Quadrilateral and Hexagonal Maps Corresponding to the Subgroups Γ (N) of the Modular Group

YAZICI GÖZÜTOK N., GÜLER B. Ö.

Graphs and Combinatorics, vol.38, no.3, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1007/s00373-022-02503-0
  • Journal Name: Graphs and Combinatorics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Keywords: Regular maps, Modular group, Normalizer, CONGRUENCE SUBGROUPS, NORMALIZER
  • Karadeniz Technical University Affiliated: Yes

Abstract

© 2022, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.Let N= 2 α3 β. The normalizer Γ B(N) of Γ (N) in PSL(2 , R) is the triangle group (2 , 4 , ∞) for α= 1 , 3 , 5 , 7 ; β= 0 , 2 and the triangle group (2 , 6 , ∞) for α= 0 , 2 , 4 , 6 ; β= 1 , 3. In this paper we examine relationship between the normalizer and the regular maps. We define a family of subgroups of the normalizer and then we study maps with quadrilateral and hexagonal faces using these subgroups and calculating the associated arithmetic structure.