关于无限p-群的几点注记  

Notes on Infinite p- Groups

作　　者：吕恒[1] 段泽勇[1] 

机构地区：[1]西南师范大学数学系,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2002年第3期301-302,共2页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目 (198710 66);教育部优秀青年教师资助计划 ([2 0 0 2 ] 40 )

摘　　要：证明了满足极大条件的可解p群是幂零群 ;p群中具有有限指数的极大子群是正规子群 ;如果群G =AB ,其中A是有限p群 ,｜A′｜=p ,且对 x Z(A) ,CA(x)是交换群 ,B是G的半正规p群 ,｜B′｜=pn,那么G的导出长度至多为n +3.It is proved proved that a soluble p group which satisfies the maximal condition is nilpotent and a maximal subgroup of a p with finite index is normal. The authors use this result and one of Morigis esult to have get that: If G=AB is a p group satisfying, and (1) A is a finite p group, C\-A(x) is Abelian while xZ(A) and |A′|=p ; (2) B is seminormal and |B′|=p\+n . Then G (n+3) =1.

关 键 词：无限p-群 导出长度 可解p-群 幂零群 多重循环群 极大子群 正规子群 

分 类 号：O152.1[理学—数学]