交错群与旗传递点本原非对称2-(v,k,3)设计  

Alternating groups and flag-transitive point-primitive non-symmetric 2-(v,k,3) designs

作　　者：王贝军 梁洪雪 周胜林[1] Wang Beijun;Liang Hongxue;Zhou Shenglin(School of Mathematics, South China University of Technology, Guang)

机构地区：[1]华南理工大学数学学院,广东广州510640

出　　处：《纯粹数学与应用数学》2016年第6期649-660,共12页Pure and Applied Mathematics

基　　金：国家自然科学基金(11471123)

摘　　要：受旗传递2-(v,k,3)对称设计和非对称2-(v,k,2)设计有关分类结果的启发,本论文继续研究旗传递非对称2-(v,k,3)设计.文章利用置换群的理论和组合设计的数量性质,借助计算机代数软件Gap和Magma,完全分类了自同构群G旗传递点本原,且基柱Soc(G)为交错群An(n≥5)的非对称2-(v,k,3)设计,证明了此类设计只能是唯一的2-(5,3,3)设计,且G=A_5或S_5.Motivated by the classification of flag-transitive 2-(v; k; 3) symmetric designs and non-symmetric2-(v; k; 2) designs, this paper continue to study flag-transitive non-symmetric 2-(v; k; 3) designs. We completelyclassify all flag-transitive point-primitive non-symmetric 2-(v; k; 3) designs with alternating socle An (n  5) byapplying the theory of permutation groups, arithmetic properties of designs and the computer algebraic systemsGAP and Magma, and show that there exists a unique 2-(5; 3; 3) design with G = A5 or S5.

关 键 词：非对称2-设计 自同构群 旗传递 点本原 交错群 

分 类 号：O157.1[理学—数学]