### COHOMOLOGY RELATIVE TO A G-SET AND FINITENESS CONDITIONS

### B. E. A. Nucinkis

We shall consider a cohomology theory
relative to group actions on sets and develop a completion analogous to
Mislin, Benson and Carlson. Later we restrict ourselves to cohomology
relative to all finite subgroups. There we shall study relative analogues
to finiteness conditions on kG-modules such as finite relative projective
dimension and being of relative type FP$_\infty$.