| 非正规子群的正规闭包较大或较小的有限$p$群 |
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| 引用本文： | 赵立博,龚律.非正规子群的正规闭包较大或较小的有限$p$群[J].数学研究及应用,2017,37(2):209-213. |
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| 作者姓名： | 赵立博 龚律 |
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| 作者单位： | 广东第二师范学院数学系, 广东 广州 510310,南通大学理学院, 江苏 南通 226007 |
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| 基金项目： | 国家自然科学基金项目(Grant Nos.11526114; 11601245), 广东省自然科学基金项目(Grant No.2015A030313791), 广东省创新强校项目(Grant No.2014KTSCX196), 广东省青年创新人才项目 (Grant No.2015KQNCX107),广东第二师范学院教授博士科研专项经费资助项目(Grant No.2013ARF07). |
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| 摘 要： | A p-group G is called a JC-group if the normal closure H~G of every cyclic subgroup H satisfies |G:H~G| ≤ p or |H~G:H| ≤ p. In this paper, we classify the non-Dedekindian JC-groups for p2.
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| 关 键 词： | $JC$-群 非Dedekind $p$ 群 正则 $p$ 群 |
Finite $p$-Groups with Large or Small Normal Closures of Non-Normal Cyclic Subgroups |
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| Libo ZHAO and Lv GONG.Finite $p$-Groups with Large or Small Normal Closures of Non-Normal Cyclic Subgroups[J].Journal of Mathematical Research with Applications,2017,37(2):209-213. |
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| Authors: | Libo ZHAO and Lv GONG |
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| Institution: | Department of Mathematics, Guangdong University of Education, Guangdong 510310, P. R. China and School of Sciences, Nantong University, Jiangsu 226007, P. R. China |
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| Abstract: | A $p$-group $G$ is called a $JC$-group if the normal closure $H^G$ of every cyclic subgroup $H$ satisfies $|G:H^G|\leq p$ or $|H^G:H|\leq p$. In this paper, we classify the non-Dedekindian $JC$-groups for $p>2$. |
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| Keywords: | $JC$-group non-Dedekindian $p$-group regular $p$-group |
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