The strong approximation theorem and computing with linear groups

05/07/2019

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by   Alla Detinko, et al.

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We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group H ≤SL(n, ℤ) for n ≥ 2. More generally, we are able to compute all congruence quotients of a finitely generated Zariski dense subgroup of SL(n, ℚ) for n > 2.