Complete Classes of GUTs with Vanishing One-Loop Beta Functions

By explicit solution of the one-loop finiteness conditions for all dimensionless coupling constants (i.~e., gauge coupling constant as well as Yukawa and quartic scalar-boson self-interaction coupling constants), two classes of grand unified theories characterized by renormalization-group beta functions which all vanish at least at the one-loop level are constructed and analyzed with respect to the (suspected) appearance of quadratic divergences, with the result that without exception in all of these models the masses of both vector and scalar bosons receive quadratically divergent one-loop contributions.