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Petrie Paths in Triangular Normalizer Maps

Yıl 2022, Cilt: 5 Sayı: 3, 89 - 95, 30.09.2022
https://doi.org/10.32323/ujma.1150466

Öz

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.

Kaynakça

  • [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.
Yıl 2022, Cilt: 5 Sayı: 3, 89 - 95, 30.09.2022
https://doi.org/10.32323/ujma.1150466

Öz

Kaynakça

  • [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.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Nazlı Yazıcı Gözütok 0000-0002-3645-0623

Yayımlanma Tarihi 30 Eylül 2022
Gönderilme Tarihi 28 Temmuz 2022
Kabul Tarihi 14 Eylül 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 3

Kaynak Göster

APA Yazıcı Gözütok, N. (2022). Petrie Paths in Triangular Normalizer Maps. Universal Journal of Mathematics and Applications, 5(3), 89-95. https://doi.org/10.32323/ujma.1150466
AMA Yazıcı Gözütok N. Petrie Paths in Triangular Normalizer Maps. Univ. J. Math. Appl. Eylül 2022;5(3):89-95. doi:10.32323/ujma.1150466
Chicago Yazıcı Gözütok, Nazlı. “Petrie Paths in Triangular Normalizer Maps”. Universal Journal of Mathematics and Applications 5, sy. 3 (Eylül 2022): 89-95. https://doi.org/10.32323/ujma.1150466.
EndNote Yazıcı Gözütok N (01 Eylül 2022) Petrie Paths in Triangular Normalizer Maps. Universal Journal of Mathematics and Applications 5 3 89–95.
IEEE N. Yazıcı Gözütok, “Petrie Paths in Triangular Normalizer Maps”, Univ. J. Math. Appl., c. 5, sy. 3, ss. 89–95, 2022, doi: 10.32323/ujma.1150466.
ISNAD Yazıcı Gözütok, Nazlı. “Petrie Paths in Triangular Normalizer Maps”. Universal Journal of Mathematics and Applications 5/3 (Eylül 2022), 89-95. https://doi.org/10.32323/ujma.1150466.
JAMA Yazıcı Gözütok N. Petrie Paths in Triangular Normalizer Maps. Univ. J. Math. Appl. 2022;5:89–95.
MLA Yazıcı Gözütok, Nazlı. “Petrie Paths in Triangular Normalizer Maps”. Universal Journal of Mathematics and Applications, c. 5, sy. 3, 2022, ss. 89-95, doi:10.32323/ujma.1150466.
Vancouver Yazıcı Gözütok N. Petrie Paths in Triangular Normalizer Maps. Univ. J. Math. Appl. 2022;5(3):89-95.

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