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