| c-截断和有限群的可解性 |
| |
| 引用本文： | 李士恒,刘冬华,王战伟.c-截断和有限群的可解性[J].河南科学,2012,30(11):1568-1570. |
| |
| 作者姓名： | 李士恒 刘冬华 王战伟 |
| |
| 作者单位： | 1. 郑州航空工业管理学院数理系,郑州,450015
2. 郑州铁路职业技术学院公共教学部,郑州,450052 |
| |
| 基金项目： | 国家自然科学基金项目（11171364）;郑州航空工业管理学院青年基金（2012113002） |
| |
| 摘 要： | 设M是群G的一个极大子群,K/L是G的一个使L≤M但K埭M的主因子.我们把(M∩K)/L叫做M的c-截断.通过特殊极大子群的c-截断的一些性质来刻画有限群的可解性,如:群G可解当且仅当G有一个可解的极大子群M使│G∶M│为素数幂且Sec(M)幂零.
|
| 关 键 词： | 有限群 c-截断 极大子群 c-正规 可解 |
c-Section and the Solvability of Finite Groups |
| |
| Li Shiheng
,
Liu Donghua
,
Wang Zhanwai.c-Section and the Solvability of Finite Groups[J].Henan Science,2012,30(11):1568-1570. |
| |
| Authors: | Li Shiheng Liu Donghua Wang Zhanwai |
| |
| Institution: | Li Shiheng, Liu Donghua, Wang Zhanwai(1. Department of Mathmatics and Physics, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou 450015, China： 2. School of Foundational Education, Zhengzhou Railway Vocational ＆ Technical College, Zhengzhou 450052, China) |
| |
| Abstract: | Let G be a finite group and M be a maximal subgroup of G. If K/L is a chief factor of G such that L ≤M and KM then （M∩M）/L is called a c-section of M. In this paper, we characterize the solubility of finite groups with c-sections of some special maximal subgroups. For example, finite group G is soluble if and only if there is a soluble maximal subgroup M of G such that ｜ G ：M ｜ is a power of some prime and Sec （.M） is nilpotent. |
| |
| Keywords: | finite group c-section maximal subgroups c-normal soluble |
| 本文献已被 维普 万方数据 等数据库收录！ |
|
