ABSTRACT
Section V in a Nutshell This section starts by considering group homomorphisms, by way of analogy with ring homomorphisms: A function between groups ϕ : G → S is a group homomorphism if ϕ(gh) = ϕ(g)ϕ(h) for every g, h ∈ G. A group homomorphism preserves the group identity and inverses, the image of G is a subgroup of S, and if G is abelian then so is ϕ(G) (Theorems 22.1 and 22.2). If ϕ is a bijection, then we say ϕ is an isomorphism, in which case ker(ϕ) = 1G.
