Commutator map-equivalent groups

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This article defines an equivalence relation over the collection of groups. View a complete list of equivalence relations on groups.

Definition

Two groups are termed commutator map-equivalent groups if there exists a bijection between them that is a commutator map-equivalence of groups.

Facts

Statistics determined up to commutator map-equivalence

The following are determined up to commutator map-equivalence:

What determines a group up to commutator map-equivalence

Relation with other equivalent relations

Stronger relations

Related relations