Difficult: As I was reading in this section, I got a little lost in the proof of 7.52 where it says that N is a normal subgroup of An. What does this subgroup look like? I think that it is just a some of the elements of Sn. So is it just a set of different cycles of An? I think I am also having a hard time figuring out what An looks like. How many elements are there? Is there a way to find this out by having a certain length of a cycle or knowing what symmetric group you are working in? Also, the proof of 7.52 is so long that I just got way lost in all of the notation and didn’t really understand what was going on.
Connections: Now that I feel like I better understand the new notation with symmetric groups, I feel like I can understand the notation used in the proofs involving cycles. I like that the cycles are pretty easy to compute the “multiplication” of them. I think that knowing this information helps me be able to follow the composition of the cycles when it is done in the proofs.
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