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

Abstract

Let $p\equiv -q\equiv 5(\mathrm{mod}8)$ 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 the $2$-class groups of the fields $L_n=\mathbb{Q}(\sqrt{p},\sqrt{q},{\zeta }_{2^{n+2}})$ and their maximal real subfelds.

18 pages

References in corpus (3)

• Units and $2$-class field towers of some multiquadratic number fields
• On the rank of the $2$-class group of some imaginary triquadratic number fields
• $2$-class groups of cyclotomic towers of imaginary biquadratic fields and applications

Cited by in corpus (1)

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