Hausdorff dimension of the second Grigorchuk group

Abstract

We show that the Hausdorff dimension of the closure of the second Grigorchuk group is [Formula: see text]. 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. We show that the Hausdorff dimension of the closure of the second Grigorchuk group is [Formula: see text]. 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.