The strong approximation theorem and computing with linear groups

Detinko, A. S.; Flannery, D. L.; Hulpke, A.

Abstract

We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group for . More generally, we are able to compute all congruence quotients of a finitely generated Zariski dense subgroup of SL(n,Q) for n > 2.

Citation

Detinko, A. S., Flannery, D. L., & Hulpke, A. (2019). The strong approximation theorem and computing with linear groups. Journal of Algebra, 529, 536-549. https://doi.org/10.1016/j.jalgebra.2019.04.011

• Journal Article Type: Article
• Acceptance Date: Apr 1, 2019
• Online Publication Date: Apr 19, 2019
• Publication Date: Jul 1, 2019
• Deposit Date: May 16, 2019
• Publicly Available Date: Apr 20, 2021
• Journal: Journal of Algebra
• Print ISSN: 0021-8693
• Electronic ISSN: 1090-266X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 529
• Pages: 536-549
• DOI: https://doi.org/10.1016/j.jalgebra.2019.04.011
• Keywords: Linear group; Strong approximation; Zariski density; Algorithm; Software
• Public URL: https://hull-repository.worktribe.com/output/1794135
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0021869319302005?via%3Dihub#!