摘要
对X={1,2,3,…,n}上任一有限变换α,首先叙述并证明了α的指数和周期与其分解式中最简变换的指数和周期的关系。然后,证明了α的有向图Γ(α)可能是非连通的,Γ(α)的连通分支Ω是一个等价类,Ω有非空核K(Ω),且K(Ω)是Ω的唯一循环圈的顶点构成的集合。最后,证明了连通分支和最简变换是一一对应的,实现了利用Γ(α)计算α的指数和周期的目标。
For any finite transformation α of X={ 1,2,3,…, n}, we claim and prove the relation between the index and period of a and the indices and periods of its simplist factors at first. Then, we verify that the directed graphs Γ（α） of α may be disconnected, every connected component Ω of Γ（α） is an equivalence class, Ω has non-empty kernel K（Ω）, and K（Ω） is also the set of vertices of the only cycle of Ω. At last, we demonstrate the one-one correspondence between connected components and simplest transformations, and realize the aim to calculate the index and period of α by Γ（α）.
出处
《青岛大学学报（自然科学版）》
CAS
2007年第4期36-40,共5页
Journal of Qingdao University(Natural Science Edition)
关键词
有限变换
指数
周期
有向图
finite transformations index, period
directed graph
