区传递的2-(v,9,1)设计的分类

Classification of block transitive 2-(υ,9,1)designs

讨论区传递的2-v,k,1)设计的分类问题.特别地,讨论自同构群的基柱为典型单群的区传递,点本原但非旗传递的2-(v,9,1)设计.设D为一个2-(v,9,1)设计,若G≤Aut(D)是区传递,点本原但非旗传递的,则G的基柱Soc(G)不是有限域GF(q)上的典型单群.结合Camina,Praeger,刘伟俊,李慧陵等人的结果,可以得到2-(v,9,1)设计的完全分类.

This article is a contribution to the study of the automorphism groups of 2-（v,k,1） designs.Let D be a 2-（v,9,1） design,G≤Aut（D） be block transitive,point primitive but not flag transitive,then Soc（G）,the socle of G,is not classical simple group over finite field GF（q）. Together with the results of Camina,Praeger et al,the classification of block transitive 2-（v,9,1） designs is completed.