Group whose automorphism group is nilpotent

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

A group is termed an group whose automorphism group is nilpotent (or group with nilpotent automorphism group) if its automorphism group is a nilpotent group.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
group whose automorphism group is abelian	automorphism group is abelian	follows from abelian implies nilpotent	nilpotent automorphism group not implies abelian automorphism group
cyclic group		via automorphism group being abelian		|FULL LIST, MORE INFO
locally cyclic group		via automorphism group being abelian		|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
nilpotent group		nilpotent automorphism group implies nilpotent of class at most one more	nilpotent not implies nilpotent automorphism group	|FULL LIST, MORE INFO