A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group
This work deals with the well-known group-theoretic graphs called coset graphs for the modular group G and its applications. The group action of G on real quadratic fields forms infinite coset graphs. These graphs are made up of closed paths. When M acts on the finite field Zp, the coset graph appea...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/3905425 |
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| author | Hanan Alolaiyan Abdul Razaq Awais Yousaf Rida Zahra |
| author_facet | Hanan Alolaiyan Abdul Razaq Awais Yousaf Rida Zahra |
| author_sort | Hanan Alolaiyan |
| collection | DOAJ |
| description | This work deals with the well-known group-theoretic graphs called coset graphs for the modular group G and its applications. The group action of G on real quadratic fields forms infinite coset graphs. These graphs are made up of closed paths. When M acts on the finite field Zp, the coset graph appears through the contraction of the vertices of these infinite graphs. Thus, finite coset graphs are composed of homomorphic copies of closed paths in infinite coset graphs. In this work, we have presented a comprehensive overview of the formation of homomorphic copies. |
| format | Article |
| id | doaj-art-066b8438532f4d8cb384211a8123a64d |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-066b8438532f4d8cb384211a8123a64d2025-02-03T07:24:00ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/39054253905425A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular GroupHanan Alolaiyan0Abdul Razaq1Awais Yousaf2Rida Zahra3Department of Mathematics, King Saud University, Riyadh, Saudi ArabiaDepartment of Mathematics, Division of Science and Technology, University of Education Lahore, Lahore, PakistanDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanDepartment of Mathematics, Govt. Girls Elementary School Narri, Khushab, PakistanThis work deals with the well-known group-theoretic graphs called coset graphs for the modular group G and its applications. The group action of G on real quadratic fields forms infinite coset graphs. These graphs are made up of closed paths. When M acts on the finite field Zp, the coset graph appears through the contraction of the vertices of these infinite graphs. Thus, finite coset graphs are composed of homomorphic copies of closed paths in infinite coset graphs. In this work, we have presented a comprehensive overview of the formation of homomorphic copies.http://dx.doi.org/10.1155/2021/3905425 |
| spellingShingle | Hanan Alolaiyan Abdul Razaq Awais Yousaf Rida Zahra A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group Journal of Mathematics |
| title | A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group |
| title_full | A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group |
| title_fullStr | A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group |
| title_full_unstemmed | A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group |
| title_short | A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group |
| title_sort | comprehensive overview on the formation of homomorphic copies in coset graphs for the modular group |
| url | http://dx.doi.org/10.1155/2021/3905425 |
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