幂零的

Theorem and Burnside Theorem about p-nilpotence.

和Burnside关于p-幂零的定理。

If every minimal p-subgroup of G is containedin Z, every cyclic subgroup of order 4 of G is conditional c-normal in G, then G isp-nilpotent.Theorem 2.3.9 Let p be a fixed prime.

定理2.3.9对某个固定的素数p，设G的每个极小p-子群包含于Z，4阶循环子群在G中条件c-正规，则G是p-幂零的。

This condition is much easier than that given by the Maximum principle in many cases.

最后，对于系统Lie代数为1或2幂零的情况下一类非线性最优控制问题，给出了解的必要条件。

We obtain some results on solvability and nilpotency of finite groups by the 9— pairs of 2—maximal subgroups.

利用2-极大子群的θ-子群偶得到了一系列有限群可解，幂零的结果。

In this paper we give the concept ob approximation nilpotent alternate algebra,and sduty the relation ot nipotency and solvability to the approximation nilpotency .

在这篇文章中给出了交错代数的近似幂零性的概念。并且，讨论了交错代数的幂零性、可解性与近似幂零性之间的关系。

Finally, we study the PLDP(n, 2) and strongly nilpotent Jacobian matrices, and we prove that if the nilpotency index of JH for a power-linear map H of degree 2 is less than 4, then JH is strongly nilpotent, and consequently the rows of JH are linearly dependent.

此外，我们特别对线性多项式2次幂映射的相关性问题进行了讨论，为此，对强幂零的Jacobi矩阵进行了研究，刻画了Gorni-Zampieri对的幂零指数之间的关系，并证明了Gorni-Zampieri对保持强幂零性。

In the present paper,we investigate solvable radicals and Hopkins nilpotent radicals for Lie triple systems and prove that both radicals are invariant under actions of deriva- tions.

本文讨论李三系的可解根基和Hopking幂零的某些性质及导子作用下的不变性，讨论了李三系次理想的某些性质，证明了李三系为幂零的当且仅当每个子系都是次理想。

By using Jordan-Hlder type theorem of table algebras, we prove that table algebras satisfying nilpotent extension condition are nilpotent, which does not correspond to extension problems of nilpotent groups exactly.

本文研究了幂零表代数的一个有趣的性质，利用表代数的Jorda-Hlder型定理，证明了表代数满足幂零被幂零扩张仍是幂零的，但有限幂零群没有这样的扩张。

In this paper, by using conditional cnormalityof some special subgroups(such as minimal subgroups, maximal subgroups, Sylowsubgroups, maximal subgroups of Sylow subgroups)of G, we obtain some sufficient or necessaryconditions for a finite group to be solvable, supersolvable, nilpotent. Some previouslyknown results are generalized.

本文结合有限群的某些特殊子群(如，极小子群，极大子群，Sylow子群，Sylow子群的极大子群)的条件c-正规性来研究有限群的可解性，超可解性，幂零性，得到了有限群可解，超可解，幂零的若干充分和充要条件，推广了有限群的一些结果。

In the fifth chapter,we study dipolarizations in some quadratic Lie algebras.Inthe first section,we obtain some results on the classification of dipolarizations in gen-eral quadratic Lie algebras,and prove that there exist dipolarizations in the solvablequadratic Lie algebras whose Cartan subalgebras consist of semisimple elements.

第五章讨论了某些二次李代数的双极化，在第一节中，我们给出了二次李代数的双极化的一些分类结果；特别证明Cartan子代数是由半单元组成的二次李代数上存在双极化，第二节确定了四维扩张Heisenberg代数的所有双极化，在第三节中，我们构造了2n+2维扩张Heisenberg代数的六类双极化，我们发现两个不同于半单李代数情形的有趣事实：（1）在扩张Heisenberg代数上同时存在对称和非对称双极化；（2）对应于扩张Heisenberg代数的双极化的特征元有的是半单的有的是幂零的。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷