Geodesic
Note on the Hilbert 2-class field tower
Mathematica Bohemica, Tome 147 (2022) no. 4, pp. 513-524
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Let $k$ be a number field with a 2-class group isomorphic to the Klein four-group. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields $\Bbbk =\Bbb {Q}\big (\sqrt d, \sqrt {-1}\big )$, which leads to a correction of some parts in the main results of A. Azizi and A. Zekhini (2020).
Let $k$ be a number field with a 2-class group isomorphic to the Klein four-group. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields $\Bbbk =\Bbb {Q}\big (\sqrt d, \sqrt {-1}\big )$, which leads to a correction of some parts in the main results of A. Azizi and A. Zekhini (2020).
DOI : 10.21136/MB.2022.0056-21
Classification : 11R11, 11R16, 11R20, 11R27, 11R29, 11R37
Keywords: multiquadratic field; fundamental systems of units; 2-class group; 2-class field tower; capitulation 
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Azizi, Abdelmalek; Chems-Eddin, Mohamed Mahmoud; Zekhnini, Abdelkader. Note on the Hilbert 2-class field tower. Mathematica Bohemica, Tome 147 (2022) no. 4, pp. 513-524. doi: 10.21136/MB.2022.0056-21

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