Spring 2023  MATH 341 D100
Algebra III: Groups (3)
Class Number: 5260
Delivery Method: In Person
Overview

Course Times + Location:
Mo, We, Fr 3:30 PM – 4:20 PM
WMC 2810, Burnaby 
Exam Times + Location:
Apr 15, 2023
8:30 AM – 11:30 AM
BLU 10921, Burnaby

Instructor:
Amarpreet Rattan
rattan@sfu.ca

Prerequisites:
MATH 340 or 342 or 332, with a minimum grade of C.
Description
CALENDAR DESCRIPTION:
Finite groups and subgroups. Cyclic groups and permutation groups. Cosets, normal subgroups and factor groups. Homomorphisms and isomorphisms. Fundamental theorem of finite abelian groups. Sylow theorems. Students with credit for MATH 339 may not take this course for further credit.
COURSE DETAILS:
Course Details:
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 [OrbitStabilizer 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
 Indirect Products
Grading
 Assignments (≈10) (weighted equally) 15%
 Midterm 30%
 Final Exam 55%
Materials
REQUIRED READING:
A First Course in Abstract Algebra: Rings, Groups, and Fields
3rd Edition
Marlow Anderson, Todd Feil
ISBN: 9781482245523
REQUIRED READING NOTES:
Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/coursematerials/mypersonalizedcoursematerials.
Registrar Notes:
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.
Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s1001.html