  Under certain conditions, we prove that the set of zeros of an elliptic net
forms an Abelian group. We present two applications of this fact. Firstly we
give a generalization of a theorem of Ayad on valuations of division
polynomials in the context of net polynomials. Secondly we generalize a theorem
of Ward on symmetry of elliptic divisibility sequences to the case of elliptic
nets.
