Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
EnglishFrançais
Journal of the London Mathematical Society Journal of the London Mathematical Society

Article contents

HOMOLOGICAL FINITENESS CONDITIONS FOR MODULES OVER GROUP ALGEBRAS

Published online by Cambridge University Press:  01 August 1998

JONATHAN CORNICK  and
PETER H. KROPHOLLER
JONATHAN CORNICK
Affiliation:
Centre de Recerca Matematica, Institut d'Estudis Catalans, Apartat 50, E 08193 Bellaterra, Spain. E-mail: ICRM6@cc.uab.es
PETER H. KROPHOLLER
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS. E-mail: P.H.Kropholler@qmw.ac.uk
Get access

Abstract

We develop a theory of modules of type FP∞ over group algebras of hierarchically decomposable groups. This class of groups is denoted H[Fscr ] and contains many different kinds of discrete groups including all countable polylinear groups. Amongst various results, we show that if G is an h[Fscr ]-group and Mis a ℤG-module of type FP∞ then M has finite projective dimension over ℤH for all torsion-free subgroups H of G. We also show that if G is an h[Fscr ]-group of type FP∞ and M is a ℤG-module which is ℤF-projective for all finite subgroups F of G, then M has finite projective dimension over ℤG. Both of these results have as a special case the striking fact that if G is an h[Fscr ]-group of type FP∞ then the torsion-free subgroups of G have finite cohomological dimension. A further result in this spirit states that every residually finite h[Fscr ]-group of type FP∞ has finite virtual cohomological dimension.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 58 , Issue 1 , August 1998 , pp. 49 - 62
Copyright
The London Mathematical Society 1998

Access options

Get access to the full version of this content by using one of the access options below.
If you should have access and can't see this content please contact technical support.

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 20 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 22nd January 2021. This data will be updated every 24 hours.

16 Cited by
Hostname: page-component-76cb886bbf-rm8z7 Total loading time: 0.348 Render date: 2021-01-22T23:41:40.331Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false }

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

HOMOLOGICAL FINITENESS CONDITIONS FOR MODULES OVER GROUP ALGEBRAS
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

HOMOLOGICAL FINITENESS CONDITIONS FOR MODULES OVER GROUP ALGEBRAS
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

HOMOLOGICAL FINITENESS CONDITIONS FOR MODULES OVER GROUP ALGEBRAS
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *