SOME RESULTS ON NILPOTENT LIE ALGEBRAS

Let L be a finite dimensional Lie algebra over an arbitrary field F. In this paper, we prove that the class of finite nilpotent (solvable) Lie algebras is an example of formation. Furthermore, we conclude that every finite Lie algebra has a nilpotent (solvable) residual. Finally we prove some results on Frattini and Fitting subalgebras of the nilpotent Lie algebra L.