The Hausdorff dimension of the generalized Brunner–Sidki–Vieira groups

Abstract

We compute the Hausdorff dimension of the closure of the generalized Brunner–Sidki–Vieira group acting on the $m$-adic tree for $m\ge 2$, providing the first examples of self-similar topologically finitely generated closed subgroups of transcendental Hausdorff dimension in the group of $m$-adic automorphisms for $m\ge 4$ even.