References & Citations
Mathematics > Number Theory
Title: Arithmetic of some real triquadratic fields; Units and 2-class groups
(Submitted on 9 Aug 2021 (v1), last revised 10 Mar 2024 (this version, v2))
Abstract: In this paper, we compute the unit groups and the $2$-class numbers of the Fr\"ohlich's triquadratic fields $\KK=\mathbb{Q}(\sqrt{2},\sqrt{p},\sqrt{q})$, where $p$ and $q$ are two prime numbers such that ($p\equiv 1 \pmod8$ and $q\equiv 3 \pmod4$) or ($p\equiv 5$ or $3 \pmod8$ and $q\equiv 3 \pmod4$). Furthermore, we determine some families of the fields $\KK$ whose $2$-class groups are trivial or cyclic non trivial, and some other families with $2$-class groups isomorphic to the Klein group.
Submission history
From: Mohamed Mahmoud Chems-Eddin [view email][v1] Mon, 9 Aug 2021 16:58:30 GMT (19kb)
[v2] Sun, 10 Mar 2024 18:17:07 GMT (18kb)
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