Generalized classes of suborbital graphs for the congruence subgroups of the modular group
Let \( \Gamma \) be the modular group. We extend a nontrivial \( \Gamma \)-invariant equivalence relation on \( \widehat{\mathbb{Q}} \) to a general relation by replacing the group \( \Gamma_0(n) \) by \( \Gamma_K(n) \), and determine the suborbital graph \( \mathcal{F}^K_{u,n} \), an extended conce...
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| Дата: | 2019 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2019
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/319 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-319 |
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admjournalluguniveduua-article-3192019-04-09T04:52:54Z Generalized classes of suborbital graphs for the congruence subgroups of the modular group Jaipong, Pradthana Tapanyo, Wanchai modular group, congruence subgroups, suborbital graphs 05C20; 05C40; 05C63; 05C05; 05C60; 20H05 Let \( \Gamma \) be the modular group. We extend a nontrivial \( \Gamma \)-invariant equivalence relation on \( \widehat{\mathbb{Q}} \) to a general relation by replacing the group \( \Gamma_0(n) \) by \( \Gamma_K(n) \), and determine the suborbital graph \( \mathcal{F}^K_{u,n} \), an extended concept of the graph \( \mathcal{F}_{u,n} \). We investigate several properties of the graph, such as, connectivity, forest conditions, and the relation between circuits of the graph and elliptic elements of the group \( \Gamma_K(n) \). We also provide the discussion on suborbital graphs for conjugate subgroups of \( \Gamma \). Lugansk National Taras Shevchenko University (Pradthana Jaipong, Research Center in Mathematics and Applied Mathematics), (Wanchai Tapanyo, Chiang Mai University) 2019-03-23 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/319 Algebra and Discrete Mathematics; Vol 27, No 1 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/319/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/319/503 Copyright (c) 2019 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2019-04-09T04:52:54Z |
| collection |
OJS |
| language |
English |
| topic |
modular group congruence subgroups suborbital graphs 05C20 05C40 05C63 05C05 05C60 20H05 |
| spellingShingle |
modular group congruence subgroups suborbital graphs 05C20 05C40 05C63 05C05 05C60 20H05 Jaipong, Pradthana Tapanyo, Wanchai Generalized classes of suborbital graphs for the congruence subgroups of the modular group |
| topic_facet |
modular group congruence subgroups suborbital graphs 05C20 05C40 05C63 05C05 05C60 20H05 |
| format |
Article |
| author |
Jaipong, Pradthana Tapanyo, Wanchai |
| author_facet |
Jaipong, Pradthana Tapanyo, Wanchai |
| author_sort |
Jaipong, Pradthana |
| title |
Generalized classes of suborbital graphs for the congruence subgroups of the modular group |
| title_short |
Generalized classes of suborbital graphs for the congruence subgroups of the modular group |
| title_full |
Generalized classes of suborbital graphs for the congruence subgroups of the modular group |
| title_fullStr |
Generalized classes of suborbital graphs for the congruence subgroups of the modular group |
| title_full_unstemmed |
Generalized classes of suborbital graphs for the congruence subgroups of the modular group |
| title_sort |
generalized classes of suborbital graphs for the congruence subgroups of the modular group |
| description |
Let \( \Gamma \) be the modular group. We extend a nontrivial \( \Gamma \)-invariant equivalence relation on \( \widehat{\mathbb{Q}} \) to a general relation by replacing the group \( \Gamma_0(n) \) by \( \Gamma_K(n) \), and determine the suborbital graph \( \mathcal{F}^K_{u,n} \), an extended concept of the graph \( \mathcal{F}_{u,n} \). We investigate several properties of the graph, such as, connectivity, forest conditions, and the relation between circuits of the graph and elliptic elements of the group \( \Gamma_K(n) \). We also provide the discussion on suborbital graphs for conjugate subgroups of \( \Gamma \). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2019 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/319 |
| work_keys_str_mv |
AT jaipongpradthana generalizedclassesofsuborbitalgraphsforthecongruencesubgroupsofthemodulargroup AT tapanyowanchai generalizedclassesofsuborbitalgraphsforthecongruencesubgroupsofthemodulargroup |
| first_indexed |
2025-12-02T15:46:09Z |
| last_indexed |
2025-12-02T15:46:09Z |
| _version_ |
1850411968980058112 |