| 1. | And element x=a is nilpotent .
元素XA是幂零的。 |
| 2. | And element x = a is nilpotent
元素x a是幂零的。 |
| 3. | In section 4 , in the case of finite and infinite non - nilpotent we mainly study the soluble structure of s ( a , c ) - groups
最后主要研究非幂零的4 … …卜群，在有限和无限条件下得到了一些可解结构 |
| 4. | In order to characterize the linear operators that strongly preserve nilpotence and that strongly preserve invertibility , we first study the case of the binary boolean algebra
为了刻画强保持幂零的线性算子和强保持可逆的线性算子，我们首先研究二元布尔代数上的情况 |
| 5. | By the means of the extension of linear operator , we characterize the linear operators that strongly preserve nilpotence and that strongly preserve invertibility over any boolean algebra
再利用线性扩张这一工具,我们刻画了在一般布尔代数上强保持幂零的线性算子和强保持可逆的线性算子 |
| 6. | We prove that the strong and weak topological contractions for automorphisms of connected lie groups are equivalent . we also get that the connected lie group which admits a topological contractive automorphism must be a nilpotent lie group
证明了连通李群自同构的强拓扑压缩性质与弱拓扑压缩性质等价；存在拓扑压缩自同构的连通李群是幂零的。 |
| 7. | 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 |
| 8. | Also , by the means of the pattern of matrix and the pattern of linear operator , we characterize the linear operators that strongly preserve nilpotence and that strongly preserve invertibility over antinegative commutative semirings without zero divisors
另外,利用矩阵模式和算子模式等工具，我们在非负无零因子半环上刻画了强保持幂零的线性算子和强保持可逆的线性算子 |
| 9. | In l , the author gives main definitions and basic results what are needed in the paper . in 2 , the author determines the structures of some groups by using s - normality of sylow subgroups and the maximal subgroups of sylow subgroups . there are the main theorems that 1 ) a group g is metanilpotent if and only if every sylow subgroup of g is s normal in g
我们在1中将给出本文所需的主要概念和基本结果，在2中讨论sylow子群、 sylow子群的极大子群的s -正规性对群的结构的影响，主要结论是1 )群g是亚幂零的当且仅当g的每个sylow子群在g中s -正规。 |
| 10. | In this aspect , kondrat ' ev [ ll ] has shown that a group g is 2 - nilpotent if the normalizer of each sylow subgroup of g is of odd index in g . in 1995 , zhang [ 13jhas proved that a group g is soluble if the index of the normalizer of every sylow subgroup in g is a prime power
1988年， kondrat ’ ev卜11证明了:如果群g的任意西洛子群的正规化子在g中的指数为奇数，则g是2一幂零的。 1995年， zhang卜习证明了如果群g的任意西洛子群的正规化子有素数幂指数，则g是可解的。 |
