非交换群

Group is an important concept in Modem Algebra. Viewed from a different angle it may be divided into two different categories: finite group and infinite group; and Abelian group and non-Abelian group.

群是《近世代数》的一个重要概念，从不同的角度出发，群可以分为有限群和无限群两大类，又可以分为交换群和非交换群两大类。

Suppose G is a finite group, then QG is a semisimple Q-algera, obviously ZG is a Z-order of QG,we denote the maximal Z-order by ?.If G is not abelian, it is not an easy thing to determine г; if G is an abelian group, then QG is isomorphic to the direct sum of a finite number of number fields, and r is the direct sum of these rings of algebraic integers of those number fields, but which elements of QG belong to r is not clear.

设G是一个有限群，那么QG是一个半单代数，ZG是QG的一个Z-序，设Γ是QG的一个极大Z-序，当G是一个非交换群时，Γ的求解是困难的问题；当G是一个交换群时，QG同构于有限多个数域的直和，Γ相应的就是各数域代数整数环的直和，但Γ具体是QG中那些元素不清楚。

In particular, when thereis an alternating group A_5 action on a Spin 4-manifold X, we obtain: If X is smooth Spin4-manifold with non-positive signature and b_1=0, denote k=-σ/16 and m=b_2~+,then 2k+3≤m if b_2~++b_2~+≠2b_2~+(Z/A_5) and b_2~+≠0,where and are subgroups of A_5 generated by the elements s=∈A_5and t=∈A_5 respectively.

特别地，在Spin 4-流形具有非交换群A_5作用时，我们得到了：若X为光滑的具有非正符号差的Spin 4-流形，b_1=0，令k=-σ／16，m=b_2~+，如果X上具有Spin交错群A_5作用，且满足b_2~++b_2~+≠2b_2~+(X／A_5)，b_2~+≠0，则2k+3≤m，其中和分别为s=∈A_5和t=∈A_5生成的A_5的子群。

The braid group is infinite non-commutative group, and it has many hard problems that can be utilized to design cryptographic primitives, such as the word problem, conjugacy problem and root problem.

辫群是一种非交换的无限群，该群中有许多困难问题是不可解的，如字问题、共轭问题和根问题等，利用这些困难问题可以去设计一些密码协议。

We establish a relation between μ and the stucture of the group G, and obtain the lower bound of the ratio by the mininal prime divisor of the order and commutator of the group G, and give a necessary and sufficient condition under which this lower bound is attained.

第一部分，记有限群G的阶与不可约特征标个数的比值为μ，我们研究了一般的非交换有限群G的结构和μ之间的关系，通过群G的阶的最小素因子和换位子群G′的最小素因子得到了μ的一个下界，同时给出了达到下界的一个充分必要条件。

In this paper, we investigate some basic properties of the noncommuting graph associated with a finite group and their effects on the structure of the group.

本文主要研究了有限群的非交换图的一些基本性质及其对群结构的影响。

We anew confirm every generated relation of non-commutative group of 16 orders by using Hlder, O.

通过群的同构分类的观点，分析了16阶非交换群的生成关系，并使用霍尔德定理、N/C定理及元素阶的分析，重新确定了16阶非交换群的生成关系。

Although the quantum double of a finite Clifford monoid is indeed a generalization of the quantum double of a finite group, the quantum doubles in [L2] can not usually be regarded as

作为特殊情况，非交换的半格分次弱Hopf代数的量子偶同样可以构造出来。作为群和非交换非余交换Hopf代数的量子偶的构

Its main goal is to explore information in the K-theory groups of the index C*-algebras, the Roe algebras C*, by using the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other relating problems, say, the Novikov conjecture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature, the idempotent problem in the theory of C*-algebras.

粗几何上的指标理论是"非交换几何"领域九十年代以来发展起来的重要研究方向，它孕育于非紧流形上的指标理论，其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）的大尺度几何结构探索指标代数，即 Roe代数，的K-理论群的信息，从而建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Gromov-Lawson-Rosenberg正标量曲率猜测、群C*-代数幂等元问题等。

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，。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。