Geodesic
Flag-transitive automorphism groups of 2-designs with λ ≥ (r, λ)^2 and an application to symmetric designs
Ars Mathematica Contemporanea, Tome 14 (2018) no. 1, pp. 187-195.

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Let D be a 2-(v, k, λ) design with λ ≥ (r, λ)2. If G ≤ Aut(D) is flag-transitive, then G cannot be of simple diagonal or twisted wreath product type, and if G is product type then the socle of G has exactly two components and G has rank 3. Furthermore, we prove that if D is symmetric, then G must be an affine or almost simple group.
DOI : 10.26493/1855-3974.1165.105
Keywords: 2-design, automorphism group, primitivity, flag-transitivity. 
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Shenglin Zhou; Xiaoqin Zhan. Flag-transitive automorphism groups of 2-designs with λ ≥ (r, λ)^2 and an application to symmetric designs. Ars Mathematica Contemporanea, Tome 14 (2018) no. 1, pp. 187-195. doi : 10.26493/1855-3974.1165.105. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1165.105/

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