Unit groups of some multiquadratic number fields and 2-class groups

Abstract

Let pequiv -q equiv 5pmod 8 be two prime integers. In this paper, we investigate the unit groups of the fields L_1 =mathbb {Q}(sqrt{2}, sqrt{p}, sqrt{q}, sqrt{-1} ) and L_1^+=mathbb {Q}(sqrt{2}, sqrt{p}, sqrt{q} ). Furthermore , we give the second 2-class groups of the subextensions of L_1 as well as the 2-class groups of the fields L_n =mathbb {Q}( sqrt{p}, sqrt{q}, zeta _{2^{n+2}} ) and their maximal real subfields.