Some restrictions on possible supergroups and flavor groups

It is pointed out that a suggestion of Nambu which yields diquark currents from the usual flavor or color quark currents may be relevant for classifying similar currents which arise in gauge theories unifying strong, weak, and electromagnetic interactions. The requirement that charges of ${\mathrm{SU}\mathrm{}\left(3\right)\mathrm{}}_{\mathrm{color}}\times {\mathrm{SU}\mathrm{}\left(n\right)\mathrm{}}_{\mathrm{flavor}}$ plus the new diquark currents complete the generators of a simple vectorlike supergroup $G$ can be met only in the cases $n = 3$, $G = {\mathrm{F}}_4$; $n = 6$, $G = {\mathrm{E}}_7$; and $n = 7$, $G = \mathrm{SU}\mathrm{}\left(15\right)\mathrm{}$ for $n\le 30$. Black-hole "no-hair" theorems seem to indicate an interesting but speculative motivation for diquark and leptoquark currents. The exceptional groups ${\mathrm{G}}_2$ and ${\mathrm{E}}_6$ result from an analogous generalization of SU(3) and SU(3) × SU(3) × SU(3). Explicit generators involving diquark and leptoquark charges are constructed for the groups ${\mathrm{G}}_2$ and ${\mathrm{F}}_4$.