SQ-universal group

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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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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

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