一类传递置换群的极小基

Minimal Bases of a Class of Transitive Permutation Groups

摘要: 群G作用在有限集合Ω上，Δ⊆Ω，G_(Δ)={x∈G|δ^x=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S_d与S_r的圈积S_dwrS_r以及它的子群D_2rwrS_r，Z_rwrS_r在某种非本原作用下的极小基。

Abstract: A group G acting on a finite set Ω, Δ⊆Ω, G_(Δ)={x∈G|δ^x=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 S_dwrS_r of symmetric groups S_d and S_r, the minimal basis of its subgroups D_2rwrS_r and Z_rwrS_r under some imprimitive action are calculated.