Algorithms for experimenting with Zariski dense subgroups

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

Abstract

We give a method to describe all congruence images of a finitely generated Zariski dense group . The method is applied to obtain efficient algorithms for solving this problem in odd prime degree n; if n = 2 then we compute all congruence images only modulo primes. We propose a separate method that works for all n as long as H contains a known transvection. The algorithms have been implemented in GAP, enabling computer experiments with important classes of linear groups that have recently emerged.

Citation

Detinko, A. S., Flannery, D. L., & Hulpke, A. (2020). Algorithms for experimenting with Zariski dense subgroups. Experimental Mathematics, 29(3), 296-305. https://doi.org/10.1080/10586458.2018.1466217

• Journal Article Type: Article
• Acceptance Date: May 1, 2018
• Online Publication Date: Jun 4, 2018
• Publication Date: Sep 1, 2020
• Deposit Date: May 22, 2019
• Journal: Experimental Mathematics
• Print ISSN: 1058-6458
• Publisher: Taylor & Francis
• Peer Reviewed: Peer Reviewed
• Volume: 29
• Issue: 3
• Pages: 296-305
• DOI: https://doi.org/10.1080/10586458.2018.1466217
• Keywords: Algorithm; Zariski dense; Congruence subgroup; Strong approximation
• Public URL: https://hull-repository.worktribe.com/output/1794321
• Publisher URL: https://www.tandfonline.com/doi/full/10.1080/10586458.2018.1466217
• Related Public URLs: https://research-repository.st-andrews.ac.uk/handle/10023/17812
• Additional Information: Peer Review Statement: The publishing and review policy for this title is described in its Aims & Scope.; Aim & Scope: http://www.tandfonline.com/action/journalInformation?show=aimsScope&journalCode=uexm20; Published: 2018-06-04