On groups of type (FP)

  title={On groups of type (FP)},
  author={Peter H. Kropholler},
  journal={Journal of Pure and Applied Algebra},
  • P. Kropholler
  • Published 19 November 1993
  • Mathematics
  • Journal of Pure and Applied Algebra

Projective Resolutions for Modules over Infinite Groups

We define a notion of complexity for modules over group rings of infinite groups. This generalizes the notion of complexity for modules over group algebras of finite groups. We show that if M is a

A Criterion for Projective Modules

In case G is a finite group, there is a well-known criterion for projective modules: A ℤ G-module M is projective if and only if it is ℤ -free and has finite projective dimension. We first

Homological Finiteness Conditions for Modules Over Group Algebras

We develop a theory of modules of type FP∞ over group algebras of hierarchically decomposable groups. This class of groups is denoted hF and contains many different kinds of discrete groups including


Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut.G/ such that for ’ 2 H the Reidemeister number R.’/ is infinite. This includes all finitely

Some groups of type VF

Abstract.A group is of type VF if it has a finite-index subgroup which has a finite classifying space. We construct groups of type VF in which the centralizers of some elements of finite order are

Groups acting on nite dimensional spaces with nite stabilizers

It is shown that every HF-group G of type FP1 admits a nite dimensional G-CW- complex X with nite stabilizers and with the additional property that for each nite subgroup H, the xed point subspace X

Complexity and Varieties for Infinite Groups, I☆

This two-part paper generalizes the usual notion of complexity and varieties for modules over the group algebra of a finite group, to a large class of infinite groups. The context is modules of

2 4 Fe b 20 05 On Cohomology rings of infinite groups

Let R be any ring (with 1), Γ a group and RΓ the corresponding group ring. Let Ext∗ RΓ (M,M) be the cohomology ring associated to the RΓ-module M . Let H be a subgroup of finite index of Γ which



Linear groups of finite cohomological dimension

Our main result provides necessary and sufficient conditions for a finitelygenerated subgroup of GLn(C), n > 0, to have finite virtual cohomological dimension. A group has finite virtual

Groups Acting on Graphs

Preface Conventions 1. Groups and graphs 2. Cutting graphs and building trees 3. The almost stability theorem 4. Applications of the almost stability theorem 5. Poincare duality 6. Two-dimensional