THE THETA PAIRS FOR PROPER SUBALGEBRAS AND THE SOLVABILITY

For a proper subalgebra K of a finite dimensional Lie algebra L, a pair (A;B) of subalgebras of L is called a µ-pair if L = hA;Ki, B is the largest ideal of L contained in A \ N and for each proper subalgebra C=B of A=B which is an ideal of L=B, we have L 6= C +K. In this article, using this concept, we give some characterizations of solvability and supersolvability of a finite dimensional Lie algebra