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.

Item Type: | Journal Article |

Journal or Publication Title: | Linear and Multilinear Algebra |

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

Uncontrolled Keywords: | Lie algebra ; two generator ; solvable ; supersolvable ; triangulable |

Subjects: | ?? qa ?? |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 872 |

Deposited By: | Dr David A. Towers |

Deposited On: | 20 Dec 2007 13:54 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 14 Apr 2018 00:10 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/872 |
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