关于由群与幂等元生成半群的若干组合结果

The combinatorial results of semigroups generated by a group and an idempotent

全变换半群是由它自身的对称群和任意一个秩为n-1的幂等元生成的。特别地,在一个有限集合X上,由置换群和秩为n-1的幂等元生成的半群都是正则的。考虑了Hamilton四元数群的所有子群与幂等元生成纯正半群和逆半群的组合结果。同时,也考虑循环群与二面体群的所有子群与幂等元生成纯正半群与逆半群的情形。

It is well know that semigroup of all transformations on a finite set of order n is generated by its group of units,the symmetric group,and any idempotent of rank n- 1. Similarly,the semigroup is regular and is generated by its group of units and idempotent of rank n- 1. In this paper we go a step further to investigate semigroups generated by a group and an idempotent. The first section consists of preliminaries while the second contained some combinatorial results of Hamilton quaternion group,cyclic group and dihedral group.