循环群

When G is a finite abelian group, the abelian group K_1, iscalculated completely mainly using the Bass-Milnor-Serre theorem, then the structure of K_1{ZG,|G|г is clear.

K_1。 3。利用Bass-Milnor-Serre定理，我们首先计算出了G是一个有限交换群时的K_1，也就计算出了(来源：e2ABC论文网www.abclunwen.com)K_1；当G是2阶和3阶循环群时，我们计算出了K_2=1，这个结果有待于继续推广，对于计算一些环的K_2群会有所帮助。

It is prove that groups of order p2 can be divided into two kinds in the isomorphism sense:(1) cycle group ;(2)commutative group which can be written as a product of two cycle proper-subgroup of order p.

证明了在同构意义下p2阶群共有两类：一类是循环群，一类是可分解为两个p阶真循环子群乘积的可换群。

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。

This article proves that a finite cyclic group can be isomorphically represented by direct product of some cyclic groups.

摘要本文运用基础代数中有关循环群、直积、同构等理论，证明了一个循环群可以用另一组循环群的直积形式来同构表示。

Metacyclic group, which is the expansion of a cyclic group by a cyclic group, is a special group generated by two elements.

亚循环群，即循环群被循环群的扩张，是特殊的二元生成群，Otto Hlder曾研究并给出了有限亚循环群的构造；G。

The cyclic group of order 3, above, and {1,-1} under ordinary multiplication, also above, are both examples of abelian groups, and inspection of the symmetry of their Cayley tables verifies this.

上述的 3 阶的循环群和{1，-1}在普通乘法下的群都是阿贝尔群，可以通过检查其凯莱表的对称性来验证。

In Chapter 3, by using the technique of finite dimensional approximation of Seiberg-Wittentheory, the equivariant K-theory and some other methods, we study the problem of topologicalrestriction when there are smooth groups acting on Spin 4-manifolds such as the alternatinggroup A_5, cyclic group Z_6 and symmetric group S_3 with actions of odd type, consequently weimprove Furutas 10/8 theorem under the condition of group actions.

第三章运用Seiberg-Witten理论的有限维逼近技巧和等变K-理论等工具，研究了Spin 4-流形X上分别存在光滑交错群A_5、循环群Z_6和奇型三阶对称群S_3作用时，X的拓扑限制问题，在群作用下改进了Furuta的10／8定理。

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。

Metacyclic group, which is the expansion of a cyclic group by a cyclic group, is a special group generated by two elements.

亚循环群，即循环群被循环群的扩张，是特殊的二元生成群，Otto H？

Pazderski once proved the conditions which the order of metacyclic group have; And many domestic group-researchers such as, Xu Minyao , Fan Yun , Huang Ping-an Chen Guiyun ,etc, all of them had done much useful researc...

Pazderski曾证明了有限群G恒为亚循环群时G之阶|G|所具备的条件；徐明曜、樊恽、黄平安、陈贵云等国内群论学者，也都先后对亚循环群的各类性质做过研究，得到了许多具有重要价值的结论。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失