Rational nonlinear characters of metabelian groups
HTML articles powered by AMS MathViewer
- by B. G. Basmaji PDF
- Proc. Amer. Math. Soc. 85 (1982), 175-180 Request permission
Abstract:
Let $G$ be a finite metabelian group with all nonlinear irreducible characters rational. Then the exponent of the commutator group $G’$ is a prime or divides 16, 24, or 40. If $G’$ is also cyclic, then its order is a prime or divides 12.References
- B. G. Basmaji, Monomial representations and metabelian groups, Nagoya Math. J. 35 (1969), 99–107. MR 244394
- B. G. Basmaji, Modular representations of metabelian groups, Trans. Amer. Math. Soc. 169 (1972), 389–399. MR 310050, DOI 10.1090/S0002-9947-1972-0310050-9
- Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0144979
- Roderick Gow, Groups whose characters are rational-valued, J. Algebra 40 (1976), no. 1, 280–299. MR 409620, DOI 10.1016/0021-8693(76)90098-3
- I. Martin Isaacs, Character theory of finite groups, Pure and Applied Mathematics, No. 69, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0460423
- Frank M. Markel, Groups with many conjugate elements, J. Algebra 26 (1973), 69–74. MR 330287, DOI 10.1016/0021-8693(73)90034-3
- A. L. Višneveckiĭ, Finite groups with rational characters, Dokl. Akad. Nauk Ukrain. SSR Ser. A 10 (1977), 876–878, 958 (Russian, with English summary). MR 0470054
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 175-180
- MSC: Primary 20C15
- DOI: https://doi.org/10.1090/S0002-9939-1982-0652436-0
- MathSciNet review: 652436