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

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

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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:
Journal 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.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
50002
Deposited By:
Deposited On:
28 Sep 2011 15:30
Refereed?:
Yes
Published?:
Published
Last Modified:
08 Aug 2020 02:42