有限群的p-幂零性和极小子群  

On p-Nilpotence and Minimal Subgroups of Finite Groups

作　　者：李世荣[1] 农国平[1] 周龙桥[1] 何俊[1] 

机构地区：[1]广西大学数学与信息科学学院,南宁530004

出　　处：《数学年刊（A辑）》2009年第5期623-630,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金项目(No.10161001);广西自然科学基金(No.0249001)资助的项目

摘　　要：从有限群构造的角度来看,p-幂零群和p-可分解群很相似,前者是p-群和p′-群的半直积,后者是p-群和p′-群的直积.有限群G的p-可分解剩余是P(G)=∩{H|H■G,而且G/H是p-可分解}.通过观察p-可分解剩余和极小子群的性质得到了几个关于p-幂零的充要条件.There are many similar structures between p-nilpotent groups and p-decomposable groups. The former is a semidirect product of a p-group and a p′-group, and the latter is a direct product of a p-group and a p′-group. The p-decomposable residual of G is P（G） = ∩{H ｜ H ｜ G and G/H is p-decomposable}. In this paper, the authors obtain some necessary and sufficient conditions for p-nilpotence by investigating characterizations of p-decomposable residual and minimal subgroups.

关 键 词：有限群 极小子群 P-幂零 p-可分解剩余 

分 类 号：O152.1[理学—数学]