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
class two normal subgroup				Commutator-in-center subgroup|FULL LIST, MORE INFO
hereditarily 2-subnormal subgroup				Commutator-in-center subgroup|FULL LIST, MORE INFO