The Auslander conjecture for NIL-affine crystallographic groups

Let N be a simply connected, connected real nilpotent Lie group of finite dimension n. We study subgroups in Aff(N)=NAut(N) acting properly discontinuously and cocompactly on N. This situation is a natural generalization of the so-called affine crystallographic groups. We prove that for all dimensions 1n5 the generalized Auslander conjecture holds, i.e., that such subgroups are virtually polycyclic.