Group Analyzer page

Dr. Paul G. Glenn
Department of Mathematics
Catholic University of America
Washington, DC 20064
glenn AT cua DOT edu

Abstract for Group Analyzer

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Group Analyzer is an application for performing various finite group computations in a calculator-like manner with groups of order up to 400. It is intended for use by students (and their instructors) in courses introducing elementary finite group theory. There are two mathematically and functionally equivalent versions, one for MacOs 8.1 - 9.x and one for Mac OS X.

The Group Analyzer applications, the group data file maker application and the documentation are copyright 1992-2005, all rights reserved, by Paul G. Glenn. They are offered FREE to the academic community. The package may be distributed by others provided it is done so intact and whole, and free of charge.

Why use such software?

In their first course in abstract algebra, students work, typically, with two types of finite group examples. One type involves very small order groups in which explicit calculations are easy for beginners. A second type, requiring familiarity with the basics and some experience, involves larger groups whose properties and characteristics are found using theorems and ad hoc mathematical reasoning. With this type of example, one would almost certainly not want to hand-calculate lists of elements such as cosets, the set of commutators, etc.

Group Analyzer makes it possible to work directly with a larger selection of finite examples. As with hand-calculated very small groups, the students have access via Group Analyzer to an explicit specification of the group's operation in the form of a table.  (However, the table is stored in the computer's memory and the user doesn't get to see it.) The groups Group Analyzer works with are big enough to illustrate various ideas of finite groups in non-trivial ways.

With such examples, students can illustrate or conjecture theorems, search for counter-examples and check assertions arrived at using, or suggested by, indirect reasoning. Thus Group Analyzer serves both as an adjunct to indirect reasoning and as a tool to enable students to work with larger groups similar to their work with very small groups.

Some of Group Analyzer's features:

• Group data files: The group information which Group Analyzer (= GA) uses for calculations is contained in a separate file for that group called a "group data file" (gdf). To do calculations in a particular group, one starts GA itself, then commands GA to load a group data file. During a session with GA one may load in new files at will, but one may work with only file at a time.
  
  There is a separate application "GDF Maker" with which instructors or students can create gdf's.
  


• A user controls GA with a combination of button clicks, menu commands and keyboard shortcuts. There is a built-in "Help" facility for all terms used and commands.
  
  
• The essential core of GA consists of its calculation commands. Depending on the command, its input consists of zero, one or two subsets of the group and its output consists of one or more subsets of the group. All input/output appears onscreen in a text field called the "stack".
  
  Other commands yield information about the group, displayed in various ways.
  
  
• Once a group has been loaded in, one can also set GA to do its calculations in the homomorphic image of any subgroup of the original group.
  
  
• GA also has features which make it easier to understand and use the results of its calculations. The main one is the "session record", a separate text window which shows all the calculations done during a session. It is an editable and searchable plain text file, and can be saved as a separate text file.
  
  
• Group Analyzer is designed so that students can begin using it early in a course before they know much group theory. Initially, they would use GA in simple and restricted ways, then use it in more elaborately as they learn more about groups.
  

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Hardware requirements and earlier versions of Group Analyzer

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Group Analyzer (classic) works on Macintosh computers running MacOS 8.1 through 9.x.

Group Analyzer (OS X) works on Macs running OS 10.2 - 10.3.x

The current version is 7.2, compiled in February, 2005.

Earlier versions of Group Analyzer are still available here. Group Analyzer 6 will run in Systems 7.0 on up and Group Anayzer 5.5 will work on 68k Macintoshes.

Screen shots

Download links

In addition to Group Analyzer itself, there is:

• Documentation (a user's guide and a tutorial, in PDF format). There is also a description of how to use GAP ("Groups, Algorithms, Programming") to make gdf files.
  
• Installation instructions (plain text).
• A folder of sample group data files.
• A separate application called GDF Maker for creating more group data files.
• Activity sampler: that is, a collection of guided activities for students. (PDF format).
  

OS X package
This includes Group Analyzer 7.2 (OS X), GDF Maker (OS X), the installation instructions, the user guide, the tutorial, instructions for using GAP to make GDF files and a small selection of sample group data files. (2.7 MB, dmg file)

"Classic" package
This includes Group Analyzer 7.2 (OS8-9), GDF Maker (classic), the installation instructions, the user guide, the tutorial, instructions for using GAP to make GDF files and a small selection of sample group data files. (2.6 MB, compressed self-extracting)

Note: If you are using  MacOS 8.x and have difficulty unstuffing the "Classic" package, please contact me for another form of these files.

Documentation only (uncompressed)

User Guide (318 KB)
Tutorial (141 KB)
Instructions for using GAP to make GDF files (53 KB)

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