The unit group and the 2-class number of some fields of the form $\mathbb{Q}(\sqrt{2},\sqrt{pq},\sqrt{ps})$ and $\mathbb{Q}(\sqrt{2},\sqrt{pq},\sqrt{ps},\sqrt{-\ell })$

Moha Ben Taleb El Hamam

Let $\LL^+=\mathbb{Q}(\sqrt{2}, \sqrt{pq}, \sqrt{ps})$ and $\LL=\mathbb{Q}(\sqrt{2}, \sqrt{pq}, \sqrt{ps}, \sqrt{-\ell})$ be two fields, where $q$, $p$ and $s$ three different prim…