Abelian group

Maximal Z-Orders of Integral Group Rings of Finite Abelian Group and Relative K_1-Group

有限交换群的整群环的极大序及其相对K1-群

And Abelian group and non-Abelian group. The order of an element is a significant concept in group.

而元的阶又是群的一个重要概念，元的阶和群的阶有着内在的联系；

A class of rings constructed by an abelian group

由一个加群构造的一类交换环

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

具有有限秩的无扭阿贝尔群的结构

The automorphism groups of Cayley digraphs of finite Abelian group with degree 2

2度可换群上的有向Cayley图的自同构群

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.

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。

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.

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。

( Lemma 2) Let G be a finite Abelian group.

（引理2）设G是有限交换群，S（？）

The authors show that the Lies Theorem holds for Lie color algebras with a torsion-free abelian group G.

作者证明了无挠群上的色李代数的李定理，同时，也给出例子说明无挠性是必要的。

If the permutation group is not an Abelian group, we can find an Abelian subgroup included in the group, and then we can use the method as above.

若给出的置换群不是一个Abelian群，则我们可以在这个群中，找一个Abelian子群，因此同样可以用上述方法。

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

阿贝尔手征群陪集纯规范场的量子化

Extends the binary morphological rank operator to grey-scale images based on fuzzy logic and studies grey-scale morphological rank operators in a finite additive Abelian group.

在有限Abelian群中，基于模糊逻辑将二值形态学分级算子推广到灰度图像，研究灰度形态学分级算子。

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.

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。

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.

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。

Some Public Key Cryptosystem Extended to Abelian Group

一些公钥密码体制在阿贝尔群上的扩展

Generalizing a single involutive automorphism to a finite Abelian group of automorphisms of G, we obtain a homogeneous space called generalized symmetric space and some of its properties.

本文把李群的单个对合自同构推广为由李群G的一些自同构组成的有限可换群，从而决定了一个广义对称空间，并讨论了它的某些性质。

In terms of sub-shifts of finite type determined by an irreducible matrix, affine maps of compacted connected metric abelian group and continuous maps of tree, the two concepts of topologically ergodic map and topologically transitive map are identical.

指出对于由不可约方阵所决定的符号空间有限型子转移而言，或紧致交换群的仿射变换及树上连续自映射而言，拓扑遍历与拓扑可迁这两个概念是一致的。

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.

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。

Where A is abelian group.

其中A是交换群。

Let Г be an abelian group.

设Г是交换群.

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.

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。

In this paper we study Toeplitz operator and Toeplitz algebra on discrete abelian group.

研究了离散交换群上的Toeplitz算子和Toeplitz代数.

Archimedean property of a free Abelian lattice group

自由可换格群的阿基米德性质

This paper proves that the omni-direction permutations constructed by recurring shift Latin square Dp and Latin square Wp on the finite primary field Fp must be complete mappings on Abelian group Fp, and prove that these omni-direction permutations are also linear functions on Fp.

证明了利用有限素域Fp上的循环移位拉丁方Dp和拉丁方Wp产生的全向置换必定是Fp加群上的完全映射，而且这类全向置换一定是F上的线性函数。

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

阿贝尔群上函数的傅里叶谱特征