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Integrality and arithmeticity of solvable linear groups

Detinko, A. S.; Flannery, D. L.; de Graaf, W. A.

Authors

A. S. Detinko

D. L. Flannery

W. A. de Graaf



Abstract

We develop a practical algorithm to decide whether a finitely generated subgroup of a solvable algebraic group G is arithmetic. This incorporates a procedure to compute a generating set of an arithmetic subgroup of G. We also provide a simple new algorithm for integrality testing of finitely generated solvable-by-finite linear groups over the rational field. The algorithms have been implemented in Magma.

Citation

Detinko, A. S., Flannery, D. L., & de Graaf, W. A. (2015). Integrality and arithmeticity of solvable linear groups. Journal of Symbolic Computation, 68(P1), 138-145. https://doi.org/10.1016/j.jsc.2014.08.011

Journal Article Type Article
Acceptance Date Mar 10, 2014
Online Publication Date Aug 11, 2014
Publication Date 2015-05
Deposit Date May 16, 2019
Journal Journal of Symbolic Computation
Print ISSN 0747-7171
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 68
Issue P1
Pages 138-145
DOI https://doi.org/10.1016/j.jsc.2014.08.011
Keywords Arithmetic group; Algorithm; Algebraic group; Lattice
Public URL https://hull-repository.worktribe.com/output/1794556
Publisher URL https://www.sciencedirect.com/science/article/pii/S0747717114000613?via%3Dihub