  The product replacement algorithm is a practical algorithm to construct
random elements of a finite group G. It can be described as a random walk on a
graph whose vertices are the generating k-tuples of G (for a fixed k). We show
that if G is PSL(2,q) or PGL(2,q), where q is a prime power, then this graph is
connected for any k>=4. This generalizes former results obtained by Gilman and
Evans.
