AutoMorphism

A structure-preserving BiJection of a mathematical object into itself.

The set of AutoMorphism of an object forms a group with the composition law.

When it is possible to build transformation of an object by selecting one of its elements and applying operations to the object, one can separate

• inner AutoMorphisms
• outer AutoMorphisms

The latter being transformations for which there is no correspondance with an element of the object.

---

(I am not satisfied with that, it is too much jargon, there should be an example, it does not convey the power of the concept and is just a definition) -- Olivier.