A CHARACTERIZATION OF UNIFORM PRO-p GROUPS

被引：5

作者：

Klopsch, Benjamin ^{[1
]}

Snopce, Ilir ^{[2
]}

机构：

[1] Univ Dusseldorf, Math Inst, D-40225 Dusseldorf, Germany

[2] Univ Fed Rio de Janeiro, Inst Matemat, BR-20785050 Rio De Janeiro, RJ, Brazil

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2014年 / 65卷 / 04期

关键词：

POWER-STRUCTURE; SUBGROUPS;

D O I：

10.1093/qmath/hau005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, we propose and supply evidence for the following conjecture, aimed at characterizing uniform pro-p groups. Suppose that pa parts per thousand yen3 and let G be a torsion-free pro-p group of finite rank. Then G is uniform if and only if its minimal number of generators is equal to the dimension of G as a p-adic manifold, i.e. d(G) = dim(G). In particular, we prove that the assertion is true whenever G is soluble or p > dim(G).

引用

页码：1277 / 1291

页数：15

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