一类2-(v,k,1)设计的可解区传递自同构群

Soluble block-transitive automorphism groups of a class 2-(v,k,1) designs

设G是一个2-(v,k,1)设计的可解区传递自同构群,且k≥3.若v>〔k(k-1)/2-1〕2,则v=pn,其中p为素数.进一步,当n为两个不同奇素数幂的乘积时,G是旗传递的或者G≤AΓL(1,pn).

Let G be a soluble block-transitive automorphism group of a 2-（v,k, 1） design and k≥3.If v〉（k（k-1）/2-1）^2 , where p is a prime number and n is a positive integer. Furthermore, if n=q＇r＇ , where q and r are two different odd primes and s and t are two positive integers, G is flag-transitive or G≤AГL（1,p^n）.