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

DOI10.1007/BF02940830zbMath0919.11075OpenAlexW2512467417MaRDI QIDQ1378249

Franz Lemmermeyer

Publication date: 1 September 1999

Published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02940830

zbMATH Keywords

class groupsunit groups2-class groupimaginary quadratic number field2-class field tower

Mathematics Subject Classification ID

Quadratic extensions (11R11) Units and factorization (11R27) Class field theory (11R37) Class numbers, class groups, discriminants (11R29)

Related Items (20)

On the $2$-class group of some number fields of $2$-power degree ⋮ Capitulation of the 2-ideal classes of type \((2, 2, 2)\) of some quartic cyclic number fields ⋮ The distribution of second \(p\)-class groups on coclass graphs ⋮ Computation of Galois groups associated to the 2-class towers of some quadratic fields. ⋮ Asymptotic Fermat for signatures (p,p,2)$(p,p,2)$ and (p,p,3)$(p,p,3)$ over totally real fields ⋮ Galois action on class groups ⋮ On Hilbert 2-class fields and 2-towers of imaginary quadratic number fields ⋮ The computation of $\mathrm{Gal}(k^\infty /k)$ for some complex quadratic number fields $k$ ⋮ Grün's theorems and class groups ⋮ Imaginary quadratic fields with \(Cl_2(k)\simeq (2,2,2)\). ⋮ On \(2\)-class field towers of some real quadratic number fields with \(2\)-class groups of rank \(3\) ⋮ On the second 2-class group \(\mathrm{Gal}(K_2^{(2)} / K)\) of some imaginary quartic cyclic number field \(K\) ⋮ Structure of \(\mathrm {Gal}(\Bbbk _2^{(2)}/\Bbbk)\) for some fields \(\Bbbk=\mathbb {Q}(\sqrt{2p_1p_2},i)\) with \(\mathbf {C}l_2(\Bbbk)\simeq (2, 2, 2)\) ⋮ Group Theory and the Capitulation Problem for Some Number Fields ⋮ Maximal unramified extensions of imaginary quadratic number fields of small conductors ⋮ Maximal unramified extensions of imaginary quadratic number fields of small conductors ⋮ 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 ⋮ Principalization of 2-class groups of type (2, 2, 2) of biquadratic fields ${\mathbb Q}(\sqrt{p_1p_2q}, \sqrt{-1})$ ⋮ On the 2-class field tower conjecture for imaginary quadratic number fields with 2-class group of rank 4

Cites Work

• Unnamed Item
• Real quadratic fields with abelian 2-class field tower
• On a theorem of Koch
• Unramified quaternion extensions of quadratic number fields
• Über die Lösbarkeit einiger nicht-Abelscher Einbettungsprobleme
• Kuroda's class number formula
• Capitulation in unramified quadratic extensions of real quadratic number fields
• Ideal class groups of cyclotomic number fields I

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