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Flag-transitive point-primitive 2-(v,k,4) symmetric designs and two dimensional classical groups 被引量:5
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作者 ZHOU Sheng-lin TIAN De-lu 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第3期334-341,共8页
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
关键词 Symmetric design flag-transitive point-primitive two dimensional classical group.
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Flag-Transitive 6-(v, k, 2) Designs
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作者 Xiaolian Liao Shangzhao Li Guohua Chen 《Advances in Pure Mathematics》 2014年第5期203-208,共6页
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
关键词 flag-transitive Combinatorial Design PERMUTATION GROUP AFFINE GROUP 3-Homogeneous PERMUTATION Groups
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On 2-(v,k,λ)Designs with Flag-Transitive Automorphism Groups of Product Action Type
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作者 Zhilin Zhang Shenglin Zhou 《Algebra Colloquium》 SCIE CSCD 2023年第2期351-360,共10页
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
关键词 flag-transitive 2-(v k λ) design O'Nan-Scott theorem product action type
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Exceptional groups of Lie type and flag-transitive triplanes 被引量:7
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作者 ZHOU ShengLin & DONG HuiLi Department of Mathematics, South China University of Technology, Guangzhou 510640, China 《Science China Mathematics》 SCIE 2010年第2期447-456,共10页
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
关键词 SYMMETRIC design triplane flag-transitive point-primitive exceptional GROUPS of LIE type
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Sporadic groups and flag-transitive triplanes 被引量:7
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作者 ZHOU ShengLin DONG HuiLi 《Science China Mathematics》 SCIE 2009年第2期394-400,共7页
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
关键词 triplane symmetric design flag-transitive point-primitive sporadic simple group 05B05 05B25 20B25
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Affine groups and flag-transitive triplanes 被引量:2
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作者 DONG HuiLi ZHOU ShengLi 《Science China Mathematics》 SCIE 2012年第12期2557-2578,共22页
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
关键词 symmetric design triplane flag-transitive point-primitive affine group
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Flag-Transitive 3-(v,k,3)Designs and PSL(2,q)Groups
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作者 Shaojun Dai Shangzhao Li 《Algebra Colloquium》 SCIE CSCD 2021年第1期33-38,共6页
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
关键词 flag-transitive 3-designs PSL(2 q)groups
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Flag-transitive 2-(v,5,λ)designs with sporadic socle
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作者 Jiaxin SHEN Shenglin ZHOU 《Frontiers of Mathematics in China》 SCIE CSCD 2020年第6期1201-1210,共10页
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
关键词 2-design PRIMITIVITY flag-transitivity sporadic simple group
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On Transposed Translation Planes
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作者 K. Satyanarayana K. V. V. N. S. Sundari Kameswari 《Open Journal of Discrete Mathematics》 2012年第1期35-43,共9页
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
关键词 t-Spread Sets TRANSLATION PLANES Transposed TRANSLATION PLANES flag-transitive TRANSLATION PLANES COLLINEATIONS TRANSLATION COMPLEMENT
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Block-Transitive 4-(v,k,4) Designs and Ree Groups
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作者 Shaojun Dai Ruihai Zhang 《Advances in Pure Mathematics》 2016年第5期317-320,共4页
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
关键词 flag-transitive BLOCK-TRANSITIVE T-DESIGN Ree Group
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