Recognizing finite matrix groups over infinite fields

Authors:
A. S. Detinko;D. L. Flannery;E. A. Obrien
Affiliations:
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland;School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland;Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand
Venue:
Journal of Symbolic Computation
Year:
2013

Citing 4
Cited 0

Deciding finiteness of matrix groups in deterministic polynomial time

ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
The MAGMA algebra system I: the user language

Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Algorithms for computing with nilpotent matrix groups over infinite domains

Journal of Symbolic Computation
On deciding finiteness of matrix groups

Journal of Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.