Speaker: Robert Gilman

Abstract:
Consider a finite presentation, P, for a group G. The most important question about P is probably whether or not G is finite. Like most decision problems in combinatorial group theory, this one is recursively unsolvable. Nevertheless there is a well-known procedure, coset enumeration, which will give the correct answer when G is finite. For infinite G coset enumeration runs forever. Although there is no computable upper bound for the running time of coset enumeration when G is finite, the procedure works very well in practice. We will discuss results which suggest that the running time of coset enumeration is subexponential in the length of P for almost all cases in which G is finite.