on permutably complemented subalgebras of finite dimensional lie algebras

Let $l$ be a finitedimensional lie algebra. we say a subalgebra $h$ of $l$ is permutably complemented in $l$ if there is a subalgebra $k$ of $l$ such that $l=h+k$ and $hcap k=0$. also, if every subalgebra of $l$ is permutably complemented in $l$, then $l$ is called completely factorisable. in this article, we consider the influence of these concepts on the structure of a lie algebra, in particular, we obtain some characterizations for supersolvability of a finitedimensional lie algebra in terms of permutably complemented subalgebras.