| 关于有限群的$CAP$-嵌入子群 |
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| 引用本文： | 郭鹏飞,郭秀云.关于有限群的$CAP$-嵌入子群[J].数学研究与评论,2009,29(6):992-998. |
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| 作者姓名： | 郭鹏飞 郭秀云 |
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| 作者单位： | 海大学数学系, 上海 200444;连云港师范高等专科学校数学系, 江苏 连云港 222006 |
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| 基金项目： | 国家自然科学基金(No.10771132);2006年度江苏省高校``青蓝工程'优秀青年骨干教师项目. |
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| 摘 要： | A subgroup H of a finite group G is said to be CAP-embedded subgroup of G if, for each prime p dividing the order of H, there exists a CAP-subgroup K of G such that a Sylow p-subgroup of H is also a Sylow p-subgroup of K. In this paper some new results are obtained based on the assumption that some subgroups of prime power order have the CAP-embedded property in the group.
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| 关 键 词： | 嵌入式 有限群 子群 Sylow 黄金分割 |
| 收稿时间： | 2007/9/20 0:00:00 |
| 修稿时间： | 1/4/2008 12:00:00 AM |
On $CAP$-Embedded Subgroups in Finite Groups |
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| GUO Peng Fei and GUO Xiu Yun.On $CAP$-Embedded Subgroups in Finite Groups[J].Journal of Mathematical Research and Exposition,2009,29(6):992-998. |
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| Authors: | GUO Peng Fei and GUO Xiu Yun |
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| Institution: | Department of Mathematics, Shanghai University, Shanghai 200444, China; Department of Mathematics, Lianyungang Teachers College, Jiangsu 222006, China;Department of Mathematics, Shanghai University, Shanghai 200444, China |
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| Abstract: | A subgroup $H$ of a finite group $G$ is said to be $CAP$-embedded subgroup of $G$ if, for each prime $p$ dividing the order of $H$, there exists a $CAP$-subgroup $K$ of $G$ such that a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of $K$. In this paper some new results are obtained based on the assumption that some subgroups of prime power order have the $CAP$-embedded property in the group. |
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| Keywords: | $CAP$-embedded subgroups maximal subgroups $p$-nilpotent groups supersolvable groups |
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