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On quasi-toral restricted Lie algebras. (English) Zbl 1105.17008
In the paper some properties of finite-dimensional restricted Lie algebras $$L$$ satisfying the condition: $$x^{[p]^{n(x)}}=x$$ for any $$x\in L$$, are obtained. According to Jacobson’s conjecture a restricted Lie algebra $$L$$ such that $$x^{[p]^{n(x)}}=x$$ for any $$x\in L$$, is abelian. In the finite-dimensional case the conjecture was proved by A. Premet [Izv. Akad. Nauk SSSR 50, No. 4, 788–800 (1986; Zbl 0613.17009)].

##### MSC:
 17B50 Modular Lie (super)algebras 17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
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##### References:
 [7] H. Strade and R. Farnsteiner, Modular Lie Algebras and Their Representations (Marcel Dekker Inc., New York, 1988) p. 300. · Zbl 0648.17003
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