  Let G be the product of an abelian variety and a torus defined over a number
field K. Let R be a K-rational point on G of infinite order. Call n_R the
number of connected components of the smallest algebraic K-subgroup of G to
which R belongs. We prove that n_R is the greatest positive integer which
divides the order of (R mod p) for all but finitely many primes p of K.
Furthermore, let m>0 be a multiple of n_R and let S be a finite set of rational
primes. Then there exists a positive Dirichlet density of primes p of K such
that for every l in S the l-adic valuation of the order of (R mod p) equals
v_l(m).
