1) π-nilpotent
π-幂零
2) π-nilpotent group
π-幂零群
1.
giving many necessary and sufficient conditions of π-nipotent groups, and obtaining the relevant charaterizations of π-nilpotent groups by introduction to the relevant chardcteristic subgroups π-hypercenter and π-nilpotent residual.
本文给出了π-幂零群的若干刻划;引进了相关的特征子群π-超中心和π-幂零剩余,得到了π-幂零相应的特征性质;特别讨论了内、外π-幂零群的结构,获得了有意义的结果,最后讨论了π-Abel群。
3) upper π nilpotent series
上π-幂零列
1.
In this paper, the upper π nilpotent series and the lower π nilpotent series of finite groups are introduced, and one necessary and sufficient condition for a finite group to be a π soluble group is obtained.
通过建立上π－幂零列和下π－幂零列，得到了判别有限群为π－可解群的一个充要条件。
4) lower π nilpotent series
下π-幂零列
1.
In this paper, the upper π nilpotent series and the lower π nilpotent series of finite groups are introduced, and one necessary and sufficient condition for a finite group to be a π soluble group is obtained.
通过建立上π－幂零列和下π－幂零列，得到了判别有限群为π－可解群的一个充要条件。
5) locally π-nilpotent group
局部π-幂零
6) π-quasinilpotent group
π-拟幂零群
1.
In this paper,with defination and properties of π-quasinilpotent group in ,some sufficient conditions for the solvable and supersolvable group are obtained and a conclusion is developed.
在参考文献[1]中π-拟幂零群的定义和性质下,利用其子群的π′-正规性来得到可解及超可解的充分条件,并推广了参考文献[1]的一个结论。
2.
Based on normality of Sylow subgroups of finite group, in [1] the author gave the definition of π-quasinilpotent group, and obtained the properties and some sufficient conditions with π -quasinormolity of its subgroups, and discussed the relationship between π - quasinilpotent group and supersolvable group.
[1]借助有限群的Sylow子群的正规性给出π-拟幂零群的概念,并利用子群的π-拟正规性得到π-拟幂零群的性质及几个充分条件,也探讨了π-拟幂零群与超可解群的关系。
3.
In this paper, we obtain some sufficient conditions for supersolvability of finite groups with the properties of the π-quasinilpotent group.
本文利用 π-拟幂零群的性质得到了有限超可解群的若干充分条
补充资料：幂零Lie代数
幂零Lie代数
Lie algebra, nilpotent
幂零lie代数【liealgebI’a.浦训t即t;瓜朋~。代Hm明盯e6Pal 域k上满足下列等价条件之一的代数(司罗bla)g: l)有g的理想的有限降链{9.}。“、。，使得g。=g，g。={o}，且对o簇i
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参考词条