# 3-abelian group

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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## Definition

A group is termed 3-abelian if it is n-abelian for $n = 3$, i.e., the cube map is an endomorphism of the group.

## Facts

For more on power maps being endomorphisms, see n-abelian group.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
abelian group
group of exponent three

### Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
2-Engel group Follows from Levi's characterization of 3-abelian groups