Definition:Trivial Character
(Redirected from Definition:Principal Character)
Jump to navigation
Jump to search
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 $G$.