A self-similar group in the sense of iterated function system

Abstract

In this paper, first we give an iterated function system whose attractor is G m, a subgroup of the automorphism group of an (m + 1) -ary rooted tree. We also show that G m is a self-similar group in the sense of IFS. Then we prove that G m is both isomorphic and isometric to a compact topological group on k-ary Cantor set C k in the case of k = 2m + 1