Let G be a group. ACG to be we have defined the centralizer of a subset C(A) = {G| for every y A, ry = yr} the set of group elements that commute with every element of A. We have seen that C(A) is a subgroup of G. Let's define for two subsets A. BCG: AB= (ab a A and be B). So AB is the set of all group elements that can be obtained by picking a member a of A, a member b of B, and multiplying them (using G's group operation). Now suppose HSG is a subgroup of G. Your problem is to show that HC(H)