1. The problem statement, all variables and given/known data I have attached the problem below. 2. Relevant equations 3. The attempt at a solution I have tried to use the natural epimorphism from G x G x ... x G to (G x G x ... x G)/(K1 x K2 x ... x Kn), but I do not believe that this is an injective function. Then I tried to use a function f from G to (G/K1) x (G/K2) x ... x (G/Kn) defined by f(g) = (k1g, k2g, ..., kng) for all g in G. I found that this function was injective (and a homomorphism) but not surjective. I've also been trying to find a way to use the first isomorphism theorem, but with no luck. Any hints would be greatly appreciated!