1. As far as I could tell to check and see if a subgroup of a group is normal, you just take each element of the group and 'multiply' it on the right and left side of each element in the subgroup and see if you get the same thing. I think this is wrong though - if Na=aN, then this means na is an element of Na AND aN, not that na=an. I'll have to remember that...
2. I liked the proof of Theorem 7.33. I think the theorem will be useful in proving other things too, such as possibly with quotient rings in the next section. I think I am going to have to spend a little more time on Theorem 7.34 though, it was long but I am sure very powerful! :)
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