Flag-transitive, point-imprimitive symmetric 2-(v,k,λ) designs with k>λ(λ-3 )/2

2022/03/17 by Montinaro, Alessandro
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.09261

Abstract

Let D=(P,B ) be a symmetric 2-(v,k,λ) design admitting a flag-transitive, point-imprimitive automorphism group G that leaves invariant a non-trivial partition Σ of P. Praeger and Zhou \citePZ have shown that, there is a constant k₀ such that, for each B ∈ B and Δ∈ Σ, the size of \vert B ∩ Δ \vert is either 0 or k₀. In the present paper we show that, if k>λ(λ-3 )/2 and k₀ ≥ 3, D is isomorphic to one of the known flag-transitive, point-imprimitive symmetric 2-designs with parameters (45,12,3) or (96,20,4).

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