Computational Group Theory

University of Arizona, Department of Mathematics

Master's Thesis work by Rachel Baumann

My research is on the structure of the socle and radical series for projective indecomposable modules (PIMs) of finite simple groups with Klaus Lux here at the University of Arizona. Because of the size of the PIMs, I use the Groups, Algorithms, and Programming (GAP) GAP software package designed for computational group theory. For more information, here is some of my recent work:

• Paper: The Structure of the Socle and Radical Series for Projective Indecomposable Modules of Simple Groups

• Presentation: The Structure of the Socle and Radical Series for Projective Indecomposable Modules of Simple Groups

Results

A list of all groups and characterisitics for which I computed and compared the socle and radical series is given here.

• Results of groups in characteristic 2
• Results of groups in characteristic 3
• Results of groups in characteristic 5
• Results of groups in characteristic 7
• Results of groups in characteristic 11 and 13
• Results of groups in characteristic 19, 23, 29, 31, and 37

GAP Code

To recreate the above results you will need a working copy of or access to the Basic package. Also many of the basic algebras have already been computed by Klaus Lux or by myself, which can be a lenght process. So having access to these basic algebra files would be beneficial. At present almost all are located on chivo.math.arizona.edu in /scratch/rbaumann/basicAlgebras or can be obtained from myself or Klaus Lux. Below is my working source code used for this project and files they use:

• ReadSRseries Source Code
• GAPssrsCheck Source Code
• LandrockCheck Souce Code
• Compute2 Source Code

Files

• modatlasgroups File
• ReadAlgebras File

Organizing Data and Creating Tables

• groupsSRComputed Source Code
• OrderTable Source Code
• CreateTable Source Code
• PrintTableToLaTeX Source Code

Some Resources

Groups, Algorithms, and Programmming: GAP

See references at the end of my paper: The Structure of the Socle and Radical Series for Projective Indecomposable Modules of Simple Groups

Atlas of Finite Group Representations - Version 3

Small Groups Library

Javascript code prettifier: PrettyPrint

University of Arizona, Math Department Webpage: Rachel Baumann

University of Arizona, Math Department Webpage: Klaus Lux