| Abstract: | A subalgebra H of a finite dimensional Lie algebra L is said to be a SCAP-subalgebra if there is a chief series 0 = L0 ? L1 ?... ? Lt = L of L such that for every i = 1, 2,..., t, we have H + Li = H + Li-1 or H ∩ Li = H ∩ Li-1. This is analogous to the concept of SCAP-subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its SCAP-subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable. |
