The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant (Q634710)

The authors study the dynamics of properly discontinuous and crystallographic affine groups leaving a quadratic form of signature \((p, q)\) invariant. The main results are: (i) if \(p - q \geq 2\), then the linear part of the group is not Zariski dense in the corresponding orthogonal group; (ii) if \(q = 2\) and the group is crystallographic, then the group is virtually solvable. So the Auslander conjecture is proven for this case.