Group whose automorphism group is nilpotent

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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 aut-nilpotent 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
Aut-abelian group	automorphism group is abelian	follows from abelian implies nilpotent	aut-nilpotent not implies aut-abelian
Cyclic group		via aut-abelian		|FULL LIST, MORE INFO
Locally cyclic group		via aut-abelian		|FULL LIST, MORE INFO

Weaker properties

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