基柱为A6的旗传递2-设计
Flag-Transitive 2-Designs with Socle A6
DOI: 10.12677/pm.2024.1412423, PDF,    国家科技经费支持
作者: 申佳昕, 夏雨晴*：五邑大学数学与计算科学学院，广东 江门
关键词: 旗传递；2-设计；交错群；自同构群；Flag-Transitive； 2-Design； Alternating Group； Automorphism Group
摘要: 2-设计是一个点–区关联结构，使得每个区组与相同个数的点关联，而且任意两个点都与相同个数的区组关联。如果2-设计的自同构群在旗集合上传递，则称该自同构群是旗传递的。本文分类了基柱为交错群 A 6 的旗传递2-设计，得到18个两两不同构的2-设计，并决定了其对应的旗传递自同构群。
Abstract: A 2-design is point-block incidence structure, such that any block is incident with a constant number of points, and any two points are incident with a constant number of blocks. An automorphism group of a 2-design is said to be flag-transitive, if it acts transitively on the flag set of this design. In this paper, we classify the flag-transitive 2-designs with socle A 6 . We obtain 18 pairwise non-isomorphic designs, and determine the corresponding automorphism groups.
文章引用：申佳昕, 夏雨晴. 基柱为A6的旗传递2-设计[J]. 理论数学, 2024, 14(12): 220-226. https://doi.org/10.12677/pm.2024.1412423

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