Alternating Groups and Flag-Transitive 2-(v, k, 4) Symmetric Designs

作者：Dong Huili; Zhou Shenglin^*

来源：Journal of Combinatorial Designs, 2011, 19(6): 475-483.

DOI：10.1002/jcd.20294

• symmetric design
• flag-transitive
• point-primitive
• alternating group

In this article, we study the classification of flag-transitive, point-primitive 2-(v, k, 4) symmetric designs. We prove that if the socle of the automorphism group G of a flag-transitive, point-primitive nontrivial 2-(v, k, 4) symmetric design D is an alternating group An for n >= 5, then (v, k)=(15,8) and D is one of the following: (i) The points of D are those of the projective space PG(3,2) and the blocks are the complements of the planes of PG(3,2), G= A(7) or A(8), and the stabilizer G(x) of a point x of D is L(3)(2) or AGL(3)(2), respectively. (ii) The points of D are the edges of the complete graph K(6) and the blocks are the complete bipartite subgraphs K(2,4) of K(6), G= A(6) or S(6), and G(x) = S(4) or S(4) x Z(2), respectively.

• 出版日期2011-11
• 单位华南理工大学