Almost simple groups as flag-transitive automorphism groups of 2-designs with λ = 2

2023/07/11 by Alavi, Seyed Hassan
#05B05 #05B25 #20B25 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2307.05195

Abstract

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 ((3ⁿ-1)/2,3,2) and X=PSL_n(3) for some n≥ 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).

Related

• Flag-transitive 2-(v,k,λ) designs with λ≥ (r,λ)²
• Flag-transitive block designs and finite exceptional simple groups of Lie type
• On flag-transitive automorphism groups of 2-designs with λ prime
• Classification of the non-trivial 2-(k²,k,λ) designs, with λ| k, admitting a flag-transitive almost simple automorphism group
• Analysing 2-(v,k,2) designs admitting a flag-transitive almost simple automorphism group with socle PSL(2,q) by means of conics and hyperovals of PG(2,q)