The 2-Class Group of Certain Families of Imaginary Triquadratic Fields

Author:

Chems-Eddin Mohamed Mahmoud1,El Fadil Lhoussain1

Affiliation:

1. Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University , Fez , MOROCCO

Abstract

ABSTRACT Our goal in this paper is to compute the 2-rank of the class group of the fields K = ( 2 , q , d ) \[\mathbb{K}=\mathbb{Q}\left( \sqrt{-2},\sqrt{q},\sqrt{d} \right)\] for any odd positive squarefree integer d and any prime integer q ≡ 5 (mod 8). Furthermore, we give the list of these fields whose 2-class groups are trivial, cyclic, of type (2, 2), (2, 4) or (2, 2, 2).

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference25 articles.

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2. AZIZI, A.: Units de certains corps de nombres imaginaires et abliens sur ℚ \[\mathbb{Q}\] , Ann. Sci. Math. Qubec 23 (1999), 15–21.

3. AZIZI, A.—BENHAMZA, I.: Dtermination des corps K=ℚ(d,−2) \[K=\mathbb{Q}\left( \sqrt{d,}\sqrt{-2} \right)\] dont les 2-groupes de classes sont de type (2, 2) (in French); [Determining fields K=ℚ(d,−2) \[K=\mathbb{Q}\left( \sqrt{d,}\sqrt{-2} \right)\] whose class 2-groups are of type (2, 2)] Rend. Istit. Mat. Univ. Trieste 33 (2001), 83–104.

4. AZIZI, A.—BENHAMZA, I.: Sur la capitulation des 2-classes d’idaux de ℚ(d,−2) \[\mathbb{Q}\left( \sqrt{d,}\sqrt{-2} \right)\] , Ann. Sci. Math. Qubec 29 (2005), 1–20.

5. AZIZI, A.—CHEMS-EDDIN, M. M.—ZEKHNINI, A.: On the rank of the 2-class group of some imaginary triquadratic number fields, Rend. Circ. Mat. Palermo (2) 70 (2021), 1751–1769.

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