The materials given below were used in various abstract algebra courses which I taught at Eastern Illinois University, Charleston, IL. The projects were developed while I was on sabbatical leave at the Centre for Interdisciplinary Research in Computational Algebra at the University of St. Andrews, Scotland. Several of them were tested by students at St. Andrews.

For further information about GAP (Groups, Algorithms, and Programming), including how to obtain it, see GAP’s home page.

If you would like modify any of these materials for your personal use, contact me. The LaTEX source is freely available.

You will need to have Acrobat Reader (freely available) in order to read many of files.

Note: This is a one-semester introduction to groups, rings and fields.

Fall 2000

Laboratory 1

Introduction

Laboratory 2

Permutation Groups and Conjugates

Laboratory 3

Modular Arithmetic: Primitive Elements and Square Roots

Laboratory 4

Cosets and Factor Groups

Reference Guide

Linux/GAP/emacs Reference Guide

Laboratory 1

The Euclidean Algorithm

Laboratory 2

Permutations

Laboratory 3

Generators and Relations, Isomorphisms and Cosets

Laboratory 4

Lattices of Subgroups

Projects

• Groups of Order 16   Description  No File needed
• Subgroup Lattices of Groups of Order 16   Description  No File needed
• The Probability of Two-Generation   Description  File needed
• Graphs and Their Groups   Description  File needed
• Simple Groups of Small Order   Description  No File needed
• Additive Semigroups of Z⁺   Description  No File needed
• Multiplicative Semigroups of Z⁺   Description  No File needed
• The Group of a Sliding Block Puzzle   Description  No File needed
• Solving a Sliding Block Puzzle   Description  File needed
• Using Schreier Elements to Compute the Order of a Group   Description  File needed

Laboratory 1

Introduction

Laboratory 2

Lattices of Subgroups

Laboratory 1

Introduction

Laboratory 2

Group Actions and the Sylow Theorems

Reference Guide

Linux/GAP/emacs Reference Guide

Laboratory 1

Introduction

Laboratory 2

Equivalence Classes and Normal Subgroups

Laboratory 3

Group Actions

Laboratory 4

Simple Groups

Please direct any question to Duane Broline