%0 Journal Article
%T $B_{h}[g]$ modular sets from $B_{h}$ modular sets
%A Nidia Y. Caicedo
%A Carlos A. G¨Žmez
%A Jhonny C. G¨Žmez
%A Carlos A. Trujillo
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1411.5741v2