Schur indices in finite quaternion-free groups

Author:
A. D. Oh

Journal:
Proc. Amer. Math. Soc. **85** (1982), 514-516

MSC:
Primary 20C15

MathSciNet review:
660593

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite, quaternion-free group with exponent , let be a field of characteristic zero and let be an absolutely irreducible character of . Suppose that a Sylow -subgroup of the Galois group of over is cyclic. It is shown that if is not real valued, then the Schur index of over is odd.

**[1]**I. Martin Isaacs,*Character theory of finite groups*, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Pure and Applied Mathematics, No. 69. MR**0460423****[2]**D. M. Goldschmidt and I. M. Isaacs,*Schur indices in finite groups*, J. Algebra**33**(1975), 191–199. MR**0357570****[3]**Burton Fein,*Schur indices and sums of squares*, Proc. Amer. Math. Soc.**51**(1975), 31–34. MR**0374249**, 10.1090/S0002-9939-1975-0374249-6**[4]**Larry Joel Goldstein,*Analytic number theory*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR**0498335****[5]***The theory of numbers*(1975), xi+541. With contributions by T. Tannaka, T. Tamagawa, I. Satake, Akira Hattori, G. Fujisaki and H. Shimizu; Translated from the Japanese by K. Iyanaga; North-Holland Mathematical Library, Vol. 8. MR**0444603****[6]**Larry Dornhoff,*𝑀-groups and 2-groups*, Math. Z.**100**(1967), 226–256. MR**0217174**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
20C15

Retrieve articles in all journals with MSC: 20C15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1982-0660593-5

Article copyright:
© Copyright 1982
American Mathematical Society