Finiteness conditions on groups and quasi-isometries
type: Item
instance of: scholarly article
title: Finiteness conditions on groups and quasi-isometries
zbMATH Open document ID: 0823.20034
DOI: 10.1016/0022-4049(94)90069-8
author: Juan Miguel Alonso
published in: Journal of Pure and Applied Algebra
publication date: 1995-10-15T00:00:00Z
review text: Let \(G\) be a finitely generated group equipped with a word-metric. A major theme, which has been developed mainly by Gromov, is to study the properties of \(G\) which are invariant under quasi-isometries. A group \(G\) is said to be of type \(F_ n\) (\(n\geq 1\)) if there exists an Eilenberg-MacLane complex \(K(G,1)\) with finite \(n\)-skeleton. Condition \(FP_ n\) is a homological version. Conditions \(F_ 1\) and \(F_ 2\) are equivalent, respectively, to \(G\) being finitely generated and finitely presented. The author shows that conditions \(F_ n\) and \(FP_ n\) are quasi- isometry invariants. The paper contains also an application for properties \(F_ n\) and \(FP_ n\) for group extensions.
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 55U10
zbMATH DE Number: 681814
zbMATH Keywords: finiteness properties of groups
zbMATH Keywords: finitely generated groups
zbMATH Keywords: word-metrics
zbMATH Keywords: Eilenberg-MacLane complex
zbMATH Keywords: finitely presented groups
zbMATH Keywords: quasi-isometry invariants
zbMATH Keywords: group extensions
reviewed by: Athanase Papadopoulos
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90069-8
OpenAlex ID: W2012833225
cites work: Q3350312
cites work: Q4002533
cites work: Semihyperbolic Groups
cites work: Finiteness properties of groups
cites work: Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
description: scientific article; zbMATH DE number 681814