Cohomological dimension of soluble groups
type: Item
instance of: scholarly article
title: Cohomological dimension of soluble groups
zbMATH Open document ID: 0603.20033
DOI: 10.1016/0022-4049(86)90069-1
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: This paper turns a conjecture of Gildenhuys and Strebel into the following Theorem. Let G be a soluble group. Then the following are equivalent: (i) \(cd_{{\mathbb{Z}}}G=hd_{{\mathbb{Z}}}G<\infty\). (ii) G is of type FP. (iii) G is a duality group. (iv) G is torsion-free and constructible. The proof is based on an important reduction due to Gildenhuys and Strebel. Their result allows to restrict attention to a special kind of metabelian groups. The skillful combination of homological tools with elementary commutative algebra and point set topology is reminiscent of earlier work by the same author.
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20E34
zbMATH DE Number: 3973157
zbMATH Keywords: (co)homological dimension
zbMATH Keywords: constructible group
zbMATH Keywords: finiteness conditions
zbMATH Keywords: soluble group
zbMATH Keywords: type FP
zbMATH Keywords: duality group
zbMATH Keywords: metabelian groups
author: Peter H. Kropholler
reviewed by: Hans Rudolf Schneebeli
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90069-1
OpenAlex ID: W2086465972
cites work: On the cohomology of soluble groups. II
cites work: A note on the cohomology of metabelian groups
description: scientific article; zbMATH DE number 3973157