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.