# Weakly normal automorphism

From Groupprops

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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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## Definition

An automorphism of a group is termed a **weakly normal automorphism** if, for every normal subgroup of , .

## Relation with other properties

### Stronger properties

- Inner automorphism
- Normal automorphism: A normal automorphism is a weakly normal automorphism whose inverse is also weakly normal.
- Uniform power automorphism
- Power automorphism
- Class-preserving automorphism
- Subgroup-conjugating automorphism
- Strong monomial automorphism
- Monomial automorphism