7.6 part 2

1. Not much of this was difficult, especially since we went over some of it in class.  The hardest part was probably following the proof of the interconnecting parts of Theorem 7.34.

2. It's interesting to me that even though Na = aN does not imply that na = an, that doesn't end up mattering for quotient groups.  Having the entire subgroup commute ends up being enough.