Quadrilateral and Hexagonal Maps Corresponding to the Subgroups Gamma(0)(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
  • Marmara University Affiliated: Yes

Abstract

Let N = 2(alpha)3(beta). The normalizer Gamma(B)(N) of Gamma(0)(N) in PSL(2, R) is the triangle group (2, 4, infinity) for alpha = 1, 3, 5, 7; beta = 0, 2 and the triangle group (2, 6, infinity) for alpha = 0, 2, 4, 6; (beta) = 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.