a1 Department of Mathematics, Åbo Akademi, Henriksgatan 9, SF-20500 Åbo 50, Finland.
Let X be a finite set and S a semigroup of transformations of X. We investigate the trace on X of a random walk on S. We relate the structure of the trace process, which turns out to be a Markov chain, to that of the random walk. We show, for example, that all periods of the trace process divide the period of the random walk.
(Received May 20 1975)
(Revised February 01 1977)