  In this paper, we study the Ising model with general spin $S$ in presence of
an external magnetic field by means of the equations of motion method and of
the Green's function formalism. First, the model is shown to be isomorphic to a
fermionic one constituted of $2S$ species of localized particles interacting
via an intersite Coulomb interaction. Then, an exact solution is found, for any
dimension, in terms of a finite, complete set of eigenoperators of the latter
Hamiltonian and of the corresponding eigenenergies. This explicit knowledge
makes possible writing exact expressions for the corresponding Green's function
and correlation functions, which turn out to depend on a finite set of
parameters to be self-consistently determined. Finally, we present an original
procedure, based on algebraic constraints, to exactly fix these latter
parameters in the case of dimension 1 and spin $\frac32$. For this latter case
and, just for comparison, for the cases of dimension 1 and spin $\frac12$ [F.
Mancini, Eur. Phys. J. B \textbf{45}, 497 (2005)] and spin 1 [F. Mancini, Eur.
Phys. J. B \textbf{47}, 527 (2005)], relevant properties such as magnetization
$<S>$ and square magnetic moment $<S^2 >$, susceptibility and specific heat are
reported as functions of temperature and external magnetic field both for
ferromagnetic and antiferromagnetic couplings. It is worth noticing the use we
made of composite operators describing occupation transitions among the 3
species of localized particles and the related study of single, double and
triple occupancy per site.
