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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.

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More information

Published date: 19 November 1993
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 349609
URI: https://eprints.soton.ac.uk/id/eprint/349609
PURE UUID: 82753e11-2302-42a2-9223-2f35ac0b61c9

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Date deposited: 15 Apr 2013 11:27
Last modified: 18 Jul 2017 04:40

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