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

DOI10.1007/S13348-013-0085-4zbMath1338.11099OpenAlexW2134121484MaRDI QIDQ486327

Abdelmalek Azizi, Mohammed Taous, Abdelkader Zekhnini

Publication date: 15 January 2015

Published in: Collectanea Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13348-013-0085-4

zbMATH Keywords

class field towersclass groupsclass numbersclass fieldsbiquadratic extensionsHilbert class

Mathematics Subject Classification ID

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

Related Items (5)

ON THE -RANK OF CLASS GROUPS OF DIRICHLET BIQUADRATIC FIELDS ⋮ On the unit index of some real biquadratic number fields ⋮ Structure of \(\mathrm {Gal}(\Bbbk _2^{(2)}/\Bbbk)\) for some fields \(\Bbbk=\mathbb {Q}(\sqrt{2p_1p_2},i)\) with \(\mathbf {C}l_2(\Bbbk)\simeq (2, 2, 2)\) ⋮ 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) ⋮ 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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