  A Lie group as a 4-dimensional pseudo-Riemannian manifold is considered. This
manifold is equipped with an almost product structure and a Killing metric in
two ways. In the first case Riemannian almost product manifold with
nonintegrable structure is obtained, and in the second case - a
pseudo-Riemannian one. Each belongs to a 4-parametric family of manifolds,
which are characterized geometrically.
