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The structure of the second $2$ -class group of some special Dirichlet fields

Abdelmalek Azizi

Mathematics Department, Sciences Faculty, Mohammed First University, Oujda, Morocco

E-mail Address: abdelmalekazizi@yahoo.fr

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and

Abdelkader Zekhnini

Mathematics Department, Pluridisciplinary Faculty, Mohammed First University, Nador, Morocco

E-mail Address: zekha1@yahoo.fr

Corresponding author.

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https://doi.org/10.1142/S1793557120500539Cited by:0 (Source: Crossref)

Abstract

Let $k$ be a number field and $k_{2}^{(1)}$ (respectively, $k_{2}^{(2)}$ ) its first (respectively, second) Hilbert $2$ -class field. Let $G = Gal (k_{2}^{(2)} / k)$ be the Galois group of $k_{2}^{(2)} / k$ . The purpose of this note is to determine the structure of $G$ for some special Dirichlet fields $k = ℚ (\sqrt{d}, \sqrt{- 1})$ .

Communicated by V. A. Artamonov

Keywords:

AMSC: 11R11, 11R16, 11R20, 11R27, 11R29

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