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King Creativity at Southwestern

Finding All Solvable Groups of Size Less than 2002

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by: Jason Jones
Major: computational mathematics

The goal of my project was to find all the groups up to order 2002 that we re both soluble and non-nilpotent. This was originally to be part of an honor’s project that started in the spring of 2001 under the supervision of Dr. Walter Potter. The funding from the King Creativity Fund gave me the means to add the computational power to generate and test all of these groups.

The majority of the testing was done on a 6-node linux cluster located in the Ralph M. Whitmore lounge in Mood-Bridwell Hall. My major task was to generate the groups of these orders and use these in a program called GAP (http://www.gap-system.org) to determine if they had the properties that I was seeking. I was able to successfully complete the generation and testing of all of these groups, but not in the way that was originally hoped. Generating all of these groups in the way that I originally attempted proved to be very difficult and the libraries of groups contained in GAP were used for those orders that I was not able to generate. There ended up being a total of 3,767,799 groups with the properties that we were seeking. The results from this may be used by Dr. Potter in future research that he will do.