In this Research Experiences for Undergraduates award, six students will concentrate on applications of probability to the analysis of basic questions in group theory. The principal goal is one of determining in a probabilistic sense the likelihood that two elements of a group commute. Specifically, the team will construct confidence intervals for the location parameter of a symmetric random variable. The method uses the notion of resampling introduced by Tukey for determining what are called typical values for the subsample means. To attack the problems, students will be introduced to the high level programming language, CAYLEY, which enables the user to define algebraic structures in which various structural properties can then be classified. This important tool is generally not available to undergraduates. Reports will be prepared at the end of the program. Those students who have made significant progress will refine the work into publishable form; efforts will be made to have students present their work at forthcoming professional meetings. This is the third year of support for this program. Results to date have been substantial.
