Alternating groups as flag-transitive automorphism groups of 2-designs with block size seven

2023/07/11 by Ashraf Daneshkhah, Daneshkhah, Ashraf
Mathematics · Computer Science · Engineering · #Finite Group Theory Research #Coding theory and cryptography #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2307.05190

Abstract

In this article, we prove that if D is a 2-design with k=7 admitting flag-transitive almost simple automorphism group with socle an alternating group, then D is PG₂(3,2) with parameter set (15,7,3) and G=A₇, or D is the 2-design with parameter set (55, 7, 1680) and G=A₁₁ or S₁₁.

Related

• Block-transitive 3-(v,k,1) designs associated with alternating groups
• Classification of flag-transitive 2-(v, k, λ) designs with alternating group A_n(n ≤ 10) as socle
• Almost simple groups as flag-transitive automorphism groups of 2-designs with λ = 2
• Block designs with gcd(r,λ)=1 admitting flag-transitive automorphism groups
• A classification of flag-transitive block designs