MATH 4550 - Modern Algebra I

Class information:

Notes:

  • 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:

  • 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!):

week 1, week 2, week 3, week 4, week 5,
week 6, week 7, week 8, week 9, week 10,
week 11, week 12, week 13, week 14, week 15