The generalized Dyson boson mapping is extended to multifermion systems
containing three- particle substructures as occuring in nuclear matter. Two
different approaches are described. The first one leads to a mapping involving
equal numbers of bosons and fermions, where each boson, as usual, represents a
fermion pair. The second possibility consists of the introduction of new kinds
of fermions carrying the quantum numbers of the original three-fermion
subsystems. Both transformations are nonunitary.