In this paper the Lie algebra
analogues to groups with property E of Bechtell are investigated. Let χ be the class
of solvable Lie algebras with the following property: if H is a subalgebra
of L, then ϕ(H) ⊆ ϕ(L) where ϕ(L) denotes the Frattini subalgebra of L;
that is, ϕ(L) is the intersection of all maximal subalgebras of L. Groups
with the analogous property are called E-groups by Bechtell. The class X is
shown to contain all solvable Lie algebras whose derived algebra is nilpotent.
Necessary conditions are found such that an ideal N of L ∈ χ be the Frattini
subalgebra of L. Only solvable Lie algebras of finite dimension are considered
here.
