1. The problem statement, all variables and given/known data For any integer K, the map ø_k: Z → Z given by ø_k(n) = kn is a homomorpism. Verify this 2. Relevant equations if ø(gh) = ø(g)ø(h) for all g,h in G then the map ø: G → H is a group homomorpism 3. The attempt at a solution So I have barely any linear algebra so many taking this summer course wasn't the best idea, but I have PF so i'm good. So... if ø(xy) = ø(x)ø(y) for all x,y in Z then the map ø: Z → Z is a group homomorphism. ø_k(x) = kx and ø_k(y) = ky but then ø(xy) = kxy and ø(x)ø(y) = (xy)k^2 i'm new to this type of thinking, can anyone help me out here?