Remark on infinite unramified extensions of number fields with class number one
type: Item
instance of: scholarly article
title: Remark on infinite unramified extensions of number fields with class number one
zbMATH Open document ID: 1215.11123
author: David Brink
published in: Journal of Number Theory
publication date: 2010-01-08T00:00:00Z
review text: \textit{C. Maire} [On infinite unramified extensions, Pac. J. Math. 192, No. 1, 135--142 (2000; Zbl 1037.11074)] constructed some examples of biquadratic number fields, with trivial class group (and so, by class field theory, with no unramified abelian extensions) and an infinite unramified Galois extension. In this short paper the author modifies Maire's method to obtain other such examples, but with considerably smaller root discriminants.
reviewed by: Alessandro Cobbe
Mathematics Subject Classification ID: 11Y40
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R32
zbMATH DE Number: 5654996
zbMATH Keywords: non-solvable unramified extensions
zbMATH Keywords: biquadratic number fields
MaRDI profile type: Publication
full work available at URL: j.jnt.2009.08.013
OpenAlex ID: W1976252294
cites work: The imaginary bicyclic biquadratic fields with class-number 1.
cites work: Q4407980
cites work: Algebraic number fields with the discriminant equal to that of a quadratic number field
cites work: On infinite unramified extensions.
cites work: Q3952202
cites work: Tours de corps de classes et estimations de discriminants
cites work: Q4692759
cites work: Die Zerlegungs- und Trägheitsgruppe als Permutationsgruppen
cites work: On unramified Galois extensions of real quadratic number fields
cites work: Maximal unramified extensions of imaginary quadratic number fields of small conductors
DOI: 10.1016/J.JNT.2009.08.013
description: scientific article; zbMATH DE number 5654996