Character of a finite abelian group
= Character of a finite abelian group
{title2=$\chi:G\to S^1$}
= Characters of a finite abelian group
{synonym}
A character of a <finite abelian group> is a homomorphism into the complex unit circle. Equivalently it is a <linear character>; finite order forces each character value to be a root of unity. These are the elements of the <character group of a finite abelian group> and form the orthogonal Fourier basis of functions on the group.