Unit groups of some multiquadratic number fields of degree 16. (English) Zbl 1514.11070
Let \(p\) and \(q\) be two primes, and let \(\ell\) be an odd positive square-free integer distinct from \(1,p,q,pq\). In this paper the authors compute the unit group of some number fields of the form \({\mathbb Q}(\sqrt{2},\sqrt{p},\sqrt{q},\sqrt{-\ell})\). The answer is split into \(7\) cases which depend of the residues of \(p,q\) modulo \(8\) and on whether \(p\) is a quadratic residue modulo \(q\) or not.
Reviewer: Artūras Dubickas (Vilnius)
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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