Group satisfying Tits alternative for finitely generated subgroups

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

A group is said to satisfy the Tits alternative for finitely generated subgroups if for every finitely generated 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).