Principalization of 2-class groups of type (2, 2, 2) of biquadratic fields ${\mathbb Q}(\sqrt{p_1p_2q}, \sqrt{-1})$

DOI10.1142/S1793042115500645zbMath1319.11079arXiv1404.3761OpenAlexW2075870789MaRDI QIDQ5253879

Daniel C. Mayer, Mohammed Taous, Abdelmalek Azizi, Abdelkader Zekhnini

Publication date: 5 June 2015

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

Full work available at URL: https://arxiv.org/abs/1404.3761

zbMATH Keywords

Galois groupcapitulationbiquadratic fieldsclass-field tower

Mathematics Subject Classification ID

Galois theory (11R32) Class field theory (11R37) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29)

Related Items (10)

On some metabelian 2-groups and applications III ⋮ Unnamed Item ⋮ Capitulation of the 2-ideal classes of type \((2, 2, 2)\) of some quartic cyclic number fields ⋮ ON THE -RANK OF CLASS GROUPS OF DIRICHLET BIQUADRATIC FIELDS ⋮ Capitulation in the absolutely abelian extensions of some number fields. II ⋮ Unnamed Item ⋮ On the second 2-class group \(\mathrm{Gal}(K_2^{(2)} / K)\) of some imaginary quartic cyclic number field \(K\) ⋮ Group Theory and the Capitulation Problem for Some Number Fields ⋮ 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

Cites Work

• The distribution of second \(p\)-class groups on coclass graphs
• On the 2-class field tower of \(\mathbb Q (\sqrt{2p_1p_2},i)\) and the Galois group of its second Hilbert 2-class field
• Real quadratic fields with abelian 2-class field tower
• On 2-class field towers of some imaginary quadratic number fields
• Imaginary quadratic fields with \(Cl_2(k)\simeq (2,2,2)\).
• On 2-class field towers of imaginary quadratic number fields
• Über die Lösbarkeit der Gleichung \(t^2-Du^2=-4\)
• Computation of Galois groups associated to the 2-class towers of some imaginary quadratic fields with 2-class group \(C_2 \times C_2\times C_2\)
• Classifying 2-groups by coclass
• Sur une question de capitulation

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