UNIT GROUPS OF SOME MULTIQUADRATIC NUMBER FIELDS

Abstract

Let \( p\), \(q \) and \( s \) be three different prime integers such that \( p \equiv 1 \pmod{8} \), \( q \equiv 3 \pmod{8} \) and \( s \equiv 7 \pmod{8} \), with\(\left( \frac{p}{q} \right) = \left( \frac{p}{s} \right) = \left( \frac{q}{s} \right) = -1\). In this paper, we investigate the unit groups of the number fields of the form \(\mathbb{L^+} = \mathbb{Q}(\sqrt{2}, \sqrt{pq}, \sqrt{ps})\)