The fixed-point-space dimension function for a finite group representation
HTML articles powered by AMS MathViewer
- by I. Martin Isaacs
- Proc. Amer. Math. Soc. 107 (1989), 867-872
- DOI: https://doi.org/10.1090/S0002-9939-1989-0982403-5
- PDF | Request permission
Abstract:
Given a complex representation of a finite group $G$, construct the integer valued function $\alpha$ on $G$ by setting $\alpha (g)$ to be the dimension of the fixed-point-space of $g$ in the module corresponding to the given representation. Usually, $\alpha$ is not a generalized character of $G$ and for trivial reasons $|G|\alpha$ is always a generalized character. The main result of this paper is that $e\alpha$ is always a generalized character, where $e$ is the exponent of $G$.References
- 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
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 867-872
- MSC: Primary 20C15
- DOI: https://doi.org/10.1090/S0002-9939-1989-0982403-5
- MathSciNet review: 982403