Math 322: Group Theory

Fall Term 2015
Lior Silberman

General Information

This is the introductory course in algebra, intended for honours students. Students who wish to buy a single abstract algebra book should buy the book [1], which will serve you for both 322 and 323 this year, and also covers the material of 422 and 423. The gentler and less-terse alternative is the book [2]. If you want a group-theory specific textbook, the best book in my opinion is Rotman's (reference [3] below). You can download a copy by following the link while on the UBC network. That said, any book titled "Group Theory" (topic-specific) or "algebra" or "abstract algebra" (wide-coverage) is fine.

References

  1. Dummit and Foote, Abstract Algebra
  2. Gallian, Contemporary Abstract Algebra
  3. Rotman, An Introduction to the Theory of Groups, also available from SpringerLink.

During the course, we will study three classical theorems by Sylow. They are, of course, discussed in detail in the textbooks. Sylow's original paper from 1872 (written in French) is available online from the Göttingen University Library.

Final Exam

Midterm Exam

Problem Sets

  1. Problem Set 1, due 17/9/2015 (hint to 2b fixed). Solutions.
  2. Problem Set 2, due 24/9/2015. Solutions.
  3. Problem Set 3, due 1/10/2015. Solutions.
  4. Problem Set 4, due 8/10/2015. Solutions.
  5. Problem Set 5, due 15/10/2015. Solutions.
  6. Problem Set 6, due 27/10/2015, Problem 6 postponed to PS7. Solutions.
  7. Problem Set 7, due 5/11/2015. Solutions.
  8. Problem Set 8, due 12/11/2015. Solutions.
  9. Problem Set 9, due 19/11/2015. Solutions.
  10. Problem Set 10, due 26/11/2015. Solutions.
  11. Problem Set 11, not for submission. Solutions.

Lecture-by-Lecture information

Readings are generally from Dummit and Foote (sections marked "N" are in the lecture notes). Those reading Rotman can find the material there

Week Date Material Reading Notes
1 Th 10/9 Introduction
The Integers
 
§0.2
Putnam Sessions
T 15/9 Modular arithmetic §§0.3,0.1 Relations
Th 17/9 (continued)   PS1 due
2 T 22/9 Permutations §1.3  
Th 24/9 (continued)   PS2 due
3 T 29/9 Groups and subgroups §§1.1,1.2,1.5,2.1 Concepts to review
Th 1/10 Homomorphisms, Cyclic groups   PS3 due
4 T 6/10 Cosets and Lagrange's Theorem
Normal Subgroups
§3.2  
Th 8/10 Quotient groups §3.3 PS4 due
5 T 13/10 Isomorphism Theorems
Simplicity of A_n
§3.3
§4.6
Feedback form
6 Th 15/10 Group actions §1.7, §§4.1-4.2 PS5 due
T 20/10 Midterm Exam Midterm Midterm
7 Th 22/10 Conjugation §4.3 Zagier's Trick
T 27/10 Orbits, stabilizers   Examples
PS6 due
8 Th 29/10 p-groups N4.1 Groups of order p^3
T 3/11 pq-groups N4.2  
9 Th 5/11 (continued) N4.2 PS7 due
T 10/11 Sylow's Theorems §4.5  
10 Th 12/11 Applications   PS8 due
T 17/11 Groups of medium order §6.2  
Th 19/11 Finite Abelian groups §6.1 PS9 due
11 T 24/11 Finitely generated abelian groups §5.2  
Th 26/11 Nilpotent groups §6.1 PS10 due
12 T 1/12 Solvable groups §6.1  
Th 3/12 Last lecture §6.1  
  M 7/12 Review: 10:00-12:00 at MATH 225    
T 8/12 Final exam: 15:30-18:00 at IBLC 182    


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