The strong approximation theorem and computing with linear groups

Abstract 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 .