# Difference between revisions of "Automorphism"

From Encyclopedia of Mathematics

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An [[Isomorphism|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|Algebraic system, automorphism of an]]). | An [[Isomorphism|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|Algebraic system, automorphism of an]]). |

## Latest revision as of 20:25, 3 May 2014

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://encyclopediaofmath.org/index.php?title=Automorphism&oldid=12546