A note on two families of \(2\)-designs arose from Suzuki-Tits ovoid
In this note, we give a precise construction of one of the families of \(2\)-designs arose from studying flag-transitive \(2\)-designs with parameters \((v,k,\lambda)\) whose replication numbers \(r\) are coprime to \(\lambda\). We show that for a given positive integer \(q=2^{2n+1}\geq 8\), there...
Збережено в:
| Дата: | 2023 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2023
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1687 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543029878325248 |
|---|---|
| author | Alavi, S. H. |
| author_facet | Alavi, S. H. |
| author_sort | Alavi, S. H. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2023-03-06T16:39:17Z |
| description | In this note, we give a precise construction of one of the families of \(2\)-designs arose from studying flag-transitive \(2\)-designs with parameters \((v,k,\lambda)\) whose replication numbers \(r\) are coprime to \(\lambda\). We show that for a given positive integer \(q=2^{2n+1}\geq 8\), there exists a \(2\)-design with parameters \((q^{2}+1,q,q-1)\) and the replication number \(q^{2}\) admitting the Suzuki group \(\mathsf{Sz}(q)\) as its automorphism group. We also construct a family of \(2\)-designs with parameters \((q^{2}+1,q(q-1),(q-1)(q^{2}-q-1))\) and the replication number \(q^{2}(q-1)\) admitting the Suzuki groups \(\mathsf{Sz}(q)\) as their automorphism groups. |
| first_indexed | 2025-12-02T15:39:07Z |
| format | Article |
| id | admjournalluguniveduua-article-1687 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:39:07Z |
| publishDate | 2023 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-16872023-03-06T16:39:17Z A note on two families of \(2\)-designs arose from Suzuki-Tits ovoid Alavi, S. H. Suzuki group, Suzuki-Tits ovoid, \(2\)-design, automorphism group 05B05, 05B25, 20B25, 20D05 In this note, we give a precise construction of one of the families of \(2\)-designs arose from studying flag-transitive \(2\)-designs with parameters \((v,k,\lambda)\) whose replication numbers \(r\) are coprime to \(\lambda\). We show that for a given positive integer \(q=2^{2n+1}\geq 8\), there exists a \(2\)-design with parameters \((q^{2}+1,q,q-1)\) and the replication number \(q^{2}\) admitting the Suzuki group \(\mathsf{Sz}(q)\) as its automorphism group. We also construct a family of \(2\)-designs with parameters \((q^{2}+1,q(q-1),(q-1)(q^{2}-q-1))\) and the replication number \(q^{2}(q-1)\) admitting the Suzuki groups \(\mathsf{Sz}(q)\) as their automorphism groups. Lugansk National Taras Shevchenko University 2023-03-06 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1687 10.12958/adm1687 Algebra and Discrete Mathematics; Vol 34, No 2 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1687/pdf Copyright (c) 2023 Algebra and Discrete Mathematics |
| spellingShingle | Suzuki group Suzuki-Tits ovoid \(2\)-design automorphism group 05B05 05B25 20B25 20D05 Alavi, S. H. A note on two families of \(2\)-designs arose from Suzuki-Tits ovoid |
| title | A note on two families of \(2\)-designs arose from Suzuki-Tits ovoid |
| title_full | A note on two families of \(2\)-designs arose from Suzuki-Tits ovoid |
| title_fullStr | A note on two families of \(2\)-designs arose from Suzuki-Tits ovoid |
| title_full_unstemmed | A note on two families of \(2\)-designs arose from Suzuki-Tits ovoid |
| title_short | A note on two families of \(2\)-designs arose from Suzuki-Tits ovoid |
| title_sort | note on two families of \(2\)-designs arose from suzuki-tits ovoid |
| topic | Suzuki group Suzuki-Tits ovoid \(2\)-design automorphism group 05B05 05B25 20B25 20D05 |
| topic_facet | Suzuki group Suzuki-Tits ovoid \(2\)-design automorphism group 05B05 05B25 20B25 20D05 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1687 |
| work_keys_str_mv | AT alavish anoteontwofamiliesof2designsarosefromsuzukititsovoid AT alavish noteontwofamiliesof2designsarosefromsuzukititsovoid |