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multiplicative groups
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  乘群
     The first part of this paper deals with two extreme classes of finite rings of characteristic 2 in their general forms namely,the classes of such rings of order 2~m,the multiplicative groups of the invertible elements which have orders 1 and 2~m-1 respectively M being any given positive integer。
     本文的第一部份研究了特征为2的某些2~m 阶的有限环的两种极端情形:其可逆元作成分别为1和2~m-1阶的乘群,其中 m 是任意给定正整数。
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  “multiplicative groups”译为未确定词的双语例句
     ON THE STRUCTURE OF MULTIPLICATIVE GROUPS OF DISCRETELY VALUATIONAL PERFECT FIELD
     离散赋值完满域的乘法群的构造
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     ON THE MULTIPLICATIVE GROUPS OF DIVISION ALGEBRAS OVER DISCRETELY VALUATIONAL PERFECT FIELD.
     关于离散赋值完满域上可除代数的乘法群
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     ON THE STRUCTURE OF MULTIPLICATIVE GROUPS OF DISCRETELY VALUED COMPLETE FIELDS(Ⅱ)
     离散赋值完满域的乘法群的构造(Ⅱ)
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     Multiplicative Groups Used for Coding Three Dimensional Signals
     面向三维信号的非线性纠错码
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     This note discusses the two-cocycles on Sweedler′s 4-dimensional Hopf algebra. The structures of all normal two-cocycles and their convolution-inverses are given by giving the table of values of these two-cocycles on the generators of Sweedler′s 4-dimensional Hopf algebra. The braiding structures and their classification are also given by using convolution and some multiplicative groups.
     讨论 Sweedler四维 Hopf代数上的 2余循环 ,首先通过 2余循环在 Sweedler四维 Hopf代数生成元上的赋值给出所有正规 2余循环及其卷积逆的结构 ,然后利用卷积和某些乘法群给出了 Sweedler四维 Hopf代数上辫子结构及其分类
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  相似匹配句对
     Automorphism Groups of Multiplicative Circulant Networks
     乘积循环网络的自同构群
     Multiplicative Groups Used for Coding Three Dimensional Signals
     面向三维信号的非线性纠错码
短句来源
     On E_q~*-Groups
     关于E_q~*—群
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     FUZZY GROUPS I
     Fuzzy 群 1
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  multiplicative groups
A useful class of systems of topological generators for the additive and multiplicative groups is described.
      
Letdet∝(a) denote the principal minor of order |α|?n of the matrixa ? G (б) corresponding to the indices in α, and let' Φ(б) be the Cartesian product of the multiplicative groups of the quotient rings R/б(α) over all subsets α? I.
      
The problem of the rationality of stably rational tori consists of disentangling the complicatedly knotted linear representations of multiplicative groups of fields.
      
Representations of the Galois group and of multiplicative groups of division rings over local fields
      
The algebraic structure of the infinite sets of labels that represent the "units" has been established: such sets WB are infinite Abelian multiplicative groups with a finite basis.
      
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The following theorem is proved in this paper:Let F* be a multiplicative group of a field F and F* = <α1, …, αn>, then Fis a finite field.

本文主要得到一个定理:若域F的乘群F~·为有限生成:F~·=〈a_1,…,a_3,〉则F为有限域。

The first part of this paper deals with two extreme classes of finite rings of characteristic 2 in their general forms namely,the classes of such rings of order 2~m,the multiplicative groups of the invertible elements which have orders 1 and 2~m-1 respectively M being any given positive integer。For the first case a matrix representation is abtained while it is proved that for the second case it can be reduced to GF (2~m)。of course the rings to be studied are assumed to have identities 1≠0 Owing to the...

The first part of this paper deals with two extreme classes of finite rings of characteristic 2 in their general forms namely,the classes of such rings of order 2~m,the multiplicative groups of the invertible elements which have orders 1 and 2~m-1 respectively M being any given positive integer。For the first case a matrix representation is abtained while it is proved that for the second case it can be reduced to GF (2~m)。of course the rings to be studied are assumed to have identities 1≠0 Owing to the limitation of space,Some lengthy proofs are omitted。

本文的第一部份研究了特征为2的某些2~m 阶的有限环的两种极端情形:其可逆元作成分别为1和2~m-1阶的乘群,其中 m 是任意给定正整数。文中还得到了第一种情形的矩阵表示,证明了第二种情形可化为 GF(2~m)。

In this paper, we prove the following theorem and its corollary.Theorem. Let take the values 0,+l independently, if the integer 9 apart from and if one of following conditions-2) andthen equationhas only the zero solution Xj=0(j=1,n) over the finite field Ft, wherc 1, -, n), the Fp is a multiplicative group of F,.Cor. Under the same conditions as in the theorem, the Diophantine equationhas no Integral solutions apart from xj=0 (j=1, -, n).

本文证明了以下主要结果:对于丢番图方程除开x_j=0(j=1,…,n)外,无其他的整数解,这里p是一个奇素数,满足p=1(mod 3)或p=1(mod 4)

 
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