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| 子群的S-条件置换性对有限群结构的影响 | |
| 引用本文： | 牛文娟,郭文彬,刘玉凤.子群的S-条件置换性对有限群结构的影响[J].数学研究及应用,2011,31(1):173-179. |
| 作者姓名： | 牛文娟 郭文彬 刘玉凤 |
| 作者单位： | 徐州师范大学数学科学院, 江苏 徐州 221116;徐州师范大学数学科学院, 江苏 徐州 221116; 中国科学技术大学数学系, 安徽 合肥 230026;烟台大学数学系, 山东 烟台 264005 |
| 基金项目： | 国家自然科学基金项目(Grant No.11071229),江苏省高校自然科学研究项目(Grant No.10KJD110004),徐州师范大学研究生创新工程项目资助. |
| 摘 要： | Let G be a finite group. Fix a prime divisor p of IGI and a Sylow p-subgroup P of G, let d be the smallest generator number of P and Ma（P） denote a family of maximal subgroups P1, P2 , Pd of P satisfying ∩^di=1 Pi = Ф（P）, the Frattini subgroup of P. In this paper, we shall investigate the influence of s-conditional permutability of the members of some fixed .Md（P） on the structure of finite groups. Some new results are obtained and some known results are generalized. |
| 关 键 词： | finite groups s-conditionally permutable groups saturated formations supersoluble groups nilpotent groups. |
| 收稿时间： | 2009/5/31 0:00:00 |
| 修稿时间： | 2009/9/18 0:00:00 |
The Influence of $s$-Conditional Permutability of Subgroups on the Structure of Finite Groups |
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| Wen Juan NIU,Wen Bin GUO and Yu Feng LIU.The Influence of $s$-Conditional Permutability of Subgroups on the Structure of Finite Groups[J].Journal of Mathematical Research with Applications,2011,31(1):173-179. | |
| Authors: | Wen Juan NIU Wen Bin GUO and Yu Feng LIU |
| Institution: | 1. Department of Mathematics,Xuzhou Normal University,Jiangsu 221116,P.R.China 2. Department of Mathematics,Xuzhou Normal University,Jiangsu 221116,P.R.China;Department of Mathematics,University of Science and Technology of China,Anhui 230026,P.R.China 3. School of Mathematical and Informational Science,Shandong Institute of Business and Technology,Shandong 264005,P.R.China |
| Abstract: | Let $G$ be a finite group. Fix a prime divisor $p$ of $|G|$ and a Sylow $p$-subgroup $P$ of $G$, let $d$ be the smallest generator number of $P$ and ${\cal M}_{d}(P)$ denote a family of maximal subgroups $P_{1}, P_{2}, \ldots, P_{d}$ of $P$ satisfying $\bigcap_{i=1}^{d}P_{i}=\Phi(P)$, the Frattini subgroup of $P$. In this paper, we shall investigate the influence of $s$-conditional permutability of the members of some fixed ${\cal M}_{d}(P)$ on the structure of finite groups. Some new results are obtained and some known results are generalized. |
| Keywords: | finite groups $s$-conditionally permutable groups saturated formations supersoluble groups nilpotent groups |
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