1) I guess I don't why we look at an automorphism in groups but not rings. Is it because an automorphism in rings is just trivial? I also don't totally understand Cayley's Theorem. What does it mean for a group G to be isomorphic to a group of permutations? I don't see how that can be true if the cardinalities are different?
2) Other than that everything is pretty straightforward - it is cool to see the parallels and differences between groups and rings, and it is easier to understand the proofs and ideas since we started with rings. I wonder how it would be different if we did groups before rings.
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