Difficult:
As I read section 8.4, I had difficulty distinguishing between C and C(a). I know that C(a) is the centralizer of a. But then they used C in place of C(a) and then they used it as the representation of the conjugacy class and I got a little confused. Also, with how intricate all of the details are becoming about all the theorems and what we can and cannot say about any given group, it is difficult for me to really understand the why behind all of the theorems, especially those in 8.5, because to me many of them seem somewhat trivial. It seems random, even though I know it is not. I know that there are a lot of good reasons why someone discovered these theorems but, like I said, a couple of more examples would be quite help.
Reflective:
It is a sad thought, but I think I am just now starting to really appreciate abstract algebra better. It really is a fine, and complicated art. What is so funny about it is that there are times when the book seems to be making things so very simple and easy. And then all of a sudden it comes to a theorem and its proof and all simplicity gets thrown out the window at times. I just hope that I can study enough so that I can look at the final from the simplest view possible rather than trying to cram everything in and only make it unnecessarily complicated for myself.
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