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| 恰有4个非循环子群共轭类的有限幂零群 | |
| 引用本文： | 孟伟,卢家宽,李世荣.恰有4个非循环子群共轭类的有限幂零群[J].广西大学学报(自然科学版),2009,34(6). |
| 作者姓名： | 孟伟 卢家宽 李世荣 |
| 作者单位： | 1. 云南民族大学,数学与计算机科学院,云南,昆明,650031 2. 上海大学理学院数学系,上海,200444 3. 广西大学数学与信息科学学院,广西,南宁,530004 |
| 基金项目： | 国家自然科学基金资助项目，上海大学研究生创新基金 |
| 摘 要： | 设G是有限群,用δ(G)表示G的非循环子群共轭类的个数.δ(G)对G的结构有比较强的影响.例如,δ(G)=0当且仅当G循环.δ(G)=1当且仅当G非循环而G的所有真子群循环,即G内循环群.2007年,李世荣,赵旭波给出了有限δ-群(即每个可解子群日满足δ(H)≤2的有限群)的完全分类.作为以上问题的继续,使用群论的初等方法,给出δ(G)=4的幂零群的完全分类. |
| 关 键 词： | 幂零群 极大子群 p-群 |
Finite nilpotent groups with four non-cyclic subgroups |
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| MENG Wei,LU Jia-kuan,LI Shi-rong.Finite nilpotent groups with four non-cyclic subgroups[J].Journal of Guangxi University(Natural Science Edition),2009,34(6). | |
| Authors: | MENG Wei LU Jia-kuan LI Shi-rong |
| Abstract: | Let G be a finite group, the number of conjugate classes of the non-cyclic subgroups of G is denoted by δ(G). It is quite clear that δ(G) give a lot of information about the structure of G. For instance, δ(G) =0 if and only of G is cyclic. Δ(G) = 1 if and only if G is non-cyclic but every proper subgroup of G is cyclic. In 2007, LI and ZHAO investigated the finitegroups (I. E. A finite group in which every soluble subgroup H satisfies δ(H) ≤ 2). In this paper, the finite nilpotent groups with δ(G) =4 are classifed. |
| Keywords: | nilpotent groups maximal subgroups p-groups |
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