Icosahedral Group and Classification of PSL(2, Z)-Orbits of Real Quadratic Fields

Tianlan Chen, Muhammad Nadeem Bari, Muhammad Aslam Malik, Hafiz Muhammad Afzal Siddiqui, Jia-Bao Liu and Shaofang Hong

Journal of Mathematics, 2020, vol. 2020, 1-10

Abstract: Reduced numbers play an important role in the study of modular group action on the PSL2,ℤ-subset of Qm/Q. For this purpose, we define new notions of equivalent, cyclically equivalent, and similar G-circuits in PSL2,ℤ-orbits of real quadratic fields. In particular, we classify PSL2,ℤ-orbits of Qm/Q=∪k∈NQ∗k2m containing G-circuits of length 6 and determine that the number of equivalence classes of G-circuits of length 6 is ten. We also employ the icosahedral group to explore cyclically equivalence classes of circuits and similar G-circuits of length 6 corresponding to each of these ten circuits. This study also helps us in classifying reduced numbers lying in the PSL2,ℤ-orbits.

Date: 2020
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2020/9568254.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2020/9568254.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9568254

DOI: 10.1155/2020/9568254

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().