# Normal subgroup whose automorphism group is abelian

From Groupprops

(Redirected from Aut-abelian normal subgroup)

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 |