# Definition:Semigroup Automorphism

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## Definition

Let $\left({S, \circ}\right)$ be a semigroup.

Let $\phi: S \to S$ be a (semigroup) isomorphism from $S$ to itself.

Then $\phi$ is a semigroup automorphism.

## Also see

• Results about semigroup 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.