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Zariski density and computing in arithmetic groups

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


A. Detinko

D. L. Flannery

A. Hulpke


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.

Journal Article Type Article
Publication Date Aug 7, 2017
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
APA6 Citation Detinko, A., Flannery, D. L., & Hulpke, A. (2017). Zariski density and computing in arithmetic groups. Mathematics of Computation, 87(310), 967-986.
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