Suzuki群与旗传递点本原2-(ν,Κ,λ)设计

Suzuki Group and Flag-Transitive Point-Primitive 2-(ν,Κ,λ)Designs

群论与组合设计有着紧密的内在关系,主要通过设计的自同构群的旗传递性、点本原性等性质来体现。本文研究D是一个非平凡的2-(ν,Κ,λ)设计,其中λ≤10。若G≤Aut(D)是旗传递、点本原的群,且G=Sz(q),则D是一个2-(65, 8, 7)设计,且G=Sz(8)。

There are important internal connections between groups and combinatorial designs,which re-flected by the flag-transitivity,point-primitivity or other properties of the automorphism groups.Let D be non-trivial 2-designs with λ≤10.Assume that G=Sz(q)is a flag-transitive point-primitive automorphism group of D.Then D is a 2-(65,8,7)design and G=Sz(8).