On the 2-class group of \(\mathbb{Q}(\sqrt{d},i)\)
type: Item
instance of: scholarly article
title: On the 2-class group of \(\mathbb{Q}(\sqrt{d},i)\)
zbMATH Open document ID: 0920.11076
DOI: 10.1007/BF02844380
author: Abdelmalek Azizi
publication date: 1999-06-01T00:00:00Z
review text: The author determines all positive squarefree integers \(d\) such that the \(2\)-class group of the biquadratic number field \(\mathbb Q(\sqrt{d},i)\) has type \((2,2)\). The methods used include genus theory, the class number formula for biquadratic extensions, and the ambiguous class number formula.
reviewed by: Franz Lemmermeyer
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R16
zbMATH DE Number: 1279152
zbMATH Keywords: biquadratic number fields
zbMATH Keywords: class number formula
zbMATH Keywords: 2-class group
MaRDI profile type: Publication
cites work: Note on primes of type x2 + 32y2, class number, and residuacity.
cites work: Binary quadratic forms of determinant \(-pq\)
cites work: Q4184930
cites work: Q5811275
cites work: On the congruences for the class numbers of the quadratic fields whose discriminants are divisible by 8
cites work: The genus fields of algebraic number fields
cites work: Divisibility by 8 of the class number of quadratic fields whose 2-class group is cyclic, and biquadratic reciprocity
cites work: Sur le 2-groupe des classes d'idéaux des corps quadratiques.
cites work: Über die Beziehung der Klassenzahlen der Unterkörper des bizyklischen bizuadratischen Zahlkörpers
cites work: Über Den Bizyklischen Biquadratischen Zahlkörper
cites work: Q5840258
cites work: Q4117900
cites work: Q3856855
cites work: A Remark on the Class Field Tower*
cites work: Determination of certain real quadratic fields with class number two
cites work: Q3882616
cites work: Congruences modulo 8 for class numbers of general quadratic fields \(\mathbb{Q}(\sqrt{m})\) and \(\mathbb{Q}(\sqrt{-m})\)
cites work: Q5541475
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1279152