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Construction of elements in the closure of Grigorchuk group

Goulnara Arzhantseva·Zoran Sunic
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Abstract

We describe constraints that need to be satisfied ``near the top'' of the portraits of the elements in Grigorchuk group. These constraints, if satisfied by the portraits of all sections of some binary tree automorphism, guarantee that this automotphism belongs to the closure of Grigorchuk group in the pro-finite group of binary tree automorphisms. The constraints may be viewed as an effective version of a more conceptual description given earlier by Grigorchuk.

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Goulnara Arzhantseva, Zoran Sunic. 2006-07-31. Construction of elements in the closure of Grigorchuk group. https://arxiv.org/abs/math/0607778

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