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.