Block transitive automorphism groups of designs
The authors prove the following result: Let G be a block-transitive group of automorphisms of a 2-(v,k,l)design, where k divides v. Then (i) G is transitive on flags and (ii) G/S(G) has a simple socle. (Note: flag is an incident point pair and S(G) denotes the maximal soluble normal subgroup of G.) The proof of (i) is straightforward. Then (i) implies that G is primitive on points. The use of the O'Nan and Scott theorem together with some results of \textit{C. Hering} [Geom. Dedicata 2, 425-460 (1974; Zbl 0292.20045)] then enables (ii) to be proved.
scientific article; zbMATH DE number 3861173