The hardest part of this material for me was understanding Theorem 7.17. I don't quite understand what is going on with the subgroup generated by S. I was also wondering in regards to the example under Theorem 7.13, why every unit mulitiplied by another unit must be a unit. It seems to make sense, I am just not connecting why this must be true.
The most interesting part of this section was the center. I found this interesting and was wondering if the center of a group is sort of like an ideal of a ring. They seem similar and so I was wondering if they are related in any way.
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