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Some groups of type VF

Some groups of type VF
Some groups of type VF
A group is of type VF if it contains a finite-index subgroup which has a finite classifying space. We construct groups of type VF in which the centralizers of some elements of finite order are not of type VF and groups of type VF containing infinitely many conjugacy classes of finite subgroups. From these examples it follows that a group G of type VF need not admit a finite-type or finite classifying space for proper actions (sometimes also called the universal proper G-space). We construct groups G for which the minimal dimension of a universal proper G-space is strictly greater than the virtual cohomological dimension of G. Each of our groups embeds in some general linear group over the rational integers. Applications to algebraic K-theory of group algebras and topological K-theory of group C*-algebras are also considered. The groups are constructed as finite extensions of Bestvina-Brady groups.
0020-9910
135-165
Leary, None
57bd5c53-cd99-41f9-b02a-4a512d45150e
Nucinkis, Brita E.A.
0b1c337c-36ae-4ef3-add4-b49a7c23810c
Leary, None
57bd5c53-cd99-41f9-b02a-4a512d45150e
Nucinkis, Brita E.A.
0b1c337c-36ae-4ef3-add4-b49a7c23810c

Leary, None and Nucinkis, Brita E.A. (2003) Some groups of type VF. Inventiones Mathematicae, 151 (1), 135-165. (doi:10.1007/s00222-002-0254-7).

Record type: Article

Abstract

A group is of type VF if it contains a finite-index subgroup which has a finite classifying space. We construct groups of type VF in which the centralizers of some elements of finite order are not of type VF and groups of type VF containing infinitely many conjugacy classes of finite subgroups. From these examples it follows that a group G of type VF need not admit a finite-type or finite classifying space for proper actions (sometimes also called the universal proper G-space). We construct groups G for which the minimal dimension of a universal proper G-space is strictly greater than the virtual cohomological dimension of G. Each of our groups embeds in some general linear group over the rational integers. Applications to algebraic K-theory of group algebras and topological K-theory of group C*-algebras are also considered. The groups are constructed as finite extensions of Bestvina-Brady groups.

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Published date: 2003

Identifiers

Local EPrints ID: 29841
URI: http://eprints.soton.ac.uk/id/eprint/29841
ISSN: 0020-9910
PURE UUID: 203dcf3d-2ca5-4c7d-8ade-63cabda5b52a
ORCID for None Leary: ORCID iD orcid.org/0000-0001-8300-4979

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Date deposited: 12 May 2006
Last modified: 16 Mar 2024 04:04

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Contributors

Author: None Leary ORCID iD
Author: Brita E.A. Nucinkis

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