1. The problem statement, all variables and given/known data Let G be an abelian group of order n, and let k be an nonnegative integer. If k is relatively prime to n, show that the subgroup generated by a is equal to the subgroup generated by ak 2. Relevant equations 3. The attempt at a solution I'm not sure where to start. I know that we are equating two sets, so I think that I need to show that one is a subset of the other and vice versa, but I can't see where to use the fact that G is abelian and that k is relatively prime to n.