Levi's characterization of 3-abelian groups

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This article gives a proof/explanation of the equivalence of multiple definitions for the term 3-abelian group
View a complete list of pages giving proofs of equivalence of definitions

Statement

The following are equivalent for a group G:

  1. G is a 3-abelian group, i.e., the cube map of G is an endomorphism of G.
  2. G is a 2-Engel group (also called a Levi group) and the derived subgroup of G is either trivial or has exponent dividing three.

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