In  Thompson showed that a finite group G is solvable if and only if every twogenerated subgroup is solvable (Corollary 2, p. 388). Recently, Grunevald et al.  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.
The final, definitive version of this article has been published in the Journal, Linear and Multilinear Algebra, 55 (5), 2007, © Informa Plc