  Let G be the product of an abelian variety and a torus defined over a number
field K. Let P and Q be K-rational points on G. Suppose that for all but
finitely many primes p of K the order of (Q mod p) divides the order of (P mod
p). Then there exist a K-endomorphism f of G and a non-zero integer c such that
f(P)=cQ. Furthermore, we are able to prove the above result with weaker
assumptions: instead of comparing the order of the points we only compare the
radical of the order (radical support problem) or the l-adic valuation of the
order for some fixed rational prime l (l-adic support problem).
