群的同态及意义

本文在群同态定义的基础上,整理和深入研究了群同态的诸多性质及群同态的基本定理,特别是它的意义.它是研究群与群之间关系的有利工具,根据我们可知一定可以找到G一个不变子群K,使得的性质和商群G/K的完全一样.且我们可以利用同构这一有利工具将抽象群的问题具体化.

This article in the group homomorphism definition foundation,the rerganization and has thoroughly studied group homomorphism many nature and the group homomorphism foundamental therems,specially its signifcance.It studies the advantageous tool which between the group and the group relates,we may know according to the theorem certainly may find G mormal divisor K,cases naturequotient group G/K is completely same.Also we mingt abstract the group using iaomrphism this advantageous tool the question concrete applicatio