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.