| 素数幂阶子群的s-半置换性对有限群结构的影响 |
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| 引用本文： | 王丽芳,张勤海.素数幂阶子群的s-半置换性对有限群结构的影响[J].数学研究与评论,2005,25(3):423-428. |
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| 作者姓名： | 王丽芳 张勤海 |
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| 作者单位： | 1. 中山大学数学系,广东,广州,510275
2. 山西师范大学数计学院,山西,临汾,041004 |
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| 基金项目： | NNSF of China (10471085)
NSF of Shanxi Province of China (20011004)
Key Proj. of Ministry of Education(02023)
the Returned Overseas Students Foundation of Shanxi Province of China ([2004]7) |
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| 摘 要： | 设G为有限群,G的一个子群H称为半置换的,若对任意的K≤G,只要(|K|,|H|)=1,就有KH=HK;H称为s-半置换的,若对任意的p||C|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G).本文考察了素数幂阶子群的s-半置换性对有限群的超可解性的影响.
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| 关 键 词： | s-半置换子群 Sylow塔 超可解群 |
| 文章编号： | 1000-341X(2005)03-0423-06 |
| 收稿时间： | 6/5/2003 12:00:00 AM |
| 修稿时间： | 2003年6月5日 |
Influence of s-Semipermutability of Some Subgroups of Prime Power Order on Structure of Finite Groups |
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| WANG Li-fang and ZHANG Qin-hai.Influence of s-Semipermutability of Some Subgroups of Prime Power Order on Structure of Finite Groups[J].Journal of Mathematical Research and Exposition,2005,25(3):423-428. |
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| Authors: | WANG Li-fang and ZHANG Qin-hai |
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| Institution: | School of Mathematics, Zhongshan University, Guangzhou 510275, China;School of Mathematics and Computer, Shanxi Teachers'University, Linfen 041004, China |
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| Abstract: | A subgroup H of a finite group G is called semipermutable if it is permutable with every subgroup K of G with (|H|,|K|) = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p,|H|) = 1. In this paper, we investigate the influence of s-semipermutablity of some subgroups of prime power order of a finite group on its supersolvablility. |
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| Keywords: | s-semipernutable subgroups Sylow tower supersolvable groups |
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