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

被引：4
|
作者：
Azizi, Abdelmalek [1 ]
Rezzougui, Mohammed [1 ]
Taous, Mohammed [2 ]
Zekhnini, Abdelkader [3 ]
机构：
[1] Mohammed First Univ, Sci Fac, Math Dept, Oujda, Morocco
[2] Moulay Ismail Univ, Sci & Tech Fac, Math Dept, Errachidia, Morocco
[3] Mohammed First Univ, Pluridisciplinary Fac, Math Dept, Nador, Morocco
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2019年 / 15卷 / 04期
关键词：
Quadratic field; Hilbert 2-class field; 2-class group; metacyclic; 2-group;
D O I：
10.1142/S179304211950043X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we investigate the cyclicity of the 2-class group of the first Hilbert 2-class field of some quadratic number field whose discriminant is not a sum of two squares. For this, let p(1) p(2) -q 1 (mod 4) be different prime integers. Put k = Q(root p(1)p(2)q), and denote by C-k,C-2 its 2-class group and by k(2)((1)) (respectively k(2)((2))) its first (respectively second) Hilbert 2-class field. Then, we are interested in studying the metacyclicity of G = Gal(k(2)((2))/k) and the cyclicity of Gal(k(2)((2))/k(2)((1))) whenever the 4-rank of C-k,C-2 is 1.
引用
收藏
页码：807 / 824
页数：18
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