The most difficult part of this material for me was trying to understand the proof of Cayley's Theorem. Also, I didn't really understand the second example of the section. I also don't remember what it means when they put two stars next to R, and whether that is just to denote something or if it is supposed to mean a certain something.
The most interesting part of this section for me was trying to figure out how isomorphisms of groups could be applied to the real world and if this is even a possibility. I was also wondering if certain things are preserved in a group isomorphism. Also, what is the difference between an isomorphism of rings and groups in a visual sense. Does it just sort of copy something more general whereas in the case of rings it is a copy of something more detailed? Or is the actual isomorphism different when dealing with rings?
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