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 of a group
is termed a normal subgroup whose inner automorphism group is central in automorphism group if
is a normal subgroup of
and
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 |