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arXiv · 1012.1688

Pattern closure of groups of tree automorphisms

Zoran Sunic
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Abstract

It is shown that a group defined by forbidding all patterns of size s+1 that do not appear in a given self-similar group of tree automorphisms is the topological closure of a self-similar, countable, regular branch group, branching over its level s stabilizer. As an application, it is shown that there are no infinite, finitely constrained, topologically finitely generated groups of binary tree automorphisms defined by forbidden patterns of size two.

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Zoran Sunic. 2010-12-09. Pattern closure of groups of tree automorphisms. https://arxiv.org/abs/1012.1688

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