区传递的2-(v，k，1)设计与李型单群E_8(q)

Block transitive 2-(v,k,1) design and the groups E_8(q)

分类自同构群的基柱为李型单群E_8(q)的区传递2-(v,k,1)设计,得到如下定理:设D为一个2-(v,k,1)设计,G≤Aut(D)是区传递、点本原但非旗传递的.若q>((k_rk-k_r+1)f)^(1/24)(这里k_r=(k,v-1),q=p^f,p是素数,f是正整数),则Soc(G)■ E_8(q).

A 2-（v, k, 1） design admitting a block transitive automorphism group whose socle is the simple groups Es（q） of Lie type is classified and the following theorem is proved. Let D be a 2-（v, k, 1） design admitting a block-transitive, point-primitive but not flag-transitive automorphism group G. Let kr = （k,v - 1）, q = p^f for prime p and positive integer number f. If q 〉 24√（krk-kr＋1）f, then Soc（G）≌/ E8（q）.