Fixed points of endomorphisms of trace monoids
  It is proved that the fixed point submonoid and the periodic point submonoid of a trace monoid endomorphism are always finitely generated. Considering the Foata normal form metric on trace monoids and uniformly continuous endomorphisms, a finiteness theorem is proved for the infinite fixed points of the continuous extension to real traces. 
Pedro V. Silva and Emanuele Rodaro
math.GR cs.FL