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Flag-transitive 2-(v,5,λ)designs with sporadic socle

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Frontiers of Mathematics in China 2020年第6期15卷 1201-1210页

作者： Jiaxin SHEN shenglin zhou School of Mathematics South China University of TechnologyGuangzhou 510640China

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... 详细信息

关键词： 2-design primitivity flag-transitivity sporadic simple group

Flag-transitive 2-（v, k, λ） symmetric designs with （k, λ） =1 and alternating socle

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Frontiers of Mathematics in China 2015年第6期10卷 1483-1496页

作者： Yan ZHU Haiyan GUAN shenglin zhou School of Mathematics South China University of Technology Guangzhou 510640 China Department of Mathematics China Three Gorges University Yichang 443002 China

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）... 详细信息

关键词： Symmetric design automorphism group alternating group flagtransitive

Line-transitive point-imprimitive linear spaces with Fang-Li parameter gcd（k, r） at most ten

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Frontiers of Mathematics in China 2012年第6期7卷 1095-1112页

作者： Haiyan GUAN Delu TIAN shenglin zhou Department of Mathematics South China University of Technology Guangzhou 510640China

This paper is a further contribution to the classification of line- transitive finite linear spaces. We prove that if y is a non-trivial finite linear space such that the Fang-Li parameter gcd（k, r） is 9 or 10, and the group G ≤ Aut（Y） is line-transitive and point-imprimitive, then y is the Desarguesian projective plane PG（2, 9）.

关键词： Linear space line-transitive point-imprimitive

Sporadic groups and flag-transitive triplanes

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Science China Mathematics 2009年第2期52卷 394-400页

作者： zhou shenglin DONG HuiLi Department of Mathematics South China University of TechnologyGuangzhou 510640China Department of Mathematics Shantou UniversityShantou 515063China

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... 详细信息

关键词： triplane symmetric design flag-transitive point-primitive sporadic simple group 05B05 05B25 20B25

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Exceptional groups of Lie type and flag-transitive triplanes

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Science China Mathematics 2010年第10期53卷 447-456页

作者： zhou shenglin & DONG HuiLi Department of Mathematics, South China University of Technology, Guangzhou 510640, China Department of Mathematics South China University of Technology Guangzhou China

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... 详细信息

关键词： symmetric design triplane flag-transitive point-primitive exceptional groups of Lie type

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Flag-Transitive Point-Primitive（v, k, 4）-Symmetric Designs with PSL_n（q） as Socle

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Journal of Mathematical Research with Applications 2018年第1期38卷 34-42页

作者： Yan ZHU shenglin zhou School of Basic Education Sciences Xuzhou Medical University School of Mathematics South China University of Technology

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） = PSL2（9）.

关键词： symmetric design flag-transitive point-primitive classical group

Classification of Flag-Transitive Primitive Symmetric(v, k, λ) Designs with PSL(2, q) as Socle

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Journal of Mathematical Research with Applications 2016年第2期36卷 127-139页

作者： Delu TIAN shenglin zhou Department of Mathematics Guangdong University of Education School of Mathematics South China University of Technology

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 ... 详细信息

关键词： symmetric design flag-transitive primitive group

On Vasantha Kandasamy's Problem

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Journal of Mathematical Research with Applications 2014年第2期34卷 249-252页

作者： Hanbin ZHANG shenglin zhou Department of Mathematics South China University of Technology

In this paper, we solve the problem proposed by Vasantha Kandasamy about the torsion-free non-abelian groups.

关键词： essential group torsion-free non-abelian group.

Finite Line-transitive Linear Spaces:Theory and Search Strategies

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Acta Mathematica Sinica,English Series 2009年第9期25卷 1399-1436页

作者： Anton BETTEN Anne DELANDTSHEER Maska LAW Alice C. NIEMEYER Cheryl E. PRAEGER shenglin zhou Colorado State University Department of Mathematics Fort Collins CO 80523 U.S.A. Universite Libre de Bruxelles Facultd des Sciences appliquges CP165J11 av. F.D. Roosevelt 50 B 1050 Brussels Belgium The University of Western Australia School of Mathematics and Statistics 35 Stirling Highway Crawley 6009 Australia Department of Mathematics South China University of Technology Guangzhou 510641 China

The paper summarises existing theory and classifications for finite line-transitive linear spaces, develops the theory further, and organises it in a way that enables its effective application. The starting point is a theorem of Camina and the fifth author that identifies three kinds of line-transitive automorphism groups of linear spaces. In two of these cases the group may be imprimitive on points, that is, the group leaves invariant a nontrivial partition of the point set. In the first of these cases the group is almost simple with point-transitive simple socle, and may or may not be point-primitive, while in the second case the group has a non-trivial point-intransitive normal subgroup and hence is definitely point-imprimitive. The theory presented here focuses on point-imprimitive groups. As a non-trivial application a classification is given of the point-imprimitive, line-transitive groups, and the corresponding linear spaces, for which the greatest common divisor gcd（k, v - 1） ≤ 8, where v is the number of points, and k is the line size. Motivation for this classification comes from a result of Weidong Fang and Huffing Li in 1993, that there are only finitely many non-trivial point-imprimitive, linetransitive linear spaces for a given value of gcd（k, v - 1）. The classification strengthens the classification by Camina and Mischke under the much stronger restriction k ≤ 8： no additional examples arise. The paper provides the backbone for future computer-based classifications of point-imprimitive, line- transitive linear spaces with small parameters. Several suggestions for further investigations are made.

关键词： linear space line-transitive automorphism group combinatorial design combinatorial search algorithm

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