| 引用本文： |
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李世荣,何宣丽,史江涛.有限群的极小子群与超可解性[J].广西科学,2006,13(2):81-84. [点击复制]
- LI Shi-rong,HE Xuan-li,SHI Jiang-tao.Minimal Subgroups and Supersolvability of Finite Groups[J].Guangxi Sciences,2006,13(2):81-84. [点击复制]
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| 摘要: |
| 利用群G的Fitting子群、广义Fitting子群的极小子群F-s-补条件刻划群G的结构,得到新的结果,即:设F是含U的饱和群系,G是一有限群,则G∈F的充分必要条件是存在G的可解正规子群N(或正规子群N)使得G/N∈F且F(N)(或F*(G))的所有素数阶子群在G中均有超可解-s-补. |
| 关键词: 群系 Fitting子群 F-s-补 超可解群 |
| DOI： |
| 投稿时间：2005-08-04修订日期：2005-09-23 |
| 基金项目:广西自然科学基金(0249001)资助项目 |
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| Minimal Subgroups and Supersolvability of Finite Groups |
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LI Shi-rong, HE Xuan-li, SHI Jiang-tao
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| (College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| We characterize the structure of finite group G under the assumpations that minimal subgroups of Fitting subgroup and generalized Fitting subgroup of G are F-s-supplemented, and have the following new results:Let F be a saturated formation containing U and let G be a finite group.Then G ∈ F if and only if there exists a solvable normal subgroup N (respectively a normal subgroup N) of G such that G/N ∈ F and all prime order subgroups of F (G) (respectively F* (G)) are supersolvables-supplemented in G. |
| Key words: formation Fitting subgroup F-s-supplement supersolvable group |
