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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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

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