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Hausdorff dimension of the second Grigorchuk group

Marialaura Noce

Mathematisches Institut, Georg-August Universität zu Göttingen, Bunsenstr. 3-5, Göttingen 37073, Germany

E-mail Address: mnoce@unisa.it

Corresponding author.

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and

Anitha Thillaisundaram

School of Mathematics and Physics, University of Lincoln, Brayford Pool, Lincoln LN6 7TS, UK

E-mail Address: anitha.t@cantab.net

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https://doi.org/10.1142/S0218196721400038Cited by:3 (Source: Crossref)

This article is part of the issue:

Special Issue on Papers From the Conference “Semigroups and Groups, Automata, Logics” SandGAL 2019
Guest Editors: Achille Frigeri, Victoria Gould, Patrizia Longobardi and Emanuele Rodaro

Abstract

We show that the Hausdorff dimension of the closure of the second Grigorchuk group is $43 / 128$ $43 / 128$ . Furthermore, we establish that the second Grigorchuk group is super strongly fractal and that its automorphism group equals its normalizer in the full automorphism group of the tree.

Communicated by all the special editors

Keywords:

AMSC: 20E08, 20E18, 28A78

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