Maximal subalgebras of Lie algebras containing Engel subalgebras

Relationships between certain properties of maximal subalgebras of a Lie algebra L and the structure of L itself have been studied by a number of authors. Some maximal subalgebras, however, exert a greater influence on particular results than others. Here we study properties of those maximal subalgebras that contain Engel subalgebras, and of those that also have codimension greater than one in L.