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

SALTAN M., Demir B.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.408, sa.2, ss.694-704, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 408 Sayı: 2
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1016/j.jmaa.2013.06.040
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.694-704
  • Anahtar Kelimeler: Iterated function system, Self-similar set, Cantor set, Profinite group, Fractal, Topological group
  • Anadolu Üniversitesi Adresli: Evet

Özet

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.