Levi's characterization of 3-abelian groups
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
The following are equivalent for a group :
- is a 3-abelian group, i.e., the cube map of is an endomorphism of .
- is a 2-Engel group (also called a Levi group) and the derived subgroup of is either trivial or has exponent dividing three.