Bounding the orders of finite subgroups
Bounding the orders of finite subgroups
Suppose that G is a group of rational cohomological dimension n and that G is of type FP(n) over the integers. Under these hypotheses we show that there is a bound on the orders of finite subgroups of G. This extends a result of P. H. Kropholler, who obtained the same conclusion for G of finite rational cohomological dimension and of type FP(infinity) over the integers. For each n, there are groups G of type FP(n-1) over the integers and of rational cohomological dimension n for which there is no bound on the orders of finite subgroups.
finiteness conditions, finite subgroups
259-264
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Nucinkis, Brita E.A.
0b1c337c-36ae-4ef3-add4-b49a7c23810c
2001
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Nucinkis, Brita E.A.
0b1c337c-36ae-4ef3-add4-b49a7c23810c
Leary, Ian J. and Nucinkis, Brita E.A.
(2001)
Bounding the orders of finite subgroups.
Publicacions Matematiques, 45 (1), .
Abstract
Suppose that G is a group of rational cohomological dimension n and that G is of type FP(n) over the integers. Under these hypotheses we show that there is a bound on the orders of finite subgroups of G. This extends a result of P. H. Kropholler, who obtained the same conclusion for G of finite rational cohomological dimension and of type FP(infinity) over the integers. For each n, there are groups G of type FP(n-1) over the integers and of rational cohomological dimension n for which there is no bound on the orders of finite subgroups.
This record has no associated files available for download.
More information
Published date: 2001
Additional Information:
This is an improved version of a preprint by IJL alone that appeared late in 2000.
Keywords:
finiteness conditions, finite subgroups
Identifiers
Local EPrints ID: 29838
URI: http://eprints.soton.ac.uk/id/eprint/29838
ISSN: 0214-1493
PURE UUID: 862a841b-dd21-4f61-a780-224a16be0757
Catalogue record
Date deposited: 11 May 2006
Last modified: 12 Dec 2021 03:47
Export record
Contributors
Author:
Brita E.A. Nucinkis
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
