New Relations for the Normal Subgroups of Hecke Groups
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For an integer q ≥ 3, Hecke groups H(λq) are an important class of discrete groups with the most important member being the famous modular group obtained in the case of q = 3. They were defined by E. Hecke in 1936 when he was studying with Dirichlet series. There are a number of research papers on the properties of Hecke groups, their normal subgroups and the relation with regular maps. Here we add some recent results to state new relations between the parameters of the normal subgroups of Hecke groups and the corresponding regular maps which are also graphs in combinatorial sense by means of a new graph invariant called omega which was recently defined in 2018.
Abstract
For an integer q ≥ 3, Hecke groups H(λq) are an important class of discrete groups with the most important member being the famous modular group obtained in the case of q = 3. They were defined by E. Hecke in 1936 when he was studying with Dirichlet series. There are a number of research papers on the properties of Hecke groups, their normal subgroups and the relation with regular maps. Here we add some recent results to state new relations between the parameters of the normal subgroups of Hecke groups and the corresponding regular maps which are also graphs in combinatorial sense by means of a new graph invariant called omega which was recently defined in 2018.
참고문헌 (12)
- I. N. Cangul, "Normal Subgroups of the Hecke Group H(p 2)", Commun. Fac. Sci. Univ. Ank. Series A1, 43, pp.129~135 (1994)
- I. N. Cangul, "Normal Subgroups of the Hecke Groups and Regular Maps", Hacettepe Bull. of Nat. Sci. and Eng., 24, pp.15~23 (1995)
- I. N. Cangul, "The Group Structure of Hecke Groups H(λq)", Tr. J. of Mathematics, 20, pp.203~207 (1996)
- I. N. Cangul, "Normal Subgroups of Hecke Groups and Regular Maps", Math. Proc. Camb. Phil. Soc., 123, pp.59~74 (1998)
- S. Delen, "A New Graph Invariant", Turkish Journal of Analysis and Number Theory, 6(1), pp.30~33 (2018)
- S. Delen, "Extremal Problems on Components and Loops in Graphs", Acta Mathematica Sinica, English Series, 35(2), pp.161~171 (2019)
- Delen, S, "Omega Invariant of Graphs and Cyclicness", Applied Sciences, 21, pp.91~95 (2019)
- M. Demirci, "Diophantine Equations and Congruence Subgroups of the Hecke Groups H(√2) and H(√3)", Adv. Studies in Contemporary Maths, 12, pp.309~313 (2006)
- E. Hecke, "Über die Bestimmung Dirichletcherreichen durch ihre Funktionalgleichungen", Math. Ann., 112, pp.664~699 (1936)
- G. A. Jones, "Theory of Maps on Orientable Surfaces", Proc. L. M. S., 37(3), pp.273~307 (1978)
- Hasan Basri Özdemir, "A method for finding normal subgroups of Hecke groups", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 9(1), pp.51~55 (2006), 장전수학회
- Sanli, U, "Connectedness Criteria for Graphs by Means of Omega Invariant", FILOMAT, 34(2), pp.647~652 (2020)