Weakly normal automorphism

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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 $\sigma$ of a group $G$ is termed a weakly normal automorphism if, for every normal subgroup $N$ of $G$, $\sigma (N)\subseteq N$.

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