- Notes on the dihedral group can be found here.
- Lemma about the identity element and inverses in subgroups.
- Lemma about what cyclic subgroups look like.
- The division algorithm statement and proof
- Classification of homomorphisms from cyclic groups: lemma and main theorem.
- A proof that the set of permutations of a set is a group under composition.
- Homework #1: problems and solutions
See this for a better way to do the solutions for 2,3,13
Typos: The solutions on problem 5 should say "Thus, e = 2 and e = 1. This is a contradition."
- Homework #2: problems and solutions
See this for a better way to do #2,9,10 and for two extra problems to do
- Homework #3: problems and solutions.
Typo: At the end of the proof 5(a) it says "By the lemma, k divides the order of phi(x)." It should say "By the lemma, the order of phi(x) divides k."
- Homework #4: problems and solutions.
Typos: In the solutions for problem 6 I found the homomorphisms from Z_6 to Z_8. It should have been Z_8 to Z_6 as stated in the problem set. But my solution is correct for the Z_6 to Z_8 problem. Try doing Z_8 to Z_6 in the same way.
- Homework #5: problems and solutions.
- Homework #6: problems and solutions.
- Homework #7: problems and solutions.
- Homework #8: problems and solutions.
- Homework #9: problems and solutions.
Student notes from F16 (Thanks Cynthia!):