On some metabelian 2-group and applications II

被引：2

作者：

Azizi, Abdelmalek ^{[1
]}

Zekhnini, Abdelkader ^{[1
]}

Taous, Mohammed ^{[2
]}

机构：

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

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

来源：

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA | 2016年 / 34卷 / 02期

关键词：

2-group; metabelian; capitulation; Hilbert class fields;

D O I：

10.5269/bspm.v34i2.27016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be some metabelian 2-group such that G/GI similar or equal to 2/2Z 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 C, where k(2)((2)) is the second Hilbert 2-class field of k.

引用

页码：75 / 85

页数：11

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