1. Although there were lots of proofs and lemmas in the section to go through and understand, the hardest one to grasp was theorem 8.7 - the fundamental theorem of finite abelian groups. It makes me think that this theorem is most important because its name is the "fundamental theorem." However, I think it is really confusing that it is so important and fundamental to know about finite abelian groups that they are direct sums of cyclic groups, each of prime power order. Why is this so important? And why do we care? I do not understand.
2. The most interesting part of this section was that there was sooo many different proofs and properties for finite abelian groups. I would have never thought they were so important or unique in the sense that they have all these special theorems that people have discovered, studied, and now teach to anyone in abstract algebra. It is pretty cool.
No comments:
Post a Comment