  This paper answers a question raised by Grothendieck in 1970 on the
"Grothendieck closure" of an integral linear group and proves a conjecture of
the first author made in 1980. This is done by a detailed study of the
congruence topology of arithmetic groups, obtaining along the way, an
arithmetic analogue of a classical result of Chevalley for complex algebraic
groups. As an application we also deduce a group theoretic characterization of
thin subgroups of arithmetic groups.
