A note on class number of certain real cyclotomic field

TL;DR

This paper constructs an infinite family of real cyclotomic fields with non-trivial class groups, expanding previous results and demonstrating the existence of such fields more broadly.

Contribution

It introduces a new infinite family of real cyclotomic fields with non-trivial class groups, generalizing earlier specific cases.

Findings

Existence of infinite family of real cyclotomic fields with non-trivial class group

Generalization of previous isolated results to a broader family

Method for constructing such fields

Abstract

We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.