Dihedral group and classification of G-circuits of length 10

Bari M.N. Malik M.A. Al-Kaseasbeh S. Afzal Siddiqui H.M. Issakhov A. Rahimi-Gorji M. Hassani M.
1 November 2023 Walter de Gruyter GmbH

International Journal of Nonlinear Sciences and Numerical Simulation
2023 #24 Issue 7 2447 - 2459 pp.

In this paper, we classify G-circuits of length 10 with the help of the location of the reduced numbers lying on G-circuit. The reduced numbers play an important role in the study of modular group action on PSL(2,Z)-subset of Q( v m)Q. For this purpose,we define new notions of equivalent, cyclically equivalent, and similar G-circuits in PSL(2,Z)-orbits of real quadratic fields. In particular, we classify PSL(2,Z)-orbits of Q( v m)Q= ? k?NQ* (v k2m ) containingG-circuits of length 10anddeterminethat thenumberof equivalence classes of G-circuits of length 10 is 41 in number.We also use dihedral group to explore cyclically equivalence classes of circuits and use cyclic group to explore similar G-circuits of length 10 corresponding to 10 of these circuits. By using cyclically equivalent classes of circuits and similar circuits, we obtain the exact number of G-orbits and the structure of G-circuits corresponding to cyclically equivalent classes. This study also helps us in classifying the reduced numbers lying in the PSL(2,Z)-orbits.

cyclically equivalence classes of G-circuits , dihedral group , equivalence classes of G-circuits , reduced numbers , similar circuits

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Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, 54590, Pakistan
Department of Mathematics, Faculty of Science, Tafila Technical University, Tafila, Jordan
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Kazakh-British Technical University, Almaty, Kazakhstan
Faculty of Medicine and Health Sciences, Ghent University, Gent, 9000, Belgium

Department of Mathematics
Department of Mathematics
Department of Mathematics
Al-Farabi Kazakh National University
Kazakh-British Technical University
Faculty of Medicine and Health Sciences

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