Group having no free non-abelian subgroup

Definition
A group having no free non-abelian subgroup is a group satisfying the following equivalent conditions:


 * It has no subgroup that is a free non-abelian subgroup.
 * It has no subgroup isomorphic to the free group on two generators.
 * For fixed $$r > 1$$, it has no subgroup isomorphic to a free group on $$r$$ generators.
 * It has no subgroup isomorphic to a free group on a countably infinite number of generators.

Stronger properties

 * Weaker than::Finite group
 * Weaker than::Abelian group
 * Weaker than::Nilpotent group
 * Weaker than::Virtually abelian group
 * Weaker than::Virtually nilpotent group
 * Weaker than::Virtually solvable group
 * Weaker than::Periodic group
 * Weaker than::Group satisfying a nontrivial identity