Symmetric designs and projective special unitary groups $\text{PSU}_{5}(q)$
In this article, we prove that if a nontrivial symmetric $(v, k, \lambda)$ design admit a flag-transitive and point-primitive automorphism group $G$, then the socle $X$ of $G$ cannot be a projective special unitary group of dimension five. As a corollary, we list all exist nineteen non-i...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2022-09-01
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| Series: | International Journal of Group Theory |
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| Online Access: | https://ijgt.ui.ac.ir/article_25912_7bf6160b47aac2e1727152ec1fac1175.pdf |
| _version_ | 1829456180940898304 |
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| author | Ashraf Daneshkhah |
| author_facet | Ashraf Daneshkhah |
| author_sort | Ashraf Daneshkhah |
| collection | DOAJ |
| description | In this article, we prove that if a nontrivial symmetric $(v, k, \lambda)$ design admit a flag-transitive and point-primitive automorphism group $G$, then the socle $X$ of $G$ cannot be a projective special unitary group of dimension five. As a corollary, we list all exist nineteen non-isomorphism such designs in which $\lambda\in\{1,2,3,4,6,12, 16, 18\}$ and $X=\text{PSU}_n(q)$ with $(n,q)\in\{(2,7),(2,9),(2,11),(3,3),(4,2)\}$. |
| first_indexed | 2024-04-11T08:43:07Z |
| format | Article |
| id | doaj.art-62d6c96dc9c64905b1ad7d090425bc6b |
| institution | Directory Open Access Journal |
| issn | 2251-7650 2251-7669 |
| language | English |
| last_indexed | 2024-04-11T08:43:07Z |
| publishDate | 2022-09-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | International Journal of Group Theory |
| spelling | doaj.art-62d6c96dc9c64905b1ad7d090425bc6b2022-12-22T04:34:02ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692022-09-0111317518510.22108/ijgt.2021.123581.163025912Symmetric designs and projective special unitary groups $\text{PSU}_{5}(q)$Ashraf Daneshkhah0Department of Mathematics, Bu-Ali Sina University, Hamedan, IranIn this article, we prove that if a nontrivial symmetric $(v, k, \lambda)$ design admit a flag-transitive and point-primitive automorphism group $G$, then the socle $X$ of $G$ cannot be a projective special unitary group of dimension five. As a corollary, we list all exist nineteen non-isomorphism such designs in which $\lambda\in\{1,2,3,4,6,12, 16, 18\}$ and $X=\text{PSU}_n(q)$ with $(n,q)\in\{(2,7),(2,9),(2,11),(3,3),(4,2)\}$.https://ijgt.ui.ac.ir/article_25912_7bf6160b47aac2e1727152ec1fac1175.pdfsymmetric designflag-transitivepoint-primitiveautomorphism group |
| spellingShingle | Ashraf Daneshkhah Symmetric designs and projective special unitary groups $\text{PSU}_{5}(q)$ International Journal of Group Theory symmetric design flag-transitive point-primitive automorphism group |
| title | Symmetric designs and projective special unitary groups $\text{PSU}_{5}(q)$ |
| title_full | Symmetric designs and projective special unitary groups $\text{PSU}_{5}(q)$ |
| title_fullStr | Symmetric designs and projective special unitary groups $\text{PSU}_{5}(q)$ |
| title_full_unstemmed | Symmetric designs and projective special unitary groups $\text{PSU}_{5}(q)$ |
| title_short | Symmetric designs and projective special unitary groups $\text{PSU}_{5}(q)$ |
| title_sort | symmetric designs and projective special unitary groups text psu 5 q |
| topic | symmetric design flag-transitive point-primitive automorphism group |
| url | https://ijgt.ui.ac.ir/article_25912_7bf6160b47aac2e1727152ec1fac1175.pdf |
| work_keys_str_mv | AT ashrafdaneshkhah symmetricdesignsandprojectivespecialunitarygroupstextpsu5q |