Normal subgroup whose automorphism group is abelian
From Groupprops
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 automorphism group is abelian
View a complete list of such conjunctions
Statement
A subgroup of a group
is termed an normal subgroup whose automorphism group is abelian of
if it satisfies both these conditions:
-
is a normal subgroup of
.
-
is a group whose automorphism group is abelian: the automorphism group
is an abelian group.
Relation with other properties
Stronger properties
Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|
cyclic normal subgroup | cyclic group and normal subgroup | cyclic implies abelian automorphism group | abelian automorphism group not implies abelian | |FULL LIST, MORE INFO |