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 |
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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 | |
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