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
基金项目:
作者单位
王丽芳 中山大学数学系,广东,广州,510275 
张勤海 山西师范大学数计学院,山西,临汾,041004 
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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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