几类传递置换群的秩和次级数
The Rank and Subdegree of Several Transitive Permutation Groups
DOI: 10.12677/PM.2020.1012145, PDF,   
作者: 汪 畅, 肖仁兵：云南师范大学数学学院，云南 昆明
关键词: 置换群；传递作用；秩；次轨道；Permutation Group； Transitive Action； Rank； Suborbit
摘要: 设群G是作用在有限集合Ω上的传递置换群。G在Ω上的次轨道定义为点稳定子群Gα作用在集合Ω上的轨道，这里α∈Ω。次轨道的个数称为群G作用在Ω上的秩，次轨道的长度称为群G作用在Ω上的次级数。在本文中我们通过利用圈积的乘积作用和某种非本原作用构造了几类传递置换群，并确定了它们的秩和次级数。
Abstract: Let G be a transitive permutation group acting on a finite set Ω. The suborbits of G on Ω are defined as the orbits of a point stabilizer on Ω. The number of suborbits is called the rank of G and the length of suborbits is called the subdegree of G. In this paper, we construct several kinds of transi-tive permutation groups by using the product action and some imprimitive action of the wreath product, and determine their rank and subdegree.
文章引用：汪畅, 肖仁兵. 几类传递置换群的秩和次级数[J]. 理论数学, 2020, 10(12): 1220-1228. https://doi.org/10.12677/PM.2020.1012145

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