ABSTRACT
In Chapter 27 we introduced the idea of group homomorphism. Let’s recall the corresponding development that we followed, after introducing the idea of ring homomorphism. We obtained the Fundamental Isomorphism Theorem for Rings 19.1, which asserts that knowing about homomorphisms is equivalent to knowing about ideals: Each homomorphism gives rise to an ideal (its kernel) and each ideal in turn gives rise to a homomorphism (of which it is the kernel) to a ring of cosets. We would like to emulate this powerful and useful theory in the theory of groups, so that we can better understand group homomorphisms. This will be the goal of the next three chapters.
