Deskins’s conjecture on Lie algebras

Abstract

We investigate relationships between the properties of maximal sub- algebras of L and the members of P(M) and solvability and supersolv- ability in Lie algebras. that corresponds to similar relationships in the group-theory. Further, we show that if L be a Lie algebra and algebri- caly closed field of zero characteristic, there exists a θ-subalgebra C such that L=M+C and  is abelian for all maximal subalgebras M and L, L is solvable.