ON SOME METABELIAN 2-GROUPS AND APPLICATIONS I

被引：1

作者：

Azizi, Abdelmalek ^{[1
]}

Zekhnini, Abdelkader ^{[2
]}

Taous, Mohammed ^{[3
]}

机构：

[1] Mohammed First Univ, Fac Sci, Dept Math, Oujda, Morocco

[2] Mohammed First Univ, Polydisciplinary Fac Nador, Dept Math, Nador, Morocco

[3] Moulay Ismail Univ, Fac Sci & Technol, Dept Math, Errachidia, Morocco

来源：

COLLOQUIUM MATHEMATICUM | 2016年 / 142卷 / 01期

关键词：

2-group; metabelian; capitulation; Hilbert class field; 2-class field tower; 2-CLASS FIELD;

D O I：

10.4064/cm142-1-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be some metabelian 2-group satisfying the condition G/G' similar or equal to Z/2Z x Z/2Z x Z/2Z. In this paper, we construct all the subgroups of G of index 2 or 4, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem of the 2-ideal classes of some fields k satisfying the condition Gal(k(2)((2))/k) similar or equal to G, where k(2)((2)) is the second Hilbert 2-class field of k.

引用

页码：99 / 113

页数：15

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