# Spring 2022 - MATH 341 D100

## Overview

• #### Course Times + Location:

Mo, We, Fr 3:30 PM – 4:20 PM
WMC 2810, Burnaby

• #### Exam Times + Location:

Apr 26, 2022
3:30 PM – 6:30 PM
WMC 3220, Burnaby

• #### Instructor:

Jonathan Jedwab
jed@sfu.ca
1 778 782-3337
• #### 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

• Assignments 15%
• Midterm 30%
• Final Exam 55%

## Materials

Contemporary Abstract Algebra
Joseph A. Gallian
9th Edition
ISBN: 9781305657960

Visual Group Theory
Nathan Carter
ISBN: 9780883857571