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Groupprops β

3-abelian group

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

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