Group whose automorphism group is solvable

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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