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On some problems of group theory and Lie algebras. (Russian) Zbl 0673.17007
This paper is an intermediate step in the complete solution of the restricted Burnside problem recently achieved by the author. It is proved here that the above problem reduces to the local nilpotence of Lie algebras over \({\mathbb{Z}}_ p\) satisfying the Engel condition \(E_ n\) and its linearizations. As for this latter, the author proves here that Lie rings with \(E_ 6\) as well as Lie algebras over \({\mathbb{Z}}_ p\) with \(E_{p^ 2-p}\) are locally nilpotent. There are also some remarks on Engel groups in the final part of the paper.
Reviewer: Yu.A.Bakhturin

MSC:
17B30 Solvable, nilpotent (super)algebras
20F45 Engel conditions
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
20F50 Periodic groups; locally finite groups
20F40 Associated Lie structures for groups
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