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...
Saved in:
| Date: | 2019 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2019
|
| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/319 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | 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 \( \Gamma \). |
|---|