半群HS_((n,k))的秩

On Rank of Semigroup HS_((n,k))

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.