Character group
= Character group
{title2=$\widehat G=\operatorname{Hom}_{\rm cont}(G,S^1)$}
The character group of a <topological group> that is an <abelian group> consists of its continuous <group homomorphisms> to the <circle group>, with pointwise multiplication. For a <finite group>, all characters are continuous and their values are <roots of unity>, so this agrees with the <character group of a finite abelian group>.