| ■-可补子群对有限群结构的影响 |
| |
| 引用本文： | 唐娜,黎先华. ■-可补子群对有限群结构的影响[J]. 吉林大学学报(理学版), 2014, 52(2): 266-268 |
| |
| 作者姓名： | 唐娜 黎先华 |
| |
| 作者单位： | 1. 淮阴师范学院 数学科学学院, 江苏 淮安 223300； 2. 苏州大学 数学科学学院, 江苏 苏州 215006 |
| |
| 基金项目： | 国家自然科学基金(批准号:11171243);国家自然科学基金天元基金(批准号:11226285) |
| |
| 摘 要： | 利用■-可补子群研究p-超可解群,得到了两个主要结果:1)令G是p-可解的且p G,则G是p-超可解的当且仅当Fp(G)中包含Op′(G)的所有极大子群在G中■-可补,这里■是所有p-超可解群组成的群类;2)令G是p-可解的且p G,则G是p-超可解的当且仅当Fp(G)的非循环Sylowp-子群的极大子群在G中■-可补,这里■是包含所有p-超可解群组成的群类.
|
| 关 键 词： | F-可补子群 p-超可解群 饱和群系 Fitting子群 |
| 收稿时间： | 2013-04-07 |
Influence of F Supplemented Subgroups onthe Structure of Finite Group |
| |
| TANG Na,LI Xian hua. Influence of F Supplemented Subgroups onthe Structure of Finite Group[J]. Journal of Jilin University: Sci Ed, 2014, 52(2): 266-268 |
| |
| Authors: | TANG Na LI Xian hua |
| |
| Affiliation: | 1. School of Mathematics Science, Huaiyin Normal University, Huai’an 223300, Jiangsu Province, China;2. School of Mathematics Science, Soochow
University, Suzhou 215006, Jiangsu Province, China |
| |
| Abstract: | We took the advantage of F supplemented subgroups to study the structure of p-supersolvable groups and obtained two main results. 1) Let G be p-solvable and p||G|, then G is p-supersolvable if and only if every maximal subgroup of Fp(G) containing Op′(G) is F supplemented in G, where F is the class of all p-supersolvable groups. 2) Let G be p-solvable and p||G|, then G is p-supersolvable if and only if every maximal subgroup of non cyclic Sylow p-subgroups of Fp(G) isF supplemented in G, where F is the class of all p-supersolvable groups. |
| |
| Keywords: | supplemented subgroup p-supersolvable group saturated formation Fitting subgroup |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《吉林大学学报(理学版)》浏览原始摘要信息 |
|
点击此处可从《吉林大学学报(理学版)》下载全文 |
|
