So I forgot to post on the first part of section 7.6... but here is the second stuff
Difficult: For me, the most difficult thing about normal subgroups is just realizing that aN=Na, not that an=na. The It is hard for me to realize that the sets just have to be equal, not that every element has to commute. Another thing that I find difficult is just being able to find whether aNa^(-1) is a subset of N. I just have a hard time remembering how to find if something is a subset... its just something that I need to review.
Connections: Theorem 7.33 is similar to most of the congruence theorems that we have seen this semester about multiplying two things that are congruent modulo something. However, this one is a little different because the two things are congruent modulo a normal subgroup. This one seems to have a little bit more of a restriction. I also noticed that there wasn't a theorem for adding two things that are congruent modulo a normal subgroup. Is this not allowed?
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