Lincoln, Mark and Towers, David (1997) *The Frattini p-subalgebra of a solvable Lie p-algebra.* Proceedings of the Edinburgh Mathematical Society, 40 (1). pp. 31-40. ISSN 0013-0915

## Abstract

In this paper we continue our study of the Frattini p-subalgebra of a Lie p-algebra L. We show first that if L is solvable then its Frattini p-subalgebra is an ideal of L. We then consider Lie p-algebras L in which L^2 is nilpotent and find necessary and sufficient conditions for the Frattini p-subalgebra to be trivial. From this we deduce, in particular, that in such an algebra every ideal also has trivial Frattini p-subalgebra, and if the underlying field is algebraically closed then so does every subalgebra. Finally, we consider Lie p-algebras L in which the Frattini p-subalgebra of every subalgebra of L is contained in the Frattini p-subalgebra of L itself.

Item Type: | Article |

Journal or Publication Title: | Proceedings of the Edinburgh Mathematical Society |

Additional Information: | http://journals.cambridge.org/action/displayJournal?jid=PEM The final, definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, 40 (1), pp 31-40 1997, © 1997 Cambridge University Press. |

Subjects: | |

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

ID Code: | 50002 |

Deposited By: | ep_importer_pure |

Deposited On: | 28 Sep 2011 16:30 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 13 Jan 2016 13:44 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/50002 |
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