Zelmanov's theorem on Engel Lie rings

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This article gives a proof/explanation of the equivalence of multiple definitions for the term locally nilpotent Lie ring
View a complete list of pages giving proofs of equivalence of definitions

Statement

The statement has many equivalent versions:

  1. For any natural number n, any finitely generated n-Engel Lie ring is a nilpotent Lie ring. Note that finite generation is as a Lie ring, not necessarily as an abelian group.
  2. For any natural number n, any n-Engel Lie ring is a locally nilpotent Lie ring.
  3. A Lie ring is a locally nilpotent Lie ring if and only it is a (not necessarily bounded) Engel Lie ring.

Related facts

Similar facts for Lie rings

Similar facts for groups