~2F_4(q^2)群与2-(v,k,5)对称设计

Simple Group ~2F_4(q^2) and 2-(v,k,5) Symmetric Designs

如果一个非凡的t-设计是一个对称设计,则t=2.设2-(v,k,λ)是一个非平凡的对称设计,G是它的一个旗传递自同构群.在过去正对λ≤4情形研究的基础上,本文讨论λ=5的情况.证明了如果G是2-(v,k,5)对称设计的一个旗传递点本原自同构群,并且G是几乎单群,则G的基柱不能为2F4(q2)群.证明中需使用2F4(q2)群的极大子群的分类,同时也需要考虑2F4(q2)群的置换表示.

If a non-trivial t--design is a symmetric design, t = 2. 2-（v, k, k） will be a non-trivial symmetric design, and G will be a flag-transitive automorphism group. Cases λ≤ has been discussed by some scholars, and this paper attempts to discuss A = 5. In this paper, it is to be proved that if G is point-primitive automorphism group acting 2 2 fiag-transitive on a 2-（v, k, 5） symmetric design, then scole of G is not F, （q）. In proof, the classification of max- imum subgroups should be used and permutation representation of 2F4 （q2） should also be taken into account.