Real quadratic fields with abelian 2-class field tower
From MaRDI portal
Publication:1277178
DOI10.1006/jnth.1998.2291zbMath0919.11073OpenAlexW2083567129MaRDI QIDQ1277178
Elliot Benjamin, Franz Lemmermeyer, Chip Snyder
Publication date: 16 August 1999
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/dd826169ce14b55f5b52f047eef71d3aa14bd114
Related Items
On the 2-class group of real multiquadratic fields, The class number one problem for the normal CM-fields of degree 32, A note on the 3-class field tower of a cyclic cubic field., On the rank of the 2-class group of some imaginary biquadratic number fields, Imaginary quadratic fields \(k\) with cyclic \(\text{Cl}_2(k^1)\), On 2-class field towers of some imaginary quadratic number fields, 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, Capitulation of the 2-ideal classes of type \((2, 2, 2)\) of some quartic cyclic number fields, On the maximal unramified pro-2-extension over the cyclotomic \(\mathbb Z_2\)-extension of an imaginary quadratic field, On metabelian 2-class field towers over -extensions of real quadratic fields, The computation of $\mathrm{Gal}(k^\infty /k)$ for some complex quadratic number fields $k$, On the Hilbert 2-class field of some quadratic number fields, Some real quadratic number fields whose Hilbert 2-class fields have class number congruent to 2 modulo 4, Sur le rang du 2-groupe de classes de 𝑄({√{𝑚}},{√{𝑑}}) où 𝑚=2 ou un premier 𝑝≡1(𝑚𝑜𝑑4), 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 \(\mathbb Q(\sqrt{p},\sqrt{q},\sqrt{-1})\), The narrow 2-class field tower of some real quadratic number fields, On \(2\)-class field towers of some real quadratic number fields with \(2\)-class groups of rank \(3\), On the unit index of some real biquadratic number fields, On the 2-class field tower of \(\mathbb Q (\sqrt{2p_1p_2},i)\) and the Galois group of its second Hilbert 2-class field, 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 \(\mathbf {C}l_2(\Bbbk)\simeq (2, 2, 2)\), Abelian 2-class field towers over the cyclotomic \({\mathbb {Z}_2}\)-extensions of imaginary quadratic fields, Group Theory and the Capitulation Problem for Some Number Fields, On unramified Galois $2$-groups over $\mathbb Z_2$-extensions of real quadratic fields, 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), Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group, On \(p^2\)-ranks in the class field tower problem, Necessary condition and sufficient for certain Galois group to be metacyclic, On the parity of the class number of multiquadratic number fields, Real quadratic number fields with metacyclic Hilbert $2$-class field tower, On the 2-class field towers of some imaginary quartic cyclic number fields, Refined lower bounds on the 2-class number of the Hilbert 2-class field of imaginary quadratic number fields with elementary 2-class group of rank 3, Unnamed Item, Principalization of 2-class groups of type (2, 2, 2) of biquadratic fields ${\mathbb Q}(\sqrt{p_1p_2q}, \sqrt{-1})$, Tame pro-2 Galois groups and the basic ℤ₂-extension
Cites Work
- A note on the group of units of an algebraic number field
- Unramified abelian extensions of number fields
- Number fields with class number congruent to 4 mod 8 and Hilbert's Theorem 94
- Tours de corps de classes et estimations de discriminants
- Unramified quaternion extensions of quadratic number fields
- Über die zentrale Klassenzahl eines relativ-Galoisschen Zahlkörpers
- Über Den Bizyklischen Biquadratischen Zahlkörper
- Central Extensions, Galois Groups, and Ideal Class Groups of Number Fields
- Infinite class field towers of quadratic fields.
- Central class numbers in central class field towers
- Sur le 2-groupe des classes d'idéaux des corps quadratiques.
- Capitulation in unramified quadratic extensions of real quadratic number fields
- Real Quadratic Number Fields with 2-Class Group of Type (2,2).
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
