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)
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Publication:2788566
DOI10.1142/S0219498816500274zbMath1335.11091OpenAlexW2140537044MaRDI QIDQ2788566
Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous
Publication date: 19 February 2016
Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0219498816500274
Galois theory (11R32) Quadratic extensions (11R11) Class field theory (11R37) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29)
Related Items (8)
Invariant generalized ideal classes -- structure theorems for \(p\)-class groups in \(p\)-extensions ⋮ On some metabelian 2-groups and applications III ⋮ Capitulation of the 2-ideal classes of type \((2, 2, 2)\) of some quartic cyclic number fields ⋮ ON THE -RANK OF CLASS GROUPS OF DIRICHLET BIQUADRATIC FIELDS ⋮ Capitulation in the absolutely abelian extensions of some number fields. II ⋮ On the second 2-class group \(\mathrm{Gal}(K_2^{(2)} / K)\) of some imaginary quartic cyclic number field \(K\) ⋮ Group Theory and the Capitulation Problem for Some Number Fields ⋮ The group Gal(k3(2)|k) for k = ℚ(−3,d) of type (3,3)
Cites Work
- 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
- Real quadratic fields with abelian 2-class field tower
- On 2-class field towers of some imaginary quadratic number fields
- Divisibility by 8 of the class number of quadratic fields whose 2-class group is cyclic, and biquadratic reciprocity
- Imaginary quadratic fields with \(Cl_2(k)\simeq (2,2,2)\).
- On 2-class field towers of imaginary quadratic number fields
- Imaginary bicyclic biquadratic fields with cyclic 2-class group
- Structure of \(\mathrm {Gal}(\Bbbk _2^{(2)}/\Bbbk)\) for some fields \(\Bbbk=\mathbb {Q}(\sqrt{2p_1p_2},i)\) with \(\mathbf {C}l_2(\Bbbk)\simeq (2, 2, 2)\)
- Principalization of 2-class groups of type (2, 2, 2) of biquadratic fields ${\mathbb Q}(\sqrt{p_1p_2q}, \sqrt{-1})$
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