| 有限群的PCSM-子群 |
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| 引用本文： | 李华,钱国华.有限群的PCSM-子群[J].青岛大学学报(自然科学版),2008,21(3):12-14. |
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| 作者姓名： | 李华 钱国华 |
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| 作者单位： | 1. 江苏大学理学院,江苏,镇江,212013;常熟理工学院数学系,江苏,常熟,215500
2. 常熟理工学院数学系,江苏,常熟,215500 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 设G是一个有限群,H为G的子群,如果对于G的任意Sylow子群的极大子群M,至少存在M的一个共轭子群Mx,x∈G,使得HMx=MxH,则称子群H为G的PCSM-子群。考察了某些子群是PCSM-子群时的有限群结构,特别地获得了超可解群的一些充分条件。
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| 关 键 词： | PCSM-子群 极大子群 超可解 |
Pcsm Subgroups of Finite Groups |
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| LI Hua,QIAN Guo-hua.Pcsm Subgroups of Finite Groups[J].Journal of Qingdao University(Natural Science Edition),2008,21(3):12-14. |
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| Authors: | LI Hua QIAN Guo-hua |
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| Institution: | LI Hua , QIAN Guo-hua (1. Faculty of Science. , Jiangsu University, Zhen jiang 212013, China; 2. Department of Mathematu, Changshu Institute of Technology, Changshu 215500, China) |
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| Abstract: | A subgroup H of a group G is called PCSM-subgroup in G if there exists at least one G-conjugate of each maximal subgroup M of any Sylow subgroup of G such that HMx=MxH for some x∈G. The aim of this paper is to investigate the structure of a finite group under the assumption that certain subgroups are PCSM-subgroups. Furthermore some sufficient conditions for supersolvability are obtained. |
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| Keywords: | PCSM-subgroup Maximal subgroup Supersolvable group |
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