交换群

Furthermore,we consider the relations between the general linear groups and the corresponding BN-pairs and show that they satisfy a commutative diagram of groups.In Chapter 2,we study the structure of unitary groups over finite group rings R and its applications.

第一章考虑任意局部环上典型群的BN-对问题，构造了局部环上一般线性群、辛群、正交群的BN-对，并且证明了局部环上一般线性群与对应的BN-对之间满足群交换图关系。

After new station just had been done, the site PR of the friend that you can look for you to be familiar with is tall exchange a link with him, do not know who does impossibly also with you, this I am to have the same feeling greatly, when I stand newly, be in stationmaster group in call commutative link every day, all the time nobody is willing to be exchanged with you, although stand with what you exchange, his station PR also is 0, if your popularity should grasp an opportunity only so very much, believe you also can find the site with tall PR to exchange.

新站刚做好以后，你可以找你熟悉的朋友的站点PR高的和他交换链接，不认识的谁也不可能和你做的，这个我是深有同感，我新站的时候在站长群里天天喊交换连接，一直没人愿意和你交换，即使和你交换的站，他的站PR也是0，如果你人缘好那么只要把握住机会，相信你也可以找到PR高的站点来交换。

Add a few head of a station more group, be in next group in call commutative link, undertake leaving exchange with a few way station, let stationmaster advise more next, come down opinion record, improve slowly.

多加几个站长群，然后在群里喊交换链接，和一些小站进行下交换，然后多让站长提意见，把意见记录下来，慢慢改进。

Finite commutative group; Symmetric bicharacter; Lie color superalgebra ; Left color symmetric algebra ; Left color symmetric structure

基础科学，数学，代数、数论、组合理论有限交换群；对称双特征标；着色李超代数；左着色对称代数；左着色对称结构

We establish a relation between μ and the stucture of the group G, and obtain the lower bound of the ratio by the mininal prime divisor of the order and commutator of the group G, and give a necessary and sufficient condition under which this lower bound is attained.

第一部分，记有限群G的阶与不可约特征标个数的比值为μ，我们研究了一般的非交换有限群G的结构和μ之间的关系，通过群G的阶的最小素因子和换位子群G′的最小素因子得到了μ的一个下界，同时给出了达到下界的一个充分必要条件。

This paper extends the ant colony algorithm which is used for solving 0-1 knapsack problem in reference [7], and gets enlightenment from the ant colony algorithm with 2-opt local optimization for solving traveling salesman problems: Exchange strategy can make the algorithm have faster convergence rate and get better quality solution. So this paper presents the ant colony algorithm based on exchange stragegy.

本文推广了文献[7]中求解单维0-1背包问题的蚁群算法，并从结合2-opt等局部优化的蚁群算法求解旅行商问题中得到启示：通过交换策略可以加快算法的收敛速度和获取更高质量的解，因此提出了基于交换策略的蚁群算法。

Not every subgroup of a D-group is also a D-group. If a subgroup is a D-group we call the subgroup "sub- D -group." The "commutator ideal" of G is the smallest sub-D-group containing its commutator subgroup. We found that the commutator ideal can be viewed as a finitely generated module over a ring when G is a finitely generated metabelian D-group.

并非每个子群都是一个可除群，若一个子群是可除群，我们称之为子可除群(sub-D-group)，而G 的交换子理想则是在G中包含其导出群的最小子可除群，我们发现当G是一个有限生成亚交换可除群时，其交换子理想是一个有限生成模。

With the help of its structure, this paper points out that the non-commutative finite solvable subsimple group will necessarily be a qualitative element group. And referring to the nature of qualitative element group, it can be easily identified the conditions that the ordered prime divisors in a solvable initial finite subsimple group should meet. Suppose that G is always a finite group.

利用其结构，指出了非交换可解有限次单群必为质元群，从而利用质元群的性质，可以很容易地初步确定了可解有限次单群的阶中素因子之间所必须满足的条件，主要得到下面的一些结论：定理1 G是非交换的可解有限次单群，则G′是G的唯一的非平凡正规子群，并且G′是初等交换p -群，此时| G |= p~n q，|G′|=p~n，。

A subgroup of a finite group G is called π-quasinormal in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be c-supplemented in G if there exists a subgroup N of G such that G=HN and H∩N≤H=Core.

有限群G的一个子群称为在G中是π-拟正规的若它与G的每一个Sylow-子群是交换的。G的一个子群H称为在G中是c-可补的若存在G的子群N使得G=HN且H∩N≤H＝Core。

Ni6 cluster is an octahedron belonging to Oh point group. Its 3Eg orbital presents strong negative exchange coupling and has a trend of antiferromagnetic couplings. Ni5 cluster is of three-side pyramidal structure belonging to point group C3v. The magnetic moment direction of Ni atom lying on vertex of the pyramid is antiparallel to the moment direction of the Ni atoms lying on underside of the pyramid, which present the characteristic of ferrimagnetic couplings.

具有Oh点群对称的八面体原子簇Ni6的3Eg轨道上存在很强的负交换耦合，呈现反铁磁耦合趋势；具有C3v点群对称的三边金字塔结构的原子簇Ni5位于塔顶点的Ni原子与基面上的Ni原子磁矩方向相反，但大小不等，呈现出亚铁磁交换耦合特征。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。