Three-generation models with chiral-color interactions

Chiral color for strong interactions requires that the gauge group of elementary-particle interactions be at least $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_L\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_R\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_Y$. Under this symmetry the conventional quarks have triangle anomalies associated with chiral-color and weak hypercharge gauge interactions. These anomalies are canceled by adding exotic-quark representations of the group $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_L\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_R\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_Y$. Models with three generations of conventional quarks and leptons are presented as solutions to the constraints of anomaly cancellation.