  In 1964 L. Auslander conjectured that every crystallographic subgroup of an
the affine group is virtually solvable, i.e. contains a solvable subgroup of
finite index. D. Fried and W. Goldman proved Auslander's conjecture for n = 3
using cohomological arguments. We prove the Auslander conjecture for n < 7. The
proof is based mainly on dynamical arguments. In some cases, we use the
cohomological argument which we could avoid but it would significantly lengthen
the proof.
