# Automorphism

From Encyclopedia of Mathematics

An isomorphism (isomorphic mapping) of a system of objects onto itself. The totality of all automorphisms of an arbitrary algebraic system forms a group, and the study of this group is an important and powerful tool in the study of the properties of the system itself (cf. Algebraic system, automorphism of an).

**How to Cite This Entry:**

Automorphism.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Automorphism&oldid=12546