On the Hilbert 2-class field of some quadratic number fields-Reference-Cited by-同舟云学术

On the Hilbert 2-class field of some quadratic number fields

Published:2019-04-29 Issue:04 Volume:15 Page:807-824
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Azizi Abdelmalek¹,Rezzougui Mohammed¹,Taous Mohammed²,Zekhnini Abdelkader³

Affiliation:

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

2. Mathematics Department, Sciences and Techniques Faculty, Moulay Ismail University, Errachidia, Morocco

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

Abstract

In this paper, we investigate the cyclicity of the [Formula: see text]-class group of the first Hilbert [Formula: see text]-class field of some quadratic number field whose discriminant is not a sum of two squares. For this, let [Formula: see text] be different prime integers. Put [Formula: see text], and denote by [Formula: see text] its [Formula: see text]-class group and by [Formula: see text] (respectively [Formula: see text]) its first (respectively second) Hilbert [Formula: see text]-class field. Then, we are interested in studying the metacyclicity of [Formula: see text] and the cyclicity of [Formula: see text] whenever the [Formula: see text]-rank of [Formula: see text] is [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179304211950043X

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