7.7

1. What was the hardest part of the reading for you?
Oh man, I hate to be a Negative Nancy here, but this is where I started to get lost and feel frustrated when talking about rings and quotient rings and yadda yadda. I feel nervous about going into this chapter and what it'll do for the rest of the semester. The part that was difficult for me was the part that talked about the structure of the groups. For example, Theorem 3.37 kind of lost me, along with 7.38. I don't like that they changed notation of the center of the group during the proof -- who just does that?!? and I really just didn't follow that proof very well.

2. Why the confusion?
This was the question I asked myself at the very beginning of this section. The first thing this chapter says is, "Let N be a normal subgroup of a group G. Then G/N denotes the set of all right cosets of N in G." Okay, my question is this: Why state that N is a NORMAL subgroup then make a notation for the right cosets? Why can't G/N just be notation for the normal cosets? Is there going to be a different notation for left cosets? I just don't really understand this part of it. I know that if N is normal to G then the right and left cosets of N will be the same, but why make the distinction here when talking about a normal set? That is what I would like to know.