Unit groups and Iwasawa lambda invariants of some multiquadratic number fields
type: Item
instance of: scholarly article
title: Unit groups and Iwasawa lambda invariants of some multiquadratic number fields
zbMATH Open document ID: 1468.11223
author: Mohamed Mahmoud Chems-Eddin
author: Abdelmalek Azizi
author: Abdelkader Zekhnini
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 2021-05-03T00:00:00Z
review text: The authors consider the field \(L=\mathbb Q(\sqrt{q_1},\sqrt{q_2},\sqrt2,i)\), where \(q_1,q_2\) are primes satisfying \(q_1\equiv 7\pmod 8, q_2\equiv3\pmod 8\) and determine the fundamental units and the \(2\)-class-group of \(L\) and its maximal real subfield. As an application they show that the Iwasawa coefficient \(\lambda(F)\) equals three for the cyclotomic \(\mathbb Z_2\)-extension of \(F=\mathbb Q(\sqrt{p_1},\sqrt{p_2},i)\), where \(p_1,p_2\) are primes with \(p_1\equiv7\pmod{16}, p_2\equiv3\pmod8\).
Mathematics Subject Classification ID: 11R20
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 7342807
zbMATH Keywords: multiquadratic number fields
zbMATH Keywords: unit groups
zbMATH Keywords: 2-class groups
zbMATH Keywords: cyclotomic \(\mathbb{Z}_2\)-extensions
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
full work available at URL: s40590-021-00329-z
OpenAlex ID: W3129713793
cites work: On the 2-class group of \(\mathbb{Q}(\sqrt{d},i)\)
cites work: Sur la capitulation des 2-classes d'idéaux de
cites work: Units of certain imaginary abelian number fields over \(\mathbb Q\).
cites work: Q5447689
cites work: Units and2-class field towers of some multiquadratic number fields
cites work: On the strongly ambiguous classes of some biquadratic number fields.
cites work: Q3994474
cites work: The Iwasawa invariant \(\mu_p\) vanishes for abelian number fields
cites work: Remarks on \(\mathbb{Z}_ p\)-extensions of number fields
cites work: On Γ-extensions of algebraic number fields
cites work: Sur le 2-groupe des classes d'idéaux des corps quadratiques.
cites work: Cyclotomic Z//2-extensions of J-fields
cites work: Über die Klassenzahlen algebraischer Zahlkörper
cites work: Q5541475
DOI: 10.1007/S40590-021-00329-Z
description: scientific article; zbMATH DE number 7342807