1. The multiplicative notation for cosets will take a bit of getting used to, since cosets in rings and vector spaces use addition as the operation. The fact that right cosets aren't necessarily left cosets is also new, although it makes sense given that our operation may not be commutative.
2. I thought Lagrange's Theorem was quite interesting. It's the kind of result that isn't intuitive without looking at examples. This theorem will definitely make it easier to classify finite groups, especially with Corollary 7.27.
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