Faithful characters and the Chebotarev density theorem

Choose a finite group G and a number field F. We show that, given any large family of G-extensions of F, almost all are subject to a strong effective form of the Chebotarev density theorem. As one consequence, given a prime p, we are able to give nontrivial upper bounds for the size of the p-torsion of the class group of most G-extensions of F.

To prove this result requires a tool we have developed in the character theory of finite groups. More specifically, it requires a strengthened form of Artin's induction theorem that applies to faithful irreducible characters.

(jt. with Robert Lemke-Oliver)