8.1, due April 6

One thing that confused me in this section came when they defined the coordinatewise operation on the Cartesian product G1xG2x....xGn.  I expected it to be an ordered pair with n entries.  Instead it was like to cycles each with n elements composed together.  I thought the with M={0, 3}, N={0, 2, 4}, and Z_6 was EXTREMELY fascinating!  Things weren't as awesome after that (How could you top something that cool?) and I think there's a typo in the last example.  They claim that M={1, 11} has cyclic order 4 and N={1, 2, 4, 8} has cyclic order 2.  I'm pretty sure that's supposed to be the other way around.