# nilpotent group in Chinese

• 幂零群
###### Examples
• Some sufficient and necessary conditions of - nilpotent group
幂零群的几个充要条件
• Theorem 3 . 10 if g is locally nilpotent group and c * - group , then g is baer nilpotent and hypercentral group
定理3若局部幂零群g是c二群，则g是baer幂零而且是超限上中心群
• Theorem 3 . 11 if g is torsion locally nilpotent group and c ( p ) - group , then the nilpotent class of g is at most 3
定理3 11若周期的局部幂零群g是c ” …卜群，则g的类最多为3
• So we can easily obtain nilpotent class of s * ( a * , c * ) - groups and the structure of their derived subgroup in the case of torsion and locally nilpotent group
从而进一步得到了周期的局部幂零群的幂零类及导群的结构。
• At the same time , we get some new characterization of supersolvable and nilpotent groups by introduce the new concepts of u ( g ) and v ( g ) . the following theorems are some of the main results in this thesis . 1
特别地，引进群g的两个特征子群u ( g )及v ( g ) ，用这两个子群来刻划有限群的结构，得到了有限群超可解，幂零的一些充分条件，减弱了某些已知定理的条件
• It is important to study the structures of finite groups by combining some subgroups with some properties in the researches on finite groups . in this paper , we discuss the following : ( 1 ) the relations between the - pairs of maximal subgroups and c - normality , weak c - normality , s - normality , the normal index of maximal subgroups ; ( 2 ) some results on solvablity of finite groups that are obtained by using the s - normality of subgroups ; ( 3 ) the - pairs of general proper subgroups of finite groups as the generalization of the - pairs of maximal subgroups that is used to describe c - normal subgroups , weak c - normal subgroups and s - normal subgroups , by which some new results on finite groups are obtained ; ( 4 ) some new results on p - quasinilpotent groups and p * - nilpotent groups
本文在前人的基础上，讨论了以下内容： ( 1 )极大子群的子群偶和c正规性、弱c正规性、 s正规性、正规指数之间的关系； ( 2 )利用s正规性得到了关于有限群可解性的几个结果； ( 3 )将极大子群的子群偶推广为有限群的一般真子群的偶，证明了有限群的c正规、弱c正规以及s正规子群都可以用一般真子群的偶来描述和几个新的结果； ( 4 )研究p拟幂零群和p ~ *幂零群，得到了一些新的结构定理。
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