This is a computer program which computes information about the groups of orders 1-32.  You can find the orders of elements, list the subgroups, find cosets, search for a finitely presented group, work with permutations, and more.

 

 

 

 

 

 

 

 

John J Wavrik 

Dept of Math 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 
 
 
 
 

 

 


 
 
 
 

An older version of the program is available online via ssh. 

From a ssh client program, type “ssh groups32@math.ucsd.edu” and supply the password  “groups32”.

 

A new version of the Groups32 program can now be downloaded by clicking here.  This provides a .zip file that contains the executable Groups32.exe, an Introduction and Sample Session. This program is only for Windows.

 

Read the Sample Session (pdf format) while using Groups32 for the first time.   View or download Sample Session

 

 

 

An article about the development of Groups32 was published in the Journal of Online Mathematics and its Applications (JOMA) the online journal of the MAA.

The article, “Evolution of a Computer Application” is an attempt to combine exposition with access to a computer program. The executable files which originally accompanied the article can be obtained by clicking here. A new version of Groups32 can be obtained here.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 




All files are in .pdf format and require Adobe Reader or equivalent

 

INTRODUCTION

An introductory demonstration on Groups and the use of Groups32 

A script which presents an overview of most of the commands. Either print the script on paper or run the script and Groups32 in separate windows.

ABOUT GROUPS32

Click here  for information about the history and technical background of Groups32.

ADVANCED

There is a file of  sample problems with solutions. These are taken from various parts of a course in modern algebra - they are intended to show how Groups32 can be used. They are not beginners exercises. 

COURSE HANDOUTS

Click here for a list of handouts for an undergraduate course in Applied Modern Algebra which used Groups32.

 

 

 

 


 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 
 
 
 






 


 
 



 


 

    1. Tables / Backtracking Algorithms
    2. Cayley Tables
    3. Introduction to Groups32
    4. Sample Session - Groups32
    5. Greatest Common Divisor
    6. Permutations
    7. Normal Subgroups
    8. Quotient Groups
    9. Generators and Relations


 
 









 

 

 

 

Where can I get SSH for my personal computer?
this information was supplied by the UCSD Math Dept Computer Support
If the computer you're using does not already have a SSH client installed, the following SSH clients are available for free download and use:

PLATFORM

RECOMMENDED

ALTERNATIVE

NOTES

Microsoft
Windows

SSH Secure Shell
for Workstations

DOWNLOAD via
HTTP or FTP

PuTTY

DOWNLOAD via
HTTP or FTP

The SSH Secure Shell for Workstations client has BOTH SSH remote terminal and SFTP secure file transfer capabilities built-in.

However, if you do not have local administrative privileges to install software on the PC you're using, then use the PuTTY client instead (SSH remote terminal only).

Mac OS X

Mac OS X comes with SSH pre-installed.

Go to Applications -> Utilities -> Terminal

At the prompt, type "ssh -l username euclid.ucsd.edu"
OR "ssh username@euclid.ucsd.edu"

Use Software Update to update to the latest SSH version.

For a graphical SFTP secure file transfer client, use Cyberduck or Fugu. Or use the pre-installed command-line "sftp" and "scp" clients.

To run Unix X11 graphical programs, use the Apple X11 client under Applications -> Utilities -> X11 (or download from Apple X11). At the prompt, type "ssh -X -l username euclid.ucsd.edu" to login with automatic X11 port forwarding enabled.

Classic Mac OS
(9.x or older)

MacSSH

DOWNLOAD for
PPC or 68K

NiftyTelnet SSH

DOWNLOAD via
HTTP

MacSSH and NiftyTelnet SSH only have SSH remote terminal capability.

For SFTP secure file transfer, use MacSFTP ($15 shareware).

Unix/Linux

Most Unix/Linux distributions now
come with SSH pre-installed.

At the prompt, type "ssh -l username euclid.ucsd.edu"
OR "ssh username@euclid.ucsd.edu"

If SSH is not installed, please consult your system documentation on how to update your system or ask your system administrator to install OpenSSH.

Use the command-line "sftp" or "scp" clients for secure file transfer.

To run Unix X11 graphical programs, type "ssh -X -l username euclid.ucsd.edu" to login with automatic X11 port forwarding enabled.

Web/Java

If you have a Java-enabled web browser,
you can use the

MindTerm SSH Java Applet

To run MindTerm SSH properly, your web browser must use a recent Java Virtual Machine (JVM) runtime environment. If a working JVM is not already installed:

Microsoft Windows: Install the latest Sun J2SE JRE.
Mac OS X: Use Software Update to update to the latest Mac OS X Java.
Classic Mac OS: Install the latest Mac OS Runtime for Java (MRJ).
Unix/Linux: Install the latest Sun J2SE JRE.

For Classic Mac OS, you must install the latest MRJ and use Microsoft Internet Explorer 5.x to use MindTerm SSH. The internal JVM in Netscape Communicator 4.x lacks certain features needed to run MindTerm SSH successfully. It is recommended that Classic Mac OS users use the MacSSH or NiftyTelnet SSH clients instead.