Two Generator Subalgebras of Lie Algebras

Details Two Generator Subalgebras of Lie Algebras Two Generator Subalgebras of Lie Algebras

2007-04-20

arxiv.org/abs/0704.2723v1

Mathematics

Rings and Algebras

12 pages

Scientific paper

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.

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