# Direct factor-preserving automorphism

From Groupprops

This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)

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## Contents

## Definition

### Symbol-free definition

An automorphism of a group is said to be **direct factor-preserving** if it takes each direct factor to itself, that is, if every direct factor is invariant under the automorphism.

### Definition with symbols

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