Isoclinic groups

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

Definition

Two groups are said to be isoclinic if there is an isoclinism between them.

Facts

Groups isoclinic to the trivial group

A group is isoclinic to the trivial group if and ony if it is Abelian. In that case, the inner automorphism group and commutator subgroup are both trivial, and thus the isomorphisms are just the trivial maps.