阿贝尔群

令t（G）为有限阿贝尔群G的单因子个数.本文得到了∑｜G｜≤xt（G）带有更好余项的渐近公式。

Let t ( G ) be the number of unitary factors of finite Abelian group G. In this paper , we obtain an asymptotic formula of t ( G ) with a better error term .

结合抽象代数，组合数学，矩阵理论等知识，提出一种有限阿贝尔群上Jacket矩阵的构造方法，扩展了Jacket矩阵家族。

The combination of abstract algebra , combinatorial mathematics and the matrix theory knowledge , we propose a new construction of Jacket matrix based on finite Abelian group , which expand the Jacket matrix family .

本文将定域规范不变的平均场方法由分立的阿贝尔群情况推广至非阿贝尔连续群情况，计算了SU（2）Yang-Mills场和Higgs场耦合系统的相图。

The locally gauge invariant mean field approach is generalized from Abelian gauge groups to non-Abelian gauge groups . The SU ( 2 ) Yang-Mills-Higgs field coupling system is analyzed .

具有有限生成元的阿贝尔群的自同态环的矩阵表示

The representations of matrix of endomorphism ring of finitely generated Abel groups

具有有限秩的无扭阿贝尔群的结构

The structure of the torsion - free Abelian group with finite rank

关于有限阿贝尔群单因子个数的均值（Ⅱ）

On the Average Number of Unitary Factors of Finite Abelian Groups (ⅱ)

局部紧阿贝尔群上的势位论和一种推广的广义函数

The Potential Theory and a Class of Generalized Distributions on a LCA Group

阿贝尔群上函数的傅里叶谱特征

On the Characterization of the Fourier Spectra of Functions Defined on an Abelian Group

一些公钥密码体制在阿贝尔群上的扩展

Some Public Key Cryptosystem Extended to Abelian Group

阿贝尔群被超-（循环或有限）群的可裂扩张（Ⅰ）（英文）

Splitting extensions of Abelian by hyper - ( cyclic or finite ) groups (ⅰ)

本文讨论了有限阿贝尔群上的希尔伯特变换和张&哈特莱变换的性质。由于引入了群元素排序的概念和定义了函数的奇偶性，从而能够将函数划分出真函数与虚函数两种类别。

This paper discloses properties of the Hilbert and Zhang-Hartley Transforms in Finite Abe-lian Groups .

给出了有限阿贝尔群同构的一个判定算法。

In this paper , the author gives an algorithm for testing isomorphism of finite Abelian groups .

对于任意给定的有限阿贝尔群，迄今尚未见有文献给出其自同构群的群阶的一般计算公式。

Up to now , for any given finite abelian group , it havn 't been found any paper gave a general formula to calculate the order of the automorphism group of the group .

本文给出一些不是集合的群类，如扭阿贝尔群，无扭非阿贝尔群、非阿贝尔群。

In this paper , we have given some classes of groups that are not sets , such as the classes of torsion abelian groups , abelian groups , torsion-free non-abelian groups , non-abelian groups .

使用椭圆曲线作为公钥密码体制的基础是由于定义在有限域上的椭圆曲线上的点的集合可构成阿贝尔群，由此可定义其上的离散对数，即椭圆离散对数。

The base using elliptic curves as public-key cryptosystem is that because the points set of elliptic curve on finite field can form Abelian group . By this , the discrete logarithm on elliptic curve can be defined .

并说明在有限生成的阿贝尔群范畴内F-同构是一等价关系，否则不然。

We also consider the Five Lemma in the case of F-isomorphism and F & exactness , It is shown that in the category of finitely generated abelian groups the F-isomorphism is an equivalent relation but is not true out of this category .

H为非阿贝尔单群，K为素数阶群。

H is a non-abelian simple group , K is of prime order .

G/H的阶为素数，H为非阿贝尔单群且在G内无正规补子群。

G / H is of prime order , H is the non-abelian simple group which without normal complement in G.

给出Minkowski空间的临界维数与内部非阿贝尔规范群的秩的关系。

The relation between critical dimension of Minkowski space and the rank of internal nonabelian gauge group is given .

对于非阿贝尔规范群，这里给出的有效作用量所含的项比Witten的要少。

In the non-abelian ease , the gauge invariant effective action presented here contains less terms than the one obtained by Witten .

p~m阶阿贝尔p-群同构的判定

Decision of p ~ m - order Abel p-group Isomorphism

阿贝尔半群图

A Graph of An Abelian Semigroup

弱阿贝尔格序群簇及其在L1中的积

The variety of weakly Abelian 1 - groups and its product varieties in l_ 1

阿贝尔手征群陪集纯规范场的量子化

On the quantization of pure gauge fields on coset space of Abelian chiral group

利用此恒等式建造了重整化方程，并由方程的解将阿贝尔手征群陪集纯规范场理论重整化。

With this identity the renormalization equations are established . The renormalization of the pure gauge field theory in coset space of the Abelian chiral group is carried out by solving these equations .

导出了与阿贝尔手征群陪集空间纯规范场的生成泛函路径积分测度和有效作用量联合起来在手征群变换下具有不变性相应的恒等式。

We derived the identity which combines the measure of the path-integral of the generating functional and the effective action of the pure gauge field in the coset space of the Abelian chiral group , and is invariant under chiral transformation .