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Dergiler / Conference Proceedings of Science and Technology / 2026 / Cilt: 3 Sayı: 1

Investigation of Γ-Invariant Equivalence Relations of Modular Groups and Subgroups

İbrahim Gökcan(KARADENİZ TEKNİK ÜNİVERSİTESİ)0000-0002-6933-8494
Ali Hikmet Değer(KARADENIZ TECHNICAL UNIVERSITY, FACULTY OF SCIENCE)0000-0003-0764-715X
Sayfa
110–114
Yayın Tarihi
2020-12-15
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Similarly, we study subgroups H containing Γ_(x/y) and we examine its the invariants equivalence relations on Q ̂.

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Amaç & Hipotez:In [3], the modular group, the movement of an element of the modular group on Q ̂ (extended set of rational numbers) in hyperbolic geometry, and Farey graph, G_(u,n) and F_(u,n) were investigated.
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Temel Bulgular & Veri:In the same study, H, the subgroups of Γ of containing Γ_∞ are obtained and its invariant equivalence relations are generated on Q ̂.
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Sonuç & Katkı:Similarly, we study subgroups H containing Γ_(x/y) and we examine its the invariants equivalence relations on Q ̂.
🔬Tür:Konferans Bildirisi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Infinite period · Invariant equivalence relations · Modular group

Abstract

In [3], the modular group, the movement of an element of the modular group on Q ̂ (extended set of rational numbers) in hyperbolic geometry, and Farey graph, G_(u,n) and F_(u,n) were investigated. Furthermore, it is indicated that the fixed of any two points is conjugated in Γ, and the element of the modular group that leaves constant an element on Q ̂ is infinite period. Hence, the element of the modular group that leaves the ∞ element constant is symbolized as Γ_∞. In the same study, H, the subgroups of Γ of containing Γ_∞ are obtained and its invariant equivalence relations are generated on Q ̂. Taking these points into account, in this study, we show that, the element that fixed x/y in modular group based on the choice of x/y for x,y∈Z and (x,y)=1, instead of a special value of set Q ̂, such as ∞. Similarly, we study subgroups H containing Γ_(x/y) and we examine its the invariants equivalence relations on Q ̂.

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Bu Makaleye Atıf Yap

Gökcan, İ., Değer, A. H. (2020). Investigation of Γ-Invariant Equivalence Relations of Modular Groups and Subgroups. Conference Proceedings of Science and Technology, Cilt: 3 Sayı: 1, 110–114. https://ajindex.com/articles/1648717

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Kaynakça (7)

  1. 1 B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, Berlin, Heidelberg, New York,(1974).
  2. 2 C.C. Sims, Graphs and Finite Permutation Groups, Math. Z. 95 (1967), 75-86.
  3. 3 G.A. Jones,D. Singerman and K. Wicks, The Modular Group and Generalized Farey Graphs, London Math. Soc. Lecture Notes, CUP, Cambridge, 160 (1991), 316-338.
  4. 4 N. L. Biggs and A. T. White, Permutation Groups and Combinatorial Structures, London Math. Soc. Lecture Notes 33, Cambridge University Press, Cambridge, (1979).
  5. 5 M. Akbas, On Suborbital Graphs for The Modular Group, Bull. London Math. Soc., 33 (2001), 647-652.
  6. 1 B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, Berlin, Heidelberg, New York,(1974).
  7. 4 N. L. Biggs and A. T. White, Permutation Groups and Combinatorial Structures, London Math. Soc. Lecture Notes 33, Cambridge University Press, Cambridge, (1979).