Generic groups acting on regular trees

Miklós Abért; Yair Glasner

doi:10.1090/S0002-9947-09-04662-5

Generic groups acting on regular trees

Miklós Abért, Yair Glasner

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Let T be a k-regular tree (k ≥ 3) and A = Aut(T) its automorphism group. We analyze a generic finitely generated subgroup Γ of A. We show that Γ is free and establish a trichotomy on the closure Γ̄ of Γ̄ in A. It turns out that Γ̄ is either discrete, compact or has index at most 2 in A.

Original language	English
Pages (from-to)	3597-3610
Number of pages	14
Journal	Transactions of the American Mathematical Society
Volume	361
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9947-09-04662-5
State	Published - 1 Jul 2009

ASJC Scopus subject areas

Mathematics (all)
Applied Mathematics

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10.1090/S0002-9947-09-04662-5

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abstract = "Let T be a k-regular tree (k ≥ 3) and A = Aut(T) its automorphism group. We analyze a generic finitely generated subgroup Γ of A. We show that Γ is free and establish a trichotomy on the closure {\=Γ} of {\=Γ} in A. It turns out that {\=Γ} is either discrete, compact or has index at most 2 in A.",

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AB - Let T be a k-regular tree (k ≥ 3) and A = Aut(T) its automorphism group. We analyze a generic finitely generated subgroup Γ of A. We show that Γ is free and establish a trichotomy on the closure Γ̄ of Γ̄ in A. It turns out that Γ̄ is either discrete, compact or has index at most 2 in A.

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Generic groups acting on regular trees

Abstract

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