1.School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410075， China; 2.School of Mathematics and Computing, Hunan University of Science and Engineering， Yongzhou, Hunan 425100， China)
Abstract：If a non-trivial t-design admitting a flag-transitive automorphism group, then t≤6 and its automorphism group is ［(t+1)／2］ homogeneous. Therefore, the automorphism group of a flagtransitive 5-(v,k,2) design is a 3-homogeneous permutation group. Using the classification theorem of 3-homogeneous permutation groups, the classification of flagtransitive 5-(v,k,2) designs is discussed. By analyzing the combination quantity relation of 5-(v,k,2) design and the characteristics of 3-homogeneous permutation groups, it is proved that if group G is a flagtransitive automorphism group of a nontrivial 5-(v,k,2)design, then Soc(G)=PSL(2,q), and q=2e or 3e.
2010, Vol. 31 
