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Classification of PSL (2, Z)-Circuits having Length Six


Affiliations
1 Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore − 54590, Pakistan
 

Objectives: To classify PSL (2, Z)-circuits contained in PSL (2, Z)-orbit having length six. Methods/Statistical Analysis: By employing coset diagrams of these orbits containing PSL (2,Z)-circuits with length 6 are explored. Findings: Thirty different types with the above mentioned property have been found in all. Applications: By using classification of PSL (2, Z)-circuits of length six we can comprehend the construction of PSL (2, Z)-orbits of Q(√m) .
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  • Mushtaq Q. Modular group acting on real quadratic fields, Bulletin of the Australian Mathematical Society. 1988; 37(2):303−09. https://doi.org/10.1017/S000497270002685X.

  • Farkhanda A, Qamar A, Malik MA. A Classification of the real quadratic irrational numbers of w.r.t Modulo, International Mathematical Forum. 2012; 7(39):1915−24.

  • Farkhanda A, Qamar A, Malik MA. Modular group action on quadratic fields by linear congruence, Novi Sad Journal of Mathematics. 2012; 42(2):127−37.

  • Mushtaq Q, Razaq A. Homomorphic Images of circuits in PSL (2, Z)-Space, Bulletin of the Malaysian Mathematical Sciences Society. 2017; 40:1115−33. https://doi.org/10.1007/s40840-016-0357-8.

  • Mushtaq Q, Razaq A. Joining of circuits in PSL (2, Z)-Space, Bulletin of the Korean Mathematical Society. 2015; 52(6):2047−69. https://doi.org/10.4134/BKMS.2015.52.6.2047.

  • Mushtaq Q, Nighat M. PSL (2, 7) and carbon allotropy D168 Schwarzite, Journal of Mathematical Chemistry. 2018; 56:2485−94. https://doi.org/10.1007/s10910-018-0900-y. https://doi.org/10.1007/s10910-018-0903-8.

  • Malik MA, Zafar MA. Real quadratic irrational numbers and modular group action. Southeast Asian Bulletin of Mathematics. 2011, 35(3), pp. 439-445.

  • Mushtaq Q, Yousaf A. Alternating groups as quotients of PSL (2, Z[i]), Proceedings – Mathematical Sciences Indian Academy of Sciences. 2018; 128(4):1−15.

  • Mushtaq Q. On word structure of the modular group over finite and real quadratic fields, Discrete Mathematics. 1998; 178(1-3):155−64. https://doi.org/10.1016/S0012-365X(97)81824-9.

  • MalikMA, Sajjad Ali. Reduced Quadratic Irrational Numbers and Types of G-circuits with Length Four by Modular Group. Indian Journal of Science and Technology. 2018, pp. 1-7 https://doi.org/10.17485/ijst/2018/v11i14/110789, https://doi.org/10.17485/ijst/2018/v11i30/127391.


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  • Classification of PSL (2, Z)-Circuits having Length Six

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Authors

Sajjad Ali
Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore − 54590, Pakistan
M. Aslam Malik
Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore − 54590, Pakistan

Abstract


Objectives: To classify PSL (2, Z)-circuits contained in PSL (2, Z)-orbit having length six. Methods/Statistical Analysis: By employing coset diagrams of these orbits containing PSL (2,Z)-circuits with length 6 are explored. Findings: Thirty different types with the above mentioned property have been found in all. Applications: By using classification of PSL (2, Z)-circuits of length six we can comprehend the construction of PSL (2, Z)-orbits of Q(√m) .

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DOI: https://doi.org/10.17485/ijst%2F2018%2Fv11i42%2F132011