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What will be be doing this week?
- Internal Direct products.
- Prove that $HK\approx H\oplus K$ under appropriate conditions. They don't need much, other than maybe a hint that they do have to show that $hk=kh$, so elements commute. This should appear as something that is obvious to show when they try to prove it's a homomorphism.
- Fundamental Theorem of Finitely Generated Abelian Groups.
- Statement of Theorem, and applications.
- Look at several U groups and decide which one it is isomorphic to.
- Start the proof.
- Sylow Theorems
- Practice with induction on order of the group.
- Geometric Group Theory.
- Growth Function in a Cayley graph.
- Infinte Cayley graphs for $Z$ and $Z\oplus Z$, compute growth functions.
- Introduction to Rings.
For more problems, see AllProblems