MATH 341, Algebra III: Groups
Hours and Location for Lecture, Tutorial and office hours
| Lectures: |
Monday, Wednesday, Friday, 15:30-16:20
First lecture is Monday January 8, 2024
|
| Instructor: |
Nils Bruin
email: nbruin@sfu.ca
|
| Course information: |
See Canvas for further notification, assignments,
solutions, and lecture notes (if required).
|
Book
A First Course in Abstract Algebra, Third Edition
by Marlow Anderson and Todd Feil
Taylor and Francis, 2015
ISBN 978-1-4822-4552-3
Note: The third edition has received an extensive rewrite and
expansion of its chapters about group theory, so earlier editions are
not suitable.
Topics covered in course
Groups:
- Definition and examples of Groups
- Elementary Properties of Groups
Finite Groups: Subgroups:
- Terminology and Notation
- Subgroup Tests
- Examples of Subgroups
Cyclic Groups:
- Properties of Cyclic Groups
- Classification of Subgroups of Cyclic Groups
Permutation Groups:
- Definition and Notation
- Cycle Notation
- Properties of Permutations
Isomorphisms:
- Motivation
- Definition and Examples
- Cayley's Theorem
- Properties of Isomorphisms
- Automorphisms
Cosets and Lagranges Theorem:
- Properties of Cosets
- Lagranges Theorem and Consequences
- An Application of Cosets to Permutation Groups [Orbit-Stabilizer Theorem]
- The Rotation Group of a Cube
Normal Subgroups and Factor Group:
- Normal Subgroups
- Factor Groups
- Applications of Factor Groups [including Cauchy's Theorem]
Group Homomorphisms:
- Definition and Examples
- Properties of Homomorphisms
- The First Isomorphism Theorem
Sylow Theorems:
- Conjugacy Classes
- The Class Equation
- The Sylow Theorems
- Applications of Sylow theorems
Other topics:
- The Fundamental Theorem of Finite Abelian Groups
- Simple Groups
- Composition Series
- Solvable Groups
- Semi-direct Products
Examination, Grading and Assignments
Scoring Formula
| Assignments: | 15% |
| Midterm: | 30% |
| Final examination: | 55% |
Cheating policy
Don't cheat. Students caught cheating on an assignment, Midterm or
on the Final Examination will receive no credit and
will be reported to the chair of the department, who may take appropriate
action.
Students are encouraged to work together on assignment problems. However,
you are not simply to copy the solutions of a fellow student. You should
understand what you hand in and you should be prepared and able to explain your
solution. I will occasionally ask students to explain their assignment solutions
to me.
As a guideline, prepare the solution you hand in on your own,
without looking at other people's work.