| 关于有限群的弱S-可补嵌入子群(英文) |
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| 引用本文： | 赵涛,黎先华,徐勇,李样明. 关于有限群的弱S-可补嵌入子群(英文)[J]. 数学进展, 2012, 0(3): 373-383 |
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| 作者姓名： | 赵涛 黎先华 徐勇 李样明 |
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| 作者单位： | 苏州大学数学科学学院;山东理工大学理学院;广东第二师范学院数学系 |
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| 基金项目： | supported by NSFC(No.11171243,No.10871032);the Natural Science Foundation of Jiangsu Province(No.BK2008156);Guangdong Province(No.S2011010004447) |
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| 摘 要： | 假定H是有限群G的一个子群.如果对于|H|的每个素因子p,H的一个Sylow p-子群也是G的某个s-可换子群的Sylow p-子群,则称H为G的s-可换嵌入子群;如果存在G的子群T使得G=HT并且H∩T≤HG,其中HG为群G含于H的最大的正规子群,则称H为G的c-可补子群;如果存在G的子群T使得G=HT并且H∩T≤Hse,其中Hse为群G含于H的一个s-可换嵌入子群,则称H为G的弱s-可补嵌入子群.本文研究弱s-可补嵌入子群对有限群结构的影响.某些新的结论被进一步推广.
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| 关 键 词： | 弱s-可补嵌入子群 超可解群 p-幂零群 饱和群系 |
On Weakly s-supplemently Embedded Subgroups of Finite Groups |
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| ZHAO Tao,LI Xianhua,XU Yong,LI Yangming. On Weakly s-supplemently Embedded Subgroups of Finite Groups[J]. Advances in Mathematics(China), 2012, 0(3): 373-383 |
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| Authors: | ZHAO Tao LI Xianhua XU Yong LI Yangming |
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| Affiliation: | (3,**) (1.School of Mathematical Science,Soochow University,Suzhou,Jiangsu,215006,P.R.China; 2.School of Science,Shandong University of Technology,Zibo,Shandong,255049,P.R.China; 3.Department of Mathematics,Guangdong University of Education,Guangzhou,Guangdong,510310, P.R.China) |
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| Abstract: | Suppose that G is a finite group and H is a subgroup of G.H is said to be s-permutably embedded in G if for each prime p dividing H,a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-permutable subgroup of G;H is called c-supplemented in G if there exists a subgroup T of G such that G = HT and H∩T≤HG,where HG is the largest normal subgroup of G contained in H.H is said to be weakly s-supplemently embedded in G if there are a subgroup T of G and an s-permutably embedded subgroup Hse of G contained in H such that G =HT and H∩T≤Hse.We investigate the influence of weakly s-supplemently embedded subgroups on the structure of finite groups.Some recent results are generalized. |
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| Keywords: | weakly s-supplemently embedded subgroup supersolvable group p-nilpotent group saturated formation |
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