commutator subgroup

We investigate the commutator subgroup of a convergence group,and obtain the relationship between the elementariness of a convergence group and the cardinal number of the fixed point set of its commutator subgroup.

讨论了收敛群的换位子群 ,建立了收敛群的初等性与它的换位子群的不动点集的基数之间的联系 。

Denote by G the commutator subgroup of G .

证明了如下结果：设Ｇ是有限群，｜Ｇ｜＝ｐｑｒ，ｐ、ｑ、ｒ为素数，ｐ＜ｑ＜ｒ，Ｇ是Ｇ的换位子群，｜Ｇ｜＝ｑｒ。

On the basis of giving the generators of special linear group SL(n,Zpr),we get the commutator subgroup of GL(n,Zm),by using the Euler′s theorem and the method created by Professor Loo Keng Hua when he investigated the general linear group over division ring.

研究了环Zm上的一类线性群GL(n,Zm),在给出特殊线性群SL(n,Zpr)生成元的基础上,利用欧拉定理和华罗康在研究体上线性群时所创造的方法,得到了GL(n,Zm)的换位子群,该结果进一步加深了对线性群GL(n,Zm)的认识。

In this paper we discusses the concept of weak commutator subgroup, consider the fundamental properties of weak commutator subgroup, and get the result which weak commutator subgroup is exactly the minimal normal subgroup of normal subgroups with their quotients being nilpotent groups, and so on.

本文给出了弱换位子群的概念，讨论了弱换位子群的性质（性质１－６），得到了弱换位子群恰为使群的商群为幂零群的正规子群之极小者等结

We obtain a few of properties from definition of n-metacyclic commutative subgroup.

从n-反换位子群的定义出发,得到了它的几条重要性质。