Algorithms for experimenting with Zariski dense subgroups
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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.
Detinko , A , Flannery , D & Hulpke , A 2018 , ' Algorithms for experimenting with Zariski dense subgroups ' , Experimental Mathematics , vol. Latest Articles . https://doi.org/10.1080/10586458.2018.1466217
© 2018 Taylor & Francis. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1080/10586458.2018.1466217
DescriptionOur work was supported by a Marie Skłodowska-Curie Individual Fellowship grant under Horizon 2020 (EU Framework Programme for Research and Innovation), and Simons Foundation Collaboration Grant 244502.
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