Schreier property

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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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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.
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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