2−(v,k,1) designs admitting automorphism groups with socle Sz(q)

摘要

The classification of all block-transitive 2−(v,k,1) designs has been known as a long-standing and still open problem. This work is a contribution to the general program to classify the pairs (D,G) in which D is a 2−(v,k,1) design and G act as a point-primitive block-transitive automorphism group of D with a Suzuki group Sz(q) socle. We determine the point-stabilizer Gα ∩ Sz(q) and the block-stabilizer GB ∩ Sz(q), and the parameter of D is given.