Minimal splitting fields in cyclotomic extensions
Authors:
Eugene Spiegel and Allan Trojan
Journal:
Proc. Amer. Math. Soc. 87 (1983), 33-37
MSC:
Primary 20C05; Secondary 12A55
DOI:
https://doi.org/10.1090/S0002-9939-1983-0677225-3
MathSciNet review:
677225
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Abstract | References | Similar Articles | Additional Information
Abstract: Suppose is a finite group of exponent
and
an irreducible character of
. In this note we give sufficient conditions for the existence of a minimal degree splitting field
with
.
- [1] Mark Benard and Murray M. Schacher, The Schur subgroup. II, J. Algebra 22 (1972), 378–385. MR 302747, https://doi.org/10.1016/0021-8693(72)90155-X
- [2] Gary Cornell, Abhyankar’s lemma and the class group, Number theory, Carbondale 1979 (Proc. Southern Illinois Conf., Southern Illinois Univ., Carbondale, Ill., 1979) Lecture Notes in Math., vol. 751, Springer, Berlin, 1979, pp. 82–88. MR 564924
- [3] Burton Fein, Minimal splitting fields for group representations, Pacific J. Math. 51 (1974), 427–431. MR 364420
- [4] Burton Fein, Minimal splitting fields for group representations. II, Pacific J. Math. 77 (1978), no. 2, 445–449. MR 510933
- [5] Burton Fein, Schur indices and sums of squares, Proc. Amer. Math. Soc. 51 (1975), 31–34. MR 374249, https://doi.org/10.1090/S0002-9939-1975-0374249-6
- [6] Charles Ford, Groups which determine the Schur index of a representation, J. Algebra 57 (1979), no. 2, 339–354. MR 533802, https://doi.org/10.1016/0021-8693(79)90227-8
- [7] D. M. Goldschmidt and I. M. Isaacs, Schur indices in finite groups, J. Algebra 33 (1975), 191–199. MR 357570, https://doi.org/10.1016/0021-8693(75)90120-9
- [8] Helmut Hasse, Number theory, Akademie-Verlag, Berlin, 1979. Translated from the third German edition of 1969 by Horst Günter Zimmer. MR 544018
- [9] Richard Anthony Mollin, Splitting fields and group characters, J. Reine Angew. Math. 315 (1980), 107–114. MR 564527, https://doi.org/10.1515/crll.1980.315.107
- [10] Eugene Spiegel and Allan Trojan, On semi-simple group algebras. II, Pacific J. Math. 66 (1976), no. 2, 553–559. MR 447385
- [11] Toshihiko Yamada, The Schur subgroup of the Brauer group, Lecture Notes in Mathematics, Vol. 397, Springer-Verlag, Berlin-New York, 1974. MR 0347957
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1983-0677225-3
Article copyright:
© Copyright 1983
American Mathematical Society