A Polycyclic Quotient Algorithm

This paper describes a generalization of the Gröbner basis method to the integral group ring of a polycyclic group. A polycyclic quotient algorithm is developed using this method. SupposeGis a group given by a finite presentation andG(n)is thenth term in the derived series ofG. A polycyclic quotient algorithm computes the quotientG/G(n)if it is polycyclic. An implementation of this algorithm in C has been developed and its efficiency is encouraging.