摘要
设Xn=[n]={1,2,…,n},Singn为Xn上的奇异变换半群,H(n,k)为带k的局部循环群.令HS_((n,k))=Singn∪H(n,k),则HS_((n,k))对变换的合成构成Xn上的一个半群,并称之为带k的局部循环变换半群.通过对半群HS_((n,k))中的元素进行分析,证明了当k≥2,n-k≥3时,变换半群HS_((n,k))的秩为(n-k)(n-k-1)2+n-k+2+k2.
Let Xn=[n]={1,2,…,n},Singn is the singular transformation semigroup on Xn,and H(n,k)is the local cyclic group with k.HS_((n,k))=Singn∪H(n,k),then HS_((n,k))forms a semigroup of composition of transformation on Xn,which is called the local cyclic transformation semigroup with k.By analyzing the elements of the semigroup HS_((n,k)),it is shown that for k≥2,n-k≥3,the rank of the transformation semigroup HS_((n,k))is equal to(n-k)(n-k-1)2+n-k+2+k2.
作者
黄朝霞
高荣海
罗永贵
HUANG Zhao-xia;GAO Rong-hai;LUO Yong-gui(School of Mathematics and Sciences, Guizhou Normal University, Guiyang 550025, China)
出处
《西南师范大学学报(自然科学版)》
CAS
2021年第4期4-8,共5页
Journal of Southwest China Normal University(Natural Science Edition)
基金
贵州师范大学博士科研项目(GZNUD[2019]23).
关键词
奇异变换半群
带k的局部循环群
秩
singular transformation semigroup
local cyclic group with k
rank