Group in which every automorphism is normal-extensible

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

Symbol-free definition

A group in which every automorphism is normal-extensible is a group with the property that given any automorphism of it, and any embedding of it as a normal subgroup of a bigger group, the automorphism extends to an automorphism of the bigger group.

Relation with other properties

Stronger properties

• Complete group
• Group in which every automorphism is inner
• Centerless group that is maximal in its automorphism group: For full proof, refer: Centerless and maximal in automorphism group implies every automorphism is normal-extensible
• Group in which every automorphism is center-fixing and whose inner automorphism group is maximal in its automorphism group: For full proof, refer: Every automorphism is center-fixing and inner automorphism group is maximal in automorphism group implies every automorphism is normal-extensible