# Definition:Trivial Character

## Definition

Let $G$ be a finite abelian group.

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

$\forall g \in G: \chi_0 \left({g}\right) = 1$

is the trivial character on $G$.

## Also known as

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