### On groups acting on contractlible spaces with stabilizers of prime power order

### Ian J. Leary Brita E. A. Nucinkis

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).