 Automorphism group

The automorphism group of a group $G$ is the group of all isomorphisms $G\to G$ under composition.

In mathematics, specifically in the field of group theory and abstract algebra, an automorphism group is a concept that involves the symmetries of a mathematical structure. ### Definition An **automorphism** is an isomorphism from a mathematical object to itself. In other words, it is a bijective mapping that preserves the structure of the object.