Section 8.1, Due Monday, April 2

The section for today was 8.2: Finite Abelian Groups.

This section was very complicated. The hardest part to follow was the proof of Lemma 8.6.

I thought that Lemma 8.8 was interesting. We used on the very first test, and now it's proof is understandable because we have learned so much since then.

Section 8.1, Due Friday, March 30

The section for today was 8.1: Direct Products.

The most difficult part for me was in the proof of Theorem 8.1 when they showed that f was a homomorphism.

I thought that it was an interesting section. The fact that you can create an internal direct product, made up of normal subgroups, that is isomorphic to the original group, is pretty neat.

Section 7.10, Due Wednesday, March 28

The section for today was 7.10: The Simplicity of An.

This section was pretty abstract. I thought that the proof of Theorem 7.52 was the most difficult to understand.

I think that the fact that was revealed at the end was the most interesting. It stated that If n>=5, then (1), An, and Sn are the only normal subgroups of Sn.

Section 7.9, Due Monday, March 26

The section for today was 7.9: The Symmetric and Alternating Groups.

This section was kind of confusing. I think that most difficult part was the proof of Lemma 7.49. The whole concept about even/odd is pretty abstract.

I thought that the cycles were pretty cool and that the notation was fun and interesting.

Section 7.8, Due Friday, March 23

The section for today was 7.8: Quotient Groups and Homomorphisms.

I thought that the most difficult part of this section was the proof of theorem 7.44.

I thought the end was cool when they talked about Group Theory research. I can't believe that that proof was 10,000 pages.

Section 7.7, Due Wednesday, March 21

The section for today was 7.7: Quotient Groups.

The most difficult part of this section was the proof of theorem 7.36.

I thought that the most interesting thing about this section was theorem 7.37.

Section 7.6 (second half), Due Monday, March 19

The section for today was 7.6: Normal Subgroups.

The most difficult part in this section was Theorem 7.34 and its proof.

The most interesting part was 7.33 which uses normal subgroups to convert theorem 6.5 to groups.

Section 7.6 (first half), Due Friday, March 16

The section for today was 7.6: Normal Subgroups.

The most difficult part of this section so far was the fact that aN=Na does not imply that an=na for all n.

I thought that this was an interesting parrallel between rings and groups. I guess normal subgroups are the equivalent (kind of) to Ideals in rings.

Section 7.5 (second half), Due Wednesday, March 14

The section for today was 7.5: Congruence and Lagrange's Theorem.

I thought that the most difficult part of this section was Theorem 7.30; its proof is very complicated.

I thought that it was interesting that mathematicians are trying to to classify all finitie groups up to isomorphism. That sounds like a really massive project. It would be really handy if they were able to do that.

Section 7.4 (first half), Due Monday, March 12

The section for today was 7.5: Congruence and Lagrange's Theorem.

The most difficult part for me was Lagrange's Theorem.

I think that it is neat that congruence also transfers from rings to groups, with modification of course.

Section 7.4, Due Friday, March 9

Today's section was 7.4: Isomorphism and Homomorphisms.

The most difficult part of today's reading was understanding what it means to have an automorphism or an inner automorphism.

I thought it was cool at the end when they said that by the use of representations the study of group theory can be reduced to the study of permutation groups. That is a really convenient fact.

Midterm 2 Review

Q: What topics and theorems do you think are the most important out of those we have studied?

A: I think that the most important topics/theorems are the ideals, the first isomorphism theorem, criteria for groups and cyclic groups.

Q: What questions do you expect to see on the exam?

A: I expect to see questions like those on the study guide. Proofs, examples etc.

Q: What do you need to work on understanding better before the exam?

A: I need to work on finding examples of different things.

A problem I would like to see worked out in class is Give an example of a maximal ideal in a ring that does not contain all proper ideals of the ring.

and #7 on the review sheet.

Section 7.3, Due Monday, March 5

The section for today was 7.3: Subgroups.

The most difficult part of this section was understanding Generators of Groups.

I think that this section is interesting. Cyclic Groups seem very neat, I liked reading about them.

Section 7.2, Due Friday, March 2

The section for today was 7.2: Basic Properties of Groups.

I did not understand Corollary 7.9. Hopefully we go over it in lecture.

I thought that it was interesting that groups have these properties. I liked the example you did last time where we were able to find all the elements of D4 by multipling random ones together.