On Algebraic Characterizations For Finiteness of the Dimension of Eg

Certain algebraic invariants of the integral group ring zg of a group g were introduced and investigated in relation to the problem of extending the farrell-tate cohomology, which is defined for the class of groups of finite virtual cohomological dimension. it turns out that the finiteness of these invariants of a group g implies the existence of a generalized farrell-tate cohomology for g which is computed via complete resolutions. in this article we present these algebraic invariants and their basic properties and discuss their relationship to the generalized farrell-tate cohomology. in addition we present the status of conjecture which claims that the finiteness of these invariants of a group g is equivalent to the existence of a finite dimensional model for eg, the classifying space for proper actions.