  J. G. Thompson showed that a finite group G is solvable if and only if every
two -generated subgroup is solvable. Recently, Grunevald, Kunyavskii, Nikolova,
and Plotkin have shown that the analogue holds for finite-dimensional Lie
algebras over infinite fields of characteristic greater than 5. It is a natural
question to ask to what extent the two-generated subalgebras determine the
structure of the algebra. It is to this question that this paper is addressed.
Here, we consider the classes of strongly-solvable and of supersolvable Lie
algebras, and the property of triangulability.
