We show that a complete flat pseudo-Riemannian homogeneous manifold with
non-abelian linear holonomy is of dimension at least 14. Due to an example
constructed in a previous article by Oliver Baues and the author, this is a
sharp bound. Also, we give a structure theory for the fundamental groups of
complete flat pseudo-Riemannian manifolds in dimensions less than 7. Finally,
we observe that every finitely generated torsion-free 2-step nilpotent group
can be realized as the fundamental group of a complete flat pseudo-Riemannian
manifold with abelian linear holonomy.Comment: 16 page
