Fermion mass hierarchy without flavor symmetry

We discuss a supersymmetric grand unified model which has the gauge group $\mathrm{SU}\left(5\right)\mathrm{}\times \mathrm{SU}\left(5\right)\mathrm{}\times \mathrm{SU}\left(5\right)\mathrm{},$ with matter fields transforming asymmetrically under different gauge SU(5) groups. We observe that the gauge structure of the model leads to approximate texture zero structures in fermion mass matrices and a natural hierarchy in the Yukawa couplings. The proton lifetime is estimated to be larger than ${10}^{34}\mathrm{yr}$ in this model. As in more conventional supersymmetric grand unified theory models with product gauge groups, this model possesses no tensor fields with rank higher than 2, so that it might arise from a level 1 string construction.