$B_{h}[g]$ modular sets from $B_{h}$ modular sets

Abstract

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 G\'omez and Trujillo look at for the suitable homomorphism that allows us to preserve the cardinal of this types of sets.