Let F denote the class of finite groups, and let P de- note the subclass consisting of groups of prime power order. We study group actions on topological spaces in which either (1) all stabilizers lie in P or (2) all stabilizers lie in F. We compare the classifying spaces for actions with stabilizers in F and P, the Kropholler hierarchies built on F and P, and group cohomology relative to F and to P.

Preprint (2009).