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Free subgroups of groups with nontrivial Floyd boundary
KTH, Superseded Departments, Mathematics.
2003 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 31, no 11, 5361-5376 p.Article in journal (Refereed) Published
Abstract [en]

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 by Floyd (Floyd, W. J. (1980). Group completions and limit sets of Kleinian groups. Invent. Math. 57: 205-218) as well as giving an elementary proof of a conjecture stated in that same paper. We also show that if the Floyd boundary of a finitely generated group is nontrivial, then it is a boundary in the sense of Furstenberg and the group acts on it as a convergence group.

Place, publisher, year, edition, pages
2003. Vol. 31, no 11, 5361-5376 p.
Keyword [en]
geometric group theory, convergence group action, hyperbolic groups, group-completions, kleinian-groups, sets
URN: urn:nbn:se:kth:diva-22872DOI: 10.1081/agb-120023961ISI: 000185773200011OAI: diva2:341570
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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