On the Hilbert 2-class field of some quadratic number fields

Galois theory (11R32) Quadratic extensions (11R11) Class field theory (11R37) Class numbers, class groups, discriminants (11R29) Finite nilpotent groups, (p)-groups (20D15)

Related Items (2)

On the metacyclic 2-groups whose abelianizations are of type \((2, 2^n)\), \(n\geq 2\) and applications ⋮ On the maximal unramified pro-2-extension of certain cyclotomic \(\mathbb{Z}_2\)-extensions

Uses Software

PARI/GP

Cites Work

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Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group
Capitulation of the 2-ideal classes of biquadratic fields whose class field differs from the Hilbert class field
Number fields with class number congruent to 4 mod 8 and Hilbert's Theorem 94
Real quadratic fields with abelian 2-class field tower
Imaginary quadratic fields \(k\) with cyclic \(\text{Cl}_2(k^1)\)
Sur les \(\ell\)-classes d'idéaux dans les extensions cycliques rélatives de degré premier \(\ell\). I
Classification of metabelian 2-groups \(G\) with \(\mathbf{G}^{\mathrm{ab}} (\mathbf{2},\mathbf{2}^{\mathbf n})\), \(\mathbf n\geq \mathbf 2\), and rank \(\mathbf d(\mathbf G^{\prime})=\mathbf 2\). Applications to real quadratic number fields
Sur le rang du 2-groupe de classes de 𝑄({√{𝑚}},{√{𝑑}}) où 𝑚=2 ou un premier 𝑝≡1(𝑚𝑜𝑑4)
Some real quadratic number fields whose Hilbert 2-class fields have class number congruent to 2 modulo 4
Generalizations of Certain Elementary Theorems on p -Groups
Sur le 2-groupe des classes d'idéaux des corps quadratiques.
Kuroda's class number formula
Sur la capitulation des 2-classes d'idéaux de
Real Quadratic Number Fields with 2-Class Group of Type (2,2).
On the rank of the 2-class group of the Hilbert 2-class field of some quadratic fields
Imaginary quadratic fields \(k\) with \(\text{Cl}_ 2(k)\simeq(2,2^ m)\) and rank \(\text{Cl}_ 2(k^ 1)=2\).

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