Computing ray class groups, conductors and discriminants

Abstract

We use the algorithmic computation of exact sequences of Abelian groups to compute the complete structure of ( Z K / m ) ∗ (\mathbb {Z}_{K}/\mathfrak {m})^{*} for an ideal m \mathfrak {m} of a number field K K , as well as ray class groups of number fields, and conductors and discriminants of the corresponding Abelian extensions. As an application we give several number fields with discriminants less than previously known ones.