1. The problem statement, all variables and given/known data I got this question from contemporary abstract algebra : http://gyazo.com/7a9e3f0603d1c0dcfde256e7b05276cd 2. Relevant equations One step subgroup test : 1. Find my defining property. 2. Show that my potential subgroup is non-empty. 3. Assume that we have some a and b in our potential subgroup. 4. Prove that ab-1 is in our potential subgroup. 3. The attempt at a solution 1. Defining property : xh = hx for x in G and for all h in H. 2. C(H) ≠ ∅ because the identity element e is in C(H) and satisfies xe = ex. 3. Suppose a and b are in C(H), then xa = ax and xb = bx. 4. Show that ab-1 is in H whenever a and b are in H. So we want : xab-1 = ab-1x Start with : xa = ax x(ab-1) = (ax)b-1 x(ab-1) = (xa)b-1 x(ab-1) = x(ab-1) x(ab-1) = (ab-1)x I know this is probably horribly wrong, but for some reason I can't seem to see how to do this properly. Any help would be appreciated.