Divisibility Theory and Complexity of Algorithms in Free Partially   Commutative Groups
  The original version of the paper was published in Contemporary Mathematics 378 ``Groups, Languages, Algorithms''; 2005, pp. 319-348. This is a modified version with Appendix that holds a corrected formulation of Proposition 4.1. 
E. S. Esyp, I. V. Kazachkov and V. N. Remeslennikov