The MathNet Korea
Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Journal of Pure and Applied Algebra
( Vol. 90 NO.1 / (1993))
On Groups of Type (FP)$_infty$
Peter H. Kropholler,
Pages. 55-67
Abstract Let $G$ be a group. A $mathbb{Z}G$-module $M$ is said to be of
type (FP)$_infty$ over $mathbb{Z}G$ if and only if there is a
projective resolution $P_* twoheadrightarrow M$ in which every
$P_i$ 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 $mathbb{Z}G$-module of
type (FP)$_infty$ has finite projective dimension. We also prove
that every soluble or linear group of type (FP)$_infty$ 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.
Contents 1. Introduction
2. Closure operations
3. Cohomological functors
4. Mislin's generalization of Tate cohomology
5. Some general properties of (FP)$_infty$-groups
Key words
Mathmatical Subject Classification