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| 关于由群与幂等元生成半群的若干组合结果 | |
| 引用本文： | 李旺威,徐波. 关于由群与幂等元生成半群的若干组合结果[J]. 贵州师范大学学报(自然科学版), 2014, 32(6): 60-62 |
| 作者姓名： | 李旺威 徐波 |
| 作者单位： | 贵州师范大学数学与计算机科学学院,贵州贵阳,550001 |
| 摘 要： | 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。 |
| 关 键 词： | 群 半群 幂等元 |
The combinatorial results of semigroups generated by a group and an idempotent |
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| LI Wangwei,XU Bo. The combinatorial results of semigroups generated by a group and an idempotent[J]. Journal of Guizhou Normal University(Natural Sciences), 2014, 32(6): 60-62 | |
| Authors: | LI Wangwei XU Bo |
| Affiliation: | LI Wangwei;XU Bo;School of Mathematics and Computer Science,Guizhou Normal University; |
| Abstract: | 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. |
| Keywords: | group idempotent semigroup |
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