On the descriptive power of special Thue systems

This paper proves two results on the descriptive power of special Thue systems. Let T be a special Thue system on A and let M(A; T) be the monoid presented by T. If the center of M(A; T) is nontrivial, then M(A; T) is the infinite cyclic monoid or a group; if M(A; T) has only a finite number of R (or L)-classes, then M(A; T) is a group.