Free Subgroups of Groups with Nontrivial Floyd Boundary
نویسنده
چکیده
We prove that when a countable group admits a nontrivial Floyd-type boundary, then every nonelementary and metrically proper subgroup contains a noncommutative free subgroup. This generalizes the corresponding well-known results for hyperbolic groups and groups with infinitely many ends. It also shows that no finitely generated amenable group admits a nontrivial boundary of this type. This improves on a theorem in [Fl 80] as well as giving an elementary proof of a conjecture stated in that same paper. We also show that in case the Floyd boundary of a finitely generated group is nontrivial, then it is a boundary in the sense of Furstenberg.
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