Schur indices in finite quaternion-free groups

Author:
A. D. Oh

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

MSC:
Primary 20C15

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

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. M. Isaacs,*Character theory of finite groups*, Academic Press, New York, 1976. MR**0460423 (57:417)****[2]**D. M. Goldschmidt and I. M. Isaacs,*Schur indices in finite groups*, J. Algebra**33**(1975), 191-199. MR**0357570 (50:10038)****[3]**B. Fein,*Schur indices and sums of squares*, Proc. Amer. Math. Soc.**51**(1975), 31-34. MR**0374249 (51:10449)****[4]**L. J. Goldstein,*Analytic number theory*, Prentice-Hall, Englewood Cliffs, N. J., 1971. MR**0498335 (58:16471)****[5]**S. Iyanaga,*The theory of numbers*, North-Holland, Amsterdam, 1975. MR**0444603 (56:2953)****[6]**L. Dornhoff,*-groups and**-groups*, Math. Z.**100**(1967), 226-256. MR**0217174 (36:265)**

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