Section 7.6, due on November 10

The most difficult part of this material for me was following the all of the details that come along with Theorem 7.4. It was more difficult for me to understand in general why aN=N does not means that an=n for each n in N but rather that an=n1 for some n1 in N. The differences between these statements are a little confusing to me (ie. top of page 213).

The most interesting part of this material for me was the concept of a normal subgroup and how it is analagous to an ideal. It also made me wonder if it is at all related to a normal vector that we study in multivariable calculus and linear algebra. It is interesting, but still a little confusing, that normal subgroups aren't necessarily made up of elements that commute with all other elements of the group.