Group Homomorphism and Abelian Groups
Let phi: G ---> H be a group homomorphism. Show that phi[G] is abelian if and only if for all x, y in G, we have xyx^(-1)y^(-1) in ker(phi).
proving (=>) seems almost obvious since if it is abelian that means xyx^(-1)y^(-1) = xx^(-1)yy^(-1)=ee which is in the kernel, but I'm not sure about how to do the reverse (<=) and show that phi is abelian?