| p~4阶群与李环结构之间的关系 |
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| 引用本文： | 包德喜,张陆,张天宇. p~4阶群与李环结构之间的关系[J]. 高师理科学刊, 2012, 0(1): 41-43 |
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| 作者姓名： | 包德喜 张陆 张天宇 |
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| 作者单位： | 内蒙古民族大学数学学院,内蒙古通辽028043 |
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| 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.
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| 关 键 词： | 有限p群 p4阶群 换位子 李环 子群 |
Relation between the group of order p~4 and the structure of Lie ring |
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| BAO De-xi,ZHANG Lu,ZHANG Tian-yu. Relation between the group of order p~4 and the structure of Lie ring[J]. Journal of Science of Teachers＇College and University, 2012, 0(1): 41-43 |
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| Authors: | BAO De-xi ZHANG Lu ZHANG Tian-yu |
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| Affiliation: | (School of Mathematics,Inner Mongolia University for Nationalities,Tongliao 028043,China) |
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| Abstract: | 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. |
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| Keywords: | finite groups group of order p~4 commutator Lie ring subgroup |
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