We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm that, given such a finite group as input, in practice successfully constructs an isomorphic copy over a finite field, and uses this copy to investigate the group’s structure. Implementations of our algorithms are available in Magma.
|Number of pages||10|
|Journal||Journal of Symbolic Computation|
|Early online date||14 Jun 2012|
|Publication status||Published - 1 Mar 2013|