Block designs with gcd(r,λ)=1 admitting flag-transitive automorphism groups

2022/04/05 by Alavi, Seyed Hassan, Bayat, Mohsen, Biliotti, Mauro +12
#05B05 #05B25 #20B25 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2204.02439

Abstract

In this paper, we present a classification of 2-designs with gcd(r,λ)=1 admitting flag-transitive automorphism groups. If G is a flag-transitive automorphism group of a non-trivial 2-design D with gcd(r,λ)=1, then either (D,G) is one of the known examples described in this paper, or D has q = p^d points with p prime and G is a subgroup of AΓL₁(q).

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