Classification of PSL (2, Z)-Circuits having Length Six

Sajjad Ali and M  Aslam Malik

doi:10.17485/ijst/2018/v11i42/132011

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Classification of PSL (2, Z)-Circuits having Length Six

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2018/v11i42/132011

Year: 2018, Volume: 11, Issue: 42, Pages: 1-18

Original Article

Classification of PSL (2, Z)-Circuits having Length Six

Sajjad Ali and M. Aslam Malik

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore − 54590, Pakistan; [email protected], [email protected]

^*Author for correspondence
Sajjad Ali,
Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore − 54590, Pakistan; [email protected]

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

Abstract

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 ( ) .

Keywords: Classification of Types Containing 6 Length PSL (2, Z)-Circuits, Coset Diagrams, Reduced Numbers, PSL (2, Z)