This article is a contribution to the study of the automorphism groups of designs. Let be a non-trivial design where for some positive integer , and is block-transitive. If the socle of G is iso...This article is a contribution to the study of the automorphism groups of designs. Let be a non-trivial design where for some positive integer , and is block-transitive. If the socle of G is isomorphic to the simple groups of lie type, then G is not flag-transitive.展开更多
A t-(v,k,λ)design is said to be G-point-primitive or G-block-transitive,if its automorphism group G acts primitively on the point set or transitively on the block set,respectively.In this paper we begin by extending ...A t-(v,k,λ)design is said to be G-point-primitive or G-block-transitive,if its automorphism group G acts primitively on the point set or transitively on the block set,respectively.In this paper we begin by extending some results on block-transitive Steiner 2-designs to block-transitive 3-designs,and then based on these results,investigate the G-point-primitive block-transitive 3-(v,k,λ)designs for alternating or symmetric groups G.We prove that when n≥min{λ^(2),30}the point stabilizer in G must be of intransitive type,and specifically,when n≥30 there exists no nontrivial G-point-primitive block-transitive 3-(v,k,2)design.展开更多
This article is a contribution to the study of block-transitive automorphism groups of 2-(v,k,1)block designs.Let D be a 2-(v,k,1)design admitting a block-transitive,pointprimitive but not flag-transitive automorphism...This article is a contribution to the study of block-transitive automorphism groups of 2-(v,k,1)block designs.Let D be a 2-(v,k,1)design admitting a block-transitive,pointprimitive but not flag-transitive automorphism group G.Let kr=(k,v-1)and q=pf for prime p.In this paper we prove that if G and D are as above and q(3(krk-kr+1)f)1/3,then G does not admit a simple group E6(q)as its socle.展开更多
In recent years, there has been a great deal of research concerning the flag- transitive t-designs, however, few about the block-transitive t-designs with t large （t 〉 4）. In 1993, Cameron and Praeger conjectured t...In recent years, there has been a great deal of research concerning the flag- transitive t-designs, however, few about the block-transitive t-designs with t large （t 〉 4）. In 1993, Cameron and Praeger conjectured that there are no non-trivial block-transitive 6-designs. In this paper, we prove that the conjecture is true when k ≤ 10000 and G ≤ Aut（D） is almost simple.展开更多
This paper is a contribution to the study of the automorphism groups of 2 - （v, k, 1） designs. Let D be a 2 - （v, 23, 1） design and G a block-transitive and point-primitive group of automorphism of D. Then the soc...This paper is a contribution to the study of the automorphism groups of 2 - （v, k, 1） designs. Let D be a 2 - （v, 23, 1） design and G a block-transitive and point-primitive group of automorphism of D. Then the socle of G is not Sz（q） and 2G2（q）.展开更多
文摘This article is a contribution to the study of the automorphism groups of designs. Let be a non-trivial design where for some positive integer , and is block-transitive. If the socle of G is isomorphic to the simple groups of lie type, then G is not flag-transitive.
基金supported by the National Natural Science Foundation of China(No.12471022)。
文摘A t-(v,k,λ)design is said to be G-point-primitive or G-block-transitive,if its automorphism group G acts primitively on the point set or transitively on the block set,respectively.In this paper we begin by extending some results on block-transitive Steiner 2-designs to block-transitive 3-designs,and then based on these results,investigate the G-point-primitive block-transitive 3-(v,k,λ)designs for alternating or symmetric groups G.We prove that when n≥min{λ^(2),30}the point stabilizer in G must be of intransitive type,and specifically,when n≥30 there exists no nontrivial G-point-primitive block-transitive 3-(v,k,2)design.
基金Supported by the National Natural Science Foundation of China(Grant No.10871205)China Postdoctoral Science Foundation Funded Project(Grant No.20080441323)Scientific Research Fund of Zhejiang Education Department(Grant No.Y200804780)
文摘This article is a contribution to the study of block-transitive automorphism groups of 2-(v,k,1)block designs.Let D be a 2-(v,k,1)design admitting a block-transitive,pointprimitive but not flag-transitive automorphism group G.Let kr=(k,v-1)and q=pf for prime p.In this paper we prove that if G and D are as above and q(3(krk-kr+1)f)1/3,then G does not admit a simple group E6(q)as its socle.
基金Supported by the National Natural Science Foundation of China （Grant No. 10871205, 11271208） and Hunan Provincial Science and Technology Department （2011FJ6092）.
文摘In recent years, there has been a great deal of research concerning the flag- transitive t-designs, however, few about the block-transitive t-designs with t large （t 〉 4）. In 1993, Cameron and Praeger conjectured that there are no non-trivial block-transitive 6-designs. In this paper, we prove that the conjecture is true when k ≤ 10000 and G ≤ Aut（D） is almost simple.
基金Supported by the National Natural Science Foundation of China(11271208,11471054)Supported by the Graduate Students’Scientific Research Innovation Project of Jiangsu Province Ordinary University(KYLX1213)
文摘This paper is a contribution to the study of the automorphism groups of 2 - （v, k, 1） designs. Let D be a 2 - （v, 23, 1） design and G a block-transitive and point-primitive group of automorphism of D. Then the socle of G is not Sz（q） and 2G2（q）.
