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).

Relation with other properties

Stronger properties

• Finite group
• Abelian group
• Nilpotent group
• Solvable group
• Virtually Abelian group
• Virtually nilpotent group
• Virtually solvable group
• Free group

Weaker properties

• Group satisfying Tits alternative for finitely generated subgroups