SQ-universal group

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 defining ingredient::finitely generated group is a defining ingredient::subquotient of the given group
 * 2) There exists a defining ingredient::finitely generated free group (on at least two generators) that occurs as a subquotient of the given group
 * 3) The defining ingredient::free group on two generators is a subquotient of the given group

Stronger properties

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