1. The problem statement, all variables and given/known data Let G be an abelian group and let x, y be elements in G. Suppose that x and y are of finite order. Show that xy is of finite order and that, in fact, o(xy) divides o(x)o(y). Assume in addition that (o(x),(o(y)) = 1. Prove that o(xy) = o(x)o(y). 3. The attempt at a solution I was able to prove the first part, that xy is of finite order and that o(xy) divides o(x)o(y). I'm having trouble with the second part, proving that o(xy) = o(x)o(y) if the greatest common factor of o(x) and o(y) is 1.