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Journals / Universal Journal of Mathematics and Applications / 2022 / Cilt: 5 - Sayı: 3

Petrie Paths in Triangular Normalizer Maps

Nazlı YAZICI GÖZÜTOK
Pages
89–95
Publication Date
2022-09-30
DOI
—
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AI Summary & Key Takeaways

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

Thus, for each regular map, we find the Petrie length of the corresponding map.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This study is devoted to investigate the Petrie paths in the normalizer maps and regular triangular maps corresponding to the subgroups $\Gamma_0(N)$ of the modular group $\Gamma$.
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Key Findings & Data:We show that each regular triangular map admits a closed Petrie path.
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Conclusion & Impact:Thus, for each regular map, we find the Petrie length of the corresponding map.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Normalizer · Petrie path · regular map

Abstract

This study is devoted to investigate the Petrie paths in the normalizer maps and regular triangular maps corresponding to the subgroups $\Gamma_0(N)$ of the modular group $\Gamma$. We show that each regular triangular map admits a closed Petrie path. Thus, for each regular map, we find the Petrie length of the corresponding map.

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Cite This Article

GÖZÜTOK, N. Y. (2022). Petrie Paths in Triangular Normalizer Maps. Universal Journal of Mathematics and Applications, Cilt: 5 - Sayı: 3, 89–95. https://ajindex.com/articles/819893

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References (13)

  1. B. Schoeneberg, Elliptic Modular Functions, Springer, Berlin, 1974
  2. N. Yazıcı Go¨zu¨tok, B. O¨. Gu¨ler, Suborbital graphs for the group GC(N), Bull. Iran. Math. Soc., 45 (2019), 593-605
  3. Y. Kesicio˘glu, M. Akbas¸, On suborbital graphs for the group G3, Bull. Iran. Math. Soc., 46 (2020), 1731-1744
  4. B. O¨. Gu¨ler, M. Bes¸enk, A.H. Deg˘er, S. Kader, Elliptic elements and circuits in suborbital graphs, Hacettepe J. Math. Stat., 40 (2011), 203-210
  5. P. Jaipong, W. Promduang, K. Chaichana, Suborbital graphs of the congruence subgroup G0(N), Beitr. Algebra Geom., 60 (2019), 181-192
  6. P. Jaipong, W. Tapanyo, Generalized classes of suborbital graphs for the congruence subgroups of the modular group, Algebra Discret. Math., 27 (2019), 20-36
  7. M. Akbas¸, D. Singerman, Onsuborbital graphs for the modular group, Bull. London Math. Soc., 33 (2001), 647-652
  8. N. Yazıcı Go¨zu¨tok, U. Go¨zu¨tok, B. O¨. Gu¨ler, Maps corresponding to the subgroups G0(N) of the modular group, Graphs Combin., 35 (2019), 1695-1705
  9. N. Yazıcı G¨oz¨utok, Normalizer maps modulo N, Mathematics, 10 (2022), 1046
  10. J. H. Conway, S. P. Norton, Monstrous moonshine, Bull. London Math. Soc., 11 (1977), 308-339
  11. M. Akbas¸, D. Singerman, The signature of the normalizer of G0(N), Lond. Math. Soc. Lect. Note Ser., 165 (1992), 77-86
  12. D. Singerman, J. Strudwick, Petrie polygons, Fibonacci sequences and Farey maps, Ars Math. Contemp., 10 (2016), 349-357
  13. D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525-532.