Anomaly Constraints and Number of Families

The purpose of this paper is to answer the following question : is it possible to find a gauge group G and a space-time dimension D such that anomalies constrain the fermion content to be composed of the 3 known families of quarks and leptons ? The answer is, in some way, unique and consists in taking an SU(5) gauge group in 6 dimensions. This work has been done with the collaboration of N. Borghini and M. H. Tytgat.