PUB - Publikationen an der Universität Bielefeld

Inspired by the Basilica group B, we describe a general construction which allows us to associate to any group of automorphisms G < Aut(T ) of a rooted tree T a family of Basilica groups Bass(G), s E NC. For the dyadic odometer O2, one has B = Bas2(O2). We study which properties of groups acting on rooted trees are preserved under this operation. Introducing some techniques for handling Bass(G), in case G fulfills some branching conditions, we are able to calculate the Hausdorff dimension of the Basilica groups associated to certain GGS-groups and of generalisations of the odometer, Odm. Furthermore, we study the structure of groups of type Bass(Odm) and prove an analogue of the congruence subgroup property in the case m = p, a prime.