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Home > Research > Publications & Outputs > Two Generator Subalgebras Of Lie Algebras.
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Two Generator Subalgebras Of Lie Algebras.

Research output: Contribution to journalJournal article

Published

Journal publication date09/2007
JournalLinear and Multilinear Algebra
Journal number5
Volume55
Number of pages10
Pages429-438
Original languageEnglish

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.

Bibliographic note

The final, definitive version of this article has been published in the Journal, Linear and Multilinear Algebra, 55 (5), 2007, © Informa Plc