A set of positive integers A is called a B h [g] 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 B h [g] maximal sets i.e. those with larger cardinality.We construct B h [g] modular sets from B h modular sets using homomorphisms and analyze the constructions of B h sets by Bose and Chowla, Ruzsa, and Gómez and Trujillo look at for the suitable homomorphism that allows us to preserve the cardinal of this types of sets.