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.

中文翻译：

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第二个 Grigorchuk 群的 Hausdorff 维数

我们证明了第二个 Grigorchuk 群闭包的 Hausdorff 维数是43/128. 此外，我们确定第二个 Grigorchuk 群是超强分形的，并且它的自同构群等于它在树的完全自同构群中的归一化器。