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

Unit groups and Iwasawa lambda invariants of some multiquadratic number fields. (English) Zbl 1468.11223

Bol. Soc. Mat. Mex., III. Ser. 27, No. 1, Paper No. 24, 16 p. (2021).
The authors consider the field \(L=\mathbb Q(\sqrt{q_1},\sqrt{q_2},\sqrt2,i)\), where \(q_1,q_2\) are primes satisfying \(q_1\equiv 7\pmod 8, q_2\equiv3\pmod 8\) and determine the fundamental units and the \(2\)-class-group of \(L\) and its maximal real subfield. As an application they show that the Iwasawa coefficient \(\lambda(F)\) equals three for the cyclotomic \(\mathbb Z_2\)-extension of \(F=\mathbb Q(\sqrt{p_1},\sqrt{p_2},i)\), where \(p_1,p_2\) are primes with \(p_1\equiv7\pmod{16}, p_2\equiv3\pmod8\).
Reviewer: Władysław Narkiewicz (Wrocław)

Cited in 2 Documents

MSC:

11R20 Other abelian and metabelian extensions
11R04 Algebraic numbers; rings of algebraic integers
11R23 Iwasawa theory
11R27 Units and factorization
11R29 Class numbers, class groups, discriminants

Keywords:

multiquadratic number fields; unit groups; 2-class groups; cyclotomic \(\mathbb{Z}_2\)-extensions
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\textit{M. M. Chems-Eddin} et al., Bol. Soc. Mat. Mex., III. Ser. 27, No. 1, Paper No. 24, 16 p. (2021; Zbl 1468.11223)
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References:

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