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 $L$.