| 钟祥贵,李世荣.幂零群中非正规循环子群的共轭类数[J].数学研究及应用,2006,26(3):557~561 |
| 幂零群中非正规循环子群的共轭类数 |
| The Number of Conjugacy Classes of Nonnormal Cyclic Subgroups in Nilpotent Groups |
| 投稿时间：2004-06-28 |
| DOI：10.3770/j.issn:1000-341X.2006.03.020 |
| 中文关键词: 幂零群 非正规子群 共轭类数. |
| 英文关键词:nilpotent group nonnormal subgroup number of conjugacy classes |
| 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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| 中文摘要: |
| 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)\ $v^*(G)\geq c(G)-1$; (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$D(2^n), n\geq 3$或$C_2 \times C_2$同构. |
| 英文摘要: |
| 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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