Imaginary quadratic fields \(k\) with \(\text{Cl}_ 2(k)\simeq(2,2^ m)\) and rank \(\text{Cl}_ 2(k^ 1)=2\).

DOI10.2140/PJM.2001.198.15zbMath1063.11038OpenAlexW2055981594MaRDI QIDQ5943428

Chip Snyder, Elliot Benjamin, Franz Lemmermeyer

Publication date: 24 September 2001

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.2001.198.15

zbMATH Keywords

Hilbert 2-class field

Mathematics Subject Classification ID

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

Related Items (8)

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 ⋮ On the Galois groups of the 2-class towers of some imaginary quadratic fields ⋮ On the maximal unramified pro-2-extension over the cyclotomic \(\mathbb Z_2\)-extension of an imaginary quadratic field ⋮ 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 ⋮ Necessary condition and sufficient for certain Galois group to be metacyclic

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