The University of Southampton
×
Filter your search:
University of Southampton Institutional Repository

On groups of type (FP)?

On groups of type (FP)?
On groups of type (FP)?
Let G be a group. A ZG-module M is said to be of type (FP)? over G if and only if there is a projective resolution P? ?M in which every Pi is finitely generated. We show that if G belongs to a large class of torsion-free groups, which includes torsion-free linear and soluble-by-finite groups, then every ZG-module of type (FP)? has finite projective dimension. We also prove that every soluble or linear group of type (FP)? is virtually of type (FP). The arguments apply to groups which admit hierarchical decompositions. We also make crucial use of a generalized theory of Tate cohomology recently developed by Mislin.
55-67
Kropholler, Peter H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Kropholler, Peter H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4

Kropholler, Peter H. (1993) On groups of type (FP)? Journal of Pure and Applied Algebra, 90 (1), 55-67. (doi:10.1016/0022-4049(93)90136-H).

Record type: Article

Abstract

Let G be a group. A ZG-module M is said to be of type (FP)? over G if and only if there is a projective resolution P? ?M in which every Pi is finitely generated. We show that if G belongs to a large class of torsion-free groups, which includes torsion-free linear and soluble-by-finite groups, then every ZG-module of type (FP)? has finite projective dimension. We also prove that every soluble or linear group of type (FP)? is virtually of type (FP). The arguments apply to groups which admit hierarchical decompositions. We also make crucial use of a generalized theory of Tate cohomology recently developed by Mislin.

This record has no associated files available for download.

More information

Published date: 19 November 1993
Organisations: Mathematical Sciences
Learn more about Mathematical Sciences research

Identifiers

Local EPrints ID: 349609
URI: http://eprints.soton.ac.uk/id/eprint/349609
DOI: doi:10.1016/0022-4049(93)90136-H
PURE UUID: 82753e11-2302-42a2-9223-2f35ac0b61c9
ORCID for Peter H. Kropholler: ORCID iD orcid.org/0000-0001-5460-1512

Catalogue record

Date deposited: 15 Apr 2013 11:27
Last modified: 15 Mar 2024 03:46

Export record

Altmetrics

Contributors

Author: Peter H. Kropholler ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Library staff additional information
Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×