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...
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| Дата: | 2023 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2023
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1687 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua: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 |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Suzuki group Suzuki-Tits ovoid \(2\)-design automorphism group 05B05 05B25 20B25 20D05 |
| 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 |
| topic_facet |
Suzuki group Suzuki-Tits ovoid \(2\)-design automorphism group 05B05 05B25 20B25 20D05 |
| format |
Article |
| author |
Alavi, S. H. |
| author_facet |
Alavi, S. H. |
| author_sort |
Alavi, S. H. |
| title |
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_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_sort |
note on two families of \(2\)-designs arose from suzuki-tits ovoid |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2023 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1687 |
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AT alavish anoteontwofamiliesof2designsarosefromsuzukititsovoid AT alavish noteontwofamiliesof2designsarosefromsuzukititsovoid |
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2024-04-12T06:26:05Z |
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2024-04-12T06:26:05Z |
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