On profinite groups of type FP∞

被引：5

作者：

Cook, Ged Corob ^{[1
]}

机构：

[1] Univ London, Dept Math, Egham TW20 0EX, Surrey, England

来源：

ADVANCES IN MATHEMATICS | 2016年 / 294卷

关键词：

Profinite group; Cohomology; Permutation module; Soluble; Finiteness condition; Finite rank; FINITE;

D O I：

10.1016/j.aim.2016.02.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose R is a profinite ring. We construct a large class of profinite groups (L'H(R)J) over cap, including all soluble profinite groups and profinite groups of finite cohomological dimension over R. We show that, if G is an element of (L'H(R)J) over cap is of type FP. over R, then there is some n such that H-R(n)(G, [R]) not equal 0, and deduce that torsion -free soluble pro-p groups of type FP infinity over Z(p) have finite rank, thus answering the torsion-free case of a conjecture of Kropholler. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：216 / 255

页数：40

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