Please oh please help me finish this
1,000,000 < 2^20
Know that until you have a generating set, you can show that you keep adding elements so the prodcuts of each subset are different.
Prove by induction that you can generate any group of at most 2^k elements w/ k generators. Assume that you ahve a group G w/ a subgroup H, generated by k elements.
If g is an element of G not in H, the subgroup generated by the generators of H and g contains all the products gh for all h in H.
Try to prove all elements are distinct, and none exist in H. THis means that starting w/ a subgroup H generated by k elements you can add a generator and get a subgroup twice (at least) as large as H.
Your help will be GREATLY appreciated, thank you.