Imaginary quadratic fields with \(Cl_2(k)\simeq (2,2,2)\).

DOI10.1016/S0022-314X(03)00084-2zbMath1045.11077MaRDI QIDQ1415366

Elliot Benjamin, Franz Lemmermeyer, Chip Snyder

Publication date: 3 December 2003

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

zbMATH Keywords

Hilbert 2-class fieldtower

Mathematics Subject Classification ID

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

Related Items (15)

Computation of Galois groups associated to the 2-class towers of some imaginary quadratic fields with 2-class group \(C_2 \times C_2\times C_2\) ⋮ Determination of all imaginary quadratic fields for which their Hilbert 2-class fields have 2-class groups of rank 2 ⋮ On the maximal unramified pro-2-extension over the cyclotomic \(\mathbb Z_2\)-extension of an imaginary quadratic field ⋮ The distribution of second \(p\)-class groups on coclass graphs ⋮ On Hilbert 2-class fields and 2-towers of imaginary quadratic number fields ⋮ The computation of $\mathrm{Gal}(k^\infty /k)$ for some complex quadratic number fields $k$ ⋮ Grün's theorems and class groups ⋮ The generalized Rédei-matrix ⋮ On the second 2-class group \(\mathrm{Gal}(K_2^{(2)} / K)\) of some imaginary quartic cyclic number field \(K\) ⋮ Structure of \(\mathrm {Gal}(\Bbbk _2^{(2)}/\Bbbk)\) for some fields \(\Bbbk=\mathbb {Q}(\sqrt{2p_1p_2},i)\) with \(\mathbf {C}l_2(\Bbbk)\simeq (2, 2, 2)\) ⋮ Group Theory and the Capitulation Problem for Some Number Fields ⋮ Embedding 2-groups in groups generated by involutions ⋮ Coclass of ${\rm Gal}({\mathbb K}_2^{(2)}/{\mathbb K})$ for some fields ${\mathbb K} = {\mathbb Q}(\sqrt{p_1p_2q}, \sqrt{-1})$ with 2-class groups of types (2, 2, 2) ⋮ Unnamed Item ⋮ Principalization of 2-class groups of type (2, 2, 2) of biquadratic fields ${\mathbb Q}(\sqrt{p_1p_2q}, \sqrt{-1})$

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Konstruktion imaginärquadratischer Körper mit unendlichem Klassenkörperturm
• Tours de corps de classes et estimations de discriminants
• Refined lower bounds on the 2-class number of the Hilbert 2-class field of imaginary quadratic number fields with elementary 2-class group of rank 3
• Imaginary quadratic fields \(k\) with cyclic \(\text{Cl}_2(k^1)\)
• On 2-class field towers of some imaginary quadratic number fields
• Unramified quaternion extensions of quadratic number fields
• A Contribution to the Theory of Groups of Prime-Power Order
• Ideal class groups of cyclotomic number fields I
• Real Quadratic Number Fields with 2-Class Group of Type (2,2).
• Über den 2-Klassenkörperturm eines quadratischen Zahlkörpers. I.

This page was built for publication: Imaginary quadratic fields with \(Cl_2(k)\simeq (2,2,2)\).