Families of Unramified Extensions of Number Fields

TL;DR

This paper explores algebraic techniques to construct families of unramified abelian extensions of number fields with specific Galois groups, advancing understanding of their structure and properties.

Contribution

It introduces new algebraic methods for constructing unramified abelian extensions with prescribed Galois groups in certain number fields.

Findings

Constructed explicit families of unramified abelian extensions

Identified conditions for the existence of such extensions

Enhanced understanding of Galois group structures in number fields

Abstract

Algebraic methods are used to construct families of unramified abelian extensions of some families of number fields with specified Galois groups.