1) Abelian(multiplicative)group
Abel(乘法)群
2) Abel group
Abel群
1.
A discussion on the constitution of an Abel group by the collection of n step cyclic matrix
关于n阶循环矩阵成Abel群的讨论
2.
In this paper,a new characteristic of a infinite Abel group with finite generators,and a new proof of the finite Abel group theorem were given.
Serre利用群的特征标理论给出了有限群是Abel群的一个充要条件,该文利用群的表示理论给出了无限群是有限生成Abel群的一个新刻划,且对Serre关于有限Abel群的定理给出了一个新的证明。
3.
IfΦ(G)=1, the Sylow-q subgroup of G is a regular, elementary Abel group, and a Sylow-p subgroup circulation, furthermore qb = 1 (modp).
本文对“只有两个极大子群共轭类的群的素因子个数≤2”这一结论,作了进一步的讨论,使其结果进一步深化,从而得出以下结论:只有两个极大子群共轭类的非Abel群,若Φ(G)=1,则G的Sylow-q子群为正规的初等Abel群,Sylow-P子群循环,且q~b≡1(modp)。
3) Abelian group
Abel群
1.
This paper discusses the structures of Abelian group G by oder |A(G)| of automorphism group.
利用有限Abel群G的自同构群A(G)的阶来刻划群G的构造,用一种巧妙的方法,推导出了|A(G)|=24P2(P为奇素数)的有限Abel群G的全部类型,并给出了详细的推导。
2.
The adjoint algebras of an Abelian group are studied, and it is pointed out that all adjoint algebras of an Abelian group are automorphic.
研究了Abel群的伴随代数,指出了一个Abel群的所有伴随代数都是自同构的,同时给出了广义结合BCI-代数的一个重要性质。
3.
Let the arithmetic function a(n) denote the number of non-isomorphic Abelian groups oforder n.
用算术函数a(n)表示n阶非同构Abel群的个数,令A_k(x)=sum from n≤x u(n)=k (1),A_k(x;h)=A_k(x+h)-A_k(x)。
4) multiplicative semigroup
乘法半群
1.
By a system of linear equations on multiplicative semigroup,we present a general mathematical method to solve the inverse lattice problems in physics.
用乘法半群上的线性方程组来求解晶体原子间对势反演的逆问题。
2.
In this paper, it is proved that if n≥2 and R is an effective semiring or a semiring in which all idempotents are central elements, then Φ:Tn(R)→Tn(R) is a multiplicative semigroup automorphism if and only if there exist a invertible G∈Tn(R) and a semiring automorphism τ of R such that Φ(A)=G-1τ(A)G for all A=(aij)n×n inTn(R).
证明了当R是一个幂等元都是中心元的半环时,映射Φ:Tn(R)→Tn(R)是乘法半群自同构当且仅当存在Tn(R)中的可逆矩阵G和R中的半环自同构τ使得A=(aij)n×n∈Tn(R),均有Φ(A)=G-1τ(A)G。
5) inner-Abel group
内-Abel群
1.
In this paper we have mainly proved that groups,when they have only one conjugate class of non-subnormal subgroups and the length of the conjugate class is finite,are non-nilpotent finite inner-Abel groups, and discusses the properties of the groups when the length of the conjugate class is infinite.
主要证明了仅含一个非次正规子群共轭类且此共轭类长有限的群G为非幂零的有限内-Abel群,并讨论了当此共轭类长无限时的一些群的性质。
6) finite Abel group
有限Abel群
1.
The balanced characteristics of finite Abel group is discussed, and the problems of the balanced characteristics of P—group of cycles are solved, which have not only aesthetic feeling of mathematics in form, but also some prospects for applications.
提出并讨论了有限Abel群的均衡性问题 ,并解决了P—循环群群的均衡性问题 ,得到了几个有用的结果 ,为讨论Abel的群的结果构奠出一定的基础 。
2.
If the type of deduction group G of the known automorphism group is complex,reviews of the study in finite Abel group can be made in three stages,thus providing the development process in this field.
文章对有限Abel群在该方面的研究分三阶段进行综述,提供了该领域研究的发展过程。
补充资料：乘法群
乘法群
multiplicative group
乘法群[md石函口触，，，;M拯mn~皿明印y-皿a]，除环上的 给定除环(skew一倪记)中除零元外的所有元素在该除环的乘法运算下形成的群.域的乘法群是Abel群. 0 .A.玩a肋a撰【补注】带有限非零特征的除环的有限乘法子群是循环群，特征零的情况则不然.只有有限多偶数阶群，却有无限多奇数阶群，后者的极小阶是63.分类已在【AI]中给出.在证明一类Tits二择一性(Ti招司t肛na-tive)时，有类似的问题:除环的乘法群的任一有限正规子群含一自由非循环群或为一有限可解群且有一到除环上的线性群的扩张.某些情况是已知的，例如【A2].
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条