Schreier property

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
VIEW: Definitions built on this | Facts about this: (facts closely related to Schreier property, all facts related to Schreier property) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
View a list of other standard non-basic definitions

Definition

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.

Relation with other properties

Stronger properties

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