**The Frattini p-subalgebra of a solvable Lie p-a...**Final published version, 408 KB, PDF-document

Research output: Contribution to journal › Journal article

Published

<mark>Journal publication date</mark> | 1997 |
---|---|

<mark>Journal</mark> | Proceedings of the Edinburgh Mathematical Society |

Issue number | 1 |

Volume | 40 |

Number of pages | 10 |

Pages (from-to) | 31-40 |

<mark>State</mark> | Published |

<mark>Original language</mark> | English |

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.

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.