Abstract
Supersymmetric models with preons in a self-adjoint representation of the hypercolor group ${G}_{\mathrm{HO}}$ are considered. Anomaly matching constraints and N-independence requirements of 't Hooft are imposed assuming that the flavor group ${G}_{f}$=SU(N)\ifmmode\times\else\texttimes\fi{}U(1) and supersymmetry remain unbroken. This leads to solutions which are practically unique for every choice of ${G}_{\mathrm{HO}}$ and which may be interpreted as grand unified theories containing a specific number of generations. All possible choices of ${G}_{\mathrm{HO}}$ and ${G}_{f}$ consistent with the asymptotic freedom of the former are listed. In particular, when ${G}_{\mathrm{HC}=\mathrm{S}\mathrm{O}(11)}$, ${G}_{f}$ is fixed as SU(6)\ifmmode\times\else\texttimes\fi{}U(1) and the number of generations as four.
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