Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\)
An anti-torus in a CAT(0) group is a subgroup \(\langle a,b\rangle\), where \(a\) and \(b\) do not have commuting powers. We study anti-tori in quaternionic lattices \(\Gamma_\tau\) over the field \(\mathbb{F}_q(t)\) introduced by Stix-Vdovina (2017). We determine when every pair of generators of \(...
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| Дата: | 2024 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2024
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2217 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543145227976704 |
|---|---|
| author | Bondarenko, Ievgen Bondarenko, Nataliia |
| author_facet | Bondarenko, Ievgen Bondarenko, Nataliia |
| author_sort | Bondarenko, Ievgen |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2024-06-27T08:42:43Z |
| description | An anti-torus in a CAT(0) group is a subgroup \(\langle a,b\rangle\), where \(a\) and \(b\) do not have commuting powers. We study anti-tori in quaternionic lattices \(\Gamma_\tau\) over the field \(\mathbb{F}_q(t)\) introduced by Stix-Vdovina (2017). We determine when every pair of generators of \(\Gamma_\tau\) generates an anti-torus, and establish the existence of \(a,b\in\Gamma_\tau\) such that the subgroup \(\langle a^{p^n},b^{p^n}\rangle\) is not abelian and not free for all \(n\geq 0\). Explicit examples of matrices \(a,b\in SL_3(\mathbb{F}_q(t))\) with this property are given. |
| first_indexed | 2025-12-02T15:35:34Z |
| format | Article |
| id | admjournalluguniveduua-article-2217 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:35:34Z |
| publishDate | 2024 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-22172024-06-27T08:42:43Z Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) Bondarenko, Ievgen Bondarenko, Nataliia anti-torus, quaternionic lattice, free subgroup 11R52, 20F65, 20F67 An anti-torus in a CAT(0) group is a subgroup \(\langle a,b\rangle\), where \(a\) and \(b\) do not have commuting powers. We study anti-tori in quaternionic lattices \(\Gamma_\tau\) over the field \(\mathbb{F}_q(t)\) introduced by Stix-Vdovina (2017). We determine when every pair of generators of \(\Gamma_\tau\) generates an anti-torus, and establish the existence of \(a,b\in\Gamma_\tau\) such that the subgroup \(\langle a^{p^n},b^{p^n}\rangle\) is not abelian and not free for all \(n\geq 0\). Explicit examples of matrices \(a,b\in SL_3(\mathbb{F}_q(t))\) with this property are given. Lugansk National Taras Shevchenko University 2024-06-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2217 10.12958/adm2217 Algebra and Discrete Mathematics; Vol 37, No 2 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2217/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2217/1155 Copyright (c) 2024 Algebra and Discrete Mathematics |
| spellingShingle | anti-torus quaternionic lattice free subgroup 11R52 20F65 20F67 Bondarenko, Ievgen Bondarenko, Nataliia Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) |
| title | Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) |
| title_full | Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) |
| title_fullStr | Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) |
| title_full_unstemmed | Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) |
| title_short | Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) |
| title_sort | anti-tori in quaternionic lattices over \(\mathbb{f}_q(t)\) |
| topic | anti-torus quaternionic lattice free subgroup 11R52 20F65 20F67 |
| topic_facet | anti-torus quaternionic lattice free subgroup 11R52 20F65 20F67 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2217 |
| work_keys_str_mv | AT bondarenkoievgen antitoriinquaternioniclatticesovermathbbfqt AT bondarenkonataliia antitoriinquaternioniclatticesovermathbbfqt |