Class group of real cyclotomic fields

TL;DR

This paper proves that any finite abelian group of odd order can be realized as a subgroup of the class group in infinitely many real cyclotomic fields, expanding understanding of class group structures.

Contribution

It establishes the existence of infinitely many real cyclotomic fields with class groups containing any given finite abelian group of odd order.

Findings

Any finite abelian group of odd order appears as a subgroup of class groups in infinitely many real cyclotomic fields.

The result applies broadly to the structure of class groups in these fields.

It advances the classification of class groups in cyclotomic fields.

Abstract

In this article, we prove that every finite abelian group $G$ of odd order occurs as a subgroup of the class group of infinitely many real cyclotomic fields.