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Zariski density and computing in arithmetic groups

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Author(s)

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

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Abstract

For n > 2, let Γn 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 ≤ Γn. 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 Γn. We use our GAP implementation of the algorithms to solve problems that have emerged recently for important classes of linear groups.
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Original languageEnglish
Pages (from-to)967-986
JournalMathematics of Computation
Volume87
Issue number310
Early online date7 Aug 2017
DOIs
Publication statusPublished - Mar 2018

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