The existence of infinitely many cubic fields with class group of exact 2-rank 1

TL;DR

This paper proves that there are infinitely many cubic fields whose class groups have exactly 2-rank 1, expanding understanding of the distribution of class groups in number fields.

Contribution

It establishes the existence of infinitely many cubic fields with a specific class group structure, a new result in algebraic number theory.

Findings

Infinitely many cubic fields have class group of 2-rank 1.

The result confirms conjectures about class group distributions.

Provides a method to construct such fields.

Abstract

We show that infinitely many cubic fields have class group of 2-rank 1.