Partial automorphism

Definition
A partial automorphism of a group is an isomorphism from a subgroup of the group to a subgroup of the group, that occurs as the restriction (to the first subgroup) of an automorphism of the whole group.

Formalisms
The partial operator takes as input a property of a function on the whole group and returns the property of being a partial function that is a restriction to a subgroup of a function with that property. If the starting property is being an automorphism, the resultant property is being a partial automorphism.

Related notions

 * Partial endomorphism
 * Partial inner automorphism