有限对称逆半群的极大半个传递子半群

The Maximal Half-transitive Subsemigroups of the Finite Symmetric Inverse Semigroups

设In是有限集X_n={1,2,…,n}上的对称逆半群.文章给出I_n的所有极大半个传递子半群的构造,进而得到I_n的所有极大半个传递子半群的个数,最后得到每个极大半个传递子半群的基数.

Let In be the symmetric inverse semigroup on Xn={1,2,…,n}.The maximal half-transitive subsemigroups of In are described in this paper.Further,the number of maximal half-transitive subsemigroups of In is counted.Finally,the cardinality of every maximal half-transitive subsemigroup is also obtained.