马休群与斯坦诺4-设计

Mathieu Groups and Steiner 4-Designs

讨论了马休群旗传递作用于斯坦诺4-设计上情况,得到了如下结论:设D=(X,B,I)是非平凡的斯坦诺4-设计,D的自同构群G旗传递地作用在D上。若G是几乎单群,则i)Soc(G)不同构于单群:N=Mv,v=12,22,24和N=M11,v=12;ii)若N=M11,v=11,则D是一个斯坦诺4-(11,5,1)设计,且GM11;iii)若N=M23,v=23,则D是一个斯坦诺4-(23,7,1)设计,且GM23。

Mathieu groups acting flag - transitivly on the Steiner 4 - Designs was discussed, and the following result was obtained：Let D = （X, B, I） be a non - trivial Steiner 4 - design,and G be a flag- transitive automorphism group of D,if G is almost simple type, then i） Sot（G） is not isomorphic to N= Mv,v= 12,22,24 and N= M11,v= 12; ii） If N = M11, v = 11, then D is Steiner 4 - （ 11,5,1 ） design, and G △ M11; iii）If N= M23 ,v = 23,then D is a Steiner 4- （23,7,1） design, and G △M23.