2025/05/08 by Seyed Hassan Alavi, Ashraf Daneshkhah, Alavi, Seyed Hassan +3
Computer Science · Mathematics · #05B05 #05B25 #20B25 #20D08 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2505.04985
openalex publication_date 2025/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this article, we study 2-(v,k,λ) designs D with λ prime admitting flag-transitive and point-primitive almost simple automorphism groups G with socle T a finite exceptional simple group or a sporadic simple groups. If the socle of G is a finite exceptional simple group, then we prove that D is isomorphic to one of two infinite families of 2-designs with point-primitive automorphism groups, one is the Suzuki-Tits ovoid design with parameter set (v,b,r,k,λ)=(q2+1,q2(q2+1)/(q-1),q2,q,q-1) design, where q-1 is a Mersenne prime, and the other is newly constructed in this paper and has parameter set (v,b,r,k,λ)=(q3(q3-1)/2,(q+1)(q6-1),(q+1)(q3+1),q3/2,q+1), where q+1 a Fermat prime. If T is a sporadic simple group, then we show that D is isomorphic to a unique design admitting a point-primitive automorphism group with parameter set (v,b,r,k,λ)=(176,1100,50,2), (12,22,11,6,5) or (22,77,21,6,5).