### Periodic cohomology and subgroups with bounded Bredon cohomological
dimension

### Jang Hyun Jo and Brita E. A. Nucinkis

Mislin and Talelli showed that a torsion-free group in Kropholler's class
**H**F
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)