Reduced Quadratic Irrational Numbers and Types of G-circuits with Length Four by Modular Group

M  Aslam Malik and Sajjad Ali

doi:10.17485/ijst/2018/v11i30/127391

Article

Reduced Quadratic Irrational Numbers and Types of G-circuits with Length Four by Modular Group

VIEWS 1107
PDF 435

Abstract
Full-Text HTML
Full-Text PDF
How to Cite

Indian Journal of Science and Technology

DOI: 10.17485/ijst/2018/v11i30/127391

Year: 2018, Volume: 11, Issue: 30, Pages: 1-7

Original Article

Reduced Quadratic Irrational Numbers and Types of G-circuits with Length Four by Modular Group

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]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

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