Arithmetic of some real triquadratic fields; Units and 2-class groups
Mohamed Mahmoud Chems-Eddin
Departement of Mathematics, Faculty of Sciences Dhar El Mahraz,
Sidi Mohamed Ben Abdellah University, Fez, Morocco
Pages 358–387 | Received 28 March 2024, Accepted 23 July 2024, Published 08 November 2024
Abstract
In this paper, we compute the unit groups and the 2-class numbers of the Fröhlich’s triquadratic fields \mathbb{K}=\mathbb{Q}(\sqrt{2},\sqrt{p},\sqrt{q}), where p and q are two prime numbers such that (p\equiv 1 \pmod 8 and q\equiv 3 \pmod 4) or (p\equiv 5 or 3 \pmod 8 and q\equiv 3 \pmod 4). Furthermore, we determine some families of the fields \mathbb{K} whose 2-class groups are trivial or cyclic non trivial, and some other families with 2-class groups isomorphic to the Klein group.
Keywords: Real multiquadratic fields, unit group, 2-class group, 2-class number.
MSC numbers: 11R04, 11R27, 11R29, 11R37.
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