Simon Fraser University
Engaging the World

Course Outlines

Spring 2025 - MATH 341 D100

Algebra III: Groups (3)

Class Number: 3218

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 6 – Apr 9, 2025: Mon, Wed, Fri, 3:30–4:20 p.m.
    Burnaby

  • 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 [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
  •     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/course-materials/my-personalized-course-materials.

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/s10-01.html

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.