Algorithms for Experimenting with Zariski Dense Subgroups

Alla Detinko, Dane Flannery, Alexander Hulpke

Research output: Contribution to journalArticlepeer-review

4 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
Pages (from-to)296-305
Number of pages10
JournalExperimental Mathematics
Issue number3
Early online date4 Jun 2018
Publication statusPublished - 1 Sep 2020
Externally publishedYes


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