Steinitz classes of extensions with Galois group \(A_4\)
type: Item
instance of: scholarly article
title: Steinitz classes of extensions with Galois group \(A_4\)
zbMATH Open document ID: 1026.11082
author: Marjory Godin
author: Bouchaïb Sodaïgui
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2003-06-30T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/93841
review text: Let \(k\) be a number field and \(E/k\) a cyclic extension of degree \(3\). The authors show that if \(k\) has odd class number, then the set \(R\) of Steinitz classes of the rings of integers \(O_N\) of extensions \(N/k\) containing \(E/k\) and with Galois group \(A_4\) is equal to the coset \(\text{ cl}(O_E)(N_{E/k}\text{ Cl}(E))^3\). Here \(\text{ cl}(O_E)\) is the Steinitz class of \(O_E\), and \(N_{E/k}\) is the relative norm applied to the ideal class group of \(E\).
reviewed by: Franz Lemmermeyer
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 12F10
zbMATH DE Number: 1943337
zbMATH Keywords: alternating group
zbMATH Keywords: number field
zbMATH Keywords: Steinitz class
MaRDI profile type: Publication
OpenAlex ID: W2090426213
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DOI: 10.5802/JTNB.356
description: scientific article; zbMATH DE number 1943337