On Codimension One Nilfoliations and a Theorem of Malcev

A HOMOGENEOUS space of a (connected) Lie group G is a manifold on which G acts transitively; these manifolds have been studied for many years. A particularly interesting family of non transitive actions is that of actions whose orbits are the leaves of a foliation. If one tries to describe them, one naturally restricts to the codimension 1 case. Here we study foliations defined by locally free actions of nilpotent Lie groups on compact manifolds: the so-called nilfoliations. Our aim is to generalize both