# 仿射型群与旗传递6-(v, k, 3)设计Affine Type Groups and Flag-Transitive 6-(v, k, 3) Designs

Abstract: The classification of flag-transitive designs is an important subject on algebraic combinatorics. And the automorphism groups of a flag-transitive 6-(v, k, 3) design are 3-homogeneous. Therefore, using the classification theorem of 3-homogeneous permutation groups, the classification of flag-transitive 6-(v, k, 3) designs can be discussed, and we prove that the automorphism groups of a flag-transitive 6-(v, k, 3) design are not isomorphic to affine type groups.

[1] Biggs, N.L. and Whit, E.A.T. (1979) Permutation Groups and Combinatorial Structures. Peking University Press, Beijing, 2-32.
https://doi.org/10.1017/cbo9780511600739

[2] Cameron, P.J. and Praeger, C.E. (1992) Block-Transitive t-Designs. Finite Geometry and Combinatorics, 191, 103-119.

[3] Beth, T., Jungnickel, D. and Lenz, H. (1999) Design Theory. Cambridge University Press, Cambridge, 3-28.

[4] Huber, M. (2007) A Sensus of Highly Symmetric Combinatorial Designs. Journal of Algebraic Combinatorics, 26, 453-476.
https://doi.org/10.1007/s10801-007-0065-4

[5] 徐向红, 章静. 3-齐次群与旗传递 5-(v,k,3)设计[J]. 数学理论与应用, 2009, 32(04): 5-11.

Top