Zariski dense subgroups of arithmetic groups

Abstract

E Z (in fact, r can be taken to be a maximal subgroup of G(Z)). Further, two commuting semisimple elements of S&(Z) (n 24), which generate a free abelian group of rank 2 and which are contained in a Zariski dense (in fact, maximal) subgroup of infinite index in S&(Z) are exhibited. Given an algebraic Q-subgroup H of G, one can attempt, by imitating the methods of [2], to obtain Zariski dense subgroups of infinite index in G(Z) which contain a congruence subgroup of H(E). We obtain such sub- groups of infinite index when