Computing polycyclic presentations for polycyclic rational matrix groups

Authors:
Björn Assmann;Bettina Eick
Affiliations:
School of Computer Science, University of St. Andrews, Fife, KY16 9AJ, United Kingdom;Department of Mathematics and Computer Science, TU Braunschweig, Braunschweig 38106, Germany
Venue:
Journal of Symbolic Computation
Year:
2005

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Abstract

We describe practical algorithms for computing a polycyclic presentation and for facilitating a membership test for a polycyclic subgroup of GL(d,Q). A variation of this method can be used to check whether a finitely generated subgroup of GL(d,Q) is solvable or solvable-by-finite. We report on our implementations of the algorithms for determining a polycyclic presentation and checking solvability.