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s-半置换子群对群构造的影响
引用本文:张勤海,王丽芳.s-半置换子群对群构造的影响[J].数学学报,2005,48(1):81-88.
作者姓名:张勤海  王丽芳
作者单位:山西师范大学数学与计算机科学学院,山西师范大学数学与计算机科学学院 临汾 041004,临汾 041004
基金项目:国家自然科学基金(10171086) 教育部回国留学人员基金([1999]363) 山西省自然科学基金(20011004) 回国留学人员基金([2002]16)资助项目
摘    要:群G的一个子群H称为半置换的,若对G的任意子群K,只要(|H|,|K|)=1,就有HK=KH;H称为s-半置换的,若对G的任意Sylow p-子群P,只要(p,|H|)=1,就有HP=PH.本文研究极大子群和极小子群的某些子群的s-半置换性对群构造的影响,推广和改进了Asaad及王品超等人所得的结果.

关 键 词:s-半置换子群  半正规子群  Fitting子群

The Influence of s-Semipermutable Subgroups on the Structure of Finite Groups
Qin Hai ZHANG Li Fang WANG College of Mathematics and Computer,Shanxi Teachers University,Linfen ,P. R. China.The Influence of s-Semipermutable Subgroups on the Structure of Finite Groups[J].Acta Mathematica Sinica,2005,48(1):81-88.
Authors:Qin Hai ZHANG Li Fang WANG College of Mathematics and Computer  Shanxi Teachers University  Linfen  P R China
Institution:Qin Hai ZHANG Li Fang WANG College of Mathematics and Computer, Shanxi Teachers University, Linfen 041004, P. R. China
Abstract:A subgroup H of a group G is said to be 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 extend and improve some of Asaad and Pingchao Wang's results by examining the influence of s-semipermutability on the structure of groups.
Keywords:s-semipermutable subgroups  Seminormal subgroups  Fitting subgroups
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