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Lie algebras with nilpotent length greater than that of each of their subalgebras

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<mark>Journal publication date</mark>06/2017
<mark>Journal</mark>Algebras and Representation Theory
Issue number3
Number of pages16
Pages (from-to)735-750
Publication StatusPublished
Early online date16/12/16
<mark>Original language</mark>English


The main purpose of this paper is to study the finite-dimensional solvable Lie algebras described in its title, which we call minimal non-N . To facilitate this we investigate solvable Lie algebras of nilpotent length k, and of nilpotent length ≤ k, and extreme Lie algebras, which have the property that their nilpotent length is equal to the number of conjugacy classes of maximal subalgebras. We characterise the minimal non-N Lie algebras in which every nilpotent subalgebra is abelian, and those of solvability index ≤ 3.