2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219664Let 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).13 pages; v2 results generalized; v3 incorporated referee comments, final version to appear in Journal of Number TheoryNumber Theory11G35 (Primary), 14K15, 14G25, 11R45, 14L10 (Secondary)text