This award is under the International Postdoctoral Fellows Program, which enables U.S. scientists and engineers to conduct three to twelve months of research at foreign centers of proven excellence. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad. This award will support a twelve-month postdoctoral research visit by Dr. Susan Hermiller of New Mexico State University to the University of Melbourne, Victoria, Australia, to work with Dr. John R. J. Groves. A finite complete rewriting system for a group is a presentation which solves the word problem for the group in a way that is particularly easy to implement on a computer, and which provides a regular language of normal forms. The proposed research is a study of the class of groups with such rewriting systems. Several questions will be pursued. The first - Given a group with a finite complete rewriting system, must every finite index subgroup also have one? The second - Does an automatic group necessarily have a finite complete rewriting system? The third - If a finitely presented group has finite derivation type, does it have a finite complete rewriting system? To answer these questions, it would be helpful to construct rewriting systems for more families of groups, especially Artin groups, if possible. They also intend to study a weaker property for a group, given by a subword closed regular language of normal forms. The award recommendation provides funds to cover international travel and a stipend for twelve months.
