2007/04/20 by Kevin Bowman, Bowman, Kevin, David A. Towers +3
Mathematics · Computer Science · #Finite Group Theory Research #Algebraic structures and combinatorial models #Coding theory and cryptography
paper · pdf · doi:10.48550/arxiv.0704.2723
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.