c-Sections of Lie algebras

Let M be a maximal subalgebra of a Lie algebra L   and A/BA/B a chief factor of L   such that B⊆MB⊆M and A⊈MA⊈M. We call the factor algebra M∩A/BM∩A/B a c-section of M. All such c-sections are isomorphic, and this concept is related those of c-ideals and ideal index previously introduced by the author. Properties of c-sections are studied and some new characterizations of solvable Lie algebras are obtained.