Fundamental systems of units of some multiquadratic fields of degree 8 and degree 16

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Abstract

Let $\ell\geq1$ be a positive odd square-free integer relatively prime to $q$, $p$ and $s$. In this paper, we compute the unit group of fields of the form $\LL^+=\mathbb{Q}(\sqrt{2}, \sqrt{pq}, \sqrt{ps})$ and $\LL=\mathbb{Q}(\sqrt{2}, \sqrt{pq}, \sqrt{ps}, \sqrt{-\ell}),$ where $q$, $p$ and $s$ are three different prime integers satisfying certain conditions.

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