This research is concerned with computational group theory. The principal investigator will develop improved techniques for determining the order of a permutation group from a set of generators. He will explore the connections among coset enumeration, the nilpotent quotient algorithm and the Knuth- Bendix procedure for strings in an effort to improve the performance of each of these procedures. He will also investigate the possibility of devising a practical algorithm for computing infinite solvable quotients. This research concerns the development and computer implementation of group theoretic algorithms. This project is breaking ground in computational algebra which is an underdeveloped area relative to current computational technology. The ideas that are proposed are new state-of-the-art innovations and may provide dramatic improvements in certain types of enumerations.
