Abstract
The paper studies nilpotent n-Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for n-Lie superalgebras which is a generalization of those for n-Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent n-Lie superalgebras and obtain several sufficient conditions for an n-Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal and the Jacobson radical.
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