Generators of a Dirichlet character group (reviewed)

A set of generators of the Dirichlet character group $G$ of modulus $q$ is a set of Dirichlet characters $\chi_q(n_i,\cdot)$ that generate $G$ under multiplication. These may be chosen so that $G$ is the direct product of the cyclic groups generated by each of the $\chi_q(n_i,\cdot)$.