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 |
| Summary: | 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 $(n,q)\in\{(2,7),(2,9),(2,11),(3,3),(4,2)\}$. |
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| ISSN: | 2251-7650 2251-7669 |