Hausdorff dimension of the second Grigorchuk group

Marialaura Noce; Anitha Thillaisundaram

doi:10.1142/S0218196721400038

Hausdorff dimension of the second Grigorchuk group

Marialaura Noce, Anitha Thillaisundaram

Department of Mathematical Sciences

University of Lincoln

Research output: Contribution to journal › Article › peer-review

6 Citations (SciVal)

Abstract

We show that the Hausdorff dimension of the closure of the second Grigorchuk group is 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.

Original language	English
Pages (from-to)	1037-1047
Number of pages	11
Journal	International Journal of Algebra and Computation
Volume	31
Issue number	6
Early online date	18 Jun 2021
DOIs	https://doi.org/10.1142/S0218196721400038
Publication status	Published - 30 Sept 2021

Bibliographical note

Funding Information:
The first author thanks the University of Lincoln for its excellent hospitality while this paper was being written. Both authors are grateful to the referee for very helpful comments. The first author is supported by the Spanish Government grant MTM2017-86802-P, partly with FEDER funds, and by the National Group for Algebraic and Geometric Structures and their Applications (GNSAGA – INdAM). She also acknowledges financial support from a London Mathematical Society Joint Research Groups in the UK (Scheme 3) grant. The second author acknowledges support from EPSRC, grant EP/T005068/1.

Keywords

Groups acting on trees
Hausdorff dimension
branch groups

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1142/S0218196721400038

https://arxiv.org/abs/1910.14518

Cite this

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title = "Hausdorff dimension of the second Grigorchuk group",

abstract = "We show that the Hausdorff dimension of the closure of the second Grigorchuk group is 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.",

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author = "Marialaura Noce and Anitha Thillaisundaram",

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KW - branch groups

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ER -

Hausdorff dimension of the second Grigorchuk group

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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