On the rank of the 2-class group of the Hilbert 2-class field of some quadratic fields

DOI10.1093/QMATH/HAY021zbMath1445.11127OpenAlexW2800379615MaRDI QIDQ4968783

Chip Snyder, Elliot Benjamin

Publication date: 9 July 2019

Published in: The Quarterly Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/qmath/hay021

zbMATH Keywords

class groupHilbert 2-class field

Mathematics Subject Classification ID

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

Related Items (6)

Determination of all imaginary quadratic fields for which their Hilbert 2-class fields have 2-class groups of rank 2 ⋮ 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 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 ⋮ On the maximal unramified pro-2-extension of certain cyclotomic \(\mathbb{Z}_2\)-extensions

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