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Petrie Paths in Triangular Normalizer Maps

Yıl 2022, , 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, , 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

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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