For a proper subalgebra K of a finite dimensional Lie algebra L, a pair (A,B) of subalgebras of L is called a \theta-pair if L = \langle A,K\rangle, B is the largest ideal of L contained in A\cap K and for each proper subalgebra C/B of A/B which is an ideal of L/B, we have L\neq C+K. In this article, using this concept, we give some characterizations of solvability and supersolvability of a finite dimensional Lie algebra.
SALEMKAR, ALI REZA; Chehrazi, Sara; and MOHAMMADZADEH, HAMID
"On theta pair for a proper subalgebra,"
Turkish Journal of Mathematics: Vol. 37:
4, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol37/iss4/6