Unit groups of some multiquadratic number fields of degree 16. (English) Zbl 1514.11070

Chems-Eddin, Mohamed Mahmoud; Zekhnini, Abdelkader; Azizi, Abdelmalek

São Paulo J. Math. Sci. 16, No. 2, 1091-1096 (2022).

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 \(\mathbb{Z}_2\)-extension

References:

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