Integrality and arithmeticity of solvable linear groups

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

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