc. 51 (1975), 31-34. MR 0374249 (51:10449)
  • [3] D. Goldschmidt and I. Isaacs, Schur indices in finite groups, J. Algebra 33 (1975), 191-199. MR 0357570 (50:10038)
  • [4] E. Spiegel and A. Trojan, On semi-simple group algebras. II, Pacific J. Math. 66 (1976), 553-559. MR 0447385 (56:5697)
  • [5] T. Yamada, The Schur subgroup of the Brauer group, Lecture Notes in Math., vol. 397, Springer-Verlag, Berlin and New York, 1974. MR 0347957 (50:456)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20C05, 12A55

Retrieve articles in all journals with MSC: 20C05, 12A55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0593453-8
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society