两个Fitting类的例子  

Two Examples of Fitting Classes

作　　者：高锐敏[1] 李巧利[2] 卜春霞[3] 

机构地区：[1]河南牧业经济学院基础部,河南郑州450044 [2]河南工业大学理学院,河南郑州450001 [3]郑州大学数学系,河南郑州450000

出　　处：《数学的实践与认识》2016年第8期213-219,共7页Mathematics in Practice and Theory

基　　金：河南省科技厅基础与前沿技术研究计划项目(132300410381);河南省科技发展计划基础与前沿项目(142300410018)

摘　　要：给出了两个特殊的群类,即R={H|C_H(F(H))≤F(H)}和S={G|1≠K⊿G^((∞)),G^((∞))=KC_(G(∞))(K)},证明了他们都是Fitting类,这两个Fitting类都和单群理论有密切联系.各自都包含了一些很值得注意的群,对每个Fitting类给出了群G属于该Fitting类的一个充要条件.Two group classes are given in this paper,they areR={H｜CH（F（H））≤F（H）}andS={G｜δ1≠K G^（∞）,G^（∞）=KC（G（∞））（K）},moreover they are proved to be fitting classes,and both of them are closely related to the theory of finite simple group.In addition we notice that some groups in two fitting classes have some special properties,for every fitting class,we give a sufficient and necessary condition of that G is a group in this class.

关 键 词：Fitting类 有限可解群 正规子群 单群 

分 类 号：O152.1[理学—数学]