  {Let $K$ be a number field, and $A_1,A_2$ abelian varieties over $K$. Let $P$
(resp. $Q$) be a non-torsion point in $ A_1(K)$ (resp. $A_2(K)$) such that for
almost all places $v$ of $K$, the order of $Q$ mod $v$ divides the order of $P$
mod $v$. Then we prove (under some conditions on $A_i, i=1,2$) that there is a
homomorphism $j$ from $A_1$ to $A_2$ such that $j(P) = Q$. We formulate and
extend such a result for any subgroups of $A_i(K), i=1,2$. These results in
particular extend the work of Corrales and Schoof from elliptic curves to
abelian varieties.
