# character of a finite group

###### Definition.

Let $G$ be a finite group, and let $K$ be a field. A character from $G$ to $K$ is a group homomorphism $\chi\colon G\to K^{\times}$, where $K^{\times}$ is the multiplicative group $K\setminus\{0_{K}\}$.

Example: The Dirichlet characters are characters from $\mathbb{Z}/m\mathbb{Z}$ to $\mathbb{C}$.

Title character of a finite group CharacterOfAFiniteGroup 2013-03-22 14:10:27 2013-03-22 14:10:27 alozano (2414) alozano (2414) 6 alozano (2414) Definition msc 11A25 character DirichletCharacter