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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generic groups acting on regular trees


Authors: Miklós Abért and Yair Glasner
Journal: Trans. Amer. Math. Soc. 361 (2009), 3597-3610
MSC (2000): Primary 20E08, 20E06; Secondary 20B15
Published electronically: March 3, 2009
MathSciNet review: 2491892
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Abstract: Let $ T$ be a $ k$-regular tree ($ k\geq 3$) and $ A=\mathrm{Aut}(T)$ its automorphism group. We analyze a generic finitely generated subgroup $ \Gamma $ of $ A$. We show that $ \Gamma $ is free and establish a trichotomy on the closure $ \overline{\Gamma }$ of $ \Gamma $ in $ A.$ It turns out that $ \overline{\Gamma }$ is either discrete, compact or has index at most $ 2$ in $ A$.


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Additional Information

Miklós Abért
Affiliation: Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, Illinois 60637

Yair Glasner
Affiliation: Department of Mathematics, Ben Gurion University of the Negev, 84105 Beer Sheva, Israel

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04662-5
PII: S 0002-9947(09)04662-5
Received by editor(s): March 8, 2007
Published electronically: March 3, 2009
Additional Notes: Part of this work was carried out at the Institute for Advanced Studies and supported by NSF grant DMS-0111298
Article copyright: © Copyright 2009 American Mathematical Society