Zariski density and computing in arithmetic groups

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

Abstract

For n > 2, let Gamma _n denote either SL(n, {Z}) or Sp(n, {Z}). We give a practical algorithm to compute the level of the maximal principal congruence subgroup in an arithmetic group H\leq \Gamma _n. This forms the main component of our methods for computing with such arithmetic groups H. More generally, we provide algorithms for computing with Zariski dense groups in Gamma _n. We use our GAP implementation of the algorithms to solve problems that have emerged recently for important classes of linear groups.

Citation

Detinko, A., Flannery, D. L., & Hulpke, A. (2018). Zariski density and computing in arithmetic groups. Mathematics of Computation, 87(310), 967-986. https://doi.org/10.1090/mcom/3236

• Journal Article Type: Article
• Acceptance Date: May 1, 2017
• Online Publication Date: Aug 7, 2017
• Publication Date: Jan 1, 2018
• Deposit Date: May 16, 2019
• Publicly Available Date: May 17, 2019
• Journal: Mathematics of Computation
• Print ISSN: 0025-5718
• Electronic ISSN: 1088-6842
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 87
• Issue: 310
• Pages: 967-986
• DOI: https://doi.org/10.1090/mcom/3236
• Public URL: https://hull-repository.worktribe.com/output/1794385
• Publisher URL: http://www.ams.org/journals/mcom/2018-87-310/S0025-5718-2017-03236-1/