SQ-universal group

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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Definition

Symbol-free definition

A group is termed SQ-universal with respect to finitely generated groups (or simple SQ-universal) if it satisfies the following equivalent conditions:

1. Every finitely generated group is a subquotient of the given group
2. There exists a finitely generated free group (on at least two generators) that occurs as a subquotient of the given group
3. The free group on two generators is a subquotient of the given group

Relation with other properties

Stronger properties

• Non-Abelian finitely generated free group (i.e. a finitely generated free group on at least two generators)