Examples of nonproper affine actions (Q1803916)

This paper is concerned with free subgroups of the affine group that act properly discontinuously on \(\mathbb{R}^ 3\). These subgroups are conjugate to free subgroups of \(H\), the group of motions of Lorentz 3-space. The author gives a condition on a free subgroup of \(H\) which implies that the action is not properly discontinuous. He then constructs a free subgroup which does not satisfy this condition and which also does not act properly discontinuously.