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.
|Number of pages||19|
|Journal||Journal of Symbolic Computation|
|Early online date||17 Aug 2007|
|Publication status||Published - 1 Jan 2008|