Refined solvable presentations for polycyclic groups

‎We describe a new type of presentation that‎, ‎when consistent‎, ‎describes a polycyclic group‎. ‎This presentation is obtained by‎ ‎refining a series of normal subgroups with‎ ‎abelian sections‎. ‎These presentations can be described effectively in‎ ‎computer-algebra-systems like Gap or‎ ‎ Magma‎. ‎We study these‎ ‎presentations and‎, ‎in particular‎, ‎we obtain consistency criteria for them‎. ‎The‎ ‎consistency implementation demonstrates that there are situations where‎ ‎the new method is faster than the‎ ‎existing methods for polycyclic groups‎.

Keywords:

Polycyclic , presentation , nilpotent