  Engel subalgebras of finite-dimensional n-Lie algebras are shown to have
similar properties to those of Lie algebras. Using these, it is shown that an
n-Lie algebra, all of whose maximal subalgebras are ideals, is nilpotent. A
primitive 2-soluble n-Lie algebra is shown to split over its minimal ideal and
that all the complements to its minimal ideal are conjugate. A subalgebra is
shown to be a Cartan subalgebra if and only if it is minimal Engel, provided
that the field has sufficiently many elements. Cartan subalgebras are shown to
have a property analogous to intravariance.

Rings and Algebras