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 $\chi \mathrm{:}G\mathrm{\to }{K}^{\mathrm{\times }}$, where $K^{\mathrm{\times }}$ is the multiplicative group $K\mathrm{\setminus }\mathrm{\{}{\mathrm{0}}_K\mathrm{\}}$.

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

Title	character of a finite group
Canonical name	CharacterOfAFiniteGroup
Date of creation	2013-03-22 14:10:27
Last modified on	2013-03-22 14:10:27
Owner	alozano (2414)
Last modified by	alozano (2414)
Numerical id	6
Author	alozano (2414)
Entry type	Definition
Classification	msc 11A25
Synonym	character
Related topic	DirichletCharacter