University of Isfahan International Journal of Group Theory 2251-7650 1 2 2012 06 01 Refined solvable presentations for polycyclic groups 1 17 452 10.22108/ijgt.2012.452 EN René Hartung Gunnar Traustason Journal Article 2011 12 19 ‎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. https://ijgt.ui.ac.ir/article_452_1d810507574aaf0c521c12a424179a4e.pdf