Self-similar groups in the sense of an iterated function system and their properties

The notion of self-similarity in the sense of iterated function system (IFS) for compact topological groups is given by Ş. Koçak in Definition 3. In this work, first we give the definition of strong self-similar group in the sense of IFS. Then, we investigate the main properties of these groups. We also obtain the relations between profinite groups and strong self-similar groups in the sense of IFS. Finally, we construct some examples of these groups.