一类传递置换群的极小基  

Minimal Bases of a Class of Transitive Permutation Groups

作　　者：陈媛媛 

机构地区：[1]云南师范大学数学系,云南 昆明

出　　处：《理论数学》2022年第1期103-108,共6页Pure Mathematics

摘　　要：群G作用在有限集合Ω上,Δ⊆Ω,G(Δ)={x∈G|δx=δ,∀δ∈Δ}称为G在Δ上的逐点稳定子。若G(Δ)=1,则称Δ为G群的基。若Σ⊆Ω是使得G(Σ)=1成立的最小集合,则称Σ为群G的极小基。本文计算出对称群Sd与Sr的圈积SdwrSr以及它的子群D2rwrSr,ZrwrSr在某种非本原作用下的极小基。A group G acting on a finite set Ω, Δ⊆Ω, G(Δ)={x∈G|δx=δ,∀δ∈Δ} is called a pointwise stabilizer on G. If G(Δ)=1, Δ is called the basis of group G. If Σ⊆Ω is the smallest set that makes G(Σ)=1 true, then Σ is called the minimal basis of group G. In this paper, the wreath product SdwrSr of symmetric groups Sd and Sr, the minimal basis of its subgroups D2rwrSr and ZrwrSr under some imprimitive action are calculated.

关 键 词：对称群 圈积 非本原作用 极小基 

分 类 号：O153[理学—数学]