Group isomorphic to its inner automorphism group

Definition
A group is termed a group isomorphic to its inner automorphism group if the group is isomorphic to its defining ingredient::inner automorphism group, or equivalently, the group is isomorphic to the quotient by its center.

Related properties

 * Group isomorphic to its automorphism group

Facts
For a finite group, and more generally for a Hopfian group, being isomorphic to its inner automorphism group is equivalent to being centerless.