On flag-transitive automorphism groups of symmetric designs - Alavi, Seyed Hassan (Ars mathematica contemporanea, 2019)
In this article, we study flag-transitive automorphism groups of non-trivial symmetric ?$(v, k, λ )$? designs, where ?$λ$? divides ?$k$? and ?$k \geqslant λ^2$?. We show that such an automorphism group is either point-primitive of affine or almost simple type, or point-imprimitive with parameters ?$v = λ^2(λ + 2)$? and ?$k = λ(λ + 1)$?, for some positive integer ?$λ$?. We also provide some examples in both possibilities.
Keywords: automorphism group; flag-transitive; grupa avtomorfizmov; point-imprimitive; point-primitive; praporno tranzitiven; simetrični načrt; symmetric design; točkovno neprimitiven; točkovno primitiven