Reduced Quadratic Irrational Numbers and Types of G-circuits with Length Four by Modular Group
Muhammad Aslam Malik, Ali Sajjad · Indian Journal of Science and Technology · 2018
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