Ideal class groups of real cyclotomic fields

Dongho Byeon

doi:10.1007/s11139-026-01324-6

January 30, 2026The Ramanujan JournalOpen Access

Ideal class groups of real cyclotomic fields

View Full Paper

Ask AI

Bookmark

Share

Key Points

The aim is to demonstrate the existence of certain ideal class groups within real cyclotomic fields.
Mathematical proof techniques applied to finite abelian group theory.
Analysis of the structure of real cyclotomic fields.
Investigation into the relationship between ideal class groups and subgroups.
Established that a positive density of real cyclotomic fields has ideal class groups with a subgroup isomorphic to G.
Provided examples of such cyclotomic fields.
Assured the relevance to the study of algebraic number theory.

Implication

This research proves a positive density of cyclotomic fields containing specific ideal class group substructures.

Abstract

Let G be a finite abelian group. We prove that there exists a positive density subfamily of real cyclotomic fields whose ideal class groups contain a subgroup isomorphic to G .

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Dongho Byeon (2026) studied this question.

synapsesocial.com/papers/6980ff08c1c9540dea811ac6 https://doi.org/10.1007/s11139-026-01324-6

View Full Paper

Ask AI

Bookmark

Share

Ideal class groups of real cyclotomic fields

Key Points

Implication

Abstract

Discussion

Cite This Study

Ideal class groups of real cyclotomic fields

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading