Ray Class Groups of Quadratic and Cyclotomic Fields

TL;DR

This paper investigates the structure of ray class groups in quadratic and cyclotomic fields, providing explicit computations and restrictions on possible Galois groups in these number fields.

Contribution

It offers explicit calculations of ray class groups for certain number fields and establishes restrictions on Galois groups arising from these fields.

Findings

Ray class groups computed for specific quadratic and cyclotomic fields

Restrictions on finite Galois groups based on ray class group structure

Explicit structure of ray class groups in regular cyclotomic fields

Abstract

This paper studies Galois extensions over real quadratic number fields or cyclotomic number fields ramified only at one prime. In both cases, the ray class groups are computed, and they give restrictions on the finite groups that can occur as such Galois groups. Also the explicit structure of ray class groups of regular cyclotomic number field is given.