商群

Group, Subgoup, Permutation Group, Cyclic Group, Commutative Group, Normal Subgroup, Factor Group, Isomorphism, Ring, Ideal, Field, Polynomial Ring, Factor Ring.

课程内容：群，子群，置换群，循环群，交换群，正规子群，商群，群之同构，环，理想，体，多项式环，商环等。

Subgroup, Factor Group, Isomorphism, Ring, Ideal, Field, Polynomial Ring, Factor

课程内容：群，子群，置换群，循环群，交换群，正规子群，商群，群之同构，环，理想，体，多项式环，商环等。

In this chapter, firstly, the definition of rough semigroups is given afresh. Then based on rough groups, rough subgroups, rough cosets, rough invariant subgroups, some properties of rough subgroups and rough invariant subgroups and the concept of rough quotient groups are introduced. Finally, based on some concepts of homomorphism and isomorphism of rough groups, basic homomorphism theorem and isomorphism theorem of rough groups are put forward and proved.

在这一章中，首先重新给出了粗糙半群的定义，其次在粗糙群、粗糙子群、粗糙陪集、粗糙不变子群的基础上，给出了粗糙子群的若干性质、粗糙不变子群的三个重要性质和粗糙商群的定义，最后在粗糙群同态与同构的基础上，给出了粗糙群同态基本定理与同构定理。

In this part, we will study some basic and important concepts such as semi-group, group, isomorphism, homomorphism, subgroup, invariant subgroup, factor group, and transformation group.

本部分考虑的主要概念有半群、群、同构、同态、子群、不变子群、商群以及变换群等。

And a way to find the elements ofthat are conjugate to is proposed. Then we prove that the quotient group is isomorphic to, the symmetric group of order , and is a semidirect product group of with the classical binary simplex code in the linear case. Finally, we generalize a result due to Calderbank et al..

本文刻画了商群与集合的关系，给出了一个确定集合中那些与共轭的元素的方法，还证明了在线性情形下，商群与阶对称群是同构的，而且是与经典单形码的一个半直积，并且推关广了Calderbank等人的一个结果。

In addition, the concept of generalized fuzzy quotient group is introduced and the correspondence theorems of generalized fuzzy quotient groups and fuzzy quotient subgroups are obtained respectively under group homomorphism.

另外，我们引入广义模糊商群概念，建立了环同态下广义模糊商群的对应定理及模糊商子群的对应定理。

We consider Theorem 1 to be highly significant and apply it to obtaining the rank of a certain augmentation quotient group by proposing Theorem 3 and giving its complete proof.

应用具有Np-序列有限p-群的特殊性质和重量函数，基本序列等概念以及已有的一些结果，分别研究了类为1的pk(k 2)阶A bel基本p-群和类为2的p4阶基本p-群之增广商群Qn的结构，得到了当n足够大时Qn作为A bel基本p-群的秩。

In this dissertation, a theorem to describe the relationship between the quotient group Aut/H and the set F_f is presented. And a way to find the elements of F_f that are conjugate to f is proposed. Then we prove that the quotient group Aut/H is isomorphic to S_3, the symmetric group of order 3, and H is a semidirect product group of GL_(m/2)(4) with the classical binary simplex code S_m in the linear case.

本文刻画了商群Aut／H与集合F_f的关系，给出了一个确定集合F_f中那些与f共轭的元素的方法，还证明了在线性情形下，商群Aut／H与3阶对称群S_3是同构的，而且H是GL_(m/2)(4)与经典单形码S_m的一个半直积，并且推关广了Calderbank等人的一个结果。

Let G be a finite group, ZG its integral group ring and Δ~n the nth power of the augmentation ideal Δ, denote Q_n=Δ~n/Δ~ n+1 the augmentation quotient group s of G.

对任意有限群G的整群环ZG，设Δn是ZG的n次增广理想，记Qn=Δn/Δn+1为G的增广商群。

On the other hand, a is invariant in G/N if χ is viewed as a character of G/N for normal subgroup N≤kerχ.

另外，我们定义的特征标次数的商a与我们将χ看成那个商群G／N无关。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。