Schreier property

Symbol-free definition
A group is said to have the Schreier property if its outer automorphism group (viz the quotient of its automorphism group by its inner automorphism group) is solvable.

Definition with symbols
A group $$G$$ is said to have the Schreier' property if $$Out(G) = Aut(G)/Inn(G)$$ is solvable.

Stronger properties

 * Finite simple non-Abelian group: This fact, known as the Schreier conjecture, follows from the classification of finite simple groups