On the 2-component of the class group of certain cyclic extensions of degree \(2^ n\)
type: Item
instance of: scholarly article
title: On the 2-component of the class group of certain cyclic extensions of degree \(2^ n\)
zbMATH Open document ID: 0833.11054
author: Graziella Guerry
published in: Journal of Number Theory
publication date: 1996-03-17T00:00:00Z
review text: For a totally imaginary number field \(K\), cyclic over \(\mathbb{Q}\) of degree \(2^n\) \((n\geq 2)\), the author shows that the 2-class group of \(K\) is cyclic if and only if the relative class number of \(K\) is congruent to \(2\bmod 4\), and in this case, the exponent of this 2-group is \(\leq n\) and is completely determined by the ramification indices of the prime factors of the conductor of \(K\). This contrasts with the case of imaginary quadratic fields, for which the determination of the exponent of the 2-class group -- when it is cyclic -- is still an open problem.
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R20
zbMATH DE Number: 792474
zbMATH Keywords: totally imaginary cyclic number field
zbMATH Keywords: 2-class group
zbMATH Keywords: relative class number
zbMATH Keywords: imaginary quadratic fields
reviewed by: Thong Nguyen Quang Do
MaRDI profile type: Publication
full work available at URL: jnth.1995.1084
OpenAlex ID: W2061985811
DOI: 10.1006/JNTH.1995.1084
description: scientific article; zbMATH DE number 792474