Hausdorff dimension of the second Grigorchuk group

Marialaura Noce, Anitha Thillaisundaram

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)


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 languageEnglish
Pages (from-to)1037-1047
Number of pages11
JournalInternational Journal of Algebra and Computation
Issue number6
Early online date18 Jun 2021
Publication statusPublished - 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.


  • Groups acting on trees
  • Hausdorff dimension
  • branch groups

ASJC Scopus subject areas

  • Mathematics(all)


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