On the construction of pure number fields of odd degrees with large 2-class groups
type: Item
instance of: scholarly article
title: On the construction of pure number fields of odd degrees with large 2-class groups
zbMATH Open document ID: 0592.12005
published in: Proceedings of the Japan Academy. Series A
publication date: 1986-01-01T00:00:00Z
review text: Let \(n\) be an odd integer \(>1\) and let \(\Delta_ n\) denote the number of positive divisors of \(n\) smaller than \(n\). In a previous paper [Arch. Math. 42, 53-57 (1984; Zbl 0531.12006)] the author constructed infinitely many pure number fields of degree \(n\) whose ideal class groups have 2-rank at least \(2\Delta_ n\). In the present paper he proves a stronger result where \(2\Delta_ n\) is replaced by \(3\Delta_ n\).
Mathematics Subject Classification ID: 11R23
zbMATH DE Number: 3950655
zbMATH Keywords: pure number fields
zbMATH Keywords: ideal class groups
author: Shin-Ichi Nakano
reviewed by: Veikko Ennola
Wikidata QID: Q114023247
MaRDI profile type: Publication
full work available at URL: pjaa.62.61
OpenAlex ID: W2004135534
cites work: A type of class group for imaginary quadratic fields
cites work: A construction for irregular discriminants
cites work: On the 2-rank of the ideal class groups of pure number fields
cites work: On unramified Galois extensions of quadratic number fields
DOI: 10.3792/PJAA.62.61
description: scientific article; zbMATH DE number 3950655