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.
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
关键词
有限P群
p4阶群
换位子
李环
子群
finite groups
group of order p^4
commutator
Lie ring
subgroup