Group satisfying Tits alternative

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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

Weaker properties