Lancaster EPrints

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

[img]
Preview
PDF - Published Version
Download (408Kb) | Preview

    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: 09 Apr 2014 22:43
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/50002

    Actions (login required)

    View Item