| 幂零群中非正规循环子群的共轭类数 |
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| 引用本文： | 钟祥贵,李世荣.幂零群中非正规循环子群的共轭类数[J].数学研究与评论,2006,26(3):557-561. |
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| 作者姓名： | 钟祥贵 李世荣 |
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| 作者单位： | 1. 广西师范大学数学与计算机科学学院,广西,桂林,541004
2. 广西大学数学与信息科学学院,广西,南宁,530004 |
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| 基金项目： | 国家自然科学基金(10161001)，广西科学基金(桂科基0575050) |
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| 摘 要： | 设G是有限幂零群,v~*(G)是其非正规循环子群的共轭类数,则下列结论之一成立：(1) v~*(G)≥c(G)-1；(2)G是Hamilton群；(3)G中存在正规子群K使K/Z(K)有一个同态像与二面体群D(2~n),n≥3或C_2×C_2同构．
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| 关 键 词： | 幂零群 非正规子群 共轭类数 |
| 文章编号： | 1000-341X(2006)03-0557-05 |
| 收稿时间： | 06 28 2004 12:00AM |
| 修稿时间： | 05 11 2005 12:00AM |
The Number of Conjugacy Classes of Nonnormal Cyclic Subgroups in Nilpotent Groups |
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| ZHONG Xiang-gui and LI Shi-rong.The Number of Conjugacy Classes of Nonnormal Cyclic Subgroups in Nilpotent Groups[J].Journal of Mathematical Research and Exposition,2006,26(3):557-561. |
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| Authors: | ZHONG Xiang-gui and LI Shi-rong |
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| Institution: | School of Math. \& Comput. Sci., Guangxi Normal University, Guilin 541004, China;School of Math. \& Info. Sci., Guangxi University, Nanning 530004, China |
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| Abstract: | This paper proves that for a nilpotent group $G$ of nilpotency class $c=c(G),$ the number $v^*(G)$ of conjugacy classes of nonnormal cyclic subgroups satisfies the inequality $v^*(G)\geq c(G)-1,$ or $G$ is a Hamiltonian group, or there is a normal subgroup $K$ of $G$ such that $K/Z(K)$ has a homomorphic image isomorphic to the dihedral group $D(2^n)$ with $n\geq 3$ or $C_2\times C_2.$ |
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| Keywords: | nilpotent group nonnormal subgroup number of conjugacy classes |
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