Some comments on flipped SU(5)×U(1) and flipped unification in general

A general group-theoretical discussion of flipped embeddings is given. In addition to the well-known flipped SU(5) and flipped SO(10), the existence of flipped ${\mathrm{E}}_6$ and ${\mathrm{E}}_7$ is shown, as well as several families and special cases of flipped embeddings. A possible physical reason, essentially based on the group theory of flipped embeddings, why nature prefers the low-energy group SU(3)×SU(2)×U(1) to alternatives such as SU(4)×U(1) and SU(5) is pointed out.