  Using the exact solution in terms of the generalized classical transfer
matrix method we presented a detailed analysis of the magnetic properties and
ground state structure of the simplified model of the single-chain magnet,
trimetallic coordination polymer compound, [{(CuL)_2 Dy}{Mo(CN)_8}] 2CH_3CN
H_2O is N,N'-propylenebis(3-methoxysalicylideneiminato). Due to appearance of
highly anisotropic Dy3+ ion this material is an unique example of the
one-dimensional magnets with Ising and Heisenberg bonds, allowing exact
statistical-mechanical treatment. We found two zero-temperature ground states
corresponding to different part of the magnetization curve of the material. The
zero-filed ground state is shown to be an antiferromagnetic configuration with
spatial modulation of the local Dy3+(which is proven to posses well defined
Ising like properties due two large anisotropy of g-factors) and composite
S=1/2 spin of the quantum spin trimer Cu-Mo-Cu in the form
"up"-"down"-"down"-"up". Another important feature of this compound is the
appearance of the quasi-plateau at non rational value of magnetization due to
difference of the g-factors of the Cu- and Mo-ion in quantum spin trimers. The
quasi-plateau is an almost horizontal part of the magnetization curve where the
corresponding zero-temperature ground state of the chain demonstrate slow but
monotonous dependence of the magnetization on the external magnetic field,
while the $z$-projection of the total spin is constant.
