Lincoln, Mark and Towers, David (1997) The Frattini psubalgebra of a solvable Lie palgebra. Proceedings of the Edinburgh Mathematical Society, 40 (1). pp. 3140. ISSN 00130915

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Abstract
In this paper we continue our study of the Frattini psubalgebra of a Lie palgebra L. We show first that if L is solvable then its Frattini psubalgebra is an ideal of L. We then consider Lie palgebras L in which L^2 is nilpotent and find necessary and sufficient conditions for the Frattini psubalgebra to be trivial. From this we deduce, in particular, that in such an algebra every ideal also has trivial Frattini psubalgebra, and if the underlying field is algebraically closed then so does every subalgebra. Finally, we consider Lie palgebras L in which the Frattini psubalgebra of every subalgebra of L is contained in the Frattini psubalgebra 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 3140 1997, © 1997 Cambridge University Press. 
Uncontrolled Keywords:  /dk/atira/pure/subjectarea/asjc/2600 
Subjects:  
Departments:  Faculty of Science and Technology > Mathematics and Statistics 
ID Code:  50002 
Deposited By:  ep_importer_pure 
Deposited On:  28 Sep 2011 15:30 
Refereed?:  Yes 
Published?:  Published 
Last Modified:  20 Oct 2019 23:43 
URI:  https://eprints.lancs.ac.uk/id/eprint/50002 
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