On quasi-toral restricted Lie algebras (Q2483724)

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 \textit{A. Premet} [Izv. Akad. Nauk SSSR 50, No. 4, 788--800 (1986; Zbl 0613.17009)].