A set of positive integers A is called a  set if there are at most g different sums of h elements from A with the same result. This definition has a generalization to abelian groups and the main problem related to this kind of sets is to find  maximal sets, i.e., those with larger cardinality.

We construct  modular sets from  modular sets using homomorphisms and analyze the constructions of  sets by Bose and Chowla, Ruzsa, and Gómez and Trujillo look at for the suitable homomorphism that allows us to preserve the cardinal of these types of sets.

Sidon sets,  sets,  sets, finite fields, homomorphism of groups.