SavedAdd your journal

Journals / Turkish Journal of Mathematics / 2008 / Cilt: 32 - Sayı: 1

Trace classes and fixed points for the extended modular group $overlineGamma$

Sebahattin İKİKARDEŞ
Recep ŞAHİN
Özden KORUOĞLU
Pages
11–19
Publication Date
2022-11-05
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Using this, we classify the elements of $overlineGamma$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The extended modular group $overlineGamma$ = PGL(2,$Bbb{Z}$) is the group obtained by adding the reflection R(z) = 1/$overline z$ to the generators of the modular group $overlineGamma$ = PSL(2,$Bbb{Z}$).
📊
Key Findings & Data:In this paper, we find the trace classes of the extended modular group $overlineGamma$.
💡
Conclusion & Impact:Using this, we classify the elements of $overlineGamma$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The extended modular group $overlineGamma$ = PGL(2,$Bbb{Z}$) is the group obtained by adding the reflection R(z) = 1/$overline z$ to the generators of the modular group $overlineGamma$ = PSL(2,$Bbb{Z}$). In this paper, we find the trace classes of the extended modular group $overlineGamma$. Using this, we classify the elements of $overlineGamma$.

🔖

Cite This Article

İKİKARDEŞ, S., ŞAHİN, R., KORUOĞLU, Ö. (2022). Trace classes and fixed points for the extended modular group $overlineGamma$. Turkish Journal of Mathematics, Cilt: 32 - Sayı: 1, 11–19. https://ajindex.com/articles/609049

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. Fine, B. Trace classes and quadratic forms in the modular group, Canad. Math. Bull. Vol.37(2), 202-212, (1994)
  2. Jones, G. A.; Thornton, J. S. Automorphisms and congruence subgroups of the extended modular group, J. London Math. Soc. (2) 34, 26-40, (1986)
  3. Kern-Isberner, G.; Rosenberger, G. A note on numbers of the form n = $x^2 + Ny^2$. Arch.Math. (Basel) 43 (2), 148–156 (1984)
  4. Kulkarni, R. S. An arithmetic-geometricmethod in the study of the subgroups of the modular group, Am. J. Math. 113, No.6, 1053-1133, (1991)
  5. Lang, M. L. Normalisers of subgroups of the modular group, J. Algebra, 248, No.1, 202-218,(2002)
  6. Newman, M. The structure of some subgroups of the modular group, Illinois J. Math. 6,480-487, (1962)
  7. Newman, M. Free subgroups and normal subgroups of the modular group, Illinois J. Math.8, 262-265, (1964)
  8. Sahin, R.; İkikardes S.; Koruoğlu, Ö. On the power subgroups of the extended modular group $overlineGamma$, Tr. J. of Math., 29, 143-151, (2004)
  9. Schmidt, T.A.; Sheingorn, M. Length spectra of the Hecke triangle groups, Math. Z. 220,no. 3, 369–397 (1995)
  10. Singerman, D. PSL(2,q) as an image of the extended modular group with applications to group actions on surfaces, Proc. Edinb. Math. Soc., II. Ser. 30, 143-151, (1987)
  11. Özgür, N. Y.; Sahin, R. On the extended Hecke groups $overline H(lambda q )$, Tr. J. of Math., 27, 473-480, (2003).