Algorithms for experimenting with Zariski dense subgroups
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.
Citation
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
Publication
Experimental Mathematics
Status
Peer reviewed
ISSN
1058-6458Type
Journal article
Description
Our 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.Collections
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