Open main menu

Groupprops β

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 inner automorphism group, or equivalently, the group is isomorphic to the quotient by its center.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Centerless group center is trivial isomorphic to inner automorphism group not implies centerless |FULL LIST, MORE INFO

Related properties

Facts

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