1. The problem statement, all variables and given/known data If H and K are subgroups of G, show HUK is a subgroup of G if and only if H < K or K < H ( the < meaning that all the elements of H are in K or all the elements of K are in H). 2. Relevant equations None 3. The attempt at a solution I believe the problem here is HUK might not be a closed group. Certainly all the elements of HUK are also in G. If all the elements of H are in K, then hk is an element of HUK for all h,k. If the intersection of H and K does not equal H or K, that means that hk may not be in HUK as it is not closed. These are my thoughts so far. Am I on the right track here? How do I start turning this into a proof?