Intersecting subvarieties of with algebraic subgroups

Let be an irreducible closed subvariety defined over . We bound the height of algebraic points on X that are in a certain sense close to the union of all algebraic subgroup of of dimension m < n /dim X . The bound we obtain is effective and will be expressed as a function of the height of X , the degree of X , and n . We then apply this bound to derive certain finiteness results if m is also strictly less than n − dim X .