Class groups of real cyclotomic fields

TL;DR

This paper proves that any finite abelian group 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 universality of class groups of real cyclotomic fields for all finite abelian groups, a significant advancement in algebraic number theory.

Findings

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

The result applies broadly across all finite abelian groups, not just specific cases.

Provides new insights into the structure and diversity of class groups in cyclotomic fields.

Abstract

We prove that every finite abelian group G occurs as a subgroup of the class group of infinitely many real cyclotomic fields.