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

SALTAN M., Demir B.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.408, no.2, pp.694-704, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 408 Issue: 2
  • Publication Date: 2013
  • Doi Number: 10.1016/j.jmaa.2013.06.040
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.694-704
  • Keywords: Iterated function system, Self-similar set, Cantor set, Profinite group, Fractal, Topological group
  • Anadolu University Affiliated: Yes

Abstract

The notion of self-similarity in the sense of iterated function system (IFS) for compact topological groups is given by S. Kocak 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. (C) 2013 Elsevier Inc. All rights reserved.