Definition:Trivial Character

Definition
Let $G$ be a finite abelian group.

The character $\chi_0: G \to \C_{\ne 0}$ defined as:


 * $\forall g \in G: \map {\chi_0} g = 1$

is the trivial character on $G$.

Also see

 * Constant Mapping to Identity is Homomorphism, which demonstrates that $\chi_0$ is indeed a character.


 * Definition:Trivial Dirichlet Character, a similar concept

Also known as
The trivial character is also known as the principal character on $G$.