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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Бібліографічні деталі
Дата:2019
Автори: Jaipong, Pradthana, Tapanyo, Wanchai
Формат: Стаття
Мова:English
Опубліковано: 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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spelling 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
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
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