Mislin and Talelli showed that a torsion-free group in Kropholler's class HF with periodic cohomology after some steps has finite cohomological dimension. In this note we look at similar questions for groups with torsion by considering Bredon cohomology. In particular we show that every elementary amenable group acting freely and properly on some R^n x S^m admits a finite dimensional classifying space for proper actions.

Preprint (2006)