Refined solvable presentations for polycyclic groups

Abstract

We describe a new type of polycyclic presentations, that we will call refined solvable presentations, for polycyclic groups. These presentations are obtained by refining a series of normal subgroups with abelian sections. These presentations can be described effectively by presentation maps which yield the basis data structure to define a polycyclic group in computer-algebra-systems like {\scshape Gap} or {\scshape Magma}. We study refined solvable presentations and, in particular, we obtain consistency criteria for them. This consistency implementation demonstrates that it is often faster than the existing methods for polycyclic groups.

Preprint