Almost simple groups as flag-transitive automorphism groups of 2-designs with λ = 2
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910826264264704 |
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| author | Alavi, Seyed Hassan |
| author_facet | Alavi, Seyed Hassan |
| contents | In this article, we study $2$-designs with $λ=2$ admitting a flag-transitive almost simple automorphism group with socle a finite simple exceptional group of Lie type, and we prove that such a $2$-design does not exist. In conclusion, we present a classification of $2$-designs with $λ=2$ admitting flag-transitive and point-primitive automorphism groups of almost simple type, which states that such a $2$-design belongs to an infinite family of $2$-designs with parameter set $((3^n-1)/2,3,2)$ and $X=PSL_n(3)$ for some $n\geq 3$, or it is isomorphic to the $2$-design with parameter set $(6,3,2)$, $(7,4,2)$, $(10,4,2)$, $(10,4,2)$, $(11,5,2)$, $(28,7,2)$, $(28,3,2)$, $(36,6,2)$, $(126,6,2)$ or $(176,8,2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05195 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Almost simple groups as flag-transitive automorphism groups of 2-designs with λ = 2 Alavi, Seyed Hassan Group Theory Combinatorics 05B05, 05B25, 20B25 In this article, we study $2$-designs with $λ=2$ admitting a flag-transitive almost simple automorphism group with socle a finite simple exceptional group of Lie type, and we prove that such a $2$-design does not exist. In conclusion, we present a classification of $2$-designs with $λ=2$ admitting flag-transitive and point-primitive automorphism groups of almost simple type, which states that such a $2$-design belongs to an infinite family of $2$-designs with parameter set $((3^n-1)/2,3,2)$ and $X=PSL_n(3)$ for some $n\geq 3$, or it is isomorphic to the $2$-design with parameter set $(6,3,2)$, $(7,4,2)$, $(10,4,2)$, $(10,4,2)$, $(11,5,2)$, $(28,7,2)$, $(28,3,2)$, $(36,6,2)$, $(126,6,2)$ or $(176,8,2)$. |
| title | Almost simple groups as flag-transitive automorphism groups of 2-designs with λ = 2 |
| topic | Group Theory Combinatorics 05B05, 05B25, 20B25 |
| url | https://arxiv.org/abs/2307.05195 |