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Algorithms for experimenting with Zariski dense subgroups

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Author(s)

Alla Detinko, Dane Flannery, Alexander Hulpke

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Abstract

We give a method to describe all congruence images of a finitely generated Zariski dense group H ≤ SL (n,ℤ). 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.

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Original languageEnglish
Number of pages10
JournalExperimental Mathematics
VolumeLatest Articles
Early online date4 Jun 2018
DOIs
Publication statusE-pub ahead of print - 4 Jun 2018

    Research areas

  • Algorithm, Zariski dense, Congruence subgroup, Strong approximation

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