This web site is a repository for my thesis and all of the work created and presented to the faculty. The work was performed over a one year period while a graduate student in the Computer Science department of San Diego State University (SDSU). I defended the thesis at the end of April 2005 and graduated the following May. I have been working in the high tech industry since 1993 after graduating from Cornell University with a Bachelors of Science degree in Mechanical Engineering.

My work on this thesis resulted in a program that could be used to generate, identify, and analyze finite groups presented in the form of a Cayley Table as well as visualize the groups that are generated. The abstract of the thesis is located here including a lot of links to some basic group theory definitions.

The code can be tried here. The code requires that Java 2, Edition 5.0 is installed as the run-time engine on your system. One can also use the code as a teaching tool to allow introductory group theory students to better understand what a group is as well as visualize the differences between groups and perform some simple analysis of the groups that are input and/or generated.

The entire thesis is located here.

The presentation for my oral defense is located here.

The JavaDoc for the code is located here.

A zip file containing the source code, including the Netbeans project files, is located here. I have released the code under the GNU General Public License (GPL).

**Useful Links:**

Dog School of Mathematics: This site provides a good introduction to basic group theory for those just starting out.

Groups15 and Groups32: This site provides information and visualization tools for groups of order 1-32. There are two programs available. Groups15 is a Java applet for displaying all the finite groups of order 1-15. Groups32 is an application that provides information about finite groups of order 1-32 and is available via telnet. I found both programs very interesting.

Groups of Small Order: This site provides the list of all groups of order 1-31, including some Cayley Tables and characteristics of some of the groups.

The
MOD-2 Cohomology of 2-Groups: An advanced group theory site that gives
links to all of the finite groups of order 2^{n}
where 1 < n < 7.

Wikipedia: A lot of basic information and definitions of terms used throughout my thesis.

Labor Law Encyclopedia: Surprisingly enough, this site has an excellent section of definitions and explanations of many mathematic concepts and areas of focus.

Permutation Generator: Java code used in a side project I describe in my thesis to analyze the creation of groups by brute force.