# Schreier property

From Groupprops

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.VIEW: Definitions built on this | Facts about this: (factscloselyrelated to Schreier property, all facts related to Schreier property) |Survey articles about this | Survey articles about definitions built on this

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## 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 is said to have the **Schreier' property** if 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