What is primitive character?

A primitive character is a mathematical concept used in number theory. It refers to a multiplicative character on a finite abelian group that is not induced by a character from a proper subgroup. In other words, a primitive character is a character that cannot be decomposed into simpler characters.

Primitive characters have many important properties, including orthogonality relations and the ability to generate all other characters on the group. They are also used in the study of L-functions and in the proof of many important theorems, such as Dirichlet's theorem on primes in arithmetic progressions.

In some contexts, the term "primitive character" may also refer to a character that is not a constituent of a larger character induced from a subgroup. However, this usage is less common than the definition given above.