中文摘要：

设S（Xn,A）是具有稳定子集A的有限奇异变换半群.借助已有的研究方法,首先考虑了半群S（Xn,A）中E（Jn＊-1）的图论性质,得到了与E（J＊n-1）相关联的有向图是极大强完备的.其次,确定了Jn＊-1中所有由幂等元生成的元素以及由E（Jn＊-1）的两个子集I1、I2生成的半群结构.这些结果对进一步研究该类半群的结构奠定了基础.

英文摘要：

Let S（Xn,A） be finite singular transformation with a stable subset A.By using methods used by others,some digraph properties associated with E（Jn＊-1） in S（Xn,A） are considered.It is proved that the directed digraph associated with E（Jn＊-1） is maximal strongly complete.Moreover the elements generated by idempotents in Jn＊-1 are characterized,and the structure of the subsemigroup generalted by the subsets I1,I2 of E（Jn＊-1） is also given.The present results are useful to further study the properties of the semigroups.