Algorithms for experimenting with Zariski dense subgroups

Alla Detinko, Dane Flannery, Alexander Hulpke

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

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


  • Algorithm
  • Zariski dense
  • Congruence subgroup
  • Strong approximation


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