We construct finite Dyson boson-fermion mappings of general collective
algebras extended by single-fermion operators. A key element in the c
onstruction is the implementation of a similarity transformation which
transforms boson-fermion images obtained directly from the supercoher
ent state method. In addition to the general construction, we give det
ailed applications to SO(2N), SU(l+1), SO(5), and SO(8) algebras.