The Auslander conjecture for NIL-affine crystallographic groups
Abstract
Let N be a simply connected, connected real nilpotent Lie group of finite dimension n. We study subgroups in (N)=N (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 1 n 5 the generalized Auslander conjecture holds, i.e., that such subgroups are virtually polycyclic.
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