Flag-transitive point-primitive quasi-symmetric 2-designs and exceptional groups of Lie type

2025/06/12 by Jianbing Lu, Lu, Jianbing
Computer Science · Materials Science · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2506.10266

openalex publication_date 2025/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let D be a non-trivial quasi-symmetric 2-design with two block intersection numbers x=0 and 2≤ y≤10, and suppose that G is an automorphism group of D. If G is flag-transitive and point-primitive, then it is known that G is either of affine type or almost simple type. In this paper, we show that the socle of G cannot be a finite simple exceptional group of Lie type.

Citations

• Flag-transitive point-primitive quasi-symmetric 2-designs with block intersection numbers 0 and y≤10
• A Classification of the flag-transitive 2-(v,k,2) designs
• On the Maximal Subgroups of E₇(q) and Related Almost Simple Groups
• On flag-transitive 2-(v,k,2) designs
• Flag-transitive block designs and finite exceptional simple groups of Lie type
• Flag-transitive point-primitive non-symmetric 2-(v,k,2) designs with alternating socle
• Large subgroups of simple groups
• Linear spaces with flag-transitive automophism groups

Related

• Flag-transitive point-primitive quasi-symmetric 2-designs with block intersection numbers 0 and y≤10
• Flag-transitive non-symmetric 2-designs with (r,λ)=1 and exceptional groups of Lie type
• Flag-transitive block designs and finite exceptional simple groups of Lie type
• Finite exceptional groups of Lie type and symmetric designs
• Almost simple groups as flag-transitive automorphism groups of 2-designs with λ = 2