3-abelian group

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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