Unramified quaternion extensions of quadratic number fields

DOI10.5802/jtnb.189zbMath0890.11031arXiv1310.6606OpenAlexW2040314999MaRDI QIDQ1382093

Franz Lemmermeyer

Publication date: 25 March 1998

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.6606

zbMATH Keywords

number fieldsunramified dihedral extensions of quadratic number fieldsunramified quaternion extensions

Mathematics Subject Classification ID

Quadratic extensions (11R11) Other number fields (11R21)

Related Items (15)

The class number one problem for the normal CM-fields of degree 32 ⋮ Quaternion extensions with restricted ramification ⋮ Determination of all imaginary quadratic fields for which their Hilbert 2-class fields have 2-class groups of rank 2 ⋮ Imaginary quadratic fields \(k\) with cyclic \(\text{Cl}_2(k^1)\) ⋮ On 2-class field towers of some imaginary quadratic number fields ⋮ The computation of $\mathrm{Gal}(k^\infty /k)$ for some complex quadratic number fields $k$ ⋮ Arithmetic Chern–Simons Theory II ⋮ Imaginary quadratic fields with \(Cl_2(k)\simeq (2,2,2)\). ⋮ Cohen-Lenstra moments for some nonabelian groups ⋮ The narrow 2-class field tower of some real quadratic number fields ⋮ The class number one problem for some non-abelian normal CM-fields of degree 24 ⋮ Maximal unramified extensions of imaginary quadratic number fields of small conductors ⋮ Real quadratic fields with abelian 2-class field tower ⋮ A note on unramified quaternion extensions over quadratic number fields. ⋮ Unramified subextensions of ray class towers

Cites Work

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• A characterization of C-fields via Galois groups
• An elementary construction of Galois quaternion extension
• Number fields with class number congruent to 4 mod 8 and Hilbert's Theorem 94
• Quaternionic compositum genus
• A classical invitation to algebraic numbers and class fields. With two appendices by Olga Taussky: `Artin's 1932 Göttingen lectures on class field theory' and `Connections between algebraic number theory and integral matrices'.
• On 2-class field towers of imaginary quadratic number fields
• Groups of order 16 as Galois groups
• Class number parity of \(S_ 4\)-extensions of \(\mathbb{Q}\) and elliptic curves
• On central extensions of elementary abelian fields
• Constructing quaternionic fields
• Sur les extensions de groupe de Galois Ã₄
• Plongement d'une extension qudratique dans une extension quaternionienne.
• Extra-Special Groups of Order 32 as Galois Groups
• Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one
• The Class Number One Problem for Some Non-Abelian Normal CM-Fields of 2-Power Degrees
• Arithmetischer Beweis des Satzes über die Anzahl der durch vier teilbaren Invarianten der absoluten Klassengruppe im quadratischen Zahlkörper.
• Sur les extensions de ℚ à groupe de Galois S₄ et S̃₄
• On 2-Groups as Galois Groups
• Explicit Classifications of Some 2-Extensions of a Field of Characteristic Different from 2
• Determination of all Quaternion Octic CM-Fields with Class Number 2
• Über den 2-Klassenkörperturm eines quadratischen Zahlkörpers. I.

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