Tate-Farrell Cohomology
Farrell extended Tate cohomology groups to the case of all groups G of finite virtual cohomological dimension. In Farrell's theory, the groups are isomorphic to the usual cohomology groups whenever n is greater than the virtual cohomological dimension of the group G. Finite groups have virtual cohomological dimension 0, and in this case Farrell's cohomology groups are the same as those of Tate.
Read more about this topic: Tate Cohomology Group