Here are solutions to the final exam. Thanks ofr all your hard work, and have a great summer. Good luck next year.

Final Exam solutions

Here is a link to the MAT 511 web page, for homework and exam solutions some of which are relevant for our current study,

MAT 511 web page

One final correction from last semester: the long, complicated proof of the non-simplicity of groups G of order 36 = 2²3² is completely unnecessary. I was missing the obvious, standard argument: the number of Sylow 3-subgroups is either 1 or 4. If it were 4 then there would be a subgroup of index 4, the normalizer of a Sylow 3-subgroup. Then, if G were simple, the action on cosets gives an injection into S₄, implying |G| is at most 4! = 24. Contradiction.

I've started writing up some solutions to 12.1 exercises, by request. See the link called "Answers" below the exercise list.

Here are some notes on quotient modules that are needed for Exercise 10.3.2.

Quotient modules

And here is something about torsion that might help with Exercise 10.3.5.

Torsion in modules

Syllabus (includes tentative exam dates)

Exams

• Exam 1

• Solutions

• Exam 2

• Solutions

Homework Sheets

• HW #1, due 2/3
  • Solutions
• HW #2, due 2/12
  • Solutions
• HW #3, due 2/22
  • Solutions
• HW #4, due 3/12
  • Solutions
• HW #5, due 3/31
  • Solutions
• HW #6, due 4/7
  • Do any four of these exercises: 9.3.1, 9.4.2, 9.4.6(a) (use 9.4.1(b)), 9.4.7, 13.1.1, 13.1.2, 13.2.2
  • Solutions
• HW #7, due 4/23
  • Solutions
• HW #8, due 4/28
  • Solutions

 

Exercises (from the text Abstract Algebra, by David Dummit and Richard Foote, 3rd ed.)

10.3 / 1,2,5,13,18,27.

Hints: 10.3.13

12.1 / 1(b), 2,3,4,5,6,8,9.

12.2 / 9,11,16,18.

Exercises (from the text Computational Algebraic Geometry, by Hal Schenck)

Appendix A / 2.4, 2.5, 2.8, 3.6.

Chapter 1 / 1.5, 3.1, 3.5, 3.9, 3.11, 3.12.

 

Answers

• 12.1

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