My mind was overwhelmed with this section. It was interesting but I'm not sure what I read. I was really confused by the proof of theorem 8.1. In fact I had no idea what was going on to prove that f is a homomorphism. I would also like to go over the general idea on which the whole section is based which is writing the elements of a group as sums or products of elements of two subgroups. I don't really understand why that works.
I think it is interesting to look at the problem of what a group is isomorphic to by crossing some of its normal subgroups. How do we know which normal subgroups to use? Is it based on the size of the subgroup or is it trial and error?
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