Euler classes and Bredon cohomology for groups with restricted families of finite subgroups

We explore some of the special features with respect to Bredon cohomology of groups having all its finite subgroups either nilpotent or p-groups or cyclic p-groups. We get some results on dimensions and also a formula for the equivariant Euler class for certain groups. We consider the generalization for Bredon cohomology of the properties of being duality or Poincar\'e duality and study their behavior under p-power index extensions with coefficients in a field of characteristic p.