p^4阶群与李环结构之间的关系  

Relation between the group of order p^4 and the structure of Lie ring

作　　者：包德喜[1] 张陆[1] 张天宇[1] 

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028043

出　　处：《高师理科学刊》2012年第1期41-43,共3页Journal of Science of Teachers＇College and University

摘　　要：继单群分类定理完成之后,有限p群逐渐成为有限群研究的热点.证明了在p^4阶群G关于其子群N(G)={a-pb-papbp,c-p2b-p2ap 2-pbp2c pa,b,c∈G}的商群中定义加法和Lie乘运算为aN(G)bN(G)=(ab)pN(G),aN(G)bN(G)[a,b]N(G),则GN(G)成为Lie环.由于Lie环的可算性,这一结论有利于对p4阶群的结构进行研究.After the accomplishment of the classification of finite simple groups,peoples′ attention focus on the study of finite p-groups more and more.Proved that if we define the addition and muliplication in the factor group of subgroup N（G）={a-pb-papbp,c-p2b-p2ap 2-pbp2c pa,b,c∈G} in G of order p4 as aN（G）bN（G）=（ab）pN（G）,aN（G）bN（G）[a,b]N（G）,respectively then will become a Lie ring.Because the Lie ring is easy to calculate so this conclusion is helpful in studying the structure of the group of order.

关 键 词：有限P群 p4阶群 换位子 李环 子群 

分 类 号：O152[理学—数学]