子群陪集与群同态基本定理的一种几何模型

A GEOMETRIC MODEL OF SUBGROUP COSET AND FUNDAMENTAL THEOREM OF GROUP HOMOMORPHISMS

本文研究了子群、群同态基本定理的几何意义.利用二、三维几何空间图形,得到了子群陪集、不变子群对群的分类、商群、同态满射和群同态基本定理的几何模型,为认识上述抽象的代数内容提供了直观的几何解释,同时也给出了其几何表示.

In this article,we study the geometric meanings of subgroup coset,normal subgroup,quotient group and the fundamental theorem of group homomorphisms.By using the two-and three-dimensional geometric space graphics,we obtain the geometric models of subgroup coset,normal subgroup,quotient group and the fundamental theorem of group homomorphisms,which provide us the intuitive geometry interpretation for the abstract algebra and also recuperate a geometric representation for the above mentioned abstract algebra.