Page "Automorphism" Paragraph 0

In mathematics, an automorphism is an isomorphism from a mathematical object to itself.

It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure.

The set of all automorphisms of an object forms a group, called the automorphism group.

It is, loosely speaking, the symmetry group of the object.