Mathieu群与旗传递2-(v,k,λ)设计
Mathieu Groups and Flag-Transitive 2-(v,k,λ) Designs
DOI: 10.12677/PM.2018.81008, PDF,    科研立项经费支持
作者: 陈佳楠*, 周胜林：华南理工大学数学学院，广东 广州
关键词: 2-设计；旗传递；基柱；Mathieu群；2-Design； Flag-Transitive； Socle； Mathieu Group
摘要: 旗传递性是群作用在2-(v,k,λ) 设计上的重要性质之一。对满足一定条件的旗传递2-设计进行分类是一个比较有意思的问题。Dembowski已经证明了满足条件(v-1,k-1)≤2 的旗传递2-(v,k,λ) 设计的自同构群G是本原群。据此，本文在条件(v-1,k-1)≤2 下，研究自同构群旗传递且其基柱Soc(G)是五个Mathieu 群之一时的2-(v,k,λ) 设计的分类问题，得到了在同构意义下存在62个这样的设计。
Abstract: Flag-transitivity is one of the important conditions that can be imposed on the automorphism group of a 2-(v,k,λ) design. The classification of flag-transitive 2-designs is an important problem in the algebraic combinatorial theory. Dembowski has proved that if G≤Aut(D) is flag-transitive and (v-1,k-1)≤2, then G is also point-primitive. According to this result, in this paper we completed the classification of this type of designs, with Soc(G) was one of five Mathieu groups Mi, where i=11, 12, 22, 23 or 24. We prove that there exists 62 2-designs satisfying the assumption.
文章引用：陈佳楠, 周胜林. Mathieu群与旗传递2-(v,k,λ)设计[J]. 理论数学, 2018, 8(1): 47-54. https://doi.org/10.12677/PM.2018.81008

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