Flag-transitive 4-(v, k, 3) designs and PSL(2, q) groups

摘要

Among the properties of homogeneity of incidence structures, flag-transitivity obviously is a particularly important and natural one. Originally, Buekenhout et al. reached a classification of flag-transitive Steiner 2-designs. Recently, Huber completely classified all flagtransitive Steiner t-designs with t 6 using the classification of the finite 2-transitive permutation groups. Hence the determination of all flag-transitive t-designs with lambda 2 has remained of particular interest and has been known as a long-standing and still open problem.