| Norm商群的Sylow子群皆循环的有限群 |
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| 引用本文： | 陈松良,樊恽.Norm商群的Sylow子群皆循环的有限群[J].数学研究及应用,2022,42(2):153-161. |
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| 作者姓名： | 陈松良 樊恽 |
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| 作者单位： | 贵州师范学院数学与大数据学院, 贵州 贵阳 550018;华中师范大学数学与统计学学院, 湖北 武汉 430079 |
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| 基金项目： | 国家自然科学基金(Grant No.11661023), 贵州省服务业发展引导资金投资计划项目(Grant No.黔发改服务[2018]1181号). |
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| 摘 要： | 设$G$是有限群, $N(G)$为$G$的norm, 则$N(G)$是$G$的正规化G的每个子群的特征子群. 我们在下列条件之一下,研究了$G$的结构：1) Norm商群$G/N(G)$是循环群；2) Norm商群$G/N(G)$的所有Sylow子群都是循环群,特别地当$G/N(G)$的阶是无平方因子数时.
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| 关 键 词： | norm(范) 戴德金群 哈密顿群 $\phi$-群 有限群的构造 西洛子群 |
| 收稿时间： | 2021/2/5 0:00:00 |
| 修稿时间： | 2021/10/16 0:00:00 |
Finite Groups Whose Norm Quotient Groups Have Cyclic Sylow Subgroups |
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| Songliang CHEN,Yun FAN.Finite Groups Whose Norm Quotient Groups Have Cyclic Sylow Subgroups[J].Journal of Mathematical Research with Applications,2022,42(2):153-161. |
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| Authors: | Songliang CHEN Yun FAN |
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| Institution: | School of Mathematics and Big Data, Guizhou Education University, Guizhou 550018, P. R. China; School of Mathematics and Statistics, Central China Normal University, Hubei 430079, P. R. China |
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| Abstract: | Let $G$ be a finite group and $N(G)$ be its norm. Then $N(G)$ is a characteristic subgroup of $G$ which normalizes every subgroup of $G$. In this paper, we will study the structure of $G$ under one of the following conditions: 1) norm quotient group $G/N(G)$ is cyclic; 2) all Sylow subgroups of $G/N(G)$ are cyclic and in particular if the order of $G/N(G)$ is a square-free number. |
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| Keywords: | norm Dedekind group Hamiltonian group $\pi$-group structure of finite group Sylow subgroup |
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