正规子群

Main results are following: Let G be a finite solvable group and N be a normal subgroup.

即：设G是一个有限可解群，H为G的正规子群。

Let H be a normal subgorup of a finite group G such that G/H is nilpotent.

2假设H是有限群G的一个正规子群使得G/H是幂零群。

In this paper, we study some basic properties of s-seminormal subgroups of finite groups and how s-seminormal subgroups of a finite group influence the structure of the group.

研究了s-半正规子群的一些基本性质和它们是如何影响群结构的。

In Chapter Ⅱ, we introduce a Suslin s famous result: when n≥3, the elementary group of general linear group of rank n is a normal subgroup.

第二章介绍了Suslin给出的一个著名结果：当n≥3且系数环为可换环，则n阶一般线性群的基本子群是正规子群。

Furthermore, when the normal subgroup is the idendity group, the basis of the first space is just as the set of irreducible Brauer characters.

进一步，当正规子群为单位元群时，前面一个空间的基就是不可约Brauer特征标的集合。

In section four, we consider a normal π-subgroup in π-separable group, a normal set and a complex value class function space defined on G, using the B_π-character theory and character-triple isomorphism, and find a classical basis of this space such that it behaves as the set of irreducible Brauer characters, and satisfies the Fong-Swan property.

在第四节中我们考虑了π-可分群G中的一个正规π-子群，以及定义在G上的一个正规集和它上面的一个复值类函数空间，利用B_π-特征标理论和特征三元组同构，我们找到了这个空间的一个经典基，使得这个基具有类似于不可约Brauer特征标的集合的性质，并且满足Fong-Swan性质。

A finite group G is called n-decomposable if every proper non-trivial normal subgroup of G is a union of n distinct conjugacy classes of G.

如果有限群G的每个非平凡真正规子群均是G的n个不同共轭类的并，则称G为n-可分解的。

Every group G has a normal subgroup N such that the quotient group G/N is a simple group.

任何群G都存在正规子群N使得G/N是单群。

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，。

Finite group; conditional c-normal; solvable group; p-supersolvable group; p-nilpotent group

基础科学，数学，代数、数论、组合理论有限群；条件c-正规子群；可解群； p-超可解群； P-幂零群

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐