Group satisfying Tits alternative

Definition
A group is said to satisfy the Tits alternative if for every subgroup of it, one of these two conditions holds:


 * 1) The subgroup is virtually solvable (i.e., has a solvable subgroup of finite index)
 * 2) The subgroup contains a free non-abelian subgroup (which is equivalent to saying that it contains a copy of free group:F2).

Stronger properties

 * Weaker than::Finite group
 * Weaker than::Abelian group
 * Weaker than::Nilpotent group
 * Weaker than::Solvable group
 * Weaker than::Virtually Abelian group
 * Weaker than::Virtually nilpotent group
 * Weaker than::Virtually solvable group
 * Weaker than::Free group

Weaker properties

 * Stronger than::Group satisfying Tits alternative for finitely generated subgroups