Some real quadratic number fields whose Hilbert 2-class fields have class number congruent to 2 modulo 4

DOI10.4064/aa8485-9-2016zbMath1401.11143OpenAlexW2591827482WikidataQ114022062 ScholiaQ114022062MaRDI QIDQ2985899

Chip Snyder, Elliot Benjamin

Publication date: 10 May 2017

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

Full work available at URL: https://doi.org/10.4064/aa8485-9-2016

zbMATH Keywords

real quadratic fieldsHilbert class field2-class groupsmetabelian 2-groups

Mathematics Subject Classification ID

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

Related Items (6)

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 ⋮ The computation of $\mathrm{Gal}(k^\infty /k)$ for some complex quadratic number fields $k$ ⋮ On the Hilbert 2-class field of some quadratic number fields ⋮ The narrow 2-class field tower of some real quadratic number fields ⋮ Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group ⋮ On some finite 2-groups in which the derived group has two generators

Cites Work

• Real quadratic fields with abelian 2-class field tower
• Imaginary quadratic fields \(k\) with cyclic \(\text{Cl}_2(k^1)\)
• Über Den Bizyklischen Biquadratischen Zahlkörper
• Kuroda's class number formula
• Endliche Gruppen I
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