Number fields with class number congruent to 4 mod 8 and Hilbert's Theorem 94
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Publication:1228507
DOI10.1016/0022-314X(76)90004-4zbMath0334.12019WikidataQ56689265 ScholiaQ56689265MaRDI QIDQ1228507
Publication date: 1976
Published in: Journal of Number Theory (Search for Journal in Brave)
Related Items (57)
A positive proportion of some quadratic number fields with infinite Hilbert 2-class field tower ⋮ Sur une question de capitulation ⋮ Algebraic number fields ⋮ On the 2-class field tower of some imaginary biquadratic number fields ⋮ Unit groups of some multiquadratic number fields and 2-class groups ⋮ Remarks concerning the 2-Hilbert class field of imaginary quadratic number fields ⋮ Galois groups of tamely ramified \(p\)-extensions ⋮ Unramified abelian extensions of number fields ⋮ Determination of all imaginary quadratic fields for which their Hilbert 2-class fields have 2-class groups of rank 2 ⋮ On a question of capitulation ⋮ Imaginary quadratic fields \(k\) with cyclic \(\text{Cl}_2(k^1)\) ⋮ Unramified quaternion extensions of quadratic number fields ⋮ On the maximal unramified pro-2-extension over the cyclotomic \(\mathbb Z_2\)-extension of an imaginary quadratic field ⋮ The distribution of second \(p\)-class groups on coclass graphs ⋮ On metabelian 2-class field towers over -extensions of real quadratic fields ⋮ THE SECOND p-CLASS GROUP OF A NUMBER FIELD ⋮ On Hilbert genus fields of imaginary cyclic quartic fields ⋮ On maximal tamely ramified pro-2-extensions over the cyclotomic \(\mathbb Z_2\)-extension of an imaginary quadratic field ⋮ On the metacyclic 2-groups whose abelianizations are of type \((2, 2^n)\), \(n\geq 2\) and applications ⋮ Konstruktion imaginärquadratischer Körper mit unendlichem Klassenkörperturm ⋮ The structure of the second 2-class group of some special Dirichlet fields ⋮ Transfers of metabelian \(p\)-groups ⋮ A note on a paper of Iwasawa ⋮ On the Hilbert 2-class field of some quadratic number fields ⋮ On the maximal unramified pro-2-extension of \(\mathbb Z_2\)-extensions of certain real quadratic fields. ⋮ Sur le rang du 2-groupe de classes de 𝑄({√{𝑚}},{√{𝑑}}) où 𝑚=2 ou un premier 𝑝≡1(𝑚𝑜𝑑4) ⋮ Pseudo-null Iwasawa modules for \(\mathbb Z_2^2\)-extensions ⋮ On the second Hilbert 2-class field of real quadratic number fields with 2-class group isomorphic to \((2,2^n)\), \(n\geq 2\) ⋮ On the rank of the 2-class group of \(\mathbb Q(\sqrt{p},\sqrt{q},\sqrt{-1})\) ⋮ On the unit index of some real biquadratic number fields ⋮ On the splitting of the Hilbert class field ⋮ Cyclicity of the unramified Iwasawa module ⋮ 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 ⋮ Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group ⋮ Quaternionic compositum genus ⋮ DISTRIBUTION OF GALOIS GROUPS OF MAXIMAL UNRAMIFIED 2-EXTENSIONS OVER IMAGINARY QUADRATIC FIELDS ⋮ A note on semidihedral 2-class field towers and \(\mathbb {Z}_{2}\)-extensions ⋮ On 2-class field towers of imaginary quadratic number fields ⋮ On the \(p\)-class tower of a \(\mathbb Z_p\)-extension ⋮ Capitulation of 2-class ideals of \(\mathbb Q\left(\sqrt{-pq(2+\sqrt 2)}\right)\) where \(p\equiv q\equiv {\pm 5} \bmod 8\) ⋮ Necessary condition and sufficient for certain Galois group to be metacyclic ⋮ Real quadratic fields with abelian 2-class field tower ⋮ Capitulation of the 2-class group of some cyclic number fields with large degree ⋮ On 2-class field towers for quadratic number fields with 2-class group of type (2,2) ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the Iwasawa invariants of certain non-cyclotomic \(\mathbb Z_2\)-extensions ⋮ On Hilbert class field tower for some quartic number fields ⋮ On the Hilbert $2$-class field tower of some imaginary biquadratic number fields ⋮ Tame pro-2 Galois groups and the basic ℤ₂-extension ⋮ On the 2-class field tower conjecture for imaginary quadratic number fields with 2-class group of rank 4 ⋮ Unramified subextensions of ray class towers ⋮ Maximal unramified extensions of imaginary quadratic number fields of small conductors. II ⋮ Note on the Hilbert 2-class field tower
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