ON THE STAR OPERATION IN FREE PARTIALLY COMMUTATIVE MONOIDS

Let X be a finite set of traces. In this paper we show that each connected iterative factor of X* has a power which may be expressed as the conjugate of a product of the elements of X. From this property we deduce that if the star of a finite set of traces is recognizable then maximal connected factors of iterative factors of X* have a power which is the conjugate of a product of the elements of X.