Sylow子群及其极大子群对有限群结构的影响  

The Influence of Sylow Subgroups and Its Maximal Subgroups on the Finite Groups

作　　者：胡玉生[1] 张利英[1] 

机构地区：[1]安徽财经大学统计与应用数学学院,安徽蚌埠233030

出　　处：《北京联合大学学报》2012年第1期70-72,共3页Journal of Beijing Union University

基　　金：安徽财经大学校级科研项目(ACKYQ1152ZC);安徽省高校人文社科项目(2011SK166);安徽省高校人文社科项目(2011SK177)

摘　　要：利用Sylow子群及其极大子群在有限群G中完全条件置换得出了G超可解的结论,并把结果推广到群系中,得到了包含超可解群类的饱和群系的充分条件,推广了一些已知结果。By using the completely conditional permutability of the Sylow subgroups and its maximal subgroups of finite group G, the sufficient conditions for a finite group G to be supersolvable are proved and the results are generalized to formations. Moreover, the sufficient condition for a saturated formation containing the class of all finite supersolvable groups is also obtained, and some known results are generalized.

关 键 词：完全条件置换子群 SYLOW子群 极大子群 超可解群 

分 类 号：O152[理学—数学]