| 李世荣,农国平,周龙桥,何俊.有限群的p-幂零性和极小子群[J].数学年刊A辑,2009,30(5):623~630 |
| 有限群的p-幂零性和极小子群 |
| On p-Nilpotence and Minimal Subgroups of Finite Groups |
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| DOI： |
| 中文关键词: 有限群 极小子群 p-幂零 P-可分解剩余 |
| 英文关键词:Finite groups, Minimal subgroups , p-Nilpotence, p-Decomposable
residual |
| 基金项目:国家自然科学基金项目，广西自然科学基金(No.0249001)资助的项目 |
| Author Name | Affiliation | E-mail | | LI Shirong | School of Mathematics and Information Sciences, Guangxi University, Nan-
ning 530004, China. | shirong@gxu.edu.cn | | NONG Guoping | School of Mathematics and Information Sciences, Guangxi University, Nan-
ning 530004, China. | nongguoping@tom.com | | ZHOU Longqiao | School of Mathematics and Information Sciences, Guangxi University, Nan-
ning 530004, China. | longqiao886@163.com | | HE Jun | School of Mathematics and Information Sciences, Guangxi University, Nan-
ning 530004, China. | hejun5170789@yahoo.com.cn |
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| 中文摘要: |
| 从有限群构造的角度来看,p-幂零群和p-可分解群很相似,前者是p-群和p'-群的半直积,后者是p-群和P'-群的直积.有限群G的p-可分解剩余是P(G)=∩{H|H(⊿) G,而且G/H是p-可分解}.通过观察p-可分解剩余和极小子群的性质得到了几个关于p-幂零的充要条件. |
| 英文摘要: |
| There are many similar structures between $p$-nilpotent groups and $p$-decomposable groups. The former is a semidirect product
of a $p$-group and a $p'$-group, and the latter is a direct product of a $p$-group and a $p'$-group. The $p$-decomposable
residual of $G$ is $P(G) = \cap\{H \mid H \unlhd G$ and $G/H$ is $p$-decomposable\}. In this paper, the authors
obtain some necessary and sufficient conditions for $p$-nilpotence by investigating characterizations of
$p$-decomposable residual and minimal subgroups. |
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