Generalised nilpotence conditions in n-engel lie algebras |
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| Authors: | David M Riley |
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| Institution: | Department of Mathematics , The University of Western Ontario , Middlesex College, London, Ontario, N6A 5B7, Canada E-mail: DMRiley@uwo. ca |
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| Abstract: | A Lie algebra is said to satisfy the Baer condition provided each of its 1-dimensional subalgebras is a subideal; if the defect is bounded then the Lie algebra is bounded Baer. We first characterise restricted enveloping algebras (of odd characteristic p) that satisfy the bounded Baer condition. Using this characterisation, we are then able to construct a Lie algebra satisfying the bounded Engel condition, in each odd characteristic p, that does not satisfy the Baer condition. Such a bounded Engel Lie algebra must contain a non-nilpotent 1-generated ideal |
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