The document discusses the relationship between the orders of elements in subgroups H and K if their direct product is equal to the group G. It shows that if G = HK, where every element g in G can be uniquely expressed as g = hk for h in H and k in K, then the orders of h, k, and g are related. Specifically, if g = hk then the order of g is the product of the orders of h and k.