This award is concerned with research on group-theoretic algorithms with emphasis on procedures for studying groups defined by finite presentations. Special attention will be given to improving the performance of two procedures of growing importance to computational group theory, the Knuth-Bendix procedure for strings and the Baumslag-Cannonito-Miller polycyclic quotient algorithm. The connection between these procedures and three other fundamental algebraic algorithms, coset enumeration, the LLL lattice reduction algorithm, and the method of Groebner bases will also be explored. It is expected that one result of the research will be a new implementation of the Knuth-Bendix procedure for strings, along with careful documentation, which can be shared with other researchers. This project is in the general area of group theory and the computer-aided computational aspects of this field. There is a growing interest in using computers to answer theoretical questions in algebra and conversely, algebra is quite useful for the development of algorithms. This project makes serious use of both the theory and practice of symbolic calculations to solve real problems in group theory.
