群的同余关系的几个性质  

SOME PROPERTIES OF THE CONGRUENCE ON A GROUP

作　　者：朱玉山[1] 

机构地区：[1]中国计量学院

出　　处：《哈尔滨师范大学自然科学学报》2006年第3期47-48,77,共3页Natural Science Journal of Harbin Normal University

摘　　要：讨论了一个任意群上的同余关系与这个群的正规子群之间的联系,给出了同余的交集与正规子群交集间的关系,在以上讨论的基础上证明了由群中一个元素对决定的同余关系对应于其中一个元和另一个元的逆元的乘积所生成的正规子群.In this paper, the relations between the congruences and the normal subgroups for a group were discussed. The connection between the intersection of congruences and the intersection of normal subgroups was established. Based on the discussion above, we determined the normal subgroup corresponding to the congruence generated by a pair of elements in a group.

关 键 词：群 同余 正规子群 

分 类 号：O153.1[理学—数学]