  We construct homogeneous flat pseudo-Riemannian manifolds with non-abelian
fundamental group. In the compact case, all homogeneous flat pseudo-Riemannian
manifolds are complete and have abelian linear holonomy group. To the contrary,
we show that there do exist non-compact and non-complete examples, where the
linear holonomy is non-abelian, starting in dimensions $\geq 8$, which is the
lowest possible dimension. We also construct a complete flat pseudo-Riemannian
homogeneous manifold of dimension 14 with non-abelian linear holonomy.
Furthermore, we derive a criterion for the properness of the action of an
affine transformation group with transitive centralizer.

Differential Geometry;Representation Theory