Geodesic
Almost simple groups of Lie type and symmetric designs with \(\lambda\) prime
Seyed Hassan Alavi1 ; Mohsen Bayat1 ; Ashraf Daneshkhah1
1Bu-Ali Sina University
The electronic journal of combinatorics, Tome 28 (2021) no. 2
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In this article, we investigate symmetric $(v,k,\lambda)$ designs $\mathcal{D}$ with $\lambda$ prime admitting flag-transitive and point-primitive automorphism groups $G$. We prove that if $G$ is an almost simple group with socle a finite simple group of Lie type, then $\mathcal{D}$ is either the point-hyperplane design of a projective space $\mathrm{PG}_{n-1}(q)$, or it is of parameters $(7,4,2)$, $(11,5,2)$, $(11,6,3)$ or $(45,12,3)$.
DOI : 10.37236/9366
Classification : 05B05, 05B25, 20B25, 05E14
Mots-clés : \((v,k,\lambda)\)-designs, flag-transitive groups, point-primitive automorphism groups

Seyed Hassan Alavi  1   ; Mohsen Bayat  1   ; Ashraf Daneshkhah  1

1 Bu-Ali Sina University 
@article{10_37236_9366,
     author = {Seyed Hassan Alavi and Mohsen Bayat and Ashraf Daneshkhah},
     title = {Almost simple groups of {Lie} type and symmetric designs with \(\lambda\) prime},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {2},
     doi = {10.37236/9366},
     zbl = {1464.05020},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9366/}
}
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Seyed Hassan Alavi; Mohsen Bayat; Ashraf Daneshkhah. Almost simple groups of Lie type and symmetric designs with \(\lambda\) prime. The electronic journal of combinatorics, Tome 28 (2021) no. 2. doi: 10.37236/9366

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