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Generic groups acting on regular trees

Miklos Abert·Yair Glasner
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Abstract

Let T be a k-regular tree (k>2) and A 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 of Gamma: it is either discrete, compact or has index at most 2 in A.

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Miklos Abert, Yair Glasner. 2007-02-25. Generic groups acting on regular trees. https://arxiv.org/abs/math/0702736

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