当前位置: X-MOL 学术Period. Math. Hung. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On the maximal unramified pro-2-extension of certain cyclotomic $$\mathbb {Z}_2$$-extensions
Periodica Mathematica Hungarica ( IF 0.6 ) Pub Date : 2020-11-20 , DOI: 10.1007/s10998-020-00362-x
Abdelmalek Azizi , Mohammed Rezzougui , Abdelkader Zekhnini

In this paper, we establish a necessary and sufficient criterion for a finite metabelian 2-group G whose abelianized $$G^{ab}$$ is of type $$(2, 2^m)$$ , with $$m\ge 2$$ , to be metacyclic. This criterion is based on the rank of the maximal subgroup of G which contains the three normal subgroups of G of index 4. Then, we apply this result to study the structure of the Galois group of the maximal unramified pro-2-extension of the cyclotomic $$\mathbb {Z}_2$$ -extension of certain number fields. Illustration is given by some real quadratic fields.

中文翻译:

关于某些分圆 $$\mathbb {Z}_2$$-extensions 的最大未分支 pro-2-extension

在本文中,我们建立了一个有限元贝尔 2 群 G 的充分必要条件,其 abelianized $$G^{ab}$$ 的类型为 $$(2, 2^m)$$ ,其中 $$m\ ge 2$$ ,为元循环。该标准基于 G 的最大子群的秩,该子群包含指数 4 的 G 的三个正规子群。然后,我们应用这个结果来研究最大非分枝 pro-2-extension 的 Galois 群的结构cyclotomic $$\mathbb {Z}_2$$ - 某些数字字段的扩展。一些真实的二次场给出了说明。
更新日期:2020-11-20
down
wechat
bug