Multiplicative character
In mathematics, a multiplicative character on a group G is a group homomorphism from G to the multiplicative group of a field, usually the field of complex numbers. If G is any group, then the set Ch of these morphisms forms an abelian group under pointwise multiplication.
This group is referred to as the character group of G. Sometimes only unitary characters are considered ; other such homomorphisms are then called quasi-characters. Dirichlet characters can be seen as a special case of this definition.
Multiplicative characters are linearly independent, i.e. if are different characters on a group G then from it follows thatExamples
