| 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(英文)[J].数学研究及应用,2005,25(3):423~428 |
| 素数幂阶子群的s-半置换性对有限群结构的影响(英文) |
| Influence of s-Semipermutability of Some Subgroups of Prime Power Order on Structure of Finite Groups |
| 投稿时间：2003-06-05 |
| DOI：10.3770/j.issn:1000-341X.2005.03.006 |
| 中文关键词: s-半置换子群 Sylow塔 超可解群 |
| 英文关键词:s-semipernutable subgroups Sylow tower supersolvable groups |
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| 中文摘要: |
| 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‖G|,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. |
| 英文摘要: |
| 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 influ ence of s-semipermutablity of some subgroups of prime power order of a finite group on its supersolvablility. |
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