On codimension one nilfoliations and a theorem of Malcev (Q1122833)

The authors study nilfoliations, i.e. foliations defined by locally free actions of nilpotent Lie groups on compact manifolds. They generalize Malcev's structure theorem for nilmanifolds as well as some results by Rosenberg, Roussarie, Weil and Chatelet on manifolds foliated by actions of \(R^ n\) or Heisenberg groups. In particular, they show that any nilfoliation is almost without holonomy.