Ideal class groups of cyclotomic number fields II

TL;DR

This paper investigates the structure of class groups in cyclotomic fields, focusing on maximal real subfields with even class number, plus class number implications, capitulation phenomena, and p-class group behavior in ramified extensions.

Contribution

It introduces new results on the behavior of class groups and capitulation in cyclotomic fields, especially for maximal real subfields with even class number.

Findings

Maximal real subfields with even class number identified

Implications of large plus class numbers analyzed

Capitulation and p-class group behavior in ramified extensions studied

Abstract

We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large plus class numbers of cyclotomic fields. We also discuss capitulation of the minus part and the behaviour of p-class groups in cyclic ramified p-extensions.