Sur le rang du 2-groupe de classes de 𝑄({√{𝑚}},{√{𝑑}}) où 𝑚=2 ou un premier 𝑝≡1(𝑚𝑜𝑑4)

DOI10.1090/S0002-9947-01-02753-2zbMath0986.11073OpenAlexW1530613127MaRDI QIDQ2719046

Ali Mouhib, Abdelmalek Azizi

Publication date: 14 May 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-01-02753-2

zbMATH Keywords

genus fieldnorm residue symbolKronecker symbolrank of 2-class groupbiquadratic number field2-class numberambiguous class number formulabiquadratic residue symbols

Mathematics Subject Classification ID

Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29)

Related Items (23)

On the 2-class group of real multiquadratic fields ⋮ A remark on the capitulation problem ⋮ On metabelian 2-class field towers over -extensions of real quadratic fields ⋮ The2-rankof the class group of some real cyclic quartic number fields II ⋮ Structure of 2-class groups in the \(\mathbb{Z}_2\)-extensions of certain real quadratic fields ⋮ The 2-rank of the real pure quartic number field \(K= \mathbb{Q}(\sqrt[4{pd^{2}})\)] ⋮ The 2-class group of certain families of imaginary triquadratic fields ⋮ On the Hilbert 2-class field of some quadratic number fields ⋮ On \(2\)-class field towers of some real quadratic number fields with \(2\)-class groups of rank \(3\) ⋮ On the cyclicity of the 2-class group of the fields $\mathbb{Q}(i,\sqrt{p_1},\dots,\sqrt{p_n})$ ⋮ On the rank of the 2-class group of some imaginary triquadratic number fields ⋮ Cyclicity of the unramified Iwasawa module ⋮ Cubic, quartic and sextic Pólya fields ⋮ Group Theory and the Capitulation Problem for Some Number Fields ⋮ On unramified Galois $2$-groups over $\mathbb Z_2$-extensions of real quadratic fields ⋮ LE 2-RANG DU GROUPE DE CLASSES DE CERTAINS CORPS BIQUADRATIQUES ET APPLICATIONS ⋮ The 2-rank of the class group of some real cyclic quartic number fields ⋮ On the maximal unramified pro-2-extension of certain cyclotomic \(\mathbb{Z}_2\)-extensions ⋮ Biquadratic Pólya fields with only one quadratic Pólya subfield ⋮ On the 2-rank and 4-rank of the class group of some real pure quartic number fields ⋮ On the parity of the class number of multiquadratic number fields ⋮ Real quadratic number fields with metacyclic Hilbert $2$-class field tower ⋮ Kuroda's formula and arithmetic statistics

Cites Work

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• Number fields with class number congruent to 4 mod 8 and Hilbert's Theorem 94
• Real quadratic fields with abelian 2-class field tower
• Divisibility by 8 of the class number of quadratic fields whose 2-class group is cyclic, and biquadratic reciprocity
• Sur les \(\ell\)-classes d'idéaux dans les extensions cycliques rélatives de degré premier \(\ell\). I
• On the parity of the class number of a biquadratic field
• Imaginary bicyclic biquadratic fields with cyclic 2-class group
• Über Den Bizyklischen Biquadratischen Zahlkörper
• On the Ideal Class Group of Real Biquadratic Fields

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