| Sylow p-子群的非平凡子群与有限群的p-超可解性 |
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| 引用本文： | 韦华全,李娜,周宇珍.Sylow p-子群的非平凡子群与有限群的p-超可解性[J].广西师范学院学报(自然科学版),2011,28(2):1-3. |
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| 作者姓名： | 韦华全 李娜 周宇珍 |
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| 作者单位： | 1. 广西师范学院数学科学学院
2. 继续教育学院,广西南宁,530001 |
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| 基金项目： | 国家自然科学基金项目，广西自然科学基金项目，广西教育厅科研项目 |
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| 摘 要： | 设E是有限群G的正规子群使得G/E为p-超可解群,P是E的正规的Sylowp-子群,其中p为一奇素数,如果P存在一个子群D满足以下性质：1〈︱D︱〈︱P︱,对于任意的H≤P,︱H︱=︱D︱,H在G中正规,则G为p-超可解群.
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| 关 键 词： | 正规子群 弱c^＊-正规子群 Sylow子群 p-超可解群 |
Non-trivial Subgroups of Sylow p-subgroups and the p-supersolvability of Finite Groups |
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| WEI Hua-quana,LI Naa,ZHOU Yu-zhen.Non-trivial Subgroups of Sylow p-subgroups and the p-supersolvability of Finite Groups[J].Journal of Guangxi Teachers Education University:Natural Science Edition,2011,28(2):1-3. |
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| Authors: | WEI Hua-quana LI Naa ZHOU Yu-zhen |
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| Institution: | b(a.School of Mathematical Sciences,b.School of Continuing Education,Guangxi Teachers Education University,Nanning 530001,P.R.China) |
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| Abstract: | Let E be a normal subgroup of a finite group G such that G/E is p-supersolvability,P a normal Sylow p-subgroup of E,where p is an odd prime.If there exists a subgroup D of P such that 1︱D︱︱P︱ and every subgroup H of P with order ︱D︱ is normal in G,then G is p-supersolvable. |
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| Keywords: | normal weakly c^＊-normal Sylow subgroup p-supersolvable |
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