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
Let D be a nontrivial symmetric（v, k, λ） design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G acts flag-transitively, pointprimitively on D and Soc（G） = PSL（2, q）, t...Let D be a nontrivial symmetric（v, k, λ） design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G acts flag-transitively, pointprimitively on D and Soc（G） = PSL（2, q）, then D has parameters（7, 3, 1）,（7, 4, 2）,（11, 5, 2）,（11, 6, 3） or（15, 8, 4）.展开更多
Let D be a nontrivial symmetric（v, k, 4） design, and G ≤ Aut（D） be flag-transitive and point-primitive with PSL_n（q） as socle. Then D is a 2-（15, 8, 4） symmetric design and Soc（G） = PSL_2（9）.
In recent years several authors have determined some 2-designs with flag-transitive point-primitive automorphism group G of almost simple type with sporadic socle. Here we obtain the complete classification of flag-tr...In recent years several authors have determined some 2-designs with flag-transitive point-primitive automorphism group G of almost simple type with sporadic socle. Here we obtain the complete classification of flag-transitive point-primitive non-trivial 2-designs with socle M11,and find that there are precisely 14 such nonisomorphic 2-designs.展开更多
The automorphism group of a flag-transitive 6–(v, k, 2) design is a 3-homogeneous permutation group. Therefore, using the classification theorem of 3–homogeneous permutation groups, the classification of flag-transi...The automorphism group of a flag-transitive 6–(v, k, 2) design is a 3-homogeneous permutation group. Therefore, using the classification theorem of 3–homogeneous permutation groups, the classification of flag-transitive 6-(v, k,2) designs can be discussed. In this paper, by analyzing the combination quantity relation of 6–(v, k, 2) design and the characteristics of 3-homogeneous permutation groups, it is proved that: there are no 6–(v, k, 2) designs D admitting a flag transitive group G ≤ Aut (D) of automorphisms.展开更多
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 triplane, i.e., a 2-(ν, k, 3) symmetric design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G is flag-transitive point-primitive, then the socle of G cannot be a...Let D be a triplane, i.e., a 2-(ν, k, 3) symmetric design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G is flag-transitive point-primitive, then the socle of G cannot be a sporadic simple group.展开更多
Let D be a nontrivial 2-(v, k, 3) symmetric design (triplane) and let G≤Aut(D) be flag-transitive and point-primitive. In this paper, we prove that if G is an affine group, then G≤AΓL1(q), where q is some power of ...Let D be a nontrivial 2-(v, k, 3) symmetric design (triplane) and let G≤Aut(D) be flag-transitive and point-primitive. In this paper, we prove that if G is an affine group, then G≤AΓL1(q), where q is some power of a prime p and p≥5.展开更多
In this paper we present two new families of 2-(v,k,λ)designs with a flag-transitive and point-primitive automorphism group of product action type.More sur-prisingly,one of them is still a family of 2-(v,k,λ)designs...In this paper we present two new families of 2-(v,k,λ)designs with a flag-transitive and point-primitive automorphism group of product action type.More sur-prisingly,one of them is still a family of 2-(v,k,λ)designs with a fag-transitive and point-imprimitive automorphism group.展开更多
This article is a contribution to the study of the automorphism groups of 3-(v,k,3)designs.Let S=(P,B)be a non-trivial 3-(q+1,k,3)design.If a two-dimensional projective linear group PSL(2,q)acts flag-transitively on S...This article is a contribution to the study of the automorphism groups of 3-(v,k,3)designs.Let S=(P,B)be a non-trivial 3-(q+1,k,3)design.If a two-dimensional projective linear group PSL(2,q)acts flag-transitively on S,then S is a 3-(q+1,4,3)or 3-(q+1,5,3)design.展开更多
We state that the flag-transitive automorphism group of a 2-(v,5,λ)design D is primitive of affine type or almost simple type.W e also find that there are up to isomorphism 202-(v,5,λ)designs admitting flag-transiti...We state that the flag-transitive automorphism group of a 2-(v,5,λ)design D is primitive of affine type or almost simple type.W e also find that there are up to isomorphism 202-(v,5,λ)designs admitting flag-transitive automorphism groups with socle of a sporadic simple group.展开更多
This paper is devoted to the study of a translation plane π(C) associated with a t-spread set C and its transposed t-spread set C t. In this paper, an explicit matrix form of the inverse of an isomorphism from a tran...This paper is devoted to the study of a translation plane π(C) associated with a t-spread set C and its transposed t-spread set C t. In this paper, an explicit matrix form of the inverse of an isomorphism from a translation plane into another translation plane associated with t-spread sets is derived and proved that two translation planes associated with t-spread sets are isomorphic if and only if their corresponding transposed translation planes are isomorphic. Further, it is shown that the transpose of a flag-transitive plane is flag-transitive and derived a necessary and sufficient condition for a translation plane π(C) to be isomorphic to its transposed translation plane.展开更多
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
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Supported by the National Natural Science Foundation of China(Grant Nos.1147112311426066)the Natural Science Foundation of Guangdong Province(Grant No.S2013010011928)
文摘Let D be a nontrivial symmetric（v, k, λ） design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G acts flag-transitively, pointprimitively on D and Soc（G） = PSL（2, q）, then D has parameters（7, 3, 1）,（7, 4, 2）,（11, 5, 2）,（11, 6, 3） or（15, 8, 4）.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1147112311626206)the Scientific Research Foundation for Excellent Talents of Xuzhou Medical University(Grant No.D2016002)
文摘Let D be a nontrivial symmetric（v, k, 4） design, and G ≤ Aut（D） be flag-transitive and point-primitive with PSL_n（q） as socle. Then D is a 2-（15, 8, 4） symmetric design and Soc（G） = PSL_2（9）.
基金Supported by the National Natural Science Foundation of China(Grant No.11801092)the Characteristic Innovation Project(Natural Science)of Guangdong Province(Grant No.2018KTSCX160)the Fund of Guangzhou Science and Technology(Grant No.201804010088)。
文摘In recent years several authors have determined some 2-designs with flag-transitive point-primitive automorphism group G of almost simple type with sporadic socle. Here we obtain the complete classification of flag-transitive point-primitive non-trivial 2-designs with socle M11,and find that there are precisely 14 such nonisomorphic 2-designs.
文摘The automorphism group of a flag-transitive 6–(v, k, 2) design is a 3-homogeneous permutation group. Therefore, using the classification theorem of 3–homogeneous permutation groups, the classification of flag-transitive 6-(v, k,2) designs can be discussed. In this paper, by analyzing the combination quantity relation of 6–(v, k, 2) design and the characteristics of 3-homogeneous permutation groups, it is proved that: there are no 6–(v, k, 2) designs D admitting a flag transitive group G ≤ Aut (D) of automorphisms.
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 Scientific Research Foundation for the Returned Overseas Scholars, Ministry of Education of China
文摘Let D be a triplane, i.e., a 2-(ν, k, 3) symmetric design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G is flag-transitive point-primitive, then the socle of G cannot be a sporadic simple group.
基金supported by National Natural Science Foundation of China (Grant No. 11071081)
文摘Let D be a nontrivial 2-(v, k, 3) symmetric design (triplane) and let G≤Aut(D) be flag-transitive and point-primitive. In this paper, we prove that if G is an affine group, then G≤AΓL1(q), where q is some power of a prime p and p≥5.
基金Zhilin Zhang was supported by the National Natural Science Foundation of China(12001204)Shenglin Zhou was supported by the National Natural Science Foundation of China(12271173).
文摘In this paper we present two new families of 2-(v,k,λ)designs with a flag-transitive and point-primitive automorphism group of product action type.More sur-prisingly,one of them is still a family of 2-(v,k,λ)designs with a fag-transitive and point-imprimitive automorphism group.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11301377,11701046,11671402)the Natural Science Foundation of Jiangsu Province(BK20170433)the Universities Natural Science Foundation of Jiangsu Province(16KJB110001).
文摘This article is a contribution to the study of the automorphism groups of 3-(v,k,3)designs.Let S=(P,B)be a non-trivial 3-(q+1,k,3)design.If a two-dimensional projective linear group PSL(2,q)acts flag-transitively on S,then S is a 3-(q+1,4,3)or 3-(q+1,5,3)design.
基金supported by the National Natural Science Foundation of China(Grant No.11871224).
文摘We state that the flag-transitive automorphism group of a 2-(v,5,λ)design D is primitive of affine type or almost simple type.W e also find that there are up to isomorphism 202-(v,5,λ)designs admitting flag-transitive automorphism groups with socle of a sporadic simple group.
文摘This paper is devoted to the study of a translation plane π(C) associated with a t-spread set C and its transposed t-spread set C t. In this paper, an explicit matrix form of the inverse of an isomorphism from a translation plane into another translation plane associated with t-spread sets is derived and proved that two translation planes associated with t-spread sets are isomorphic if and only if their corresponding transposed translation planes are isomorphic. Further, it is shown that the transpose of a flag-transitive plane is flag-transitive and derived a necessary and sufficient condition for a translation plane π(C) to be isomorphic to its transposed translation plane.
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.
