| 不存在恰有15个Sylow 7-子群的有限群 |
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| 引用本文： | 钟凌锋,周伟. 不存在恰有15个Sylow 7-子群的有限群[J]. 西南师范大学学报(自然科学版), 2020, 45(4): 9-12 |
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| 作者姓名： | 钟凌锋 周伟 |
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| 作者单位： | 西南大学数学与统计学院, 重庆 400715 |
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| 基金项目： | 国家自然科学基金项目（11671324）. |
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| 摘 要： | 运用极小反例来确定群的阶和它的Sylow 7-子群的阶,利用初等方法证明了不存在恰有15个Sylow 7-子群的有限群.
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| 关 键 词： | Sylow p-子群 Sylow定理 共轭 |
| 收稿时间： | 2019-10-09 |
There Exists No Finite Group with Exactly 15 Sylow 7-Subgroups |
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| ZHONG Ling-feng,ZHOU Wei. There Exists No Finite Group with Exactly 15 Sylow 7-Subgroups[J]. Journal of southwest china normal university(natural science edition), 2020, 45(4): 9-12 |
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| Authors: | ZHONG Ling-feng ZHOU Wei |
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| Affiliation: | School of Mathematics and Statistics, Southwest University, Chongqing 400715, China |
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| Abstract: | In this paper, we use minimal counterexamples to determine the order of the group and its Sylow 7-subgroups, by elementary methods, prove that there exists no finite group with exactly 15 Sylow 7-subgroups. |
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| Keywords: | Sylow p-subgroup Sylow theorem conjugate |
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