Indian Journal of Science and Technology
Year: 2018, Volume: 11, Issue: 30, Pages: 1-7
M. Aslam Malik and Sajjad Ali
Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore − 54590, Pakistan; aslam. [email protected], [email protected]
*Author for correspondence
M. Aslam Malik,
Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore − 54590, Pakistan; aslam. [email protected]
Objectives: To classify the types of G-circuits with length four in G-orbits G α 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.
Keywords: Coset Diagrams, Modular Group, Reduced Quadratic Irrational Numbers, Types of G-circuits of Length Four
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