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Ali, Sajjad
- Reduced Quadratic Irrational Numbers and Types of G-Circuits with Length Four by Modular Group
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Authors
M. Aslam Malik
1,
Sajjad Ali
1
Affiliations
1 Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore − 54590, PK
1 Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore − 54590, PK
Source
Indian Journal of Science and Technology, Vol 11, No 30 (2018), Pagination: 1-7Abstract
Objectives: To classify the types of G-circuits with length four in G-orbits αG where α is a reduced quadratic irrational number and G is the modular group. Methods/Statistical Analysis: G-orbits of real quadratic fields are evaluated using coset diagrams of modular group. Findings: There are five distinct types of the G-circuits in all. The number of disjoint G-orbits containing G-circuits of two types out of these five is four and for the remaining three types of G-circuits corresponding number of disjoint G-orbits is two. Application/Improvements: With the help of classification of G-circuits of length four we can find the structure of G-orbits of real quadratic fields.Full Text
References
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- Husnine SM, Aslam M, Majeed A. On ambiguous numbers of an invariant subset of under the action of the modular group PSL (2, Z), Studia Scientcrum Mathematic Arum Hungarica. 2005; 42(4):401−12.
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- Malik MA, Zafar MA. G-subsets of an invariant subset of under the modular group action. Utilitas Mathematica; 2013. p. 377−87.
- Mushtaq Q. On word structure of the modular group over finite and real quadratic fields, Discrete Mathematics. 1998; 178:155−64. https://doi.org/10.1016/S0012-365X(97)81824-9.
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- Classification of PSL (2, Z)-Circuits having Length Six
Abstract Views :206 |
PDF Views:0
Authors
Sajjad Ali
1,
M. Aslam Malik
1
Affiliations
1 Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore − 54590, PK
1 Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore − 54590, PK
Source
Indian Journal of Science and Technology, Vol 11, No 42 (2018), Pagination: 1-18Abstract
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) .Full Text
References
- 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.