Abstract
It is shown that every group of automorphisms of a regular rooted tree that is defined by forbidding a set of patterns of size s + 1 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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Acknowledgments
The author would like to thank Rostislav Grigorchuk for stimulating conversations and the referee for useful remarks.
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Communicated by E. Zelmanov.
Partially supported by NSF grant DMS-0805932.
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Šunić, Z. Pattern closure of groups of tree automorphisms. Bull. Math. Sci. 1, 115–127 (2011). https://doi.org/10.1007/s13373-011-0007-2
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DOI: https://doi.org/10.1007/s13373-011-0007-2