Final review questions, due on April 13

Questions: Could we do some examples of quotient rings and and Sylow stuff? Like your question 1 on the midterms kind of stuff. I'd really like to work Sylow stuff more. Doing related proofs (like number 5 on midterm 2) about rings and groups would be good too.

8.5, due on April 10

Difficult: I don't know how important class equations are, but if they are quite important could you explain them a bit in class? There were 2 lines I didn't understand in the proof of Thm 8.33.

Reflective: It's kinda nice that the book computes symmetry groups with just r and d like we've been doing in class anyway.

8.4, due on April 8

Difficult: I didn't completly understand Theorem 8.21 or the proofs of the 2nd and 3rd Sylow theorems.

Reflective: Conjugacy reminds me of similar matrices in linear algebra. Could we do more examples of those in class?

8.3, due on April 6

Difficult: So everything in this section makes sense. The problem isn't that the concepts are difficult, it's that there are so many of them. It's hard to commit it all to memory (for the test) and get an overall idea of what is going on.

Reflective: Again the concepts by themselves make sense, but could you do and example or two (like those in the book) that give an overarching idea of what is going on. The more examples, the better.

8.2, due on April 3

Difficult: So I hope we don't have to reprove the theorems, because I really didn't understand most of the proofs, but I think I got what the theorems were saying.

Reflective: So basically finite abelian groups are direct sums of cyclic groups and each has a unique set of elementary divisors. Two finite abelian groups are only isomorphic if they have the same elementary diviors. Right?

8.1, due on April 1

Difficult: So this section wasn't too bad. I would just like to see some more examples of groups that are direct products of some normal subgroups and go throught the material again.

Reflective: This makes groups seem more like numbers since they have factors. It would be kind of like the number 12 is a direct product of 1,2,3,4,6,12 where 1,2,3,4,6,12 are all normal subgroups. But it is a little different.

7.10, due on March 30

Difficult: So how in the proof for thm 7.52 does it come up with the cases, why doesn't 4 work, and where did it use Lemma 7.53?And in Cor 7.55, how does that proof go? This is tricky stuff!

Reflective: So A(sub)n is usually simple. I guess that is important so it is isomorphic to the integers mod p.