character of a finite groupCharacterOfAFiniteGroup2004-02-20 12:01:232005-04-25 14:55:39Definition% this is the default PlanetMath preamble. as your knowledge
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\newcommand{\Nats}{\mathbb{N}}
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\newcommand{\Rats}{\mathbb{Q}}\begin{defn}
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 $K\setminus\{0_K\}$.
\end{defn}
{\bf Example}:
The Dirichlet characters are characters from $\Ints/m\Ints$ to $\Complex$.