Character group

Summary

The character group of a group $G$ is the set of homomorphisms from $G$ to the multiplicative group $\C^\times$, with pointwise multiplication. It is always an abelian group. For a finite abelian group it is isomorphic to the group itself, and its elements form an orthogonal basis of the functions on the group. For locally compact abelian groups, its topological version with continuous unitary characters is the Pontryagin dual.