Normal subgroup whose inner automorphism group is central in automorphism group

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This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): group whose inner automorphism group is central in automorphism group
View a complete list of such conjunctions

Definition

A subgroup $H$ of a group $G$ is termed a normal subgroup whose inner automorphism group is central in automorphism group if $H$ is a normal subgroup of $G$ and $H$ is a group whose inner automorphism group is central in automorphism group.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
cyclic normal subgroup Normal subgroup whose automorphism group is abelian|FULL LIST, MORE INFO
abelian normal subgroup Normal subgroup whose automorphism group is abelian|FULL LIST, MORE INFO
normal subgroup whose automorphism group is abelian normal subgroup that is also a group whose automorphism group is abelian |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
commutator-in-center subgroup