| 引用本文： |
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汤恒琦,易忠,邓培民.连通不可约变换半群的自同构群结构[J].广西科学,2008,15(4):338-340. [点击复制]
- TANG Heng-qi,YI Zhong,DENG Pei-min.Structure about Connected or Irreducible Automor-phism Group of Transformation Semigroup[J].Guangxi Sciences,2008,15(4):338-340. [点击复制]
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| 摘要: |
| 给出连通变换半群导出的变换群保持连通性的充分必要条件,证明不可约变换半群导出的变换群不可约,不可约变换半群的自同构群是本原置换群,连通变换半群的自同构群是正则置换群,连通且不可约的变换半群的自同构群是一个素数阶的循环群. |
| 关键词: 变换半群 变换群 自同构群 不可约 连通 置换群 |
| DOI： |
| 投稿时间：2008-06-12修订日期：2008-07-31 |
| 基金项目:国家自然科学基金项目(60473005);广西自然科学基金项目(0640061,0832103)资助 |
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| Structure about Connected or Irreducible Automor-phism Group of Transformation Semigroup |
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TANG Heng-qi1,2, YI Zhong2, DENG Pei-min2
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| (1.Mathematics Research Group, Jinhua No.1 High School, Jinhua, Zhejiang, 321015, China;2.College of Mathematics Science, Guangxi Normal University, Guilin, Guangxi, 541004, China) |
| Abstract: |
| The sufficient and neccessory condition of the transformation group induced by a transformation semigroup maintaining connectivity is discussed. It is proved that the transformation group induced by an irreducible transformation semigroup is irreducible, that the automorphism group of an irreducible transformation semigroup is a primitive permutation group, that the automorphism group of a connected transformation semigroup is a regular permutation group, and that the automorphism group of a connected and irreducible transformation semigroup is a cyclic group with prime order. |
| Key words: transformation semigroup transformation group automorphism group irreducible connected permutation group |
