8.1, Due April 6th

• Difficult: I was confused by Theorem 8.1. When it says N_1, N_2 ..., N_k, does it mean that those are ALL of the normal subgroups of G, or can it be any number of normal subgroups of G? Or does that second part of the proof say it doesn't matter how many normal subgroups there are so long as ever element is covered? It wasn't clear. Also, because I didn't understand Theorem 8.1, I don't understand why Lemma 8.2 is important.
• Reflective: A lot of this was pretty straight forward. In fact, i wasn't really sure what we were supposed to find in this section that was NEW. It seemed like it was just showing you how to take cartesian products of groups, and isn't that what we've already been doing?