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Group Theory and the Capitulation Problem for Some Number Fields - MaRDI portal

Group Theory and the Capitulation Problem for Some Number Fields (Q5738729)

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scientific article; zbMATH DE number 6729468

Language	Label	Description	Also known as
English	Group Theory and the Capitulation Problem for Some Number Fields	scientific article; zbMATH DE number 6729468

Statements

scholarly article

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Group Theory and the Capitulation Problem for Some Number Fields (English)

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Abdelmalek Azizi

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Abdelkader Zekhnini

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Non-Associative and Non-Commutative Algebra and Operator Theory

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publication date

12 June 2017

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zbMATH Keywords

genus field

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capitulation

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Hilbert class field

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/978-3-319-32902-4_1

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On the 2-class group of \(\mathbb{Q}(\sqrt{d},i)\)

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Construction of the 2-Hilbert class field tower of some biquadratic fields

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

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Capitulation des 2-classes d'idéaux de k=Q (\sqrt 2p, i)

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On the $2$-groups whose abelianizations are of type $(2, 4)$ and applications

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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)

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Structure of \(\mathrm {Gal}(\Bbbk _2^{(2)}/\Bbbk)\) for some fields \(\Bbbk=\mathbb {Q}(\sqrt{2p_1p_2},i)\) with \(\mathbf {C}l_2(\Bbbk)\simeq (2, 2, 2)\)

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

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Real quadratic fields with abelian 2-class field tower

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

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Principal ideal theorems in the genus field for absolutely abelian extensions

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Number fields with class number congruent to 4 mod 8 and Hilbert's Theorem 94

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Ideal class groups of cyclotomic number fields I

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On 2-class field towers of some imaginary quadratic number fields

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Imaginary bicyclic biquadratic fields with cyclic 2-class group

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Algebraic investigations of Hilbert's theorem 94, the principal ideal theorem and the capitulation problem

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A principal ideal theorem in the genus field

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Identifiers

zbMATH Open document ID

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10.1007/978-3-319-32902-4_1

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:5738729

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