半群SY_(n-1)的秩

On the Rank of the Semigroup SY_(n-1)

设X_(n)=[n]={1,2,…,n},Sing_(n)为[n]上的奇异变换半群,Y_(n-1)为n元置换群的某个二阶子群。令SY_(n-1)=Sing_(n)∪Y_(n-1),则SY_(n-1)为[n]上的一个变换半群,是T_(n)的子半群。通过对半群SY_(n-1)中的元素分析,证明了当n≥5时,变换半群SY_(n-1)的秩为C_(n-1)^(2)+[n-1]/2/2+n/2+2。

Let X_(n) be[n]={1,2,…,n},Sing_(n) is the singular transformation semigroup on[n],and Y_(n-1)is the subgroup of order 2.SY_(n-1)=Sing_(n)∪Y_(n-1),then SY_(n-1)is a transformation semigroup on[n],and is a subsemigroup of T_(n).By analyzing the elements of the semigroup SY_(n-1),it is shown that for n≥5,the rank of the transformation semigroup SY_(n-1)is equal to C_(n-1)^(2)+[n-1]/2/2+n/2+2.