Hausdorff dimension of the second Grigorchuk group
Marialaura Noce, Anitha Thillaisundaram
TL;DR
This paper calculates the Hausdorff dimension of the closure of the second Grigorchuk group as 43/128, and explores its fractal properties and automorphism group structure.
Contribution
It provides the first explicit Hausdorff dimension calculation for this group and analyzes its fractal and automorphism properties.
Findings
Hausdorff dimension of the closure is 43/128
The second Grigorchuk group is super strongly fractal
Its automorphism group equals its normaliser in the full automorphism group of the tree
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 normaliser in the full automorphism group of the tree.
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