summary: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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机译：摘要：本文研究了特征零域上的幂立$ n $ -Lie超级代数。更具体地讲，我们证明了恩格尔定理关于$ n $ -Lie超级代数，这是对$ n $ -Lie代数和Lie超级代数的推广。另外，作为恩格尔定理的一个应用，我们给出了幂等n元-李超代数的一些性质，并通过使用最大子代数（弱理想和雅各布森激进派。
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