The narrow 2-class field tower of some real quadratic number fields

DOI10.4064/aa190517-23-8zbMath1462.11101OpenAlexW3007449965MaRDI QIDQ3298860

Elliot Benjamin, Chip Snyder

Publication date: 16 July 2020

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa190517-23-8

zbMATH Keywords

real quadratic fieldclass field2-class groupnarrow class groupnarrow 2-class field tower

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Finite nilpotent groups, (p)-groups (20D15)

Related Items (1)

Determination of all imaginary quadratic fields for which their Hilbert 2-class fields have 2-class groups of rank 2

Cites Work

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• Real quadratic fields with abelian 2-class field tower
• Unramified quaternion extensions of quadratic number fields
• Classification of metabelian 2-groups \(G\) with \(\mathbf{G}^{\mathrm{ab}} (\mathbf{2},\mathbf{2}^{\mathbf n})\), \(\mathbf n\geq \mathbf 2\), and rank \(\mathbf d(\mathbf G^{\prime})=\mathbf 2\). Applications to real quadratic number fields
• Über die Lösbarkeit der Gleichung \(t^2-Du^2=-4\)
• Some real quadratic number fields whose Hilbert 2-class fields have class number congruent to 2 modulo 4
• Über Den Bizyklischen Biquadratischen Zahlkörper
• Kuroda's class number formula
• Ideal class groups of cyclotomic number fields I
• Real Quadratic Number Fields with 2-Class Group of Type (2,2).
• Imaginary quadratic fields \(k\) with \(\text{Cl}_ 2(k)\simeq(2,2^ m)\) and rank \(\text{Cl}_ 2(k^ 1)=2\).

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