Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group

DOI10.1016/J.JNT.2016.09.030zbMath1377.11114OpenAlexW2554007565MaRDI QIDQ730066

Elliot Benjamin

Publication date: 23 December 2016

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2016.09.030

zbMATH Keywords

class groupdiscriminantHilbert 2-class fieldreal quadratic number fieldcommutator subgroupunramified quadratic extension

Mathematics Subject Classification ID

Quadratic extensions (11R11) Class numbers, class groups, discriminants (11R29)

Related Items (3)

Corrigendum to: ``Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group. ⋮ On the metacyclic 2-groups whose abelianizations are of type \((2, 2^n)\), \(n\geq 2\) and applications ⋮ On the Hilbert 2-class field of some quadratic number fields

Cites Work

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• On determining the 4-rank of the ideal class group of a quadratic field
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• Real quadratic fields with abelian 2-class field tower
• Imaginary quadratic fields \(k\) with cyclic \(\text{Cl}_2(k^1)\)
• On the second Hilbert 2-class field of real quadratic number fields with 2-class group isomorphic to \((2,2^n)\), \(n\geq 2\)
• 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
• On the $2$-groups whose abelianizations are of type $(2, 4)$ and applications
• Real Quadratic Number Fields with 2-Class Group of Type (2,2).
• Endliche Gruppen I

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