Semiautomorphism of a group

Definition
Let $$G$$ be a group. A semiautomorphism of $$G$$ is a semihomomorphism of groups from $$G$$ to itself, which has an inverse that is also a semihomomorphism of groups. Equivalently, it is a bijective semihomomorphism of groups from $$G$$ to itself.

Stronger properties

 * Automorphism of a group
 * Antiautomorphism of a group

Weaker properties

 * 1-automorphism of a group