1. One question that I had was the example on page 184 - it says that the multiplicative group of units in the ring Z(15) is U(15)={1,2,4,7,8,11,13,14} by Theorem 2.11, but I don't see how this theorem would prove this. Then it says that 7 has order 4 in U(15) but they only checked 4 of them - or is that just part of the construction?
2. It seems like there are SO many more applications in groups than there where in rings! I hope I can remember them all, because there are a lot. One that I found interesting was the center of a group - it commutes with all other elements like how the identity element does.
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