On groups acting on contractible spaces with stabilizers of prime power order

Description/Abstract

Let F denote the class of finite groups, and let P denote 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. In terms of standard notations, we show that F C H1P C H1F, with all inclusions proper; that HF = HP; that FH*(G;−) = PH*(G;−); and that EpG is finite-dimensional if and only if EfG is finite-dimensional and every finite subgroup of G is in P