A triplane is a ( v, k, 3)-symmetric design. Let G be a subgroup of the full automorphism group of a triplane D. In this paper we prove that if G is flag-transitive and point-primitive, then the socle of G cannot be a...A triplane is a ( v, k, 3)-symmetric design. Let G be a subgroup of the full automorphism group of a triplane D. In this paper we prove that if G is flag-transitive and point-primitive, then the socle of G cannot be a simple exceptional group of Lie type.展开更多
Let D be a 2-（v, k, 4） symmetric design and G be a flag-transitive point-primitive automorphism group of D with X ≥G ≤Aut（X） where X ≌ PSL2（q）.Then D is a 2-（15,8,4） symmetric design with X = PSL2（9） and ...Let D be a 2-（v, k, 4） symmetric design and G be a flag-transitive point-primitive automorphism group of D with X ≥G ≤Aut（X） where X ≌ PSL2（q）.Then D is a 2-（15,8,4） symmetric design with X = PSL2（9） and Xx = PGL2（3） where x is a point of D.展开更多
Consider the flag-transitive 2-（v, k, λ） symmetric designs with （k, λ）= 1. We prove that if （） is a nontrivial 2-（v, k, λ）symmetric design with （k,λ） = 1 and G ≤ Aut（） is flag-transitive with Sot（G）...Consider the flag-transitive 2-（v, k, λ） symmetric designs with （k, λ）= 1. We prove that if （） is a nontrivial 2-（v, k, λ）symmetric design with （k,λ） = 1 and G ≤ Aut（） is flag-transitive with Sot（G） = An for n ≥5, then is the projective space PG2（3, 2） and G = A7.展开更多
文摘A triplane is a ( v, k, 3)-symmetric design. Let G be a subgroup of the full automorphism group of a triplane D. In this paper we prove that if G is flag-transitive and point-primitive, then the socle of G cannot be a simple exceptional group of Lie type.
基金Supported by the National Natural Science Foundation of China(11071081)
文摘Let D be a 2-（v, k, 4） symmetric design and G be a flag-transitive point-primitive automorphism group of D with X ≥G ≤Aut（X） where X ≌ PSL2（q）.Then D is a 2-（15,8,4） symmetric design with X = PSL2（9） and Xx = PGL2（3） where x is a point of D.
基金Acknowledgements The authors would like to thank the anonymous referees for their valuable suggestions and comments which helped to improve this paper. This work was supported by the National Natural Science Foundation of China （Grant No. 11471123） and the Natural Science Foundation of Guangdong Province （Grant No. $2013010011928）.
文摘Consider the flag-transitive 2-（v, k, λ） symmetric designs with （k, λ）= 1. We prove that if （） is a nontrivial 2-（v, k, λ）symmetric design with （k,λ） = 1 and G ≤ Aut（） is flag-transitive with Sot（G） = An for n ≥5, then is the projective space PG2（3, 2） and G = A7.
