Bowman, Kevin and Towers, David A. and Varea, Vicente R.
(2007)
*Two Generator Subalgebras Of Lie Algebras.*
Linear and Multilinear Algebra, 55 (5).
pp. 429-438.
ISSN 1563-5139

## Abstract

In [14] 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. [10] 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.