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Algorithms for experimenting with Zariski dense subgroups

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

Authors

A. S. Detinko

D. L. Flannery

A. Hulpke



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.

Journal Article Type Article
Journal Experimental Mathematics
Print ISSN 1058-6458
Electronic ISSN 1944-950X
Publisher Taylor & Francis
Peer Reviewed Peer Reviewed
APA6 Citation Detinko, A. S., Flannery, D. L., & Hulpke, A. (in press). Algorithms for experimenting with Zariski dense subgroups. Experimental Mathematics, https://doi.org/10.1080/10586458.2018.1466217
DOI https://doi.org/10.1080/10586458.2018.1466217
Keywords Algorithm; Zariski dense; Congruence subgroup; Strong approximation
Publisher URL https://www.tandfonline.com/doi/full/10.1080/10586458.2018.1466217
Additional Information Peer Review Statement: The publishing and review policy for this title is described in its Aims & Scope.; Aim & Scope: http://www.tandfonline....ope&journalCode=uexm20; Published: 2018-06-04
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