# Definition:Group Automorphism

## Definition

Let $\struct {G, \circ}$ be a group.

Let $\phi: G \to G$ be a (group) isomorphism from $G$ to itself.

Then $\phi$ is a group automorphism.

## Also see

• Results about group automorphisms can be found here.

## Linguistic Note

The word automorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix iso- meaning equal.

Thus automorphism means self structure.