Lie p-algebras of finite p-subalgebra rank |
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Authors: | D M Riley |
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Institution: | Department of Mathematics, Middlesex College, The University of Western Ontario,? London, Ontario N6A 5B7, Canada, e-mail: DMRiley@uwo.ca, CA
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Abstract: | We say that a Lie p-algebra L has finite p-subalgebra rank if the minimal number of generators required to generate every finitely generated p-subalgebra is uniformly bounded by some integer r. This paper is concerned with the following problem: does L being of finite p-subalgebra rank force ad(L) to be finite-dimensional? Although this seems unlikely in general, we show that this is indeed the case for Lie p-algebras in a large class including all locally, residually, and virtually soluble Lie p-algebras. |
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