Flag-transitive 4 - (v, k, 4) designs and P5L(2, q) groups
Abstract
Among the properties of homogeneity of incidence structures flag-transitivity obviously is a particularly important and natural one. Originally, F. Buekenhout et al. reached a classification of flag-transitive Steiner 2-designs. Recently, Huber completely classified all flag-transitive 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 λ ≥ 2 has remained of particular interest and has been known as a long-standing and still open problem. This article is a contribution to the study of the automorphism groups of 4 - (v, k,4) designs. Let S = (P, B) be a non-trivial 4 - (q + l,K,4) design. If G acts flag-transitively on S, then G is not two-dimensional projective linear group PSL(2,q). © 2017 Utilitas Mathematica Publishing Inc.. All rights reserved.
