Received April 27, 2021. Published online January 18, 2022.
Abstract: 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).
Keywords: multiquadratic field; fundamental systems of units; 2-class group; 2-class field tower; capitulation
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Affiliations: Abdelmalek Azizi, Department of Mathematics, Faculty of Sciences, Mohammed First University, Oujda, Morocco, e-mail: abdelmalekazizi@yahoo.fr; Mohamed Mahmoud Chems-Eddin, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco, e-mail: 2m.chemseddin@gmail.com; Abdelkader Zekhnini, Department of Mathematics, Faculty of Sciences, Mohammed First University, Oujda, Morocco, e-mail: zekha1@yahoo.fr
