Group whose automorphism group is solvable

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A group is termed a group whose automorphism group is solvable or a group with solvable automorphism group if its automorphism group is a solvable 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 solvable |FULL LIST, MORE INFO
group whose automorphism group is nilpotent automorphism group is nilpotent follows from nilpotent implies solvable |FULL LIST, MORE INFO
complete solvable group solvable group that is also complete |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
solvable group aut-solvable implies solvable of derived length at most one more
Schreier property outer automorphism group is solvable