Unit groups of some multiquadratic number fields and 2-class groups. (English) Zbl 1513.11178
Summary: Let \(p \equiv -q \equiv 5 \pmod 8\) be two prime integers. In this paper, we investigate the unit groups of the fields \(L_1 = Q(\sqrt{2},\sqrt{p},\sqrt{q},\sqrt{-1})\) and \(L_1^+ = Q(\sqrt{2},\sqrt{p},\sqrt{q})\). Furthermore, we give the second 2-class groups of the subextensions of \(L_1\) as well as the 2-class groups of the fields \(L_n = Q(\sqrt{p},\sqrt{q},\zeta_{2^{n+2}})\) and their maximal real subfields.
Reviewer: Nikolai L. Manev (Sofia)
MSC:
| 11R04 | Algebraic numbers; rings of algebraic integers |
| 11R27 | Units and factorization |
| 11R29 | Class numbers, class groups, discriminants |
| 11R37 | Class field theory |
Keywords:
multiquadratic number fields; unit group; 2-class group; Hilbert 2-class field tower; cyclotomic \(\mathbb{Z}_2\)-extensionReferences:
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