Real quadratic number fields with metacyclic Hilbert $2$-class field tower

DOI10.21136/MB.2018.0102-17zbMath1474.11187OpenAlexW2889368766MaRDI QIDQ5227163

Ali Mouhib, Ahmed Dakkak, Said Essahel

Publication date: 5 August 2019

Published in: Mathematica Bohemica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.21136/mb.2018.0102-17

zbMATH Keywords

class field towerclass groupreal quadratic number fieldmetacyclic group

Mathematics Subject Classification ID

Quadratic extensions (11R11) Class field theory (11R37) Class numbers, class groups, discriminants (11R29)

Related Items (2)

On the rank of the 2-class group of some imaginary biquadratic number fields ⋮ On the cyclicity of the 2-class group of the fields $\mathbb{Q}(i,\sqrt{p_1},\dots,\sqrt{p_n})$

Cites Work

• A positive proportion of some quadratic number fields with infinite Hilbert 2-class field tower
• On \(2\)-class field towers of some real quadratic number fields with \(2\)-class groups of rank \(3\)
• On subgroups of finite \(p\)-groups.
• Capitulation of the 2-ideal classes of biquadratic fields whose class field differs from the Hilbert class field
• On the parity of the class number of multiquadratic number fields
• Tours de corps de classes et estimations de discriminants
• Real quadratic fields with abelian 2-class field tower
• Sur le rang du 2-groupe de classes de 𝑄({√{𝑚}},{√{𝑑}}) où 𝑚=2 ou un premier 𝑝≡1(𝑚𝑜𝑑4)
• A Remark on the Class Field Tower^*

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