Algorithms for computing with nilpotent matrix groups over infinite domains
We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical nilpotency testing algorithm for matrix groups over an infinite field. We also provide algorithms to answer a number of structural questions for a nilpotent matrix group. The main algorithms have been implemented in GAP, for groups over the rational number field. (c) 2007 Elsevier Ltd. All rights reserved.
matrix group nilpotent group nilpotency testing infinite field