For the most part I followed this section well. The most confusing parts were parts 3 and 4 of theorem 7.8 and their proofs, and the proof of corollary 7.9. I understood what corollary 7.9 was saying but I couldn't follow the proof (probably because I didn't the references of how to use theorem 7.8 part 4.
I was glad we had already spent a few minutes of class discussing the order of an element because I don't know that I would have understood the discussion without having already gone through some examples. I'm curious to know how order plays a role in groups. Like it was mentioned in class, we will be using it probably in conjunction with isomorphism between groups. Because of theorem 7.8 part 3 where a^i=a^j iff i is congruent to j mod n, I'm wondering if we'll be making congruence classes in groups and using those in different ways. I can see how this chapter could go from relatively easy to understand to completely abstract relatively quickly.
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