Bounding the orders of finite subgroups 

Ian J. Leary and Brita E. A. Nucinkis  

Abstract 
We give homological conditions on groups such that whenever the conditions
hold for a group $G$, there is a bound on the orders of finite 
subgroups of $G$.  This extends a result of P. H. Kropholler.  
We also suggest a weaker condition under which the same 
conclusion might hold.