Arithmetic of some real triquadratic fields; Units and 2-class groups

Abstract

In this paper, we compute the unit groups and the $2$-class numbers of the Fröhlich's triquadratic fields $\KK=\mathbb{Q}(\sqrt{2},\sqrt{p},\sqrt{q})$, where $p$ and $q$ are two prime numbers such that ($p\equiv 1(\mathrm{mod}8)$ and $q\equiv 3(\mathrm{mod}4)$) or ($p\equiv 5$ or $3(\mathrm{mod}8)$ and $q\equiv 3(\mathrm{mod}4)$). 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.

This is a new revised version, 33 pages

References in corpus (2)

• Units and $2$-class field towers of some multiquadratic number fields
• Unit groups of some multiquadratic number fields and $2$-class groups