1. I think the hardest part for me is still getting used to the multiplicative notation for cosets. I'm sure it will come more naturally after I've done some homework on it.
2. I think it's interesting that the lack of commutativity is what makes quotient groups difficult to define, but that we don't actually need commutativity for each pair of elements in the group to make them work, only for the left and right congruence classes.
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