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The Frattini p-subalgebra of a solvable Lie p-algebra

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<mark>Journal publication date</mark>1997
<mark>Journal</mark>Proceedings of the Edinburgh Mathematical Society
Issue number1
Number of pages10
Pages (from-to)31-40
Publication StatusPublished
<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.

Bibliographic note

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.